Process Control and Common Terms

Process Control and Common Terms For Practinioners

Common terms in the process control terminologyAnalog SignalAnalog signals are like voltage or electric current signal, representing temperature, pressure, level etc. Usually the electrical current signal is of magnitude 4-20 mA where 4 mA is the minimum point of span and 20 mA is the maximum point of span.

Analog to Digital Converting, A-D ConvertingElectronic hardware converts analog signal like voltage, electric current, temperature, or pressure into digital data a computer can process and interpret.

Auto ModeIn auto mode the output is calculated by the controller using the error signal - the difference between set point and the process variable.

Closed LoopController in automatic mode.

CascadeTwo or more controllers working together. The output of the master controller is the set point for the "slave" controller.

Controller Output - COOutput signal from the controller.

DDE Windows Dynamic Data ExchangeA standard Microsoft operating system method for communicating between applications. Replaced by OLE for process control - OPC.

Dead BandThe range through which an input can be varied without initiating a response.

Dead TimeDead time is the amount of time it takes for the process variable to start changing after changing output as a control valve, variable frequency drive etc.

Derivative - DThe derivative - D - part of a PID controller. With derivative action the controller output is proportional to the rate of change of the process variable or process error.

DelayA term commonly used in stead of dead time.

DeviationAny departure from a desired or expected process value.

Digital SignalA discrete value at which an action is performed. A digital signal is a binary signal with two distinct states - 1 or 0, often used as an on - off indication.

Digital Control System - DCSDigital Control System - DCS refers to larger digital control systems.

Discrete LogicRefers to digital "on - off" logic.

Discrete I/OOn or off signals sent or received to the field.

Distributed Control System - DCSA control system where the controller elements are not central in location but distributed throughout the system with each component sub-system controlled by one or more controllers.

Dominant Lag ProcessMost processes consist of both dead time and lag. If the lag time is larger than the dead time, the process is a dominant lag process. Most process plant loops are dominant lag types. This includes most temperature, level, flow and pressure loops.

ErrorIn the control loop the error = set point - process value.

GainGain = 100 / Proportional Band. More gain in the controller gives a faster loop response and a more oscillatory (unstable) process.

Gain in the process is defined as the change in input divided by the change in output. A process with high gain will react more to the controller output changing.

Gain MarginThe difference in the logarithms of the amplitude ratios at the frequency where the combined phase angle is 180 degrees lag is the gain margin.

HysteresisThe signal change before the output unit (valve or similar) moves.

Input/Output - I/OElectronic hardware where the field devices are wired.

Integral Action - I

The integral part of the PID controller. With integral action, the controller output is proportional to the amount and duration of the error signal. If there is more integral action, the controller output will change more when error is present.

Load Upset An upset to the process not from changing the set-point (process disturbance).

Lag TimeLag time is the amount of time after the dead time that the process variable takes to move 63.3% of its final value after a step change in valve position.

MeasurementMeasurement is the same as the process value.

Manual ModeIn manual mode the output is set manual.

ModeThe controller can be set in auto, manual, or remote mode.

Man Machine Interface - MMIRefers to the software that the process operator operates the process with.

OutputOutput of the controller.

OvershootThe amount a process exceed the set point during a change in the system load or change in the set point.

PID ControllerController including Proportional, Integrating and Derivative controller functions. Cfr. ANSI/IEE Standard 100-1977.

Process Value - PVThe actual value in the control loop, temperature, pressure, flow, composition, pH, etc

Programmable Logic Controller - PLCControllers replacing relay logic, usually with PID controllers.

Process Variable - PVThe actual value in the control loop, temperature, pressure, flow, composition, pH, etc. See Process Value.

Proportional Band - PWith proportional band the controller output is proportional to the error or a change in process variable. Proportional Band = 100/Gain

RateSame as the derivative or "D" part of PID controllers.

RegisterA data storage location in a PLC.

RegulatorA controller changing the a output variable to move the process variable back to the set point

RepeatabilityThe variation in outputs for the same change of input.

ResetSame as the integral or "I" part of PID controllers.

Reset WindupIntegral action continuing to change the controller output value after the actual output reaches a physical limit.

Response TimeThe rate of interrogating a transmitter.

Sample IntervalThe rate at which a controller samples the process variable and calculates a new output.

Set PointThe set point is the desired value of the process variable.

Time ConstantSame as lag time.

TransmitterA transmitter sense the actual value of a system and transforms the value to a standardized signal - 4-20 mA is common for analog signals - as input for the control system.

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Glossary of Process Control Terms

By John Gerry, P.E., and George Buckbee, P.E., ExperTune Inc.

"A to D" or A/D Converter: A to D means Analog to Digital. This electronic hardware converts an analog signal like voltage, electric

current, temperature, or pressure into a digital number that a computer can process and interpret.

Active Model Capture: This technology involves the automated capture of process models from naturally-occurring process data. For example, when the operator makes a setpoint change, a process model can be developed. For more on active model capture, click here

Auto Mode: In auto mode the controller calculates the output based its calculation using the error signal (difference between setpoint and PV). See Mode.

Anti-Reset Windup: Same as reset windup.

Bump Test:To determine a process model, there needs to be some "excitation" of the process. This is typically accomplished through bump testing. Bump tests can be performed many ways. Some ways to do this include:

Make a Setpoint Change WIth the loop in MANUAL, change the controller output Perform a Fast Plant Test

Closed Loop: Controller in automatic mode. See Mode.

Cascade: With 2 or more controllers. The output of the "Master" controller is the setpoint for the "Slave" controller. A classic example is the control of a reactor (a large vessel with a steel jacket around it). The product temperature (master) controller's output is the setpoint of the jacket temperature (slave) controller.

Composition: A process variable. Represents the amount of one material in a solution, or gas.

CO or Controller Output: Same as output.

Corner Frequency: For first order time constants, the "corner frequency" is the frequency where the amplitude ratio starts to turn and the phase lag equals 45 degrees. Also:

corner frequency = 1/(time constant) radians/time

DDE Windows Dynamic Data Exchange. A standard software method for communicating between applications under Microsoft Windows. Created by Microsoft starting with Windows 3.1. DDE is being replaced by OLE for process control, OPC.

Dead Time: Dead time is the amount of time that it takes for your process variable to start changing after your valve changes. If you were taking a shower, the dead time is the amount of time it would take for you (the controller) to feel a change in temperature after you have adjusted the hot or cold water.

Pure dead time processes are usually found in plug flow or solids transportation loops. Examples are paper machine and conveyor belt loops. Dead time is also called delay. A controller cannot make the process variable respond before the process dead time.

To a controller, a process may appear to have more dead time than what it actually has. That is, the controller cannot be tuned tight enough (without going unstable) to make the process variable respond appreciably before an equivalent dead time. More accurately, the characteristic time of the loop is determined by equivalent dead time. Equivalent dead time consists of pure dead time plus process components contributing more than 180 degrees of phase lag.

The phase of dead time increases proportionally with frequency. Any process having more than 180 degrees phase lag has equivalent dead time.

Derivative: The "D" part of PID controllers. With derivative action, the controller output is proportional to the rate of change of the process variable or error. Some manufacturers use the term rate or pre-act instead of derivative. Derivative, rate, and pre-act are the same thing. Derivative action can compensate for a changing process variable. Derivative is the "icing on the cake" in PID control, and most people don't use it. It can make the controller output jittery on a noisy loop and most people don't use derivative on noisy loops for this reason. See presentation on Derivative Action, the Good, the Bad, and the Ugly.

Delay: This term is often used in place of dead time. See dead time.

DCS: Digital Control System. DCS refers to larger analog control systems like Fisher, Foxboro, Honeywell, and Bailey systems. DCSs were traditionally used for PID control in the process industries, whereas PLCs were used for discrete or logic processing. However, PLCs are gaining capability and acceptance in doing PID control. Most utilities, refineries and larger chemical plants use DCSs. These systems cost from twenty thousand to millions of dollars.

Discrete Logic: Refers to digital or "on or off" logic. For example, if the car door is open and the key is in the ignition, then the bell rings.

Discrete I/O: Senses or sends either "on or off" signals to the field. For example a discrete input would sense the position of a switch. A discrete output would turn on a pump or light.

Dominant Dead Time Process: If the dead time is larger than the lag time the process is a dominant dead time process.

Dominant Lag Process: Most processes consist of both dead time and lag. If the lag time is larger than the dead time, the process is a dominant lag process. Most process plant loops are dominant lag types. This includes most temperature, level, flow and pressure loops.

Error: Error = setpoint - PV. In auto mode, the controller uses the error in its calculation to find the output that will get you to the setpoint.

Equivalent Dead Time: To a controller, a process may appear to have more dead time than what it actually has. That is, the controller cannot be tuned tight enough (without going unstable) to make the process variable respond appreciably before anequivalent dead time. More accurately, the characteristic time of the loop is determined by equivalent dead time consisting of pure dead time plus process components contributing more than 180 degrees of phase lag.

The phase of dead time increases proportionally with frequency. Any process having more than 180 degrees phase lag has equivalent dead time.

Fast Plant Test: A process test designed to quickly gather process model information from slow processes. This method works well with slow loops such as temperatures, compositions, and some tank levels.

Gain (of the controller): This is another way of expressing the "P" part of the PID controller. GAIN = 100/(Proportional Band). The more gain a controller has the faster the loop response and more oscillatory the process.

Gain (of the process): Gain is defined as the change in input divided by the change in output. A process with high gain will react more to the controller output changing. For example, picture yourself taking a shower. You are the controller. If you turned the hot water valve up by half a turn and the temperature changed by 10 degrees this would be a higher gain process than if the temperature changed only 3 degrees.

Gain Margin: The difference in the logarithms of the amplitude ratios at the frequency where the combined phase angle is 180 degrees lag is the GAIN MARGIN.

Hysteresis: In a valve with loose linkages, the air signal to the valve will have to change by an amount equal to the hysteresis before the valve stem will move. Once the valve has begun to move in one direction it will continue to move if the air signal keeps moving in the same direction. When the air signal reverses direction, the valve will not move until the air signal has changed in the new direction by an amount equal to the hysteresis.

I/O: Input/Output. Refers to the electronic hardware where the field devices are wired. Discrete I/O would have switches for inputs and relay outputs to fire solenoid valves or pump motors. Analog I/O would have process variable inputs, and variable controller outputs.

Integrating Process: With these loops, making a small change in the controller ouptut, will cause the process variable to ramp until it hits a limit. The larger the change, the faster the ramp. Also the smaller the integral time the faster it will move. It is a common mis-conception that integral time in the controller is not required to hold setpoint with an

integrating process. Most control loops are self-regulating. Self-regulating means that with a change in the controller output, the process variable will move and then settle. Integrating loops are also described as non-self-regulating. The most common example of an integrating processes is Tank Level.

Integral Action: The "I" part of the PID controller. With integral action, the controller output is proportional to the amount andduration of the error signal. If there is more integral action, the controller output will change more when error is present. If your units on integral are in "time/rep" or "time" then decreasing your integral setting will increase integral action. If your units on integral are in "rep/time or "1/time" then increasing your integral setting increases integral action.

Load Upset: An upset to the process (that is not from changing the set-point). A simple example: you are taking a shower and someone flushes the toilet. The temperature suddenly changes on you, the controller. Another example: you are injecting steam into flowing cold water to get lukewarm water, and the inlet cold water changes temperature.

Lag Time: Lag time is the amount of time after the dead time that the process variable takes to move 63.3% of its final value after a step change in valve position. Lag time is also called a capacity element or a first order process. Very few real processes are pure lag. Almost all real processes contain some dead time.

Measurement: Same as "process variable."

Manual Mode: In manual mode, the user sets the output. See Mode.

Mode: Auto, manual, or remote. In auto mode the controller calculates the output based its calculation using the error signal (difference between setpoint and PV). In manual mode, the user sets the output. In remote, the controller is actually in auto but gets its setpoint from another controller.

MMI: Man Machine Interface. Also known as "HMI" or Human-Machine Interface. Refers to the software and hardware that the process operator "sees" the process with. An example MMI screen may show you a tank with levels and temperatures displayed with bar graphs and values. Valves and pumps are often shown and the operator can "click" on a device to turn it on, off or make a setpoint change. Examples are Intellution's FIX DMACS, Wonderware's Intouch, Genesis's ICONICS, TA Engineering's AIMACS, and Intec's Paragon.

Open Loop: Controller in manual mode. See Mode.

OPC or OLE for Process Control is a standard set by the OPC Foundation for fast and easy connections to controllers. ExperTune Inc, is an OPC Foundation Member.

Output: Output of the PID controller. In auto mode the controller calculates the output based its calculation using the error signal

(difference between setpoint and PV). In manual mode, the user sets the output.

Phase Margin: The difference in phase at the frequency where the combined process and controller amplitude ratio is 0 is the PHASE MARGIN.

PID Controller: Controllers are designed to eliminate the need for continuous operator attention. Cruise control in a car and a house thermostat are common examples of how controllers are used to automatically adjust some variable to hold the process variable (or process variable) at the set-point. The set-point is where you would like the process variable to be. Error is defined as the difference between set-point and process variable.

(error) = (set-point) - (process variable)

The output of PID controllers will change in response to a change in process variable or set-point.

pH: A measure of how acidic or basic a solution is. pH is often a process variable to control.

PLC: Programmable Logic Controller. These computers replace relay logic and usually have PID controllers built into them. PLCs are very fast at processing discrete signals (like a switch condition). The most popular PLC manufacturers are Allen Bradley, Modicon, GE, and Siemens (or TI).

PV or Process Variable: What you are trying to control: temperature, pressure, flow, composition, pH, etc. Also called the measurement.

Proportional Band: The "P" of PID controllers. With proportional band, the controller output is proportional to the error or a change in process variable. Proportional Band = 100/Gain.

Proportional Gain: This is the "P" part of the PID controller. See gain. (of the controller). (Proportional gain)=100/(Proportional Band).

PV Tracking: An option on many controllers. When a control loop is in MANUAL, with PV Tracking turned on, the controller setpoint will follow the PV. When the loop is returned to AUTO, there is no sudden movement of the process, because the PV is already at setpoint. If PV Tracking is turned off, returning to AUTO will drive the loop to its previous setpoint.

Rate: Same as the derivative or "D" part of PID controllers.

Register: A storage location in a PLC. The ExperTune PID Tuner needs to know certain register addresses to tune loops in PLCs.

Regulator: When a controller changes a process variable to move the process variable back to the setpoint, it is called a regulator.

Reset: Same as the integral or "I" part of PID controllers.

Reset Windup: With a simple PID controller, integral action will continue to change the controller output value (in voltage, air signal or digital computer value) after the actual output reaches a physical limit. This is called reset (integral) windup. For example, if the controller is connected to a valve which is 100% open, the valve cannot open farther. However, the controller's calculation of its output can go past 100%, asking for more and more output even though the hardware cannot go past 100%. Most controllers use an "anti-reset windup" feature that disables integral action using one of a variety of methods when the controller hits a limit.

Robust: A loop that is robust is relatively insensitive to process changes. A less robust loop is more sensitive to process changes. See a presentation on Loop Stability, The Other Half of the PID Tuning Story

Sample Interval: The rate at which a controller samples the process variable, and calculates a new output. Ideally, the sample interval should be set between 4 and 10 times faster than the process dead time. See a presentation on What Sample Interval Should I Use?

Set-Point: The set-point is where you would like the process variable to be. For example, the room you are in now has a setpoint of about 70 degrees. The desired temperature you set on the thermostat is the setpoint.

Servo: When a controller changes a process variable to move the process variable in response to a setpoint change, it is called a servo.

Time Constant: Same as lag time.

Dead Time versus Time ConstantThe dynamic response of self-regulating processes can be described reasonably accurately with a simple model consisting of process gain, dead time and lag (time constant). The process gain describes how much the process will respond to a change in controller output, while the dead time and time constant describes how quickly the process will respond.

Although the dead time and time constant both seem to describe the same thing, there are several fundamental differences between how dead time and time constant affects a control loop. The first difference is that dead time describes how long it takes before a process begins to respond to a change in controller output, and the time constant describes how fast the process responds once it has begun moving.

Measuring the Dead Time and Time Constant of a ProcessLet’s begin with the measurement of dead time and time constant of a self-regulating process. Typically, one will place the controller in manual control mode, wait for the process variable to settle down, and then make a step change of a few percent in the controller output. At first the process variable does nothing (dead time) and then it begins changing (time constant) until finally it settles out at a new level.

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Measuring Dead Time and Time Constant

To measure the dead time and time constant, draw a horizontal line at the same level as the original process variable. We’ll call this the baseline. Then find the maximum vertical slope of the process variable response curve. Draw a line tangential to the maximum slope all the way to cross the baseline. We’ll call this crossing the intersection.

- The process dead time is measured along the time axis as the time spanned between the step change in controller output and the intersection.

Next, measure the total change in process variable. Then find the point on the process response curve where the process variable has changed by 0.63 of the total change in process variable. We’ll call this point P63.

- The process time constant is measured along the time axis as the time spanned between the intersection (described previously) and P63.

Dead Time versus Time ConstantWe can draw a chart with a continuum of dead time through time constant (see figure below). Processes woth dynamics consisting of pure dead time will be on the left and pure lag (time constant) on the right. In the middle the process dead time will equal its time constant.

We’ll find that flow loops and liquid pressure loops fall just about in the middle of the continuum, because their dead time and time constant are almost equal. Gas pressure and temperature loops will be located more toward the right – they are lag (time constant) dominant. Serpentine channels in water treatment plants and conveyors with downstream mass meters will appear on the left side – they are dead-time dominant.

Level loops should actually be treated differently, but can be approximated on the continuum by replacing the time constant with their residence time (time they will take to fill or empty out at full flow rate.) Most level loops will be located far to the right, having relatively short dead times.

The ratio of dead time to time constant affects the controller modes and tuning rules we use, the controllability of the process, and the minimum possible loop settling time.

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A continuum from pure Dead Time to pure Lag

Controller ModesThe derivative control mode works well where process variables continue to move in the same direction for some time, i.e. lag-dominant processes. Derivative control does not work well on processes where the process variable changes sporadically – typically processes with relatively short time constants, located in the middle and to the left on the continuum.

Applicability of Tuning RulesMost tuning rules will work on lag-dominant processes. However, the Ziegler-Nichols rules have only a narrow range of applicability. Lambda / IMC tuning rules apply to a broader spectrum of processes, while Cohen-Coon has the widest coverage. The Dead-Time tuning rule, applies to processes on the left, as its name implies.

ControllabilityLag-dominant loops are easier to control than dead-time-dominant loops. Operators find that lag-dominant processes respond much more intuitively than dead-time-dominant processes and are easier to control in manual mode.

Loop Settling TimeWhen tuning a loop for the shortest possible settling time, one finds that there is a minimum limit on settling time. If you tune the controller any tighter, the loop will begin oscillating. The minimum settling time depends mostly on the amount of dead time in a control loop, and will be between two and four times the length of the dead time. The ratio of time constant to dead time determines where the minimum settling time falls between two and four times the process dead time.

Fascinating stuff, right? To learn more, consider getting an in-house training workshop for you and your colleagues.

Let me know if you have questions, and feel free to leave a comment.

Tuning Rule for Dead-Time Dominant ProcessesDecember 15, 2010

Processes with lags or time constants (tau) longer than their dead times (td) are reasonably easy to tune. Most tuning rules work well for processes where tau > 2 td (lag dominant). The opposite is not true. Many tuning rules work very poorly when td > 2 tau (dead-time dominant).


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http://blog.opticontrols.com/wp-content/uploads/2011/06/td-versus-tau.png

Lag DominantWhen a process has a time constant that is much longer than the dead time, problems like overshoot and having to use high controller gains begin to appear. However, loops with long time constants still act in an intuitive way – if we add more control action we can make the process respond faster, like stepping down harder on the accelerator will get our car to the desired speed quicker.

Dead-Time DominantOn the other side of the spectrum, when a process’ dead time is significantly longer than its time constant, it behaves much less intuitively – adding more control action does not make the process respond faster. For example, if your shower water is a little cold, opening the hot water tap a lot more is not going to get you to the right temperature any quicker, and it is going to have some serious side-effects.

I once saw several operators struggle to manually control the outlet temperature of a three-pass kiln. The kiln was a dead-time dominant process and its dead time was about 10 minutes long. The operators would notice the temperature is below set point and increase the firing rate. When they see no effect, they increase the firing rate more. And then some more, and more. Finally, when changes have made their way through the dead time, the temperature overshoots its set point by a large margin. Then the operators take the same actions and make the same mistakes in the opposite direction.

Needless to say, controller tuning also becomes difficult on dead-time dominant processes.

Tuning

Step response of a dead-time dominant process.

You will find that the Ziegler-Nichols tuning rules don’t work well at all on a dead-time dominant process. For example, the following process characteristics were measured from the step-response of a dead-time dominant process in the previous plot:

td = 0.276 minutestau = 0.013 minutesgp = 0.89

Applying the Ziegler-Nichols tuning rules to this process gives the following controller settings: Kc = 0.05; Ti = 0.92 minutes. The result is an extremely sluggish control loop (see below).


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Dead-time dominant loop tuned with the Ziegler-Nichols tuning rules.

Processes with time constants (tau) longer than their dead times (td) are reasonably easy to tune. Most tuning rules work well for processes where tau > 2 td (lag dominant). The opposite is not true. Most tuning rules work very poorly when td > 2 tau (dead-time dominant).

The Lambda tuning rules were designed for lag dominant processes and do not work all that well on dead-time dominant processes either. The Cohen-Coon tuning rules work much better than the Ziegler-Nichols rules, but they too aren’t the best tuning rule when the dead time is five or ten times as long as the time constant.

So what type of tuning rule will work well for controlling dead-time dominant processes? First, we need a lag-dominant controller, to make up for the absence of lag in the process. But if we just crank up the integral term, the loop will become unstable. So, second, we have to compensate by decreasing the controller gain.

The Cohen-Coon PI tuning rules will work reasonably well up to td = 2 tau, but it becomes sluggish after that. When td > 2 tau, it is better to use the dead-time tuning rule. It is as follows:

Kc = 0.36 / (gp * SM)Ti = td / 3No derivative.

SM is the stability margin and can be set to a value between 1 and 4. A value of 1 is equivalent to the 1/4-amplitude damping response. It is considered unsafe – the loop is very sensitive to changes in process conditions. A value of 2 or higher is recommended. It will reduce the overshoot, eliminate unnecessary cycling, and make the loop far more robust to changes in process conditions.

Hint: measure dead time in the same units of time as your controller’s integral setting. E.g. if your controller’s Ti setting is in minutes, measure td in minutes.

Notes:- The tuning rules above are designed to work on controllers with interactive or non-interactive algorithms, but not controllers with parallel algorithms.- Furthermore, they will work only on controllers with a controller gain setting and not a proportional band (found on Foxboro I/A controllers, for example).- The rules assume the controller’s integral setting is in units of time (minutes or seconds), and not integral gain or rate (repeats per minute or repeats per second).

If your controller is different, parameter conversions will allow you to use these rules.

Applying the dead-time tuning rules to the process described above gives the following controller settings: Kc = 0.2; Ti = 0.092 minutes. The result is significantly better than what can be obtained with other tuning rules.





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Dead-time dominant loop tuned with the Dead-Time tuning rules.

Better loop response can be obtained with a Smith Predictor, but that is more complex to implement, more tedious to tune, sensitive to changes in process characteristics, and perhaps the topic of a future blog.

Process ControllersBasic process controllers with proportional, integrating and derivative functions

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Basic ControllerThe Basic Controller for an application can be visualized as

The controller consists of

a measuring unit with an appropriate instrument to measure the state of process, a temperature transmitter, pressure transmitter or similar.

a input set point device to set the desired value. a comparator for comparing the measured value with the set point, calculating the

difference or error between the two. a control unit to calculate the output magnitude and direction to compensate the

deviation from the desired value.

http://www.engineeringtoolbox.com/process-controllers-d_499.html

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a output unit converting the output from the controller to physical action, a control valve, a motor or similar.

Controller PrinciplesThe Control Units are in general build on the control principles

proportional controller integral controller derivative controller

Proportional Controller (P-Controller)One of the most used controllers is the Proportional Controller (P-Controller) who produce an output action that is proportional to the deviation between the set point and the measured process value.

OP = -kP Er (1)

where

OP = output proportional controller

kP = proportional gain or action factor of the controller

Er = error or deviation between the set point value and the measured value

The gain or action factor - kP

influence on the output with a magnitude of kP

determines how fast the system responds. If the value is too large the system will be in danger to oscillate and/or become unstable. If the value is too small the system error or deviation from set point will be very large.

can be regarded linear only for very small variations.

The gain kP can be expressed as

kP = 100 / P (1b)

where

P = proportional band

The proportional band P, express the value necessary for 100% controller output. If P = 0, the gain or action factor kP would be infinity - the control action would be ON/OFF.

Note! A proportional controller will have the effect of reducing the rise time and will reduce, but never eliminate, the steady-state error.

Integral Controller (I-Controller)With integral action, the controller output is proportional to the amount of time the error is present. Integral action eliminates offset.

OI = - kI Σ(Er dt) (2)

where

OI = output integrating controller

kI = integrating gain or action factor of the controller

dt = time sample

The integral controller produce an output proportional with the summarized deviation between the set point and measured value and integrating gain or action factor.

Integral controllers tend to respond slowly at first, but over a long period of time they tend to eliminate errors.

The integral controller eliminates the steady-state error, but may make the transient response worse. The controller may be unstable.

The integral regulator may also cause problems during shutdowns and start up as a result of the integral saturation or wind up effect. An integrating regulator with over time deviation (typical during plant shut downs) will summarize the output to +/- 100%. During start up the output is set to 100%m which may be catastrophic.

Derivative Controller (D-Controller)With derivative action, the controller output is proportional to the rate of change of the measurement or error. The controller output is calculated by the rate of change of the deviation or error with time.

OD = - kD dEr / dt (3)

where

OD = output derivative controller

kD = derivative gain or action factor of the controller

dEr = deviation change over time sample dt

dt = time sample

The derivative or differential controller is never used alone. With sudden changes in the system the derivative controller will compensate the output fast. The long term effects the controller allow huge steady state errors.

A derivative controller will in general have the effect of increasing the stability of the system, reducing the overshoot, and improving the transient response.

Proportional, Integral, Derivative Controller (PID-Controller)The functions of the individual proportional, integral and derivative controllers complements each other. If they are combined its possible to make a system that responds quickly to changes (derivative), tracks required positions (proportional), and reduces steady state errors (integral).

Note that these correlations may not be exactly accurate, because P, I and D are dependent of each other. Changing one of these variables can change the effect of the other two.

Controller Response Rise Time Overshoot Settling Time Steady State Error

P Decrease Increase Small Change Decrease

I Decrease Increase Increase Eliminate

D Small Change Decrease Decrease Small Change

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Control NotesReflections of a Process Control Practitioner

Below are the contents of the Control Notes website, not the contents of the book.To see the contents of the book, click the book’s image on the right, and then click the “Look Inside” link.

1. General

o Introduction to Control Systems and Optimization

o Quarter Amplitude Damping

o Settings in the Controller were Closer than they Appeared

o Tools of the Tuner

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2. Process Characteristics

o Causes of Dead Time in a Control Loop

o Dead Time versus Time Constant

o Inverse Response

o Level Control Loops

3. PID Controllers

o Bumpless Transfer and Bumpless Tuning

o Derivative Control

o Gap Control

o PID Controller Algorithms

o PID Controllers Explained

o Settings in the Controller were Closer than they Appeared

o Unraveling Controller Algorithms

4. Controller Tuning

o Cohen-Coon Tuning Rules

o Comments on the Ziegler-Nichols tuning method

o Detuning Control Loops

o Is Lambda a Bad Tuning Rule?

o Lambda Tuning Rules

o Level Controller Tuning

o Minimum IAE Tuning Rules

o Quarter Amplitude Damping

o Surge Tank Level Control

o Tank Level Tuning Complications

o Tuning Rule for Dead-Time Dominant Processes

o Typical Controller Settings

o When to Use which Tuning Rule

o Ziegler-Nichols Closed-Loop Tuning Method

o Ziegler-Nichols Open-Loop Tuning Rules

5. Control Valves

o Butterfly Valves and Control Performance

o Control Valve Linearization

o Control Valve Problems

o Equal Percentage Control Valves and Applications

o Valve Diagnostics on a Level Loop

6. Loop Performance, Problems, and Diagnostics

o An Oscillating Level Control Loop


o Caster Level Control Improvement

o Control Loop Performance Monitoring

o Control Valve Problems

o Diagnosing and Solving Control Problems

o Q&A on Loop Performance

o Valve Diagnostics on a Level Loop

7. Control Strategies

o A Tutorial on Cascade Control

o A Tutorial on Feedforward Control



o Control Valve Linearization

o Drum Level Control

o Improving pH Control

o Ratio Control

o Steam Temperature Control

8. Case Studies

o A pH Control Success Story

o An Oscillating Level Control Loop



o Flow Control Conundrum

o How to Fill a Container

o Inverse Response

o Level Versus Flow Control

o Pressure and Flow Control Loop Interaction

o Process Oscillations from Afar

o Ratio Control

o Tank Level Tuning Complications

9. Tips and Work-Process

o Best Practices for Control Loop Optimization

o Diagnosing and Solving Control Problems

o Process Control for Practitioners

o Testing Control Loop Performance

o Tools of the Tuner

o Tuning Tips - How to Improve Your Results

o When to Use which Tuning Rule

o Why Tuning Rules Don't Always Work

1. General o Introduction to Control Systems and Optimization

o Quarter Amplitude Damping o Settings in the Controller were Closer than they Appeared o Tools of the Tuner

Introduction to Control Systems and OptimizationJanuary 2, 2010

Since my company, OptiControls Inc, specializes in the optimization of process control systems, I thought it would be appropriate to begin my blog with a non-technical description of the problem it solves for customers, and how it is done.

What is automatic control?

Cruise Control

One of the best-known domestic examples of automatic controls would be the cruise control of a motor car. The cruise control keeps the car’s speed constant, despite road gradient and wind direction. When the road runs uphill or downhill, the cruise control automatically changes the accelerator position to keep the car’s speed constant.

Similarly, industrial processes have automatic control systems for keeping them under control and maintaining all process conditions close to their specified operating levels. For example, at a power station, the water level in the boiler, steam temperature, and steam pressure (as well as many other items) are kept in check by the automatic control system. Complex process plants can have hundreds or even thousands of individual temperatures, flows, levels, pressures and other conditions that are controlled simultaneously.

Simple Flow Control Loop

At the core of an automatic control system are individual controllers – each controlling one aspect of the process. Each controller monitors a specific process condition via feedback from a sensor and compares it to the desired value (set point). The controller tries to correct any difference between the measurement and set point by changing its output to the process, which changes the position of a final control element (like a valve) and drives the process back towards the set point. This loop consisting of the measurement, controller, final control element, and process, is called the control loop.

So what’s the challenge with this?




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Three-Loop Controller

Industrial controls need to be properly tuned to do a good job of regulating all the process conditions. Improperly tuned controls can cause unsafe process conditions, poor product quality, unnecessary plant shut-downs, longer start-up times and higher operating and maintenance costs.

An example of where humans act like controllers is when we regulate the water temperature while taking a shower. If the water is too cold, we open the hot water tap a bit and when the water is too hot we close it a bit. And we all know from experience how important it is to turn the tap the right amount and at the right speed. If we turn it too much or too fast we will get burnt or chilled, if we turn it too little or too slow we will be uncomfortable for a longer period.

A controller has adjustable settings that govern the magnitude and rate of the changes it will make to the process. The magnitude and rate of the controller’s output changes should be optimized for the dynamics of the process it is controlling. If the controller reacts too fast the process will overshoot its set point. If the controller reacts too slow it will take too long to get to set point. Getting the right tuning settings for some complex processes can be quite challenging.

How well are industrial controls performing?

Unfortunately, poorly functioning controls are very common in industry. Various studies have shown that up to 30% of controllers do not function in automatic control mode at all, while another 30% of control loops function quite poorly in automatic control mode.

In many cases the problems exist because the personnel who originally installed the control system were not well skilled at optimizing the controls. The controllers were tuned very roughly and only well enough to get the process up and running, frequently leaving much room for improvement. In addition to this bad start, process dynamics often change during operation, and the integrity of control equipment deteriorates over time, which further reduces the effectiveness of the controls.

How should automatic controls be optimized?

You should always do control loop optimization in a systematic way, working closely with the process operator and process engineer. Before a controller is tuned, the purpose of the control loop and the control objective are established. Then the design of the control loop is reviewed and diagnostic tests are run to ensure proper performance of the measuring device and final control element. Assuming no problems are found, the controller is tuned to work in harmony with the dynamics of the process it is controlling, and to meet the overall control objective of the loop.

The dynamic behavior of the process is determined by analyzing data from a simple process response test. Appropriate controller settings are calculated using tuning formulas or a computer program. Finally, the new settings are entered into the controller and one or more response tests are done to ensure the process is being controlled properly and that the control objective is met. Ideally, the controller’s performance will be monitored periodically for a few days after tuning and under different process conditions to verify improved operation.

Quarter Amplitude Damping







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October 4, 2013

Quarter-amplitude damping is likely the best-known tuning objective, but it’s a poor choice for process stability. Also called quarter amplitude decay or QAD, many tuning rules, including the famous Ziegler-Nichols and Cohen-Coon tuning rules, were designed for this objective. The idea behind quarter-amplitude damping is to eliminate any error between the setpoint and process variable very fast. In fact, the controller responds so fast that the process variable actually overshoots its setpoint and oscillates a few times before it finally comes to rest (Figure 1). The deviation from setpoint gets smaller with each successive cycle at a ratio of 4:1. In Figure 1, the ratio of B/A = 1/4.

Figure 1. A quarter-amplitude-damping response after a process disturbance.

When developing their tuning rules, Ziegler and Nichols chose quarter-amplitude damping to be “optimum” control loop response. Although QAD performance lies in the middle between a completely dead controller and an unstable control loop, you should realize that quarter-amplitude damping, by design, causes the process to overshoot its set point and to oscillate around it a few times before eventually settling down. Practitioners with solid experience in controller tuning will all tell you that quarter-amplitude-damping is a very poor choice for tuning industrial control loops.Problems with Quarter-Amplitude Damping

Although the quarter-amplitude damping tuning objective provides very fast rejection of disturbances, it creates three problems:

1. It makes the loop very oscillatory, often causing interactions with similarly tuned loops. If control

loops in a highly interactive process, such as a paper machine, power plant boiler, or

hydrodealkylation process, are tuned for quarter-amplitude damping, oscillations affecting the

entire process often occur.

2. It causes a loop to overshoot its setpoint when recovering from a process disturbance and after a

setpoint change. Many processes cannot tolerate overshoot.

3. QAD-tuned loops are not very stable and have low robustness. They can very easily become

completely unstable if the process characteristics change. For example, such a loop will become

unstable if its process gain doubles, which can happen very easily in industrial processes.

Solution

An easy way to minimize all three problems is to reduce the controller gain (detune the controller). The minimum reduction I recommend is to use the calculated Kc divided by two (or more if necessary). For example, if a quarter-amplitude-damping tuning rule suggests using a controller gain of 0.9, then use 0.45 instead. This will greatly reduce oscillations and overshoot in the control loop, and it will increase the loop’s robustness by a factor of two. (Please note that if your controller uses a parallel algorithm, you have to reduce Kp, Ki, and Kd to achieve the equivalent effect).

Stay tuned!

Jacques SmutsPrincipal Consultant at OptiControls, and author of Process Control for Practitioners.

Posted in 1. General, 4. Controller Tuning

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One Response to “Quarter Amplitude Damping” Don Parker :

October 8, 2013 at 5:11 pm

Jacques,I have worked with boiler/turbine controls for many years and could not agree more. So many of the processes are interactive that they must be tuned wthout oscillation, generally with maximum overshoot of about 5%.

Of course there is also the problem of over-active actuators, which can cause premature aging, wear, linkage hysteresis, etc.

I have found Lambda tuning to be a very successful method for many power plant control loops.

Settings in the Controller were Closer than they Appeared

May 17, 2012

Before I do step-testing to analyze and tune a control loop, I always take a look at the current tuning settings in the controller.

The controller’s gain setting gives me some indication of the sensitivity of the process, e.g. if the

controller gain is 0.1 the process could be very sensitive to controller output changes.

The controller’s integral time gives me an idea of the speed of the process dynamics, i.e. a short

integral time usually means fast process dynamics and vice versa.

The derivative time (if used) can reveal if the last person tuning the loop lacked understanding of

the tuning process, e.g. if the derivative time is set to more than half the integral time, or less than

one-eighth of it.

Earlier this month I optimized control loops on an oil platform. A few of the loops were oscillating. One of the oscillating loops, a gas pressure control loop on a separator, had a controller gain of 16! I facetiously told the control engineer: “Well, there’s your problem!” A value of 16 did seem like an abnormally large controller gain, but I know there are many exceptions from “normal” in process control.

A closer look revealed the reason for the high controller gain. Even though the set point was set to the normal operating pressure of 200 PSI, the pressure transmitter was calibrated to measure between 0 and 4000 PSI. So the operating pressure was at only 5% of the measurement range! A more appropriate measurement range would have been 0 – 400 PSI, since the maximum design pressure for the vessel was 380 PSI. In this case, the calibration range was ten times larger than it should have been. Considering that the measurement span was ten times over-ranged, the controller gain had to be ten times larger than “normal” to compensate. This means the effective gain of the controller was only 1.6, which is a reasonable value, especially for gas pressure control. In other words, the high controller gain was not responsible for causing the control loop instability. It turned out that the control loop was oscillating because of control valve stiction.

Based on these findings I recommended a replacement / recalibration of the pressure transmitter and the subsequent reranging of the signals in the DCS. After doing this, the controller gain must be set to 1.6. I also recommended that the sticky control valve be repaired or replaced to fix the oscillations.

The high controller gain cancelled out by the large measurement span reminded me of the warning on a passenger-side rear-view mirror: “Objects in the mirror are closer than they appear.”

Objects in the mirror are closer than they appear.

Learn more about controller settings from the book Process Control for Practitioners.Try it out for yourself using the OptiControls Loop Simulator.

Stay Tuned!

Jacques SmutsFounder and Principal ConsultantOptiControls Inc.

Tools of the TunerJuly 8, 2013

A control loop tuner should be proficient in using a variety of tools to be effective in any tuning situation. Customers often ask me how I tune loops, and my answer is that I use several tools – depending on the situation. Here is an overview of the tools I frequently use when analyzing and optimizing control loops.

Process Historian

Indispensable for much more than tuning, the process historian is one of my most-used tools. I use it to check valve linearity, analyze process interactions, compare loop performance before and after tuning, design feedforward controllers and characterizers, and to analyze the step-response of a process for tuning the controller.

Some plants where I work have no OPC connection for retrieving real-time process data, or don’t allow installing data collection software to collect real-time process data. Then their process historian is my only way to access plant data. I often analyze the step response for tuning purposes using the historian’s user interface, but if it is easy enough to export data to Excel, I will go that route and analyze the data using tuning software on my laptop.

For fast-responding loops, I ask the system administrator to speed up the sampling rate, because the default sampling interval on most historians is 30 to 60 seconds, which is too slow for analyzing fast loops. A one-second sampling interval is required for flow and liquid pressure loops, five seconds for most other loops, while 30 to 60 seconds serve only the slowest loops.

Some control loops I work on have processes that take hours to respond. In more than half of these cases I can go back in history and find sufficiently large operator-induced step changes that I can use for analysis and tuning. That saves me from having to do step tests and wait hours for the process to respond. I always try to get at least three of these step changes, but I prefer to have more if the process models change from one step-test to the next. This saves me a lot of time on slow-responding processes because the complete response is already in the historian. This also minimizes the need for disturbing the process with additional step tests.





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Process Historian

Excel

When I analyze step-test data directly on the historian, I use a pre-built Excel spreadsheet to simplify the data analysis and controller tuning calculations. I take down a few readings from the historian and enter them into the spreadsheet, and it calculates the process characteristics, and recommends tuning settings. It supports self-regulating and integrating process types, and has Cohen-Coon, Ziegler-Nichols, Lambda/IMC, Dead-Time, Surge-Tank, and Level-Averaging tuning rules. It also allows me to speed up or slow down the loop response by calculating different tuning settings, based on my tuning objective. Every thing I need for my tuning calculations!

Excel Tuning Calculator

Loop Simulation Software

Loop Explorer is a simulation and tuning software tool that I developed to give me insights into how a loop would respond to setpoint changes and disturbances. This is essential for obtaining optimal tuning settings for the loop’s control objective. The simulator is especially handy when I use the spreadsheet to analyze the step response, since the spreadsheet does not have its own simulator. I also use the Loop Explorer software in my training classes to demonstrate many concepts related to process characteristics, PID controllers, and controller tuning.







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Loop Explorer Software

Tuning Software

Of course I also use commercial tuning software. I recommend that every plant who does tuning in-house invest in good tuning software and have it accessible in every control room. If I work at a plant that already has high-end tuning software installed, I use their software. Otherwise I use the tuning software I have on my laptop. High-end tuning software applications analyze process response and automatically identify process characteristics. They provide access to different tuning methods, and render simulations of loop response with the new tuning settings. They also have databases of controller types, so one doesn’t have to deal with manually converting tuning constants to suit a specific controller.

One very important point: Tuning software is just a tool and is no substitute for understanding process dynamics, PID controllers, and the tuning process. If you can’t tune control loops by manually determining process characteristics from step-response data, and applying an appropriate tuning rule to calculate tuning constants, you will likely not be successful with software either.

Operator Time Trends

When I do step testing, I mostly sit right next to the operator. Then we use his/her real-time trends for the control loop to monitor the response. When sitting next to the operator I can point to certain anomalies, and explain why I do certain tests. It is also a great time to get to know the operator, learn about the process he controls, and become familiar with the culture of the company.

P&ID and Operator Graphics

Before analyzing and tuning a control loop, I ask the operator to explain the process to me. He/she will often use their operator graphics to show me the streams into and out of the process, and the location of valves, pumps, heat exchangers etc. Process engineers will often give me a set of P&IDs that I refer to.

In several occasions I discovered that other interacting or subordinate loops have to be tuned first, or placed in manual, before I could attend to the loop of concern. I also find flow measurements, not being used for control, that I can trend for supplemental information on the control valve’s performance, or if there might be a need for implementing cascade control.

Operator Graphic


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Pen, Paper, and Calculator

And don’t forget the traditional pen, paper and calculator. I find it handy and convenient to quickly draw a diagram on paper, take notes, or to quickly run through calculations. I would often transfer my written notes to electronic format for inclusion in my report after the day’s tuning, or while waiting for step-test results on a slow loop.

Hand Calculations

Process Walk-Down

Whenever possible, I go out to the plant with an experienced operator or engineer to take a look at the process, equipment, and physical location and condition of the control valves and instrumentation. One time I was dealing with a vastly oversized nitrogen injection control valve that was used to control pressure on a distillation column. The loop was completely unstable, regardless of any tuning settings we tried. We tried making 0.1% steps in controller output with the controller in manual mode. Stepping the controller output upwards from 1.5% to 2.4% the column pressure showed no response (no physical change in valve opening), but at 2.5% the pressure sharply decreased. When the operator and I went out to the valve and radioed back to the control room to repeat the test, we noticed that the valve position bumped by about 5% instead of the 0.1% change in controller output. We would never have known this if we did not go to the valve. After the faulty positioner was replaced we could stabilize the loop. (However, control was still poor because the valve was grossly oversized.)

Process Walkdown

Literature


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I have several really good books on process control, instrumentation, control valves, processes, PID controllers, and tuning. Some of them are academically inclined, making them virtually useless for tuning controllers in real plants. But some others are much more practical in nature. The latter is obviously more suitable for practitioners. I track the sales of eight of these practical books on amazon.com and the top seller, Process Control for Practitioners, has sold more copies over the last two years than the next three books together.

Summary

Even though I am a big proponent of tuning software, it is not the only tool available for analyzing and tuning control loops. It is important to consider the situation, and use the most appropriate tool or technique for analyzing and optimizing control loops – even if it comes down to doing manual calculations on a piece of paper.

2. Process Characteristics o Causes of Dead Time in a Control Loop o Dead Time versus Time Constant o Inverse Response o Level Control Loops

Causes of Dead Time in a Control LoopOctober 18, 2010

I always cover process characteristics as part of the process control training classes I present. It’s necessary for understanding process behavior and controller tuning.

The picture below shows the typical response of a self-regulating process after a step change in controller output. The process dead time (td) follows the change in controller output (CO). The process time constant is indicated with the Greek symbol τ (tau).

Dynamic Process Response to a Step Test

During the discussion on process characteristics, I show students how dead time affects the minimum settling time of a control loop. Even with the best possible tuning, a loop will still need a minimum of four times the dead time to settle out after a set point change or a disturbance. (Some people say a loop needs the equivalent of 10 dead times to settle, but appropriate tuning can normally do better than that if speed is the objective.)

Loop Response after a Disturbance

During a training class on controller tuning that I recently presented, one of the students pondered the relationship between dead time and minimum settling time for a while and then asked me how one can

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decrease the dead time of a process. I answered that the length of dead time is mostly determined by the process design, but if you consider all the contributors to dead time, there might be some of them you can reduce or eliminate.

Here is a list of contributors to dead time:

Actual process transportation lag. This is the time it takes your control action to progress through

the process equipment and reach the sensor. There is seldom something you can do about

transportation lag, but in some cases you may be able to move the sensor closer to the control

action to shorten the time delay.

Small lags in control loop. Although these are technically not true dead time, small lags increase

the apparent dead time of a loop, and has the same effect on tuning and settling time as true dead

time. Small lags creep in all along the control loop, and can be a significant contributor to overall

dead time:

o Thermowell thickness. Use the thinnest allowable thermowell for the fastest response.

o Thermocouple or RTD response time. Use fast-responding devices to reduce dead time.

For example, grounded thermocouples respond significantly faster than ungrounded ones.

o Tightness of fit of thermocouple or RTD. A less-than-tight fit of a temperature sensor inside

a thermowell can add an enormous lag to the control loop. Consider using heat transfer

compound to improve temperature response if conditions allow.

o Instrument dampening or filtering. Unless you have a good reason for using instrument

dampening or filtering, turn this feature off or set it to zero.

o Pneumatic tubing. 500 feet of ¼” tubing has a lag of about 4 seconds. This is very long,

considering that a 4-20 mA signal will have no delay along the same length. There is very

little reason to still have long runs of pneumatic tubing in plants today.

o Old positioner. Positioners used to be so slow that they were not recommended for use on

valves in flow control loops. Nowadays they respond very fast. If you have old positioners

on a loop you want to tune faster, consider replacing it with a new, fast positioner.

o Slew rate of valve. A control valve can take a considerable time to slew to a new position.

The larger the position change, the longer it takes to get there. Installing high-volume

positioners can dramatically shorten the slew time on slow valves.

o Velocity limiting of controller output. Some controllers are set up to limit the rates at which

their outputs change. This may be necessary to protect process equipment, but consider

setting this as fast as allowed by the equipment.

Controller scan interval. The periodic-execution nature of a digital controller will add an average

dead time of one half of the scan interval to the dead time of a loop.

Analyzer sampling time. Similar to controller scan interval, but normally much longer in duration. If

an analyzer samples the process every 5 minutes, the periodic sampling adds an average of 2.5

minutes to the loop dead time.

Some of these contributors to dead time may seem small or even trivial, but if you consider that 5 seconds of additional dead time increase the minimum loop settling time by 20 seconds or more, the value in finding and eliminating the small lags in a loop is more obvious.

Contact me if you have any questions.

Dead Time versus Time ConstantJune 21, 2011

The dynamic response of self-regulating processes can be described reasonably accurately with a simple model consisting of process gain, dead time and lag (time constant). The process gain describes how much the process will respond to a change in controller output, while the dead time and time constant describes how quickly the process will respond.

Although the dead time and time constant both seem to describe the same thing, there are several fundamental differences between how dead time and time constant affects a control loop. The first difference is that dead time describes how long it takes before a process begins to respond to a change in controller output, and the time constant describes how fast the process responds once it has begun moving.

Measuring the Dead Time and Time Constant of a Process

Let’s begin with the measurement of dead time and time constant of a self-regulating process. Typically, one will place the controller in manual control mode, wait for the process variable to settle down, and then make a step change of a few percent in the controller output. At first the process variable does nothing (dead time) and then it begins changing (time constant) until finally it settles out at a new level.

Measuring Dead Time and Time Constant

To measure the dead time and time constant, draw a horizontal line at the same level as the original process variable. We’ll call this the baseline. Then find the maximum vertical slope of the process variable response curve. Draw a line tangential to the maximum slope all the way to cross the baseline. We’ll call this crossing the intersection.

- The process dead time is measured along the time axis as the time spanned between the step change in controller output and the intersection.

Next, measure the total change in process variable. Then find the point on the process response curve where the process variable has changed by 0.63 of the total change in process variable. We’ll call this point P63.

- The process time constant is measured along the time axis as the time spanned between the intersection (described previously) and P63.

Dead Time versus Time Constant

We can draw a chart with a continuum of dead time through time constant (see figure below). Processes woth dynamics consisting of pure dead time will be on the left and pure lag (time constant) on the right. In the middle the process dead time will equal its time constant.

We’ll find that flow loops and liquid pressure loops fall just about in the middle of the continuum, because their dead time and time constant are almost equal. Gas pressure and temperature loops will be located more toward the right – they are lag (time constant) dominant. Serpentine channels in water treatment plants and conveyors with downstream mass meters will appear on the left side – they are dead-time dominant.

Level loops should actually be treated differently, but can be approximated on the continuum by replacing the time constant with their residence time (time they will take to fill or empty out at full flow rate.) Most level loops will be located far to the right, having relatively short dead times.

The ratio of dead time to time constant affects the controller modes and tuning rules we use, the controllability of the process, and the minimum possible loop settling time.

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A continuum from pure Dead Time to pure Lag

Controller Modes

The derivative control mode works well where process variables continue to move in the same direction for some time, i.e. lag-dominant processes. Derivative control does not work well on processes where the process variable changes sporadically – typically processes with relatively short time constants, located in the middle and to the left on the continuum.

Applicability of Tuning Rules

Most tuning rules will work on lag-dominant processes. However, the Ziegler-Nichols rules have only a narrow range of applicability. Lambda / IMC tuning rules apply to a broader spectrum of processes, while Cohen-Coon has the widest coverage. The Dead-Time tuning rule, applies to processes on the left, as its name implies.

Controllability

Lag-dominant loops are easier to control than dead-time-dominant loops. Operators find that lag-dominant processes respond much more intuitively than dead-time-dominant processes and are easier to control in manual mode.

Loop Settling Time

When tuning a loop for the shortest possible settling time, one finds that there is a minimum limit on settling time. If you tune the controller any tighter, the loop will begin oscillating. The minimum settling time depends mostly on the amount of dead time in a control loop, and will be between two and four times the length of the dead time. The ratio of time constant to dead time determines where the minimum settling time falls between two and four times the process dead time.

Fascinating stuff, right? To learn more, consider getting an in-house training workshop for you and your colleagues.

Let me know if you have questions, and feel free to leave a comment.

Stay tuned!Jacques Smuts – Author of the book Process Control for Practitioners

Posted in 2. Process Characteristics

4 Responses to “Dead Time versus Time Constant” Tejaswinee:

October 9, 2012 at 8:01 am

Sir, you explained the method for self-regulating processes. How we calculate delay, tau and Ts for processes which are not self-regulating?

Jacques :


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Tejaswinee, please see this article on level controller tuning for determining dead time on non-self-regulating (integrating) processes. For integrating processes, process time constants contribute to the apparent dead time, so we don’t have to consider them independently. And the estimated minimum closed-loop settling time will be four times as long as the apparent dead time.- Jacques

Nay:

May 21, 2013 at 12:26 am

Hi ! please help me on dead time also. For my case , pressure control PID ( reverse acting)at first PV is higher than SP(52) , so CV is 100% open. but eventually PV goes down and pass SP(52) , for example: PV(51.5 or 51 ) . but PID not start closing and take long time 5-15 min to start tuning. Recently , PID parameters are Kp 6.5 , Ki 0.3 and Kd 0. Kindly advise me …Thanks in advance

Jacques :

May 21, 2013 at 8:58 am

Nay, you have to do step-tests and use the process’s dynamic characteristics to calculate appropriate tuning settings.Se this writeup for more details: Cohen Coon Tuning Rules.

nverse ResponseAugust 5, 2013

When you push down on your car’s accelerator, you expect the car to speed up, right? What if it slows down? Or even worse: You lift your foot off the accelerator and your car speeds up. And the more you lift your foot, the more the car speeds up. These are almost unthinkable and certainly scary situations, yet they occur every day in thousands of boilers and some other processes around the world. The phenomenon is called an inverse response. One of the most common occurrences of inverse response is found in the control of boiler drum level.

Boiler Drum Level Control

In a boiler, water is converted to steam. Steam and water separates in the boiler drum, with the steam then leaving through a pipe at the top of the drum. It is important to keep the level of water in the drum away from this pipe or water will exit with the steam and damage downstream equipment. Even more important is to always have some water in the drum – when the boiler runs dry there is no water to cool it, and this will result in severe damage to the boiler. So the water level in the drum is normally maintained close to its centerline.

The drum level is controlled by adding water to the boiler, called feedwater. A closed-loop controller looks at the drum level and if it is lower than the setpoint it opens the feedwater control valve to increase the feedwater flow rate and vice versa (Figure 1). This brings us to inverse response…

Figure 1. Boiler drum level control diagram.

Inverse Response


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The temperature of the feedwater flowing into the drum is normally below boiling point. When we add more of this colder water to the boiler, some of the steam bubbles in the boiler condense. This causes the drum level to decrease and the effect is called inverse response. However, the effect is only temporary. After a while, the higher rate of feedwater flow overcomes the lost volume and the drum level rises (Figure 2). The opposite is also true: when we decrease the flow rate of the colder feedwater, steam production increases, and the additional steam bubbles cause the drum level to rise. But after a while, the drum level begins to fall, as expected.

Figure 2. With inverse response, the process first responds in the wrong (inverse) direction, and then in the expected direction.

I have not seen many other processes exhibiting inverse response. Two that come to mind are distillation column bottom level control (very similar to drum level control) and crystal size control in certain crystallizers (see case study below).

Tuning Implications

Processes exhibiting inverse response can easily cause control loop stability problems. Using derivative control is questionable from a stability perspective, and certainly not useful. Using a high controller gain is not possible since it will “chase” the inversely responding process and create a snowball (runaway) effect. But when you use a low controller gain on an integrating process, you also have to use a long integral time (low integral gain). So you end up with a very slow-responding control loop, and any attempt to speed it up significantly lowers its stability. This is why three-element control is the strategy of choice for drum level control.

When you do step-testing on a process with an inverse response and determine the process characteristics to tune the controller, you should treat the entire duration of the inverse response as dead time (Figure 3). Then you can apply your usual level controller tuning rules using this pseudo dead time.

Figure 3. Dead-time (td) measurement on an inversely responding process.

Case Study

Below is an example of dealing with inverse response in a different process.

A few weeks ago I was optimizing control loops on an ammonium sulfate crystallizer. The crystal size was very important, but it could not be measured directly. Instead the agitator motor amps were used as an indication of crystal size. Control was done by changing the feed rate of saturated liquid to the crystallizer, thereby changing the residence time of slurry in the crystallizer, and subsequently changing



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the crystal size. However, changes in feed rate also changed the crystallizer level, which turned out to cause a profound inverse response on the agitator amps because of the mechanical design of this particular crystallizer. The plant personnel was unaware of this, but the inverse response was revealed when we did step-testing.

The control was rather poor before we got started. There were large oscillations in motor amps, caused by large variations in crystal size. After step-testing, we calculated the new controller settings, recorded a week of data as a baseline (because we increased the process historian’s sampling resolution), and then entered the new settings. A time-trend of the control performance before and after tuning is shown in Figure 4.

Figure 4. Improvement in control of an inversely-responding process through proper tuning. New tuning settings were entered during the morning of 7/9. Blue = motor amps; Green = setpoint.

Needless to say, the production manager was very happy with the control improvement and the plant is now selling the ammonium sulfate crystals at a higher price because of the improvement in quality.

Level Control LoopsApril 15, 2010

Level loops are very common in industry. In fact, around 20% of control loops in the process industry (refining, petrochemical, power, paper & pulp, steel, etc.) are level loops, second in number only to flow loops. Consequently, I have optimized a large number of level control loops over the last two decades. Although the processes are different and have their own specific problems, a large percentage of the level loops I looked at had one or both of two very common problems: the controller had too much integral action, or the controller gain was too low.

Two Integrators

Integrating Process

A level-controlled process is also called an integrating process. This means that if there is an imbalance between what goes in and what comes out, the level will continue to rise or fall. PID controllers also have an integral term, and this is useful for getting a process all the way to its set point, something that proportional control alone cannot do.

However, the combination of the two integrators (level and controller’s integral term) in a level control loop often causes problems. Problems range from overshooting the set point, to oscillations, to


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downright instability. And the integral action of the controller is to blame. (I suppose we could blame the process, but that problem is more difficult to solve than tuning.)

Careful with that Integral!

In addition to having one extra integrator in the loop, level control loops are normally quite slow to respond. And a slow-responding process requires a long integral time (or low integral gain, depending on your controller’s integral unit.) If you have a long slow oscillation in a level control loop, compare the integral time to the period of the oscillation. If integral time is shorter than the period of the oscillation, that may be your problem.

Too Little Controller Gain

Many level-type processes have a very slow rate of response after a change in controller output. You might change the output by 10% and then you have to wait 15 minutes to see the level move by a few percent. To compensate for this slow rate of response, a high controller gain should be used.

Sometimes, a seemingly ridiculous controller gain, like 25 or more, is just what the level loop needs (but do read on about loop response objectives below). Most people would consider that controller gain to be just too high, and will dial down the gain to a more reasonable value of 3 or maybe 5. Doing this vastly changes the ratio between proportional and integral in the level control loop, making it less stable. If you lower the controller gain in a level loop, you must at the same time lengthen the integral time proportionally to maintain the ratio between integral and proportional, and hence maintain loop stability. This is not necessary on self-regulating loops like flow and temperature, but it is required on level control loops.

Control Objectives

Some people apply the Ziegler-Nichols tuning rules to level control loops. This gives the loop a very fast response, meaning a quick recovery after any deviation in the level. This may be the desirable response, but the control objective may very likely be different.

Slow Response / Surge Tanks

In many cases a slow response is needed in a level control loop, like for level control in a surge tank. For these applications you can apply level-averaging control or calculate the appropriate controller gain by simply using the desired high and low level limits in the tank. For example if the level should always remain between 20% and 80%, a Proportional Band (PB) of 60% (i.e. 80% – 20%) is needed. So set your controller gain to 100/PB (= 1.67 in this case) and turn off the integral action. Then, with the controller in manual, bring the level and the setpoint to 50%, momentarily change the controller output to 50%, put the controller in auto, and voila – you have a tuned and stable surge tank level loop. The operators should be trained that the level will not always be at setpoint, but it will always remain between the high and low limits.

Fast Response

A fast response may be needed, for example when controlling the level in a high-pressure gas separator on an oil platform. Using the Ziegler-Nichols tuning rules will give a very fast response, but will result in a loop with very little tolerance for changes in process characteristics, and a low tolerance for any measurement errors you might have made. In short – the Ziegler-Nichols tuning rules set a loop up with insufficient robustness.

To improve the robustness on a level loop tuned with the Ziegler-Nichols tuning rules, you can use 0.5 of the calculated controller gain, and 2 times the calculated integral time (or 0.5 of the integral gain – depending on which integral unit the controller uses). Follow this link for more detail on tuning level loops for a fast response.

3. PID Controllers o Bumpless Transfer and Bumpless Tuning o Derivative Control o Gap Control o PID Controller Algorithms o PID Controllers Explained





o Settings in the Controller were Closer than they Appeared o Unraveling Controller Algorithms

Bumpless Transfer and Bumpless TuningFebruary 1, 2010

Bumpless Transfer

Most control practitioners have heard of bumpless transfer, a feature available in virtually all PID controllers. It prevents a sudden jump (bump) in controller output when the controller’s mode is switched from manual to auto.

Bumpless transfer is done by the controller by executing its control algorithm to calculate a pseudo controller output, comparing this to the current manual controller output, and subtracting the difference from the integral term so that the calculated output matches the manual output. Bumpless transfer can also be achieved by using a velocity algorithm and not the more intuitive positional algorithm for calculating the controller output.

Both of these methods are pre-programmed in the controller code – an area normally available only to the controller manufacturer. Luckily, most controllers nowadays come standard with bumpless transfer.

Bumpless Tuning

Similar to bumpless transfer is the concept of bumpless tuning – a term coined by Harold Wade. In this case, without a bumpless tuning feature, the bump occurs due to changing controller gain or derivative settings during controller tuning.

Again ignoring integral and derivative control actions for now, the controller output (CO) is simply:

CO(old) = Kc(old) * E

CO(new) = Kc(new) * E

If E is not exactly zero when the change in Kc is made, the controller output will jump. Similarly, changing the controller’s derivative setting (Td) can create a jump in controller output if the rate of change of the error is not zero at the moment Td is changed.

It is because of the bump in controller output caused by changing tuning settings that it is good practice to place a controller in manual momentarily while making tuning changes. Because most controllers have bumpless transfer, it eliminates the bump when switching the controller back to auto after making the tuning changes in manual mode. However, this becomes a problem if the tuning settings are changed programmatically, as in the case of gain scheduling.

Bumpless tuning can be achieved without the need to place the controller in manual mode by calculating how much the controller output will jump due to the new proportional and derivative settings, and subtracting an equal quantity from the integral term, so that the sum of the three terms (the controller output) remains unchanged. Similar to bumpless transfer, bumpless tuning can also be achieved by using a velocity algorithm.

The bumpless tuning feature is pre-programmed in the controller device – and cannot be added afterward by the user. Far fewer controllers have this feature. For example, the modern C200 controllers from Honeywell do not have Bumpless Tuning, while DeltaV controllers from Emerson do.

Derivative ControlMay 3, 2010

When doing on-site services or training, I am often asked: When should one use the derivative control mode of a PID controller? Although there is no black & white division between when to use it or not, I have a few guidelines that should help your decision. But let’s take a step back first and review the derivative control mode and its role in a PID controller.


Figure 1. PID Controller

What is Derivative?You can think of derivative control as predicting the error in future, based on the current slope of the error. How far into the future? That’s what the derivative time (Td) is for. It is the prediction horizon. (Derivative control actually uses extrapolation, not prediction. But hey, we all understand how prediction works, so we’ll just go with that.)

Once the derivative mode has predicted the future error, it adds an additional control action of Controller Gain * Future Error.

For example, if the error changes at a rate of 2% per minute, and the derivative time Td = 3 minutes, the predicted error is 6%. If the Controller Gain, Kc = 0.2, then the derivative control mode will add an additional 0.2 * 6% = 1.2% to the controller output.

You don’t Absolutely Need DerivativeThe first point to consider when thinking about using derivative is that a PID control loop will work just fine without the derivative control mode. In fact, the overwhelming majority of control loops in industry use only the proportional and integral control modes. Proportional gives the control loop an immediate response to an error, and the integral mode eliminates the error in the longer term. Hence – no derivative is needed.

Why Use DerivativeThe derivative control mode gives a controller additional control action when the error changes consistently. It also makes the loop more stable (up to a point) which allows using a higher controller gain and a faster integral (shorter integral time or higher integral gain).

These have the effect of reducing the maximum deviation of process variable from set point if the process receives and external disturbance. For a typical temperature control loop, you can expect a 20% reduction in the maximum deviation. Figure 2 shows how a loop with derivative (PID) control recovers quicker from a disturbance with less deviation than a loop with P or PI control.

Figure 2. P versus PI versus PID control.

Obviously you don’t want to use derivative to speed up a loop if the control objective is slow response, like a surge tank, for example. But for loops where fast response is the objective, derivative could help. But do read on for information on when not to use derivative.

Noisy PVUsing the derivative control mode is a bad idea when the process variable (PV) has a lot of noise on it. ‘Noise’ is small, random, rapid changes in the PV, and consequently rapid changes in the error. Because the derivative mode extrapolates the current slope of the error, it is highly affected by noise (Figure 3). You could try to filter the PV so you can use derivative, as long as your filter time constant is shorter than 1/5 of your derivative time.

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Figure 3. Effect of Noise on Derivative.

Process DynamicsOn dead-time dominant processes, PID control does not always work better than PI control (it depends on which tuning method you use). If the time constant (tau) is equal to or longer than the dead time (td), like in Figure 4, PID control easily outperforms PI control.

Figure 4. Process Dynamics.

Temperature and Level LoopsTemperature control loops normally have smooth measurements and long time constants. The process variable of a temperature loop tends to move in the same direction for a long time, so its slope can be used for predicting future error. So temperature loops are ideal candidates for using derivative control – if needed. Level measurements can be very noisy on boiling liquids or gas separation processes. However, if the level measurement is smooth, level control loops also lend themselves very well to using derivative control (except for surge tanks and averaging level control where you don’t need the speed).

Flow Control LoopsFlow control loops tend to have noisy PVs (depending on the flow measurement technology used). They also tend to have short time constants. And they normally act quite fast already, so speed is not an issue. These factors all make flow control loops poor candidates for using derivative control.

Pressure Control LoopsPressure control loops come in two flavors: liquid and gas. Liquid pressure behaves very much like flow loops, so derivative should not be used. Gas pressure loops behave more like temperature loops (some even behave like level loops / integrating processes), making them good candidates for using derivative control.

Final WordsDerivative control adds another dimension of complexity to control loops. It does have its benefits, but only in special cases. If a loop does not absolutely need derivative control, don’t bother with it. However, if you have a lag-dominant loop with a smooth process variable that needs every bit of speed it can get, go for the derivative.

To learn more about controllers and tuning, contact OptiControls to for on-site process control training.


Posted in 3. PID Controllers | Tags: Controller Tuning, Derivative Control

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3 Responses to “Derivative Control” Garcier LaCamppiello:

June 14, 2012 at 4:17 pm

I used this as a refresher-review and found it very helpful. You have done a fine job at describing the derivative control mode and I recommend it to all readers. I am an Instrumentation Technician formerly with Alyeska Pipeline Service Co., Alaska, retired but still functional.

Thank you,

abdul wahab:

February 7, 2013 at 1:27 pm

nice, i am very happy to learn this

Sivasankar:

April 17, 2013 at 1:11 pm

Really useful…since im an inst engineer, having long time doubt about usage of derivative control…i searched lot n didn’t convince any answers…but here i really got wat i wanted..thanks a lot.

Gap ControlJuly 18, 2011

Some control loops have two seemingly conflicting objectives of keeping the process variable under control, but also minimizing controller output movement. Although such a loop will have a set point, it is more important to keep its process variable within predefined bounds than to keep it exactly at set point. A typical application of gap control is averaging level control. (Averaging control is somewhat like surge tank control, but the process variable is controlled around its set point. True surge tank level control rarely controls around its set point.)

Controller manufacturers have designed a modification of the standard PID control algorithm for use on processes with these conflicting objectives. This modification is called gap control and it works on the principle of two user-definable control regions, one for each of the two control objective.

The first region is far from set point (outside the gap) and requires a strong control action to turn the process around and bring it back to set point. The normal controller settings are used outside the gap. The second region is close to set point (inside the gap) within which the controller detunes itself based on a configurable gain multiplier M (between 0.0 and 1.0). The detuning helps to minimize controller output movements.

Gap Control (click to enlarge)

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Tuning a Gap Controller

To use gap control effectively, you should set the size of the gap around the set point according to the typical variation of the process variable so that the process variable does not frequently and unnecessarily venture outside the gap. Tune the controller for fast response outside the gap to provide quick recovery from disturbances. Use a gain multiplier (M) of 0.5 or less to minimize the controller output movement inside the gap.

For integrating processes divide the calculated integral time (Ti) by M (i.e. make the integral time longer in proportion to decreasing the controller gain). This is a requirement only for integrating processes and is done to ensure a stable integral term when the controller gain is reduced inside the gap. Do not use a gain multiplier of zero when controlling integrating processes because this dead band will cause the process variable to continuously cycle through the gap.

Gap control should not be used in control loops of which the objective is to keep the process variable as close to set point as possible. Use regular PI or PID control for those loops.


Posted in 3. PID Controllers

2 Responses to “Gap Control” JC:

June 6, 2014 at 2:39 pm

Jacques, you recommend using gain multiplier of 0.5 or less. Is there any chance it will destablize the loop as PV crosses the gap limit? If so, is it higher risk of destabilizing the control loop with small Kgap? I want to use gap controller on a reactor and the normal OP range is between 20 and 25%. Currently, the feedforward control is doing a decent job handling disturbances but I want to minimize the CO movement during normal operation. I set gain multiplier to 0.7 and I do see improvement. I want to further reduce the CO movement but am concerned sudden change of K will destablize the loop or cause windup. Thank you in advance for your feedback.

Jacques :

June 8, 2014 at 10:49 am

JC: It depends a lot on the control system’s implementation of gap control. See this blog on bumpless tuning. If the control system causes a bump in controller output when the PV crosses over the edge of the gap it can cause major stability problems.

Your reference to OP makes me believe you have a Honeywell DCS. Take a look for the setting called “Legacy Gap”. When turned on, this setting changes the behavior to bumpless. The setting is not always visible on the controller faceplate (Loop Tune tab) so you may have to use Control Builder to access it.

PID Controller AlgorithmsMarch 30, 2010

Controller manufacturers arrange the Proportional, Integral and Derivative modes into three different controller algorithms or controller structures. These are called Interactive, Noninteractive, and Parallel algorithms. Some controller manufacturers allow you to choose between different controller algorithms as a configuration option in the controller software.

Interactive Algorithm

Interactive Controller Algorithm

The oldest controller algorithm is called the Series, Classical, Real or Interactive algorithm. The original pneumatic and electronic controllers had this algorithm and it is still found it in many controllers today. The Ziegler-Nichols PID tuning rules were developed for this controller algorithm.

Noninteractive Algorithm

Noninteractive Controller Algorithm

The Noninteractive algorithm is also called the Ideal, Standard or ISA algorithm. The Cohen-Coon and Lambda PID tuning rules were designed for this algorithm.

Note: If no derivative is used (i.e. Td = 0), the interactive and noninteractive controller algorithms are identical.

Parallel Algorithm

Parallel Controller Algorithm

Some academic textbooks discuss the parallel form of PID controller, but it is also used in some DCSs and PLCs. This algorithm is simple to understand, but not intuitive to tune. The reason is that it has no controller gain (affecting all three control modes), it has a proportional gain instead (affecting only the

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proportional mode). Adjusting the proportional gain should be supplemented by adjusting the integral and derivative settings at the same time. Try to not use this controller algorithm if possible (in some DCSs it is an option, so select the alternative).

Significance of Different AlgorithmsThe biggest difference between the controller algorithms is that the Parallel controller has a true Proportional Gain (Kp), while the other two algorithms have a Controller Gain (Kc). Controller Gain affects all three modes (Proportional, Integral and Derivative) of the Series and Ideal controllers, while Proportional Gain affects only the Proportional mode of a Parallel controller.

This difference has a major impact on the tuning of the controllers. All the popular tuning rules (Ziegler-Nichols, Cohen-Coon, Lambda, and others) assume the controller does not have a parallel structure and therefore has a Controller Gain. To tune a Parallel controller using any of these rules, the Integral time has to be divided and derivative time multiplied by the calculated Controller Gain.

The second difference between the controller algorithms is the interaction between the Integral and Derivative modes of the Series (Interactive) controller. This, of course, is only of significance if the Derivative mode is used. In most PID controller applications, Derivative mode is not used. Formulas have been developed for converting tuning settings between Ideal and Series controller algorithms.

Units of Measure of Tuning SettingsAnother very important difference between controllers lies in the units of measure of the tuning settings. There are three differences.

1. Most controller types (e.g. Honeywell Experion, Emerson DeltaV, ABB Bailey) use Controller Gain, while some (e.g. Foxboro I/A, Yokogawa CS3000) use Proportional Band (PB). The conversion between the two is easy once you know which one is being used: PB = 100% / Kc.

2. Many controllers (e.g. Siemens APACS) use minutes as the unit for Integral and Derivative modes, but some controllers (e.g. Emerson DeltaV) use seconds.

3. Some controllers (e.g. ABB Mod 300) use Time for their Integral unit, while others (e.g. Allen-Bradley SLC500) use Repeats/Time. These are reciprocals of each other.

The first controller I ever tried to tune used Proportional Band, but at the time, I had never heard of this concept. Needless to say, when I entered my calculated Kc of 1.2 into its PB setting, the loop became wildly unstable. It did not take me long to realize that I should read up on PID controllers before trying to tune one again.

Other DifferencesBeyond the differences mentioned above, controllers also differ in the way the changes on controller output is calculated (positional and velocity algorithms), in the way Proportional and Derivative modes act on set point changes, in the way the Derivative mode is limited/filtered, as well as a interesting array of other minor differences. These differences are normally subtle, and should not affect your tuning.

When tuning controllers, always find out what structure the controller has and what units it is using.



4 Responses to “PID Controller Algorithms” Nitin Mehta:

October 10, 2012 at 12:09 am

Nice article, thank you Jacques!

Tejaswinee:


Excellent

Marco:

February 12, 2014 at 10:08 am

If I don’t know which algorithm is implemented and the manufacturer of the controller won’t tell me., is there a simple way to identify it?

Jacques :


Marco, start with a PI controller with PV = SP = CO = 0%, mode = manual. Use a PV range of 100%. Use a gain of 1 and an integral time of 1 minute. Change mode to auto and change the SP to 10% while keeping the PV at 0%. The controller output should jump by 10% and then ramp by another 10% in the 1 minute you have as integral time. If that worked, go to manual and reset SP and CO back to 0. Change the controller gain to 2. Change the mode to auto and the SP to 10%. The controller output will now jump to 20%, but then notice the ensuing ramp over 1 minute. If the CO ramps by 10% you have a parallel algorithm, and you don’t need to read any further. If the CO ramps by 20% you have either an interactive or a noninteractive algorithm. If you plan to use PI control, this is all you need to do because interacting and noninteracting algorithms behave the same under PI control.

If you plan on using PID control, to find out if the algorithm is interacting or noninteracting, go to manual and reset SP and CO to 0. Set the derivative time to 0.25 minutes (gain is still 2 and integral time is still 1 minute). Change the mode to auto and the SP to 10%. Ignore the CO bump, look at the CO value after 1 minute. If the CO is at 45% you have an interacting algorithm. If the CO is at 40% you have a noninteracting algorithm.

PID Controllers ExplainedMarch 7, 2011

PID controllers are named after the Proportional, Integral and Derivative control modes they have. They are used in most automatic process control applications in industry. PID controllers can be used to regulate flow, temperature, pressure, level, and many other industrial process variables. This blog reviews the design of PID controllers and explains the P, I and D control modes used in them.

Manual ControlWithout automatic controllers, all regulation tasks will have to be done manually. For example: To keep constant the temperature of water discharged from an industrial gas-fired heater, an operator will have to watch a temperature gauge and adjust a fuel gas valve accordingly (Figure 1). If the water temperature becomes too high for some reason, the operator has to close the gas valve a bit – just enough to bring the temperature back to the desired value. If the water becomes too cold, he has to open the gas valve.


Figure 1. An operator doing manual control.

Feedback ControlThe control task done by the operator is called feedback control, because the operator changes the firing rate based on feedback that he gets from the process via the temperature gauge. Feedback control can be done manually as described here, but it is commonly done automatically, as will be explained in the next section.

Control LoopThe operator, valve, process, and temperature gauge forms a control loop. Any change the operator makes to the gas valve affects the temperature which is fed back to the operator, thereby closing the loop.

Automatic ControlTo relieve our operator from the tedious task of manual control, we should automate the control loop. This is done as follows:

Install an electronic temperature measurement device.

Automate the gas valve by adding an actuator (and perhaps a positioner) to it so that it can be

driven electronically.

Install a controller (in this case a PID controller), and connect it to the electronic temperature

measurement and the automated control valve.

A PID controller has a Set Point (SP) that the operator can set to the desired temperature. The Controller’s Output (CO) sets the position of the control valve. And the temperature measurement, called the Process Variable (PV) gives the controller its much-needed feedback. The process variable and controller output are commonly transmitted via 4 – 20mA signals, or via digital commands on a Fieldbus.

When everything is up and running, the PID controller compares the process variable to its set point and calculates the difference between the two signals, also called the Error (E).

Then, based on the Error and the PID controller’s tuning constants, the controller calculates an appropriate controller output that opens the control valve to the right position for keeping the temperature at the set point. If the temperature should rise above its set point, the controller will reduce the valve position and vice versa.

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Figure 2. A PID controller doing automatic control.

PID ControlPID controllers have three control modes:

Proportional Control

Integral Control

Derivative Control

Each of the three modes reacts differently to the error. The amount of response produced by each control mode is adjustable by changing the controller’s tuning settings.

Proportional Control ModeThe proportional control mode is in most cases the main driving force in a controller. It changes the controller output in proportion to the error (Figure 3). If the error gets bigger, the control action gets bigger. This makes a lot of sense, since more control action is needed to correct large errors.

The adjustable setting for proportional control is called the Controller Gain (Kc). A higher controller gain will increase the amount of proportional control action for a given error. If the controller gain is set too high the control loop will begin oscillating and become unstable. If the controller gain is set too low, it will not respond adequately to disturbances or set point changes.

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Figure 3. Proportional control action.

Adjusting the controller gain setting actually influences the integral and derivative control modes too. That is why this parameter is called controller gain and not proportional gain.

Proportional BandWhile most controllers use controller gain (Kc) as the proportional setting, some controllers use Proportional Band (PB), which is expressed in percent. Table 1 shows the relationship between Kc and PB.

Controller Gain (Kc) Proportional Band (PB) %

0.1 1000

0.2 500

0.5 200

1 100

2 50

5 20

10 10

Table 1. Relationship between Kc and PB

Proportional-only ControllerProportional controllers are simple to understand and easy to tune. The controller output is simply the output of the proportional control mode, plus a bias. The bias is needed so that the controller can maintain an output (say at 50%) while there is no error (set point = process variable).

Figure 4. A proportional-only controller algorithm.

The use of proportional control alone has a large drawback – offset. Offset is a sustained error that cannot be eliminated by proportional control alone. For example, let’s consider controlling the water level in the tank in Figure 5 with a proportional-only controller. As long as the flow out of the tank remains constant, the level will remain at its set point.

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Figure 5. Level control, with operator causing a disturbance.

But, if the operator should increase the flow out of the tank, the tank level will begin to decrease due to the imbalance between inflow and outflow. While the tank level decreases, the error increases and our proportional controller increases the controller output proportional to this error. Consequently, the valve controlling the flow into the tank opens wider and more water flows into the tank.

As the level continues to decrease, the valve continues to open until it gets to a point where the inflow again matches the outflow. At this point the tank level (and error) will remain constant. Because the error remains constant our P-controller will keep its output constant and the control valve will hold its position. The system now remains at balance, but the tank level remains below its set point. This residual sustained error is called Offset.

Figure 6 shows the effect of a sudden decrease in fuel gas pressure to the process heater described earlier, and the response of a p-only controller. The decrease in fuel-gas pressure reduces the firing rate and the heater outlet temperature decreases. This creates and error to which the controller responds. However, a new balance-point between control action and error is found and the temperature offset is not eliminated by the proportional controller.

Figure 6. A proportional controller’s response to a disturbance.

Under proportional-only control, the offset will remain until the operator manually changes the bias on the controller’s output to remove the offset. It is said that the operator manually “Resets” the controller.

Integral Control ModeThe need for manual reset as described above led to the development of automatic reset or the Integral Control Mode, as we know it today. As long as there is an error present (process variable not at set point), the integral control mode will continuously increment or decrement the controller’s output to reduce the error. Given enough time, integral action will drive the controller output far enough to reduce the error to zero.

If the error is large, the integral mode will increment/decrement the controller output fast, if the error is small, the changes will be slower. For a given error, the speed of the integral action is set by the

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controller’s integral time setting (TI). A large value of TI (long integral time) results in a slow integral action, and a small value of TI (short integral time) results in a fast integral action (Figure 7). If the integral time is set too long, the controller will be sluggish, if it is set too short, the control loop will oscillate and become unstable. In the figure, TS is the control algorithm’s execution interval, sometimes called sampling time or scan time.

Figure 7. Integral control action and an integral-only controller’s equation.

Most controllers use integral time in minutes as the unit of measure for integral control, but some others use integral time in seconds, integral gain in repeats per minute or repeats per second. Table 2 compares the different integral units of measure.

Integral Time Integral Gain

Minutes

Seconds Rep / Min Rep / Sec

0.05 3 20 0.333

0.1 6 10 0.167

0.2 12 5 0.0833

0.5 30 2 0.0333

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1 60 1 0.0167

2 120 0.5 0.00833

5 300 0.2 0.00333

10 600 0.1 0.00167

20 1200 0.05 0.00083

Table 2. Units of the integral control mode.

Proportional + Integral ControllerCommonly called the PI controller, its controller output is made up of the sum of the proportional and integral control actions (Figure 8).

Figure 8. The PI controller algorithm.

Figure 9 shows how the integral mode continues to increment the controller’s output to bring the heater outlet temperature back to its set point. Compared to Figure 6, it is clear how Integral control eliminates offset.

Figure 9. A PI controller’s response to a disturbance.

Derivative Control ModeThe third control mode in a PID controller is derivative. Derivative control is rarely used in controlling processes, but it is used often in motion control. For process control, it is not absolutely required, is very sensitive to measurement noise and it makes trial-and-error tuning more difficult. See http://blog.opticontrols.com/archives/153 for more detail. Nevertheless, using the derivative control mode of a controller can make a control loop respond a little faster than with PI control alone.


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The derivative control mode produces an output based on the rate of change of the error (Figure 10). Derivative mode is sometimes called Rate. The derivative mode produces more control action if the error changes at a faster rate. If there is no change in the error, the derivative action is zero. The derivative mode has an adjustable setting called Derivative Time (TD). The larger the derivative time setting, the more derivative action is produced. A derivative time setting of zero effectively turns off this mode. If the derivative time is set too long, oscillations will occur and the control loop will run unstable. Again TS is the controller’s execution interval.

Figure 10. Derivative control action.

Two units of measure are used for the derivative setting of a controller: minutes and seconds.

Proportional + Integral + Derivative ControllerCommonly called the PID controller, its controller output is made up of the sum of the proportional, integral, and derivative control actions (Figure 11). There are other configurations too. See http://blog.opticontrols.com/archives/124 for a description.

Figure 11. The Standard (Noninteractive) PID controller algorithm.

PID control provides more control action sooner than what is possible with P or PI control. This reduces the effect of a disturbance, and shortens the time it takes for the level to return to its set point.


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Figure 12. A PID controller’s response to a disturbance.

Figure 13 compares the recovery under P, PI, and PID control of the process heater outlet temperature (PV) after a sudden change in fuel gas pressure as described above.

Figure 13. The result of a P, PI, and PID controllers’ response to a disturbance.



13 Responses to “PID Controllers Explained” mohd redzuwan:

December 13, 2011 at 9:14 pm

hye, I’m looking forward to know more about PID controller and try to find a suitable books or reference regarding this topic since i teach control engineering subject. thanks

Jacques :


Mohd, you could take a look at this book: Process Control for PractitionersJacques

sn Maiti:

June 19, 2012 at 12:03 am

http://blog.opticontrols.com/archives/344/comment-page-1#comment-2472

http://www.amazon.com/gp/product/0983843805/ref=as_li_tf_tl?ie=UTF8&tag=contnote-20&linkCode=as2&camp=217145&creative=399373&creativeASIN=0983843805




http://blog.opticontrols.com/archives/category/pid-controllers


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while I appreciate for the physical example given for the proportional control action, could you please explain the interal action by physical explanation? From mathematical, the reset action is not comprehensible.

Jacques :

June 19, 2012 at 9:03 pm

Maiti: Here is a practical example of everyday integral action. You perform a type of integral action when you change your shower water’s temperature. Let’s say the water is way too cold. You might know from experience you have to turn the hot water tap at least 1/4 turn. This is equivalent to proportional action. Then the temperature might be closer, but still not exactly on target. So you slowly turn the tap some more. The closer you get to the desired temperature, the slower you turn the tap. You continue turning the tap slower and slower until the temperature is exactly on target and then you stop turning the tap. This secondary action is a pseudo integral action. The larger the error, the faster the corrective action is done, and it continues until the error is zero.

Ahniel:

July 22, 2012 at 12:10 pm

What is manual bias in a controller?

Jacques :

July 23, 2012 at 12:48 pm

Let’s say a proportional-only controller with a setpoint of 70 kg/hr is in manual, and the output is zero. The operator increases the output manually to 40% to bring the actual flow to 70 kg/hr. Then he puts the controller in auto. Now since CO = Kc x Error for a proportional controller, and the error is zero, one would expect the output to drop to 0%. However, the controller output remmains at 40%. That is the manual bias that biases the output by 40%. So actually CO = Kc x Error + Bias.

Nilesh:

May 15, 2013 at 9:51 am

It was quite nice going through it…thanks.. these examples helped me a lot in understanding it physically…

Darus :

November 26, 2013 at 10:03 am

I have a very simple question. I have a secondary controller in a cascade loop that is controlling 3 control valves maintaining the secondary’s Set-point so as to maintain the primary’s Set-point. Before any tuning should be attempted, wouldn’t the first thing to do would be to try to linearized each valve independently as much as is possible with the controller/positioner you have. As in Honeywell analog outputs only having 4 points for non-linear correction. Some positioners also have more advanced non-linear correction capabilities, but comes with cost’s but, that might not even be a consideration. I have been in the PID control tuning business one way or another for over 20 years. I am looking for conformation on what I consider the first and foremost property necessary to have a 1 chance in 1000000 times to control the primary(control Set-point)in all ranges. Thank You!

Jacques :



http://opticontrols/







November 26, 2013 at 12:37 pm

Darus – Yes, if you are looking for the best possible performance from the flow control loops, you should do tests or use historical data to determine if the valves have a linear installed flow characteristic. Considering the normal operating range of each valve, if the maximum gain is more than 2 – 3 times the minimum gain, you should consider linearizing the flow characteristic. A four-point characterizer should be sufficient for this – except for valves that have an S-shaped characteristic, such as butterfly valves (and dampers). You can also use a function generator or F(x) block to do the linearization. I don’t like putting characterizers in positioners, because when a positioner is replaced the chance is good that the characterizer will not be configured in the new one. You should also implement gain scheduling in the primary loop if your system sometimes uses fewer than three valves for control.

aditya:


Sir,

Can you please explain the proportional controllers offset error with another example.Because when inflow matches the outflow, level shall remain constant, but our measured variable i.e. level, will still be different fom setpoint isnt it?so controller will have to open up control valve more and more so that level reaches setpoint again till error is zero.so where is the offset coming into picture?

Jacques :


A mechanical example of a P-only controller is a spring on which a weight hangs. If you add more weight, the spring stretches out a bit more to uphold the additional weight. The difference in spring length is offset.

Leo:

June 7, 2014 at 6:14 am

I don’t understand Table 1.

0,1 is 10% and so on. In my mind the left or right column should be inverted.

Jacques :

June 8, 2014 at 10:53 am

Leo: PB is not simply the Kc expressed in percent, PB = 100% / Kc, or differently, Kc = 100% / PB. Table 1 is correct.

Leave a Reply

Settings in the Controller were Closer than they Appeared

May 17, 2012

Before I do step-testing to analyze and tune a control loop, I always take a look at the current tuning settings in the controller.

The controller’s gain setting gives me some indication of the sensitivity of the process, e.g. if the

controller gain is 0.1 the process could be very sensitive to controller output changes.








The controller’s integral time gives me an idea of the speed of the process dynamics, i.e. a short

integral time usually means fast process dynamics and vice versa.

The derivative time (if used) can reveal if the last person tuning the loop lacked understanding of

the tuning process, e.g. if the derivative time is set to more than half the integral time, or less than

one-eighth of it.

Earlier this month I optimized control loops on an oil platform. A few of the loops were oscillating. One of the oscillating loops, a gas pressure control loop on a separator, had a controller gain of 16! I facetiously told the control engineer: “Well, there’s your problem!” A value of 16 did seem like an abnormally large controller gain, but I know there are many exceptions from “normal” in process control.

A closer look revealed the reason for the high controller gain. Even though the set point was set to the normal operating pressure of 200 PSI, the pressure transmitter was calibrated to measure between 0 and 4000 PSI. So the operating pressure was at only 5% of the measurement range! A more appropriate measurement range would have been 0 – 400 PSI, since the maximum design pressure for the vessel was 380 PSI. In this case, the calibration range was ten times larger than it should have been. Considering that the measurement span was ten times over-ranged, the controller gain had to be ten times larger than “normal” to compensate. This means the effective gain of the controller was only 1.6, which is a reasonable value, especially for gas pressure control. In other words, the high controller gain was not responsible for causing the control loop instability. It turned out that the control loop was oscillating because of control valve stiction.

Based on these findings I recommended a replacement / recalibration of the pressure transmitter and the subsequent reranging of the signals in the DCS. After doing this, the controller gain must be set to 1.6. I also recommended that the sticky control valve be repaired or replaced to fix the oscillations.

The high controller gain cancelled out by the large measurement span reminded me of the warning on a passenger-side rear-view mirror: “Objects in the mirror are closer than they appear.”

Objects in the mirror are closer than they appear.

Learn more about controller settings from the book Process Control for Practitioners.Try it out for yourself using the OptiControls Loop Simulator.

Stay Tuned!


Unraveling Controller AlgorithmsOctober 27, 2012

Someone recently asked me which controller algorithm the Emerson Provox PID controller uses. She pointed me to the PID equations given in the Provox manual (Figure 1).

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Figure 1. PID Algorithm given in the Emerson Provox Manual (click to enlarge)

The author of this documentation has obviously given little thought to the information sought by the end user:

1. What algorithm does the controller use (interactive, noninteractive, parallel)?

2. Is the integral setting in units of time (min/sec) or gain (repeats/min, repeats/sec)?

3. Do the proportional and derivative terms act on error or PV?

The answers to these questions are critical for tuning the controller and understanding its response to setpoint changes. But the information given in the manual does not give one of these pieces of information in a straightforward manner. (It may seem obvious from Figure 1 that the integral setting is in units of time, but this is wrong.)

To help decipher controller algorithms as documented by many manufacturers, I thought it may be useful to summarize the building blocks of a PID controller and their Laplace representations (Figure 2).

Figure 2. Controller algorithm building blocks used in manufacturer documentation. (Click to enlarge.)

TI = Integral timeTD = Derivative timeTF = Filter time constanta = Derivative filter ratio. Also called derivative gain limiter, or rate action limiter. Usually set between 0.1 and 0.125.

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Now back to the Provox PID algorithm…

Rearranging the equation at the top of Figure 1 to reflect the blocks given in Figure 2, and substituting IVP (implied valve position) with CO (controller output) we obtain the equation in Figure 3.

Figure 3. Rearranged Provox PID equation. (Note that 1/Ti should actually be Ki - see text).

The equation in Figure 3 indicates that the Provox uses the interactive PID control algorithm because the derivative term is multiplied by the proportional and integral terms, not added to them. The rearranged equation in Figure 3 also tells me that the Provox uses a lead-lag block, which provides derivative action with the numerator (lead) and derivative filtering with the denominator (lag). This answers the first question.

The equation and text in Figure 1 would have led me to believe that the controller uses integral time, but… WATCH OUT, the part of Emerson’s manual I pasted in Figure 1 turned out to be wrong in this aspect! Many pages later, the Provox manual says that the integral tuning constant (called RESET), is actually a gain expressed in repeats per minute. In their own peculiar way the second question has been answered.

Finally, doing some extensive rearrangement of the math at the bottom of Figure 1, I concluded that the derivative term acts on PV and not Error. Admittedly, the latter is difficult to do with the interactive controller algorithm. Luckily the manual actually tells the reader “the set point term of the PID algorithm has been isolated so that rate action occurs only on changes to the PV”. If you know what you are looking for – this line says it. Tediously, the last question was answered.

To summarize, the Emerson Provox PID controller uses:

1. The interactive control algorithm

2. Integral gain in repeats/minute

3. Derivative on PV and proportional on error

As a consultant working on many controller types, I have been compiling a database of controller algorithms and tuning units over that past 20+ years. I learned that you often have to rearrange the manufacturer’s equations into a familiar format to see what algorithm they are using (Emerson is not the only culprit here and not the worst I have seen). And you should question the accuracy of the information given in controller equations – try to find text to back it up.

Stay tuned,

Jacques Smuts – author of Process Control for Practitioners.


5 Responses to “Unraveling Controller Algorithms” Allan Zadiraka:


Jacques –

Very interesting article, especially when read with your linked article on PID Controller Algorithms. I disagree with your statement in that article that the parallel arrangement is non-intuitive and should be avoided.

I spent most of my career with the Bailey 721/820 and Network 90 function codes 18 & 19 controllers which include both controller (Kc) and proportional gains (Kp). My training was to keep the controller gain at 1.0 since a parallel arrangement is much easier to tune. Changing Kc means you have to change Ki & Kd as well.

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To me, controller gain is a legacy of the mechanical arm adjustment in pneumatic controllers which needs to be eradicated.

I have no problem with using PID control, just with the cookie cutter PID controllers that we are stuck with.

Said:


We are working on a sliimar quadrotor project and we are newbeeies in the control algorithm. We have a working IMU now with precise Euler angle outputs. Our struggle is with the PID control. We just implemented a very simple PID control and tried tuning it to balance just pitch axis while keeping the other axis fixed on a stand. However, we could not get to a good enough result especially in high throttle. I would really appreciate if you could give us some feedback on the PID control you guys implemented.ThanksGuinness

Jacques :


We have to use the PID control algorithm supplied by the control system vendor in their hardware. That is why we have to understand what algorithm they provide so that we can tune it properly. If you tell me more about your algorithm and tuning methods I might be able to give you some direction.- Jacques

Anu:


Interesting article. I have got a driver for a dc motor. I know my system and motor specifications. The driver software allows the user to decide the gains of the controller. But am required to tune the PI controller. How will I know what algorithm they have coded in the DSP of the driver? Without knowing the algorithm, how am I supposed to tune the controller? Please do give your inputs and suggestions.

Jacques :


Anu – I suggest you contact the supplier to obtain the algorithm and the units of measure for the tuning parameters. You could potentially also determine the algorithm by looking how the controller reacts to a setpoint change while holding the process variable constant when using different values for the tuning parameters, e.g. 0 and 1; 1 and 0; 1 and 1.

4. Controller Tuning o Cohen-Coon Tuning Rules o Comments on the Ziegler-Nichols tuning method o Detuning Control Loops o Is Lambda a Bad Tuning Rule? o Lambda Tuning Rules o Level Controller Tuning o Minimum IAE Tuning Rules

o Quarter Amplitude Damping o Surge Tank Level Control o Tank Level Tuning Complications o Tuning Rule for Dead-Time Dominant Processes o Typical Controller Settings o When to Use which Tuning Rule o Ziegler-Nichols Closed-Loop Tuning Method o Ziegler-Nichols Open-Loop Tuning Rules

Cohen-Coon Tuning RulesMarch 24, 2011

Based on the number of Google searches in 2010, the Cohen-Coon tuning rules are second in popularity only to the Ziegler-Nichols tuning rules. Cohen and Coon published their tuning method in 1953, eleven years after Ziegler and Nichols published theirs.

More Flexible than Ziegler-NicholsThe Cohen-Coon tuning rules are suited to a wider variety of processes than the Ziegler-Nichols tuning rules. The Ziegler-Nichols rules work well only on processes where the dead time is less than half the length of the time constant.

The Cohen-Coon tuning rules work well on processes where the dead time is less than two times the length of the time constant (and you can stretch this even further if required).

Cohen-Coon provides one of the few sets of tuning rules that has rules for PD controllers – should you ever need this.

Quarter-Amplitude DampingLike the Ziegler-Nichols tuning rules, the Cohen-Coon rules aim for a quarter-amplitude damping response. Although quarter-amplitude damping-type of tuning provides very fast disturbance rejection, it tends to be very oscillatory and frequently interacts with similarly-tuned loops. Quarter-amplitude damping-type tuning also leaves the loop vulnerable to going unstable if the process gain or dead time doubles in value. However, the easy fix for both problems is to reduce the controller gain by half. E.g. if the rule recommends using a controller gain of 1.8, use only 0.9. This will prevent the loop from oscillating around its set point as described above, and will provide an acceptable stability margin.

Target PID Controller AlgorithmThere are three types of PID controller algorithms: Interactive, Noninteractive, and Parallel. The Cohen-Coon tuning rules were designed for controllers with the noninteractive controller algorithm. If you are not using the derivative control mode (i.e. using P, PI, of PD control), the rules will also work for the interactive algorithm. However, if you are using derivative (i.e. PID control) on an interactive controller, or if your controller has a parallel algorithm, you should convert the calculated tuning settings to work on your controller.

Noninteractive Controller Structure

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A Note on Integral TimeThe original Cohen-Coon paper expressed the tuning constant for the integral control mode in terms of reset rate (or integral gain) in repeats per minute. Virtually all the modern texts on process control use integral time, and this article follows that trend. Therefore, the tuning rules below use integral time. If your controller uses integral gain or reset rate, you’ll have to invert the calculated integral time (use 1/Ti).

Also, if your controller’s integral time unit is in minutes, you must make your measurements of dead time and time constant in minutes. Likewise if your controller uses seconds, make your measurements in seconds.

When to use the Cohen-Coon Tuning RulesThe Cohen-Coon tuning rules are suitable for use on self-regulating processes if the control objective is having a fast response, but I recommend you divide the calculated controller gain by two, as described above.

If the control objective is to have a very stable, robust control loop that absorbs disturbances, rather use the Lambda tuning rules.

Tuning ProcedureAssuming the control loop is linear and the final control element is in good working order, you can continue with tuning the controller. The Cohen-Coon tuning rules use three process characteristics: process gain, dead time, and time constant. These are determined by doing a step test and analyzing the results.

Step Test for Tuning – (click to enlarge)

1. Place the controller in manual and wait for the process to settle out.

2. Make a step change of a few percent in the controller output (CO) and wait for the process

variable (PV) to settle out at a new value. The size of this step should be large enough that the

process variable moves well clear of the process noise/disturbance level. A total movement of

five times the noise/disturbances on the process variable should be sufficient.

3. Convert the total change obtained in PV to a percentage of the span of the measuring device.

4. Calculate the process gain (gp) as follows:

o gp = change in PV [in %] / change in CO [in %]

5. Find the maximum slope on the PV response curve. This will be at the inflection point(where the

PV stops curving upward and begins curving downward). Draw a line tangential to the PV

response curve through the point of inflection. Extend this line to intersect with the original level

of the PV (before the step change in CO). Take note of the time value at this intersection.

6. Measure the dead time (td) as follows:

o td = time difference between the change in CO and the intersection of the tangential line

and the original PV level.

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7. Calculate the value of the PV at 63% of its total change. On the PV reaction curve, find the time

value at which the PV reaches this level.

8. Measure the time constant (Greek symbol tau) as follows:

o tau = time difference between intersection at the end of dead time, and the PV reaching

63% of its total change.

9. Convert your measurements of dead time and time constant to the same time-units your

controller’s integral mode uses. E.g. if your controller’s integral time is in minutes, use minutes

for this measurement.

10. Do two or three more step tests and calculate process gain, dead time, and time constant for

each test to obtain a good average of the process characteristics. If you get vastly different

numbers every time, do even more step tests until you have a few step tests that produce similar

values. Use the average of those values.

11. Calculate new tuning settings using the Cohen-Coon tuning rules below. Note that these rules

produce a quarter-amplitude damping response. See the next step.

oThe Cohen-Coon Tuning Rules – click to enlarge

12. Divide the calculated controller gain by two to reduce oscillations and improve loop stability.

13. Compare the newly calculated controller settings with the ones in the controller, and ensure that

any large differences in numbers are expected and justifiable.

14. Make note of the previous controller settings, the new settings, and the date and time of change.

15. Implement and test the new controller settings. Ensure the response is in line with the overall

control objective of the loop.

16. Leave the previous controller settings with the operator in case he/she wants to revert back to

them and cannot find you to do it. If the new settings don’t work, you have probably missed

something in one or more of the previous steps.

17. Monitor the controller’s performance periodically for a few days after tuning to verify improved

operation under different process conditions.


*G.H. Cohen and G.A. Coon, Theoretical Consideration of Retarded Control, Trans. ASME, 75, pp. 827-834, 1953

Posted in 4. Controller Tuning

2 Responses to “Cohen-Coon Tuning Rules” ija:

http://blog.opticontrols.com/wp-content/uploads/2011/03/CohenCoonRules1.png

December 22, 2011 at 8:33 am

why level of water cannot use Cohen-Coon’s to calculate the gain and intergral time? instead use Zieglar-Nichols’s method to calculate gain and intgral time.

Jacques :


Ija,

The Cohen-Coon tuning method requires a measurement of the process time constant, while the way we normally model integrating processes (like liquid level) this measurement is not available.

The original Ziegler-Nichols method does not require a measurement of the process time constant and therefore lends itself very well to tuning level controllers for a fast response. See this poset for details: http://blog.opticontrols.com/archives/697

- Jacques

Comments on the Ziegler-Nichols tuning methodJanuary 11, 2010

The overwhelming majority of control practitioners are familiar with the Ziegler-Nichols tuning methods. If not from personal experience, then at least from reading or hearing about the tuning rules they developed. Although their tuning rules are widely published and referenced (do a Google search on Ziegler Nichols), I have met only a few control practitioners who have actually read their original paper Optimum Settings for Automatic Controllers published in Transactions of the A.S.M.E., November 1942, and pondered the fundamental premises of their work, and applicability to processes in general.

I think the Ziegler-Nichols tuning rules were indeed ground-breaking and still are elegant, however, there are a few potential problems to consider when applying theses rules.

Issue #1 – Quarter-amplitude damping

Ziegler and Nichols chose quarter-amplitude damping to be “optimum” control loop response. Although this result lies neatly in the middle between a completely dead controller and an unstable control loop, you should realize that quarter-amplitude damping, by design, causes the process to overshoot its set point and to oscillate around it a few times before eventually settling down. For many processes, overshoot cannot be tolerated and oscillations are a bad thing. For these sensitive processes, the Ziegler-Nichols tuning rules cannot be used, unless the controller is detuned from the original settings.

Issue #2 – Low robustness (Close to unstable)

Ziegler and Nichols describe in detail how they designed their tests and how they arrived at the “optimum” tuning settings. Quite simply, they increased controller gain until they reached the point of instability and then backed the controller gain down by a factor of 0.5 (e.g. if a controller gain of 0.8 makes a loop border-line unstable, they recommend using a gain of 0.4). This gave them exactly the quarter-amplitude damping they were aiming for, but it makes the margin to loop instability very small. An equal-percentage control valve’s gain can easily increase by a factor of 10 as the valve position changes between closed and fully open. The gain of a feed heater temperature loop can quadruple if the process flow through the heater goes from maximum down to 25%. In both of these examples (and numerous others), a control loop tuned with the Ziegler-Nichols rules can quickly go unstable.

Issue #3 – Poor response on dead-time-dominant processes

Under Ziegler-Nichols tuning, the controller’s integral setting is set proportional to the process dead time: the longer the dead time, the slower the integral will be. This is acceptable where dead times are short in relation to the process time constant, but not so for dead-time-dominant processes. For the latter, the integral action becomes too slow, and the loop’s ability to recover from a process upset is diminished.

Issue #4 – Very sensitive to underestimating the dead time

The Ziegler-Nichols open-loop response test (called the “reaction curve” method in their paper) requires graphically measuring the process dead time and time constant on a plot of the process’ response after changing the controller’s output. If the dead time is significantly smaller than the time constant, its

measurement becomes exceptionally difficult – especially due to the effect of process noise and disturbances on the process’ response curve. Because the Ziegler-Nichols tuning method relies on an accurate measurement of dead time for the calculation of controller gain, integral, and derivative settings, an incorrectly measured dead time will result in a very poorly tuned controller.

Issue #5 – Very sensitive to control valve problems

The ultimate cycling, or ultimate sensitivity, method of Ziegler-Nichols tuning can produce grossly incorrect controller settings if the control loop has a faulty control valve. This tuning method requires a very linear response between the controller output and process response to obtain the ultimate gain and ultimate period. Control valve dead band and stiction will affect both the ultimate gain and ultimate period, and you will end up with a poorly tuned control loop.

General considerations

In addition to the issues listed above, there are a few additional items to keep in mind when using the Ziegler-Nichols tuning rules:

The time units of your process measurements must be the same as your controller’s integral and

derivative time units. For example, if your controller’s integral and derivative time units are in

minutes, make your process measurements in minutes or convert them to minutes.

The rules were developed for the series (interactive) controller algorithm. Controller settings

calculated using the Ziegler-Nichols tuning rules must be converted when applied to PID

controllers with the ideal (non-interactive) algorithm and PID or PI controllers with the parallel

algorithm.

The original rules had an integral unit (reset rate as they called it in their paper) of 1/minute,

while many controller types also have their integral unit in minutes (or of course, 1/second or

seconds). Also, the rules calculate controller gain (called sensitivityin their paper) and not

proportional band, which is used by a few controller types. Be sure to do the proper conversions

between calculated controller settings in the units used by Ziegler-Nichols to the units used by

your controller.

In Ziegler and Nichols’ defense

In Ziegler and Nichols’ defense, I’ll be quick to point out that many of these issues and most considerations apply to several other tuning rules too. It is important that you, as a controls practitioner, don’t just blindly apply a tuning rule, but that you understand its objectives and how controllers and tuning rules work.

One Response to “Comments on the Ziegler-Nichols tuning method”

Glen:


The problem is that Ziegler Nichols is based on a faulty premise. One normally does not adjust the controller gains to alter time domain response. Time domain response should be adjusted via a prefilter. One adjusts the controller to obtain desired frequency domain characteristics.

The other fundamental flaw involved here is that the PID controller is a low order controller. Such a low order controller unnecessarily restricts the ability to realize desired frequency domain characteristics.

Detuning Control LoopsOctober 3, 2012


Many tuning rules are designed to produce a super-fast control loop response. These rules include Ziegler-Nichols, Cohen-Coon, and Minimum IAE tuning rules. When tuned with one of these fast-response tuning rules, the controller responds so aggressively to disturbances and setpoint changes that the process variable overshoots its setpoint and oscillates around the setpoint a few times before it finally settles out. You might have heard of the Quarter-Amplitude-Damping response that Ziegler and Nichols and others aimed for (Figure 1).

Figure 1. Simulated response of a temperature control loop tuned for Quarter-Amplitude Damping.

Perhaps even more concerning than the oscillatory response, is the fact that these aggressive tuning methods push a control loop very close to instability. This could become a huge problem because a small change in the process gain or dynamics can cause a control loop tuned in this way to become completely unstable. We say the control loop is not robust.

Detuning a Controller

Since oscillatory response and low robustness can both be detrimental to control loop performance, it is therefore good practice to tune controllers in a way that will produce a more stable control loop. Starting from tuning settings calculated with an aggressive tuning rule, we can detune the controller to obtain a more stable response and increased robustness. In this sense, detuning is a good thing and it simply means that we are slightly backing away from the aggressive, oscillatory, and semi-unstable tuning, to obtain a loop that is less oscillatory and more tolerant to changes in process characteristics.

On controllers with interactive and noninteractive algorithms, detuning is done by simply reducing the controller gain (Kc). Detuning the controller by a factor of two simply means dividing the controller gain by two. For simplicity, I call this detuning factor the stability margin(SM):

Kc to use = (calculated Kc) / SM.

On controllers with the parallel algorithm, the proportional, integral, and derivative gains need to be lowered in equal proportions.

Detuning a control loop by too little leaves it oscillatory and close to instability. Detuning a control loop by too much makes it very stable and robust, but slow to respond to disturbances and setpoint changes. Detuning the controller by a factor of 2 to 3 (using a stability margin of 2 to 3) is normally sufficient for eliminating oscillations and improving loop robustness.







http://blog.opticontrols.com/wp-content/uploads/2012/10/Quarter-Amplitude-Damping.png

Figure 2. Simulated response of a control loop tuned for quarter-amplitude-damping response (SM = 1), compared to detuning it by factors of 2 and 4 (SM = 2 and SM = 4).

To summarize, if you use one of the aggressive tuning rules to calculate controller settings, you should detune the controller by dividing the calculated controller gain by a stability margin of 2 or more to reduce overshoot, eliminate oscillations, and improve control loop robustness.

Stay tuned!Jacques Smuts

Author of Process Control for Practitioners, available from Amazon.com:http://www.amazon.com/gp/product/0983843813

Is Lambda a Bad Tuning Rule?July 6, 2012

Control Global recently published an article titled: “The Case Against Lambda Tuning”. In this article, controls guru Greg Shinskey makes the argument that Lambda tuning fails miserably for a loop responding to a disturbance. He bases his argument on two loop performance measures:

Maximum deviation from set point

Integral of error

He then goes on to describe optimum tuning as a balance between the two performance objectives and provides tuning guidelines for achieving this. A very nice explanation indeed.

Although the article is technically correct, I don’t fully agree with its premise: that all controllers should be tuned to respond fast and reject disturbances.

It’s like arguing against buying a minivan because it does not perform as well as a Corvette. However, minivans are less expensive and can seat several kids. So if economy and seat count are the objectives for your large family’s car, the minivan makes a fine choice. Similarly, if robustness and stability are your control loop performance objectives, Lambda tuning makes a good choice.

I am not saying Shinskey is wrong for promoting fast loop response, but keep in mind that fast response is only one of the possible performance objectives. Stability and robustness are also valid control objectives, and Lambda tuning caters to these needs. It is a fine tuning rule if you want to stabilize control loops in complex, interactive plants. For example, the paper industry makes widespread use of Lambda tuning to keep their highly-interactive paper machines stable. It is also a unique tuning rule that allows you to specify the loop’s speed of response to a set point change, i.e. the closed loop time constant.

You may wonder about the downside of using Lambda tuning. Well, the penalty one pays for increased control loop stability is a slower rejection of disturbances. So, to Greg’s point, Lambda tuning is not well suited for fast disturbance rejection on processes with long time constants. But it sure is a useful tuning rule for improving loop stability or dialing in a specific speed of response.


http://blog.opticontrols.com/wp-content/uploads/2012/10/Detuning.png

Once you understand the pros and cons of using Lambda tuning, you can decide if it meets your needs for any particular control loop.

Learn more about Lambda and other tuning rules from the book Process Control for Practitioners.Then try it out for yourself using the OptiControls Loop Simulator.

Stay Tuned!



One Response to “Is Lambda a Bad Tuning Rule?” Víctor D. Parra:

July 10, 2012 at 3:47 pm

I agree with you.

As you exposed in your minivan vs Corvette example, everything in engineering is a question of use and balance. Our job as engineer is always to find the solution that match with our requirements (about functionality, safety, isolation, endurance, etc) but respecting our constraints (price, weight, dimensions, legislation, etc)

A loop tuned very agressively intending to achieve the fastest response can be very harmful in another part of your plant downstream (think on a very agressive primary controller in a cascade loop, it will “fight” with the secondary controller). Your “performance parameter” for a loop depends on what objective you want to achieve (speed, stability, slow movement, less valve displacement, etc).

Lambda Tuning RulesNovember 22, 2010

The Lambda tuning rules, sometimes also called Internal Model Control (IMC)* tuning, offer a robust alternative to tuning rules aiming for speed, like Ziegler-Nichols, Cohen-Coon, etc. Although the Lambda and IMC rules are derived differently, both produce the same rules for a PI controller on a self-regulating process.

While the Ziegler-Nichols and Cohen-Coon tuning rules aim for quarter-amplitude damping, the Lambda tuning rules aim for a first-order lag plus dead time response to a set point change. The Lambda tuning rules offer the following advantages:

The process variable will not overshoot its set point after a disturbance or set point change.

The Lambda tuning rules are much less sensitive to any errors made when determining the

process dead time through step tests. This problem is common with lag-dominant processes,

because it is easy to under- or over-estimate the relatively short process dead time. Ziegler-

Nichols and Cohen-Coon tuning rules can give really bad results when the dead time is

measured incorrectly.

The tuning is very robust, meaning that the control loop will remain stable even if the process

characteristics change dramatically from the ones used for tuning.

A Lambda-tuned control loop absorbs a disturbance better, and passes less of it on to the rest of

the process. This is a very attractive characteristic for using Lambda tuning in highly interactive

processes. Control loops on paper-making machines are commonly tuned using the Lambda

tuning rules to prevent the entire machine from oscillating due to process interactions and

feedback control.

The user can specify the desired response time (actually the closed loop time constant) for the

control loop. This provides one tuning factor that can be used to speed up and slow down the

loop response.

Unfortunately, the Lambda tuning rules have a drawback too. They set the controller’s integral time equal to the process time constant. If a process has a very long time constant, the controller will consequently have a very long integral time. Long integral times make recovery from disturbances very slow.

It is up to you, the controls practitioner, to decide if the benefits of Lambda tuning outweigh the one drawback. This decision must take into account the purpose of the loop in the process, the control performance objective, the typical size of process disturbances, and the impact of deviations from set point.

Below are the Lambda tuning rules for a PI controller. Although Lambda / IMC tuning rules have also been derived for PID controllers, there is little point in using derivative control in a Lambda-tuned controller. Derivative control should be used if a fast loop response is required, and should therefore be used in conjunction with a fast tuning rule (like Cohen Coon). Lambda tuning is not appropriate for obtaining a fast loop response. If speed is the objective, use another tuning rule.

To apply the Lambda tuning rules for a self-regulating process, follow the steps below. Also, please read the paragraph in red text following the tuning equations.

1. Do a step-test and determine the process characteristics

a) Place the controller in manual and wait for the process to settle out.

b) Make a step change in the controller output (CO) of a few percent and wait for the process variable (PV) to settle out. The size of this step should be large enough that the PV moves well clear of the process noise/disturbance level. A total movement of five times the noise/disturbances on the process variable should be sufficient.

c) Calculate the process characteristics as follows:

Process Gain (gp)

Convert the total change in PV to a percentage of the measurement span.

gp = change in PV [in %] / change in CO [in %]

Dead Time (td)

Note: Make this measurement in the same time-units your controller’s integral mode uses. E.g. if your controller’s integral time is in minutes, use minutes for this measurement.

Find the maximum slope of the PV response curve. This will be at the point of inflection. Draw a line tangential through the PV response curve at this point. Extend this line to intersect with the original level of the PV before the step in CO. Take note of the time value at this intersection.

td = time difference between the change in CO and the intersection of the tangential line and the original PV level

Time Constant (tau)

Calculate the value of the PV at 63% of its total change. On the PV reaction curve, find the time value at which the PV reaches this level

tau = time difference between intersection at the end of dead time, and the PV reaching 63% of its total change

Note: Make this measurement in the same time-units your controller’s integral mode uses. E.g. if your controller’s integral time is in minutes, use minutes for this measurement.

Step Test for Lambda Tuning

d) Repeat steps b) and c) two more times to obtain good average values for the process characteristics. If you get vastly different numbers every time, do even more step tests until you have a few step tests that produced similar values. Use the average of those values.

2. Pick a desired closed loop time constant (taucl) for the control loop

A large value for taucl will result in a slow control loop, and a small taucl value will result in a faster control loop. Generally, the value for taucl should be set between one and three times the value of tau.

Use taucl = 3 x tau to obtain a very stable control loop. If you set taucl to be shorter than tau, the advantages of Lambda tuning listed above soon disappear.

3. Calculate PID controller settings using the equations below

Controller Gain (Kc)

Kc = tau/(gp x (taucl + td))

Integral Time (Ti)

Ti = tau

Derivative Time (Td)

Td = zero.

Important Notes!

The tuning equations above are designed to work on controllers with interactive or noninteractive

algorithms, but not controllers with parallel (independent gains) algorithms.

The rules calculate controller gain (Kc) and not proportional band (PB). PB = 100/Kc.

The rules assume the controller’s integral setting is integral time Ti (in minutes or seconds), and

not integral gain Ki (repeats per minute or repeats per second). Ki = 1/Ti.

Read this posting for more details.

If your controller is different from the above, simple parameter conversions will allow you to use the Lambda rules.

Contact me to learn more, or to schedule an in-house training session on controller tuning techniques.


*Rivera, D.E., M. Morari, and S. Skogestad, Internal Model Control 4. PID Controller Design, Industrial Engineering and Chemical Process Design and Development, 25, p. 252, 1986



22 Responses to “Lambda Tuning Rules” Trevor:


I have a negative relationship between my CO and my PV, in other words I raise my CO and my PV decreases. Should I use a negative Gp (and get a resultant negative Kc) or should I just use the absolute value?

Thanks!

Jacques :


Trevor – Very few controllers support a negative Kc. Check your controller documentation. Most likely you will have to use the absolute value of the calculated gp and configure your controller to be a direct-acting controller.

Tejaswinee:


Cohen-Coon and Ziegler-Nichols can be stated as first order-+time delay process model; because we estimate same parameters like dead time, time constant and process gain. Isn’t it?

Jacques :


Tejaswinee, yes the Ziegler-Nichols, Cohen-Coon, Lambda, Minimum IAE, and many other tuning rules use the first-order + dead time process model for tuning control loops with self-regulating processes. Since the model is only an approximation of the real process, the resultant tuning settings are only approximately correct, but in most cases good enough to use without further adjustment, provided that the loop wasdetuned appropriately.

ajay:


Hey all,

Very nice article.

I Have a question anybody tried to implement this method using any software.. !!!I am a student i am trying to implement a PID controller for controlling the flow rate of air. The problem i am facing is I want to use automatic tuning of the controller but i am not sure which method shall i use and then there are some question which can not figure out how to do it.so i just wanted if somebody already implemented can help me with this.thanks and regardsajai

Jacques :


Ajai, I suggest you search for “relay auto tuning” on Google. Most PID controllers with integrated auto tuning use this technique in some form and it is reasonably easy to

implement. The most difficult part of implementation is handling abnormal data, and very fast, very slow, noisy, and disturbed processes. But if this is a lab project you probably don’t have to worry about these factors.

Marco:

March 18, 2013 at 10:42 am

I did the response test with an Oxford Instrument ITC503 temperature controller. My problem is the proportional band used by the controller is in Kelvin. How should I convert the gain?

Jacques :

March 18, 2013 at 11:59 pm

Marco,Kc = controller gain.PB = proportional band.

100%/Kc = PB[%] = PB[Kelvin] / (PV Range [Kelvin]) * 100%So,1/Kc = PB[Kelvin] / (PV Range)Then:PB[Kelvin] = (PV Range) / Kc

- Jacques

Marco:

March 21, 2013 at 5:22 am

One more question. Wenn performing the Step response test, should CO changes e.g. 1%, 2%, 3%,… have the same time constant tau?

Jacques :

March 22, 2013 at 12:31 pm

In theory the time constant should be the same. In practice it normally varies a bit, sometimes a lot. If the valve travels slower than the actual process responds, the apparent dead time and time constant will get longer as the step sizes increase. Also, when making really small steps such as 1% – 2%, some control valves react differently from one step top the next because of friction, stiction, and deadband. I prefer making 5% steps (sometimes larger) for tuning, but the processes don’t always allow it.

RobW:

April 18, 2013 at 8:25 pm

Great article. Very direct and straight forward.

I have a question regarding intergrating processes.How are the lambda tuning rules applied if the process is intergrating?Could you outline the tuning method for this thype of process also?

Regards,RobW

Jacques :

April 18, 2013 at 11:28 pm

Rob: With IMC tuning for level controllers, you would use the following settings for a PI controller:Kc = 1/ri x (2 taucl + td) / (taucl + td)^2Ti = 2 taucl + tdWhere:ri is the integration rate of the process in dPV%/(dCO% x time). Time must be in the same units as td, taucl, and your controller’s Ti.

Greg:


What do you use for tau (for calculating taucl) when the process is integrating?

Thanks!

Greg<

Jacques :


Greg – You can normally use td x 3. But be aware that some level loops have a negligibly short dead time compared to their integration rate ri. Then the IMC and modified Ziegler Nichols rules will give you a very large controller gain. If you want to use a lower gain, use a larger taucl or use the level averaging tuning rule.

ravi:


Sir,To calculate “ri”, Can we used only one slope (The slope produce after making a step change in controller out put) and then what will be the procedure to calculate ri, Kc, Ti, in this case.An integrating process responds with a steady ramp instead of reaching a stable value, so how can we calculate “Tau” (63% of total PV change) and how can we calculate “Taucl”.

Jacques :

March 1, 2014 at 3:34 pm

1. Yes, but only if your initial slope was zero, i.e. PV1 = PV2 using the method described on this page: http://blog.opticontrols.com/archives/6972. For integrating loops, pick a Taucl as required by the process, but make sure it is several times longer than dead time. If you don’t know what the process requires, then decide if you want to use the level as a surge tank, or you the level to remain steadyand use the appropriate tuning methods.

umair:

April 10, 2014 at 9:48 am

Hi, I have a question. Can we use this tuning method on cascade control like Level and Flow cascade.

umair:

April 10, 2014 at 9:54 am

i use Yokogawa controller US1000 and limit of its proportional gain is 999. should i multiply my KC by 10?

Jacques :

April 11, 2014 at 9:39 pm

Umair: Yes you can if you require a relatively slow response and a system that will remain stable under most adverse and interactive conditions. When needed, I have used it on cascade loops with great success.

Jacques :

April 11, 2014 at 9:40 pm

No. Why do you want to do that?

Daniel O.:

June 9, 2014 at 3:22 pm

When performing a bump test on a liquid flow controller I get about a 20% overshoot of the PV before it settles to a steady state PV on bumps up and down. When calculating the gain of the process should i be using the maximum/minimum PV or the steady state value that occurs 5-10 seconds after the peak. Also for calculating the integral time which one would PV would you apply.

Link to the graph below(the orange is the output change of 2% on a different scale not shown)http://imgur.com/nYvGFT1

Jacques :

June 9, 2014 at 9:04 pm

Daniel: A simple flow loop should not overshoot after a controller output step change in manual. I would question the valve positioner, it seems to be overshooting. See this article on valve problems.However, if this is the response you have to deal with, the safest is to use the max change in PV to calculate the process gain. For Lambda tuning’s integral time, the safest would also be to calculate the time constant from 63% of the max change in PV.

Level Controller TuningDecember 16, 2011

Level control loops are common in industrial processes, but tuning level controllers can be challenging. Many level loops oscillate, sometimes causing large parts of their adjacent processes to oscillate with them. This article describes how to tune level controllers.

http://blog.opticontrols.com/wp-content/uploads/2011/12/Level-Control.png

Figure 1: A level control loop.

An important thing we need to know about level loops is that liquid level in a vessel is an integrating process, which responds differently from a self-regulating process. Therefore it has a different process model that requires a different set of tuning rules. See my article onlevel control loops for some general guidance.

Level controller tuning really is not all that difficult if you follow a few basic steps. There are always a few outliers, but in general I like tuning level loops and find them reasonably easy to tune. If the level controller output cascades to a flow controller (more info here), you have to tune the flow control loop first. I’ll assume you have done that already and are now ready to tune the level loop.

You should tune any controller based on the process’ dynamic response. Obtaining a model for the dynamic response of a tank’s level is easy:

Make sure as far as possible that the uncontrolled flow into/out of the vessel is as constant as

possible.

Place the level controller in manual control mode.

Wait for a steady slope in the level. If the level is volatile, wait long enough to be able to

confidently draw a straight line though the general slope of the level.

Make a step change in the controller output. Try to make the step change 5% to 10% in size, if

the process can tolerate it.

Wait for the level to change its slope and settle into a new direction. If the level is volatile, wait

long enough to be able to confidently draw a straight line though the general slope of the level.

Restore the level to an acceptable operating point and place the controller back in auto.

Now determine the process model:

Draw a line (Slope 1) through the initial slope, and extend it to the right (Figure 2).

Draw a line (Slope 2) through the final slope, and extend it to the left to intersect Slope 1.

Measure the time between the beginning of the change in controller output and the intersection

between Slope 1 and Slope 2. This is the process dead time (td), the first parameter you require

for tuning the controller.

Note: Express your dead time measurement in the same time-base your controller uses for its

integral time setting, i.e. minutes or seconds.

Pick any two points (PV1 and PV2) on Slope 1, located conveniently far from each other to make

accurate measurements.

Pick any two points (PV3 and PV4) on Slope 2, located conveniently far from each other to make

accurate measurements.

Calculate the difference in the two slopes as follows:

DS = (PV4 – PV3)/T2 – (PV2 – PV1)/T1

Note: Express your T1 and T2 measurements in the same time-base your controller uses for its

integral time setting, i.e. minutes or seconds.

If your PV is not ranged 0 – 100 %, convert DS to a percentage of the range as follows:

DS% = 100 x DS / (PV range max – PV range min)

Calculate the process integration rate (ri) which is the second and final parameter you need for

tuning the controller:

ri = DS% / dCO

Figure 2: Measurements for tuning a level loop.

Now that you have the dead time (td) and the process integration rate (ri), you can tune the controller. If the control objective is a nice and fast response to quickly recover from disturbances, you can use a modification of the Ziegler-Nichols (Z/N) tuning rules. The modification involves a slight detuning of the controller because the original Z/N tuning rules result in a very aggressive loop response and low tolerance for any change in operating conditions. I call the amount of detuning the stability margin, denoted by SM. You should set SM to a value of 2.0 or larger. The larger you make SM, the slower the loop will respond. In this way you can use SM as a fine-tuning factor.

Note:

The tuning rules below assume your controller’s proportional setting is in gain Kc, not

Proportional Band, PB. If not: PB = 100 / Kc.

The tuning rules below also assume your controller’s integral setting is in units of time Ti (i.e

minutes or seconds), not repeats per time Ki. If not: Ki = 1 / Ti.

The tuning rules below also assume you have a controller with an interacting algorithm (although

they work fairly well on noninteracting algorithms too), but not a parallel algorithm. For controllers

with the parallel algorithm, you need to divide Ti by Kc, and multiply Td by Kc, to obtain their

integral and derivative settings, respectively.

See my article on PID controller algorithms for more details.

To calculate tuning constants for a PI controller:

Kc = 0.9 / (SM x ri x td)

Ti = 3.33 x SM x td

Td = 0

And for a PID controller:

Kc = 1.2 / (SM x ri x td)

Ti = 2 x SM x td

Td = td / 2

Important Note:Some level controllers should not respond fast, e.g. when controlling the level of a surge tank. Surge tanks need a different set of tuning rules to ensure you make maximum use of the surge capacity, while not exceeding the upper and lower level limits. Follow this link for tuning surge tank level controllers.


http://blog.opticontrols.com/wp-content/uploads/2011/12/Integration-Rate-Meas-NonSteady.png

Posted in 4. Controller Tuning | Tags: level control, tuning, Ziegler-Nichols

5 Responses to “Level Controller Tuning” Andrew:


Used this method this week to tune a level loop that has not run in automatic since installation (4+ years). Operators have been controlling level manually. Problem was that the level filled at a faster rate than it emptied. By taking into account both the filling and emptying rates in this formula, the loop was successfully tuned and has been running in automatic all week. The operators are extremely happy.

Thanks for the great blog and I look forward to reading your book.

Andrew

Ted Mortenson:


Maybe I’m missing something here.You state “Make sure as far as possible that the uncontrolled flow into/out of the vessel is as constant as possible. Place the level controller in manual control mode. Wait for a steady slope in the level.”If flow in equals flow out, won’t level remain constant? How will you ever see a steady state slope in level?

Love your blog BTW.

Jacques :


Ted, although it would make the calculations easier, this tuning method does not require that inflow = outflow. In practice, it is very difficult to get the level to remain absolutely constant. The level normally slopes up or down over time when the controller is in manual. As long as the inflow remains constant, and the outflow remains constant, the slope will be constant. That is why the procedure asks for a “steady slope” and not a constant level.

belami:

May 25, 2014 at 10:43 pm

How can we make level control valve (or all level control loop ) responding faster to level change. especialy when the level rises and we dont want to over flow.there is any improvement to add to level control loop to have that.

thanks

Jacques :

June 5, 2014 at 12:04 pm

Belami – it is mostly the controller gain that determines how fast the valve responds to an increase in level. Increasing the controller gain will make the valve respond faster. However, using too much gain will cause the loop to become unstable. Using derivative control mode can speed up the response a little bit too. Use the tuning methods on this page. If the response is too slow, consider using feedforward control.

Minimum IAE Tuning RulesSeptember 13, 2012

I came across the Minimum IAE and other error-integral tuning rules very early in my career, but until recently I did not have the original paper describing the development of these rules. A few weeks ago I contacted Dr. C.L. Smith to get a copy of the paper he coauthored in 1967: Tuning Controllers with Error-Integral Criteria (Reference at end of this article). The error-integral tuning rules described in this paper minimize the area that develops over time if a process variable deviates from its setpoint, shown as shaded areas in Figure 1.

Figure 1. Shaded areas indicate the integral of absolute error after a disturbance to a process.

Explain, please!

You may wonder exactly what you are looking at in Figure 1, so let me explain. Imagine we have a running pump for pumping chemicals into a reactor, and a second pump on standby (Figure 2). If the operator starts the second pump, the flow rate (process variable) will increase. As a result, the flow controller will close the control valve a little to get the flow back to setpoint. The control action is not shown in Figure 1, but it is so strong that it over-corrects, causing the flow rate to undershoot the setpoint and oscillate a few times before finally settling out. The shaded areas between the process variable and setpoint are the integral of the error.

Figure 2. The total flow rate will be disturbed when pump 2 starts up.

Tuning Objectives

So, let’s get back to the technical paper. The paper describes tuning rules for minimizing several error-related integrals:

1. Integral of the error squared (ISE)

2. Integral of the absolute error (IAE)

3. Integral of the absolute error multiplied by time (ITAE)

The authors recognized that a controller’s integral and derivative times should be based not only on the length of the process time constant (or dead time as in the case of Ziegler & Nichols), but also on the ratio of dead time to time constant (td / tau).

Optimized for Disturbance Response

The tuning rules were developed for optimizing a control loop’s disturbance response. Tuning for a setpoint change will require different controller settings. However, Smith and Murrill did develop tuning rules for minimizing IAE and ITAE on setpoint changes, but these are outside the scope of this article.

Target Process

The authors also stated that the rules were developed for a 1st-order plus dead-time process. One shortfall is that their tuning rules were designed only for processes with time-constants equal to or longer than dead times (tau >= td). This is not a major restriction since most processes do fall in this category. But it excludes these tuning rules from being used on dead-time dominant processes.

http://blog.opticontrols.com/wp-content/uploads/2012/09/Integral_Error.png

http://blog.opticontrols.com/wp-content/uploads/2012/09/Flow_Disturbance.png

Target Controller and Tuning Rules

The authors developed tuning rules for P, PI and PID controllers for a non-interactingcontroller algorithm with controller gain, integral time, and derivative time. Since P-only control is hardly ever used, I list only their PI and PID tuning rules in Table 1 below.

The process characteristics are denoted in Table 1 by:

- Process gain = gp

- Dead time = td

- Time Constant = Greek letter tau

Table 1. Minimum ISE, IAE, and ITAE Tuning Rules. Click to enlarge.

Performance Assessment

So, how well do these tuning rules perform? I tested them on simulations of flow and temperature control loops. The PI control rules left the temperature loop with a very oscillatory response, but the PID tuning rules worked a bit better. As expected, the PID rules did not work well at all on the flow loop. Their Minimum ITAE tuning rules seemed to work the best in my opinion because they had the fewest oscillations (Figure 3).

Figure 3. Minimum ITAE tuning on a simulated temperature control loop responding to a disturbance.

Low Stability Margin

My biggest concern is that all of the tuning rules pushed the control loop very close to instability. To analyze stability, we can calculate a loop’s stability margin. The stability margin tells us how much the process gain can increase before a loop will become unstable with its current tuning settings. The stability margin on the temperature loop under Minimum ITAE’s PI control was only 0.7. The PID loop was marginally better at 1.1. Their other tuning rules fared even worse.

The control characteristics of industrial processes can change substantially based on valve position, process throughput, head pressure, pH, etc. Using these tuning rules on real processes will very likely cause stability problems because of their small stability margins. In all fairness this would be similar to using the unmodified Ziegler-Nichols, Cohen-Coon, and many other high-performance tuning rules.

The solution would be to detune the controller (use a lower controller gain) to increase the stability margin and tolerate these changes. I normally use a stability margin of 2 to 3 on loops I tune, sometimes even more. But this would contradict the authors’ original tuning objective of super-fast response. This is yet another example of the inevitable tradeoff between a loop’s speed of response and stability.

Reference to Minimum IAE Paper

Tuning Controllers with Error-Integral Criteria, A.M. Lopez, J.A. Miller, C.L. Smith, and P.W. Murrill, Instrumentation Technology, November 1976, pp. 57 – 62.

More Info

http://blog.opticontrols.com/wp-content/uploads/2012/09/IAE_Tuning_Rules.png

http://blog.opticontrols.com/wp-content/uploads/2012/09/Minimum_ITAE.png

Read more about tuning methods and loop stability in Process Control for Practitioners.

Stay tuned!

Jacques SmutsOptiControls Inc.


3 Responses to “Minimum IAE Tuning Rules” Ron Compton:


Is loop tuning software recommended rather then manually calculating the tuning parameters?

Jacques :


Ron, I definitely recommend using a good software program for tuning. It makes the model identification, tuning, and analysis so much easier. However, a tuning tool is no replacement for understanding your process, PID controllers, and the tuning process.Note that there are more than a dozen commercially available tuning software packages. Make sure you try out a few and pick one that is easy to use and meets your criteria.- Jacques

Peter Nachtwey :

April 3, 2013 at 12:04 pm

I agree that minimum IAE, ITAE or SSE will result in barely stable systems. One gets more robust results if you add extra terms to the cost function that is being minimized. For instance one can add a cost for the magnitude of the control output or changes in the control output. However, if one does this then it isn’t simply a minimum IAE, ITAE or SSE any more and is closer to linear quadratic control.

My other problem with minimum IAE etc, is that it minimizes what case? Minimizing the the response in a step from 0 to 1 will be different from minimizing the step between 0 and 2. Also, minimum IAE etc methods don’t take into account that the control output is limited.

I calculated the minimum IAE, ITAE and SSE coefficients using Mathcad and Scilab. Scilab is free.

Quarter Amplitude DampingOctober 4, 2013

Quarter-amplitude damping is likely the best-known tuning objective, but it’s a poor choice for process stability. Also called quarter amplitude decay or QAD, many tuning rules, including the famous Ziegler-Nichols and Cohen-Coon tuning rules, were designed for this objective. The idea behind quarter-amplitude damping is to eliminate any error between the setpoint and process variable very fast. In fact, the controller responds so fast that the process variable actually overshoots its setpoint and oscillates a few times before it finally comes to rest (Figure 1). The deviation from setpoint gets smaller with each successive cycle at a ratio of 4:1. In Figure 1, the ratio of B/A = 1/4.

Figure 1. A quarter-amplitude-damping response after a process disturbance.

When developing their tuning rules, Ziegler and Nichols chose quarter-amplitude damping to be “optimum” control loop response. Although QAD performance lies in the middle between a completely dead controller and an unstable control loop, you should realize that quarter-amplitude damping, by design, causes the process to overshoot its set point and to oscillate around it a few times before eventually settling down. Practitioners with solid experience in controller tuning will all tell you that quarter-amplitude-damping is a very poor choice for tuning industrial control loops.Problems with Quarter-Amplitude Damping

Although the quarter-amplitude damping tuning objective provides very fast rejection of disturbances, it creates three problems:

1. It makes the loop very oscillatory, often causing interactions with similarly tuned loops. If control

loops in a highly interactive process, such as a paper machine, power plant boiler, or

hydrodealkylation process, are tuned for quarter-amplitude damping, oscillations affecting the

entire process often occur.

2. It causes a loop to overshoot its setpoint when recovering from a process disturbance and after a

setpoint change. Many processes cannot tolerate overshoot.

3. QAD-tuned loops are not very stable and have low robustness. They can very easily become

completely unstable if the process characteristics change. For example, such a loop will become

unstable if its process gain doubles, which can happen very easily in industrial processes.

Solution

An easy way to minimize all three problems is to reduce the controller gain (detune the controller). The minimum reduction I recommend is to use the calculated Kc divided by two (or more if necessary). For example, if a quarter-amplitude-damping tuning rule suggests using a controller gain of 0.9, then use 0.45 instead. This will greatly reduce oscillations and overshoot in the control loop, and it will increase the loop’s robustness by a factor of two. (Please note that if your controller uses a parallel algorithm, you have to reduce Kp, Ki, and Kd to achieve the equivalent effect).

Stay tuned!

Jacques SmutsPrincipal Consultant at OptiControls, and author of Process Control for Practitioners.

Posted in 1. General, 4. Controller Tuning

One Response to “Quarter Amplitude Damping” Don Parker :


Jacques,I have worked with boiler/turbine controls for many years and could not agree more. So many

http://blog.opticontrols.com/wp-content/uploads/2013/10/qad1.png

of the processes are interactive that they must be tuned wthout oscillation, generally with maximum overshoot of about 5%.

Of course there is also the problem of over-active actuators, which can cause premature aging, wear, linkage hysteresis, etc.

I have found Lambda tuning to be a very successful method for many power plant control loops.

Surge Tank Level ControlNovember 23, 2012

A surge tank is placed between two processing units to absorb flow rate fluctuations coming from the upstream process and keep the flow rate to the downstream process more constant. To do this, the tank level has to go up and down. Consequently, the level controller should not try to hold the level as close as possible to its set point; the controller should simply keep the surge tank’s level between its upper and lower limits, and do this with the least possible amount of change to its output.

Figure 1. Surge tank level control loop.

Although there are other methods of controlling surge tank level, the level-averaging method [1] is preferred by most operators and process engineers. This method minimizes control valve movement during disturbances, keeps the level between its limits, and brings the level back to setpoint in the long term (Figure 2). Another method of surge tank control does not bring the level back to setpoint but potentially provides more surge capacity [2]; I’ll write about that method another day.

Surge Tank Level Controller Tuning

To tune the controller for level-averaging control, you need to know the following three things:

1. The residence time of the vessel (tres)The residence time is the time it would take for the surge tank to drain from 100% level to 0% level if there is no flow into the tank and the outlet valve is 100% open. You can calculate this as the volume of liquid contained in the vessel between 0% and 100% of the span of its level measurement, divided by the maximum flow rate with the outlet valve wide open: tres = V/Qmax. Use the same engineering unit for volume in V and Qmax. If you don’t know the volume and/or maximum flow rate, you can estimate the residence time as the inverse of the process integration rate, tres = 1/ri. You can determine ri through step testing. Be sure to express tres in the same time-base as your controller’s integral time (minutes versus seconds).

2. The largest expected change in flow rate (Δfmax).This should be expressed as a percentage of maximum valve capacity. You can review historical trends of the loop and find the largest change the controller output has made (under automatic control) to control the level.

3. The maximum tolerable deviation from setpoint (ΔLmax).This should be expressed as a percentage of the span of the level measurement.

Once you have all of these, calculate tuning settings for the controller with the equations below.




http://blog.opticontrols.com/wp-content/uploads/2012/11/Surge-Tank-Level-Control.png

For a controller with an interactive or noninteractive algorithm:

KC = 0.74 Δfmax / ΔLmax

TI = 4 tres / KC

TD = 0

KC is controller gain.If your controller uses proportional band, PB = 100/KC.TI is integral time in the same units as tres.If your interactive or noninteractive controller uses integral gain, KI = 1/TI.TD is the derivative time.

For a controller with a parallel algorithm:

KP = 0.74 Δfmax / ΔLmax

KI = KP2 / (4 tres)

KD = 0

KP is proportional gain and KI is integral gain using the same time-base as tres.If your parallel controller uses integral time: TI = 1 / KI

KD is the derivative time.

Figure 2. Response of a surge tank level control loop to a disturbance in inlet flow rate.

Faster tuning is also possible. The following equations will produce tuning settings to bring the level back towards the setpoint much quicker. The level will slightly overshoot the setpoint as a result of the faster response (Figure 3).

For a controller with an interactive or noninteractive algorithm:

KC = 0.5 Δfmax / ΔLmax

TI = 0.74 tres / KC

TD = 0

For a controller with a parallel algorithm:

KP = 0.5 Δfmax / ΔLmax

KI = KP2 / (0.74 tres)

KD = 0

The same parameter descriptions and conversions given previously, apply to the faster tuning equations too.



http://blog.opticontrols.com/wp-content/uploads/2012/11/Averaging-Response.png

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Figure 3. A faster response to the same disturbance in inflow.

Figure 3. A faster response to a disturbance in inflow.

With these tuning rules, you should be able to get your surge tanks under control, and have them respond appropriately to surges in inflow. Let me know if you need help.

Stay tuned.

Jacques Smuts – author of Process Control for Practitioners.

References:[1] H.L. Wade, Basic and Advanced Regulatory Control: System Design and Application, 2ndEdition, ISA, 2004.[2] F.G. Shinskey, Process Control Systems: Application, Design, and Tuning, 4th Edition, McGraw-Hill, 1996.

Tank Level Tuning ComplicationsNovember 4, 2013

Level control loops are strange creatures. This strangeness can make them difficult to tune. On average, level control loops are tuned the worst of all process types. Although I have seen poorly tuned loops of all types, poorly tuned level controllers typically have tuning settings that are the furthest from optimal. Most level processes are very robust in nature, allowing them to function surprisingly well with suboptimal tuning.

But it does not have to be this way. If controller tuning is based on the dynamic response of a process, most level control loops are actually easy to tune and provide very robust control. However, as you probably know, most control loops are tuned “intuitively” using trial and error. More often than not, this approach results in poor control loop performance.

Case Study

A few weeks ago, I helped an engineer at a power plant with the tuning of a demineralized (demin) water storage tank. It was a large tank – about 40 feet (12 m) high and 20 feet (6 m) in diameter. Water was pumped from the demin water production plant into the tank, and this flow rate was manipulated with a control valve (Figure 1). Under normal operating conditions the unit consumesd demin water at an almost constant rate (most of which was discharged through the continuous boiler blowdown).

Figure 1. Demineralized water storage tank level control.

To do the tuning correctly, the engineer executed a few step tests (Figure 2) and we analyzed the data. We calculated the process integration rate (or process gain) to be 0.0045 / minute. This means if the level is at steady state and the controller output is changed manually by X percent, it will take 1/0.0045 minutes (3.7 hours) for the level to change by the same percentage. The dead time was measured to be roughly 2.5 minutes.


http://www.opticontrols.com/contact-us

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Figure 2. The two step tests used for tuning.

Once we had this information on the dynamic properties of the process, we used the modified Ziegler-Nichols tuning rules for Integrating Processes and calculated new tuning settings for this control loop. We used a “stability margin” of 2.5 and obtained the following tuning settings:

Controller Gain (Kc) = 32Integral Time (Ti) = 20 minutes.

The high controller gain was a concern. Although the level was quite smooth during our step tests, a historical trend of level revealed some jittering was present at times. And since a 1% jitter in level would cause the controller output to ”jitter” by 32% (Kc x delta PV), we decided to use a lower controller gain since tight control was not a requirement. We felt that Kc = 10 would be a good compromise between control performance and jitter tolerance.

Tuning Complications

Many level loops have small integration rates (or process gains). Integration rate (ri) is inversely proportional to the vessel’s residence time. Typically, the larger the tank, the smaller the integration rate. The process with the smallest integration rate that I personally worked with was a city water reservoir, which had a residence time of 48 hours (ri = 0.000347 / minute). For good control, a very low integration rate theoretically requires a very high controller gain, sometimes in excess of 100. Practically we cannot use controller gains of this magnitude because of the severe control action that would result from noise and setpoint changes. (Note that one can also overcome severe control action by using a noise filter and either the P&D-on-error control algorithm or a setpoint filter).

This mandatory reduction of the controller gain brings me to the reason why most level loops have grossly suboptimal tuning settings. For integrating control loops (such as tank level), when you reduce the controller gain you have to increase the integral time, otherwise the loop can become very oscillatory.

Unenlightened tuners do not know of this requirement and end up using disproportionately short integral times on level loops, resulting in very oscillatory behavior. When they try to stabilize the loop by further reducing the controller gain, the situation deteriorates even more.

Example

For example, let’s look at how Billy, our unenlightened but fictitious tuner, might have tuned the tank level controller. Assuming he did step tests, he then used the original Ziegler-Nichols tuning rules (I did mention he is unenlightened) for calculating the controller settings. He obtained the following controller settings: Controller Gain (Kc) = 80 and Integral Time (Ti) = 8.3 minutes. He realized that the controller gain of 80 was too high, and reduced it to 10. But he left the integral time at 8.3 minutes, as calculated.

Then he tested the new tuning settings and noticed overshoot and oscillations in level. Too much gain, right? So he set the Kc value to 5 and retested the performance. The loop still oscillated with the adjusted tuning settings, but he realized that this tuning effort was taking too much of his time, so he left the tuning settings as they were and moved on to other work. Billy’s tuning results are shown in Figure 3.

Figure 3. The result of using decreased controller gains on a level loop, while leaving the integral time at the originally calculated value.

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How it’s Done

Now back to our own tuning efforts on the demin water storage tank. When the engineer and I reduced the controller gain from 32 to 10, we simultaneously increased the integral time from 20 to 64 minutes, which we calculated using the equation below.

Equation for calculating a new integral time when reducing the controller gain in a level loop:Ti(new) = Ti(old) x Kc(old) / Kc(new)

Figure 4 compares the level loop’s response to a 5% change in outflow using the initial and refined controller settings. The control loop is significantly more stable compared to the alternatives shown in Figure 3.

Figure 4. Stable level control loop response obtained from increasing integral time while decreasing controller gain.

As I said at the beginning, level controller tuning does not have to be difficult. Do step-tests to understand the process dynamics, use proven tuning rules to calculate controller settings, and remember to adjust the integral time inversely to any subsequent change you make in controller gain.

Stay tuned!

Jacques SmutsFounder and Principal Consultant, OptiControlsAuthor of Process Control for Practitioners

Posted in 4. Controller Tuning, 8. Case Studies

2 Responses to “Tank Level Tuning Complications” Nhan:


Dear Jaques,

Referred to the response curve, I calculate out the ri= 0.045/min, how come to 0.0045 as said, please advise, thanks

Jacques :


Nhan, let’s consider the first step change, dCO = 25% in size.Before the step has any effect, the level decreased by 1% over 32 minutes. S1 = -0.031%/minAfter the step change, the level increased by 1.1% over 13 minutes. S2 = 0.085%/minri = (S2 – S1) / dCO = (0.085 + 0.031) / 25= 0.0046 (which I rounded down to 0.0045 for convenience).

Tuning Rule for Dead-Time Dominant ProcessesDecember 15, 2010

Processes with lags or time constants (tau) longer than their dead times (td) are reasonably easy to tune. Most tuning rules work well for processes where tau > 2 td (lag dominant). The opposite is not true. Many tuning rules work very poorly when td > 2 tau (dead-time dominant).

http://blog.opticontrols.com/wp-content/uploads/2013/11/Proper-Tuning.png

Lag DominantWhen a process has a time constant that is much longer than the dead time, problems like overshoot and having to use high controller gains begin to appear. However, loops with long time constants still act in an intuitive way – if we add more control action we can make the process respond faster, like stepping down harder on the accelerator will get our car to the desired speed quicker.

Dead-Time DominantOn the other side of the spectrum, when a process’ dead time is significantly longer than its time constant, it behaves much less intuitively – adding more control action does not make the process respond faster. For example, if your shower water is a little cold, opening the hot water tap a lot more is not going to get you to the right temperature any quicker, and it is going to have some serious side-effects.

I once saw several operators struggle to manually control the outlet temperature of a three-pass kiln. The kiln was a dead-time dominant process and its dead time was about 10 minutes long. The operators would notice the temperature is below set point and increase the firing rate. When they see no effect, they increase the firing rate more. And then some more, and more. Finally, when changes have made their way through the dead time, the temperature overshoots its set point by a large margin. Then the operators take the same actions and make the same mistakes in the opposite direction.

Needless to say, controller tuning also becomes difficult on dead-time dominant processes.

Tuning

Step response of a dead-time dominant process.

You will find that the Ziegler-Nichols tuning rules don’t work well at all on a dead-time dominant process. For example, the following process characteristics were measured from the step-response of a dead-time dominant process in the previous plot:

td = 0.276 minutestau = 0.013 minutesgp = 0.89

Applying the Ziegler-Nichols tuning rules to this process gives the following controller settings: Kc = 0.05; Ti = 0.92 minutes. The result is an extremely sluggish control loop (see below).

Dead-time dominant loop tuned with the Ziegler-Nichols tuning rules.

Processes with time constants (tau) longer than their dead times (td) are reasonably easy to tune. Most tuning rules work well for processes where tau > 2 td (lag dominant). The opposite is not true. Most tuning rules work very poorly when td > 2 tau (dead-time dominant).

The Lambda tuning rules were designed for lag dominant processes and do not work all that well on dead-time dominant processes either. The Cohen-Coon tuning rules work much better than the Ziegler-


http://blog.opticontrols.com/wp-content/uploads/2010/12/zntuned.png

Nichols rules, but they too aren’t the best tuning rule when the dead time is five or ten times as long as the time constant.

So what type of tuning rule will work well for controlling dead-time dominant processes? First, we need a lag-dominant controller, to make up for the absence of lag in the process. But if we just crank up the integral term, the loop will become unstable. So, second, we have to compensate by decreasing the controller gain.

The Cohen-Coon PI tuning rules will work reasonably well up to td = 2 tau, but it becomes sluggish after that. When td > 2 tau, it is better to use the dead-time tuning rule. It is as follows:

Kc = 0.36 / (gp * SM)Ti = td / 3No derivative.

SM is the stability margin and can be set to a value between 1 and 4. A value of 1 is equivalent to the 1/4-amplitude damping response. It is considered unsafe – the loop is very sensitive to changes in process conditions. A value of 2 or higher is recommended. It will reduce the overshoot, eliminate unnecessary cycling, and make the loop far more robust to changes in process conditions.

Hint: measure dead time in the same units of time as your controller’s integral setting. E.g. if your controller’s Ti setting is in minutes, measure td in minutes.

Notes:- The tuning rules above are designed to work on controllers with interactive or non-interactive algorithms, but not controllers with parallel algorithms.- Furthermore, they will work only on controllers with a controller gain setting and not a proportional band (found on Foxboro I/A controllers, for example).- The rules assume the controller’s integral setting is in units of time (minutes or seconds), and not integral gain or rate (repeats per minute or repeats per second).

If your controller is different, parameter conversions will allow you to use these rules.

Applying the dead-time tuning rules to the process described above gives the following controller settings: Kc = 0.2; Ti = 0.092 minutes. The result is significantly better than what can be obtained with other tuning rules.

Dead-time dominant loop tuned with the Dead-Time tuning rules.

Better loop response can be obtained with a Smith Predictor, but that is more complex to implement, more tedious to tune, sensitive to changes in process characteristics, and perhaps the topic of a future blog.



2 Responses to “Tuning Rule for Dead-Time Dominant Processes”

Trevor:

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I am trying to calculate the Gp of the step response from the Dead Time Dominant process graph and not getting your value. I see the CO goes from 40.5 to 45 and the PV goes from 50 to 54. Utilizing the Gp equation given on another page, Gp = %changePV/%changeCO.((54-50)/50)/((45-40.5)/40.5) = 0.72. The number you listed above is 0.89. Am I calculating the Gp incorrectly?

Jacques :


Trevor – You should convert the changes in CO and PV to a percentage of full scale. In this case I did not state the scaling, but both the PV and CO are scaled 0 – 100%. So gp = dPV[%] / dCO[%] = (54-50)/(45-40.5) = 4/4.5 = 0.89

Typical Controller SettingsOctober 10, 2010

If you design processes or control loops, you might have to come up with reasonable controller settings before you have the chance of doing any tuning. If you are faced with this situation, you could use the table of typical controller settings below to give you more appropriate starting values for a controller.

The table can also be used to validate tuning settings on problem control loops. Sometimes one setting is so far off that simple trial-and-error tuning seems to make no difference. If you compare your controller settings to those in this table, you might find the culprit setting.

Important:

Settings in this table are for information only. Process characteristics can vary widely from the “typical” process, requiring greatly different controller settings. You should always tune a controller according to the actual process dynamics (by doing step tests and applying the appropriate tuning rules) before anyone places it in automatic control mode.

The controller settings are for controllers with the noninteractive algorithm, using controller gain for proportional and minutes for integral and derivative. If your controller has a different algorithm or uses different engineering units, you have to do the appropriate conversions.

If you have any questions or suggestions about the settings, please contact me.


Controller Setting

Likely Minimum

Likely Maximum

Typical Value

Unit of Settings

Flow and Liquid PressureGain 0.2 1.5 0.5 gainIntegral 0.05 0.5 0.2 minutesDerivative 0 0 0 minutesFilter 0 0.2 0.02 minutesSampling 0.5 2 1 seconds

Inline TemperatureGain 0.5 4 1 gainIntegral 0.2 1 0.5 minutesDerivative 0 0.25 0.1 minutes

Filter 0 0.1 0 minutesSampling 1 5 2 secondsColumn or Reactor Temperature, Gas Pressure

Gain 2 10 5 gainIntegral 2 20 5 minutesDerivative 0 5 1 minutesFilter 0 0.2 0 minutesSampling 1 15 10 seconds

Tight Level ControlGain 1 10 5 gainIntegral 2 30 10 minutesDerivative 0 2 1 minutesFilter 0 0.5 0.2 minutesSampling 1 5 2 seconds

Surge Tank LevelGain 1 4 2 gainIntegral 10 None 60 minutesDerivative 0 0 0 minutesFilter 0 1 0 minutesSampling 5 30 10 seconds

CompositionGain 0.1 1 0.5 gainIntegral 10 30 20 minutesDerivative 2 5 3 minutesFilter 0 0.5 0 minutesSampling 10 30 20 seconds


4 Responses to “Typical Controller Settings” Ravi Mishra:


I have absorbed that when steam temperature is below the set point (Set point: 560C, Process value: 545C), the temperature control valve (spray valve) remain close but when process value start to increase (By tilting up the burner or any other way) at that time temperature control PID start to open the spray valve which affect the temperature raising.I have asked this point with one of DCS engineer; he said that, “PID follow the trends of process value if it is in increasing trends then the temperature control PID will take action and generates the out put”.Why this is happing, while we need to increase the temperature up to desire level. If the temperature goes more than set point then only PID should take action.

This is happening not only in temperature loop even some other loop also like pressure control.Can you please explain me about these phenomena?

Jacques :


Ravi,

Let’s take a PI controller for simplicity:CO = Kc (E + Int(E)/Ti), where CO is the controller output, E is the error (PV – SP), Kc is the controller gain, Int(E) is the integral of the error and Ti is the integral time. To simplify it further, lets assume Kc = 1 and Ti = 1.

Then (Eq. 1): CO = E + Int(E).

Now if CO = 0, and E < 0, the Integral term will be blocked from further decrease to prevent windup. So, a further simplification would be to make Int(E) constant.

You told me CO = 0, and E = 545 – 560 = -15. Substituting into Eq. 1, we find that Int(E) = 15. So your integral term is sitting at +15, but it is balanced by the negative error of -15, so the CO = 0.

Now, let’s say the temperature increases to 550, then E = -10.Now CO = -10 + 15 = 5.And this is how your controller output can increase while you have the steam temp below setpoint.

Think of it this way: When you approach a red traffic light with your car, you will begin to decelerate before you get to the light. You won’t wait until you have crossed over the light to begin applying brakes. The PID controller does roughly the same thing. It begins taking action before the error is 0.

- Jacques

Ravi:


Sir,In first case E is ( -15) then according to Eq.-1CO = -15+15 = 0In second case when PV increase Then E become -10 but why Int(E) is still sitting at 15, it should be also at Int(-10). It means integral action will run behind proportional action or it will respond after some time (Lagging response).

Sir, how can I stop increasing of PID out put valve in this case where the PV is still lower than SP and it is trying to reach the SP (PV is increasing like 550, 551, 552 and SP=560). PID should start taking action when PV goes further beyond the SP (When PV≥560 and SP= 560).I observed that when the Operator or control loop increase the burner tilt to increase the RH temperature (to meet RH temperature set point), RH Spray control PID also start increase its out put and open the spray valve which slow down the temperature rise. Same thing I have seen in some other control loop also like pressure and temperature control loop. I want PID to wait and allow PV to increase and meet the set point and if it continues to increase even beyond the SP, then only PID should take action.Please explain me any solution to eliminate this problem.

Jacques :


A1: The proportional mode responds immediately on an error, the integral action occurs over time. The slower your integral, the more pronounced the lag.

A2: It seems the problem is that your temperature controller does not know that the operator has adjusted the burner tilt. You will need to bring the burner-tilt position into your temperature control strategy.

When to Use which Tuning RuleDecember 29, 2012

There are more than 400 tuning rules for PI and PID controllers [1]. How can one possibly choose the best or most appropriate tuning rule from all of these? To simplify matters, the main differences between the tuning rules can be grouped into four categories:

1. Type of process

2. Tuning objective

3. Process information required

4. Type of controller

Most of the tuning rules apply to first-order plus dead time (self-regulating) and integrator plus dead time (integrating) process types. These two process types adequately cover the vast majority of control loops in process plants. Other tuning rules apply to higher-order, oscillating, or unstable processes. Most of the documented tuning rules apply only to processes with dominant time constants. This limits their practical application. The Cohen-Coon tuning rules are an exception.

Tuning objectives include quarter-amplitude damping, minimization of some error integral, a specific percentage overshoot, critically damped, robust tuning, and a specified closed-loop time constant. It is rare to find a tuning rule with an adjustable tuning factor that allows you to change the speed of response. The IMC / Lambda tuning rules are one exception.

The process information required for the tuning rules based on first-order plus dead time and integrator plus dead time process types can be obtained by doing process step tests. A few tuning rules are based on the ultimate cycling or relay tuning methods. Many of the academic tuning rules are based on high-order process models, but they never tell you how to obtain the process model; they just base the tuning on some fictitious model chosen by the author, which largely makes them useless for practical application.

Most tuning-rule authors developed tuning rules for both PI and PID controllers, but with no guidance when to use which one. Some PID tuning rules apply to the interactive algorithm, while most apply to the noninteractive algorithm. It is reasonably easy to convert from one type to the other.

To reduce all these complexities to something we can work with on most control loops, we can consider two process types (self-regulating and integrating), and two tuning objectives (fast and slow or very robust). And ideally we need an easy tuning factor to adjust the speed of response.

When to Use Which Tuning Rule

You could probably use any of the 400 tuning rules, as long as it applies to your situation. I have successfully tuned most (but not all) control loops using just a few tuning rules. Here is what I recommend for most loops:

For self-regulating processes, use the Cohen-Coon PI tuning rule with the following exceptions:

Use a stability margin of two or more to improve robustness and adjust speed of response.

If td > 4tau, use the tuning rule for dead-time-dominant processes.

If you find it difficult to accurately measure the dead time, use the Lambda tuning rule.

If you want the loop to have a specific speed of response, use the Lambda tuning rule.

If you want the loop to absorb disturbances rather than pass them on to the next process, use

the Lambda tuning rule with the closed loop time constant set three tomes the open loop time

constant.

Use the derivative control mode (PID tuning rule) only when you need every last bit of speed, and

then only when the process lends itself well to the use of derivative.

For integrating processes, use the Ziegler-Nichols tuning rule, except for surge tanks andlevel averaging, where you should use the two tuning rules named after these control objectives.

Fast Response Slow / Robust ResponseSelf-Regulating Process

Cohen-Coon (adjust the stability margin (SM) to change the speed of response)

Lambda (adjust the closed-loop time constant to change the speed of response)

Integrating Process

Ziegler-Nichols (adjust the stability margin (SM) to change the speed of response)

Level-averaging (adjust the specification for maximum deviation from setpoint)

If you use a PID tuning rule and an interactive controller algorithm, or a controller with theparallel algorithm, remember to convert the calculated tuning parameters to ones suitable for your controller algorithm. Also remember to measure your process characteristics in the same time-units your controller’s integral uses. And remember to integral time to integral gain – if that is what your controller uses. Finally, when tuning any control loop, watch out for control valve problems.

You can find much more information in my book Process Control for Practitioners.

Stay tuned!

Jacques Smuts

Principal Consultant – OptiControls

Reference

1. O’Dwyer, A Summary of PI and PID Controller Tuning Rules for Processes with Time Delay. Part

1: PI Controller Tuning Rules, Proceedings of PID ’00: IFAC Workshop on Digital Control,

Terrassa, Spain, April 4-7, 2000, pp. 175-180.

Posted in 4. Controller Tuning, 9. Tips and Work-Process

Ziegler-Nichols Closed-Loop Tuning MethodMarch 31, 2010

J.G. Ziegler and N.B. Nichols published two tuning methods for PID controllers in 1942.

This article describes in detail how to apply one of the two methods, sometimes called the Ultimate Cycling method. (The other one is called the process reaction-curve method .) I have seen many cryptic versions of this procedure, but they leave a lot open for interpretation, and a practitioner may run into difficulties using one of these abbreviated procedures.

Before we get started, here are a few very important notes:

Read the entire procedure before beginning.

This tuning method does not work for inherently unstable processes like temperature control of

exothermic reactions.

This procedure cannot be used if the Process Variable oscillates when the controller is in Manual

control mode. If the loop is already oscillating in Auto, make sure the cycling stops in Manual.

If the controller drives a control valve or damper, and this device has dead band or

stiction problems, this tuning method cannot be used and will lead to inaccurate results and poor

tuning at best.

Care should be taken to always keep the process in a safe operating region.

An experienced operator should oversee the entire test and must have the authority to terminate

the test at any time.

Keep note of the original controller settings and leave them with the operator in case he/she

needs to revert back to them later. Process conditions can change significantly, and your new

tuning settings might only work for the conditions at which the process tests were done.

The steps below apply to a controller with a Controller Gain setting. If your controller uses Proportional Band instead, do the reciprocal of any Controller Gain changes. E.g. if the procedure calls for increasing the Controller Gain by 50%, the Proportional Band should be decreased by 50%, etc.

To apply the Ziegler-Nichols Closed-Loop method for tuning controllers, follow these steps:

1. Stabilize the process. Make sure no process changes (e.g. product changes, grade changes,

load changes) are scheduled.

2. If the loop is currently oscillating, make sure that the Process Variable stops oscillating when the

controller is placed in Manual mode.

3. Remove Integral action from controller.

o If your controller uses Integral Time (Minutes or Seconds per Repeat), set the Integral

parameter to a very large number (e.g. 9999) to effectively turn it off.

o If your controller uses Integral Gain (Repeats per Minute or Repeats per Second), set the

Integral parameter to Zero.

4. Remove Derivative action by setting the Derivative parameter to Zero.

5. Place the controller in Automatic control mode if it is in Manual mode.

6. Make a Set Point change and monitor the result.

7. If the Process Variable does not oscillate at all, double the Controller Gain.

8. If the Process Variable oscillates and the amplitude of the peaks decreases, increase the

Controller Gain by 50% (or less if you are getting close to a constant amplitude).

9. If the Process Variable oscillates and the amplitude of the peaks increases, decrease the

controller gain by 50% (or less if you are getting close to a constant amplitude).

10. If the Process Variable or Controller Output hits its upper or lower limits, decrease the controller

gain by 50%. The Process Variable and Controller Output must oscillate freely for this method to

work.

11. If the oscillations have died out, go to Step 6.

12. If the loop is oscillating, but not with a constant amplitude, repeat Steps 8, 9, and 10 until

oscillations with a constant amplitude are obtained.

13. If the Process Variable is oscillating with constant amplitude, and neither the Process Variable

nor the Controller Output hits its limits, do the following:

o Take note of the “Ultimate” Controller Gain (Ku). If your controller has Proportional Band,

note down the “Ultimate Band” (PBu).

o Measure the period of the oscillation (tu). If your controller’s Integral and Derivative units

are in minutes, measure tu in minutes. It the controller uses seconds, measure tu in

seconds.

14. Cut the Controller Gain in half to let the control loop stabilize while you do the calculations.

15. Calculate new controller settings using the equations below, enter them into the controller, and

make a Set Point change to test them.

The Ziegler-Nichols Closed-Loop Tuning Method

The Ziegler-Nichols tuning rules were designed for a ¼ amplitude decay response. This results in a loop that overshoots its set point after a disturbance or set point change. The response in general is somewhat oscillatory, the loop is only marginally robust and it can withstand only small changes process conditions. I recommend using slightly different settings (also shown below) to obtain a robust loop with increased stability.

Rules for a PI Controller

The PI tuning rule can be used on controllers with interactive or noninteractive algorithms .


Ziegler-Nichols Rule: Kc = 0.45 Ku

For robust control use: Kc = 0.22 Ku

Proportional Band (PB)

Ziegler-Nichols Rule: PB = 2.2 PBu

For robust control use: PB = 4.4 PBu

Integral Time in Minutes per Repeat or Seconds per Repeat

Ziegler-Nichols Rule: Ti = 0.83 tu

For level control (integrating processes) use: Ti = 1.6 tu

Integral Gain in Repeats per Minutes or Repeats per Seconds

Ziegler-Nichols Rule: Ki = 1.2 / tu

For level control (integrating processes) use: Ki = 0.6 / tu

Rules for a PID Controller

The PID tuning rule was designed for a controller with the Interactive algorithm. The tuning settings should be converted for use on controllers with Noninteractive and Parallelalgorithms.


Ziegler-Nichols Rule: Kc = 0.6 Ku

For robust control use: Kc = 0.3 Ku

Proportional Band (PB)

Ziegler-Nichols Rule: PB = 1.7 PBu

For robust control use: PB = 3.3 PBu

Integral Time in Minutes per Repeat or Seconds per Repeat

Ziegler-Nichols Rule: Ti = 0.5 tu

http://blog.opticontrols.com/wp-content/uploads/2010/03/Ultimate_Cycle.png

For level control (integrating processes) use: Ti = 1.0 tu

Integral Gain in Repeats per Minutes or Repeats per Seconds

Ziegler-Nichols Rule: Ki = 2.0 / tu

For level control (integrating processes) use: Ki = 1.0 / tu

Derivative Time or Derivative Gain

Td or Kd = 0.125 x tu

Good luck, and if you have any questions, contact me.



8 Responses to “Ziegler-Nichols Closed-Loop Tuning Method”

Davor :

July 25, 2013 at 2:53 am

What do you mean with tuning settings should be converted for noniteractive – idealalgorithems. How to convert?

Jacques :

July 25, 2013 at 10:09 am

For PI control, no conversion is needed.For PID control, to convert from interactive controller parameters to noninteractive:Set the controller gain to Kc x (Ti + Td) / TiSet the integral time to Ti + TdSet the derivative time to Ti x Td / (Ti + Td).

Davor :

July 30, 2013 at 1:08 am

Can I use the same parameters for nointeractive and parallel pid controller.

Jacques :

July 30, 2013 at 8:06 am

To convert from noninteractive controller parameters to parallel:Set proportional gain (Kp) to Kc.Set integral gain (Ki) to Kc/Ti, or for integral time (Ti) use Ti/Kc.Set derivative gain (Kd) to Kc x Td.

Dreni :

September 22, 2013 at 2:55 pm

Hello Jacques,

Can you please help me understand how do you define the ultimate controller gain Ku?

Thanks in Advance

Dreni

Jacques :


Ku is the controller gain that gives you the ultimate cycle. You determine it experimentally through trial and error as described above. If the cycle amplitude increases, reduce the controller gain. If the amplitude decreases, increase the controller gain. If the amplitude remains constant, then controller gain = Ku.

Harini:

March 25, 2014 at 4:23 am

If the manufacturer’s DCS is designed such that the derivative term acts on PV and not on error, will there be any change in the rules for PID parameter settings? If so, please provide the same for Zeigler Nichols and Cohen coon methods.

Thanks in advance,Harini.

Jacques :

March 26, 2014 at 3:48 pm

Harini, you can use the same rules without modification.

Ziegler-Nichols Open-Loop Tuning RulesMay 18, 2011

J.G. Ziegler and N.B. Nichols published two tuning methods for PID controllers in 1942*.

The Ultimate Cycling method, and

The Process Reaction-Curve method, often called the Ziegler-Nichols Open-Loop tuning method.

This article describes the second method. But before we jump right into the tuning method, here are a few important things you should know first.

Quarter-Amplitude DampingThe Ziegler-Nichols tuning methods aim for a quarter-amplitude damping response. Although the quarter-amplitude damping type of tuning provides very fast rejection of disturbances, it makes the loop very oscillatory, often causing interactions with similarly-tuned loops. Quarter-amplitude damping-type tuning also leaves the loop vulnerable to going unstable if the process gain or dead time increases.

The easy fix for both problems is to reduce the controller gain by half. However, if the control objective for the loop you are tuning is to have a very stable, robust control loop that absorbs disturbances, rather use the Lambda tuning rules.

Designed for the Interactive Controller AlgorithmThere are three types of PID controller algorithms: Interactive, Noninteractive, and Parallel. The Ziegler-Nichols tuning rules were designed for controllers with the interactive controller algorithm. If you are not using the derivative control mode (i.e. using P or PI control), the rules will also work for the nonteractive

algorithm. However, if you plan to use derivative (i.e. PID control) and have a noninteractive controller, or if your controller has a parallel algorithm, you should convert the calculated tuning settings to work on your controller.

Use of Integral TimeThe original Ziegler-Nichols tuning rules were designed for controllers using reset rate (integral gain in repeats per minute) and not integral time (in minutes or seconds). However, virtually all the modern texts on process control use integral time. This article follows that trend and uses integral time. If your controller uses integral gain or reset rate, you’ll have to invert the calculated integral time (use 1/Ti).

Limited Range of Process DynamicsThe Ziegler-Nichols tuning rules work well on processes of which the time constant is at least two times as long as the dead time. For example temperature and gas pressure. They work moderately poorly on flow loops and liquid pressure loops where the dead time and time constant are about equal in length. And they work very poorly on dead-time dominant processes. The Cohen-Coon tuning rules work better on a wider range of processes.

Slight Modification for Self-Regulating ProcessesThe tuning method described below is actually a widely-used modification of the published Ziegler-Nichols Process Reaction Curve method. The reaction-curve method was designed for use on integrating and self-regulating processes. The modified method works only on self-regulating processes, but then more accurately so. The modified method is so popular that few people know about the original reaction-curve method. I will describe the reaction-curve method in a future post, because it works very well for integrating processes.

Tuning ProcedureAssuming the control loop is linear and the final control element is in good working order, you can continue with tuning the controller. The Ziegler-Nichols open-loop tuning rules use three process characteristics: process gain, dead time, and time constant. These are determined by doing a step test and analyzing the results.

Step Test for Tuning – (click to enlarge)

1. Place the controller in manual and wait for the process to settle out.

2. Make a step change of a few percent in the controller output (CO) and wait for the process

variable (PV) to settle out at a new value. The size of this step should be large enough that the

process variable moves well clear of the process noise/disturbance level. A total movement of five

times the noise/disturbances on the process variable should be sufficient.

3. Convert the total change obtained in PV to a percentage of the span of the measuring device.

http://blog.opticontrols.com/wp-content/uploads/2010/03/series.png

http://blog.opticontrols.com/wp-content/uploads/2011/03/StepTest.png

4. Calculate the process gain (gp) as follows:

o gp = change in PV [in %] / change in CO [in %]

5. Find the maximum slope on the PV response curve. This will be at the inflection point(where the

PV stops curving upward and begins curving downward). Draw a line tangential to the PV

response curve through the point of inflection. Extend this line to intersect with the original level of

the PV (before the step-change in CO). Take note of the time value at this intersection.

6. Measure the dead time (td) as follows:

o td = time difference between the step-change in CO and the intersection described above.

7. Calculate the value of the PV at 63% (0.63) of its total change. On the PV reaction curve, find the

time value at which the PV reaches this level.

8. Measure the time constant (Greek symbol tau) as follows:

o tau = time difference between intersection at the end of dead time, and the PV reaching

63% of its total change.

9. Convert your measurements of dead time and time constant to the same time-units your

controller’s integral mode uses. E.g. if your controller’s integral time is in minutes, use minutes for

these measurements.

10. Do two or three more step tests and calculate process gain, dead time, and time constant for each

test to obtain a good average of the process characteristics. If you get vastly different numbers

every time, do even more step tests until you have a few step tests that produce similar values.

Use the average of those values.

11. Calculate settings for Controller Gain (Kc), Integral Time (Ti), and Derivative Time (Td), using

the Ziegler-Nichols tuning rules below. Note that these rules produce a quarter-amplitude damping

response and the calculated controller gain values should be divided by two.

o For P control: Kc = tau / (gp * td)

o For PI control: Kc = 0.9 * tau / (gp * td); Ti = 3.33 * td

o For PID control: Kc = 1.2 * tau / (gp * td); Ti = 2 * td; Td = 0.5 * td

12. IMPORTANT: If you have not already done so, divide the calculated controller gain (Kc) by two to

reduce overshoot and improve stability.

13. Compare the newly calculated controller settings with the ones in the controller, and ensure that

any large differences in numbers are expected and justifiable.

14. Make note of the previous controller settings, the new settings, and the date and time of change.

15. Implement and test the new controller settings. Ensure the response is in line with the overall

control objective of the loop.

16. Leave the previous controller settings with the operator in case he/she wants to revert back to

them and cannot find you to do it. If the new settings don’t work, you have probably missed

something in one or more of the previous steps.

17. Monitor the controller’s performance periodically for a few days after tuning to verify improved

operation under different process conditions.

*J.G. Ziegler and N.B. Nichols, Optimum settings for automatic controllers. Transactions of the ASME, 64, pp. 759–768, 1942.

5. Control Valves

o Butterfly Valves and Control Performance o Control Valve Linearization o Control Valve Problems o Equal Percentage Control Valves and Applications o Valve Diagnostics on a Level Loop

Butterfly Valves and Control PerformanceFebruary 23, 2012

Because butterfly valves cost less than “real” control valves like globe valves or characterized ball valves, they are sometimes used in place of control valves to save money. This decision is often costly in the long term because of the poor control performance resulting from butterfly valves.

Late last year I optimized several control loops at a mid-sized manufacturer of specialty chemicals. Similar to most plants I have worked at, I found a number of control loops that were oscillating. Many of them oscillated because of valve stiction, incorrect controller settings, or process interactions. One of the loops, a distillation column level control loop, oscillated as a result of using a butterfly valve as the final control element.

Figure 1. Oscillating level control loop.

To perform well, a PID control loop needs (among other things) that the process gain remains constant. In other words, the process variable must change linearly with changes in controller output. A small degree of nonlinearity can be tolerated, especially if we apply robust tuning methods, but if the process gain changes by more than a factor of 2, we can expect control problems. And this is why a butterfly valve makes a poor choice for a control valve – it has a highly nonlinear, S-shaped flow curve, as shown in Figure 2.

Figure 2. Typical butterfly valve flow characteristic.

Figure 3 shows how the gain of a typical butterfly valve changes from less than 0.2 to almost 3 over the span of the controller output. The process gain varies by a factor of 15! This large variation in process gain makes it impossible to have consistently good control at all valve positions.

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Figure 3. Typical butterfly valve gain.

At the chemical company the butterfly valve was used to control the bottom level of a distillation column. The distillation column was the last one in a train of three columns, of which each column had a progressively smaller diameter. Moderate increases in feed rate to the first column easily caused high-level alarms when they propagated to the small final column. The level controller originally seemed to be responding too slowly to handle these upsets, so the loop tuner increased the controller gain to achieve fast response at high flow rates. However, at normal flow rates, where the process gain was 15 times higher, the loop was unstable and oscillated continuously as shown in Figure 1.

The correct solution to this problem would have been to replace the butterfly valve with a control valve that has a linear flow characteristic and then retune the control loop. However, this could only be done during the plant’s annual maintenance shutdown. In the mean time we installed a characterizer to linearize the butterfly valve (Figure 4). The characterizer compensated for the butterfly valve’s nonlinearity and made the flow through the valve follow the controller output in a reasonably linear fashion.

Figure 4. Level control loop with characterizer.

With the characterizer in place we retuned the controller. After this the oscillations stopped and the loop performed much better than it did before. However, the control performance was still not as good as what a linear control valve would have provided. The real solution to the problem remained replacing the butterfly valve with control valve, but this had to wait for the next maintenance shutdown.


Posted in 5. Control Valves, 6. Loop Performance, Problems, and Diagnostics, 7. Control Strategies,8. Case Studies

3 Responses to “Butterfly Valves and Control Performance”

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mohamed elsadig:

May 18, 2013 at 11:11 pm

Dear Jacques,would you please the implementation of the Characterizer is in term of software (functional block or hardware).thank youmohamed

Jacques :

May 19, 2013 at 7:59 am

Mohamed, in this case we implemented the characterizer in the DCS using a function block. You could also do the characterization in the valve positioner if the positioner supports it (most digital valve positioners do). My preference is to do it in the control system because if the positioner is replaced, the new positioner might be put in service without the characterizer.

H.B.R:

May 27, 2014 at 2:16 am

Dear, Mr. Jacques.I’m an I&C engineer working for an EPC contractor. In the site where I worked last year, there was the exactly same problem as described in the figure no.4 of this article.The process was distillate water level and it was controlled by the butterfly type control valve.The process value was hunted like figure no.1 but with bigger magnitude. I think the problem was because of the actuator or positioner. When PID output sent a demand signal to the valve, the positioner feedback value followed the demand signal after 1~2 seconds.(i,e. there was a deadtime in the actuator.) I couldn’t detect that it was caused by the sticky actuator or positioner problem because the plant was under the commercial operation.(now, I’m working the head office and that problem is still remaining in the site.)Can you imagine the status of the process?? It’s oscillated with really big magnitude.(bigger than figure no.1)The action I did during the commissioning was only adjusting PID value at that time due to the tight commissioning time. After that, only the oscillation magnitude became smaller and the symptom alarming every minute disappeared but still big oscillation has existed.Thank you for your helpful information.

Control Valve LinearizationNovember 26, 2011

A control valve’s flow characteristic is an X-Y curve that maps the percentage of flow you’ll get for any given valve opening (Figure 1). The design characteristic (also called inherent flow characteristic) of a valve assumes a constant pressure differential across the valve. More relevant to us is the installed characteristic, which is the way the valve operates in the real process. The installed characteristic of a valve can be determined by plotting the measured flow rate at different valve openings. You can do tests on the live process to get this data, or you can get it from the process historian (make sure you use steady-state data).

Figure 1 - A Nonlinear Flow Characteristic

The installed flow characteristic of a control valve directly affects the process gain. It is essential that the installed characteristic is linear (the above plot is a straight line) so that the process gain is constant, regardless of the controller output. If the gradient of the curve varies by more than a factor of two, control loop performance will be noticeably affected. If nothing is done to linearize the valve the controller will have to be detuned to accommodate the maximum process gain. This leads to sluggish control loop response over much of the valve’s operating range.

A nonlinear flow characteristic should be linearized to obtain good control performance throughout the valve’s operating range. This is done with a linearizer (also called a characterizer). The linearizer is a control block, function generator, f(x) curve, or a lookup table, placed between the controller and the valve (Figure 2). Although the linearization can be done in a digital positioner, the DCS/PLC is the best location for it. This allows replacement of the positioner without having to reprogram the linearization curve in the new positioner.

Figure 2 - Linearizing a Nonlinear Valve Characteristic

Linearization is done with an X-Y curve or function generator that is configured to represent the reciprocal (inverse) of the control element’s flow curve (Figure 3).

Figure 3 - How a Linearizer Works

To design the linearizer, you have to first determine the flow characteristic curve of the valve operating in the actual process. For this you should take readings of the flow or process variable (PV) and controller output (CO) under steady-state conditions at various controller output levels. You need a minimum of three (PV, CO) data pairs for this, but four or five would be better for characterizing a nonlinear relationship.

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Make sure you span the entire operating range of the controller output, and try to obtain readings spaced equally across the controller output span. You can do process tests to obtain these values, or examine data from your process historian. Then convert the process variable data from engineering units to a percentage of full scale of the measurement.

Sort the data pairs in ascending order, and enter them into a function generator. The PV readings in percent become the X values (input side) and the CO readings become the Y values (output side). Include a (0, 0) point if you don’t already have one in your dataset and be sure to estimate a (100, Y) point also if you don’t have one. Also, if your valve opens as the CO decreases, your Y column will obviously have to reflect this.

For example, you get the following (PV, CO) pairs form historical data: (120, 22); (280, 39); (530, 63). The PV is ranged 0 to 1000 kg/hr. You plot the data and estimate that 1000 kg/hr will occur at about 85%. The characterizer will look like this:

Flow measurement in percent of full scale Controller output readings (in %)These values go on the input-side of the

linearizerThese values go on the output-side of the

linearizer0 (you must have a zero point) 0

12 2228 3953 63

100 (you must have a full-scale point) 85 (this can be an estimation)

After implementing a linearizer in the DCS or PLC, you can test its accuracy by checking whether the controller output and flow measurement are roughly at the same percentage of full scale. For example: 20% and 50% controller output should result in roughly 20% and 50% flow rate. You should retune the controller after implementing the linearizer because it likely had changed the process gain.

Although this discussion mentioned only control valves, the same applies to other final control elements, like vanes, dampers, feeders, etc.

Stay tuned!

Jacques SmutsAuthor of the book Process Control for Practitioners

Posted in 5. Control Valves, 7. Control Strategies

3 Responses to “Control Valve Linearization” Jack:

April 29, 2012 at 1:58 pm

We currently have a non-linear characterization on one of our boiler air dampers. I didn’t quite understand the purpose of the characterization until I read this article. It was a good thing I did too, because I almost removed the characterization. Thanks.

siby:

March 8, 2013 at 7:01 am

I have read about some situations where the control valves are deliberately chosen to have non-linear behavior like an equi-percentage characteristic because the process it is controlling is also non-linear. Will introducing a linearizer then adversely affect the loop performance?

Jacques :

March 8, 2013 at 7:19 am

Siby, if the nonlinear flow characteristic of the control valve cancels out the nonlinear characteristic of the process, the combination of the two should be linear and no characterization is required. For example, the steam flow control valve to a heat exchanger is likely better being equal percentage than linear.

Control Valve ProblemsFebruary 22, 2010

Control valve

Control valve problems can severely affect control loop performance and, unless eliminated, they can make controller tuning a challenging (sometimes impossible) task. Some problems are quite obvious to the trained eye and can easily be detected by loop performance assessment software. Others can be more difficult to detect without running specific tests. When doing on-site services, I always make sure to watch out and/or test for valve problems.

Four problems with control valves are found at a high frequency in poorly performing control loops. These are:- Dead band- Stiction- Positioner overshoot- Incorrect valve sizing- Nonlinear flow characteristic

Let’s take a closer look at each of these problems.

Dead bandA valve with dead band acts like there is some backlash between the controller output and the actual valve position. Every time the controller output changes direction, the dead band has to be traversed before the valve physically starts moving. Although dead band may be caused by mechanical backlash (looseness or play in mechanical linkages), it can also be caused by excessive friction in the valve, an undersized actuator, or a defective positioner.

Many people use the term Hysteresis instead of dead band (I used to be one of them). But theISA and Wikipedia define hysteresis as something else. The ISA clearly calls the mechanical backlash phenomenon in control valves ”dead band”.

http://blog.opticontrols.com/wp-content/uploads/2010/02/bluevalve.jpg

A control valve with dead band will cause oscillations in a level loop under PI or PID control if the controller directly drives the control valve (non-cascade). A control valve with dead band can also cause oscillations after a set point change in control loops on self-regulating processes – especially if the integral action of the controller is a little excessive.

StictionAnother very common problem found in control loops is stiction. This is short for Static Friction, and means that the valve internals are sticky.

If a valve with stiction stops moving, it tends to stick in that position. Then additional force is required to overcome the stiction. The controller continues to change its output while the valve continues to stick in position. Additional pressure mounts in the actuator. If enough pressure builds up to overcome the static friction, the valve breaks free. The valve movement quickly absorbs the excess in pressure, and often the valve overshoots its target position. After this, the valve movement stops and the valve sticks in the new position.

Frequently, this overshoot in valve position causes the process to overshoot its set point. Then the valve sticks at the new position, the controller output reverses direction and the whole process repeats in the opposite direction. This causes an oscillation, called a stick-slip cycle. If loop oscillations are caused by stiction, the controller output’s cycle often resembles a saw-tooth wave, while the process variable may look like a square wave or an irregular sine wave.

Stiction might be caused by an over-tight valve stem seal, by sticky valve internals, by an undersized actuator, or a sticky positioner.

Positioner OvershootOne control valve problem that is more common now than a decade ago, is that of positioner overshoot. Positioners are fast feedback controllers that measure the valve stem position and manipulate the valve

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actuator until the desired valve position is achieved. Most positioners can be tuned. Some are tuned too aggressively for the valve they are controlling. This causes the valve to overshoot its target position after a change in controller output. Sometimes the positioner is simply defective in a way that causes overshoot. If the process controller is also tuned aggressively, the combination with positioner overshoot can cause severe oscillations in the control loop.

Valve SizingThe fourth common problem with control valves are oversized valves. Valves should be sized so that full flow is obtained at about 70%-90% of travel, depending on the valve characteristic curve and the service conditions. In most cases, however, control valves are sized too large for the flow rates they need to control. This leads to the valve operating at small openings even at full flow conditions. A small changes in valve position has a large effect on flow. This leads to poor control performance because any valve positioning errors, like stiction and dead band, are greatly amplified by the oversized valve.

NonlinearityA valve with a nonlinear flow characteristic can also lead to tuning problems. A control valve’s flow characteristic is the relationship between the valve position and the flow rate through the valve under normal service conditions. Ideally the flow characteristic should be linear. With a nonlinear characteristic, one can have optimal controller response only at one operating point. The loop could become quite unstable or sluggish as the valve position moves away from this operating point.

ConclusionBefore attempting to tune a control loop, check the valve for dead band, stiction and nonlinearity and have all problems attended to. This could save hours of effort tuning a loop in which the control valve is actually the item needing attention.


Posted in 5. Control Valves, 6. Loop Performance, Problems, and Diagnostics

2 Responses to “Control Valve Problems” mandar:

July 30, 2011 at 9:47 am

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Hi, what will happen if we u 4 solenoid valve,4 separate regulators with range 02,0.4,0.6 and 0.8 and 1kg and 4 controller input instead of 1 positioner to change position of valves.

Jacques :

July 30, 2011 at 10:40 am

With the solenoid setup you describe, the system will come close to set point, but at minimum the 0.2 kg solenoid will keep on opening and closing, causing an oscillation around the set point.- If this is a problem, you can implement a dead band (slightly larger than 0.2 kg) in the control logic. The system may not be on set point, but it will not oscillate.- If you need to run the system at set point with no oscillations, you should use a control valve with an actuator (not a solenoid) so the contoller can change the valve position by tiny fractions required to keep the process variable to set point.Good luck!Jacques

Equal Percentage Control Valves and ApplicationsApril 26, 2013

Far too often, equal percentage control valves are found in applications where linear control valves should have been used. This article explains equal percentage control valves and sets guidelines for their use.

What is an Equal Percentage Control Valve?

The relationship between valve stem position and the flow rate through a control valve is described by a curve called the valve’s flow characteristic curve, or simply the valve characteristic. An equal percentage flow characteristic is a nonlinear curve of which the slope increases as the valve opens, while a linear flow characteristic is a straight line (Figure 1).

Figure 1. Equal percentage and linear flow characteristics.

Control valves manipulate the rate of liquid/gas flow through them by altering the open area through which the liquid/gas passes. Linear valves increase the open area linearly with valve travel, while equal percentage valves open progressively more area with valve travel (Figure 2).


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Figure 2. Port shapes of linear and equal percentage valves.

Why do we need Equal Percentage Valves?

PID controllers are linear devices and for optimal performance, the process should behave linearly too. That is, if the controller output changes from 10% to 20%, the process should respond just as much as it would if the controller output changes from 80% to 90%. From this requirement, it seems that linear control valves should be sufficient.

However, up to now we have been talking about the inherent/design flow characteristic of control valves. This is the flow characteristic that a valve exhibits if the pressure difference across it remains constant throughout its operating range. But in practice this is often not the case. The pressure difference across a valve is often a function of flow, and it changes with valve position. Consequently, the inherent flow characteristic is often distorted by the process and we refer to the resulting curve as the installed valve characteristic.

So we have to refine our linearity requirement to reflect the installed valve characteristic. Sometimes we need to use a control valve with an equal percentage inherent characteristic to obtain a linear installed characteristic. Two distinctly different scenarios follow.

Scenario 1a

Consider a centrifugal pump for providing pressure, and a control valve for controlling the flow (Figure 3). As the pump delivers more flow, its capability for generating pressure decreases. Therefore the pressure differential across the control valve is high and low flow rates; and it is low at high flow rates. An equal percentage valve can offset this change in differential pressure to exhibit a more linear installed characteristic.

Figure 3. Simple flow control loop with centrifugal pump.

Scenario 1b

However, we can’t just assume that because we have a centrifugal pump, we need an equal percentage valve. If the system pressure (backpressure) downstream of the valve remains high, for example when pumping into a pressurized system, the pump will likely stay high on its curve, and the pressure across the control valve will not change appreciably. In this case a linear valve might be a better choice.

If we consider the pressure differential across the valve versus flow, we can make the right choice in Scenarios 1a and 1b. If the pressure differential remains reasonably constant, a linear valve is required

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(but please read Scenario 2 below). If the pressure differential drops by more than 50%, equal percentage can provide better linearity. To remove the guesswork, use valve-sizing software. The software should allow you to specify a few pressure-differential versus flow points and based on that, it will recommend the best valve for the application.

Scenario 2

Let’s consider a steam-condensing heat exchanger (Figure 4). The pressure upstream of the valve is kept constant by the boiler and steam pressure controller. The pressure downstream of the valve is determined by the condensate temperature, which is roughly equal to the outlet temperature, which is controlled to a constant setpoint.

Figure 4. Steam-condensing heat exchanger.

In other words, the pressure differential across the steam control valve remains relatively constant, regardless of the flow. Should we then use a linear valve. Well, we should actually use ratio control in which we control the steam flow rate as a ratio of the process flow rate and use a linear valve, but that is another story. Most heat exchanger control designs are as simple as shown in Figure 4.

Even though the constant differential pressure across the valve calls for a linear control valve, this process calls for an equal percentage valve. At low process flow rates, the outlet temperature is very sensitive to changes in steam flow. At high process flow rates, the steam flow must be changed much more to affect the heater outlet temperature to the same degree. This can be accomplished by using an equal percentage control valve. At small valve openings, the valve sensitivity is very low, which cancels the high sensitivity of the process. The valve sensitivity increases as the valve opens more – which is exactly what is required because the sensitivity of our heat exchanger decreases with increased process flow rates.

Conclusion

An equal percentage control valve should be used when the pressure differential across the valve decreases with increases in flow rate. Valve sizing software should be able to find the right valve characteristic for the job. Also, equal percentage control valves should be used in control loops of which the process gain decreases with increases in flow rate. If none of these conditions apply, the loop is likely better off with a linear control valve.

Stay tuned!

Jacques SmutsPrincipal consultant of OptiControls, and author of Process Control for Practitioners.

Posted in 5. Control Valves

Valve Diagnostics on a Level LoopApril 10, 2012

Determining the condition of the control valve on a level loop can be challenging, but it is an important aspect of successful tuning. Control loop performance can be greatly affected bycontrol valve dead band, stiction, and nonlinear flow curve, and this is no different on a level control loop. If the level controller directly drives the control valve, both dead band and stiction will cause a level control loop to oscillate continuously.






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A level control loop oscillating because of control valve dead band.

Doing valve diagnostic tests is easy on a self-regulating loop, but not so on an integrating loop, like liquid level. On a level loop the process variable itself does not in any way reflect the actual control valve position (or the flow into/out of the vessel for that matter). So how then does one determine the condition of a control valve in a level loop?

The answer is to analyze the rate of change of the level at different control valve positions. For example, if you want to check for control valve dead band, you would put the controller in manual, make two controller output steps (typically 5% in size) in one direction, and make another step in the opposite direction – just like on a flow control loop, for example. However, instead of using the level measurement directly, you would analyze the rate of change of the measurement.

A dead-band test on a level loop. Normally the controller output steps would be equal in size, but very often smaller steps are required to keep the level within limits.

This takes some planning because the level always needs to be kept within a safe operating range and you need to allow enough time between controller output steps to obtain steady ramps in level that are long enough that you can take measurements from them. I often have to adapt my test plan to keep the process safe but still obtain the data I need for analysis. Don’t worry if your steps are not all the same size, the calculation below will compensate for this.

Once you have collected your test data, return command of the controller back to the operator to be placed in auto and/or monitored. Import the controller output (CO) and process variable (PV) data into Microsoft Excel or your spreadsheet of choice.

Add a new column of calculations that take the difference (dPV) between two successive PV samples, e.g.: C2 = B3 – B2, assuming your PV data is in Column B and the dPV calculations are in Column C.

You will likely find that the new dPV data is very noisy. In that case you should include an averaging filter in your calculation like this:


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Calculating a filtered rate of change.

Once you’re done you can plot the data and take measurements from the plot or the data. Use the average of the dPV values as shown below.

Analyzing dead band on a level loop.

You can then calculate the dead band in the valve, as a percentage of its full travel (0 – 100% open):

% Valve Dead Band = (CO3 – CO2) – (dPV3 – dPV2) / (dPV2 – dPV1) x (CO2 – CO1)

A stiction analysis can be done in the same way, but you will make 5 to 10 small changes in controller output (typically 0.5% in size). Remember to leave enough time between successive steps to obtain a steady gradient. Make sure that you take up any dead band first by preceding the small steps with one large dead-band-eliminating step in the same direction as you are planning for the small stiction steps.

Since a level loops will oscillate if its output drives a valve having dead band or stiction, you want these to be as low as possible. Installing a flow controller as an inner loop to the level controller in a cascade control arrangement will go a long way to reduce the effects of valve issues on a level control loop.

Stay Tuned!

Jacques Smuts, author of the book Process Control for Practitioners


6. Loop Performance, Problems, and Diagnostics o An Oscillating Level Control Loop o Butterfly Valves and Control Performance o Caster Level Control Improvement o Control Loop Performance Monitoring o Control Valve Problems o Diagnosing and Solving Control Problems o Q&A on Loop Performance o Valve Diagnostics on a Level Loop

An Oscillating Level Control LoopAugust 3, 2011

When I do onsite control loop optimization services I often see level controllers oscillating. Most often they oscillate because of one or more of the following reasons:

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The control valve has a dead band. (Yes, level loops with dead band oscillate continuously if you

are using a PI or PID controller.)

The control valve has stiction.

The integral time is set too short for the amount of controller gain being used.

However, these are not the only problems and I have often been amazed at the actual cause of oscillations.

So to keep me from guessing, I systematically analyze a loop for problems before I tune the controller. I always try to follow the same basic sequence of tests, and then delve deeper into any problems I notice. The sequence of tests:

1. See how the loop performs in automatic control under normal operating conditions.

2. Do a set point change (this is very helpful for various reasons that I’ll write about in future).

3. Place the controller in manual.

4. Do various valve performance tests (these can be quite challenging on a level loop).

5. Assuming no insurmountable problems were found, do step-tests for tuning (if you don’t have

enough data already).

6. Tune the controller and repeat steps 2 and 1 to ensure the loop meets its performance

objectives.

Some (non-readers of this blog) may try to address all control problems with tuning. But the simple steps listed above have served me very well over the years and I often smile to think that someone could be wasting hours of fruitless tuning if a loop really has other problems.

Case in PointA few weeks ago I was optimizing the control performance of loops an oil platform in the Gulf of Mexico. Quite early in the project I got to a level control problem on one of their separator vessels. Step 1 of my test sequence revealed the oil level control loop was oscillating. The period of the oscillations was slightly shorter than one minute.

Level loop oscillating.

Going on to Step 2, we made a set point change. I noticed the loop actually performed very well on the change in set point (ignoring the oscillation). From that I concluded the problem is not the controller’s tuning.

I also noticed that the process variable took about two minutes to cross over its set point for the first time and about six minutes to settle out at set point. This meant the response time of the loop was far slower than the period of its oscillations. It would be impossible for stiction or dead band to cause the loop to oscillate with a one-minute period if it takes the loop so much longer to reach set point. Although I would later test for stiction and dead band, I basically ruled them out as causes of the oscillation.

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Loop performed well on a set point change.

Step 3 calls for placing the controller in manual control mode. This provides a good test to see if the oscillations are caused by something in the control loop. We placed the loop in manual, and the oscillations continued. At this point I concluded that the oscillations were not caused by controller tuning, stiction, or dead band.

Oscillations continued with controller in manual.

So what could it be? A quick inspection of the level control valve indicated that the valve was rock-solid in holding its position with the controller in manual. The oscillations were not coming from the valve and therefore they had to be coming from the process. We looked at time trends of the flow rate into the separator vessel and the gas pressure inside the vessel, but these were not oscillating (at least not at one-minute periods).

Then we found the cause. The vessel is a three-phase separator: gas, oil, and water. The oil floats on a layer of water in the bottom of the separator. It was the oil-water interface level that was oscillating, moving the oil level up and down with it. After some more investigation, we found the water level control loop was operating virtually in on-off control mode. Only then could we focus on solving the real problem.

We are all sometimes tempted to tweak controller settings without looking any further, but a systematic approach to analyzing control loops and solving control problems really pays off.


Posted in 6. Loop Performance, Problems, and Diagnostics, 8. Case Studies

4 Responses to “An Oscillating Level Control Loop” Mary:

September 26, 2011 at 11:08 am

How did you solve the problem?

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Jacques :


We did step tests and properly tuned the water level controller. That solved the problem.

Nhan:


Which tuning rule did you apply for the oil level control loop, level averaging or lambda? Thanks

Jacques :


Nhan, the tuning rule of choice should always depend on the application:- For fast response, the Ziegler-Nichols rules for integrating processes work well, provided you divide the controller gain by two, and multiply the integral time by two.- For slow response, I recommend level-averaging (I still need to write an article about it).

In the case of the oil level, I proposed using level averaging to make maximum use of the surge capacity of the separator, but the operations personnel wanted the oil to stay as close to setpoint as possible (fast control). So we ended up using Z/N for tuning the oil level loop.

I think Lambda tuning for levels is good as an academic exercise, but I don’t see its need for tuning level controllers, and I have never used it for tuning levels. However, theLambda tuning rules certainly have a place with self-regulating processes.



















mohamed elsadig:

May 18, 2013 at 11:11 pm


Jacques :

May 19, 2013 at 7:59 am


H.B.R:

May 27, 2014 at 2:16 am

Dear, Mr. Jacques.I’m an I&C engineer working for an EPC contractor. In the site where I worked last year, there was the exactly same problem as described in the figure no.4 of this article.The process was distillate water level and it was controlled by the butterfly type control valve.The process value was hunted like figure no.1 but with bigger magnitude. I think the problem was because of the actuator or positioner. When PID output sent a demand signal to the


valve, the positioner feedback value followed the demand signal after 1~2 seconds.(i,e. there was a deadtime in the actuator.) I couldn’t detect that it was caused by the sticky actuator or positioner problem because the plant was under the commercial operation.(now, I’m working the head office and that problem is still remaining in the site.)Can you imagine the status of the process?? It’s oscillated with really big magnitude.(bigger than figure no.1)The action I did during the commissioning was only adjusting PID value at that time due to the tight commissioning time. After that, only the oscillation magnitude became smaller and the symptom alarming every minute disappeared but still big oscillation has existed.Thank you for your helpful information.

Caster Level Control ImprovementJanuary 31, 2013

Recently, I helped a foundry with a level control problem in their casting process. A batch of metal is melted in a furnace, after which the furnace is slowly tilted to pour the metal into a trough above the caster. The level of molten metal in the caster trough must be kept constant so that the metal flows into the mould at a constant rate. This is done by manipulating the tilt rate of the furnace. The foundry had problems maintaining a constant level in the caster trough. An investigation of the system and equipment revealed the problem.

System Description

The level of the molten metal in the casting trough is measured with a non-contact level sensor and sent to a PID controller. The controller compares the level to its setpoint and manipulates the valve that controls the furnace’s tilt rate (Figure 1). If the level is below setpoint, the PID controller opens the valve more and the furnace tilts faster. Likewise, if the level is above setpoint, the valve position is reduced.

Figure 1. Caster Trough Level Control (click to enlarge)

The Problem

The tuning parameters of any PID controller should be set according to the gain and dynamics of the process it is controlling. A control loop can tolerate small changes in process characteristics, but large changes will cause poor control, unless the control design somehow compensates for this. And herein lay the problem – during the casting process the process gain changed vastly.

At the beginning of the cast, when the molten metal in the furnace has a large surface area, a 1° change in tilt angle will pour a large quantity of metal into the caster trough. At the end of the cast, when the furnace is tilted significantly and the molten metal has a small surface area, a 1° change in tilt angle will pour only a small quantity of metal (Figure 2). This causes the process gain to change by a factor of almost 10 during the casting process.





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Figure 2. Origin of Process Nonlinearity

It is impossible to have good feedback control from a simple control loop if the process gain changes this much. The loop performance will range from being close to instability (when the process gain is high at low tilt angles early in the cast) to being very sluggish (when the process gain is low at high tilt angles late in the cast). This is why the foundry had so much trouble with this control loop.

The Solution

The solution was to either use gain scheduling on the controller or to implement a linearizer between the controller output and the process. Both of these would essentially keep the loop gain constant by either changing the controller gain based on tilt angle, or by compensating for the nonlinear process gain at different tilt angles. To simplify tuning, we chose the linearizer. The linearizer would multiply the controller output by a certain factor that would be changed automatically, based on the furnace’s tilt position (Figure 3).

Figure 3. Level Control Improvement through Linearization

We used trigonometry to calculate the appropriate multiplier for different tilt positions and implemented this into a function generator block in the control system. After this the loop was linear and the control performance vastly improved.

When tuning control loops, it is always important to understand the process and its characteristics, and how these characteristics might change in relation to the process conditions. A process control practitioner should always look for the true reason of poor control. In many cases this goes far beyond controller tuning.

Find out more about process nonlinearity, gain scheduling, controller tuning, and much more in my book Process Control for Practitioners.

Stay tuned!

Control Loop Performance MonitoringAugust 8, 2010

Control loop performance directly affects the operability and profitability of industrial plants. Considering the importance of control loops, one would expect that they always perform at their peak, but this is not the case. In fact, several studies have shown that roughly one third of industrial control loops perform poorly.


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Poorly performing control loops can make a plant difficult to operate and may have several costly side-effects, including:

Reduced production rate

Increased emissions

Lower efficiency

Plant trips following process upsets

Poor product quality

Slower startup and transition times

More off-spec product or rework

Premature equipment wear

For these reasons, control loop performance should always be kept at the highest possible level. This is achieved through continuously monitoring loop performance and taking the appropriate corrective actions when sub-optimal performance is detected.

Loop Performance Monitoring

To effectively manage, improve, or sustain control loop performance, it is important to monitor how well loops perform. Loop performance monitoring can provide valuable feedback on the success of control optimization projects; it helps maintaining a high standard of loop performance in the long run; and it can be used to pinpoint offending control loops for corrective action.

Loop Performance Assessment

Loop performance should be evaluated from various perspectives. A control loop needs to be in its correct mode (mostly auto), stable and responsive, and must reduce process variability. Loop performance can be calculated in terms of these perspectives and expressed as a numerical value, or metric. The following metrics are essential for assessing the performance of the control loop:

Percentage of time the controller is not in its correct mode

Percentage of time the controller output is at its limits

Standard deviation in error

Tendency of loop to oscillate

Controller responsiveness

Many other metrics can provide useful additional information on the performance of the control loop, control valve, and measurement device, for example:

Process variable noise

Cumulative control valve travel per day (can be used for predictive maintenance)

Number of direction changes in control valve travel per day

Mean value of controller output (can be used to indicate oversized and undersized valves or

incorrectly ranged transmitters)

Number of times the operator changed controller mode and/or output

Number of tuning constant changes on the controller

In most cases it is sufficient to calculate loop performance metrics daily. These metrics should be averaged over a period of a week to obtain KPIs for average loop performance over the week.

Some metrics can be easily computed in the process historian, while others are best done by control loop performance monitoring software applications. The monitoring process should run autonomously and automatically by using control loop performance monitoring software, or by writing a custom application in the process historian (process information management system).

Overall Loop Health

Each metric can be compared to a threshold for proper loop performance. If one or more metrics exceed their threshold, the loop should be flagged as having poor performance and maintenance or engineering staff should attend to the problem.

Practical Matter

It is important to consider the operational state of the plant when evaluating loop performance. For example when a plant has been shut down, many loops will be in manual control mode and most of the remaining controllers will have their outputs saturated at 0 or 100 percent. These control loops should not be flagged as problem loops while the plant remains shut down.

Loop Monitoring Software

Several control performance monitoring software packages are available from many vendors including ABB, AspenTech, Control Arts, ControlSoft, Control Station, Emerson, ExperTune, Honeywell / Matrikon, PAS, and RoviSys. These packages help to identify problem loops which can then be addressed to minimize the impact on production.

Summary

Good control loop performance is essential for running a process economically. Because many control loops have never been tuned properly, while the performance of others has decreased over time, control loop monitoring has become an important function at most industry-leading and many other plants.

Monitoring the performance of control loops is not difficult. Basic algorithms for assessing loop performance can be programmed in a process historian, or full-featured software can be acquired to simplify the task.

For more information, or to get a complete assessment of the performance of your control loops, or for training on this topic and others, please contact OptiControls.


Control Valve ProblemsFebruary 22, 2010

Control valve

Control valve problems can severely affect control loop performance and, unless eliminated, they can make controller tuning a challenging (sometimes impossible) task. Some problems are quite obvious to the trained eye and can easily be detected by loop performance assessment software. Others can be more difficult to detect without running specific tests. When doing on-site services, I always make sure to watch out and/or test for valve problems.

Four problems with control valves are found at a high frequency in poorly performing control loops. These are:- Dead band- Stiction- Positioner overshoot- Incorrect valve sizing- Nonlinear flow characteristic

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Let’s take a closer look at each of these problems.

Dead bandA valve with dead band acts like there is some backlash between the controller output and the actual valve position. Every time the controller output changes direction, the dead band has to be traversed before the valve physically starts moving. Although dead band may be caused by mechanical backlash (looseness or play in mechanical linkages), it can also be caused by excessive friction in the valve, an undersized actuator, or a defective positioner.

Many people use the term Hysteresis instead of dead band (I used to be one of them). But theISA and Wikipedia define hysteresis as something else. The ISA clearly calls the mechanical backlash phenomenon in control valves ”dead band”.

A control valve with dead band will cause oscillations in a level loop under PI or PID control if the controller directly drives the control valve (non-cascade). A control valve with dead band can also cause oscillations after a set point change in control loops on self-regulating processes – especially if the integral action of the controller is a little excessive.

StictionAnother very common problem found in control loops is stiction. This is short for Static Friction, and means that the valve internals are sticky.

If a valve with stiction stops moving, it tends to stick in that position. Then additional force is required to overcome the stiction. The controller continues to change its output while the valve continues to stick in position. Additional pressure mounts in the actuator. If enough pressure builds up to overcome the static friction, the valve breaks free. The valve movement quickly absorbs the excess in pressure, and often the valve overshoots its target position. After this, the valve movement stops and the valve sticks in the new position.

Frequently, this overshoot in valve position causes the process to overshoot its set point. Then the valve sticks at the new position, the controller output reverses direction and the whole process repeats in the opposite direction. This causes an oscillation, called a stick-slip cycle. If loop oscillations are caused by stiction, the controller output’s cycle often resembles a saw-tooth wave, while the process variable may look like a square wave or an irregular sine wave.

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Stiction might be caused by an over-tight valve stem seal, by sticky valve internals, by an undersized actuator, or a sticky positioner.

Positioner OvershootOne control valve problem that is more common now than a decade ago, is that of positioner overshoot. Positioners are fast feedback controllers that measure the valve stem position and manipulate the valve actuator until the desired valve position is achieved. Most positioners can be tuned. Some are tuned too aggressively for the valve they are controlling. This causes the valve to overshoot its target position after a change in controller output. Sometimes the positioner is simply defective in a way that causes overshoot. If the process controller is also tuned aggressively, the combination with positioner overshoot can cause severe oscillations in the control loop.

Valve SizingThe fourth common problem with control valves are oversized valves. Valves should be sized so that full flow is obtained at about 70%-90% of travel, depending on the valve characteristic curve and the service conditions. In most cases, however, control valves are sized too large for the flow rates they need to control. This leads to the valve operating at small openings even at full flow conditions. A small changes in valve position has a large effect on flow. This leads to poor control performance because any valve positioning errors, like stiction and dead band, are greatly amplified by the oversized valve.

NonlinearityA valve with a nonlinear flow characteristic can also lead to tuning problems. A control valve’s flow characteristic is the relationship between the valve position and the flow rate through the valve under normal service conditions. Ideally the flow characteristic should be linear. With a nonlinear characteristic, one can have optimal controller response only at one operating point. The loop could become quite unstable or sluggish as the valve position moves away from this operating point.

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ConclusionBefore attempting to tune a control loop, check the valve for dead band, stiction and nonlinearity and have all problems attended to. This could save hours of effort tuning a loop in which the control valve is actually the item needing attention.



2 Responses to “Control Valve Problems” mandar:

July 30, 2011 at 9:47 am

Hi, what will happen if we u 4 solenoid valve,4 separate regulators with range 02,0.4,0.6 and 0.8 and 1kg and 4 controller input instead of 1 positioner to change position of valves.

Jacques :

July 30, 2011 at 10:40 am

With the solenoid setup you describe, the system will come close to set point, but at minimum the 0.2 kg solenoid will keep on opening and closing, causing an oscillation around the set point.- If this is a problem, you can implement a dead band (slightly larger than 0.2 kg) in the control logic. The system may not be on set point, but it will not oscillate.- If you need to run the system at set point with no oscillations, you should use a control valve with an actuator (not a solenoid) so the contoller can change the valve position by tiny fractions required to keep the process variable to set point.Good luck!Jacques

Diagnosing and Solving Control ProblemsApril 30, 2011

While many control loops are easy to tune and present almost no control problems, a few control loops can be very problematic and never seem to control right. Control practitioners can spend many hours or even days trying to improve the performance of these challenging control loops, but the results often remain unsatisfactory. This article presents strategies for diagnosing control problems and improving the performance of challenging control loops.

Symptoms of Poor Loop PerformanceAlthough poor control performance come in many forms, it can be grouped into three categories:

Oscillations and instability – the loop tends to cycle around its set point.

Large deviations from set point – the loop struggles to remain at set point and the process

variable is frequently pushed away from set point.

Sluggish performance – the loop takes too long to get to its set point after a disturbance or set

point change.

A Control Loop with Several Problems

I’ve seen many cases where attempts to address poor performance were limited to controller tuning, because the person attending to the problem did not know of all the other causes of poor performance. To properly address and improve control loop performance, it is necessary to establish what the real cause of the poor performance is, and then to take the appropriate corrective action.

Fault DiagnosisTo guide your diagnosis efforts, a fault diagnosis tree is provided below. The first level of diagnosis is the three symptoms of poor control listed above. Depending on which of these symptoms your control loop displays, you can find the possible causes below each symptom. These are described in more depth throughout this article.

Diagnosing Control Problems

1. OscillationsOscillations can originate from within the control loop or be caused by external factors. To find out which is the case, place the controller in manual and see if the oscillation stops. If it does, the oscillation is generated from within the loop.

Oscillations Stopping when Controller is Placed in Manual

Internal OscillationsOscillations generated internally can be caused by faulty equipment or by tuning. Check first for faulty equipment, because you can spend a long time trying to tune a loop if the real cause of poor performance is the control valve.

The most common control valve problems causing oscillations are:

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Control valve stiction. Do a stiction test with the controller in manual to determine if this is the

case.

Positioner overshoot. Do step tests of various sizes and be on the lookout for signs of overshoot

in the process variable.

Both of these control valve problems and cannot be fixed by tuning the process controller. The valve needs maintenance or the positioner needs tuning.

TuningA loop that is tuned too aggressively (overly fast response) can quickly develop oscillations. Do step tests on the process and determine the dominant process characteristics (gain, dead time, lag). Do more than one step test (try to do four at least) in different directions. Then use tuning rules to calculate new controller settings. If you are using rules designed to producequarter-amplitude damping, use only half of the recommended controller gain. If you have tuning software, then use it to analyze the step-test data and calculate new controller settings.

Nonlinear valve CharacteristicMany control valves control flow differently, depending on how far they are open. The valve is said to have a nonlinear installed characteristic. If tuning is done at the one end, the settings might not work at the other end, and could cause oscillations or sluggish behavior. If this is the case, a function generator (X-Y curve) can be placed in the path of the controller output to cancel out the control valve nonlinearity.

Nonlinear ProcessSome processes react differently based on operating point, production rate, or the product being made. If these differences are large the loop can begin oscillating or become sluggish. Then different tuning settings are required for the various operating conditions. This is called gain scheduling.

External OscillationsExternally sourced oscillations can be caused by interactions between loops with the same dynamics or simply by another loop in the process oscillating and causing several other loops to oscillate with it.

Coupled InteractionInteractions between loops with the same dynamics can cause the two loops to “fight” each other. A simple example of this is if two valves control the flow and pressure in the same pipe. Because the dynamics of liquid pressure control loops and flow control loops are similar, the two controllers might be tuned very similarly, causing the hunting between the two loops. To solve this, the most important loop needs to be tuned for fast response, and the loop of secondary importance needs to be tuned significantly slower (three times or longer settling time).

Dynamically Coupled Control Loops

Process InteractionOne loop in the process could be oscillating, causing several other loops in the same process to oscillate with it. Use a process and instrumentation diagram (P&ID) to locate possible offenders. Then use historical process trends of these other loops to find the oscillating loop. Several software vendors

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like ExperTune, PAS, and Matrikon/Honeywell have products to help with locating the offending loop in a plant-wide oscillation scenario.

2. SluggishnessThe next category of poor control loop performance is sluggishness. Sluggish control loop response can be caused by equipment problems or by poor tuning.

Control Valve Dead BandDead band (also called hysteresis), can cause a loop to exhibit sluggish behavior. Every time the process variable undergoes a disturbance in a different direction from the previous disturbance, the controller output has to traverse the dead band before the valve begins moving. Dead band can be detected very reliably through simple process tests. It is a mechanical problem and cannot be addressed with tuning.

Other Equipment ProblemsA control loop may also appear to have sluggish response if the controller output becomes saturated at its upper or lower limit. Similarly, if the process variable runs into limits, the control action effectively ends. Also, if the controller output has a rate-of-change limit, it may cause sluggish response, regardless of how well the controller is tuned.

TuningComments made earlier about tuning apply here too. Furthermore, realize that loops have internal “speed limits” depending mostly on the length of the dead time in the process. It will take a well-tuned loop three to four times the dead time to get back to its set point after a disturbance or set point change. If disturbances cause large deviations from set point, and tuning is unable to correct it fast enough, see the next section.

Upper Limit to Loop Speed – any faster tuning will cause larger oscillations

3. DisturbancesThe third category of poor loop performance is that of disturbances pushing the process variable away from its set point. Disturbances are frequently the nemesis of good loop performance. As described above, feedback control is limited in how fast it can eliminate the effects of a disturbance and bring the process back to set point. Two classes of disturbances exist, depending on how they enter the loop.

Control-Flow DisturbancesControl-flow disturbances affect the loop by changing the flow rate through the final control element. For example, if steam is used to heat the process flowing through a heat exchanger, and the pressure of the steam decreases, the steam flow rate will be affected and this will disturb the outlet temperature.

Cascade control can be used very effectively to virtually eliminate the effects of a control-flow disturbance. The outer loop controls the main process variable (temperature in this case) by changing

http://blog.opticontrols.com/wp-content/uploads/2011/04/speedlimit.png

the set point for flow to an inner loop. The inner loop measures and controls the actual flow rate and immediately corrects any deviations from set point.

Cascade Control for Handling Control-Flow Disturbances

Process DisturbancesIn contrast to control-flow disturbances, all other disturbances to the process that affect the process variable are simply called process disturbances. If a process disturbance is measurable, and its effect on the process variable is known, feedforward control can be used to vastly reduce its impact.

Feedforward Control for Handling Process Disturbances


Posted in 6. Loop Performance, Problems, and Diagnostics, 9. Tips and Work-Process

6 Responses to “Diagnosing and Solving Control Problems”

Jam:

January 28, 2013 at 3:52 pm

Hello,

I have a flow control valve that operates OK in automatic. This valve only really operates between 25-40%. However when the valve tries to maintain 25%, it keeps osciallating with the around the setpoint. What could be causing this? Here are my theories:

1. Valve may have a non-linear characteristic and that may need to be placed on the output of the PID – I have yet to confirm this2. Could the valve be oversized?

Are these correct and are there other factors that could be attributing to this?

Thanks

http://blog.opticontrols.com/wp-content/uploads/2011/04/cascade.png

http://blog.opticontrols.com/wp-content/uploads/2011/04/feedforward.png

Jacques :


Jam,1. It could be that the valve has a quick-opening (nonlinear) type of flow characteristic. Is it a butterfly valve? If so, see this article: It could also be that the valve is sticky around 25% – see this article: 2. It seems that your valve is a bit oversized – control valves should ideally operate around 75% – 85% open at design flow rates.- Jacques

William Love:


In an article or post that I can’t find right now I recalled the author said you can prevent excessive valve wear by not letting the valve move unless the PID output changed by more than some amount.This idea was greeted with derision in a group discussion, so I’m trying to figure out whether the idea has any merit.

Jacques :


As with many things in process control – it depends. If you have a noisy measurement signal, and a high-gain controller, your controller output will likely move around much more than you like and wear out the valve prematurely. You have a few options, depending on your controller’s features.1. You can filter the process variable (my preferred option), but realize that this adds additional dynamics to the loop that requires slower tuning which slows down the loop response. If your process is already a slow-responding process, the additional dynamics may go virtually unnoticed, making it a very good solution. However, if you have very low-frequency noise, you need a very long filter time-constant, which can make this an infeasible solution. (Your filter time constant should be substantially shorter than your process dead time and lag to achieve fast loop response).2. You can also set a deadband around the process variable or controller output, which brings me to your question. If apply a deadband, the controller will move the control valve only when the limit of the deadband has been reached. The wider the dead band, the less often your controller will move the valve (and make smaller movements). If you set dead band larger than the noise, the controller does not respond until there has been a significant change in the process. This effectively adds pseudo-deadtime to the loop, making the control loop behave very sluggishly. So,, for fast loop performance, just as the lag in a measurement filter should be set much shorter than your process dynamics, you should ensure that the additional deadtime added by a deadband is also much shorter than your process dynamics.3. You can also look at using a different measurement technology, if the problem is measurement noise.Also, make sure you are not using derivative control on a noisy measurement signal, and if you have to use it, consider lengthening the controller scan time to reduce the gradients the derivative term sees.

William Love:


Just to clarify, the method I’m describing involves ignoring a change in the PID output (CV)unless it is more than some amount. If the CV = 45.0 %, I would hold that number in a register and keep sending that to the valve. I’d not change that signal going to the valve until say CV 45.5% (my deadband is 0.5%). So if I saw the PID output reach 45.6%, I’d update the hold register and start sending that to the valve. Then, until CV 46.1% I would keep sending the hold register value 45.6% to the valve. Is this what you thought I was saying?

One person opined this is equivalent to putting a deadband on the error between PV and SP (which in Rockwell is implemented with a parameter called “CV Zero Crossing Deadband”.) But I’m not so sure.

Is my proposal to keep the valve at the hold value until the CV changes by more than a deadband have a history in the field. I think I got the idea from a post by Greg McMillan and thought it sounded good. To your knowledge has this been done?

Jacques :


William, thanks for clarifying what you mean.First, the 0.5% “deadband” seems far too small for reducing excessive valve wear.Second, the method you propose artificially introduces the equivalent of stiction, which is very bad for stability.I don’t know if it has been done, but I will advise against it.

Q&A on Loop PerformanceFebruary 12, 2010

I was recently asked for my input on control loop performance by means of a few questions. Here is a somewhat modified version of the questions and answers.

Q: What is the percentage of control loops that operate properly in the average process plant?

A: Two papers dating back to 1993, authored individually by Ender [1] and Bialkowski [2], claimed that roughly 30% of loops were left in manual, 30% actually increased variability, and that only 20% of loops performed well. In 2001 Desborough and Miller [3, 4] confirmed that control loop performance was on average still the same. In 2008, VanDoren [5] also reported a very similar bleak state of loop performance.Our experience from loop performance audits supports these findings, although the distribution between loops in manual, those with poor performance, and those with good performance, can vary significantly between different sites and process types.

Q: When does a loop operate properly?

A: Proper operation can be subjective, and it is easier to define improper operation. Loops that increase variability when running in auto compared to manual control would not be considered as operating properly. Nor would controllers reacting mainly to noise and high-frequency disturbances, or those causing oscillations in the loop. Controllers with outputs running into limits, and controllers tuned too sluggishly are also not operating properly. So, for a loop to be “operating properly,” it needs to reduce variability, and do so in a repeatable fashion, consistent with its function in the larger process.

Q: What can cause control loops to operate poorly?

A: Improper operation can be caused by incorrect controller tuning settings, incorrect process variable (PV) filter settings, faulty or incorrectly positioned instrumentation, or mechanically defective, non-linear, oversized, or undersized final control elements. It can also be caused by not making use of an appropriate control strategy (like feedforward or gain scheduling), or improper design of such a control strategy (like dividing one flow by another for doing ratio control).

Q: What are the consequences poor loop performance?

A: A poorly performing control loop can decrease product quality, limit maximum production rates, extend process start-up and transition times, increase the likelihood of unplanned process shut-downs, increase maintenance costs, consume more energy, and make the process difficult to operate.

Q How should control loop problems be resolved?

A: The first step is to find the problem loops. Some problematic control loops are obvious due to their impacts on operations, while others might be less obvious or remain hidden to operators and process engineers. A comprehensive list of control problems can be obtained most effectively by using software to assess the performance of all control loops. The second step is to distill the performance survey down to a list of “bad actors” by looking both at the performance and the relative importance of each control loop. Bad actors would be loops performing poorly and also significantly impact the process. Loop assessment software can do this automatically if they are configured properly. The third step is to


diagnose the root cause of the problems. Loop assessment software is helpful in doing this, but engineering and process knowledge is also required. The final step is fixing the problem according to the diagnosis, for example by tuning a controller, fixing a control valve, or implementing the appropriate control strategy.

Q: Why are some control loop problems so persistent?

A: Control problems persist mostly because the root causes of the problems are not being addressed. For example: An engineer may spend hours tuning and re-tuning a control loop, but his efforts are futile if the problem actually is a sticky control valve requiring maintenance, or a nonlinear process requiring gain scheduling.

Q: What is the most important factor when optimizing control loops?

A: The single biggest factor in loop optimization is the skill level of the person doing the optimization work. Software has come a long way to simplify loop performance analysis and tuning, but the software is just a tool, and the validation of its diagnoses and execution of corrective actions need to be done by an adequately skilled human. Skills can either be hired, or learned. In both cases OptiControls can help with our services and training.


References:[1] D.B. Ender, Process Control Performance: Not as Good as You Think, Control Engineering 40 (10), 1993, 173 – 186.[2] W.L. Bialkowski, Dreams Versus Reality: A View From Both Sides of the Gap, Pulp & Paper Canada, 1993, 94 (11), 19 – 27.[3] L. Desborough and R. Miller, Increasing Customer Value of Industrial Control Performance Monitoring: Honeywell’s Experience, Proc. 6th Int. Conf. on Chemical Process Control (CPC VI), Arizona, USA, 2001, 172–192.[4] L. Desborough, P. Nordh, R. Miller, Control System – Process out of Control, Industrial Computing, August 2001, 52 – 55.[5] V. VanDoren, Advances in Control Loop Optimization, Control Engineering, March 2008, 48 – 52.

Valve Diagnostics on a Level LoopApril 10, 2012

Determining the condition of the control valve on a level loop can be challenging, but it is an important aspect of successful tuning. Control loop performance can be greatly affected bycontrol valve dead band, stiction, and nonlinear flow curve, and this is no different on a level control loop. If the level controller directly drives the control valve, both dead band and stiction will cause a level control loop to oscillate continuously.

A level control loop oscillating because of control valve dead band.

Doing valve diagnostic tests is easy on a self-regulating loop, but not so on an integrating loop, like liquid level. On a level loop the process variable itself does not in any way reflect the actual control valve









http://www.opticontrols.com/services


http://blog.opticontrols.com/wp-content/uploads/2012/04/oscillatinglevelloop.png

position (or the flow into/out of the vessel for that matter). So how then does one determine the condition of a control valve in a level loop?

The answer is to analyze the rate of change of the level at different control valve positions. For example, if you want to check for control valve dead band, you would put the controller in manual, make two controller output steps (typically 5% in size) in one direction, and make another step in the opposite direction – just like on a flow control loop, for example. However, instead of using the level measurement directly, you would analyze the rate of change of the measurement.

A dead-band test on a level loop. Normally the controller output steps would be equal in size, but very often smaller steps are required to keep the level within limits.

This takes some planning because the level always needs to be kept within a safe operating range and you need to allow enough time between controller output steps to obtain steady ramps in level that are long enough that you can take measurements from them. I often have to adapt my test plan to keep the process safe but still obtain the data I need for analysis. Don’t worry if your steps are not all the same size, the calculation below will compensate for this.

Once you have collected your test data, return command of the controller back to the operator to be placed in auto and/or monitored. Import the controller output (CO) and process variable (PV) data into Microsoft Excel or your spreadsheet of choice.

Add a new column of calculations that take the difference (dPV) between two successive PV samples, e.g.: C2 = B3 – B2, assuming your PV data is in Column B and the dPV calculations are in Column C.

You will likely find that the new dPV data is very noisy. In that case you should include an averaging filter in your calculation like this:

Calculating a filtered rate of change.

Once you’re done you can plot the data and take measurements from the plot or the data. Use the average of the dPV values as shown below.

http://blog.opticontrols.com/wp-content/uploads/2012/04/levelloopdeadbandtest.png

http://blog.opticontrols.com/wp-content/uploads/2012/04/rateofchangecalcs.png

Analyzing dead band on a level loop.

You can then calculate the dead band in the valve, as a percentage of its full travel (0 – 100% open):

% Valve Dead Band = (CO3 – CO2) – (dPV3 – dPV2) / (dPV2 – dPV1) x (CO2 – CO1)

A stiction analysis can be done in the same way, but you will make 5 to 10 small changes in controller output (typically 0.5% in size). Remember to leave enough time between successive steps to obtain a steady gradient. Make sure that you take up any dead band first by preceding the small steps with one large dead-band-eliminating step in the same direction as you are planning for the small stiction steps.

Since a level loops will oscillate if its output drives a valve having dead band or stiction, you want these to be as low as possible. Installing a flow controller as an inner loop to the level controller in a cascade control arrangement will go a long way to reduce the effects of valve issues on a level control loop.

Stay Tuned!

Jacques Smuts, author of the book Process Control for Practitioners

7. Control Strategies o A Tutorial on Cascade Control o A Tutorial on Feedforward Control o Butterfly Valves and Control Performance o Caster Level Control Improvement o Control Valve Linearization o Drum Level Control o Improving pH Control o Ratio Control o Steam Temperature Control

A Tutorial on Cascade ControlMarch 15, 2010

What is Cascade Control?In single-loop control, the controller’s set point is set by an operator, and its output drives a final control element. For example: a level controller driving a control valve to keep the level at its set point.




http://blog.opticontrols.com/wp-content/uploads/2012/04/levelloopdeadbandanalysis.png

Single Loop Control

In a cascade control arrangement, there are two (or more) controllers of which one controller’s output drives the set point of another controller. For example: a level controller driving the set point of a flow controller to keep the level at its set point. The flow controller, in turn, drives a control valve to match the flow with the set point the level controller is requesting.

Cascade Control

The controller driving the set point (the level controller in the example above) is called the primary, outer, or master controller. The controller receiving the set point (flow controller in the example) is called the secondary, inner or slave controller.

What are the Advantages of Cascade Control?There are several advantages of cascade control, and most of them boil down to isolating a slow control loop from nonlinearities in the final control element. In the example above the relatively slow level control loop is isolated from any control valve problems by having the fast flow control loop deal with these problems.

Imagine that the control valve has a stiction problem (see blog on valve problems.) Without the flow control loop, the level control loop (driving the sticky valve) will continuously oscillate in a stick-slip cycle with a long (slow) period, which will quite likely affect the downstream process. With the fast flow control loop in place, the sticky control valve will cause it to oscillate, but at a much shorter (faster) period due to the inherent fast dynamic behavior of a well-tuned flow loop. It is likely that the fast oscillations will be attenuated by the downstream process without having much of an adverse effect.

Or imagine that the control valve has a nonlinear flow characteristic (see blog on valve problems.) This requires that the control loop driving it be detuned to maintain stability throughout the possible range of flow rates. (Of course there are better ways to deal with nonlinearities, but that is the topic of another blog.) If the level controller directly drives the valve, it must be detuned to maintain stability – possibly resulting in very poor level control. In a cascade control arrangement with a flow control loop driving the valve, the flow loop will be detuned to maintain stability. This will result in relatively poor flow control, but because the flow loop is dynamically so much faster than the level loop, the level control loop is hardly affected.

When Should Cascade Control be Used?Cascade control should always be used if you have a process with relatively slow dynamics (like level, temperature, composition, humidity) and a liquid or gas flow, or some other relatively-fast process, has to be manipulated to control the slow process. For example: changing cooling water flow rate to control condenser pressure (vacuum), or changing steam flow rate to control heat exchanger outlet temperature. In both cases, flow control loops should be used as inner loops in cascade arrangements.

http://blog.opticontrols.com/wp-content/uploads/2010/03/Single-Loop-Control1.png

http://blog.opticontrols.com/wp-content/uploads/2010/03/Cascade-Control1.png

Does Cascade Control Have any Disadvantages?Cascade control has three disadvantages. One, it requires an additional measurement (usually flow rate) to work. Two, there is an additional controller that has to be tuned. And three, the control strategy is more complex – for engineers and operators alike. These disadvantages have to be weighed up against the benefits of the expected improvement in control to decide if cascade control should be implemented.

When Should Cascade Control Not be Used?Cascade control is beneficial only if the dynamics of the inner loop are fast compared to those of the outer loop. Cascade control should generally not be used if the inner loop is not at least three times faster than the outer loop, because the improved performance may not justify the added complexity.

In addition to the diminished benefits of cascade control when the inner loop is not significantly faster than the outer loop, there is also a risk of interaction between the two loops that could result in instability – especially if the inner loop is tuned very aggressively.

How Should Cascade Controls be Tuned?A cascade arrangement should be tuned starting with the innermost loop. Once that one is tuned, it is placed in cascade control, or external set point mode, and then the loop driving its set point is tuned. Do not use quarter-amplitude-damping tuning rules (such as the unmodified Ziegler-Nichols and Cohen-Coon rules) to tune control loops in a cascade structure because it can cause instability if the process dynamics of the inner and outer loops are similar.


Posted in 7. Control Strategies

11 Responses to “A Tutorial on Cascade Control” lndas:

October 18, 2011 at 10:32 am

Excellent treatment on the subject. I could get an idea about cascade control as practiced in industries.Thanks for the article.

alex:


really very useful. thank you.

DF:

August 9, 2012 at 7:25 am

Excellent overview, I’ve liked the site so much I’ve bought the book Thanks!

Jan:


I like your articles. Simple, short and useful. Thank you!

Is there an article on detuning controllers? I’ve hear the term a lot but it is not completely clear to me what it actually means and when it should be done (or not)

Jacques :


Jan, I have made a note to write my next article about detuning controllers. Thanks for the suggestion.

Shweta Garg:


A simple and clear explanation with all the necessary and important points mentioned.Thank you Sir for such an effort u made for othersLooking for new articles!

Jeff:

October 11, 2012 at 10:58 pm

Thanks for such a wonderful summary of cascade control!

frank:


I have a cascade loop that seems to favor the low side of my setpoint. The process will edge up slowly and achieve a small but acceptable overshoot and then the output will plummet down causing a large overshoot, only to have the process repeat itself again. It does not appear to be an oscillatory process as it controls slowly under the setpoint but on the other hand it reacts extremely fast when the pv is above the setpoint. It appears that the master controller is the culprit in my situation. I fear that if I lower my gain any more, it will take the process too long to reach its setpoint from below. Have any ideas on why this might be occuring/ how to fix?

Thanks,Frank

Jacques :

January 31, 2013 at 9:02 am

Frank, from your description it seems that you might have too much gain and too little integral action in your controller. I often see this on flow loops that have been tuned using trial and error, but it occurs on other loops too. Please take a look at this article for a good method to tune your controller: http://blog.opticontrols.com/archives/383- Jacques

Jarret:


Hi, I just wanted to say thank you for putting this stuff in plain English. I’m training for a career in process operations and these blogs are excellent. Thank you sir.

Rocketman:

July 11, 2013 at 10:49 am

The course I had in college left me scratching my head with how to implement it; thanks for bring reality into the subject.

A Tutorial on Feedforward ControlJanuary 17, 2011

Feedforward control can be used very successfully to improve a control loop’s response to disturbances. Feedforward control reacts the moment a disturbance occurs, without having to wait for a deviation in process variable. If any process control loop is subject to large, measurable disturbances, it can benefit greatly from feedforward control.

Feedforward control reducing effects of a disturbance

To understand feedforward control, let’s first review feedback control.

Feedback Control

Feedback control is typically done with PID (proportional + integral + derivative) controllers. The process variable of interest is measured and the controller’s output is calculated based on the process variable and its set point. Although external disturbances often affect the process variable, they are not used directly for control. Instead, if a disturbance affects the process variable, the control action is based on the process variable and not the disturbance.

As an example, the outlet temperature of a heat exchanger can be measured and used for feedback control. The feedback controller will manipulate the steam flow to the heat exchanger and keep the outlet temperature as close to set point as possible.

Feedback Control

Feedback Control and Disturbances

Many process control loops are affected by large disturbances. Feedback control can act only on the result of a disturbance, which means feedback control cannot do anything until the process variable has been affected by the disturbance.

In the example of the heat exchanger above, changes in process flow rate will be a major source of disturbances to the outlet temperature. If the process flow rate through the heater is increased, the original steam flow rate will not be enough to heat up the increased amount of process liquid and the outlet temperature will decrease. Feedback control will eventually increase the steam flow rate and bring the outlet temperature back to its set point, but not until there has been a significant deviation in temperature.

Feedforward Control

In contrast to feedback control, feedforward control acts the moment a disturbance occurs, without having to wait for a deviation in process variable. This enables a feedforward controller to quickly and

http://blog.opticontrols.com/wp-content/uploads/2011/01/FF-Effects.png

http://blog.opticontrols.com/wp-content/uploads/2011/01/Feedback-Control1.png

directly cancel out the effect of a disturbance. To do this, a feedforward controller produces its control action based on a measurement of the disturbance.

When used, feedforward control is almost always implemented as an add-on to feedback control. The feedforward controller takes care of the major disturbance, and the feedback controller takes care of everything else that might cause the process variable to deviate from its set point.

Feedforward + Feedback Control

In our example of the heat exchanger, in which the major disturbances come from changes in process flow rate, the latter can be measured and used for adjusting the steam flow rate proportionally. This is done by the feedforward controller.

Implementing Feedforward Control

Many PID controllers have an external connection for adding an input from a feedforward controller. Otherwise the output of the feedforward controller can be externally added to the output of the feedback controller. Review your controller documentation and take special care with scaling the feedforward signal. Many PID controllers expect the feedforward signal to be scaled between -100% and +100%.

Feedforward and feedback control is often combined with cascade control, to ensure that their control actions manipulate the physical process linearly, eliminating control valve nonlinearities and mechanical problems.

If several major disturbances exist, a feedforward controller can be implemented for each of them. The outputs of all the feedforward controllers can be added together to produce one final feedforward signal. Only consider disturbances that meet these criteria:

Measurable – if it can’t be measured you can’t control from it

Predictable effect on the process variable – most disturbances will fall in this class

Occur so rapidly that the feedback control cannot deal with them as they happen.

Feedforward Controller Design and Tuning

A feedforward controller essentially consists of a lead-lag function with an adjustable gain. A dead-time function (Ttd) can be added if the effect of the disturbance has a long time delay while the control action is much more immediate.

Feedforward controller design

The feedforward gain (Kff) is set to obtain the required control action for a given disturbance. For example, it controls the ratio of steam flow to process flow in the example used previously. The lead and lag time constants are set to get the right timing for the control action. The feedforward’s lead (Tld) will speed up control action should be set equal to the process lag between the controller output and the process variable. The feedforward’s lag (Tlg) will slow down the control action and should be set equal to the process lag between the disturbance and the process variable.

You can use an alternative design for a feedforward controller that makes tuning easy. This is to simply use a function generator as the feedforward controller. Before implementing the feedforward controller,

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http://blog.opticontrols.com/wp-content/uploads/2011/01/FF-Design.png

take note of the feedback controller’s output and the disturbance measurement at various levels of the disturbance. Use this relationship to set up the curve in the function generator.

Simplified feedforward controller design

For the heat exchanger example, we should tabulate the temperature controller’s output and process flow rates under various steady-state production rates. Then we program a curve in the function generator to produce the desired controller output at each of the process flow rates we measured.

Let me know if you have a control problem you need help with, or if you are interested in process control training (contact info).



6 Responses to “A Tutorial on Feedforward Control” Noel Guiriba:


Hi. I’m dealing with a process that involves a heated bath where product is dipped for about 100 minutes. We control the temperature of the bath to about 190°F. When product is initially immersed in the bath, the bath temperature drops 3F° for the first 15 minutes and gradually rises to the set temperature, about 45 minutes after the product was initially loaded. When the set temperature is reached, temperature is kept at +/-0.1°F of setpoint. We currently use a PID temperature controller and I think a feedforward controller will help us a lot. I was thinking of a function generator that is triggered by a signal of the product coming into the bath. I’d appreciate any comment or suggestions you may have. Thanks!

Jacques :


Noel, it sounds like your process might benefit from using feedforward, however use this only if the feedback controller has been tuned optimally and the temperature still deviates excessively. I don’t know the size of your process, but it sounds like the loop is responding very slow. See this link for a recommended tuning method:http://blog.opticontrols.com/archives/383If you do end up using a feedforward, I think you should consider using a lead/lag with a dominant lead. It will give you a large initial increase in controller output that will die away over time. Contact me if you need more help with this:http://www.opticontrols.com/contact-us- Jacques

dhruv prajapati:


sir i wanted to know that how the feedforward and cascade control scheme can be combined…pls give some idea on it. thank you.

http://blog.opticontrols.com/wp-content/uploads/2011/01/FF-Design-2.png

Jacques :


Dhruv, you can take a look at three-element drum level control at this link:http://blog.opticontrols.com/archives/165. This is feedforward and cascade control combined.

Andrew:

June 10, 2014 at 3:07 am

Hi. I would like to implement feedforward control on boiler outlet steam temperature.We have a base loaded chemical recovery boiler. To manage the variable steam loads in our pulp mill we have a single wood waste boiler who’s boiler master is driven by the main site 650psi header pressure. Our wood waste boiler outlet steam flow is quite variable depending on our users. The steam passes through a primary and secondary superheater. Between the primary and secondary superheaters we add feed water through a de-superheater station to control the secondary superheater outlet temperature. Currently there is only feedback control for this temperature control. Normal operation can have a dead time through the secondary superheater of about 20 to 60 seconds but could be outside this range also. The feedback control struggles to control temperature and is tuned aggressively to compensate for this dead time.

I wish to add feed forward control to this loop. I have no intermediate temperature measurement but we do measure outlet steam flow. I have the following questions and comments regarding the modelling and implementation of feedforward using the outlet steam flow.

1. What is the best way to determine the model of the steam flow influence on outlet steam flow? This is particularly tricky given that the steam demand on the wood waste boiler is so variable.2. Will the feedforward model and therefore the feedforward signal to the outlet steam temperature control become the main control action?3. How accurate does the feedforward model for this application need to be?4. Once the feedforward control is implemented does the feedback control only become a trim for non-measured variations in the process that affect the outlet steam temperature?5. Once feedforward control is implemented how should the tuning parameters for the feedback control be determined?

Please find a link to the P&ID part for this below.https://docs.google.com/file/d/0B3A30WvckCixT0hCOUZ4RFIyV1k/edit?usp=docslist_api

Jacques :

June 29, 2014 at 12:57 pm

Andrew,1. You should plot the steam temperature controller’s output against steam flow rates. If you get a nice line or curve, feedforward will likely work well. If you get a lot of scatter, don’t bother using feedforward. Assuming there is a good correlation, make the fastest possible step change in steam flow with the temperature controller in manual to determine the dynamics (dead time and lag) between changes in steam flow and temperature. You also need to do this for your steam temperature controller. The feedforward should have a lead lag comprising both system’s dynamics. I describe how to do this in detail in my book, Process Control for Practitioners.2. It depends if the line you get in the previous step has a 0,0 origin (when extrapolated). But I doubt that it will.3. The improvement in control is directly proportional to the accuracy of the feedforward. In other words, if your model is only half accurate, you’ll get only half the potential improvement.4. Yes.5. If the feedforward becomes the main control action, you will likely need to back down the temperature controller’s gain. This is best determined by looking for signs of overcorrection during testing with the feedforward in place.




















mohamed elsadig:

May 18, 2013 at 11:11 pm


Jacques :

May 19, 2013 at 7:59 am


H.B.R:

May 27, 2014 at 2:16 am

Dear, Mr. Jacques.I’m an I&C engineer working for an EPC contractor. In the site where I worked last year, there was the exactly same problem as described in the figure no.4 of this article.The process was distillate water level and it was controlled by the butterfly type control valve.The process value was hunted like figure no.1 but with bigger magnitude. I think the problem was because of the actuator or positioner. When PID output sent a demand signal to the valve, the positioner feedback value followed the demand signal after 1~2 seconds.(i,e. there was a deadtime in the actuator.) I couldn’t detect that it was caused by the sticky actuator or positioner problem because the plant was under the commercial operation.(now, I’m working the head office and that problem is still remaining in the site.)Can you imagine the status of the process?? It’s oscillated with really big magnitude.(bigger than figure no.1)The action I did during the commissioning was only adjusting PID value at that time due to the tight commissioning time. After that, only the oscillation magnitude became smaller and the symptom alarming every minute disappeared but still big oscillation has existed.Thank you for your helpful information.



System Description





The Problem





The Solution











Stay tuned!

Jacques SmutsPrincipal ConsultantOptiControls

Control Valve LinearizationNovember 26, 2011

A control valve’s flow characteristic is an X-Y curve that maps the percentage of flow you’ll get for any given valve opening (Figure 1). The design characteristic (also called inherent flow characteristic) of a valve assumes a constant pressure differential across the valve. More relevant to us is the installed characteristic, which is the way the valve operates in the real process. The installed characteristic of a valve can be determined by plotting the measured flow rate at different valve openings. You can do tests on the live process to get this data, or you can get it from the process historian (make sure you use steady-state data).

Figure 1 - A Nonlinear Flow Characteristic

The installed flow characteristic of a control valve directly affects the process gain. It is essential that the installed characteristic is linear (the above plot is a straight line) so that the process gain is constant, regardless of the controller output. If the gradient of the curve varies by more than a factor of two, control loop performance will be noticeably affected. If nothing is done to linearize the valve the controller will have to be detuned to accommodate the maximum process gain. This leads to sluggish control loop response over much of the valve’s operating range.

A nonlinear flow characteristic should be linearized to obtain good control performance throughout the valve’s operating range. This is done with a linearizer (also called a characterizer). The linearizer is a control block, function generator, f(x) curve, or a lookup table, placed between the controller and the valve (Figure 2). Although the linearization can be done in a digital positioner, the DCS/PLC is the best location for it. This allows replacement of the positioner without having to reprogram the linearization curve in the new positioner.


http://blog.opticontrols.com/wp-content/uploads/2011/11/Nonlinear-Characteristic.png

Figure 2 - Linearizing a Nonlinear Valve Characteristic

Linearization is done with an X-Y curve or function generator that is configured to represent the reciprocal (inverse) of the control element’s flow curve (Figure 3).

Figure 3 - How a Linearizer Works

To design the linearizer, you have to first determine the flow characteristic curve of the valve operating in the actual process. For this you should take readings of the flow or process variable (PV) and controller output (CO) under steady-state conditions at various controller output levels. You need a minimum of three (PV, CO) data pairs for this, but four or five would be better for characterizing a nonlinear relationship.

Make sure you span the entire operating range of the controller output, and try to obtain readings spaced equally across the controller output span. You can do process tests to obtain these values, or examine data from your process historian. Then convert the process variable data from engineering units to a percentage of full scale of the measurement.

Sort the data pairs in ascending order, and enter them into a function generator. The PV readings in percent become the X values (input side) and the CO readings become the Y values (output side). Include a (0, 0) point if you don’t already have one in your dataset and be sure to estimate a (100, Y) point also if you don’t have one. Also, if your valve opens as the CO decreases, your Y column will obviously have to reflect this.

For example, you get the following (PV, CO) pairs form historical data: (120, 22); (280, 39); (530, 63). The PV is ranged 0 to 1000 kg/hr. You plot the data and estimate that 1000 kg/hr will occur at about 85%. The characterizer will look like this:

Flow measurement in percent of full scale Controller output readings (in %)These values go on the input-side of the

linearizerThese values go on the output-side of the

linearizer0 (you must have a zero point) 0

12 2228 3953 63

100 (you must have a full-scale point) 85 (this can be an estimation)

After implementing a linearizer in the DCS or PLC, you can test its accuracy by checking whether the controller output and flow measurement are roughly at the same percentage of full scale. For example:

http://blog.opticontrols.com/wp-content/uploads/2011/11/Linearizer-location.png

http://blog.opticontrols.com/wp-content/uploads/2011/11/Linearization.png

20% and 50% controller output should result in roughly 20% and 50% flow rate. You should retune the controller after implementing the linearizer because it likely had changed the process gain.

Although this discussion mentioned only control valves, the same applies to other final control elements, like vanes, dampers, feeders, etc.

Stay tuned!

Jacques SmutsAuthor of the book Process Control for Practitioners

Posted in 5. Control Valves, 7. Control Strategies

3 Responses to “Control Valve Linearization” Jack:

April 29, 2012 at 1:58 pm

We currently have a non-linear characterization on one of our boiler air dampers. I didn’t quite understand the purpose of the characterization until I read this article. It was a good thing I did too, because I almost removed the characterization. Thanks.

siby:

March 8, 2013 at 7:01 am

I have read about some situations where the control valves are deliberately chosen to have non-linear behavior like an equi-percentage characteristic because the process it is controlling is also non-linear. Will introducing a linearizer then adversely affect the loop performance?

Jacques :

March 8, 2013 at 7:19 am

Siby, if the nonlinear flow characteristic of the control valve cancels out the nonlinear characteristic of the process, the combination of the two should be linear and no characterization is required. For example, the steam flow control valve to a heat exchanger is likely better being equal percentage than linear.

Drum Level ControlJuly 3, 2010

A very common control problem, and one used in many examples elsewhere, is that of controlling the level in a boiler drum. Many industrial plants have boilers for generating process steam, and of course boilers are central to thermal power generation.

The boiler drum is where water and steam are separated. Controlling its level is critical – if the level becomes too low, the boiler can run dry resulting in mechanical damage of the drum and boiler piping. If the level becomes too high, water can be carried over into the steam pipework, possibly damaging downstream equipment.

The design of the boiler drum level control strategy is normally described as single-element, two-element, or three-element control. This article explains the three designs.

Single-element Control (Feedback Control)

One or more boiler feedwater pumps push water through one or more feedwater control valves into the boiler drum. The water level in the drum is measured with a pressure and temperature-compensated level transmitter. The drum level controller compares the drum level measurement to the set point and modulates the feedwater control valves to keep the water level in the drum as close to set point as possible. Variable-speed boiler feed pumps are sometimes used to control the level instead of valves.

The simple feedback control design described above is called single-element control, because it uses only a single feedback element for control – the drum level measurement.

Drum Level Controller Tuning

1. Integrating Process

From a controls point-of-view, the boiler drum is an integrating process. This means that any mismatch between inflow (water) and outflow (steam) will cause a continuous change in the drum level.

Integrating loops are difficult to tune, and can easily become unstable if the controller’s integral time is set too short (i.e. high integral gain). The process-imposed requirement for a long integral time makes the loop slow to recover from disturbances to the drum level.

2. Inverse Response

To further complicate matters, the boiler drum level is notorious for its inverse response. If the drum level is low, and more feedwater is added to increase it, the drum level tends to decrease first before increasing. This is because the cooler feedwater causes some of the steam in the evaporator to condense, causing the volume of water/steam to decrease, and hence the drop in drum level.

Conventional feedback control has difficulty in coping with this inverse response. A control loop using high controller gain and derivative action may work well in other level applications, but it will quickly go unstable on a boiler drum level. Stability is best achieved by using a low controller gain, long integral time, and no derivative. However, these settings make the controller’s response very sluggish and not suitable for controlling a process as critical as boiler drum level.

Major Disturbances

Drum level is affected by changes in feedwater and steam flow rate. But because of the very slow response of the feedback control loop, changes in feed flow or steam flow can cause very large deviations in boiler drum level. Single-element drum level control can work well only if the residence time of the drum is very large to accommodate the large deviations, but this is seldom the case – especially in the power industry. For this reason, the control strategy is normally expanded to also include feedwater and steam flow.

Two-element Control (Cascade Control)

Many boilers have two or three feed pumps that will be switched on or off depending on boiler load. If a feed pump is started up or shut down, the total feedwater flow rate changes. This causes a deviation in drum level, upon which the drum level controller will act and change the feedwater control valve position to compensate. As explained above, the level controller’s response is likely very slow, so switching feed pumps on and off can result in large deviations in drum level.

A faster control action is needed for dealing with changes in feedwater flow rate. This faster action is obtained by controlling the feedwater flow rate itself, in addition to the drum level.

To control both drum level and feedwater flow rate, cascade control is used. The drum level controller becomes the primary controller and its output drives the set point of the feedwater flow controller, the secondary control loop. This arrangement is also called two-element control, because both drum level and feedwater flow rate are measured and used for control.

http://blog.opticontrols.com/wp-content/uploads/2010/07/Single-Element.png

Two-Element Drum Level Control

Three-element Control (Cascade + Feedforward Control)

Similar to feed flow, changes in steam flow can also cause large deviations in drum level, and could possibly trip the boiler. Changes in steam flow rate are measurable and this measurement can be used to improve level control very successfully by using a feedforward control strategy.

For the feedforward control strategy, steam flow rate is measured and used as the set point of the feedwater flow controller. In this way the feedwater flow rate is adjusted to match the steam flow. Changes in steam flow rate will almost immediately be counteracted by similar changes in feedwater flow rate. To ensure that deviations in drum level are also used for control, the output of the drum level controller is added to the feedforward from steam flow.

The combination of drum level measurement, steam flow measurement, and feed flow measurement to control boiler drum level is called three-element control.

Three-Element Drum Level Control

Low-load Conditions

Although three-element drum level control is superior to single- or two-element control, it is normally not used at low boiler loads. The reason is that steam flow measurement can be very inaccurate at low rates of steam flow. Once the boiler load is high enough for steam flow to be measured accurately, the feedforward must be activated bumplessly.

For help with tuning your drum level controller, or for process control or boiler training, pleasecontact me at OptiControls.



7 Responses to “Drum Level Control” Brent:

July 1, 2012 at 11:10 pm

If you’re trying to design a feedforward for an integrating process, such as a boiler steam drum level, how do you set up the lead-lag? In your book the FFlead should be the time constant of the process response and the FFlag should be the time constant of the disturbance response. But there is no time constant in an integrating process. My guess would be to use the integration rates instead of the time constant. Is this correct? Thanks.

Jacques :

http://blog.opticontrols.com/wp-content/uploads/2010/07/Two-Element.png

http://blog.opticontrols.com/wp-content/uploads/2010/07/Three-Element.png

July 10, 2012 at 4:51 pm

Brent,The integration rates you refer to are equivalent to the process gain of an integrating process. So if there were to be a difference between the rate at which the drum level changes after a change in steam flow versus feedwater flow, you would compensate for that with the feedforward’s gain. Generally, if your steam and feed flows are measured accurately, the integration rates will be the same, so the FF gain will be 1.0.

You ask a good question about tuning the lead-lag. Generally, on an integrating process (excluding drum level), any lags in the process will show up as dead time because of the way we model the process. So you will set your lead equal to the “dead time” after a change in control action, and your lag equal to the “dead time” after a disturbance.

However, for drum level it is not so straightforward because of the drum level’s inverse response. From my experience, people normally don’t bother with a lead-lag on drum level control. Sam Dukelow suggested using a lag on the steam flow signal to compensate for the inverse response. I have not tried it out, so I can’t speak to its effectiveness. If you tune boiler controls and don’t have Sam Dulelow’s book, I higly recommend getting it.

ajit laware:

August 11, 2012 at 11:50 pm

What are major limitations of PID controller for boiler-drum level ?Can we use any robust controller like H2, H infinitey or sliding mode controller ?Whether this research beneficial for idustry ? In what point of view ?

Jacques :

August 12, 2012 at 8:15 am

Ajit,1. The limitations of PID for drum-level control result from the drum’s inverse response. High controller gains (that can normally be used on level control of non-surge tanks) cannot be used on drum level because the loop goes unstable very easily. The same goes for using derivative control mode.2. You could probably get slightly better response with a properly-designed model-based controller, provided that the inverse response is modeled accurately. I have not seen this used in practice. The standard design is to use a feedforward from steam flow because it gives a response vastly superior to the capabilities of any feedback control.3. I don’t think improving feedback control for drum level will be widely adopted in industry because: a) a feedforward will still be the primary control action, b) industry is reluctant to use advanced control technologies where its benefits are marginal (especially the power industry).

Benny:


I worked at a power plant, the drum level was the classical three element control system using circa 1950′s pneumatic controls. The controllers were completely worn out due to their age (40 years in service). I put in a proposal to have them upgraded to digital controls. Two units were retrofitted. Unit 2 went into service with very little fuss. Unit 1, however, made me pull my hair. Through luck I found out that the non-return valve (NRV) between the economizer inlet and the feed pumps was defective (not closing), After it was repaired the loop worked flawlessly, it even kept the drum level close to set point after 3 coal feeders out of 5 tripped during a test. In a nutshell don’t only look at your transmitters, controllers and final control elements keep an eye on anything in those pipes such as NRV’s.

DOST MUHAMMAD:


Why at the start up of boiler the level of drum is control by single element control and on which stage or load it should be change over to three element control?

Jacques :


Muhammad, Flow measurements for feedwater and steam get less accurate as the flow rates decrease. Therefore, only single-element (drum level) control is used under low flow conditions. You can switch to three-element control when the flow measurements become more accurate, typically around 25% of maximum flow.

Improving pH ControlJanuary 29, 2012

Conventional pH ControlThe control of pH is at best very difficult with a conventional PID control loop (Figure 1). The challenge results from variable product flow rates and the highly nonlinear pH titration curve.

Figure 1. Conventional pH control - not recommended.

The pH of a liquid stream (let’s call it the product) is controlled by adding a flow of acid or base (called the reactant). To achieve the required product pH, a certain (but often unknown) ratio of reactant is needed. And here is the first key to pH control: we need to manipulate the ratio of reactant flow to product flow.

Ratio pH ControlWe should not simply manipulate the reactant flow independently of the product flow (as in Figure 1), because every time the product flow rate changes, the pH will first go off spec and then the pH controller will change the reactant flow to return the pH to its set point. With ratio control (as in Figure 2), if the product flow rate changes, the reactant flow rate is changed immediately to maintain a constant ratio between it and the product flow rate. The pH controller then manipulates this ratio to control the pH.

Figure 2. Ratio pH control - much better.



http://blog.opticontrols.com/wp-content/uploads/2012/01/Standard-pH-Control.png

http://blog.opticontrols.com/wp-content/uploads/2012/01/Ratio-pH-Control.png

Advanced pH ControlAs you probably know, pH control is a very nonlinear process – the gain of the process changes with pH. The process gain is very high around the equivalence point, and much lower elsewhere (Figure 3).

Figure 3. pH titration curve.

Because the process gain changes so significantly, we should dynamically adjust the controller gain to compensate. This is done by implementing gain scheduling to adjust the controller gain based on pH.

To design the gain scheduler we should determine the process gain at a few points along the titration curve by changing the ratio at different levels of pH and determining the process gain. Process gain = (change in pH in % of full scale) / (change in Ratio in % of full scale). We should also measure the process dynamics (dead time and time constant) at each point (although these will likely be quite constant throughout).

Then we calculate the controller gain settings that the controller should use at various pH levels, and implement these in a controller gain scheduler (Figure 4). Obviously we should also calculate the integral setting, and if used, the derivative setting but these will remain constant and can be set directly in the controller.

Figure 4. Advanced pH control.

The gain scheduler can be implemented with a standard f(x) curve or characterizer block provided in modern control systems. The gain scheduler’s input should come from the measured pH and its output should set the controller’s gain accordingly. And voila! We have good pH control.


Ratio ControlAugust 31, 2011

While I was recently helping a chemical company optimize several of their critical control loops, I noticed they had a ratio controller in manual control mode. I asked about the loop and they told me it has never worked in automatic control.




http://blog.opticontrols.com/wp-content/uploads/2012/01/Titration-Curve.png

http://blog.opticontrols.com/wp-content/uploads/2012/01/Advanced-pH-Control.png

I occasionally come across loops that never have worked in automatic control. Sometimes it’s a tuning problem, sometimes it’s an issue with the measurement or control valve, one time the control direction was wrong – go figure. However, when it is a ratio control loop that’s not working, most often the problem lies with the design of the control strategy.

Ratio Control Explained

Process design and operations often calls for keeping a certain ratio two or more flow rates. One of the flows in a ratio-control scenario, sometimes called the master flow or wild flow, is set according to an external objective like production rate. The ratio controller manipulates the other flow to maintain the desired ratio between the two flows. The flow controlled by the ratio controller is called the controlled flow. For example, when treating drinking water with chlorine, the water is the wild flow, and the chlorine is the controlled flow.

There are two fundamentally different designs for ratio control. One of them is the correct design, the other one does not work in practice.

The Intuitive but Incorrect Design

In this design, the ratio is calculated by dividing the one flow by the other. This calculated ratio is then used as the process variable for a ratio controller. This design creates a highly nonlinear control loop of which the process gain is inversely proportional to the flow rate in the denominator. Ratio controllers like this are frequently dead (virtually no control) or unstable. This design should be avoided at all times, and if you have one of these, correct the design!

The Correct Design

The wild flow should be multiplied by the desired ratio to calculate a set point for the controlled flow. A standard flow controller then controls the flow according to this set point. If required, you can divide the controlled flow by the wild flow to display the actual ratio to the operator, but don’t use it to control the ratio.

The figure below shows the two ratio-control designs. Ratio control should not be based on a division of flow rates as shown on the left, but rather on calculating a flow set point, as shown on the right.

Two designs for ratio control. Left: The incorrect design. Right: The correct design.

For example, the correct design for a ratio controller of fuel and air is shown below. Fuel is the wild flow and air is the controlled flow.

Controlling the ratio of combustion air to fuel flow.

http://blog.opticontrols.com/wp-content/uploads/2011/08/Right-Wrong.png

http://blog.opticontrols.com/wp-content/uploads/2011/08/Ratio-Control-Fuel-Air.png

I have seen several ratio controllers running in manual control mode because of “tuning problems.” After further investigation it often turns out that the incorrect design is in use. Now that you know the difference, you know what to look for and how to correct it.


Posted in 7. Control Strategies, 8. Case Studies

4 Responses to “Ratio Control” Teo:


Hi, your article is great…I am able to understand it even I don’t have chemical engineering background (I am mechatronic engineering student).

lndas:

October 18, 2011 at 11:13 am

Thank you for the article. I could get now a fair idea about ratio control

Matt:


Hello, thanks for this website.Question: what about you have a second control valve on wild flow line? would it have a dedicated controller or there might be a function out of existing controller?

Jacques :


Matt, it depends on the control objective. But you could potentially have two flow control loops of which you change both setpoints based on something else, such as furnace temperature or boiler pressure. The ratio between the two setpoints can be constant or it could be adjusted by a third controller such as O2 in the flue gas.

Steam Temperature ControlSeptember 8, 2010

Steam temperature is one of the most challenging control loops in a power plant boiler because it is highly nonlinear and has a long dead time and time lag. Adding to the challenge, steam temperature is affected by boiler load, rate of change of boiler load, air flow rate, the combination of burners in service, and the amount of soot on the boiler tubes.

After separation from the boiler water in the drum, the steam is superheated to improve the thermal efficiency of the boiler-turbine unit. Modern boilers raise the steam temperature to around 1000F (538C), which approaches the creep (slow deformation) point of the steel making up the superheater tubing. Steam temperatures above this level, even for brief periods of time, can shorten the usable life of the boiler. Keeping steam temperature constant is also important for minimizing thermal stresses on the boiler and turbine.

Steam temperature is normally controlled by spraying water into the steam between the first and second-stage superheater to cool it down. Water injection is done in a device called an attemperator or desuperheater. The spray water comes from either an intermediate stage of the boiler feedwater pump (for reheater spray) or from the pump discharge (for superheater spray). Other methods of steam temperature control include flue gas recirculation, flue gas bypass, and tilting the angle at which the burners fire into the furnace. This discussion will focus on steam temperature control through attemperation. The designs discussed here will apply to the reheater and superheater, but only the superheater will be mentioned for simplicity.

BASIC FEEDBACK CONTROL

The simplest method for controlling steam temperature is by measuring the steam temperature at the point it exits the boiler, and changing the spray water valve position to correct deviations from the steam temperature set point (Figure 1). This control loop should be tuned for the fastest possible response without overshoot, but even then the loop will respond relatively slowly due to the long dead time and time lag of the superheater.

Figure 1. Simple Steam Temperature Control

CASCADED STEAM TEMPERATURE CONTROL

Because of the slow response of the main steam temperature control loop, improved disturbance rejection can be achieved by implementing a secondary (inner) control loop at the desuperheater. This loop measures the desuperheater outlet temperature and manipulates the control valve position to match the desuperheater outlet temperature to its set point coming from the main steam temperature controller (Figure 2). This arrangement is calledcascade control.

Figure 2. Cascaded Steam Temperature Controls

The spray water comes from upstream of the feedwater control valves, and changes in feedwater control valve position will cause changes in spray water pressure, and therefore disturb the spray water flow rate. The desuperheater outlet temperature control loop will provide a gradual recovery when this happens. If the spray water flow rate to the attemperator is measured, a flow control loop can be implemented as a tertiary inner loop to provide very fast disturbance rejection. However, in many cases spray water flow rate is not measured at the individual attemperators and this flow loop cannot be implemented.

GAIN SCHEDULING

http://blog.opticontrols.com/wp-content/uploads/2010/09/Steam-Temperature-Simple.png

http://blog.opticontrols.com/wp-content/uploads/2010/09/Steam-Temperature-Cascade.png

The process dead time of the superheater increases with a decrease in boiler load because of the slower rate of steam flow at lower loads. This will have a negative impact on the stability of the main steam temperature control loop unless gain scheduling is implemented. Step tests need to be done at low, medium, and high boiler loads, and optimal controller settings calculated at each load level. A gain scheduler should be implemented to adjust the controller settings according to unit load. Because of the changing dead time and lag of the superheater, the integral and derivative times must be scheduled in addition to the controller gain.

The gain of the desuperheater outlet temperature loop will be affected greatly by steam flow rate. Changes in steam flow rate will affect the amount of cooling obtained from a given spray water flow rate. Less cooling will occur at high steam flow rates. In addition, at high loads the pressure differential between the feedwater pump discharge and steam pressure will be lower, reducing the spray flow rate for a given spray valve position (assuming the absence of a flow control loop on the desuperheater spray flow). To compensate for these nonlinear behavior, controller gain scheduling should be implemented on the desuperheater outlet temperature loop too. Fugure 3 shows the basic design of the steam temperature controller gain scheduler (cascaded controller is not shown for clarity). Similar to tuning the main steam temperature control loop, step tests must be done at low, medium, and high boiler loads to design the gain scheduler.

Figure 3. Steam Temperature Controller Gain Scheduling

FEEDFORWARD CONTROL

During boiler load ramps in turbine-following mode, the firing rate is changed first, followed by a change in steam flow rate a while later. With the increase in steam flow rate lagging behind fuel flow rate, the additional heat in the furnace can lead to large deviations in steam temperature. To compensate for this, a feedforward control signal from the boiler master to the steam temperature controller can be implemented.

The feedforward can use the rate of change in fuel flow or one of several other derived measurements to bias the steam temperature controller’s output. In essence, when boiler load is increasing, the spray water flow rate will be increased to counter the excess heat being transferred to the steam, and vice versa. The feedforward can be calibrated by measuring the extent of steam temperature deviation during load ramps.



14 Responses to “Steam Temperature Control” Karthi:

May 8, 2011 at 7:46 pm

Excellent effort.lucid description makes a great read.You can touch upon the integral windup problem frequent in STC. I would like to see you write about the boiler-turbine co-ordinated control.

http://blog.opticontrols.com/wp-content/uploads/2010/09/Steam-Temperature-Gain-Scheduling.png

RegardsKarthi

Jacques :

May 8, 2011 at 8:30 pm

Karthi,You bring up a good point. When the desuperheater outlet approaches saturation temperature, the inner loop should be blocked from adding more spray. The outer loop’s controller should use external reset feedback to prevent integral windup. If this is not possible, its integral term should be blocked under any one of these conditions:- When the inner loop’s controller output is at 0% or 100% (this normally happens automatically)- When the inner loop’s output is blocked because of proximity to saturation, as described in Zeke’s note below.

I have placed boiler-turbine coordinated control on my to-do list for the blog.

Thanks for your inputs.Stay tuned!Jacques

Allan Zadiraka:

August 3, 2011 at 9:08 pm

Jacques

In actual practice, you cannot permit the desuperheater outlet temperature reach saturation temperature since you have no idea of the quality of the fluid other that it could be all saturated liquid, all saturated vapor or some mixture of the two states. Unfortunately, turbines and superheater tubes do not like water. The spray flow must be limited to a temperature above saturation temperature for the pressure, typically 20 degrees F. This delta is needed to account for thermocouple accuracy and drift as well as the thermocouple/thermowell time response. In the few cases where it is necessary to spray to saturation, a simple temperature based limit cannot be used.

zeke

Imran Ahmed:

August 10, 2011 at 11:31 pm

Hi ! It is is very informative detail. I am facing a problem at 210 MW Steam Turbine with 640 t/hr Babcock boiler.

Recently Emerson OVation DCS has been installed as a Retrofit job. Main steam temperature cannot be increased from 480 C , also Air restriction is there, Air heaters are clear, air damper ( FDF dampers open almost 100%) but still air deficiency is there.

Can you give any particular reason on control side for low main steam temperature.

regards,

Imran

Jacques :

August 11, 2011 at 9:51 am

Imran,From the information you gave me it is not possible to tell exactly what the problem is.Are your measurements and controller outputs ranged exactly the same as they were before the retrofit?

Jacques

SAJEESH:


hi….

I didnt get the cascade control theory basics….i have to control the main steam temperature around 480 degree.Output of PID is limited to 0 to 100 corresponding to 4 to 20 mA for control valve.so i f i give this value (0 to 100) to inner loop as setpoint to de superheater how the cascade controller works.Please provide me more detailss…

Jacques :


Sajeesh,The temperature controller’s output has to be rescaled from its standard 0-100% to match the range of the spray flow controller’s set point (or process variable).

Some controllers (e.g. Invensys Fox I/A) allow you to rescale the output directly, while other controllers (e.g. Honeywell Experion) do the scaling for you automatically. Yet other systems (e.g. Emerson Ovation) require you to place a scaling block between the two controllers.

Jacques

Ravi Mishra:

January 24, 2013 at 3:42 am

Dear Sir,

During the Turbine follow mode operation its seems that, the main steam temperature have large deviations during the ramp up and ramp down, even with feed forward loop is implemented (from steam flow/BLI) because The firing rate is changed first, followed by the change in steam flow rate.So how can we generate the feed forward signal (logic) from the fuel flow or boiler master demand to compensate this deviation? Can you give the that logic which can implemented to reduce this problem?

Jacques :

January 24, 2013 at 11:21 pm

Ravi, there are several designs for this feedforward of which some seem to work better than others depending on the particular situation, boiler design, fuel type, etc. Some use fuel flow, or its rate of change, some use air flow, or its rate of change. Others use a combination of steam and fuel flow that alters spray flow based on the relative difference between fuel and steam flows. I recommend that you look at Sam Dukelow’s book, The Control of Boilers. It is an excellent source of technical information on boiler controls.- Jacques

Siby:

March 20, 2013 at 12:23 am

This is slightly off topic but still relevant question for Control engineers at a time when Advanced process control schemes are becoming more prevalent. Is the use of a Model predictive controller to provide set-points to the spray control valves for steam temperature control a cost effective approach?

Jacques :

March 20, 2013 at 8:37 pm

I did a comprehensive study for the Electric Power Research Institute (EPRI) on the adoption of Advanced Process Control / Model-Predictive Control (APC/MPC) in power plants. Compared to the refining, and chemical industries, the power industry lags far behind in using APC/MPC. On the flip side, the power industry is the forerunner with utilizing complex DCS-based control strategies. APC/MPC will do a fine job of controlling steam temperature, especially if you control the burners individually, instead of just one common fuel demand. Excess air, spraywater, burner tilts/recirc air/bypass dampers should all be used simultaneously as control elements. ABB, Neuco, Invensys, and probably others, have reported successes with APC on boiler plants. The power industry lacks the skills to implement and maintain APC, and the cost benefits are just not there in many cases (except perhaps for environmental controls).- Jacques

Siby:

March 22, 2013 at 3:31 am

I read the article and found it to give an objective assessment on APC in power plants. Nicely highlights the challenges involved in making APC’s more acceptable.Siby

H.B.R:


Hi, I read your article impressively.I would like to ask you if it’s possible to control steam temperature using characteristic curve.In the plant where I worked, the main and re-heat steam temperature control loop is cascade without feedforward demand. At first, the main and re-heat steam temperatures swinged and it affected MW and steam pressure. To avoid that, we applied charecteristic curve(o.g f(x) function in ovation) opening TCV position more than PID manipulated position to compensate the dead-time(time delay). Actually, it was the idea of my boss and I’m curious if it’s proper to use a characteristic curve for steam temperature control.

Jacques :


H.B.R. – Characterizers are used to compensate for some type of nonlinear process behavior, or to obtain a nonlinear control action where one is needed. A characterizer can be used very effectively in feedforward control where the relationship between the disturbance and the required compensating control action is nonlinear. It sounds like this is what your boss did, even though the design might have been different from normal. If there is a strong relationship between (e.g.) fuel input and spray valve position required to maintain reheat steam temperature, using a feedforward with a characterizer would be appropriate. However, you will likely also require some degree of feedback control to compensate for other variables such as different burners in use, boiler sooting, etc.

8. Case Studies o A pH Control Success Story o An Oscillating Level Control Loop o Butterfly Valves and Control Performance o Caster Level Control Improvement

o Flow Control Conundrum o How to Fill a Container o Inverse Response o Level Versus Flow Control o Pressure and Flow Control Loop Interaction o Process Oscillations from Afar o Ratio Control o Tank Level Tuning Complications

A pH Control Success StoryMarch 30, 2013

I recently helped a major chemical company improve the controls of one of their processes that was plagued by a persistent oscillation. The process consisted of a large process loop and the reaction was highly dependent on the pH in the loop. The pH oscillated, driving the oscillation in the entire process. If the pH control could be stabilized, the entire process would stop oscillating.

The pH was controlled with the addition of ammonia. The pH controller directly manipulated the ammonia flow control valve (Figure 1). The engineers and operators told me that the ammonia pressure fluctuated and that this affected the ammonia flow rate and consequently affected the pH. They suspected that the pH control loop and the ammonia-production boiler may even be oscillating against each other.

Figure 1. pH control design, as found.

To reduce the effect of ammonia pressure on the flow rate, we implemented a flow controller to keep constant the ammonia flow rate, regardless of the upstream pressure. This flow controller would get its setpoint from the pH controller – classical cascade control. Then, because we wanted to have very tight pH control, we needed to compensate for the change in process gain induced by the nonlinear pH titration curve. We obtained a titration curve from the lab, converted it to a process gain curve (i.e. the change in pH / change in ammonia flow), and normalized the curve around the pH setpoint of 3.5 (Figure 2).



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Figure 2. Normalized pH gain curve.

We configured the normalized pH gain curve in a characterizer function block that used pH as its input, and produced the estimated process gain as its output. Then we implemented a parameter for adjusting the gain, divided this gain by the output of the characterizer, and used the result to schedule the gain of the pH controller (Figure 3). Since the flow rate in Loop 1 remained relatively constant, we did not have to use ratio control.

Figure 3. Advanced pH control with a cascaded flow control loop and gain scheduling.

With the flow controller in place, we did small step-tests around the pH control point of 3.5 to establish the process’ dynamic characteristics. This was a major challenge, since the pH varied wildly with the controller in manual. (I’ll write an article about step-testing volatile/turbulent processes sometime, because I often have to deal with this problem). Once we had good estimates for the process gain, dead time, and time constant, we tuned the controller for a fast response.

The results we obtained were very good. Despite the substantial variance in the ammonia pressure, the pH control loop remained stable and controlled the pH very close to its setpoint.

Figure 4. Results of advanced pH Control.

After this, we tuned the ammonia pressure controller and several other loops. This further stabilized the process and reduced the pH variance even more. But it all started with our improvements on the pH loop.

Stay tuned!

Jacques F. SmutsPrincipal Consultant of OptiControls, and author of Process Control for Practitioners

An Oscillating Level Control LoopAugust 3, 2011

When I do onsite control loop optimization services I often see level controllers oscillating. Most often they oscillate because of one or more of the following reasons:

The control valve has a dead band. (Yes, level loops with dead band oscillate continuously if you

are using a PI or PID controller.)

The control valve has stiction.

The integral time is set too short for the amount of controller gain being used.





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However, these are not the only problems and I have often been amazed at the actual cause of oscillations.

So to keep me from guessing, I systematically analyze a loop for problems before I tune the controller. I always try to follow the same basic sequence of tests, and then delve deeper into any problems I notice. The sequence of tests:

1. See how the loop performs in automatic control under normal operating conditions.

2. Do a set point change (this is very helpful for various reasons that I’ll write about in future).

3. Place the controller in manual.

4. Do various valve performance tests (these can be quite challenging on a level loop).

5. Assuming no insurmountable problems were found, do step-tests for tuning (if you don’t have

enough data already).

6. Tune the controller and repeat steps 2 and 1 to ensure the loop meets its performance

objectives.

Some (non-readers of this blog) may try to address all control problems with tuning. But the simple steps listed above have served me very well over the years and I often smile to think that someone could be wasting hours of fruitless tuning if a loop really has other problems.

Case in PointA few weeks ago I was optimizing the control performance of loops an oil platform in the Gulf of Mexico. Quite early in the project I got to a level control problem on one of their separator vessels. Step 1 of my test sequence revealed the oil level control loop was oscillating. The period of the oscillations was slightly shorter than one minute.

Level loop oscillating.

Going on to Step 2, we made a set point change. I noticed the loop actually performed very well on the change in set point (ignoring the oscillation). From that I concluded the problem is not the controller’s tuning.

I also noticed that the process variable took about two minutes to cross over its set point for the first time and about six minutes to settle out at set point. This meant the response time of the loop was far slower than the period of its oscillations. It would be impossible for stiction or dead band to cause the loop to oscillate with a one-minute period if it takes the loop so much longer to reach set point. Although I would later test for stiction and dead band, I basically ruled them out as causes of the oscillation.

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Loop performed well on a set point change.

Step 3 calls for placing the controller in manual control mode. This provides a good test to see if the oscillations are caused by something in the control loop. We placed the loop in manual, and the oscillations continued. At this point I concluded that the oscillations were not caused by controller tuning, stiction, or dead band.

Oscillations continued with controller in manual.

So what could it be? A quick inspection of the level control valve indicated that the valve was rock-solid in holding its position with the controller in manual. The oscillations were not coming from the valve and therefore they had to be coming from the process. We looked at time trends of the flow rate into the separator vessel and the gas pressure inside the vessel, but these were not oscillating (at least not at one-minute periods).

Then we found the cause. The vessel is a three-phase separator: gas, oil, and water. The oil floats on a layer of water in the bottom of the separator. It was the oil-water interface level that was oscillating, moving the oil level up and down with it. After some more investigation, we found the water level control loop was operating virtually in on-off control mode. Only then could we focus on solving the real problem.

We are all sometimes tempted to tweak controller settings without looking any further, but a systematic approach to analyzing control loops and solving control problems really pays off.


Posted in 6. Loop Performance, Problems, and Diagnostics, 8. Case Studies

4 Responses to “An Oscillating Level Control Loop” Mary:


How did you solve the problem?

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Jacques :


We did step tests and properly tuned the water level controller. That solved the problem.

Nhan:


Which tuning rule did you apply for the oil level control loop, level averaging or lambda? Thanks

Jacques :


Nhan, the tuning rule of choice should always depend on the application:- For fast response, the Ziegler-Nichols rules for integrating processes work well, provided you divide the controller gain by two, and multiply the integral time by two.- For slow response, I recommend level-averaging (I still need to write an article about it).

In the case of the oil level, I proposed using level averaging to make maximum use of the surge capacity of the separator, but the operations personnel wanted the oil to stay as close to setpoint as possible (fast control). So we ended up using Z/N for tuning the oil level loop.

I think Lambda tuning for levels is good as an academic exercise, but I don’t see its need for tuning level controllers, and I have never used it for tuning levels. However, theLambda tuning rules certainly have a place with self-regulating processes.





To perform well, a PID control loop needs (among other things) that the process gain remains constant. In other words, the process variable must change linearly with changes in controller output. A small degree of nonlinearity can be tolerated, especially if we apply robust tuning methods, but if the process gain changes by more than a factor of 2, we can expect control problems. And this is why a butterfly


valve makes a poor choice for a control valve – it has a highly nonlinear, S-shaped flow curve, as shown in Figure 2.













mohamed elsadig:

May 18, 2013 at 11:11 pm


Jacques :

May 19, 2013 at 7:59 am


H.B.R:

May 27, 2014 at 2:16 am

Dear, Mr. Jacques.I’m an I&C engineer working for an EPC contractor. In the site where I worked last year, there was the exactly same problem as described in the figure no.4 of this article.The process was distillate water level and it was controlled by the butterfly type control valve.The process value was hunted like figure no.1 but with bigger magnitude. I think the problem was because of the actuator or positioner. When PID output sent a demand signal to the


valve, the positioner feedback value followed the demand signal after 1~2 seconds.(i,e. there was a deadtime in the actuator.) I couldn’t detect that it was caused by the sticky actuator or positioner problem because the plant was under the commercial operation.(now, I’m working the head office and that problem is still remaining in the site.)Can you imagine the status of the process?? It’s oscillated with really big magnitude.(bigger than figure no.1)The action I did during the commissioning was only adjusting PID value at that time due to the tight commissioning time. After that, only the oscillation magnitude became smaller and the symptom alarming every minute disappeared but still big oscillation has existed.Thank you for your helpful information.



System Description



The Problem










The Solution






Stay tuned!

Flow Control ConundrumOctober 15, 2011

I recently helped a control engineer review the control strategies used in his plant. The company was experiencing some control problems and wanted a second opinion. While most of the controls were





designed correctly, we found a few areas requiring design changes. One of these areas had to do with balancing flow rates through banks of filters in their water filtration plant.

System Description

Raw (river) water enters a clarifier to separate the heavy solids. The water flows over a weir and is pumped through two filter banks in series. Each bank has three filters. The flow rates through the individual filters have to be balanced for filter efficiency.

Filtration Plant P&ID - click to display full size

Control Design as Found

The clarifier had a level controller of which the output became the set point of the six flow controllers. Actually the flow set point of each bank of flow controllers were divided by the number of filters in service, but I left that detail out of the diagram to keep it simple.

Operational Problems

The site found that the second set of flow controllers would slowly increase their outputs until they were all at 100% and the valves were wide open. Occasionally, when certain filters were out of service, the first set of flow controllers would slowly increase their outputs until they were all at 100% and the valves wide open, while the second set of valves controlled properly.

Equivalent Control Design and Problem

The multiple filters and flow paths obscured the design problem. If we simplify the hydraulic flow paths and control design we end up with two flow controllers in series on the same pipe receiving the same set point.

Equivalent (simplified) Control Design

And here is the problem: we effectively have only one process variable (the common flow rate), but we have two controllers trying to control it. If one of the flow transmitters measure a slightly lower flow rate than the other, its controller will open its valve to get more flow. Although this might work temporarily, the flow rate in the other control loop will also have increased and that controller will close its control valve to compensate, bringing the flow back down to the original level. Eventually the control loop reading low will saturate with its controller output at 100% while the remaining control loop will do the flow control.

You cannot control the same process variable with two control loops at the same time!

Alternative Design

We had to have a common set point for the second set of flow controllers, but it had to be independent of the set point of the first set. Yet the two sets of controllers must in some way be linked to work in unison. Although there are other ways to solve this problem, here is the way we did it. We used the average position of the valves in the first bank as a set point to a position controller that controls the average position of the valves in the second bank.

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Alternative Design (only simplified version shown)

The position controller generates a flow set point to the second set of flow controllers that is independent of the flow set point of the first set of controllers. Basically, the valve position controller does not care what the actual flow rate is, as long as the valves in the second bank are on average at the same position as those of the first bank. In this way calibration errors has a negligible effect on the system as a whole.

After changing the design, we tuned the flow control loops, then the position controller, then the level controller. After that, the system worked perfectly.


How to Fill a ContainerMay 18, 2010

Recently, I helped a company with an interesting, but very commonly occurring problem. They fill containers one-by-one and stop filling at an exact weight of material. However, the final weight always overshoots its set point. A common analog to their setup is that of filling a tank or container with liquid to an exact level.

The filling sequence begins by placing an empty container on a digital scale. The scale tares the weight of the container so the fill can begin from zero weight. Then a PLC turns on a vibratory feeder to fill the container. During the fill cycle the weight is continuously sent back to the PLC. The PLC shuts off the vibratory feeder when the set point is reached. The filled container is then removed, and the next empty one is positioned on the scale. Then the fill sequence is repeated. The set point is kept constant between fills.

To improve the accuracy and repeatability of the fill, the company replaced the PLC program with a continuous controller, i.e. a PID controller. This was a very good decision indeed. The newly implemented PID controller worked very well, except that the weight always overshot the set point. And that’s when they contacted me.

I reviewed their setup and fill sequence with them and asked for the PID controller’s settings. They were using the P, I, and D modes of the controller. And there was the problem. If one uses the integral mode in a controller filling a container – the process will always overshoot its set point.

To work properly and not have overshoot, the controller’s output must go to zero when the process reaches set point. But when using integral, it tries to correct the error throughout the duration of the fill and accumulates a positive value. When the set point is reached, this accumulated value keeps the controller output at an elevated level, even though the error is zero. Then the process overshoots the set point, the error goes negative, the integral term begins to reverse the accumulation and eventually the controller output ends up to zero.

The solution is to use no integral action in a controller on systems like filling a vessel or container. Also, in this setup derivative is of no use, so that should be set to zero to simplify matters.

However, in the customer’s particular setup, simply turning off the integral term would create a new problem. The bumpless transfer feature of the controller will ignore the initial error when the controller is placed in auto at the beginning of the fill sequence. The controller output will begin at zero (this is desirable), but because of no integral action, nothing would drive the controller’s output.

The solution was to set the set point to zero before the fill begins. After the tare, the controller is placed in automatic mode. Then the set point is changed to the desired weight. The controller output responds to the set point change and the fill begins. As the container fills up, the error gets less and the controller output eventually settles back to zero in a nice exponential fashion as the set point is reached. Voila, no overshoot! Once the controller output is back at zero, it can be turned to manual control mode to be ready for the next fill.


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With proportional control only, the controller is also very easily tuned by adjusting the proportional gain (only active setting) to change the controller’s response.


Posted in 8. Case Studies

2 Responses to “How to Fill a Container” Avihu Hiram:

July 19, 2012 at 3:45 pm

I was searching for some material on “Signal Filtering” application (in your site…) – with no success.Do you have some thing about “Practical Filter design”?

Jacques :

July 22, 2012 at 7:52 am

Avihu, I describe the practical application and design of filters in my book Process Control for Practitioners, available from Amazon.com –http://www.amazon.com/gp/product/0983843813

Level Versus Flow ControlAugust 17, 2012

Earlier this year I did a controls optimization project on a process unit in a large chemical company. They had a complex and interactive process, but their controls were mostly simple control loops with no cascade, feedforward, gain scheduling etc. I am a firm believer in keeping things simple, but no simpler than they should be – which brings me to the story.

The unit had a huge tank to collect effluent from various parts of the process. The mixture was then pumped back to the front end of the process for reprocessing. The tank had a discharge pump and a valve for level control. Because of the chemical composition of the various effluents, small flakes of solids formed in the liquid. The flakes would often plug up the control valve. As a result, the discharge flow will get blocked and the level in the tank would slowly increase. The increasing level caused the valve to slowly open, but the solids kept on blocking the valve as fast as it would open. This would carry on until the high-level alarm on the tank triggered. Then the operator would stroke the valve open and closed a few times to clear out the solids.

Before long, the plant discovered that the control valve will not get blocked if it moves often enough. In an effort to make the system more reliable, the plant installed a flow control loop and gave the operator a signal selector to switch between level control and flow control (Figure 1). Because the control valve was much more active when driven by the flow controller, it seldom got blocked in flow-control mode. Consequently, most operators then ran the system using flow-control mode.

Figure 1. Control strategy allowed operator to select between flow control and level control. (Click to enlarge)

You might have realized it already, but in flow-control mode there is no level control. So the tank is either slowly filling up or draining down. This required the operator to check the level every few hours and adjust the flow controller’s set point based on the tank level at the time. If the level was too high, the operator would increase the flow set point, and if the level got too low, the operator would decrease it (Figure 2).

Figure 2. Control performance as found. Blue = tank level; Magenta = discharge flow rate; Green = level set point.

Although they operated like this for years, the plant did put the problem on my list of loops to look at because it remained a burden to the operators. The problem was that both level and flow control had their advantages but also their disadvantages.

The solution was quite simple; it drew upon the advantages of both level and flow control; and it eliminated the disadvantages of both modes. You guessed it… we implemented cascade control. We simply let the output of the level controller drive the set point of the flow controller (Figure 3). In this way the level controller kept the level in check, and adjusted the flow set point to do so.

Figure 3. Cascade control had all the benefits, but no disadvantages.

The flow controller was active enough to respond to deviations from set point and clear out blockages before the level was affected. We also tuned both controllers for optimal performance. Compared to what they had before the changes, the new control performance was quite remarkable (Figure 4).

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Figure 4. Control performance after implementing cascade control and tuning the two loops. Blue = tank level; Magenta = discharge flow rate.

Learn more about advanced control strategies and controller tuning from the book Process Control for Practitioners.

Stay Tuned!



2 Responses to “Level Versus Flow Control” Víctor D. Parra:

August 18, 2012 at 8:03 am

Nice case study. Would you complete it explaining the advantage of using average level control in these cases?

Jacques :

August 19, 2012 at 8:54 am

Victor, you are right – we could have applied averaging level control because this tank was originally designed to be a surge tank. However, the process engineer wanted the level to remain close to its set point because the volume of liquid in this large tank affected the plant’s conversion rate (efficiency) calculations. So we used standard level-control tuning rules for this, but detuned it enough so that the outflow would not overreact to level disturbances.

Pressure and Flow Control Loop InteractionDecember 6, 2013

Weird control strategies are sometimes used in lieu of proper tuning to address process interactions. A customer contacted me with a question about such a control strategy. She explained that a blower was being used for maintaining (negative) air pressure in a common clean-air header, and to deliver air flow to process equipment. The blower was fitted with a variable-frequency drive, which was used to control the pressure inside the clean-air duct, and a control valve was used to bypass air around the process equipment to control air flow (Figure 1).


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Figure 1. Process & Control Diagram

The weird part of the design was that the control strategy had an interlock that allowed only one of the two controllers to run in automatic control mode at any time. My customer was told the by company who installed the system that the interlock was necessary because interaction between the pressure and flow control loops would cause system instability. She asked me to come to her plant to determine if there was any possible way to control duct pressure and air flow rate at the same time, considering that the two variables interact on each other.

To explore the problem on site, we did step changes on the two controller outputs, one at a time, while recording pressure and flow. Then we reviewed the data to decide on the best path forward. It turned out that changes in the pressure controller’s output strongly affected both pressure and flow, but changes in the flow controller’s output mostly affected the flow, with a lesser, but still significant, effect on pressure.

The dynamic response of the two processes (dead time and time constant) was virtually identical. This meant that if both control loops were tuned aggressively, there would be a significant likelihood of cyclical interaction occurring between the two loops. Needless to say, both control loops were tuned very aggressively. If the process dynamics were significantly different from each other, cyclical interaction would not be such a concern.

We decided to suppress any possible cyclical interaction by tuning the two loops to have different response times (one fast and the other slow) which will also cause one of the loops to have a significantly damped response (which is very good for maintaining stability).

Since most of the disturbances were caused by other users on the common clean-air duct, we decided to tune the pressure controller for a fast response. For this we used the Cohen-Coon tuning rules with a stability margin of 2. Once the pressure controller was tuned, we put it in automatic control mode and redid the step tests on the flow loop, to include the effect of the pressure controller running/interacting in automatic control. We tuned the flow loop for a slow and damped response using the Lambda tuning rules.

When both control loops were properly tuned, we removed the interlock and put the flow loop in automatic control. As we expected, the system remained perfectly stable. We stopped and restarted one of the other clean-air users and the system behaved beautifully with not a hint of cycling or instability. The operators were delighted because they would no longer have to manually control either flow or pressure. In addition, the variability in air flow rate and duct pressure was significantly reduced (Figure 2).

Figure 2. Improvement in flow rate variability

Stay tuned!



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Jacques Smuts Founder and Principal Consultant, OptiControlsAuthor of Process Control for Practitioners

Process Oscillations from AfarApril 6, 2014

Oscillations in key process variables are highly undesirable, but their origins are often difficult to track down and solve. The success of a hydrocarbon incinerator control-optimization project I executed at a chemical plant last year was threatened by an inexplicable and seemingly unstoppable oscillation in the incinerator differential temperature (and other control loops). At first I thought the oscillation was caused by either poor tuning or cyclical interactions between two tightly coupled incinerator control loops, but even after putting all the incinerator’s control loops in manual the oscillation persisted.

The oscillation was obviously coming from an external process and the most likely source was the concentration of hydrocarbons in the vent gas being fed to the incinerator. The vent gas came from a stripper column that stripped most of the hydrocarbons from reactor vent gas (Figure 1). Changes in the remaining hydrocarbon content would affect the amount of heat released in the incinerator.

Figure 1. Simplified process diagram. (Click to enlarge.)

To determine if the problem originated in the stripper, I trended all the available temperature, pressure, and flow-rate signals from the stripper. I found that the temperature of wash oil used as a stripping medium oscillated at the same period as the loops on the incinerator. An oscillation in wash-oil temperature would have a direct effect on the amount of hydrocarbons stripped from the vent gas, which could explain why the incinerator loops oscillated.

But why did the wash-oil temperature oscillate? The wash oil was cooled by passing it through a heat exchanger that vaporized liquid ammonia to cool the wash oil. The temperature of the wash oil exiting the wash-oil cooler and flowing to the stripper column was controlled by manipulating a control valve on the ammonia vapor discharge end of the cooler. The wash-oil temperature, controller output, and wash-oil cooler’s shell pressure were all oscillating at the same period as the incinerator differential temperature (Figure 2). I asked the operator to put the temperature control loop in manual mode, after which all the oscillations completely stopped.

Figure 2. Key variables oscillating in unison. Incinerator DT uses right-side Y axis.

By doing a few simple valve-performance tests I discovered that the ammonia vapor control valve was sticking, causing a stick-slip cycle in the temperature control loop, in turn causing an oscillation in the hydrocarbon content of the vent gas being fed to the incinerator, finally causing and oscillation in outlet temperature (and therefore in the differential temperature across the incinerator – the critical variable). The wash-oil temperature measurement was located far away from the heat exchanger and this long distance caused the oscillation to have a very long period. This fact later was key to solving the problem.


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The temperature control valve stiction was on the order of 2% to 3% of the valve’s travel range. The operator called in the control valve technician, who then went out to attend to the valve. They stroked the valve open and closed a few times and the technician came back reporting that the valve works perfectly. I explained to him (as nicely as I could) that the controller was not asking for 25% changes at a time, but for 0.5% – 1% changes, and the valve needs to respond to these small changes for us to have good temperature control. He shrugged his shoulders, mumbled something about wanting a Prius to run like a Ferrari, and walked out of the control room. We were not getting the valve fixed.

However, it was important to stabilize the temperature loop for the project to be a success. I tried slowing down the tuning on the wash-oil temperature loop and even added some derivative control (to “kick” the valve), but the loop kept on oscillating with the controller in auto. I did eventually solve the problem, but I will write about that next month. For now, the main point of this anecdote is that oscillations are sometimes caused by a source far away from the process one wants to optimize (Figure 3). The second point is that oscillations are very often not a tuning problem.

Figure 3. Process oscillations originating from afar.

Read next time how we worked around the problem caused by the sticky control valve.

Stay tuned!

Jacques Smuts, Founder and Principal Consultant, OptiControlsAuthor of Process Control for Practitioners


2 Responses to “Process Oscillations from Afar” Akis:

June 6, 2014 at 4:15 am

Do you prefer to leave the wash-oil TC at Manual until the problem is fixed?or at Auto despite its the cause of the oscillation?

Jacques :

June 8, 2014 at 10:36 am

Akis: In this case we overcame the problem with the sticky control valve during the project, so we did not have to leave the controller in manual. However, if we could not overcome the problem, manual control would have been an attractive alternative.

Ratio ControlAugust 31, 2011

While I was recently helping a chemical company optimize several of their critical control loops, I noticed they had a ratio controller in manual control mode. I asked about the loop and they told me it has never worked in automatic control.

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I occasionally come across loops that never have worked in automatic control. Sometimes it’s a tuning problem, sometimes it’s an issue with the measurement or control valve, one time the control direction was wrong – go figure. However, when it is a ratio control loop that’s not working, most often the problem lies with the design of the control strategy.

Ratio Control Explained

Process design and operations often calls for keeping a certain ratio two or more flow rates. One of the flows in a ratio-control scenario, sometimes called the master flow or wild flow, is set according to an external objective like production rate. The ratio controller manipulates the other flow to maintain the desired ratio between the two flows. The flow controlled by the ratio controller is called the controlled flow. For example, when treating drinking water with chlorine, the water is the wild flow, and the chlorine is the controlled flow.

There are two fundamentally different designs for ratio control. One of them is the correct design, the other one does not work in practice.

The Intuitive but Incorrect Design

In this design, the ratio is calculated by dividing the one flow by the other. This calculated ratio is then used as the process variable for a ratio controller. This design creates a highly nonlinear control loop of which the process gain is inversely proportional to the flow rate in the denominator. Ratio controllers like this are frequently dead (virtually no control) or unstable. This design should be avoided at all times, and if you have one of these, correct the design!

The Correct Design

The wild flow should be multiplied by the desired ratio to calculate a set point for the controlled flow. A standard flow controller then controls the flow according to this set point. If required, you can divide the controlled flow by the wild flow to display the actual ratio to the operator, but don’t use it to control the ratio.

The figure below shows the two ratio-control designs. Ratio control should not be based on a division of flow rates as shown on the left, but rather on calculating a flow set point, as shown on the right.

Two designs for ratio control. Left: The incorrect design. Right: The correct design.

For example, the correct design for a ratio controller of fuel and air is shown below. Fuel is the wild flow and air is the controlled flow.

Controlling the ratio of combustion air to fuel flow.

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http://blog.opticontrols.com/wp-content/uploads/2011/08/Ratio-Control-Fuel-Air.png

I have seen several ratio controllers running in manual control mode because of “tuning problems.” After further investigation it often turns out that the incorrect design is in use. Now that you know the difference, you know what to look for and how to correct it.


Posted in 7. Control Strategies, 8. Case Studies

4 Responses to “Ratio Control” Teo:


Hi, your article is great…I am able to understand it even I don’t have chemical engineering background (I am mechatronic engineering student).

lndas:

October 18, 2011 at 11:13 am

Thank you for the article. I could get now a fair idea about ratio control

Matt:


Hello, thanks for this website.Question: what about you have a second control valve on wild flow line? would it have a dedicated controller or there might be a function out of existing controller?

Jacques :


Matt, it depends on the control objective. But you could potentially have two flow control loops of which you change both setpoints based on something else, such as furnace temperature or boiler pressure. The ratio between the two setpoints can be constant or it could be adjusted by a third controller such as O2 in the flue gas.

Tank Level Tuning ComplicationsNovember 4, 2013

Level control loops are strange creatures. This strangeness can make them difficult to tune. On average, level control loops are tuned the worst of all process types. Although I have seen poorly tuned loops of all types, poorly tuned level controllers typically have tuning settings that are the furthest from optimal. Most level processes are very robust in nature, allowing them to function surprisingly well with suboptimal tuning.

But it does not have to be this way. If controller tuning is based on the dynamic response of a process, most level control loops are actually easy to tune and provide very robust control. However, as you probably know, most control loops are tuned “intuitively” using trial and error. More often than not, this approach results in poor control loop performance.

Case Study

A few weeks ago, I helped an engineer at a power plant with the tuning of a demineralized (demin) water storage tank. It was a large tank – about 40 feet (12 m) high and 20 feet (6 m) in diameter. Water was pumped from the demin water production plant into the tank, and this flow rate was manipulated with a control valve (Figure 1). Under normal operating conditions the unit consumesd demin water at an almost constant rate (most of which was discharged through the continuous boiler blowdown).

Figure 1. Demineralized water storage tank level control.

To do the tuning correctly, the engineer executed a few step tests (Figure 2) and we analyzed the data. We calculated the process integration rate (or process gain) to be 0.0045 / minute. This means if the level is at steady state and the controller output is changed manually by X percent, it will take 1/0.0045 minutes (3.7 hours) for the level to change by the same percentage. The dead time was measured to be roughly 2.5 minutes.

Figure 2. The two step tests used for tuning.

Once we had this information on the dynamic properties of the process, we used the modified Ziegler-Nichols tuning rules for Integrating Processes and calculated new tuning settings for this control loop. We used a “stability margin” of 2.5 and obtained the following tuning settings:

Controller Gain (Kc) = 32Integral Time (Ti) = 20 minutes.

The high controller gain was a concern. Although the level was quite smooth during our step tests, a historical trend of level revealed some jittering was present at times. And since a 1% jitter in level would cause the controller output to ”jitter” by 32% (Kc x delta PV), we decided to use a lower controller gain since tight control was not a requirement. We felt that Kc = 10 would be a good compromise between control performance and jitter tolerance.

Tuning Complications

Many level loops have small integration rates (or process gains). Integration rate (ri) is inversely proportional to the vessel’s residence time. Typically, the larger the tank, the smaller the integration rate. The process with the smallest integration rate that I personally worked with was a city water reservoir, which had a residence time of 48 hours (ri = 0.000347 / minute). For good control, a very low integration rate theoretically requires a very high controller gain, sometimes in excess of 100. Practically we cannot use controller gains of this magnitude because of the severe control action that would result from noise and setpoint changes. (Note that one can also overcome severe control action by using a noise filter and either the P&D-on-error control algorithm or a setpoint filter).

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This mandatory reduction of the controller gain brings me to the reason why most level loops have grossly suboptimal tuning settings. For integrating control loops (such as tank level), when you reduce the controller gain you have to increase the integral time, otherwise the loop can become very oscillatory.

Unenlightened tuners do not know of this requirement and end up using disproportionately short integral times on level loops, resulting in very oscillatory behavior. When they try to stabilize the loop by further reducing the controller gain, the situation deteriorates even more.

Example

For example, let’s look at how Billy, our unenlightened but fictitious tuner, might have tuned the tank level controller. Assuming he did step tests, he then used the original Ziegler-Nichols tuning rules (I did mention he is unenlightened) for calculating the controller settings. He obtained the following controller settings: Controller Gain (Kc) = 80 and Integral Time (Ti) = 8.3 minutes. He realized that the controller gain of 80 was too high, and reduced it to 10. But he left the integral time at 8.3 minutes, as calculated.

Then he tested the new tuning settings and noticed overshoot and oscillations in level. Too much gain, right? So he set the Kc value to 5 and retested the performance. The loop still oscillated with the adjusted tuning settings, but he realized that this tuning effort was taking too much of his time, so he left the tuning settings as they were and moved on to other work. Billy’s tuning results are shown in Figure 3.

Figure 3. The result of using decreased controller gains on a level loop, while leaving the integral time at the originally calculated value.

How it’s Done

Now back to our own tuning efforts on the demin water storage tank. When the engineer and I reduced the controller gain from 32 to 10, we simultaneously increased the integral time from 20 to 64 minutes, which we calculated using the equation below.

Equation for calculating a new integral time when reducing the controller gain in a level loop:Ti(new) = Ti(old) x Kc(old) / Kc(new)

Figure 4 compares the level loop’s response to a 5% change in outflow using the initial and refined controller settings. The control loop is significantly more stable compared to the alternatives shown in Figure 3.

Figure 4. Stable level control loop response obtained from increasing integral time while decreasing controller gain.

As I said at the beginning, level controller tuning does not have to be difficult. Do step-tests to understand the process dynamics, use proven tuning rules to calculate controller settings, and remember to adjust the integral time inversely to any subsequent change you make in controller gain.

Stay tuned!

Jacques SmutsFounder and Principal Consultant, OptiControlsAuthor of Process Control for Practitioners

Posted in 4. Controller Tuning, 8. Case Studies

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2 Responses to “Tank Level Tuning Complications” Nhan:


Dear Jaques,

Referred to the response curve, I calculate out the ri= 0.045/min, how come to 0.0045 as said, please advise, thanks

Jacques :


Nhan, let’s consider the first step change, dCO = 25% in size.Before the step has any effect, the level decreased by 1% over 32 minutes. S1 = -0.031%/minAfter the step change, the level increased by 1.1% over 13 minutes. S2 = 0.085%/minri = (S2 – S1) / dCO = (0.085 + 0.031) / 25= 0.0046 (which I rounded down to 0.0045 for convenience).

9. Tips and Work-Process o Best Practices for Control Loop Optimization o Diagnosing and Solving Control Problems o Process Control for Practitioners o Testing Control Loop Performance o Tools of the Tuner o Tuning Tips - How to Improve Your Results o When to Use which Tuning Rule o Why Tuning Rules Don't Always Work

Best Practices for Control Loop OptimizationApril 15, 2011

Control Loop Optimization means improving the performance of control loops to get the best possible performance from them. The improvement task is often attempted in an ad-hoc or trial-and-error fashion, but this is mostly ineffective and seldom results in truly optimal loop performance. Effective control loop optimization is done in a systematic way, by following the best practices.

1. Know Your Process. This item seems almost too obvious to be on the list, but it is often tempting

to address a control problem through tuning without considering the broader process. Process

knowledge provides guidance on the control objective, tuning rules to use, diagnostic tests to do,

and the process conditions under which to do the tuning. Things to know about the process

include: the process type (integrating or self-regulating), ratio of process lag to dead time, if the

process’ gain or dynamic characteristics might change under varying operating conditions, type of

final control element being used and its flow characteristics, disturbances to the process and if

they are measurable, possible negative side-effects from process-variable overshoot or a rapidly

changing controller output.

2. Determine the Control Objective. Consider the following: Should the loop perform fast or slow?

Is overshoot tolerable? Should the controller output move a little as possible? Does the

controller’s set point often change? Does the loop have to compensate for process

disturbances? The control objective will dictate the type of tuning method to use. The control

objectives could be fast setpoint tracking or fast disturbance rejection (of which each could have

sub-objectives such as minimum absolute error or minimum integral of error), zero process-

variable overshoot, a specific process response to setpoint changes, minimum controller output

movement, and no overshoot in the manipulated variable. Surge tank level loops, for example,

should be tuned to minimize controller output movement while keeping the level between

predefined limits.

3. Review the Control Strategy. Review the design of the control strategy with the aid of process

and instrumentation diagrams. Does the design support the control objective established above?

Are cascade, feedforward, ratio, and other control strategies required and applied correctly? Are

there interactive control loops? If so, how is that being handled? The control strategy should

support the control objective, given the broader process with its disturbances, nonlinearities, and

other nuances. For example, a simple feedback control loop will do an awful job if ratio control is

actually needed. Cascade control should be used only if the inner loop is much faster than the

outer loop.Feedforward control should be used to compensate for process disturbances, except

when the disturbances directly affect the flow rate through the final control element – requiring

cascade control. When done correctly, control strategies can significantly contribute to control

loop stability and responsiveness. Unfortunately, the opposite is also true.

4. Do a Plant Walk-Down. Inspect the size and layout of the process equipment and the condition

and location of the instrumentation and final control element (i.e., valve, damper, or variable

speed pump). Is everything in good condition and located in the right place? Considering the size

of the equipment, you should be able to get some sense of how fast or slow the process will

respond to controller output changes. This knowledge will help when doing step-testing.

5. Examine the Measurement Device. Ensure the process measurement is good for the

application. Is the transmitter ranged appropriately? Is this the best sensing technology for the

process conditions? Is the device installed correctly?

6. Evaluate the Use of Filtering. Check if transmitter dampening or process variable filtering is

being used. Transmitters should use an anti-aliasing filter, but no more. Filtering, if required,

should be done in the control system to simplify its adjustment and facilitate replacing the

transmitter without having to worry about filtering. Inspect a time trend of the process variable and

determine if filtering is required, and how much. If a process variable filter is used, its time

constant should be reviewed to ensure that it is set appropriately and significantly shorter than the

dominant process time constant.

7. Test the Final Control Element. An improperly working final control hurts control loop

performance and can negate proper controller tuning methods. Typical problems include

deadband, stiction, a nonlinear flow curve, and positioner problems. These problems may appear

very similar to tuning problems, and an unknowing tuner may spend many hours of futile tuning if

the problem lies with the control valve. A few simple process tests should be done to detect and

diagnose final control element problems before any tuning is attempted. These problems will have

to be resolved for optimal control performance. Also, final control element problems can

significantly skew results from process tests and cause the calculation of completely incorrect

tuning parameters.

8. Review the Controller Configuration. Modern, digital controllers offer a range of options to

optimize their performance for various situations. Setpoints can be ramped or filtered internally to

obtain a smooth control response even when the operator makes an abrupt change. Setpoint

changes can also be hidden from the proportional and derivative control modes. External reset

feedback prevents integral windup under adverse conditions, and rate-of-change limits can protect

sensitive equipment downstream. Check the controller algorithm and configurable controller

options before tuning the controller.

9. Use an Appropriate Tuning Method. Contrary to popular belief, controller tuning is much more

science than art. Loop tuning can be done quickly and accurately based on the control objective,

process characteristics, and appropriate tuning rules. Process characteristics can be determined

by making a step-change in controller output and taking measurements from the resulting process

response. Although trial-and-error tuning is popular, it should be used only as a last resort, for

example with processes that are so volatile that it is impossible to get usable step-test data. As an

alternative to manually calculating tuning parameters based on step-test results, loop tuning

software offers many helpful features such as identification of process characteristics, producing

tuning settings for different tuning objectives, providing simulations of anticipated loop response,

analyzing control loop robustness, and more. However, tuning software is only a tool, and

someone incapable of manually tuning controllers using step-test data and tuning rules will likely

also find it difficult using tuning software.

10. Tune from Multiple Step Tests. Simulations may be 100% repeatable, but real processes are

not. Process disturbances, interacting control loops, nonlinearities, and operating conditions can

all affect measured process characteristics. Tuning from only one step test can result in poor

tuning settings if the process response at that instance was not normal for whatever reason. It is

essential to do multiple step tests to obtain “average” measurements of process characteristics,

and an appreciation of how much they change under normal conditions.

11. Cater for Nonlinearities and Changing Process Characteristics. The installed flow

characteristic of a final control element is often not linear. In addition, the characteristics of many

processes change under different process conditions (production rates, equipment in service,

catalyst concentration, pH, etc.). Control valves and dampers might have to be linearized using a

characterizer, and changing process characteristics might require the scheduling of controller

parameters (called gain scheduling or adaptive tuning).

12. Validate and Test the New Values. Compare the newly calculated controller settings with the

ones in the controller, and ensure that any large differences in numbers are expected and

justifiable. Implement and test the new controller settings. Ensure the controller is tuned to work in

harmony with the dynamics of the process it is controlling, and meeting the overall control

objective of the loop. First let the loop settle out and evaluate its performance under steady

conditions. Does it oscillate? Does the controller output move too much? If the loop should

respond to setpoint changes, make a setpoint change and look for overshoot, oscillations, or too

much controller output movement. If the loop should respond to disturbances, briefly put the

controller in manual, change the output by a few percent, and immediately put the controller back

in auto. This simulates a disturbance. Again, check for unnecessary overshoot, oscillations,

excessive controller output movement. Monitor the controller’s performance periodically for a few

days after tuning to verify improved performance under different process conditions.

13. Keep Records. Make note of the previous controller settings, the new settings, and the date and

time of change. You should keep a computerized or paper-based log of all changes to a control

loop. Leave the previous controller settings with the operator in case he/she wants to revert back

to them and cannot find you to do it. If the new settings don’t work, you have probably missed

something in one or more of the practices above.

If the desired control objectives cannot be met by following these practices, including repairing faulty equipment and making changes in control strategy, model-predictive control can be investigated as a possible solution. The final and perhaps most expensive alternative would be to modify the process equipment, but this is rarely needed. In the majority of cases the solution is available in the practices listed above.

Stay tuned!

Jacques Smuts – Author of the book Process Control for Practitioners

Diagnosing and Solving Control ProblemsApril 30, 2011

While many control loops are easy to tune and present almost no control problems, a few control loops can be very problematic and never seem to control right. Control practitioners can spend many hours or even days trying to improve the performance of these challenging control loops, but the results often remain unsatisfactory. This article presents strategies for diagnosing control problems and improving the performance of challenging control loops.

Symptoms of Poor Loop PerformanceAlthough poor control performance come in many forms, it can be grouped into three categories:

Oscillations and instability – the loop tends to cycle around its set point.

Large deviations from set point – the loop struggles to remain at set point and the process

variable is frequently pushed away from set point.

Sluggish performance – the loop takes too long to get to its set point after a disturbance or set

point change.

A Control Loop with Several Problems

I’ve seen many cases where attempts to address poor performance were limited to controller tuning, because the person attending to the problem did not know of all the other causes of poor performance. To properly address and improve control loop performance, it is necessary to establish what the real cause of the poor performance is, and then to take the appropriate corrective action.

Fault DiagnosisTo guide your diagnosis efforts, a fault diagnosis tree is provided below. The first level of diagnosis is the three symptoms of poor control listed above. Depending on which of these symptoms your control loop displays, you can find the possible causes below each symptom. These are described in more depth throughout this article.

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Diagnosing Control Problems

1. OscillationsOscillations can originate from within the control loop or be caused by external factors. To find out which is the case, place the controller in manual and see if the oscillation stops. If it does, the oscillation is generated from within the loop.

Oscillations Stopping when Controller is Placed in Manual

Internal OscillationsOscillations generated internally can be caused by faulty equipment or by tuning. Check first for faulty equipment, because you can spend a long time trying to tune a loop if the real cause of poor performance is the control valve.

The most common control valve problems causing oscillations are:

Control valve stiction. Do a stiction test with the controller in manual to determine if this is the

case.

Positioner overshoot. Do step tests of various sizes and be on the lookout for signs of overshoot

in the process variable.

Both of these control valve problems and cannot be fixed by tuning the process controller. The valve needs maintenance or the positioner needs tuning.

TuningA loop that is tuned too aggressively (overly fast response) can quickly develop oscillations. Do step tests on the process and determine the dominant process characteristics (gain, dead time, lag). Do more than one step test (try to do four at least) in different directions. Then use tuning rules to calculate new controller settings. If you are using rules designed to producequarter-amplitude damping, use only half of the recommended controller gain. If you have tuning software, then use it to analyze the step-test data and calculate new controller settings.

Nonlinear valve CharacteristicMany control valves control flow differently, depending on how far they are open. The valve is said to have a nonlinear installed characteristic. If tuning is done at the one end, the settings might not work at the other end, and could cause oscillations or sluggish behavior. If this is the case, a function generator (X-Y curve) can be placed in the path of the controller output to cancel out the control valve nonlinearity.

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Nonlinear ProcessSome processes react differently based on operating point, production rate, or the product being made. If these differences are large the loop can begin oscillating or become sluggish. Then different tuning settings are required for the various operating conditions. This is called gain scheduling.

External OscillationsExternally sourced oscillations can be caused by interactions between loops with the same dynamics or simply by another loop in the process oscillating and causing several other loops to oscillate with it.

Coupled InteractionInteractions between loops with the same dynamics can cause the two loops to “fight” each other. A simple example of this is if two valves control the flow and pressure in the same pipe. Because the dynamics of liquid pressure control loops and flow control loops are similar, the two controllers might be tuned very similarly, causing the hunting between the two loops. To solve this, the most important loop needs to be tuned for fast response, and the loop of secondary importance needs to be tuned significantly slower (three times or longer settling time).

Dynamically Coupled Control Loops

Process InteractionOne loop in the process could be oscillating, causing several other loops in the same process to oscillate with it. Use a process and instrumentation diagram (P&ID) to locate possible offenders. Then use historical process trends of these other loops to find the oscillating loop. Several software vendors like ExperTune, PAS, and Matrikon/Honeywell have products to help with locating the offending loop in a plant-wide oscillation scenario.

2. SluggishnessThe next category of poor control loop performance is sluggishness. Sluggish control loop response can be caused by equipment problems or by poor tuning.

Control Valve Dead BandDead band (also called hysteresis), can cause a loop to exhibit sluggish behavior. Every time the process variable undergoes a disturbance in a different direction from the previous disturbance, the controller output has to traverse the dead band before the valve begins moving. Dead band can be detected very reliably through simple process tests. It is a mechanical problem and cannot be addressed with tuning.

Other Equipment ProblemsA control loop may also appear to have sluggish response if the controller output becomes saturated at its upper or lower limit. Similarly, if the process variable runs into limits, the control action effectively ends. Also, if the controller output has a rate-of-change limit, it may cause sluggish response, regardless of how well the controller is tuned.

Tuning

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Comments made earlier about tuning apply here too. Furthermore, realize that loops have internal “speed limits” depending mostly on the length of the dead time in the process. It will take a well-tuned loop three to four times the dead time to get back to its set point after a disturbance or set point change. If disturbances cause large deviations from set point, and tuning is unable to correct it fast enough, see the next section.

Upper Limit to Loop Speed – any faster tuning will cause larger oscillations

3. DisturbancesThe third category of poor loop performance is that of disturbances pushing the process variable away from its set point. Disturbances are frequently the nemesis of good loop performance. As described above, feedback control is limited in how fast it can eliminate the effects of a disturbance and bring the process back to set point. Two classes of disturbances exist, depending on how they enter the loop.

Control-Flow DisturbancesControl-flow disturbances affect the loop by changing the flow rate through the final control element. For example, if steam is used to heat the process flowing through a heat exchanger, and the pressure of the steam decreases, the steam flow rate will be affected and this will disturb the outlet temperature.

Cascade control can be used very effectively to virtually eliminate the effects of a control-flow disturbance. The outer loop controls the main process variable (temperature in this case) by changing the set point for flow to an inner loop. The inner loop measures and controls the actual flow rate and immediately corrects any deviations from set point.

Cascade Control for Handling Control-Flow Disturbances

Process DisturbancesIn contrast to control-flow disturbances, all other disturbances to the process that affect the process variable are simply called process disturbances. If a process disturbance is measurable, and its effect on the process variable is known, feedforward control can be used to vastly reduce its impact.

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Feedforward Control for Handling Process Disturbances


Posted in 6. Loop Performance, Problems, and Diagnostics, 9. Tips and Work-Process

6 Responses to “Diagnosing and Solving Control Problems”

Jam:


Hello,

I have a flow control valve that operates OK in automatic. This valve only really operates between 25-40%. However when the valve tries to maintain 25%, it keeps osciallating with the around the setpoint. What could be causing this? Here are my theories:

1. Valve may have a non-linear characteristic and that may need to be placed on the output of the PID – I have yet to confirm this2. Could the valve be oversized?

Are these correct and are there other factors that could be attributing to this?

Thanks

Jacques :


Jam,1. It could be that the valve has a quick-opening (nonlinear) type of flow characteristic. Is it a butterfly valve? If so, see this article: It could also be that the valve is sticky around 25% – see this article: 2. It seems that your valve is a bit oversized – control valves should ideally operate around 75% – 85% open at design flow rates.- Jacques

William Love:


In an article or post that I can’t find right now I recalled the author said you can prevent excessive valve wear by not letting the valve move unless the PID output changed by more than some amount.This idea was greeted with derision in a group discussion, so I’m trying to figure out whether the idea has any merit.

Jacques :

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As with many things in process control – it depends. If you have a noisy measurement signal, and a high-gain controller, your controller output will likely move around much more than you like and wear out the valve prematurely. You have a few options, depending on your controller’s features.1. You can filter the process variable (my preferred option), but realize that this adds additional dynamics to the loop that requires slower tuning which slows down the loop response. If your process is already a slow-responding process, the additional dynamics may go virtually unnoticed, making it a very good solution. However, if you have very low-frequency noise, you need a very long filter time-constant, which can make this an infeasible solution. (Your filter time constant should be substantially shorter than your process dead time and lag to achieve fast loop response).2. You can also set a deadband around the process variable or controller output, which brings me to your question. If apply a deadband, the controller will move the control valve only when the limit of the deadband has been reached. The wider the dead band, the less often your controller will move the valve (and make smaller movements). If you set dead band larger than the noise, the controller does not respond until there has been a significant change in the process. This effectively adds pseudo-deadtime to the loop, making the control loop behave very sluggishly. So,, for fast loop performance, just as the lag in a measurement filter should be set much shorter than your process dynamics, you should ensure that the additional deadtime added by a deadband is also much shorter than your process dynamics.3. You can also look at using a different measurement technology, if the problem is measurement noise.Also, make sure you are not using derivative control on a noisy measurement signal, and if you have to use it, consider lengthening the controller scan time to reduce the gradients the derivative term sees.

William Love:


Just to clarify, the method I’m describing involves ignoring a change in the PID output (CV)unless it is more than some amount. If the CV = 45.0 %, I would hold that number in a register and keep sending that to the valve. I’d not change that signal going to the valve until say CV 45.5% (my deadband is 0.5%). So if I saw the PID output reach 45.6%, I’d update the hold register and start sending that to the valve. Then, until CV 46.1% I would keep sending the hold register value 45.6% to the valve. Is this what you thought I was saying?

One person opined this is equivalent to putting a deadband on the error between PV and SP (which in Rockwell is implemented with a parameter called “CV Zero Crossing Deadband”.) But I’m not so sure.

Is my proposal to keep the valve at the hold value until the CV changes by more than a deadband have a history in the field. I think I got the idea from a post by Greg McMillan and thought it sounded good. To your knowledge has this been done?

Jacques :


William, thanks for clarifying what you mean.First, the 0.5% “deadband” seems far too small for reducing excessive valve wear.Second, the method you propose artificially introduces the equivalent of stiction, which is very bad for stability.I don’t know if it has been done, but I will advise against it.

Process Control for PractitionersSeptember 9, 2011

OptiControls is proud to announce the release of its flagship book, Process Control for Practitioners – How to Tune PID controllers and Optimize Control Loops. Written by Dr. Jacques F. Smuts, the author

of this blog and principal consultant of OptiControls, this new book is the ultimate practical guide to control loop optimization.

Control loop optimization is not rocket science, but it is not trivial either. To be effective in optimizing the performance industrial process control systems, an engineer or technician has to know the process and its limitations, understand process dynamics, controllers and tuning, use the right techniques and tools, and follow the optimization process systematically. He also has to know how to troubleshoot control problems to find and fix their causes.

This book conveys the knowledge and techniques required to effectively troubleshoot and improve the performance of automatic control systems. It clearly and concisely covers all the topics and know-how required for being an outstanding controls practitioner. Explanations go into enough depth to make the material understandable, but discussions are kept short so the book can serve as a reference guide. The book shows you how to tune PID controllers more effectively in less time, and ensure long-term loop stability. It is your complete reference for improving control-loop performance, solving process control problems, and designing control strategies. You will refer to this guide again and again.

If you like the content of this blog, you will love the book Process Control for Practitioners!

The book’s 315 pages and 176 figures will help you discover how easy it is to:

Understand PID controllers, their control actions, settings, and options.

Identify process dynamics and their effects on loop performance and controller tuning.

Get the best possible performance from a control loop.

Tune controllers differently to achieve specific control objectives.

Identify the root cause (or causes) of poor control performance.

Use techniques such as linearization and gain scheduling to ensure consistent loop response and

long-term stability.

Design and optimize control strategies such as cascade, feedforward, and ratio control to improve

control performance and reduce variability.

Monitor loop performance and pinpoint control problems.

This concise manual on control-loop optimization will show you the fastest, surest, and most practical ways to tune controllers and solve control problems.

Process Control for Practitioners is available at Amazon.com:

Stay tuned!Jacques Smuts

Process Control for Practitioners - Front Cover

Process Control for Practitioners - Back Cover

Posted in 9. Tips and Work-Process

Testing Control Loop PerformanceFebruary 28, 2013

After tuning a control loop, it is customary to change the setpoint to test the loop’s performance. This will certainly show you how the loop responds to setpoint changes, but will it tell you anything about how the loop might respond to process disturbances? In some cases – yes, but in other cases – no. Let me explain…

Flow loops and liquid pressure respond similarly upon setpoint changes and disturbances. If you see overshoot after a setpoint change, it means that you will likely get overshoot after a disturbance. The same can be said for no overshoot (Figure 1), sluggish response, or oscillations. This similarity applies to loops with processes that have dead times and time constants of almost the same length, such as flow and liquid pressure.

Figure 1. A flow loop approaches its setpoint after a disturbance in the same way it does after a setpoint change.

But many loops respond differently to setpoint changes versus process disturbances. The difference becomes more evident when controlling processes with long time constants relative to their dead times,

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such as temperature and gas pressure control loops. The difference is most obvious in level control loops (Figure 2).

Figure 2. A level loop overshooting its setpoint after a setpoint change, but not after recovering from a disturbance.

It is often difficult or impossible to create a process disturbance to test tuning settings. So how can we be assess the loop’s disturbance response? Here is a simple sequence you can execute to simulate a process disturbance and see how a loop will respond to it.

1. Put the controller in manual mode.

2. Change the controller output by a few percent (5% is normally a good starting point).

3. Immediately put the controller back in automatic control mode.

After Step 3, the process variable and controller output will continue in a straight line for a few moments until the change has propagated through the process dead time. The process variable will then begin to deviate from setpoint, and the controller will react to it exactly as if it was a process disturbance (Figure 3).

Figure 3. Simulating a process disturbance by quickly changing the controller output in manual and immediately putting the controller back in auto.

There are many loops that rarely undergo setpoint changes but frequently have to compensate for the effect of disturbances. This method of testing is much more representative of such a loop’s real operating conditions.

By the way, you can buy a license for the loop simulator in Figure 3 from OptiControls.

Stay tuned!

Jacques Smuts

Principal Consultant at OptiControls, and author of Process Control for Practitioners

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Tools of the TunerJuly 8, 2013

A control loop tuner should be proficient in using a variety of tools to be effective in any tuning situation. Customers often ask me how I tune loops, and my answer is that I use several tools – depending on the situation. Here is an overview of the tools I frequently use when analyzing and optimizing control loops.

Process Historian

Indispensable for much more than tuning, the process historian is one of my most-used tools. I use it to check valve linearity, analyze process interactions, compare loop performance before and after tuning, design feedforward controllers and characterizers, and to analyze the step-response of a process for tuning the controller.

Some plants where I work have no OPC connection for retrieving real-time process data, or don’t allow installing data collection software to collect real-time process data. Then their process historian is my only way to access plant data. I often analyze the step response for tuning purposes using the historian’s user interface, but if it is easy enough to export data to Excel, I will go that route and analyze the data using tuning software on my laptop.

For fast-responding loops, I ask the system administrator to speed up the sampling rate, because the default sampling interval on most historians is 30 to 60 seconds, which is too slow for analyzing fast loops. A one-second sampling interval is required for flow and liquid pressure loops, five seconds for most other loops, while 30 to 60 seconds serve only the slowest loops.

Some control loops I work on have processes that take hours to respond. In more than half of these cases I can go back in history and find sufficiently large operator-induced step changes that I can use for analysis and tuning. That saves me from having to do step tests and wait hours for the process to respond. I always try to get at least three of these step changes, but I prefer to have more if the process models change from one step-test to the next. This saves me a lot of time on slow-responding processes because the complete response is already in the historian. This also minimizes the need for disturbing the process with additional step tests.

Process Historian

Excel

When I analyze step-test data directly on the historian, I use a pre-built Excel spreadsheet to simplify the data analysis and controller tuning calculations. I take down a few readings from the historian and enter them into the spreadsheet, and it calculates the process characteristics, and recommends tuning settings. It supports self-regulating and integrating process types, and has Cohen-Coon, Ziegler-Nichols, Lambda/IMC, Dead-Time, Surge-Tank, and Level-Averaging tuning rules. It also allows me to speed up or slow down the loop response by calculating different tuning settings, based on my tuning objective. Every thing I need for my tuning calculations!











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Excel Tuning Calculator

Loop Simulation Software

Loop Explorer is a simulation and tuning software tool that I developed to give me insights into how a loop would respond to setpoint changes and disturbances. This is essential for obtaining optimal tuning settings for the loop’s control objective. The simulator is especially handy when I use the spreadsheet to analyze the step response, since the spreadsheet does not have its own simulator. I also use the Loop Explorer software in my training classes to demonstrate many concepts related to process characteristics, PID controllers, and controller tuning.

Loop Explorer Software

Tuning Software

Of course I also use commercial tuning software. I recommend that every plant who does tuning in-house invest in good tuning software and have it accessible in every control room. If I work at a plant that already has high-end tuning software installed, I use their software. Otherwise I use the tuning software I have on my laptop. High-end tuning software applications analyze process response and automatically identify process characteristics. They provide access to different tuning methods, and render simulations of loop response with the new tuning settings. They also have databases of controller types, so one doesn’t have to deal with manually converting tuning constants to suit a specific controller.

One very important point: Tuning software is just a tool and is no substitute for understanding process dynamics, PID controllers, and the tuning process. If you can’t tune control loops by manually

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determining process characteristics from step-response data, and applying an appropriate tuning rule to calculate tuning constants, you will likely not be successful with software either.

Operator Time Trends

When I do step testing, I mostly sit right next to the operator. Then we use his/her real-time trends for the control loop to monitor the response. When sitting next to the operator I can point to certain anomalies, and explain why I do certain tests. It is also a great time to get to know the operator, learn about the process he controls, and become familiar with the culture of the company.

P&ID and Operator Graphics

Before analyzing and tuning a control loop, I ask the operator to explain the process to me. He/she will often use their operator graphics to show me the streams into and out of the process, and the location of valves, pumps, heat exchangers etc. Process engineers will often give me a set of P&IDs that I refer to.

In several occasions I discovered that other interacting or subordinate loops have to be tuned first, or placed in manual, before I could attend to the loop of concern. I also find flow measurements, not being used for control, that I can trend for supplemental information on the control valve’s performance, or if there might be a need for implementing cascade control.

Operator Graphic

Pen, Paper, and Calculator

And don’t forget the traditional pen, paper and calculator. I find it handy and convenient to quickly draw a diagram on paper, take notes, or to quickly run through calculations. I would often transfer my written notes to electronic format for inclusion in my report after the day’s tuning, or while waiting for step-test results on a slow loop.

Hand Calculations


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Process Walk-Down

Whenever possible, I go out to the plant with an experienced operator or engineer to take a look at the process, equipment, and physical location and condition of the control valves and instrumentation. One time I was dealing with a vastly oversized nitrogen injection control valve that was used to control pressure on a distillation column. The loop was completely unstable, regardless of any tuning settings we tried. We tried making 0.1% steps in controller output with the controller in manual mode. Stepping the controller output upwards from 1.5% to 2.4% the column pressure showed no response (no physical change in valve opening), but at 2.5% the pressure sharply decreased. When the operator and I went out to the valve and radioed back to the control room to repeat the test, we noticed that the valve position bumped by about 5% instead of the 0.1% change in controller output. We would never have known this if we did not go to the valve. After the faulty positioner was replaced we could stabilize the loop. (However, control was still poor because the valve was grossly oversized.)

Process Walkdown

Literature

I have several really good books on process control, instrumentation, control valves, processes, PID controllers, and tuning. Some of them are academically inclined, making them virtually useless for tuning controllers in real plants. But some others are much more practical in nature. The latter is obviously more suitable for practitioners. I track the sales of eight of these practical books on amazon.com and the top seller, Process Control for Practitioners, has sold more copies over the last two years than the next three books together.

Summary

Even though I am a big proponent of tuning software, it is not the only tool available for analyzing and tuning control loops. It is important to consider the situation, and use the most appropriate tool or technique for analyzing and optimizing control loops – even if it comes down to doing manual calculations on a piece of paper.

Stay tuned,

Jacques Smuts

Principal Consultant at OptiControls and author of the book Process Control for Practitioners

Posted in 1. General, 9. Tips and Work-Process

Tuning Tips – How to Improve Your ResultsFebruary 9, 2011

I have read several posts on LinkedIn where the writers state that tuning rules don’t work. Well, I politely argue that it is not the rules that don’t work. You have to know how to apply the rules properly and what to expect from them. It’s not rocket science, but if you miss a piece, your calculated tuning settings might not work. So I provide this checklist with tips to give you a better understanding of what’s involved with tuning a controller. Hopefully it will improve your results.


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Valve Performance

Is the control valve working properly? (See blog on control valve problems.) Dead band can severely affect your step-test results. Stiction and positioner overshoot can cause oscillations regardless of how well the controller is tuned.

Execute specific tests that check for dead band, stiction, and positioner overshoot in the control valve.

Step-test Procedure

Begin with a steady process variable and make a step-change large enough that the process variable’s response is clearly visible above the noise/disturbance level. A good rule-of-thumb is that the process variable must move five times as much as the peak-to-peak noise/disturbance level. You have to make measurements, and if the signal-to-noise ratio is too low (step too small) major errors could be made. If you can’t get the process variable steady enough you may have problems elsewhere that should be addressed first. There is aprocedure for step-testing at this blog.

Also, do multiple step-tests so that you can compare the calculations from different step tests with each other. If you do just one step-test, you won’t know if a disturbance affected the process during your test. For most loops I do four step tests. I have had to do more than a dozen step tests on some volatile processes to get good average values for process response. Take the time, and get good results.

Step-Test Measurements

Make sure you know how to measure process gain, dead time and time constant from a process response curve. Do this for each step test. An Excel spreadsheet could help if you don’t have tuning software. Compare the numbers from each step test, remove outliers, take the average of the remaining values.

Process Dynamic Response to a Step Test

Time Base

All the popular tuning rules assume that you are making time measurements in the same units as those used by your controller. Are your controller’s integral and derivative time settings in minutes or seconds? Convert your measured values to match you integral and derivative time units, if necessary.

Scaling

All tuning rules assume the process variable and controller output measurements are normalized. That means that changes in process variable have to be divided by the span of the measurement device, and changes in controller output have to be divided by the span of the controller output. The latter is normally 0% to 100%, but on some DCSs the controller output range can be different for outer loops in cascade control to match the range of the process variable.

Tuning Rule, Robustness, and Control Objective

The Ziegler-Nichols tuning rules were designed to provide ¼-amplitude decay, which is undesirable for most processes. The control loop is also not very robust – it can easily go unstable if the process gain or dead time increases. These two problems can easily be solved by dividing the calculated controller gain by two. Note that the Ziegler-Nichols tuning rules result in sluggish loops if the process dead time is longer than the time constant. See my comments on Z-N tuning rules for more detail.

The Cohen-Coon rules were also designed to provide ¼-amplitude decay, and have the same robustness problem as the Ziegler-Nichols rules. These can easily be solved by dividing the calculated controller gain by two.

Minimum IAE tuning rules give something close to ¼-amplitude decay, and have the same robustness problem as the Ziegler-Nichols and Cohen-Coon rules. The solution is to divide the calculated controller gain by two.







The Chien-Hrones-Reswick (CHR) tuning rules come in two sets, one for 20% overshoot (not recommended for most processes because of overshoot and low robustness) and a 0% overshoot rule (which is more robust and okay to use). Note that the CHR tuning rules result in sluggish loop response if the process dead time is longer than the time constant.

The Lambda and Internal Model Control (IMC) tuning rules give very stable response (robust control loops), and no overshoot if applied correctly. But loops with long time constants respond sluggishly to disturbances. See blog on Lambda tuning for more detail.

High-end tuning software should allow you to select your tuning objective, and calculate tuning settings accordingly. High-end tuning software should also warn you when calculated settings will result in a control loop with low robustness.

Controller Algorithm

Some tuning rules (like Ziegler-Nichols) have been developed for interactive PID algorithms, while others (like minimum IAE) have been developed for noninteractive algorithms. There are conversions available to go from PID settings on one type to the other. Note that if you don’t use derivative (most people don’t), there is no difference between interactive and noninteractive algorithms. See this article on controller algorithms.

A few DCSs and PLCs have parallel controller algorithms, and you have to convert your calculated integral and derivative settings for use on a parallel algorithm.

Integral’s Unit of Measure

All popular tuning rules assume your controller’s integral setting is in units of time (as in minutes or seconds), and not the inverse (as in repeats per minute or repeats per second). Invert the calculated integral time if necessary.

Controller Gain’s Unit of Measure

All popular tuning rules assume your controller has controller gain, and not proportional band. Does your controller use proportional band or gain? Convert your calculated controller gain to proportional band if necessary.

Process Linearity

Tuning rules assume your process gain, dead time, and time constant don’t ever change. If you have a process where these numbers change significantly (increase more than 50% or decrease more than 33%), this could severely affect loop response and stability. You should consider linearizing the final control element or measurement, or implement controller gain scheduling. (And you can schedule integral and derivative time too – it’s still called gain scheduling).

Tools

Your effectiveness and results will not only depend on what you know about controllers, tuning, and the process you are controlling, but also on what tools you are using.

Tuning software automatically identifies the process model, calculates controller settings that match the controller algorithm and its units of measure, and provides simulations of expected loop response after tuning. This can be well worth the money you pay for a software tool.

Manual tuning (not using software) can be greatly simplified by using an Excel spreadsheet to help calculate process model parameters and controller settings. If you are not using software, take the time and compile a spreadsheet to help you.

Let me know if you have questions or need more information.


When to Use which Tuning RuleDecember 29, 2012

There are more than 400 tuning rules for PI and PID controllers [1]. How can one possibly choose the best or most appropriate tuning rule from all of these? To simplify matters, the main differences between the tuning rules can be grouped into four categories:

1. Type of process





2. Tuning objective

3. Process information required

4. Type of controller

Most of the tuning rules apply to first-order plus dead time (self-regulating) and integrator plus dead time (integrating) process types. These two process types adequately cover the vast majority of control loops in process plants. Other tuning rules apply to higher-order, oscillating, or unstable processes. Most of the documented tuning rules apply only to processes with dominant time constants. This limits their practical application. The Cohen-Coon tuning rules are an exception.

Tuning objectives include quarter-amplitude damping, minimization of some error integral, a specific percentage overshoot, critically damped, robust tuning, and a specified closed-loop time constant. It is rare to find a tuning rule with an adjustable tuning factor that allows you to change the speed of response. The IMC / Lambda tuning rules are one exception.

The process information required for the tuning rules based on first-order plus dead time and integrator plus dead time process types can be obtained by doing process step tests. A few tuning rules are based on the ultimate cycling or relay tuning methods. Many of the academic tuning rules are based on high-order process models, but they never tell you how to obtain the process model; they just base the tuning on some fictitious model chosen by the author, which largely makes them useless for practical application.

Most tuning-rule authors developed tuning rules for both PI and PID controllers, but with no guidance when to use which one. Some PID tuning rules apply to the interactive algorithm, while most apply to the noninteractive algorithm. It is reasonably easy to convert from one type to the other.

To reduce all these complexities to something we can work with on most control loops, we can consider two process types (self-regulating and integrating), and two tuning objectives (fast and slow or very robust). And ideally we need an easy tuning factor to adjust the speed of response.

When to Use Which Tuning Rule

You could probably use any of the 400 tuning rules, as long as it applies to your situation. I have successfully tuned most (but not all) control loops using just a few tuning rules. Here is what I recommend for most loops:

For self-regulating processes, use the Cohen-Coon PI tuning rule with the following exceptions:

Use a stability margin of two or more to improve robustness and adjust speed of response.

If td > 4tau, use the tuning rule for dead-time-dominant processes.

If you find it difficult to accurately measure the dead time, use the Lambda tuning rule.

If you want the loop to have a specific speed of response, use the Lambda tuning rule.

If you want the loop to absorb disturbances rather than pass them on to the next process, use

the Lambda tuning rule with the closed loop time constant set three tomes the open loop time

constant.

Use the derivative control mode (PID tuning rule) only when you need every last bit of speed, and

then only when the process lends itself well to the use of derivative.

For integrating processes, use the Ziegler-Nichols tuning rule, except for surge tanks andlevel averaging, where you should use the two tuning rules named after these control objectives.

Fast Response Slow / Robust ResponseSelf-Regulating Process

Cohen-Coon (adjust the stability margin (SM) to change the speed of response)

Lambda (adjust the closed-loop time constant to change the speed of response)

Integrating Process

Ziegler-Nichols (adjust the stability margin (SM) to change the speed of response)

Level-averaging (adjust the specification for maximum deviation from setpoint)

If you use a PID tuning rule and an interactive controller algorithm, or a controller with theparallel algorithm, remember to convert the calculated tuning parameters to ones suitable for your controller

algorithm. Also remember to measure your process characteristics in the same time-units your controller’s integral uses. And remember to integral time to integral gain – if that is what your controller uses. Finally, when tuning any control loop, watch out for control valve problems.

You can find much more information in my book Process Control for Practitioners.

Stay tuned!

Jacques Smuts

Principal Consultant – OptiControls

Reference

1. O’Dwyer, A Summary of PI and PID Controller Tuning Rules for Processes with Time Delay. Part

1: PI Controller Tuning Rules, Proceedings of PID ’00: IFAC Workshop on Digital Control,

Terrassa, Spain, April 4-7, 2000, pp. 175-180.

Why Tuning Rules Don’t Always WorkJanuary 7, 2011

There are several reasons why PID controller tuning rules don’t always work as advertised. I have talked to several process control practitioners who tried them once or twice, but had no success and gave up on using them as a result. Here is a list of items to consider when using tuning rules.

ZIEGLER-NICHOLS TUNING RULESThe Ziegler-Nichols are the oldest and most popular tuning rules. They developed two methods: the Process Reaction-Curve or Open-Loop method (done with controller in manual) and the Ultimate-Cycling or Closed-Loop method (controller in automatic).

The Ziegler-Nichols open-loop tuning rules have several drawbacks:

Issue 1: It tunes the loop for quarter-amplitude-damping response, which overshoots and oscillates quite a bit.

Issue 2: It leaves the loop with very little robustness, which can lead to loop instability.

Issue 3: The rules give you very poor response if the process is dead-time dominant.

Issue 4: The rules are very sensitive to an accurate measurement of dead time, which is difficult on lag-dominant processes with short dead times.

The Ziegler-Nichols closed-loop tuning method does a little better with issues 3 and 4 above, but issues 1 and 2 remain a problem. In addition, this method is very sensitive to control valve problems like dead band or stiction. More info here: http://blog.opticontrols.com/archives/39

Issue 1 and 2 (and 4 to some degree) can be alleviated by using only half or less of the calculated controller gain.

COHEN-COON and OTHERSThe Cohen-Coon and many other open loop tuning rules do much better with issue 3, but issues 1, 2 and 4 are still problems. Again, these can be resolved by detuning the controller gain.

LAMBDA TUNING RULESLambda tuning rules give you a stable response with no overshoot, and leave the loop with plenty of robustness to accommodate measurement errors. So it seems like Lambda tuning rules overcome all of the four issues listed above. However, these rules result in a very slow response to disturbances on lag-dominant processes. More info here:http://blog.opticontrols.com/archives/260

CONTROLLER ALGORITHMSIf your controller algorithm and units of measure are not matched with the tuning rule you use, the results can be undesirable, or even dangerous.

Of the PID tuning rules mentioned above, the Ziegler-Nichols rules were developed for controllers with an interactive (series) controller algorithm, while Cohen-Coon and Lambda rules were developed for noninteractive (a.k.a. standard or ideal) controllers. The PI tuning rules (no derivative) will work on both interactive and non-interactive algorithms, while PID may require parameter conversion. If you detune the controller like explained above, the difference between interactive and noninteractive algorithms becomes much less important.

However, if you have a controller with a parallel algorithm, you definitely have to convert the calculated settings to work with it. More info here: http://blog.opticontrols.com/archives/124

And note that most tuning rules calculate controller gain, and not proportional band. And most calculate integral time (as in minutes or seconds), and not integral gain (as in repeats per minute or repeats per second). Make sure you convert the tuning settings to work on your controller.

Finally, the rules assume you are making the measurements of dead time and time constant in the same time-base used by your controller’s integral and derivative settings, i.e. minutes versus seconds. If you measure in seconds, but the controller uses minutes, you have to convert your measurements to minutes before calculating tuning settings.

CONTROLLER SCAN INTERVALTuning rules assume controllers are analog in nature – that they continuously sample the process variable and calculate an output. However, modern controllers are digital, and execute their task intermittently at a rate called the scan interval, execution period, or something similar. Controllers typically execute at 1-second intervals, but this could be much faster or slower, depending on the application.

Intermittently scanning and executing at a 1-second interval is normally not a problem for slow loops like temperature, gas pressure, level, and composition. However for fast loops like flow, liquid pressure, and motor speed, a 1-second scan interval can add a substantial proportion of dead time to the loop. If this extra dead time is ignored in the tuning rule, controller settings will be too aggressive, possibly leading to oscillations and instability on fast loops.

OTHER PROBLEMSAnother reason why tuning rules fail to deliver on our expectation could be that the control valve or damper might be defective. This includes problems like dead band and stiction. These problems can invalidate the results you get from a step test, and affects the loop performance of even a well-tuned loop. More information here:http://blog.opticontrols.com/archives/77

WHICH RULE TO USEYou should select the tuning rule according to the desired control objective for the loop, while considering the constraints above:

- If you need a very stable loop that absorbs disturbances rather than passing them on, use the Lambda tuning rules.

- If you need fast recovery from disturbances, use the Cohen Coon tuning rules, but use only half of the rule-calculated value for controller gain to overcome issues 1 and 2. However, if the process dead-time is very short (issue 4), or the PV is noisy and you can’t measure the dead time accurately, use the Lambda tuning rules.

TUNING SOFTWAREHigh-end tuning software packages can diagnose control valve problems such as dead band and stiction. They also let you specify the control objective and your controller type. They can then produce appropriate tuning settings after analyzing the process response from a step-test.


Posted in 9. Tips and Work-Process

2 Responses to “Why Tuning Rules Don’t Always Work”

Arkadiy Turevskiy:

April 27, 2011 at 2:24 pm

Thanks for the nice overview.When designing controllers (any controllers in general, including PID controllers speciically), it is a good idea to create a good plant model and to simulate your design in software before trying it on the actual process.Here is a page we put together with a comprehensive set of resources for tuning, simulating, and implementing PID controllers in MATLAB and Simulink:http://www.mathworks.com/discovery/pid-control.html

Jacques :

April 27, 2011 at 2:54 pm

Arkadiy, I totally agree with you. Without a process model, you’re tuning in the dark, and simulations help you see the effect of your changes before actually implementing them in the process. While aerospace and other high-tech industries often use more complex models and controllers, for most industrial processes, a simple first order + dead time model and PI or PID control are often sufficient.

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