Automatic Controllers & Control Modes

8/13/2019 Automatic Controllers & Control Modes

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Unit 2

Automatic Controllers & Control Modes


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A Control System is an arrangement of physical components

connected/related in such a manner as to command, direct or regulate itself

or another system.

A Control System consists of subsystems and processes (or plants)

assembled to control the outputs of a process.

What Is Control System?


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1) If the aim is to maintain a physical variable at some fixed value when thereare disturbances, this is called as regulator.Example: speed-control system on the ac generators of power utilitycompanies.

2) The second class is the servomechanism. This is a control system in which aphysical variable is required to follow (track) some desired time function.Example: an automatic aircraft landing system, or a robot arm designed tofollow a required path in space.

Classification Of Control System


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Process control operations are performed automatically by either open-loop or closed-loop systems.

Processes controlled only by set-point commands without feedback are

open-loop.

Open-loop systems are used in applications where simple processes are

performed.

Open-loop systems are relatively inexpensive.

Open-Loop Control System

Set Point Controller Process

Block Diagram of open loop control system


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Closed-Loop Control System

Closed-loop control systems are more effective than open-loop systems.

With the addition of a feedback loop they become self-regulating.

Components of a closed-loop system include:

I. The primary element sensor

II. The controlled variable

III. The measured variable

IV. The control signal

V. The final correcting element


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Block Diagram Of Closed loop Control System

SETPOINT

ERRORDETECTOR

ERRORSIGNAL CONTROLLER CONTROL

SIGNAL

ACTUATOR & FINALCONTROL ELEMENT

SENSOR(FEEDBACKELEMENT)

FEEDBACK

PROCESSCONTROLLED

VARIABLE

ACTION


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Process

Complex assembly of phenomenon that refers to some manufacturing

sequence. It utilizes the resources to produce certain product.

Many variables may be involved in such a process, some of which have

to be controlled.

Classification of processes.

Process

Based on variables Based on operation

to be controlled

Batch(sequential) Continuous

Single variable Multi variable process process

process process


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Process Behavior The objective of process control is to cause a controlled variable to

remain at a constant value at or near some desired set-point.

The controlled variable changes because of:1. A disturbance appears2. Load demands varies or3. Set points are adjusted.

Several process variables are controlled at once in a typical productionmachine.

Usually, only one individual feedback loop is required to control eachvariable.

Single-variable control loops consist of the following elements:o Measuring deviceo Transducer/transmittero Controllero Final Control Element


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Process Behavior Example

Flow through the pipe

is theprocess.

Fluid flow rate is the

controlled variable.

Valve position is

the set point.

Demand for the fluid

downstream is the load.

Variance in upstream

pressure is the disturbance.


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Sensor (Feedback Element)

It is the eye of the system.

Produces output that represents the status of the controlled variable.

The output of the sensor is called as feedback.

Examples of sensors used in process control are

Thermal sensors like RTD, Thermistor, Thermocouple etc.

Level sensors like Ultrasonic, Float, Radiation sensor etc.

Pressure sensors like Diaphragm, Bourdon tube, Bellows etc.

Flow sensors like Ventury meter, magnetic flow meter etc.

Optical sensors based on LED, LASER and Photodiode, Phototransistor.


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Pressure

Level

Flow

Temperature

pH

Humidity

Density

Speed

Thermocouples

RTDs / Thermistors

Filled Systems

Bi-metallic

Strain gauge

Piezo-electric

Capacitance

Bourdon Tube

Head meters

(orifice, venturi)

Coriolis Mass,

velocity,

Mechanical Floats

Guided Wave

Weight (load cell)

Ultrasonic

Static Pressure

Transmitters

Pressure Transmitter

Level Transmitter

Differential Pressure

Cell

Flow Transmitter

Temperature

Transmitter

Type of Signals

Pneumatic

3-15 PSI

Electrical

Current

4 20 mA

0 20 mA10 50 mA

Voltage

05 V

1 5 V

0 10 V

igitalON/OFF

Field Bus

ModBus

ProfiBus

Feedback Elements(Sensors)


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Error Detector

Compares set point(reference signal) with the feedback signal.

Produces error signal for the controller.

Error = Set point feedback signal

Examples of devices used as error detector are

OP-AMP based differential amplifier for analog signals.

Comparison soft wares for digital signals.


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Controller

The controller is the brain of the system.

Receives error signal and develops output that causes the controlled

variable to become equal to the set point value.

Examples of controller PLC, Microprocessor, OP-AMP based controller.

Different modes of controller areController modes

Discontinuous mode Continuous mode

Two position controller Proportional controller

Multiposition controller Proportional Integral controller

Floating controller Proportional Derivative

controller

Proportional Integral Derivative

controller


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Selection of a Controller

Controllers are designed to operate by using different control modes. Each ofthese modes has specific characteristics to provide different types of control

actions.

These control modes are:

1. On/Off2. Proportional3. Integral4. Derivative

The mode or combination of modes which is selected by the designer

is determined by the requirement of the process


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On-Off Controller (2 position controller)

Used for slow acting operationswhere lag is unavoidable.

Final correcting element is either

fully-on or fully-off.

The primary drawback of on-off

control is the rapid switching of the final

control element.

On-off differential or hysteresis

is programmed into the controllerto reduce cycling.

Dead band refers to the differing levels

at which a controller switches on and off


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On-Off Controller (2 position controller)The analytical equation for On-Off controller is given as

P= 0 % Ep < 0P= 100 % Ep > 0

Applications of On-Off controller: It is best adapted to large scale systems

with relatively slow process rates. Examples of such process are

1. Room heating or air conditioning system

2. Liquid bath temperature control

3. Level control in large volume tanks.


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Continuous Control

On/Off control is acceptable for process where the variable is setbetween two limits.

For processes where the variable needs to be kept at particular set point

level, proportional control is used.

Proportional action can be accomplished in two ways:

Time Proportioning Method

Amplitude Proportional Method


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Time Proportioning

Is a method whereby the output of the controller is continually switched

on and off. This method is also called as PWM(Pulse Width Modulation).

Here the ratio of On time to Off time called as duty cycle is varied as per

the changes in the feedback signal.

On versus off times are varied dependent upon process requirements.

Example: Speed control of DC Motor .


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Amplitude Proportional

Most common technique to produce a proportional signal.

The control signal is proportional in amplitude to the error signal.

The signal may be amplified and the amplification may be referred to as

proportional gain andproportional band.


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Proportional Control Smooth relationship exists between the controller output and the error.

P= Kp Ep + PoWhere Kp- Proportional gain between error and the controller output

Po- Controller output without error

The range of error to cover 0% to 100% controller output is called asproportional band.

PB = 100/ Kp

Disadvantage of proportional controller is offset or SSE or residual error.

The offset error limits use of proportional mode to only a few casesparticularly where manual reset of the operating point is available to reset

the offset.

It is generally used in process where large load changes are unlikely or withmoderate to small process lag times.


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Characteristics of Proportional Controller


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Offset Error


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Integral Control

Because of the introduction of offset in a control process, proportional

control alone is not used. It is often used in conjunction with Integralcontrol.

Offset is the difference between set point and the measured value after

corrective action has taken place.


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Integral ControlThe offset error of the proportional mode occurs because the controller can not

adapt to changing external conditions i.e. changing loads. In other words the zero

error output is a fixed value.

The Integral mode eliminates this problem by allowing the controller to adapt to

changing external conditions by changing zero error output.

Integral action is provided by summing the error over time, multiplying that sum

by a gain and adding the result to present controller output.


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Integral mode controller action the rate of output change depends on the error.


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Characteristics of Integral Controller


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Derivative Mode

For rapid load changes, the derivative

mode is typically used to prevent

oscillation in a process system.

The derivative mode responds to the

rate of change of the error signal rather

than its amplitude.

Derivative mode is never used by

itself, but in combination with

other modes.

Derivative action cannot remove offset.

P(t) = KD (dEp / dt)


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The Derivative mode must be used with great care and usually with a small

gain, because a rapid change of error can cause very large, sudden changes of

controller output which can lead to instability.

Derivative controller is not used alone because it provides no output when the

error is constant.

It is also called as rate controller or anticipatory control as it can take an action

in advance depending upon the rate of error change.


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Characteristics Of Derivative Controller


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Limitations of Derivative ControlThe derivative mode acts upon the rate of error signal change and it may cause

unnecessary upsets.

It tends to react to sudden set point changes and will amplify noise.

The control algorithm can be altered so that derivative acts on the

measurement and not on the error. This will reduce upsets.

Excessive noise and step changes in the measurements can be corrected by

filtering out any change in the measurement that occurs faster than the maximum

speed of response of the process.

DCS system provides software with adjustable filters for each variable.

The time constant of these filters is usually adjusted from 0 to 100 seconds.

In analog system Inverse Derivative control mode is often used.


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Inverse Derivative Control ModeThis control action is used on fast processes. The inverse derivative mode is

opposite of the derivative mode.

While the output of Derivative mode is directly proportional to the rate of

change in error, the output of inverse derivative mode is inversely proportional to

the rate of change in the error.

Inverse derivative is used to reduce the gain of the controller at high frequenciesand is useful in stabilizing the control loop.

The dynamic gain of the derivative function is selected to be 0.5 or less.

The gain of the inverse derivative controller decreases from the proportional gain

at low frequency to the limiting value of the proportional gain divided by this factor

at high frequency.

A proportional plus inverse derivative controller provides high gain to minimize

offset at low frequency and low gain to stabilize the loop at high frequency.


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Inverse derivative can be added to PI Controller to stabilize the loops requiring

very low proportional gains for stability.

Inverse derivative should only be added when the loop is unstable at theminimum gain setting of the PI Controller.

It is available in the separate unit can be added to the loop when stability

problem occurs.

The addition of inverse derivative when proportionally tuned has little effect on

the natural frequency of the loop.


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Proportional Integral (PI) Control Combines proportional and integral mode together and eliminates the offset

inherent in proportional controller.

However makes the action sluggish and increases the response time.

Another disadvantage of this system is that during start up of the batch process

the integral action causes a considerable overshoot of the error and the output

before settling to the operation point.


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Characteristics of PI Controller


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Proportional Derivative (PD) Control

It involves the serial (cascaded) use of the proportional and derivative modes.

The analytical expression for this mode is given as

This controller cannot eliminate the offset of proportional controllers , however it

can handle fast process load changes.


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Characteristics of PD Control


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Proportional Integral and Derivative (PID) control

One of the most powerful but complex controller mode operations combines theproportional, integral and derivative modes.

The system can be used for virtually any process condition.

The analytical expression is

This mode eliminates the offset of the proportional mode and still provides fastresponse.


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PID controller characteristics


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Control Mode Summary

Control System Design Process


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Electronic Controllers1. On Off Controller with dead band

Here VH = Vsp and VL= Vsp- (R1/R2) Vo


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2. Proportional Controller

We know that for proportional mode

p = KPEP+ PO

For implementation of electronic controller we have

Vout = GpVe+ VO

Where GP = R2/R1 = Gain of the controller

A li ti f ti l t l f F t t t l


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Application of proportional control for Furnace temperature control

Application of proportional control for Robot Arm control


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Application of proportional control for Robot Arm control


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3. Proportional Integral Controller

We know that the control mode equation for this mode is given as

For electronic implementation we have

Where Proportional gain = R2/R1

Integral gain = 1/ R2.C


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Proportional Integral Controller


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Application of Proportional Integral Controller to Robot arm control

4 P i l D i i C ll


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4. Proportional Derivative Controller

We know that for the PD Control mode the equation is given as


Where Proportional gain = R2/(R1+R3)

Derivative gain = R3.C


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Proportional Derivative Controller

5 P ti l I t l D i ti C t ll


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5. Proportional Integral Derivative Controller

We know that for PID the analytical expression is given as


Where Proportional gain= R2/R1

Integral gain = 1/RI. CI

Derivative gain = RD . CD

P ti l I t l D i ti C t ll


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Proportional Integral Derivative Controller

Application of Proportional Integral Derivative Controller for Robot Arm Control


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Application of Proportional Integral Derivative Controller for Robot Arm Control

P i R l


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Pneumatic Relay Also called as pneumatic amplifier or booster. It raises the pressure and /or air

flow volume by some linearly proportional amount from the input signal.


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Nozzle/Flapper systemIt is used to convert the pressure to mechanical motion and vice versa.


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Current to pressure converters The I/P Converter is an important element in process control and used to signal

condition the output of controller to equivalent pressure signal.

P ti C t ll


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Pneumatic Controllers

The pneumatic controller is based on the nozzle/flapper system.

Here also we can implement different control modes.

1. Proportional Controller

Pout= (x1/x2)* (A1/A2)*(Pin-Psp) + Po

Where Kp= (x1/x2)* (A1/A2)


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Pneumatic Proportional mode

2 Proportional Integral controller


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2. Proportional Integral controller

3 Proportional Derivative Controller


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3. Proportional Derivative Controller

4. Proportional Integral Derivative Controller


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p g


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Final Control Operation

Control signalSignal

conditioning

Actuator

(motor)

Final control

element(valve)

Process


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Control Systems in Robotics Perspective


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The Future of Control Systems

Tuning the Controller


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Tuning the Controller

Fine-tuning is the process to optimize the controller operation byadjusting the following settings:Gain setting (proportional mode)Reset rate (integral mode)Rate (derivative mode)

Three steps are taken when tuning a systems1. Study the control loop2. Obtain clearance for tuning procedures3. Confirm the correction operation of the system components

T i l d E T i


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Trial-and-Error Tuning

Does not use mathematical methods, instead a chart recorder is used and

several bump testsare made in the proportional and integral modes.

Trial-and-error tuning is very time consuming and requires considerable

experience on the part of the technician or operator.

Ziegler-Nichols Tuning Methods

Two formal procedures for tuning control loops:

1. Continuous cycling method

2. Reaction curve method

Continuous Cycling Method


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Continuous Cycling MethodThe continuous cycling method analyzes the process by forcing the controlled variableto oscillate in even, continuous cycles.

The time duration of one cycle is called an ultimate period. The proportional settingthat causes the cycling is called the ultimate proportional value.

These two values are then used in mathematical formulas to calculate the controllersettings.

Ziegler-Nichols Reaction Curve Tuning Method


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Ziegler Nichols Reaction Curve Tuning Method

This method avoids the forced oscillations that are found in the continuous cycletuning method.

Cycling should be avoided if the process is hazardous or critical.

This method uses step changesand the rate at which the process reacts isrecorded.

The graph produces three different values used in mathematical calculations todetermine the proper controller settings.

This method is applicable only to processes with self regulation characteristics.

From the response curve the following parameters are calculated

L: Lag time in minutesCp : Controlled variable change in %T : Process reaction time in minutesN = Cp / T = Process reaction rate in % / min.


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The calculations for Ziegler Nichols Process reaction method are

Mode Kp Ti = 1/ Ki Td = 1/ KdProportional P/ NL

Proportional

Integral (PI)

0.9 P/ NL 3.33 L

ProportionalIntegral

Derivative (PID)

1.2 P/ NL 2L 0.5 L

Frequency Response Method


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Frequency Response MethodThis method involves use of Bode Plot for the process and control loops.

The method is based on the application of the Bode plot stability criterion and

the effects that the proportional gain, integral time and derivative time have on the

Bode plot.

Bode plot stability criterion

1. If the phase is less than 140 degrees at the unity gain frequency the system is

stable. This then is 40 degrees phase margin from the limiting value of 180degrees .

2. If the gain is 5 dB below unity when the phase lag is 180 degrees the system is

stable. This is then 5 dB gain margin.

Tuning : The operations of tuning using frequency response method involveadjustments of the controller parameters until the stability is proved by the

appropriate phase and gain margins.

Proportional Action : Multiplies gain curve by a constant and no effect on phase.

Integral Action : Integral gain= Ki/ and Integral phase = - 90 degrees (lag)

Derivative Action : Derivative gain = Kd*

and Derivative phase=90 degrees (lead)


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Automatic Controllers & Control Modes