Class 37 inferential control, gain scheduling

ICE401: PROCESS INSTRUMENTATION

AND CONTROL

Class 37

Inferential Control, Gain Scheduling

Dr. S. Meenatchisundaram

Email: [email protected]

Process Instrumentation and Control (ICE 401)

Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015

Inferential Control:



• In some control applications, the process variable that is to be

controlled cannot be conveniently measured on-line.

• For example, product composition measurement may require that a

sample be sent to the plant analytical laboratory from time to time.

• In this situation, measurements of the controlled variable may not be

available frequently enough or quickly enough to be used for feedback

control.

• One solution to this problem is to employ inferential control, where

process measurements that can be obtained more rapidly are used

with a mathematical model, sometimes called a soft sensor, to infer

the value of the controlled variable.







• Above figure shows the general structure of an inferential controller.

• X is the secondary measurement, which is available on a nearly

continuous basis (fast sampling), while Y is the primary

measurement, which is obtained intermittently and less frequently

(e.g., off-line laboratory sample analysis).

• Note that X and/or Y can be used for control. One type of nonlinear

model that could be used as a soft sensor is a neural network.

• The inferential model is obtained by analyzing and fitting

accumulated X and Y data.

• Dynamic linear or nonlinear models (called observers) can also be

used for inferential control.










• Inferential control was originally used to solve the problem

caused by non-measurable main output and disturbance, and

the basic method was later widely used in the process with

measurable output and non-measurable disturbance; then the

inferential control under the condition of measurable output is

formed.

• Under the condition that output is measurable and disturbance is

immeasurable, the block diagram of inferential control system

can be simplified as in Fig.




Nonlinear Control Systems:



• Most physical processes exhibit nonlinear behavior to some

degree.

• However, linear control techniques such as conventional PID

control are still very effective if

(1) the nonlinearities are rather mild or

(2) a highly nonlinear process operates over a narrow

range of conditions.

• For some highly nonlinear processes, the second condition is

not satisfied and as a result, linear control strategies may not be

adequate. For these situations, nonlinear control strategies can

provide significant improvements over PID control.




• Three types of nonlinear control strategies are essentially

enhancements of single loop feedback control:

1. Nonlinear modifications of standard PID control algorithms

2. Nonlinear transformations of input or output variables

3. Controller parameter scheduling such as gain scheduling

• As one example of Method 1, standard PID control laws can be

modified by making the controller gain a function of the

control error.

• For example, the controller gain can be higher for larger errors and

smaller for small errors by making the controller gain vary

linearly with the absolute value of the error signal.




• where Kco and a are constants.

• The resulting controller is sometimes referred to as an error-

squared controller, because the controller output is proportional

to mod of e(t).

• Error-squared controllers have been used for level control in

surge vessels where it is desirable to take stronger action as the

level approaches high or low limits.

• However, care should be exercised when the error signal is

noisy.

(1 ( ) )c co

K K a e t= +




• The design objective for Method 2 is to make the closed-loop

operation as linear as possible.

• If successful, this general approach allows the process to be

controlled over a wider range of operating conditions and in a

more predictable manner.

• One approach uses simple linear transformations of input or output

variables.

• Common applications include using the logarithm of a product

composition as the controlled variable for high-purity distillation

columns or adjusting the ratio of feed flow rates in blending

problems.




• The major limitation of this approach is that it is difficult to

generalize, because the appropriate variable transformations are

application -specific.

• In Method 3, controller parameter scheduling, one or more

controller settings are adjusted automatically based on the

measured value of a scheduling variable.

• Adjustment of the controller gain, gain scheduling, is the most

common method.

• The scheduling variable is usually the controlled variable or set

point, but it could be the manipulated variable or some other

measured variable.




• Usually, only the controller gain is adjusted, because many

industrial processes exhibit variable steady-state gains but

relatively constant dynamics.

• The scheduling variable is usually a process variable that changes

slowly, such as a controlled variable, rather than one that

changes rapidly, such as a manipulated variable.

• To develop a parameter-scheduled controller, it is necessary to

decide how the controller settings should be adjusted as the

scheduling variable(s) change.

• Three general strategies are:




a) The controller parameters vary continuously with the scheduling

variable.

b) One or more scheduling variables are divided into regions where

the process characteristics are quite different. Different controller

settings can be assigned to each region.

c) The current controller settings are based on the value of the

scheduling variable and interpolation of the settings for the

different regions. Thus Method (c) is a combination of

methods (a) and (b). It is similar to fuzzy logic control.

Gain Scheduling:



• The most widely-used type of controller parameter scheduling

is gain scheduling. A simple version has a piecewise constant

controller gain that varies with a single scheduling variable, the

error signal e:

Kc = Kcl for e1 ≤ e < e2

Kc = Kc2 for e2 ≤ e < e3

Kc = Kc3 for e3 ≤ e ≤ e4

Gain Scheduling:



Fuzzy logic control (FLC):



• Fuzzy logic control (FLC) is a feedback control technique that

utilizes qualitative information through using verbal or

linguistic rules of the if-then form.

• To derive the control law, the FLC uses fuzzy sets theory, the

set of rules, and a fuzzy inference system.

• FLC has been used in consumer products such as washing

machines, vacuum cleaners, automobiles, battery chargers, air

conditioning systems, and camera autofocusing.







• There are many ways to set up a fuzzy logic controller.

• Figure shows a block diagram of a PI fuzzy controller, inspired by

the PI classical control law, but including a fuzzy inference system.

• Equation shows the control law for a PI fuzzy control.




• The inputs in Eq. are the error e(t) and the derivative of the error

de/dt and the output is the change of u, ∆u(t), which results from

evaluating the function f(.) that is the fuzzy system.

• Thus, to get the output u(t), an integrator is added at the output of

the FLC as is shown in Fig.

• The constants ke, ka, and ki are used as scaling factors.

• Fuzzy logic control calculations are executed by using both

membership functions of the inputs and outputs and a set of

rules called a rule base, as shown in Fig.

• Typical membership functions for the inputs, e and de/dt, are

shown in Fig.




• It is assumed that these inputs have identical membership

functions with the following characteristics: three linguistic

variables which are negative (N), positive (P), and zero (Z) with

trapezoidal, triangular and trapezoidal membership function forms

respectively.




• Membership functions for the inputs of the PI fuzzy controller (N

is negative, P is positive, and Z is zero).

References:

• http://www.enggcyclopedia.com/2012/06/split-range-control-loop/

• http://www.controleng.com/single-article/a-dual-split-range-control-

strategy-for-pressure-and-flow-

processes/e02afa4eb60717657598546e8feb895e.html



Engineering

Class 37 inferential control, gain scheduling