Class 37 inferential control, gain scheduling

ICE401: PROCESS INSTRUMENTATION
AND CONTROL
Class 37
Inferential Control, Gain Scheduling
Dr. S. Meenatchisundaram
Email: meenasundar@gmail.com
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 coK 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

Class 37 inferential control, gain scheduling

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