Self+Tuning+Regulators

7/29/2019 Self+Tuning+Regulators

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Self tuning regulators

( STR)


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Introduction to Self Tuning Regulator (STR)


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In STR, the controller parameters or the processparameters are estimated in real time.

These estimates are then used as if they are equal to thetrue parameters (i.e. the uncertainty in estimation is notconsidered). This is called the certainty equivalenceprinciple.

In an STR, the parameters of the process are estimated

online by the estimation techniques discussed Later these estimated parameters are used to design the

controller parameters.

Then these controller parameters are varied in the

controller, ultimately resulting in control of the plant.

TYPES OF STR

Indirect STR

Direct STR


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In an indirect STR,

the parameters of the process are estimated by the availableestimation technique,

and these estimated parameters are used for design of the controller.This is a time consuming process.

This approach is also referred to as explicit self tuning control.

In a direct STR,

the model is first re-parameterized in terms of the controllerparameters

then the parameters are estimated by the available estimationtechnique.

Hence the result of parameter estimation will now be directly thecontroller parameters, instead of process parameters.

Thus a lot of computation time is saved.The only computation effort here will be to re-parameterize the model

in terms of the controller parameters, which needs to be done only once,

so lot of time is saved in this approach.

This approach is also referred to as implicit self tuning control.


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Deterministic Vs Stochastic Process

A stochastic system is one which cannot be expressed

precisely but can be expressed with the help of statistical

data.A deterministic system on the other hand can be expressed

precisely. Usually deterministic systems are encountered in

case of servo systems. Stochastic systems are encountered

in case of regulator systems.Self Tuning Regulators are available both for deterministic

and stochastic systems.


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Deterministic Indirect Self Tuning

Regulators

Pole placement design

a simple method of controller design.

The idea of this method is to determine acontroller that gives desired closed-loop

poles.

In addition it is required that the systemfollow the command signals in a specified

manner


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process model be described by


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The key idea of the design method is to specify the desired closed loop

characteristic polynomial AC

The polynomials R and S can then be solved form equation (6).

Equation (6) is called the Diophantine equation or Bezout identity or the

Aryabhatta equation

The Diophantine equation given by (6) can be used to determine only the

polynomials R and S.

To determine T, some other conditions need to be introduced. This requiresthat the response from the command signal to the output be described by

the dynamics:


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This model-following condition says that the response of

the closed loop system to command signals is as

specified by the model (7).Whether model-following can be achieved or not depends

on the model, the system, and the command signal.

If it is possible to make the error zero for all command

signals, then perfect model-following is achieved.From (6), it can be deduced that there are cancellations of

factors of BT and Ac


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Now factorize the B polynomial


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Minimum Degree Pole placement

(MDPP) algorithm


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Algorithm for Indirect Self-Tuning

Regulator obtained by combining the parameter estimation and controller

design part.

An algorithm combining the Recursive Least Squares (RLS )

parameter estimation and Minimum Degree Pole Placement (MDPP)

controller design is given below:


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Deterministic Direct Self Tuning

Regulators In a direct STR, the model is first re-parameterized in

terms of the controller parameters and then theparameters are estimated by the available estimationtechnique.

Hence the result of parameter estimation will now bedirectly the controller parameters, instead of processparameters.

Thus it can be seen that a lot of computation time issaved.

The only computation effort here will be to re-parameterize the model in terms of the controllerparameters, which needs to be done only once, so lot oftime is saved in this approach.

This approach is also referred to as implicit self tuningcontrol.


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Consider a process described by:


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The equation (18) represents a process re-parameterized in terms of the coefficients B- ,Rand S.

If the parameters in the process given by (18)

are estimated, the control law is thus obtaineddirectly without any design calculations. It shouldhowever be noted that the process given by

(18) is nonlinear in parameters because the

right-hand side is multiplied by B

-

. The difficulties caused can be avoided in the

special case of minimum phase systems forwhich B- = b0= constant


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Minimum phase systems


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Direct self tuning regulator algorithm for minimum

phase systems


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Non-minimum phase systems


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Direct self tuning regulator algorithm for non-

minimum phase systems:

Self+Tuning+Regulators

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