Fuzzy Tuning of Pid Pakya

8/9/2019 Fuzzy Tuning of Pid Pakya

1/17


2/17

KHAIRUNNISA BINTI ABD AZIZ MOHD SHAHRIL BIN IBRAHIM

MOHD SUFI B AB MAJID MOHD SUPIAN B MOHD NAZIP MOKTAR BIN YAAKOP


3/17

PID CONTROLLERS :

Easy to understand, easy to explain to others, and easy to implement

Moreover, theyare often available at little extra cost since theyare often

incorporated into the programmable logic controllers (PLCs) that are used to

control manyindustrial processes.

Unfortunately, many of the PID loops that are in operation are in continual need

ofmonitoring and adjustment since they can easilybecome improperly tuned

PID controller is placed in a unity feedback control system :

i . the input to the plant is u,

ii. the plant output isy,iii. the reference input is r,

iv. the error input to the PID controller is e = r y

The basic form for the PID controller is :


4/17

where ;

i. Kp is the proportional gain

ii. Ki is the integral gain

iii. Kd is the derivative gain

Because PID controllersare often not properly tuned ,there isasignificant need

to develop methods for the automatic tuning of PID controllers.

While there exist many conventional methods for PID auto-tuning, herewe will

strictly focus on providing the basic ideas on howyou would construct a fuzzy

PID auto-tuner.

The figure in next slide show

ing how

a fuzzy PID auto-tuner mayw

ork. There, the behavior recognizer seeks to characterize the current behavior of

the plant in away thatwill be useful to the PID designer.

Thewhole (upper-level)supervisor maybe implemented in asimilar fashion to an

indirect adaptive controller .


5/17

Alternatively, simple tuning rulesmaybe used where the premises of the rules

form part of the behavior recognizer and the consequents form the PID designer.

In thisway, asingle fuzzysystemis used to implement the entire supervisory

control level.

Some candidate rules for such a fuzzysystemmayinclude the following:


6/17

Some candidate rules for such a fuzzysystemmayinclude the following:

1. Ifsteady-state error is large Then increase the proportional gain.

2. If the response is oscillatory Then increase the derivative gain.

3. If the response issluggish Then increase the proportional gain.

4. If the steady-state error is too big Then adjust the integral gain.

5. If the overshoot is too big Then decrease the proportional gain.

The Zeigler-Nichols PID tuning rules can used but represent themwith a fuzzy

system.

For some applications, it isbest to have a tuning phase and an on-line operationphasewhere tuning does not occur.

In the tuning phase, the system takes over and generatesaset of reference

inputs (e.g., astep)and observesand analyzes the step response to determine

the values of the parameters of the premises of the above rules.

Then the rule-base isapplied to these, the new PID gainsare found, and the

closed-loop control systemis put into operationwith these new gains.


7/17

Clearly, however, it maybe unacceptable to expect the system to be taken off-

line for such testsand retuning.

On the other hand, for some applications (e.g., in process control)it is possible to

followsuch a retuning scenario .

Overall,we would emphasize that fuzzy PID auto-tuners tend to be very

application dependent and it is difficult to present a general approach to on-line

fuzzy PID auto-tuning thatwillwork for awide variety ofapplications.

At this point, however, the reader who understands howa fuzzysystem operates

and hasaspecific application in mind, can probably quicklywrite down aset ofrules that quantifies how to keep the PID controller properly tuned.

Thisis often the primaryadvantage of the fuzzysystemsapproach to PID auto-

tuning over conventional methods.


8/17


9/17

Conventional gain scheduling involves using extrainformation from the plant,

environment, or users to tune (via schedules) the gains ofa controller.

There are manyapplicationswhere gain scheduling is used.

For instance, in aircraft control you often perform linear control designsabout a

whole range of operating points (e.g., for certain machsand altitudes).


10/17

These control designs provide aset of gains for the controller at each operating

condition over the entire flight envelope.

A gain schedule issimplyan interpolator that takesasinputs the operating

condition and provides values of the gainsasits outputs.

One way to construct thisinterpolator is to view the dataassociationsbetweenoperating conditionsand controller gainsas forming a large table.

Then,when we encounter an operating condition that is not in the table,we

simplyinterpolate between the onesin the table to find an interpolated set of

gains.

In thisway, as the aircraft movesabout its flight envelope, the gain schedulerwill

keep updating the gains of the controllerwith the ones thatwe would have

picked based on a linear design about an operating point.

This general gain scheduling approach iswidely used in the aircraft industry (e.g.,

also for engine control).

The fuzzysystemmethodologyalso offers three different methodologies for

gain schedule construction to conventional gain scheduling approaches.


11/17

In this case the design ofaset of linear controllers for various operating

conditionsmay not be necessaryasit maybe possible to simplyspecify, in a

heuristic fashion, how the gainsshould change.

The use of rulesmaybe particularly useful here. For example, the tank level

control application.

We could use a rule-base to schedule the gain ofa linear proportional controller

based on our knowledge that for higher liquid levelswewill have bigger

crossectional areas for the tank.


12/17

In this case the rulesmay represent thatwe want to have a lower proportional

gain for lower liquid levelssince for lower levels the tank will fill faster with

smaller amounts of liquid but for high levels the controllerwill have to pump

more liquid to achieve the same change in liquid level. We see that some practical knowledge of the tanksshape, which is not normally

used in the design ofa linear controller, can possiblybe effectively used to

schedule the gain ofa linear controller for the tank.

It is clear that the knowledge used to construct the gain schedule can be highly

application-specific; hence, it is difficult to provide a general methodology for the

heuristic construction of fuzzy gain schedulersbeyond what hasalreadybeen

presented for techniques to design standard fuzzy controllers.


13/17

In the casewhere we have aset of controller designs (based on linear or nonlinear

theory) for each set of operating conditions thatwe can measure

We can use the methods for function approximation to identify the function

that the datainherently represents.

This function that interpolatesbetween the datais the gain schedule, and the

methods of Chapter 5 can be used for its construction.

So, consider howwewould schedule just one of the (possibly)many gains of the

controller.

To do thiswe view the operating conditiongain associations produced by the

design of the controllersas data pairs

(xi, yi)G

where xi = ith operating point

yi = the gain that the controller design procedure produced at this

operating point.

G = the set ofall such data pairsthat is, operating conditioncontroller

associations.


14/17

Herewe consider the casewhere the plant to be controlled is

a nonlinear interpolation ofR linear models

Similar rules could be createdwith consequents that use a

discrete-time statespace representation or transfer

functions, either discrete or continuous.

Herewewill simply use the continuous-time linear state-space modelsas consequents for convenience, but the same

basic concepts hold for other forms.


15/17

2 ways that the rules can be constructed to represent theplant.

First, for some nonlinear systems the mathematical differentialequations describing the plant can be transformed into which is themodel resulting from the above rules.

A second approach would be to use system identification to constructthe rules (e.g., use the least squares, gradient, or clustering with optimaloutput predefuzzification methods.

While it is possible to modify the identification methods so that theyapply directly to continuous-time systems.


16/17

Recall controller for plant used the rules

where Ki, i = 1, 2, . . ., R, are 1 n vectors of control gains, and the premises

ofthe rules are identical to the premises of the plant rules.

Under certain conditions this controller can be used to stabilize the plant

Many view

parallel distributed compensation as a form of gainscheduling that we can achieve stability by designing the Kj , j = 1, 2, . . .,

R then using Equation to interpolate between these gains.


17/17

Regardless ofwhich of the above methodologies is used to construct thegain schedule, these approaches also automatically provide for the fuzzysystem implementation of the gain scheduler (interpolator),which can attimes be an advantage over conventional methods.

It is important to note that computational complexity is of concern in the

implementation ofa gain scheduler. Some may think that the fuzzy system methodologies could offer an

approach to reduce the memory storage requirements since the ruleswilltend to provide an interpolation that may make it possible to omit somedata.

The conventional methods used for gain scheduling use interpolationtechniques that are basically quite similar (sometimes identical) to whatis implemented by a fuzzy system.

If the original designers found that the extra data were needed to makethe mapping that the gain scheduler implements more accurate, thenthese extra data are probably needed for the fuzzy system also.

Fuzzy Tuning of Pid Pakya

Documents

Transcript of Fuzzy Tuning of Pid Pakya