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FUZZY PRECOMPENSA

TED PID CONTROLLER

Submitted By: Akanksha Arya0903321002EN

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CONTENTSIntroductionAdvantages and disadvantages of FPC(Fuzzy pre-compensator) controllerFuzzy precompensated PID controller

I. Control structureII. Fuzzy precompensator–

Fuzzification -

Decision making -

Defuzzification

ComparisonConclusion

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INTRODUCTIONFuzzy logic control technology has been widely used in industrial applications.Humanlike but systematic properties.Convert linguistic control rule into automatic control strategies.Well applied to control the process with un modeled and nonlinear dynamics.

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Advantages of fuzzy Precompensator controllerNo need for precise tuning. It reduces 90% of overshoot which occur

in the PID controller.It acts as an adaptive controller.It has faster settling time.Disadvantages of fuzzy

precompensator controller Complexity in forming the fuzzy membership function.

Auto tune fuzzy PID

controller

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Basic control structure

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FUZZY PRECOMPENSATOR PID CONTROLLER1. Control structure

Consists of a conventional PID control structure together with the proposed fuzzy pre compensator.

The pre compensator uses the command input ym and the plant output yp to generate a pre compensated command output y1 m described by the following equations -

Δe( k ) = e( k ) - e( k-1) ……(1)

γ( k ) = F[ e( k ), Δ e( k ) ] ……(2)

y1m ( k ) = ym (k) + γ( k ) ……..(3)

where, e( k )=tracking error between ym(k) and yp(k)

Δe( k )=change in the tracking error.

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γ ( k ) = F[ e( k ), Δe( k ) ]= pre compensation or correction term. The compensated command signal y1m( k ) is applied to conventional PID controller.The equations determining the PID controller are -

e1( k ) = y1m (k) - y(k)……..…..(4)Δ e1( k ) = e1 ( k ) - e1 ( k-1)...(5)

u (k) = u(k-1) +Kp Δ e1( k ) +K1 e1( k )……...(6)

where, e1(k) =pre compensated tracking error, Δ e1(k) =change in the pre compensated

tracking error, u(k) = applied input to the plant.

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2. FUZZY PRECOMPENSATOR

Its Purpose is to compensate for overshoots and undershoots present in the output response when the plant has unknown nonlinearities.

The pre compensator uses fuzzy logic rules that are based on the above motivation.

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The implementation of the fuzzy logic based term is γ ( k ) = F[ e( k ), Δ e( k ) ].

F is a collection of linguistic values. L= {NB, NM, NS, ZO, PS, PM, PB}

NB stands for negative big, NM for negative medium, NS for negative small, ZO for zero, PS for positive small and so on.

set L is a collection of membership functions.

μ = { μ NB, μNM, μNS, μ ZO, μPS, μPM, μ PB }

CONTINUE…

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Membership function of error e(k)

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Membership function of change in

error Δe(k)

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Fuzzy method consists of three stages

1. FUZZIFICATION,2. DECISION-MAKING , and3. DEFUZZIFICATION

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The realization of the function F[e(k), Δe(k)] deals into the setting of linguistic values.

This consists of scaling the inputs e(k) and Δe(k) and then converting them into fuzzy sets.

ne(l) = μl (Ce e( k ) ) nΔe(l) = μl (CΔe Δ e( k ) )

Where, nos. ne(l) and nΔe(l), l L are used in the computation of F{ e(k) and Δ e( k ) }, and Ce and CΔe are scaling constants.

1. FUZZIFICATION

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Inputs Rules Output

Fuzzy inference systems editor

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There is a set of fuzzy rules R = {R1, R2…Rr}, where r is the total number of rules. Each RI, I = 1,2,3,...r, is represented by a triplet ( li Δ, li Δc, li γ L ).The first two linguistic values are associated with the input variables e( k ), and Δ e( k ) while the third linguistic value with the output.

2. Decision-making

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Considering the triplet (ZO,NM,NM) ..

Let command signal is a constant ym, the error e(k) is zero and the change of error Δe( k) is negative number. This means that the output yp (k) is increasing, i.e, heading in the direction of an overshoot.

To compensate for this, the command signal is to be decrease. This corresponds to applying a correction term γ(k) as negative. Hence rule “if error is zero and change of error is negative medium, then output is negative medium, correction term”.

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Δee

NB NM NS ZO PS PM PB

NB NB NB NB NM NS NS ZO

NM NB NB NM NS NS ZO PS

NS NB NM NS NS ZO PS PM

ZO NM NM NS ZO PS PM PM

PS NM NS ZO PS PS PM PB

PM NS ZO PS PS PM PB PB

PB ZO PS PS PM PB PB PB

DML rule table of the FLC

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Maps the result of the fuzzy logic rule stage to a real number output F[e(k),Δe(k)].It is aimed at producing a non-fuzzy control action.

Membership function of Controller output (γ)

3. Defuzzification

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THE PERFORMANCE OF PID CONTROLLER AND FPC CONTROLLER (SIMULATION)

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COMPARISON

Poor response

Not able to follow the set point.Gives damped oscillations.

Better response. Even if the process parameter changes the FPC controller adapts itself and produces good response. Hence it acts as an ADAPTIVE CONTROLLER.Follows the set point.

Does not require precise tuning.

Conventional PID controller

FPC(fuzzy pre-compensator) controller

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CONCLUSIONFPC control scheme has superior performance compared to a conventional PID controller. An advantage of the present approach is that an existing PID control system can be easily modified by simply adding the fuzzy precompensator.Fuzzy methods can be used effectively to complement conventional control methods for improving performance and robustness, especially in the presence of unknown and severe nonlinearities.

Structure of fuzzy PID controller

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