Application of Fuzzy Logic to Approximate Reasoning

8/3/2019 Application of Fuzzy Logic to Approximate Reasoning

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Application of Fuzzy Logic toApproximate Reasoning Using

Linguistic Synthesis


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Introduction

This paper describes an application of fuzzy logic in designingcontrollers for industrial plants.

A Fuzzy Logic is used to synthesize linguistic control protocol of askilled operator.

The method has been applied to pilot scale plants as well as in apractical industrial situation.

The merits of this method in its usefulness to control engineeringare discussed. This work also illustrates the potential for using fuzzy

logic in modelling and decision making.

An avenue for further work in this area is described where the needis to go beyond a purely descriptive approach and explore means bywhich a prescriptive system may be implemented.


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Outline

The intention in this paper is to review the wholeprogram of investigation concerning the application ofApproximate Reasoning and to analyse the findings inorder to offer insightful comments and conclusions.

The original work in this program was done in early 1974and first published later that year.

This was the control of a pilot scale steam-engine usingfuzzy-logic to interpret linguistic rules which qualitativelyexpress the control strategy.


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A Brief Review of Fuzzy Logic

The point of view adopted here is that the variables areassociated with universes of discourse which are non-fuzzy sets.

These variables take on specific linguistic values. Theselinguistic values are expressed as fuzzy subsets of theuniverses.

Given a subset A of X (Ac X), A can be represented by acharacteristic function: XA: X -> {0,1}.

If the above mapping is from X to a closed interval [O,i]then we have a fuzzy subset.

Thus if A were a fuzzy subset of X it could berepresented by a membership function:

~A: X[O, i]


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Application of Fuzzy Controller

One aspect of control in this system is the regulation ofpressure in the boiler around a prescribed set-point.

The control is achieved by measuring the pressure at

regular intervals and inferring from this the heat settingto be used during that interval.

The essence of this work is simply that if an

experienced operator can provide the protocol forachieving such a control in qualitative linguistic terms,then fuzzy logic as described above can be used toimplement successfully this strategy.


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The protocol obtained from the operator in this

case considers pressure error (PE) and changein the

pressure error (CPE) to infer the amount ofchange in

the head (HC). The protocol consists of a set of

rules in terms of specific linguistic values ofthese

variables and is shown in figure i*.


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A list of rules used in the steam-engine control system

PRESSURE ERROR = PE, CHANGE IN PRESSURE ERROR = CPEAND HEAT INPUT CHANGE = HC

IF PE = (NB OR NM) THEN IF CPE = NS THEN HC = PMOR

IF PE = NS THEN IF CPE = PS THEN HC = PMOR

IF PE = NZ THEN IF CPE = (PB OR PM) THEN HC = PMOR

IF PE = NZ THEN IF CPE = (NB OR NM) THEN HC = NMOR

IF PE = PZ OR NZ THEN IF CPE = NZ THEN HC = NZOR

IF PE = PZ THEN IF CPE = (NB OR NM) THEN HC = PMOR

IF PE = PZ THEN IF CPE = (PB OR PM) THEN HC = NMOR

IF PE = PS THEN IF CPE = (PS OR NZ) THEN HC = NMOR

IF PE = PB OR PM) THEN IF CPE = NS THEN HC = NM


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Observation

On application of this method to the pilotscale plant, in repeated trials, it was foundthat the results compared favourably with

those from a straight application ofclassical methods from control engineeringpractice.


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Comments on Fuzzy-logic ControllerStudies

Two main conclusions have been drawnfrom this work.

First, that the results vindicate theapproach advocated by Zadeh anddemonstrate its potential.

Second, it can be asserted that themethod can easily be applied to manypractical situations.


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In recent months, this method has beenfurther tested by various research workerson other pilot scale plants such as batch

chemical reactors, heat exchangers and soon.


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Worth noting is the application of this method toa real plant - a sinter plant at the British SteelCorporation.

Results show that fuzzy control achieves usefulreduction in the standard deviation of themeasured output when compared with a manualoperation of the plant.

Furthermore it also compares favorably with aclassical control of the plant using control engg.


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A Recipe for a Prescriptive Approach

The overall schematic diagram for the control system isshown in figure:


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The goal is effectively a band within which the output is to be maintained. It is specified as fuzzy rules which give the corrections needed to keep the

output within the band. The input to these rules are time from start and the set-point deviation. The rules specify the change to be made in the controller. Examples of

these rules are:

(a) IF Timeis Small AND deviationis negative bigTHEN desiredchange is big.

(b) IF TIMEis big AND deviationis positive zeroTHEN desired changeis zero.

The result of this set of rules is used to alter the lower level control rules

appropriately~ Since these control rules are of the form Ai+Bi-~C i themodification is affected by first finding the linguisting values A i and B i thatbest describe the plant state for which a change in action is required.

This search is simply done by a supremum operation on the range oflinguistic values.

The action C i in the controller rules at Ai, B i value is then altered by thedesired amount.


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The results of applying this policy are shown in figure 5.


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Recomendation

The convergence property itself is a matter offurther investigation.

Analysis suggests that the lack of convergencemay be attributed to two factors.

Firstly it can arise because the controller isrequired to make a decision based on notenough variables.

Secondly, since the measured state of any

system is the consequences of a whole historyof past inputs it is not enough to alter the ruleaffecting only the single previous state.


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Conclusion

To conclude therefore, the advantage of theprescriptive method is that it reduces thedifficulties with deriving a good protocol

mentioned earlier providing the relevantvariables can be identified.

The protocol is then derived by a process ofaccumulation or integration of past experience.

Present work is aimed at extension of thismethod to a multi-variable situation.


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Reference

M. Black, "Vagueness", Philosophy ofScience, (1937).

S. Haack, DeViant Logic, CambridgeUniversity Press, 1974.

E.H. Mamdani and S. Assilian, "AnExperiment in Linguistic Synthesis with aFuzzy Logic Controller", Int. J. Man-Machine Studies, 1974.

Application of Fuzzy Logic to Approximate Reasoning

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