NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society

Integrated Development Platform for IntelligentControl based on Type-2 Fuzzy Logic

Roberto SepuilvedaCITEDI-IPN

Av. del Parque #13 10, Mesa de OtayTijuana, B. C., Mexico.rsepulve@citedi.mx

Oscar CastilloDepartment of Computer Science,Tijuana Institute of Technology

Tijuana, B. C., Mexicoocastilloa,tectijuana.mx

Patricia MelinDepartment of Computer Science,Tijuana Institute of Technology

Tijuana, B. C., Mexicopme1in(@,tectijuana.mx

Antonio Rodriguez-DiazFCQI-UABC

Tijuana, B. C., Mexicoardiaz(&uabc.mx

Abstract-Uncertainty is an inherent part in controllersfor real world applications. The use of new methods forhandling incomplete information is of fundamentalimportance in engineering applications. This work dealswith the creation of an integrated development platformfor intelligent control systems based on type-2 fuzzy sets.The principal idea with this platform is to give the user atool to realize an "on-line" and 'off-line" comparativeanalysis between type-I Fuzzy Logic Control (FLC), andtype-2 FLC, of the systems' response in the presence ofuncertainty.

I. INTRODUCTION

Uncertainty affects all decision making and appears in anumber of different forms. The concept of information isfully connected with the concept of uncertainty, the mostfundamental aspect of this connection is that uncertaintyinvolved in any problem-solving situation is a result ofsome information deficiency, which may be incomplete,imprecise, fragmentary, not fully reliable, vague,contradictory, or deficient in some other way [1]. Thegeneral framework of fuzzy reasoning allows handlingmuch of this uncertainty, fuzzy systems employ type-lfuzzy sets, which represents uncertainty by numbers in therange [0, 1] [2]. However, when something is uncertain,like a measurement, it is difficult to determine its exactvalue, and of course type-I fuzzy sets makes more sensethan using crisp sets, but it is not reasonable to use anaccurate membership function for something uncertain, soin this case what we need is another type of fuzzy sets, thosewhich are able to handled uncertainties, the so called type-2

Oscar MontielCITEDI-IPN

Av. del Parque #13 10, Mesa de OtayTijuana, B. C., Mexico.

orossAcitedi.mx

fuzzy sets [3-4]. So, the amount of uncertainty in a systemcan be reduced by using type-2 fuzzy logic because it offersbetter capabilities to handle linguistic uncertainties bymodeling vagueness and unreliability of information.

This work deals with the creation of an integrateddevelopment platform for intelligent control systems basedon type-2 fuzzy sets. The principal idea with this platformis to give the user a tool to realize a comparative studybetween type-I FLC, and type-2 FLC, of the systems'response in the presence of uncertainty.

II. TYPE-I FUZZY CONTROLLERS

In the 40's and 50's, many research works proved that manydynamic systems can be mathematically modeled usingdifferential equations. These previous works represent thefoundations of the Control theory which, in addition withthe Transform theory, provided an extremely powerfulmeans of analyzing and designing control systems [5].These theories were being developed until the 70's, whenthe area was called System theory to indicate itsdefmitiveness. Its principles have been used to control avery big amount of systems taking mathematics as the maintool to do it during many years. Unfortunately, in too manycases this approach could not be sustained because manysystems have unknown parameters or highly complex andnonlinear characteristics that make them not to be amenableto the full force of mathematical analysis as dictated by theControl theory [6,7].

Soft computing techniques have become a researchtopic, which are applied in the design of controllers. Theyhave tried to avoid the commented drawbacks, and they

0-7803-9187-X/05/$20.00 02005 IEEE. 607

allow us to obtain efficient controllers, which utilizes thehuman experience in a more related form than theconventional mathematical approach. In the cases in whicha mathematical representation of the controlled systemscannot be obtained, the process operator should be able toexpress the relationships existing in them, that is, theprocess behavior.

III. TYPE-2 FUZZY CONTROLLERS

A Fuzzy Logic System (FLS), described using at least onetype-2 fuzzy set is called a type-2 FLS. Type-I FLSs areunable to directly handle rule uncertainties, because theyuse type-I fuzzy sets that are certain. On the other hand,type-2 FLSs, are very useful in circumstances where it isdifficult to determine an exact certainties, and measurementuncertainties [3].

It is known that type-2 fuzzy sets let us to model and tominimize the effects of uncertainties in rule-based FLS.Unfortunately, type-2 fuzzy sets are more difficult to useand understand than type-I fuzzy sets; hence, their use isnot widespread yet. In [3] were mentioned at least foursources of uncertainties in type- I FLSs:1. The meanings of the words that are used in theantecedents and consequents of rules can be uncertain(words mean different things to different people).2. Consequents may have histogram of values associatedwith them, especially when knowledge is extracted from agroup of experts who do not all agree.3. Measurements that activate a type-I FLS may be noisyand therefore uncertain.4. The data used to tune the parameters of a type-I FLS mayalso be noisy.All of these uncertainties translate into uncertainties aboutfuzzy set membership finctions. Type-I fuzzy sets are notable to directly model such uncertainties because theirmembership functions are totally crisp. On the other hand,type-2 fuzzy sets are able to model such uncertaintiesbecause their membership functions are themselves fuzzy.A type-2 membership grade can be any subset in [0,1], theprimary membership, and corresponding to each primarymembership, there is a secondary membership (which canalso be in [0,1]) that defines the possibilities for the primarymembership. A type-1 fuzzy set is a special case of a type-2fuzzy set; its secondary membership fimction is a subsetwith only one element, unity.A type-2 FLS is again characterized by IF-THEN rules, but

its antecedent or consequent sets are now type-2. Type-2FLSs, can be used when the circumstances are too uncertainto determine exact membership grades such as whentraining data is corrupted by noise. In our case, we aresimulating that the instrumentation elements(instrumentation amplifier, sensors, digital to analog, analogto digital converters, etc.) are introducing some sort ofunpredictable values in the collected information.

In the case of the implementation of the type-2 FLC, wehave the same characteristics as in type-I FLC, but we usedtype-2 fuzzy sets as membership functions for the inputsand for the output. In [15, 16], we can see some examplesof application oftype-2 FLC.

IV. PERFORMANCE CRITERIA

For evaluating the transient closed-loop response of acomputer control system we can use the same criteria thatnormally are used for adjusting constants in PID(Proportional Integral Derivative) controllers. These are[8]:1. Integral of Square Error (ISE).

ISE = .f[e2] dt2. Integral of the Absolute value ofthe Error (IAE).

(1)

IAE = f I e dt (2)3. Integral ofthe Time multiplied by the Absolute value of

the Error (ITAE).

ITAE = ftl e dt (3)

Similar to a type-I FLS, a type-2 FLS includes fuzzifier,rule base, fuzzy inference engine, and output processor.The output processor includes type-reducer and defuzzifier;it generates a type-I fuzzy set output (from the type-reducer) or a crisp number (from the defuzzifier).The selection of the criteria is depending on the type ofresponse desired, the errors will contribute different for eachcriterion, so we have that large errors will increase the valueof ISE more heavily than to IAE. ISE will favor responseswith smaller overshoot for load changes, but ISE will givelonger settling time. In ITAE, time appears as a factor, andtherefore, ITAE will penalize heavily errors that occurs latein time, but virtually ignores errors that occurs early in time.Designing using ITAE will give us the shortest settling time,but it will produce the largest overshoot among the threecriteria considered. Designing considering IAE will give usan intermediate results, in this case, the settling time will notbe so large than using ISE nor so small than using ITAE,and the same applies for the overshoot response. Theselection of a particular criterion is depending on the type ofdesired response.

V. PLATFORM DEVELOPMENT

The integrated platform development for teaching anddevelop applications on real time is based on MATLAB. Itprovides the user a type-I fuzzy controller, and a type-2fiuzzy controller. Through this interface, it is possible toselect between a real system or an ideal one; to select agraphics mode, the time response, ISE, IA, ITAE.

608

It is also possible to select the input data source,example if they are data from a file, data from a serial(channel 1), data from a USB interface (channel 2).similar way it is possible to select where to save the oudata, or where they are going to go.

VI. EXPERIMENTAL RESULTS

We have performed some tests with linear and nonliidynamical systems. Next we will describe one ofthis te!Using the block diagram shown in Fig. 1, as a planprocess, it was selected the plant represented by equa(4).

y(i)=0.2. y(i-3).0.7y(i-2)+0.9 .y(i-l)+0.005 u(i- 1)+ 0.5 * u(i - 2)

Inputr

Error OutYA

y = y+O.005 randnLL. - -T - --J

Enableuncerm

for introducinginy to the system

forportIn a.tput

nearsts

In both cases, the type-l and type-2 fuzzy controllers, wereused the same values for mean and standard deviation forthe gaussian member functions, with the Foot OfUncertainty (FOU) for the type-2 membership functions. Infigures 3,4, and 5 we have the membership functions for thetype-2 fuzzy controller.

The system was tested using as an input a unitary step r(i)free ofnoise.

t or Table I, shows the values obtained for the differenttion performance evaluation criteria (ISE, IA, ITAE) considering

400 time units. For computing ITA, it was consideredT = 0.1 seconds as the sampling frequency. Next wedescribe the four experiments performed with this

(4) configuration.Experiment 1. Type-I ideal system.

put It was not added uncertainty in the information to theru) system.

Experiment 2. Type-2 ideal system.Here we have the same conditions as in experiment 1, butusing the membership functions showed in figures 2, 3 and4.

Experiment 3. Type-l real system (with uncertainty).The same conditions as in experiment 1, but using equation(7) in the feedback loop to add uncertainty.

Input e

Fig. 1. System used for obtaining experimental results.

In figure 2, we can observe that we are referring to type-Iand type-2 fuzzy controllers because they are used in theexperiments to make a comparative study. So we have twoinput variables to the fuzzy controller, e(t) y Ae(t), whichare defined by equations (5) and (6), respectively,

e(t) = r(t) - y(t) (5)

Ae(t) = e(t) - e(t -1) (6)

The output of the controller is applied directly to the plant.For type-l fuzzy controller, the output is feedback directlyto the input "summing". For type-2 fuzzy controller, it wasutilized equation (7) to introduce uncertainty to thefeedback,

y(i)= y(i)+ 0.05. randn (7)

Fig 2. Type-2 membership functions for the input error (e).

Experiment 4. Type-2 real system (with uncertainty).The same conditions as in experiment 2, but using equation(7) in the feedback loop to add uncertainty.

609

C

0.

D-EECD

Input de/dt

05

* .

Fig.3 Type-2 membership functions for the input change of error

with time .

Type-2 output controller

M,

MU

E

Fig.4. Type-2 membership functions for the controller's output.

TABLE I

COMPARISON OF PERFORMANCE CRITERIA FOR TYPE-1and TYPE-2 FUZZY LOGIC. RESULTS OBTAINED AFTER

400 SAMPLES.

VII. CONCLUSIONSThrough the use of the performance evaluation criteria ISE,LAE and ITAE, it was observed and quantified that insystems without uncertainty, ideal systems, using type-I is agood option, since they perform a little better, they areeasier to implement and they are faster. It is a fact that type-1 fuzzy controllers can manage non- linearities anduncertainty in some way.

For real systems where the non-linearities anduncertainty are inherent, based on our experiments andmeasures, we concluded that the type-2 fuzzy controllerscan be a better option just for its ability to manageuncertainty. However, it is necessary to continue workingin the development of efficient implementations to avoid thetime limitations in the processing of certain on lineapplications.

At the moment, the integrated developmentplatform for intelligent control systems based on type-2fuzzy logic, has the ability to perform type-I and type-2algorithms, and others developed with analytical methods,to be part of this platform. In the real time processing, weare working in the implementation of dynamical libraries tobe able to be out of MATLAB through the universal serialbus (USB).

ACKNOWLEGMENT

The authors thank the Comisi6n de Operaci6n y Fomento deActividades Academicas del I.P.N., Instituto Tecnol6gico deTijuana, and UABC for supporting our research activities.

REFERENCES

[1] Zadeh L A, Fuzzy Sets, Information and Control, Vol8, pp 338-353. 1965.

[2] George J. Klir, Bo Yuan, Fuzzy Sets and FuzzyLogic: Theory and Applications, Ed. Prentice HallUSA, 1995.

[3] Jerry M. Mendel, Uncertain Rule-Based Fuzzy LogicSystems: Introduction and new directions, Ed.Prentice Hall, USA, 2000.

[4] Nilesh N. Kamik, Jerry M. Mendel, Qilian Liang,Type-2 Fuzzy Logic Systems, IEEE Transactions onFuzzy Systems, Vol. 7, No. 6, December 1999

[5 0. Cord6n, F. Herrera, E. Herrera-Viedma, M.Lozano, Genetic Algorithms and Fuzzy Logic inControl Processes, Technical Report #DECSAI-95109, Universidad de Granada, Spain, 1995.

[6] John Van de Vegte, Feedback Control Systems, Ed.Prenctice hall, USA, 1994

[7] Fuller A. T., The Early Development of ControlTheory, J. Dyn. Syst. Meas. Control, vol 98, pp 109-118, 224-235, 1976.

[8] Pradee B. Deshpande, Raymond H. Ash, ComputerProcess Control with Advanced ControlApplications, 2nd. Edition Revised and Enlarged. Ed.Instrument Society ofAmerica, USA, 1988.

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Tyl 1l FLC Ty. ,e-2 FLCPerform. Ideal System Ideal Systemcriteria system with System with

uncertainty __ uncertaintyISE 5.2569 15.1143 5.4479 9.5516IAE 13.8092 57.9542 14.2045 45.4106ITAE 59.9589 1,111.20000 61.6360 877.5299