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Using Fuzzy Logic in ControlApplications: Beyond FuzzyPID ControlStephen Chiu

substantial portion of the literatureon fuzzy control deals with the useof fuzzy rules to implem ent nonlinear pro-portional-integral-derivative (PID) typecontrol. As a result, many control engi-neers are led to believe that using fuzzyrules to implement nonlinear PID controlis the prime use of fuzzy logic for control.However, when we examine commercialproducts in which fuzzy control is said tobe incorporated, we rarely see fuzzy logicbeing used to implement nonlinear PID(proportional-integral-derivative) con-trol; fuzzy logic is used mostly to handlehigh-level control functions that tradi-tional control methods do not address.This article discusses different waysthat fuzzy logic can be used in high-levelcontrol functions. Specifically, we exa m-ine the use of fuzzy logic for supervisorycontrol, for selecting discrete control ac-tions, for identifying the operating envi-ronment, and for evaluating controllerperformance. The purpose of this article isto stimulate the use of fuzzy logic to pro-vide new control functions that are out-s i d e t h e d o m a i n o f t r a d i t i o n a lcontrol-where fuzzy control is likely toprovide the greatest payoff.Introduction

Much of fuzzy control research is fo-cused on the set-point regulation problem,where the control objective is to drive aprocess variable (e.g., motor shaft posi-tion, oven temperature) to a comm andedset-point. If one reads a paper on fuzzycontrol, chances are the paper will de-scribe a fuzzy controller with set-point er-ro r and error change as its inputs, and theoutput is an actuator command or a

change in actuator command. The fuzzycontroller would execute control rules ofthe form: if set-point error is positive bigand error change is positive small, thenactuator output is negative big. Whenused in this way, fuzzy con trol is not muchdifferent from conventional PID con-trol-it is solving the same set-poin t regu-lation problem addressed by PID controland solving it in essentially the same w ayas PID control, except that fuzzy controlprovides a nonlinear input/output map-ping. Hence, fuzzy control is often viewedas a form of nonlinear PID control, andcomparisons of fuzzy control versus con-ventional PID control abound in litera-ture. Many engineers lose interest infuzzy control after finding the perfor-mance im provement offered by fuzzy PIDcontrol cannot offset the increased com -plexity in com putation and controller tun-ing, or after finding nonlinearPI Dcontrolcan be more efficiently implementedthrough other mechanisms (e.g., gainscheduling or look-up table) than throughfuzzy rules. Conventional PID control iswell-established and can satisfy the per-formance requirements of most set-pointregulation problems at minimal cost;there is little incentive to sw itch from con-ventional PID control to a more com plex,nonlinear form of PID control unless theconventional controller is doing an unsat-isfactory job. H ence, the fuzzy PID con-troller that is ubiquitous in technicalliterature rarely appears in actual com-mercial applications; commercial appli-cat ions o f fuzzy con t ro l are largelyfocused on high-level, task-oriented con-trol rather than set-point regulation.

The misconception in equating fuzzycontrol with nonlinear PID control hassteered many engineers away from ex-ploiting the full potential of fuzzy logic incontrol applications. The purpose of thisarticle is to point out the many ways thatfuzzy logic can be used in control applica-tions beyond fuzzy PID control. In partic-ular, the emphasis here is on the use offuzzy logic to perform high-level controlfunctions that fall outside the domain ofconventional control methods. We willexamine industrial applications wherefuzzy logic was emp loyed for supervisorycontrol, for selecting discrete control ac-tions, for identifying the operating envi-ronment, and for evaluating controllerperformance.

Supervisory ControlFuzzy control in the form of nonlinearPID control has not found much accep-tance in industry, because conventionalPID control is well entrenched, simpler,low cost, and works satisfactorily formost applications. For the instanceswhere fuzzy logic is applied to set-pointregu lat ion , i t i s typ ical ly used in ahigh-level module that supervises a con-ventional PID controller. Here we giveseveral examples to illustrate differentforms of fuzzy supervisory control.The temperature controller producedby Yokogaw a Electric [ I ] s a good exam-ple of how fuzzy logic can be used for su-pervisory control. Temperature controlusually involves processes that have along time delay; for m any processes, it isalso imperative that the temperature doesnot overshoot the desired set-point. How-ever, it is difficult to avoid overshoot

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when a process has a long time delay, ex-cept by using low feedback gains, whichresults in slow system response. InYokogawa Electrics temperature con-troller, fuzzy logic is used to determine ar-t i f i c i a l s e t -p o i n t s t h a t a r e f ed t o aconventional PID controller. The controlarchitecture is shown in Fig. 1. The PIDcontroller is allowed to have high feed-back gains for fast system response. Asthe fuzzy supervisory module detects im-pending overshoot, it fools the PID con-troller by comm anding the PID controllerto aim for a temperature value that issomew hat lower than the actual set-point.As the temperature rises to (and over-shoots) the a rtificial set-point, the fuzzymodule gradually raises the artificialset-point toward the actual set-point. Inthis way, the fuzzy supervisory moduleleads the PID controller along a tempera-ture trajectory that can quickly reach theactual set-point without overshoot.In a motion controller produced by Al-len-Bradley, fuzzy logic is used to super-vise the automatic tuner of a conventionalPID controller [2].The tuner observes thesystem response and automatically ad-justs the PID controller feedback gainsduring successive tuning cycles to obtaindesired system response characteristics.To facilitate fast convergence to the opti-mal gain values, and to protect the systemagainst incorrect gain changes, a fuzzy su-

I Artificial IPID Process

I I IemperatureIFig. 1. Conventional PID control is assisted b y a fuzz y supervisor to preventovershoot.

Setpoint-I . , II

PIDTunerChange

IControlled Variable

Fig. 2. A fuzz y supervisor scales the outputo a PID tuner based o n the effectivenessand consistency o the tuner in improvingPID controller pe$ormance.

pervisory module scales the output of thetuner (the gain adjustment commands)based on the resultant system perfor-mmce (see Fig. 2). The fuzzy moduleadaptively scales the tuners output basedon the amount of performance improve-ment after each tuning cycle and the con-sistency of the performance improvem entoaer the past few tuning cycles. Thetuiers output is scaled up if the systemperformance is consistently improving,and scaled down if the tuner becomes in-effective in further improving perfor-mince or if the performance vacillates.In a steam turbine control applicationat General Electric, a fuzzy supervisorym3dule is used to combine the output ofseveral conventional PID controllers [3].The turbine control system employs threePID controllers for regulating the turbinete nperature , speed, and stress, respec-tively. However, there is only one controlactuator (the bypass valve) for regulatingt h s e three parameters. Therefore, the dif-ferent, often conflicting actuator com-mands from the three PID controllersmust be resolved into a single command.The fuzzy supervisory module assignswl:ights to the different PID contro lleroutputs based on the high-level controlohjective specified by an operator and onthe current system state (temperature,speed, and stress). For example, if the ob-je-ti ve is to prewarm the turbine as fast aspossible, then temperature control wouldbe given higher priority than speed andstress control unless the speed or stress aresi,:nificantly misb ehavin g. This controlarchitecture is shown in Fig. 3.

In m ost process control applications, ahuman operator must determine theset-points for numerous PID controllersarid periodically adjust the set-points toadapt to changing process conditions. An-other type of fuzzy supervisory control in-volves converting the human operatorsknowledge into a set of fuzzy rules, andthus creating a high level controller thatautomatically determines the set-pointsfcr the low-level PID con trollers. Froese,et al., [4]describes an example of this typeof fuzzy supervisory control applied toslurry treatment.The capability of a control system canbe greatly enhanced by adding a supervi-sory module to complement conventionalcontrol algorithms. The implementationof intelligent supervisory functions is usu-ally straightforward using fuzzy logic.T i e examples described above provideonly a glimpse of the possibilities; other

examples of fuzzy supervisory controlcan be found in [ 5 ] .Selection of Discrete ControlActionsControl problems that require the se-

lection of discrete control actions, such aschoosing to turn left or right, are not ad-dressed by control theory. This type ofcontrol problem is surprisingly common,and each application is open to novel so-lutions simply because there is no stan-dard method for handling these problems.In other words, they are ripe for the appli-cation of fuzzy logic. The c ontrol of auto-matic transmission in automobiles is onesuch problem (i.e., choosing to shift up,shift down, or stay in the current gear).Conventional automatic transmissionsselect shift action based on only the vehiclespeed and throttle opening. Fig. 4shows atypical shift pattern for the gears as a func-tion of the ve hicle speed and throttle open-ing. In general, increasing speed andordecreasing throttle opening lead to highergears, while decreasing speed and/or in-creasing throttle opening lead to lowergears. This simple shift selection functiondoes not consider the many other factorsthat affect a human drivers shift action(e.g., type of road and the road incline) andtherefore the behavior of the automatictransmission often does not match thedrivers intention. For example, if thedriver releases the gas pedal (decreasesthrottle opening) to coast down a steep hill,the a utomatic transmissions will typicallyshift to a higher gear instead of lowe ringthe gear to provide engine braking torque.To a ddress this deficiency, Nissan M otorshas developed a fuzzy automa tic transmis-sion controller that provides more intelli-gent selection of the shift action [6].Nissans fuzzy automa tic transmissioncontroller selects shift action based onmore input information than a conven-tional automatic transmission controller.The inputs to the fuzzy controller are thevehicle speed, throttle opening, change inspeed during the last two seconds, changein speed during the last five seconds,change in throttle during the last clock pe-riod, change in throttle during the last twoclock periods, and an estimate of the vehi-cles running resistance. For each possi-ble gear, a set of fuzzy membershipfunctions is defined for these input vari-ables; the mem bership functions describethe specific condition under which theparticular gear should be used. Forexample, the set of membership functions

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for gear 2 would describe the range of spe ed,throttle open ing, change in speed, chan ge inthrottle opening , etc., that is appropriate forgear 2.The fuzzy controller evaluates the de-gree to w hich the present driving conditionmatches the c ondition defined for each gear,and thus obtains a measure between 0 and 1that indicates the suitability of each gear forthe present condition.Two additional sets of fuzzy me mber-ship functions are defined to describe suit-able conditions for upshift and downshift,respectively. The fuzzy controller alsoevaluates, according to these mem bershipfunctions, the degree to w hich the presentdriving condition calls for upshifting anddownshifting. Let the degree of suitabilityfor using the ith gear be denoted by G i,the degree of suitability for upshift be de-noted by Gup , and the degree of suitabilityfor downshift be denoted by G down; thefuzzy controller determines whether toperform an upshift or a downshift by eval-uating the following function:

where i is the present gear number. Thecontroller commands an upshift if S isgreater than one by some threshold, andcommands a downshift if S is less than oneby som e threshold. Thus, in order to com-mand an upshift, the suitability of thehigher gear and the suitability of upshiftmust both be high. The gear number i iscleverly included in the evaluation func-tion to induce apreference to remain in thesame gear as the gear become s higher.In addition to the key point that thiscontrol application requires the selectionof discre te control actions, anothe r notablepoint is that this fuz zy contro ller does notuse any fuz zy if-then rules. In this appli-cation we see that only fuzzy mem bershipfunctions are employed to obtain a mea-sure of the degree of matching betweencondition s; and the degrees of matchin gare used as parameters in an ana lytical cri-terion function for decision making.Hence, fuzzy control does not necessarilyinvolve e xplicit if-then rules; how ever,the analytical criterion function may beviewed as an imp licit rule.

Identification of OperatingEnvironmentTypically a simple control law canprovide good performance w ithin only a102

limited range of operating conditions.Th u s , man y co n t ro l sy s t ems r eq u i r eswitching between different control lawsas the operating condition changes. Gainscheduling, whereby the con troller feed-back gains are switched to different val-ue s as the plant state moves from oneoperating region to ano ther, is comm onlyused in conventional control systems tocompensate for the limitations of linearcontrol laws.For set-point regulation problems,switching between different control laws isusually a straightforward function of themeasured plant states (e.g., speed, altitude,temperature). Howeve r, at higher levels ofcontrol,switching between different controllaws, or control strate gies, is based on highlevel characterizations of the operating en-vironment (e.g., driving on a highway orcity street, cooling a room full of people oran empty room). Because the high levelcharacteristics of interest are often not di-rectly measurable, the characteristics oftenneed to be inferred from indirect sensormeasurements. In such cases, fuzzy logic isextremely useful for encoding the heuristicsto infer the characteristics.

The use of fuzzy logic to characterizethe operating environment is illustratedby another automatic transmission con-troller developed by Nissan Motors [7].This alternative automatic transmissioncontroller holds a set of conventiona l shiftpatterns that are optimized for differentdriving environments (e.g., highway driv-ing, mountain d riving, city driving), andselects the appropriate shift pattern ac-cording to the driving environmen t. Forexample, human drivers prefer to main-tain a constant gear when driving on awinding road, although the throttle mustchange constantly. Therefore, driving ona winding road calls for a shift pattern thatis less se nsitive to throttle change than ashift pattern designed for highway driv-ing. In this automatic transmission con-troller, fuzzy logic is not used to directlycontrol shifting, but to identify the drivingenvironment so that the appropriate con-ventional shift pattern can be selected tocontrol shifting.Because there are no suitable sensorsfor identifying the driving environment,Nissan engineers used fuzzy logic to inferthe driving environment from the drivers

FuzzySupervisorTemperature I

Temperature

Speed PID#2

Speed 1IStress

High Level ObjectiveSelected by OperatorFig. 3.A fuzzy supervisor assigns weights to the output of different PI D controllers accord-ing to the current system state and the control objective specij?ed by a hum an operator.

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Fig. 4. Typical shift pattern fo r conven-tional automatic transmissions. The nota-tion 23 ,for example, indicates shiftingfrom gear 2 to gear 3.Driving on Highway4

100 200 300Time (sec)

, Driving on Winding Road

U 100 200 300Time (sec)(b)

Fig. 5.A driver produ ces distinctive accel-erator input behaviors when driving on ahighway versus driving on a winding road.accelerator input. For example, the accel-erator input tends to be small and constantwhen driving on a highw ay, while the ac-celerator input fluctuates wildly whendriving on a winding road (see Fig. 5).Fuzzy membership functions were de-fined to characterize the accelerator input,variance in acce lerator input, and vehiclespeed that the driver produces in eachdriving environment (see Fig. 6 ) . Thecontroller evaluates the degree to whichthe accelerator and speed data match thecondition associated with each driving en-vironment. Based on the driving environ-ment w ith the highest degree of match, theappropriate shift pattern is applied to con-trol shifting.

In addition to using fuzzy logic to in-fer the operating environment, anotherinteresting aspect of this application is

thr: use of the human driver as theenvironment sensor. Creatively infer-ring information from indirect sensors(often sensors that seem unrelated to thecharacteristic that we want to measure)is at the heart of many successful fuzzyCOntrol applications.

The fuzzy controlled vacuum cleaneran11 washing machine from MatsushitaElectric both incorporate creative use ofsensors to infer characteristics of the envi-ronment. The Matsushita vacuum cleanerautomatically adjusts suction power andbeater bar speed based on the amount ofdust and floor type. An infrared LE D sen-sor in the vacuum cleaner counts the num-ber of dust particles that pass through theair tube. The floor type is inferred from therate of change in the num ber of dust parti-cles counted; the numb er of dust particlestends to decrease slowly when vacuumingon a thick carpet (mo re difficult to pick updust), decrease faster on a normal carpet,and decrease rapidly when vacuuming ona wood floor (see Fig. 7).The fuzzy controlled washing ma chinefrom M atsushita has an infrared LED sen-sor that measures the turbidity of the exit-in,$ water. If the turbidity increas esrapidly as a function of time, then it is in-ferred that the clothes were soiled by mud(mhich washes off ea sily). If the turbidityincreases slowly, then it is inferred thatthe clothes were soiled by oil.The intelligence of a controller is de-pendent on the amount of informationavailable to the controller. When there is alack of directly measurable information,our tendency is to try to design a robustcontroller that provides acceptable perfor-mmce under all variations of the un-known (e.g., an automatic transmissionshift pattern that works adequately for a lldrwing environments). Instead of accept-ing merely adequate performance, weshould challenge ourselves to find wa ys toobtain the information needed for optimalperformance. In many cases, the informa-tion needed to optimize control choicescan be inferred from indirect sensor mea-surements. Creativity of the system de-si::ner in inferring inform ation fromindirect sources, coupled with the powerof fuzzy logic for easily encoding theheuristics, plays an important role in im-pl Zmenting truly intelligent controllers.

Define Optimality MeasureHow do we compare two system be-haviors and judge which one is better?This issue arises when a control engineer

must specify an optimality measure fromwhich to search for the best control law.The optimality measure defines the idealsystem behavior and provides a quantita-tive measure of the closeness to the idealbehavior. Analytic optimality measures,such as the quadratic cost function, givethe human designer a very limited lan-guage for expressing how to judge whichsystem behavior is closer to the ideal. Asan example, consider the common use ofthe root-mean-square (RMS) error as anoptimality measure in system modeling.The ideal system behavior is o ne that pro-duces zero error; however, in judgingwhich system behavior is closer to theideal, a designer may want to consider notonly the RMS error, but also the maxi-mum error, the average percentage error,and whether the errors occur on the con-servative side. Complex trade-offs be-tween these error types may be involvedin selecting the best system behavior.The RM S error is only a rough approxi-mation of how the human designer udgesoptimality.The key point here is that a systemconsidered optimal according to an ana-lytic measure is not necessarily optimalaccording to human judgment. It is alsoimportant to keep in mind that analyticoptimality measures are only mathemati-cal tools for expressing what a designerwants a system to do; the true judge of

6

cW

20 40Accelerator Input (deg)(a)

200 400VarianceofAccelerator Input (des2)(b)

Fig. 6. Fuzzy membership unctions char-acterize the accelerator input and vari-ance in accelerator inputproduced by thedriver in different driving environme nts.October 1998 103

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of safety of the predicted speed, closenessof the predicted stopping position o the de-sired stopping position, amount of notchchange, and the elapsed time since the lastnotch change. Here fuzzy rules rate the dif-ferent control outcomes by balancing mul-tiple objectives in a way that reflectshumans sensibility of optimal. Thenotch position associated with the optimaloutcome is then selected as the notchcommand.In many control applications we knowhow w e want a system to behave but find itdifficult to express the desired behavior inan analytic formula. Fuzzy logic is a power-ful tool for expressing human preferencesand making the control system behavior ac-curately reflect these preferences.

ConclusionThere are m any ways that fuzzy logiccan be used in a control system to enhancecapabilities and reduce operatingThe high payoff applications are usnot in replacing a conventional PID con-troller with a fuzzy P ID c ontroller, but inusing fuzzy logic at higher levels of con-trol. The previous application examplesillustrate the wide range of opportunitiesthat exist and the many different ways thatfuzzy logic can be used to complementconventional controllers. A de signer whowishes to exploit the full potential offuzzy logic must maintain a broad view ofthe different aspects of a control problemand be creative in applying fuzzy logicwhere appropriate.

The essenc e of fuzzy logic is that it letsyou express whats on your mind. It is notsurprising that most com mercial applica-tions of fuzzy control has been for highlevel, task-onented control, where thereare no standard analytic solutions but an-ple hum an intuition.References[l] Yokogawa, UT15RJT14 Digital Indicating

Controllers, technical informatlon publication TI5B4A7-01E, Yokogawa Electnc, Tokyo, Japan,1990.[2] S Chand, On-line, self-monitoring tuner forproportional integral derivative controllers,Proc. IEEE Conf Decision and Control, Brigh-ton, England, Dec 1991[3] P Bonissone, V Badami, K Chiang, PKhedkar, K Marcelle, and M Schutten, Indus-trial applications of fuzzy logic at General Elec-tnc, Proc IEEE, vol 83, no 3, pp 450-465,March 1995[4] T Froese, C von Altrock, and S Franke, Op-timization of a water-treatment system with fuzzy

cSensor ninfrared LED -cDus\Pqrtrcl:s. Ea

Thick CarpetNormal CarpetWood Floor, Mat

FOperating Time

Fig. 7. The,fuzzy vacuum cleanerfrom Matsushita infers the floor type from the rate odecrease o dust.optimality is the hum an designer, not thenumerical value produced by the analyticmeasure. Unfor tunately , we tend tochoose an optimality measure based onwhether it has nice mathem atical proper-ties, not based on whether it can expresswhat is in the designers mind.The use of fuzzy logic to expressoptimality measures is perhaps the mostvaluable benefit that fuzzy logic brings tocontrol applications. Fuzzy membershipfunction is a natural framework for ex-pressing the human designers conceptionof the ideal system behavior and of how tomeasure c loseness to the ideal behavior.Fuzzy logic can also provide sm ooth tran-sitions in the optimality measure to em-phasize certain control objectives as th eoperating condition changes.The subway train control system de-veloped by Hitachi [8] is an examplewhere fuzzy logic was applied to evaluatethe optim ality of control actions. For thisparticular system, the trains accelera-

tion/decelerationis controlled by se tting apower lever and a brake lever at differentnotch positions. Changing the notch posi-tion frequently or in large increm ents cre-ates an uncom fortable ride. In addition toriding comfort, the controller must con-sider safety, on-time arrival, energy con-s u m p t i o n , a n d s t o p p i n g t h e t r a inaccurately at a specified position alongthe station platform. Optimizing traincontrol requires trading off betw een thesemultiple, often c onflicting objectives.The control method is based on pre-dicting the outcom e of each possible con-trol action and then choosing the actionthat corresponds to the optimal outcome.A simple simulation of the train dynamicsis used to predict the resultant speed, stop-ping position, and time of arrival for eachpossible choice of notch position. Theoptimality of each predicted outcom e isthen rated by a set of fuzzy rules, takinginto account factors such as the degree towhich the train is on schedule, the degree

StephenL.Chiu i s a Research Scientist at Rockwe ll ScienceCenter. He received the B.S. degree in mechanical engmeer-ing and nuclear engineering from U.C. Berkeley in 1983 andth e S.M. degree in mechanical engineering from M.I.T. in1985. He has conducted research in robotics, fuzzy control,and neuro-fuzzy systems. His current work is focused onneuro-fuzzy systems and on managing a sm art motor devel-opment project. He is presently an associate editor of the Jour-n a l o f h t e l l i g e n t an d Fuzzy Systems an d a mem ber of the board

of the North Am encaii Fuzzy Inform ation Processing Society. He served previ-ously as an associate editor of IEEE C ontrol Systems Magazine an d as a co-guesteditor of the Proceedings o IEEE in a special issue on fuzzy logic.The author is with Rockwell Science Center, 1049 Camino Do s Rios, Thou-sand Oaks, CA 91360 (slchiu@rsc.rockwell.com). Portions of this article werepublished in the proceedings of the IE EE/IFIP International Conferenceon Infor-mation Technology for Balanced Automation Systems, Prague, August 1998.These portions are used with permission from Kluwer Academ ic Press.

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logic control, Proc. Third IEEE Intl Con$ Fu.Systems, Orlando, USA, 161&1619, June 199[5 ]K. Passino and S. Yurkovich, Fuzzy ContiAddison-Wesley Longman, 1998.[ 6 ]H. Takahashi, Fuzzy control system for aumatic transmission, U S . Patent 4,841,815,sued June 27 , 1989.[7] H. Takahashi, A method for predicting tdriving environment using fuzzy reasonin!Proc. IEEE Round T able Discussion on Fuzzy aNeural Systems, and VehicleApplications,TokjJapan, Nov. 1991.[SI S. Yasunobu an d S. Miyamoto, Automatrain operation system by predictive fuzzy cctrol, Industrial Applications o Fuzzy Contr;ed . M. Sugeno, North-Holland, Amsterdam,1-18, 1985.

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