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A new approach to fuzzy control of interconnected systems.pdf

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SAMS, 2002, Vol. 42, pp. 1623–1637 A NEW APPROACH TO FUZZY CONTROL OF INTERCONNECTED SYSTEMS MAGDI S. MAHMOUD a, * , MANAR M. SABRY b,y and SALAH G. FODA c,z a Faculty of Engineering, Arab Academy for Sciences and Technology, P.O. Box 2033 Al-Horriya, Cairo, Egypt b Projects and Design Division, Saudi Arabian Texaco (J.O.), P.O. Box 9720, Ahmadi 61008, Kuwait c Electrical Engineering Department, King Saud University, P.O. Box 800, Riyadh 1142
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  SAMS  , 2002, Vol. 42, pp. 1623–1637 A NEW APPROACH TOFUZZY CONTROL OFINTERCONNECTED SYSTEMS MAGDI S. MAHMOUD a, *, MANAR M. SABRY b, y and SALAH G. FODA c, z a Faculty of Engineering, Arab Academy for Sciences and Technology,P.O. Box 2033 Al-Horriya, Cairo, Egypt b Projects and Design Division, Saudi Arabian Texaco (J.O.),P.O. Box 9720, Ahmadi 61008, Kuwait c Electrical Engineering Department, King Saud University,P.O. Box 800, Riyadh 11421, Saudi Arabia (Received 29May 2000) This paper develops a new approach to the control of interconnected system using fuzzysystem theory. The approach is based on incorporating a group of local estimators onthe system level to generate the input–output database. An array of feedback fuzzy con-trollers is then designed to ensure the asymptotic stability of the closed loop system. Thedeveloped technique is applied to an unstable large-scale system, and extensive simula-tion studies are carried out to illustrate the potential of the new approach. Keywords: 1. INTRODUCTION In control engineering research, problems of decentralized controland stabilization of interconnected systems are receiving considerableinterest in recent years [1,2] where most of the effort is focused on *Corresponding author. E-mail: magdi@eng.kuniv.edu.kw y E-mail: mmanar@ncc.moc.kw z E-mail: sfoda@ksu.edu.sa1623  dealing with the interaction patterns. It is concluded that a systematicapproach to deal with the problems of interconnected systems is two-fold: First is to base the analysis and design effort on the subsystemlevel using conventional control methods and second is to deal withinteractions effectively. These methods are facilitated, in general, byvirtue of several mathematical tools including linearization, delayapproximation, decomposition and model reduction. This constitutesthe so-called model-based control system approach for which wehave seen numerous techniques [3]. Most of the available resultshave so far overlooked the operational knowledge of the intercon-nected system under consideration. In [4], a knowledge-basedcontrol system approach has been suggested to deal with the analysisand design problems of interconnected systems by incorporatingboth the simplest available model as well as the best available knowl-edge about the system. For single physical systems, one of the earlierefforts along this direction has been based on the development of an expert learning system [5–6]. An alternative approach has beento integrate elements of discrete event systems with differential equa-tions [7]. A practically supported third approach has been the use of fuzzy logic control by successfully applying fuzzy sets and systemstheory [9].For interconnected systems, the foregoing approach motivates theresearch into intelligent control by combining techniques of controland systems theory with those from artificial intelligence. The mainfocus should be on integrating a knowledge base, an approximate(humanlike) reasoning and/or a learning process within a hierarchicalstructure.Fuzzy logic controllers [10] are generally considered applicable toplants that are mathematically poorly understood (there is no accept-able mathematical model for the plant) and where experiencedhuman operators are available for satisfactorily controlling the plantand providing qualitative ‘‘rules of thumb’’ (qualitative control rulesin terms of vague and fuzzy sentences).1. Hierarchical ordering of fuzzy rules is used to reduce the size of theinference engine.2. Real-time implementation, or on-line simulation of fuzzy control-lers can help reduce the burden of large-sized rule sets by fusing 1624 M.S. MAHMOUD  et al.  sensory data before imputing the system’s output to the inferenceengine.A concerted effort has been made to formally reduce the size of thefuzzy rule base to make fuzzy control attractive to interconnectedsystems. Two of the difficulties with the design of any fuzzy controlsystem are: .  The shape of the membership functions. .  The choice of fuzzy rules.The properties that a fuzzy membership function is used to charac-terize are usually fuzzy. Therefore, we may use different membershipfunctions to characterize the same description. Conceptully, there aretwo approaches to determine a membership function. The firstapproach is to use the knowledge of human experts. Usually thisapproach can only give a rough formula of the membership function;fine-tuning is required. In the second approach, data are collectedfrom various sensors to determine the membership functions.Specifically, the structures of the membership functions are specifiedfirst. Then fine-tuning of the membership function parameters shouldbe implemented based on the collected data [8].In this paper, we contribute to the further development of intelligentcontrol techniques of interconnected systems. It provides a newapproach to fuzzy control design for interconnected systems. Theapproach consists of two stages: In the first stage, a group of localstate estimators is constructed to generate the data base of input-output pairs. In the second stage, an array of feedback fuzzy controllersis designed and implemented to ensure the asymptotic stability of theinterconnected system. Simulation studies on a large-scale systemwith unstable eigenvalues are carried to illustrate the features andcapability of the new approach. 2. FUZZY SYSTEMS BACKGROUND Fuzzy control is by far the most successful application of fuzzy setsand systems theory to practical problems. Numerous applications of fuzzy logic controllers to a variety of consumer products and industrialsystems have been recorded [4,9]. FUZZY CONTROL 1625  Fuzzy systems are linguistic knowledge based system. The heart of a fuzzy system is what is so-called fuzzy IF-THEN rules. These rulesare statements in which some words are described by a continuousmembership function (Fig. 1). For example,IF vessel temperature is highTHEN small opening of fuel value is required : IF vessel temperature is lowTHEN wide opening of fuel value is required :  ð 1 Þ In general, the starting point of constructing a fuzzy system is toobtain a collection of fuzzy IF-THEN rules from human experts,experiments or based on domain knowledge.The next step is to combine these rules into a single system. There arethree types of fuzzy systems that are commonly used:1. Pure fuzzy systems,2. Takagi–Sugeno–Kang (TSK) fuzzy systems, and3. Fuzzy systems with fuzzifier and defuzzifier.The three systems are described briefly hereinafter.The configuration of a pure fuzzy system is illustrated in Fig. 2. Thefuzzy rule base represents the collection of fuzzy IF-THEN rules. Thefuzzy inference engine combines these fuzzy IF-THEN rules into amapping from fuzzy set in the input space  U   R n to fuzzy sets in theoutput space  V   R  based on fuzzy logic principles. If the dashed FIGURE 1 a. Temperature membership functions; b. Valve opening membershipfunctions.1626 M.S. MAHMOUD  et al.
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