Western Michigan University ScholarWorks at WMU Dissertations Graduate College 4-2002 Systematic Methods for the Design of a Class of Fuzzy Logic Controllers Saad Y. Yasin Western Michigan University Follow this and additional works at: https://scholarworks.wmich.edu/dissertations Part of the Navigation, Guidance, Control and Dynamics Commons Recommended Citation Yasin, Saad Y., "Systematic Methods for the Design of a Class of Fuzzy Logic Controllers" (2002). Dissertations. 1342. https://scholarworks.wmich.edu/dissertations/1342 This Dissertation-Open Access is brought to you for free and open access by the Graduate College at ScholarWorks at WMU. It has been accepted for inclusion in Dissertations by an authorized administrator of ScholarWorks at WMU. For more information, please contact [email protected]. SYSTEMATIC METHODS FOR THE DESIGN OF A CLASS OF FUZZY LOGIC CONTROLLERS By Saad Y. Yasin A Dissertation Submitted to the Faculty of the Graduate College in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Department of Mechanical and Aeronautical Engineering Western Michigan University Kalamazoo, Michigan April 2002 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SYSTEMATIC METHODS FOR THE DESIGN OF A CLASS OF FUZZY LOGIC CONTROLLERS Saad Y. Yasin, Ph.D. Western Michigan University, 2002 Fuzzy logic control, a relatively new branch of control, can be used effectively whenever conventional control techniques become inapplicable or impractical. Various attempts have been made to create a generalized fuzzy control system and to formulate an analytically based fuzzy control law. In this study, two methods, the left and right parameterization method and the normalized spline-base membership function method, were utilized for formulating analytical fuzzy control laws in important practical control applications. The first model was used to design an idle speed controller, while the second was used to control an inverted control problem. The results of both showed that a fuzzy logic control system based on the developed models could be used effectively to control highly nonlinear and complex systems. This study also investigated the application of fuzzy control in areas not fully utilizing fuzzy logic control. Three important practical applications pertaining to the automotive industries were studied. The first automotive-related application was the idle speed of spark ignition engines, using two fuzzy control methods: (1) left and right parameterization, and (2) fuzzy clustering techniques and experimental data. The simulation and experimental results showed that a conventional controller-like performance fuzzy controller could be designed based only on experimental data and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. intuitive knowledge of the system. In the second application, the automotive cruise control problem, a fuzzy control model was developed using parameters adaptive Proportional plus Integral plus Derivative (PID)-type fuzzy logic controller. Results were comparable to those using linearized conventional PID and linear quadratic regulator (LQR) controllers and, in certain cases and conditions, the developed controller outperformed the conventional PID and LQR controllers. The third application involved the air/fuel ratio control problem, using fuzzy clustering techniques, experimental data, and a conversion algorithm, to develop a fuzzy-based control algorithm. Results were similar to those obtained by recently published conventional control based studies. The influence of the fuzzy inference operators and parameters on performance and stability of the fuzzy logic controller was studied. Results indicated that, the selections of certain parameters or combinations of parameters, affect greatly the performance and stability of the fuzzy controller. Diagnostic guidelines used to tune or change certain factors or parameters to improve controller performance were developed based on knowledge gained from conventional control methods and knowledge gained from the experimental and the simulation results of this study. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. 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Copyright by Saad Y. Yasin 2002 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS This work would not have been possible without the help and support of many people. First, I would like to thank Dr. Rameshwar Sharma for his support, confidence, encouragement, advice, and valuable guidance throughout the many years of working together. I would also like to thank Dr. Subramaniam Ganesan of the Department of Computer Science and Engineering at Oakland University for his valuable guidance, stimulating thoughts and discussions, and for allowing me to use the research facilities at Oakland University. I would also like to thank Dr. Gurbux S. Alag of the Department of Electrical Engineering for his valuable and informative discussions, inputs, and feedback that made this work rich in its content and broader in its scope. I would also like to thank all members of my doctoral committee: Dr. Jerry Hamelink and Dr. Koorosh Naghshineh for their advice and guidance during my graduate studies and research. My thanks and appreciation also go to Dr. Maurice Snyder, Dr. Tim Athan, and Dr. Marcella Haghgodie at the Applied Dynamics International for their help in the experimental work conducted at their facilities. I want to express my appreciation and thanks to my wife and family, especially my parents who were very patient, understanding, and supportive. Last but not least I would like to thank Hope E. Smith who through her professionalism in the typing and editing part of this work helped greatly in producing this work in its present form. Saad Y. Yasin ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS ACKNOWLEDGMENTS.................................................................................. ii LIST OF TABLES.............................................................................................. ix LIST OF FIGURES............................................................................................ x CHAPTER I. RESEARCH OVERVIEW...................................................................... 1 Literature Review.............................................................................. 12 Dissertation Motivation .................................................................... 16 Dissertation Organization ................................................................. 22 II. BASIC MATHEMATICAL CONCEPTS OF FUZZY SETS AND NUMBERS.................................................................................... 25 Introduction ....................................................................................... 25 Fuzzy Sets and Crisp Sets ................................................................. 26 Membership Function ................................................................. 30 Fuzzy Set Operations .................................................................. 33 Linguistic Hedges and Operators ...................................................... 40 Fuzzy Inference Rules ....................................................................... 40 Fuzzy Logic Models .........................................................................