SYSTEMATIC METHODOLOGY OF FUZZY-LOGIC MODELING AND CONTROL AND APPLICATION TO ROBOTICS MOHAMMAD REZA EMAMl A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Mechanical and Industrial Engineering University of Toronto O Copyright by Mohammad R. Emami 1997 National Library Bibliothéque nationale 1+1 of Canada du Canada Acquisitions and Acquisitions et Bibliographie Senrices sewices bibliographiques 395 Wellington Street 395. rue Wellington Ottawa ON KIA ON4 Ottawa ON KiA ON4 Canada Canada Your hle Voire reference Our hk Noire reldfence The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or sell reproduire, prêter, distribuer ou copies of this thesis in rnicroform, vendre des copies de cette thèse sous paper or elec~onicformats. la forme de mÏcrofiche/k, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. TO Zohreh, Ali, Zahra, and my parents SYSTEMATIC METHODOLOGY OF FUZZY-LOGIC MODELING AND CONTROL AND APPLICATION 70 ROBOTICS Doctor of Philosophy Mohammad Reza Emami Department of Mechanical and Industrial Engineering University of Toronto II ABSTRACT (1 This thesis presents a systematic approach to füzzy-logic modeling and control of complex systerns. In the proposed methodology, the füzzy mode1 of the system and control rules are obtained from input-output data with no need of a priori information. The proposed fuzzy modeling methodology has three significant features: (i) a unified parametenzed reasoning formulation; (ii) an improved fuzzy clustering algorithm. and (iii) an efficient strategy of selecting significant system inputs and their membership functions. The proposed fuzzy control stmcture consists of a fuzzy mode1 of the system and robust hzzy rules in order to ensure stability and satisfactory system performance. We develop a generalized formulation of sliding mode control for a class of nonlinear muti-input multi-output systems. This formulation has two distinguish features: (i) it is applicable to "black box" systems with no need to identify interna1 parameters or to assume specific propenies; (ii) it is possible to design the robust controt command for each system state independently while the stabiIity and robustness of the entire system is guaranteed. We apply the generalized formulation to andysis of the stability and robustness of the proposed fuzzy-logic control system. We also derive guidelines for designing the robust fuuy control niles. We apply the methodology to rnodeling and trajectory control of a four degree-of-freedom robot rnanipulator. Results of the proposed fuuy-logic methodology are cornpared with those of a complete analytical simulation and a heunstic fuuy rnodeling technique. A supenor rnodeling performance in tems of accuracy and simplicity is obtained. The control performance is also compared with high-gain servo controllers for different trajectories. and a higher performance is achieved. iii I wish to thank my CO-supervisorProfessor Andrew A. Goldenberg for providinp me the best environment for study, research, and training. Without his invaluable guidance and advice. this work could never have been completed at this level. 1 am particularly gratehil for his moral support and encourasement in ail aspects of my life. What 1 learnt frorn him is far beyond the technical context. 1 would like to extend my sincere gratitude to my other CO-supervisor. Professor 1. Burhan Turksen for giving me a deeper understanding of fuzzy set theoiy and fuzzy logic. 1 always enjoyed discussing absuact concepts and theories with him. During my association with the Robotics and Automation Laboratory. 1 gained a lot of experience from many scientists and experts. iMy thanks are due to dl of them: specially to Professor Nenad M. Kircansky who inuoduced the IRIS facility to me. and was always there when 1 needed help. and to engineers Jacek Wiercienski. Pawei Kuzan. and Rafi Barakat for their technical help in design and implementation. Thanks to al1 my colleagues in RUfor providing a peaceful and friendly environment. 1 would dso like to thank The Minisvy of Culture and Higher Education of the Islamic Republic of Iran for its financiai support during rny snidy. My special thanks are due to Professor Reza Hosseini. the Higher Education Advisor. for his endless cffons to facilitate Our study in Canada. Last but not least. I owe thanks to my family. to whorn this thesis is dedicated. my wife Zohreh for her greatest moral support in ail moments of this research. and my parents for their everlasting patience and encouragement. ABSTRACT iii ACKNOWLEDGMENTS iv TABLE OF CONTENTS v LlST OF FlGURES viii LlST OF TABLES xii NOTATION xiii CHAPTER 1 : INTRQDUCTW.......................................................................... 1 1.1 : Motivation.................................................................................. 1.2 : Notion of Fuuy-Logic Modeling and Control ................................. 1.2.1 : Fuzzy Sets and Fuzzy Logic .................................................. 1.2.2 : Fuzzy-Logic Modeling.......................................................... 1.2.3 : Fuuy-Logic Control ............................................................ 1.3 : Background and Outline of the Thesis ......................................... 1.3.1 : Fuzzy-Logic Modeling.......................................................... 1.3.2 : Fuzzy-Logic Control ............................................................. 1.3.3 : Application of FLC to Robotics............................................... 1.4 : Contributions ............................................................................. CHAPTER 2 : WSONING PmCFSS IN MODM........................ 2.1 : Introduction................................................................................ 2.2 : Fuuy Connectives..................................................................... 2.2.1 : Fuzzy Cornplernent............................................................. 2.2.2 : Fuzzy Set Intersection and Union........................................... 2.2.3 : Extension of Triangular Nom and Conorm Functions................. 2.3 : Implication of Individual Rules..................................................... 2.4 : Aggregation of the Rules........................................................... 2.5 : lnference of the Rule Set............................................................ 2.5.1 : Reasoning Based on Mamdani's Approximation ........................ 2.5.2 : Reasoning Based on Fomal Logical Approach ......................... 2.5.3 : Unified Pararneterized Fuzzy Reasoning Method....................... 2.6 : Defuztification of the Output ....................................................... 2.7 : A Simplified Parameterized Reasoning Formulation...................... 2.8 : Conclusion .................................................................................50 CHAPTER 3 : CLUSTWG fl FmMW ........ ....... ......... 51 3.1 : Introduction................................................................................ 51 3.2 : A Brief Background............................................................... 53 3.3 : Funy c-Means Clustering Algorithm ......................................... 54 3.4 : Cluster Validity: Specification of the Number of Clusters ................ 56 3.5 : Selection of Weighting Exponent (m) in Fuuy Clustering.............. 62 3.6 : Initial Guess and Local Optimality in FCM Algorithms.................... 68 3.7 : Formation of Membership Functions............................................ 71 3.8 : Conclusion................................................................................ 74 CHAPTER 4 : ~-LOGICMRlTTHM........................... 76 4.1 : Introduction................................................................................ 4.2 : Input Selection in Fuuy Modeling................................................ 4.2.1 : Background............................................................................ 4.2.2 : The Proposed Method.............................................................. 4.3 : Assignment of Input mernberships............................................... 4.4 : Fuuy Parameter Identification.................................................... 4.4.1 : Fu- Inference Parameter Optimization .................................. 4.4.2 : Membership Parameter Tuning .............................................. 4.5 : Fuzzy Modeling Algorithm ........................................................... 4.6 : Case Study ................................................................................ 4.7 : Conclusion................................................................................. CHAPTER 5 : SYSTWTIC, D- AND AuYSIS_QF Ta ............**........................*................ 94 5.1 : Introduction............................................................................... 94 5.2 : Robust Model-Based Fuuy-Logic Control : Design and Analysis ..... 95 5.2.1