本論文將針對大規模的複雜受控系統，提出一個植基於遺傳演算法(Genetic Algorithm)的多階模糊控制器(Multistage Fuzzy Logic Controller)之設計方法，主要目的在於藉由多階模糊控制器大量地減少所需規則數，並利用遺傳演算法設計多階模糊控制器的參數，免於以費時的嘗試錯誤法(Trail and Error)設計控制器。
多階模糊控制器需要設計的參數包括了規則庫、輸出/入變數的歸屬函數和調整因子三種參數，本論文將選定由遺傳演算法搜尋調整因子、以專家設計或是由專家設計後再以遺傳演算法調整歸屬函數、以規則產生函數(Rule Generation Function)或是由遺傳演算法產生規則庫等四種不同的控制器參數設計要求，結合非對稱性樹(Skew Tree)和二元樹(Binary Tree)二種多階模糊控制器架構，因此，共設計八個植基於遺傳演算法之多階模糊控制器，最後並以倒單擺滑車系統比較其控制性能。
電腦模擬結果顯示，這八個多階模糊控制器都具有良好的控制性能，因此，可證實本論文所提的方法能提供系統性的方式設計多階模糊控制器。
關鍵字：多階模糊控制器、遺傳演算法、倒單擺、規則產生函數

This paper proposes a genetic algorithm (GA) approach to design a multistage fuzzy logic controller for large-scale and complex control system. The main purpose of this paper is to decrease the large number of rules by using multistage fuzzy logic controller , and adopt the genetic algorithm method to design the parameter on multistage fuzzy controller. This can get rid of trial and error approach on controller design.
There are three kinds of parameters on multistage fuzzy logic controller. It includes the rule base, input/output variables of membership function and scaling factors. The scaling factor are designed by GA , the membership function is determined by expert or regulated by GA after expert design , and the rule bases are generated by two ways：one is generated by rule generation function , the other is generated by GA . This can be found the four kinds of types in parameter design , and these four types of parameter design can be combined with two kinds of framework (Skew tree and Binary tree). Therefore there are eight kinds of multistage fuzzy logic controllers on the basis of GA , and we compared their performance in pendulum-cart system.
The results of simulation show that all of the multistage fuzzy controllers have good performance. The proposed approach provide a systematic way to design multistage fuzzy logic controller.
Keywords：Multistage Fuzzy Logic Controller、Genetic Algorithm、Inverted pendulum、Rule Generation Function

英文部份：
[1]C. C. Lee ,〝Fuzzy Logic in Control Systems：Fuzzy Logic Controller— PartⅠ,PartⅡ〞, IEEE Transaction on Systems , Man and Cybernetics , Vol.20 , No.2 , pp.404-434 , 1990
[2]Hung-Pin Chen and Tai-Ming Parng ,〝A new approach of multi-stage fuzzy logic inference〞, Fuzzy Sets and Systems , Vol.78 , No.1 , pp.51-72 , 1996.
[3]Zong-Mu Yeh and Hung-Pin Chen ,〝Multi-stage Inference Fuzzy Logic Control 〞, Proceeding of the sixth IEEE International Conference on Fuzzy Systems , Vol.2 , pp.1153-1158 , 1997.
[4]Jyh-Shing Roger Jang ,〝Adaptive network based fuzzy inference system〞, IEEE Transactions on Systems , Man , and Cybernetics , Vol.23 , No.3 , pp.665-685 , 1993.
[5]K. Uehara and M. Fujise , 〝Multistage fuzzy inference formulated as linguistic truth-value propagation and its learning algorithm based on back-propagating error information〞, IEEE Transactions on Fuzzy Systems , Vol.1 , No.3 , pp.305-317 , 1993
[6]Zong-Mu Yeh ,〝Adaptive multivariable fuzzy logic controller 〞, Fuzzy Sets and Systems , Vol.86 , pp.43-60 , 1997.
[7]C,D.S.〝Knowledge base decoupling in fuzzy logic control systems〞 , Proceeding of the American Control Conference , Vol.1 , pp.760-764 , 1993.
[8]Chen-Wei Xu ,〝Linguistic decoupling control of fuzzy multivariable processes〞, Fuzzy Sets and Systems , Vol.44 , pp.209-217 , 1991.
[9]Lin Shi and Sunil K. Singh ,〝Decentralized adaptive controller design for logic-scale systems with higher order interconnections〞, IEEE Transaction Automatic control , Vol.37 , No.8 , pp.1106-1117 , 1992.
[10]A. E. Gegov and P. M. Frank ,〝Decentralized fuzzy control of multivariable systems by active decomposition of control laws 〞, International Journal Control , Vol.62 , No.4 , pp.781-791 , 1995.
[11]G. V. S. Raju and Jun Zhou ,〝Adaptive hierarchical fuzzy controller〞, IEEE Transactions on Systems , Man , and Cybernetics , Vol.23 , No.4 , pp.973-980 , 1993.
[12]G. V. S. Raju and Jun Zhou and Roger. A. Kisner ,〝Hierarchical fuzzy control〞International Journal Control , Vol.54 , No.5 , pp.1201-1216 , 1991.
[13]T. C. Chin and X. M. Qi ,〝Genetic algorithms for learning the rule base of fuzzy logic controller 〞, Fuzzy Sets and Systems , Vol.97 , pp.1-7 , 1998.
[14]K. F. Man and K. S. Tang ,〝Genetic algorithms：concepts and application〞, IEEE Transactions on Industrial Electronics , Vol.43 , No.5 , 1996.
[15]Jinwoo Kim and B. P. Zeigleru ,〝Designing fuzzy logic controller using a multiresolutional search paradigm〞, IEEE Transactions on Fuzzy Systems , Vol.4 , No.3 , pp.213-226 , 1996.
[16]Y. S. Tarng and Z. M. Yeh and C. Y. Nian ,〝Genetic synthesis of fuzzy logic controllers in turning 〞, Fuzzy Sets and Systems , Vol.83 , pp.301-310 , 1996.
[17]Z. M. Yeh ,〝A Systematic Method for Design of Multivariable Fuzzy Logic Control Systems〞IEEE Transactions on Fuzzy System , Vol.4 , No.3 , pp.215-228 , 1998.
[18]Zong-Mu Yeh and Hung-Pin Chen ,〝 A novel approach for multistage inference fuzzy control〞, IEEE Transactions on Systems , Man , and Cybernetics— part B: Cybernetics , Vol.28 ,No.6 , pp.935-944 , 1998.
[19]C. Dou and J. A Macedo ,〝Complex System Inference-Control and Fuzzy Logic Modeling〞, International Journal Control , Vol.65 , No.5 , pp.373-378, 1995.
[20]Kuo-Yang Tu and Tsu-tian Lee and Wen-Jieh Wang ,〝Design of a multi-layer fuzzy logic controller for multi-input multi-output systems〞, Fuzzy Sets and Systems , Vol.111 , pp.199-214 , 2000.
[21]Yong-Tae Kim and Zeungnam Bien ,〝Robust self-learning fuzzy controller design for a class of nonlinear MIMO systems〞, Fuzzy Sets and Systems , Vol.111 , pp.117-135 , 2000.
[22]Koji Shimojima and Toshio Fukuda ,〝Self-tuning fuzzy modeling with adaptive membership function , rules , and hierarchical structure based on genetic algorithm〞, Fuzzy Sets and Systems , Vol.71 , pp.295-309 , 1995.
[23]D. A. Linkens and H. O. Nyongesa ,〝Genetic algorithms for fuzzy control part1：Offline system development and application〞, IEE Proceeding of Control Theory Application , Vol.142 , No.3 pp.161-176 , 1995.
[24]France Cheong and Richard Lai ,〝Constraining the optimization of a fuzzy logic controller using an enhanced genetic algorithm〞, IEEE Transaction on Systems , Man and Cybernetics—partB：Cybernetics , Vol.30 , No.1 , pp.31-46 , 2000
[25]H. Ishibuchi and T. Murata ,〝Minimizing the fuzzy rule base and Maximizing its performance by a multi-objection genetic algorithm〞, Proceeding of the sixth IEEE International Conference on Fuzzy Systems , Vol.2 , pp.259-264 , 1997.
[26]Khaled Belarbi and Faouzi Titel ,〝Genetic algorithm for the design of a class of fuzzy controllers：an alternative approach〞, IEEE Transactions on Fuzzy System , Vol.8 ,No.4 , pp.398-405 , 2000.
[27]Mori Shozo ,〝Control of unstable mechanical system control of pendulum〞, International Journal Control , Vol.23 , No.5 , pp.673-692 , 1976.
[28]Ren-Hou Li and Zhang Yi ,〝Fuzzy controller based on genetic algorithms〞, Fuzzy Sets and Systems , Vol.83 , pp.1-10 , 1996.
[29]K. G. Eltohamy and C. Y. Kuo ,〝Real time stabilization of s triple link inverted pendulum using single control input〞, IEE Proceeding of Control Theory Application , Vol.144 , No.5 pp.498-504 , 1997.
中文部份：
[30]孫宗瀛，楊英魁，〝Fuzzy控制：理論、實作與應用〞，台北:全華圖書，1994。
[31]陳弘斌，〝高速多階模糊邏輯推理及其數位實施〞，國立台灣大學博士論文，1997。
[32]林家德，〝植基於傳演算法之模糊控制器在倒立單擺上的應用〞，國立台灣師範大學工業教育研究所碩士論文，1994。
[33]周益生，〝利用遺傳演算法設計最佳模糊控制器〞，私立中原大學電機工程研究所碩士論文，1995。
[34]林明隆，〝基於基因演算法的最佳模糊控制器之設計〞，國立中央大學電機工程研究所碩士論文，1996。
[35]李志山，〝雙節倒單擺之數位控制〞，國立交通大學控制工程研究所碩士論文，1995。
[36]施振祥，〝倒立單擺上甩運動與定位模糊控制器設計〞，國立交通大學控制工程研究所碩士論文，1995。