本論文中提出了幾種模糊滑動模式控制器的設計方法，並且將其應用在機電系統中，以驗證所提控制器之效能和可行性。模糊滑動模式控制器的優點在於其本質上就提供良好的強健性，並且可以系統化的方式推導模糊規則表，所以在面對難以模式化的系統時，我們可以以口語的方式來架構控制法則，而省去了複雜的數學運算。首先，我們提出一個新類型的模糊控制器來處理離散時間系統，其特點為，此模糊控制器的推論法則都可以藉由Lyapunov穩定法則來產生。如此一來，就不太需要對受控系統做全盤的瞭解，而在此論文中，亦舉了三種系統來做驗證，包含線性、非線性和時間延遲系統等，由模擬的結果可知，所提模糊控制器可以有效的控制所列舉的各種不同型式的系統。其次，本文提出了完整的模糊滑動模式控制器和解耦模糊滑動控制器的設計和實現之方法和流程，並將所提控制器分別應用在倒三角系統和具彈簧連結的倒單擺系統中。所提設計和實現的流程包括受控系統的模式化、控制器的推導、穩定性的分析、電腦模擬和即時的控制實驗等五大目標。最後，我們以FPGA晶片來實現模糊控制器，並設計一倒單擺車系統來驗證此模糊控制晶片的效能。為了提昇控制的性能，我們發展了兩種模糊滑動控制器，包含具動態權重調整之模糊滑動控制器和模糊監督型動態權重調整之模糊滑動控制器。從模擬的結果可以確保所設計控制法則的有效性，然後將此模糊滑動控制法則實現在FPGA晶片上，來當作倒單擺車平衡控制的核心控制器。由即時的控制實驗可得知，此模糊控制晶片能夠成功地平衡倒單擺車上的倒單擺，達成預設之控制目的。

In this dissertation, we present design methodologies of fuzzy sliding-mode controllers (FSMCs) and apply them into mechatronic systems to examine the effectiveness and feasibility. The main advantages of FSMCs are their intrinsic robustness and the systematic derivation of fuzzy rule tables, and FSMCs are suitable for the ill-modeled systems from the linguistic representation of the control strategies. First, we present a new type of fuzzy logic controllers (FLCs) for discrete-time systems, and all the decision rules of FLCs are automatically generated by the Lyapunov stability criterion. The proposed control scheme can be easily derived with minimum information of the controlled plants, where three discrete-time systems, including a linear plant, a nonlinear plant, and a delayed plant are utilized to demonstrate the effectiveness of the proposed FLC. Second, we address the design and implementation of FSMCs and decoupled FSMCs (DFSMC) for a wedge-balancing system and spring-linked cart-pole (SLCP) systems, respectively, where five tasks are examined including modeling, controller design, stability verification, computer simulations, and real time experiments. Finally, we present the FLC design with the FPGA chip and set up an inverted pendulum car (IPC). For improving the control performance, we develop two kinds of FSMCs, the dynamic weighted FSMC (DWFSMC) and the fuzzy supervised DWFSMC (FSFSMC). Simulation results confirm the validity. Implementation of FSMC on an FPGA chip is also provided. The real-time experiments demonstrate that the proposed FSMC can successfully balance the pole of the FPGA-based IPC.

[1] C.-V. Altrock, B. Krause and H.-J. Zimmermann, “Advanced fuzzy logic control of a model car in extreme situation,” Fuzzy Sets and Systems, vol. 48, pp.41-52, 1992.
[2] G. Ambrosine, G. Gelentane, and F. Garofalo, “Variable structure model reference adaptive control systems,” Int. J. Contr., vol. 39, no. 6, pp.1339-1349, 1984.
[3] A.-E. Bryson and Y.-C. Ho, Applied Optimal Control, Hemisphere, N.Y., 1975.
[4] C.-C. Cheng and T.-H. S. Li, “Parallel fuzzy sliding-mode control of a spring-linked cart-pole system,” IEEE IECON’98, Aachen, German, 1998.
[5] C.-L. Chen, “Optimal design of fuzzy sliding-mode control: a comparative study,” Fuzzy Sets and Systems, vol. 93, pp. 37-48, 1998.
[6] C.-S. Chen, Analysis and Design of Uncertain System Using Fuzzy Control Logic, Ph. D. Dissertation, National Tsing Hua University, 1997.
[7] C.-T. Chen, Linear System Theory and Design, 3-rd Edition, Oxford University Press, New York, 1999.
[8] H.-K. Chen, Design and Applications of Fuzzy Sliding-Mode Control Chip using FPGA, Master Thesis, Dept. of Electrical Engineering, National Cheng Kung Univ., Tainan, Taiwan, R.O.C., June 1999.
[9] J.-Q. Chen and L.-J. Chen, “Study on stability of fuzzy closed-loop control system,” Fuzzy Sets and Systems, vol. 57, pp. 159-168, 1993.
[10] L.-H. Chen and C.-H. Chiang, “New approach to intelligent control systems with self-exploring process,” IEEE Trans. Systems, Man, Cyber. –Part B, vol. 33, pp. 56-66, 2003.
[11] C.-H. Chou and H.-C. Lu, “A heuristic self-tuning fuzzy controller,” Fuzzy Sets and Systems, vol. 6, pp. 249-264, 1994.
[12] M. Chung and J.-H. Oh, “Control of dynamic systems using fuzzy learning algorithm,” Fuzzy Sets and Systems, vol. 59, pp.1-14, 1993.
[13] J.-Y. Dieulot and P Borne, “Parameter tuning of stable fuzzy controllers,” J. Intelligent and Robotic Systems. vol. 33, pp. 301-312, 2002.
[14] H. Eichfeld, T. Kunemund, and M. Menke, “A 12b general-purpose fuzzy logic controller chip,” IEEE Trans. on Fuzzy Systems, vol. 4, no. 4, pp. 460-475, 1996.
[15] K. Furuta and M. Yamakita, “A new inverted pendulum apparatus for education,” Proc. of 1991 IFAC Conf. Advances in Control Education, pp. 191-196.
[16] D.-T. Gavel and D.-D. Siljak, “Decentralized adaptive control: structural conditions for stability,” IEEE Trans. on Automatic Control, vol. 34, no. 4, pp. 413-426, 1989.
[17] J.-S. Glover and J. Munighan, “Designing fuzzy controllers from a variable structure standpoint,” IEEE Trans. Fuzzy Systems, vol. 5, pp. 138-144, 1997.
[18] R. Gurumoorthy and S.-R. Sanders, “Controlling nonminimum phase nonlinear system- the inverted pendulum on a cart example,” Proc. of the 1993 ACC, vol. 1, pp. 680-685, 1993.
[19] M. Hagan, C.-D. Latino, E. Misawa, and G. Young, “An interdisciplinary control systems laboratory,” Proc. of the 1996 IEEE International Conference on Control Applications held together with IEEE International, pp. 403-408, 1996.
[20] S.-K. Halgamuge, T. Hollstein, A. Kirschbaum, and M. Glesner, “Automatic generation of application specific fuzzy controllers for rapid-prototyping,” Proc. of 3rd IEEE Conf. on Fuzzy Systems, vol.3, pp. 1638 –1641, 1994.
[21] T. Hollstein, S.-K. Halgamuge, and M. Glesner, “Computer-aided design of fuzzy systems based on generic VHDL specifications,” IEEE Trans. on Fuzzy Systems, vol. 4, no. 4, pp. 403-417, 1996.
[22] D.-L. Hung, “Custom design of a hardware fuzzy logic controller,” Proc. of the 3rd IEEE Conf. on Fuzzy Systems, vol. 3, pp. 1781 –1785, 1994.
[23] D.-L. Hung, “Design and rapid prototyping a high performance hardware fuzzy controller with adaptability,” Proc. of the IEEE Int. Conf. on Industrial Technology, pp. 263 –267, 1994.
[24] J.-Y. Hung, G. Senior, and J.-C. Hung, “Variable structure control: a survey,” IEEE Trans. Industrial Electronics, vol. 40, pp. 2-22, 1993.
[25] C.-S. Hsu, Design of Dynamic Fuzzy Controller IC Using FPGA, Master Thesis, Dept. of Electrical Engineering, National Cheng Kung Univ., Tainan, Taiwan, R.O.C., June 1999.
[26] P. Hsu, J. Wendiandt, C. Runge, D. Soderstrom, R. Bohn, W. Cahoon, T. Marketti, and D. Ward, “The wedge- a controller design experiment,” Proc. of 1991 IFAC Conf. Advances in Control Education, Boston, pp. 169-174, 1991.
[27] C.-L. Hwang, F.-Y. Sung, and M.-H. Wei, “Improved fuzzy sliding-mode control for a linear servo motor system,” Control Engineering Practice, vol. 5, pp. 219-227, 1997.
[28] G.-C Hwang and S.-C. Lin, “A stability approach of fuzzy control design for nonlinear systems,” Fuzzy Sets and Systems, vol. 48, pp. 279-287, 1992.
[29] H. S. Hwang, “Automatic design of fuzzy rule base for modeling and control using evolutionary programming,” IEE Proc. –Control Theory Appl., vol. 146, pp. 9-16, 1999.
[30] A. Ishigame, T. Furakawa, S. Kawamoto, and T. Taniguchi, “Sliding mode controller design based on fuzzy inference for nonlinear systems,” IEEE Trans. Industrial Electronics, vol. 40, no. 1, pp. 64-70, 1993.
[31] J.-S. R. Jang, “Self-learning fuzzy controllers based on temporal back propagation,” IEEE Trans. on Neural Networks, vol. 3, no. 5, pp. 714-723, 1992.
[32] J.-M. Jou, P.-Y. Chen, S.-S. Yang, “An adaptive fuzzy logic controller: its VLSI architecture and applications,” IEEE Trans. on VLSI systems, vol. 8, no.1, pp. 52-60, 2000.
[33] O. Kaynak, K. Erbatur, and M. Ertugrul, “The fusion of computationally intelligent methodologies and sliding-mode control-a survey,” IEEE Trans. Industrial Electronics, vol. 48, no. 1, pp. 4-17, 2001.
[34] S.-W. Kim and J.-J. Lee, “Design of a fuzzy controller with fuzzy sliding surface,” Fuzzy Sets and Systems, vol. 71, pp. 359-367, 1995.
[35] Youngdal Kim and H.-L. Kwang, “An architecture of fuzzy logic controller with parallel defuzzification,” Proc. of the NAFIPS, pp. 497-501, 1996.
[36] P. M. Larsen, “Industrial applications of fuzzy logic control,” Int. J. Man, Mach, Studies, vol. 12, No. 1, pp. 3-10, 1980.
[37] J.-R. Layne and K.-M. Passino, “Fuzzy model reference learning control,” Proc. of the 1st IEEE Conf. on Control Applications, pp. 686-691, Dayton, Ohio, 1992.
[38] C.-C. Lee, “Fuzzy logic in control system: fuzzy logic controller, part I and part II,” IEEE Trans. System, Man and Cyber., vol. 20, no. 2, pp. 404-435, 1990.
[39] C.-G. Lhee, J.-S. Park, H.-S. Ahn, and D.-H. Kim, “Sliding mode-like fuzzy logic control with self-tuning the dead zone parameters,” IEEE Trans. on Fuzzy Systems, vol. 9, no. 2, pp. 343-348, 2001.
[40] T.-H. S. Li and C.-Y. Tsai, “Parallel fuzzy sliding mode control of the cart-pole system,” Proc. of the IEEE IECON’95, pp. 1468-1473, Orlando, U.S.A., 1995.
[41] T.-H. S. Li, J.-H. Li, and C.-C. Cheng, “Design and implementation of fuzzy sliding-mode controllers for spring-linked two cart-pole systems,” Proc. of IEEE SMC’99, no.1, pp.343-348, 1999.
[42] T.-H. S. Li and M.-Y. Shieh, “Switching-type fuzzy sliding mode control of a cart-pole system,” Mechatronics, no. 10, pp. 91-109, 2000.
[43] C.-E. Lin and Y.-R. Sheu, “A hybrid-control approach for pendulum-car control,” IEEE Trans. on Industrial Electronics, vol. 39, no. 3, pp. 208-214, 1992.
[44] C.-T. Lin and Y.-C. Lu, “A neural fuzzy system with linguistic teaching signals,” IEEE Trans. on Fuzzy Systems, vol. 3, no. 2, pp. 169-189, 1995.
[45] S.-C. Lin and Y.-Y. Chen, “Design of adaptive fuzzy sliding mode for nonlinear system control,” Proc. of International Fuzzy Systems Conference, vol. 1, pp. 35-39, 1994.
[46] B.-D. Liu and C.-Y. Huang, “Design and implementation of the tree-based fuzzy logic controller,” IEEE Trans. on Systems, Man, and Cybernetics, vol. 27, no. 3, pp. 475-487, 1997.
[47] B.-D. Liu, C.-Y. Chen, and J.-Y. Tsao, “Design of adaptive fuzzy logic controller based on linguistic-hedge concepts and genetic algorithms,” IEEE Trans. Systems, Man, and Cybernetics – Part B, vol. 31, no. 1, pp. 32-53, 2001.
[48] S.-M. Liu and S.-H. Hu, “A method of generating control rule model and its implication,” Fuzzy Sets and Systems, vol. 52, pp. 33-37, 1992.
[49] H.-A. Malki, H. Li, and G. Chen, “New design and stability analysis of fuzzy proportional-derivative control systems,” IEEE Trans. Fuzzy Systems, vol. 2, pp. 245-254, 1994.
[50] E.-M. Mamdani, “Application of fuzzy algorithms for control of simple dynamic plant,” Proc. IEE. vol. 121, no. 12, pp. 1585-1588, 1974.
[51] E.-H. Mamdani, “Application of fuzzy logic to approximate reasoning using linguistic synthesis,” IEEE Trans Computers, vol. C-26, 1977.
[52] M.-A. Manzoul, and D. Jayabharathi, “Fuzzy controller on FPGA chip,” Proc. of IEEE Int. Conf. on Fuzzy Systems, pp. 1309-1316, 1992.
[53] A. Ouezri, N. Derbel, and A.-M. Alimi, “Automatic generation of fuzzy rules for the control of a mobile robot,” System Analysis and Modeling Simulation, vol. 42, pp.1081-1105, 2002.
[54] R. Palm, “Robust control by sliding mode,” Automatica, vol. 30, pp. 1429-1437, 1994.
[55] R. Palm, “Sliding mode fuzzy control,” Proc. of IEEE Int. Conf. on Fuzzy Systems, 519-526, 1992.
[56] R. Palm and D. Driankov, “Stability of fuzzy gain schedulers: sliding-mode based analysis,” Proc. of IEEE Int. Conf. Fuzzy Systems, pp. 177-183, 1997.
[57] R. Palm and D. Driankov, “Design of a fuzzy gain scheduler using sliding mode control principles,” Fuzzy Sets and Systems, vol. 121, pp. 13-23, 2001.
[58] M.-J. Patyra, J.-L. Grantner, and K. Koster, “Digital fuzzy logic controller: design and implementation,” IEEE Trans. on Fuzzy Systems, vol. 4, no. 4, pp. 439-459, 1996.
[59] T.-J. Procyk and E.-H. Mamdani, “A linguistic self-organizing process controller,” Automatica, vol. 15, pp. 15-30, 1997.
[60] V. Salapura, and V. Hamann, “Implementing fuzzy control systems using VHDL and statecharts,” Proc. of Design Automation Conference, EURO-DAC '96, European, pp. 53 –58, 1996.
[61] L. Shi and S.-K. Singh, “Decentralized adaptive controller design for large-scale systems with higher-order interconnections,” IEEE Trans. on Automatic Control, vol. 37, no. 8, pp. 1106-1118, 1992.
[62] L. Shi and S.-K. Singh, “Decentralized control for interconnected uncertain systems: extensions to higher-order uncertainties,” Int. J. Control, vol. 57, no. 6, pp. 1453-1468, 1993.
[63] J.-J. E. Slotine, “The robust control of robot manipulators,” Int. Journal of Robotics Research, vol. 4, pp. 49-64, 1985.
[64] J.-J. E. Slotine, Applied Nonlinear Control, Prentice-Hall, Inc., 1991.
[65] W.-C. So, “Development of a fuzzy logic controller for DC/DC converters: design, computer, simulation, and experimental evaluation,” IEEE Trans. Power Electronic, Vol. 11, No.6, pp. 24-32, 1996.
[66] M. Sugeno and M. Nishida, “Fuzzy control of model car,” Fuzzy sets and Systems, vol. 16, pp. 103-113, 1985.
[67] A. Suyitno, J. Fujikawa, H. Kobayashi, and Y. Dote, “Variable-structured robust controller by fuzzy logic for servomotors,” IEEE Trans. Industrial Electronics, vol.40, no.1, pp. 80-88, 1993.
[68] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Systems, Man, Cyber., vol. 15. pp. 116-132, 1985.
[69] K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control systems,” Fuzzy Sets and Systems, vol. 45, pp. 135-156, 1992.
[70] K. Tanaka, T. Ikeda, and H.-O. Wang, “Robust stabilization of a class of uncertain nonlinear system via fuzzy control: quadratic stabilizability, control theory, and linear matrix inequalities,” IEEE Trans. Fuzzy Systems, vol. 4, pp. 1-13, 1996.
[71] C.-W. Tao and J.-S. Taur, “Flexible complexity reduced PID-like fuzzy controllers,” IEEE Trans. Systems, Man, Cyber. - Part B, vol. 30, pp. 510-516, 2000.
[72] C.-S. Ting, T.-H. S. Li and F.-C. Kung, “An approach to systematic design of the fuzzy control system,” Fuzzy Sets and Systems, vol. 77, pp. 151-166, 1995.
[73] M. Togai, and H. Watanabe, “Expert system on a chip: an engine for real-time approximate reasoning,” IEEE Expert, pp. 55-62, 1986.
[74] C.-H. Tsai and Y.-Y. Tzou, “DSP-based balancing control of an inverted wedge using robust pole placement technique,” Proc. of Automatic Control Conference, pp. 172-179, 1994.
[75] C.-Y. Tsai and T.-H. S. Li, “Design of Lyapunov function based fuzzy logic controller,” Proc. of Int. Conf. on IEEE IECON 22nd, Vol. 1, pp. 396-401, 1996.
[76] S.-G. Tzafestas and G.-G. Regatos, “Design and stability analysis of a new sliding-mode fuzzy logic controller of reduced complexity,” Machine Intelligence and Robotic Control, vol. 1, no. 1, pp. 27-41, 1999.
[77] S.-G. Tzafestas and G.-G. Rigatos, “A simple robust sliding-mode fuzzy logic controller of the diagonal type,” J. Intelligent and Robotic Systems, vol. 26, no. 3-4, pp. 353-388, 1999.
[78] P. Ungering, K. Thuener, and K. Goser, “Architecture of a PDM VLSI fuzzy logic controller with pipelining and optimized chip area,” Proc. of 2nd IEEE Int. Conf. on Fuzzy Systems, vol. 1, pp. 447 –452, 1994.
[79] H.-O. Wang, K. Tanaka and M.-F. Griffin, “An approach to fuzzy control of nonlinear systems: stability and design issues,” IEEE Trans. on Fuzzy Systems, vol. 4, no. 1, pp. 14-23, Feb., 1996.
[80] L.-K. Wang, F.-H. F. Leung, and P.-K. S. Tam, “Lyapunov-function-based design of fuzzy logic controllers and its application on combining controllers,” IEEE Trans. Industrial Electronics, vol. 45. pp. 502-509, 1998.
[81] L.-X. Wang, “Stable adaptive fuzzy control of nonlinear systems, IEEE Trans. Fuzzy Systems, vol. 1, no. 2, pp. 146-159, 1993.
[82] L.-X. Wang, “Stable adaptive fuzzy controllers with application to inverted pendulum tracking,” IEEE Trans. on System, Man and Cyber-part B: Cybernetics, vol. 26, no. 5, pp. 677-691, 1996.
[83] Q. Wei, W.-S. Levine, and W.-P. Dayawansa, “An experiment to demonstrate the bandwidth requirements of a nonlinear controller,” 1991 IFAC Conf. Advances in Control Education, pp. 183-185.
[84] L.-K. Wong, F.-H. F. Leung, P.-K. S. Tam, “A fuzzy sliding controller for nonlinear systems,” IEEE Trans. on Industrial Electronics, vol. 48, no. 1, pp. 32-37, 2001.
[85] C.-J. Wu, “Quasi time-optimal PID control of multivariable systems: a seesaw example,” Journal of the Chinese Institute of Engineers, vol. 22, no. 5, pp. 617-625, 1999.
[86] C.-J. Wu, “Genetic tuning of PID controllers using a neural network model: a seesaw example,” Journal of Intelligent and Robotic Systems, vol. 25, pp. 43-59, 1999.
[87] T. Yamakawa, “Stabilization of an inverted pendulum by a high-speed fuzzy logic controller hardware system,” Fuzzy Sets and Systems, vol. 32, pp. 161-180, 1989.
[88] Z.-M. Yeh, “A systematic method for design of multivariable fuzzy logic control systems,” IEEE Trans. on Fuzzy Systems, vol. 7, no. 5, pp. 741-752, 1999.
[89] S.-Y. Yi and M.-J. Chung, “Systematic design and stability analysis of a fuzzy logic controller,” Fuzzy Sets and Systems, vol. 72, pp.271-298, 1995.
[90] B. Yoo and W. Ham, “Adaptive fuzzy sliding mode control of nonlinear system,” IEEE Trans. on Fuzzy Systems, vol. 6, no. 2, pp. 315-321, 1998.
[91] L.-A. Zadeh, “Fuzzy sets,” Inform. Control, vol. 8, pp. 338-353, 1965.
[92] L.-A. Zadeh, “Fuzzy Algorithms,” Inform. Control, vol. 12, pp. 94-102, 1968.
[93] MAX+PLUS II Getting Started, Altera Co., San Jose, California, U.S.A., 1995.
[94] MBSP Manual, Phimatic Enterprise Co., Ltd., Taiwan, R.O.C., 1995.
[95] Wedge Balancer User Guide, Phimatic Enterprise Co., Ltd., Taiwan, R.O.C., 1995.