本篇論文將Bartoszewicz所提出的準順滑模態控制設計（1998）從離散線性系統推廣到離散非線性T-S模糊系統，允許選用的順滑函數並不限定是線性的形式。以一類方式來設計順滑函數，並根據外界干擾之變動速率提出兩種準順滑模態控制器。其可以使系統有效的減輕切跳現象，並且降低控制所需消耗的能量提昇系統性能。本研究針對原始非線性系統與T-S模糊系統之控制器設計也進行比較，模擬結果說明了本設計的優點及其穩健性。

In this thesis, we extend Bartoszewicz’s design of quasi-sliding mode control (QSMC) for discrete-time linear systems (1998) to a class of T-S fuzzy-type discrete-time nonlinear systems. The selected sliding surface in this design is allowed to be nonlinear rather than only linear. One class of sliding surfaces is selected, and two quasi-sliding mode controllers according to the variation rate of disturbances are presented in this study. The study also compares the controllers between original nonlinear dynamics and T-S fuzzy-type systems. Simulation results demonstrate the benefits of the proposed schemes.

參考文獻
[1] 陳永平、張浚林，可變結構控制設計，(修訂版)，全華科技圖書，2006年7月。
[2] 曾仲熙，控制器設計與模擬範例，東華書局，2010年8月。
[3] 洪維恩，Matlab 7程式設計，旗標出版社，2008年1月。
[4] 俞克維，控制系統分析與設計使用Matlab，新文京開發公司，2007年2月。
[5] 王文俊，認識FUZZY，(第三版)，全華科技圖書，2008年6月。
[6] Y.-W. Ling, S.-D. Xu and L.-W. Ting, “T-S Model-Based SMC Reliable Design for a Class of Nonlinear Control Systems,” IEEE Transactions on Industrial Electronics, vol. 56,pp. 3286-3295,2009
[7] Jean-Jacques E.slotine and Weiping Li, Applied Nonlinear Control ,Englewood Cliffs, NJ:Prentice-Hall,1991
[8] Vadim I. Utkin, “Variable structure systems with sliding modes,” IEEE Transactions on Automatic Control, vol.AC-22, NO.2, Pages: 212-222, April 1977.
[9] Vadim I. Utkin, “Sliding Modes and Their application in variable structure Systems,” Moscow: Nauka, 1974 (in Russian); published in English by Mir, Moscow, 1978.
[10] Y. Dote and R. G. Hoft, “Microprocessor based sliding mode controller for dc motor drivers,” Industrial Applications Society Annual Meeting, Cincinnati, OH, 1980.
[11] C. Milosavljevic, “General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems,” Automatic remote control, vol. 46, pp. 307-314, 1985.
[12] Sami Z. Sarpturk, Yorgo Istefanopulos, and Okyay Kaynak, “On the stability of discrete-time sliding mode control systems,” IEEE Transactions on Automatic Control, vol. AC-32, NO. 10, pp. 930-932, October 1987.
[13] Katsuhisa Furuta, “Sliding mode control of a discrete system,” System & Control Letters, vol. 4, pp. 145-152, 1990.
[14] S. K. Spurgeon, ”Hyperplane design techniques for discrete-time variable structure control systems,” International Journal of Control, vol. 55, No. 2, pp. 445-456, 1992.
[15] A. Bartoszewicz, “Discrete-time quasi-sliding-mode control strategies,” IEEE Transactions on Industrial Electronics, vol. 45, pp. 633-637, 1998.
[16] Y.-W. Liang, S.-D. Xu, and C.-L. Tsai, “Study of VSC reliable designs with application to spacecraft attitude stabilization,” IEEE Transactions Control Systems Technology, Vol. 15, pp. 332-338, 2007.
[17] V. I. Utkin, “Sliding mode control in discrete-time and difference systems,” in Variable Structure and Lyapunov Control, A. S. I. Zinober, ed., London, U.K., Springer-Verlag, pp. 87-107, 1994.
[18] W. Gao, Y. Wang, and A. Homaifa, “Discrete-time variable structure control systems,” IEEE Transactions on Industrial Electronics, vol. 42, pp. 117-122, 1995.
[19] Y. Zheng, G. M. Dimirovski, Y. Jing, and M. Yang, “Discrete-time sliding mode control of nonlinear systems,” Processings American Control Conference, New York City, USA, July 11-13, pp. 3825-3830, 2007.
[20] S. Janardhanan and B. Bandyopadhyay, “Multirate feedback based quasi-sliding mode control of discrete-time systems,” IEEE Transactions on Automatic Control, vol. 52, pp. 499-503, 2007.
[21] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its application to modeling and control,” IEEE Transactions System, Man, Cybern, vol. SMC-15, pp. 116-132, 1985.
[22] E. Baily and A. Arapostathis, “Simple sliding mode control scheme applied to robot manipulator,” International Journal control, vol. 45, pp. 1197-1209, 1987.
[23] Gene H. Golub, Charles F. Van Loan, Matrix Computations, Johns Hopkins, 1996.
[24] Kazuo Tanaka and Hua O. Wang, Fuzzy Control Systems Design and Analysis, John Wiley & Sons, Inc., 2007.
[25] Yan Zheng, Georigi M. Dimirovski, Yuanwei Jing and Muyi Yang, “Discrete-Time Sliding Mode Control of Nonlinear Systems,” Proceedings of the 2007 American Control Conference, July 11-13, 2007.
[26] H. J. Lee, Jin Bae Park, and Guanrong Chen, “Robust fuzzy control of nonlinear systems with parametric uncertainties,” IEEE Transactions on Fuzzy System , 369-379, april 2001.
[27] K. Tanaka and H. O. Wang, “Fuzzy controller and observer design for backing control of a trailer-truck,” Engineering Application Artificial Intelligence vol. 10, pp. 441-452, 1997.
[28] H. K. Khalil, Nonlinear Systems, Prentice Hall, 2002.
[29] Chi-Tsong Chen, Linear System Theory and Design, New York Oxford, 1999.
[30] Y. -P. Chen and J. -L. Chang, “On discrete psedo-sliding control,” Journal of Control Systems and Technology ,vol. 6, pp. 253-258, 1998.
[31] K. D. Young ,Utkin V. I. Ozguner, “A control engineer’s guide to sliding mode control,” IEEE Transactions on Control Systems Technology, 1999
[32] D. Milosavljevic, “General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems,” Automation Remote Control, pp. 304-314, 1985
[33] S. Z. Sarpturk, Y. Istefanopulos, and O. Kaynak, “On the stability of discrete-time sliding mode control systems,” IEEE Transactions on Automation Contorl, pp. 930-932
[34] J. H. Wu, “A two-layer strategy applied to discrete time sliding-mode control,” Thesis,National Chiao Tung university, 1994
[35] Y.-W. Liang, S.-D. Xu, and C.-L. Tasi, “Study of VSC reliable designs with application to spacecraft attitude stabilization,” IEEE Transactions on Control system Technlongy, 2007, Vol.15, pp. 332-338
[36] Y. Zheng, Dimirovski, G. M., Jing,Y., and M. Yang, “Discrete-time sliding mode control of nonlinear systems” Proceedings of American Control Conference, New York ,NY, USA, July 2007, pp. 3825-3830
[37] S. Janard hanan,and B. Bandyopadhyay, “Multirate feedback based quasi-sliding mode control of discrete-time systems,” IEEE Transactions Automation Contorl, 2007
[38] R. A. Horn and C. R. Johnson, Matrix Analysis. 2009.
[39] A. M. Farahmand and M. J. Yazdanpanah, “Locally optimal Takagi-Sugeno fuzzy controllers,” proceedings of the IEEE conference on Decision and Control and the European Control Conference, Seville, Spain, December 12-15, 2005, pp. 4095-4099.
[40] Optimization Toolbox User’s Guide, for Use with MATLAB, Mathworks Ins.,Natick,MA,2001.[Online].Available:http://www.mathworks.com
[41] C.-S. Tseng, B.-S. Chen, and H.-J. Uang,“Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model,” IEEE Transactions on Fuzzy Systems, vol. 9, pp. 381-392, 2001
[42] C.-C. Chen, S.-F. Su ,and S.-S. Chen, “Robust TSK fuzzy modeling for function approximation with outliers,” IEEE Transactions on Fuzzy Systems, Vol. 9, pp. 810-821, 2001
[43] C.-C. Hsiao, S.-F. Su, T.-T. Lee, and C.-C. Chen, “Hybrid compensation control for affine TSK fuzzy control control systems,” IEEE Transactions on Systems,Man,Cybern, Part B: Cybernetics, Vol. 34, pp.1865-1873, 2004
[44] S. Chakrabarty and B. Bandyopadhyay, “Discrtete-time sliding mode control with minimal quasi sliding mode band” 12th IEEE Workshop on Variable Structure Systems, VSS’12, January 12-14, Mumbai, 2012
[45] C. Vivekanandan, R. Prabhakar, and M. Gnanambigai“A redefined quasi- sliding mode control strategy, ”World Academy of science, Engineering Technology” 39 2008
[46] T.-H. Chen, J.-Y. Su, C.-C. Kung, and S.-H. Li“The quasi-sliding mode control for a class of discrete-time bilinear systems,”IEEE, 2010
[47] 邱紹偉，“離散非線性系統之類滑模控制器設計與研究”國立交通大學電機與工程學系碩士論文, 2008。