臺灣博碩士論文加值系統

本論文我們主要討論針對在狀態與輸入含有未匹配不確定項的延遲系統之滑動模式控制器設計的問題。我們的方法是根據 Takagi-Sugeno 模糊模型和滑動模式控制所構成。我們使用 Takagi-Sugeno 模糊模型，它能結合一些簡單局部線性時間延遲系統和一些語言描述去表示原始的非線性系統，接著我們提出滑動模式控制器去處理存在未匹配不確定性項的模糊延遲系統。根據李普諾夫定理及函數分析觀念推導模糊延遲系統在具有未匹配不確定項之穩定度條件。最後，對於所提出之方法我們將以數值模擬結果來驗證其適用性。

In this thesis, we consider the problem of designing the sliding mode controller for an uncertain time-delay system with unmatched parametric uncertainties in the state and input matrix. Our approach is based on Takagi-Sugeno ( T-S ) fuzzy modeling method and sliding mode control technique. Using the Takagi-Sugeno fuzzy model, it is to combine some simple local linear systems with their linguistic description to represent original nonlinear systems. Then the sliding mode controller is developed for fuzzy delayed system with unmatched uncertainties. Based on Lyapunov theory and the concept of functional analysis, sufficient conditions for stability of fuzzy delayed system with unmatched uncertainties using sliding mode controller are given. Finally, the effectiveness of the proposed fuzzy sliding mode controller is demonstrated through numerical simulations.

CONTENTS
ABSTRACT (IN CHINESE) I
ABSTRACT (IN ENGLISH) II
ACKNOWLEDGEMENT ( IN CHINESE) III
CONTENTS IV
LIST OF FIGURES V
LIST OF TABLES VI
CHAPTER 1 INTRODUCTION 1
CHAPTER 2 SLIDING MODE CONTROLLER DESIGN OF UNCERATIN NONLINEAR TIME-DELAY SYSTEM USING FUZZY MODEL 6
2.1 T-S fuzzy systems and preliminaries 6
2.2 Sliding mode controller design for delay fuzzy system with unmatched 8
2.3 Sliding mode controller design for delay fuzzy system via an LMI approach unmatched 15
CHAPTER 3 NUMERICAL EXAMPLES AND PRACTICAL EXAMPLES 26
3.1 Numerical example 26
3.1 Practical example 34
CHAPTER 4 CONCLUSIONS 46
REFERENCES 47
LIST OF FIGURES
Fig. 3.1 Trajectory of the state . 29
Fig. 3.2 Trajectory of the state . 29
Fig. 3.3 The response of 30
Fig. 3.4 Trajectory of sliding surface. 30
Fig. 3.5 Trajectory of the state . 32
Fig. 3.6 Trajectory of the state . 33
Fig. 3.7 The response of . 33
Fig. 3.8 Trajectory of sliding surface 34
Fig. 3.9 Membership function of CSTR fuzzy model 40
Fig. 3.10 State response under operating point (0.4472, 2.7520). 41
Fig. 3.11 The response of 41
Fig. 3.12 State response under operating point (0.4472, 2.7520) 42
Fig. 3.13 The response of 42
Fig. 3.14 State response under operating point (0.4472, 2.7520) 44
Fig. 3.15 The response of 45
Fig. 3.16 State response under operating point (0.4472, 2.7520) 45
Fig. 3.17 The response of 46
LIST OF TABLES
Table 3.1 CSTR parameters 40

[1] E.H. Mamdani, S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic controller,” Int. J. Man-Machine Studies, vol. 7, pp.1-13, 1975.
[2] T. Takagi, M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans, Systems Man Cybernet. SMC-15(1), pp.116-132, 1985.
[3] H. O.Wang, K. Tanaka, and M. F. Griffin, “An approach to fuzzy control of nonlinear systems: Stability and design issues,” IEEE Trans. Fuzzy Syst., vol. 4, pp. 14—23, Feb. 1996.
[4] L.A. Zadeh, “Fuzzy sets,” Inform. And Control, vol. 8, pp. 338—353, 1965.
[5] M.C.M. Teixerira, S.H. Zak, “Stabilizing controller design for uncertain nonlinear systems using fuzzy models,” IEEE Trans. Fuzzy Sys., vol. 7, pp.133-142, 1999.
[6] S.G. Cao, N.W. Rees, G. Feng, “Analysis and design for a class of complex control systems part I: Fuzzy modelling and identification,” Automatica, vol.33, pp. 1017—1028, 1997.
[7] V. I. Utkin, Sliding Modes in Control and Optimization. New York: Springer-Verlag, 1992.
[8] A. DeCarlo, S. H. Zak, and G. P. Mattews, “Variable structure control of nonlinear multivariable systems: a tutorial,” Proc. IEEE, vol. 76, pp. 212-232, Mar. 1988.
[9] B. Draxenovic, “The invariance condition in variable structure system,” Automatic, vol. 5, pp. 287-295, 1969.
[10] H.S. Tan and Y. K. Chin, “Vehicle traction control: variable structure control approach,” ASME J. Dyna. Syst., Measure., Control, vol. 113, pp. 223-230, 1991.
[11] K. S. Yeung, C. C. Cheng and C. M. Kwan, “A unifying design of sliding model and classical controllers,” IEEE Trans. Automat. Contr., vol. 38, pp. 1422-1427.
[12] S. Beyhtash, “Robust output tracking for nonlinear systems,” Int. J. Control, Vol. 51, No. 6, pp. 1381-1407, June 1990.
[13] I. Tunay and O. Kaynak, “A new variable structure controller for affine nonlinear systems with non-matching uncertainties,” International Journal of Control, Vol. 62, pp.917-939, June 1995.
[14] Y. Y. Cao and P. M. Frank, “Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach,” IEEE Trans. Fuzzy Sys., vol. 8, pp.200-211, Apr. 2000.
[15] R. Bellman and K. L. Cooke, Differential-difference equations, New York: Academic Press, 1993.
[16] T. Mori, K. Fukuma, and M. Kuwahara, “Simple stability criteria for single and composite linear systems with time delays,” International Journal of Control, Vol. 34, pp.1175-1184, 1981.
[17] E. Hille, “Lectures on ordinary differential equation,” London, Addison-Wesley, 1969.
[18] B. Lehman and E. I. Verriest, “Stability of a continuous stirred reactor with delay in the recycle stream,” in Pro. 30th IEEE Conf. Dec. Contr., Brighton, U.K., 1911, pp. 1875-1876.
[19] M. C. M. Teixeira and S. H. Zak, “Stabilizing controller design for uncertain nonlinear systems using fuzzy models,” IEEE Trans. Fuzzy Sys., vol. 4, pp.14-23, Feb. 1996.
[20] Z. Yi, and P. A. Heng, “Stability of fuzzy control systems with bounded uncertain delays,” IEEE Trans. Fuzzy Sys., vol. 10, pp.92-97, Feb. 2002.
[21] F. Zheng, Q. G. Wang, and T. H. Lee, “Output tracking control of mimo fuzzy nonlinear systems using variable structure control approach,” IEEE Trans. Fuzzy Sys., vol. 10, pp.686-696, Dec. 2002.
[22] X. Li, R. A. DeCarlo, “Memoryless sliding mode control of uncertain time-delay systems,” proceedings of the American Control Conference Arlington, VA June 25-27, 2001.
[23] B. S. Chen and C. S. Tseng, and H. J. Uang, “Robustness design of nonlinear dynamic system via fuzzy linear control,” IEEE Trans. Fuzzy Sys., vol. 7, pp. 571-584, Oct. 1999.
[24] S. Tong, H. H. Li, “Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties, Fuzzy Sets and System vol. 131, pp. 165-184, 2002.
[25] W. Chang, J. B. Park, Y. H. Joo, and G. Chen, “Design of robust fuzzy—model —based controller with sliding mode control for SISO nonlinear systems,” Fuzzy Sets and System vol. 125, pp. 1-22, 2002.
[26] G. Feng, S. D. Cao, and N. W. Rees, “Stable adaptive control of fuzzy dynamic systems”, Fuzzy Sets and System vol. 131, pp. 217-224, 2002.