Analysis and control of a rotation inverted pendulum using dynamic structure fuzzy systems 周晏鈴、陳昭雄
E-mail: [email protected]
ABSTRACT
Inverted pendulum systems are typical nonlinear and unstable systems. They are experimentation equipment which usually used to verify the feasibility of the control theory. This paper presents a dynamic structure fuzzy system for model reference adaptive control of nonlinear systems whose dynamic models are poorly understood. The dynamic structure fuzzy system is to reconstruct the unknown nonlinearities of the dynamic systems. In the dynamic structure system, the reference model provides closed-loop
performance feedback for generating or modifying a fuzzy approximation knowledge base. The number of fuzzy rules can be either increased or decreased with time based on the required accuracy. The tracking error converges to the required precision through the adaptive control law derived by combining the dynamic structure fuzzy system and the Lyapunov synthesis approach. At last we simulate an inverted-pendulum system control demonstrate the effectiveness of our scheme.
Keywords : fuzzy control ; nonlinear uncertain system ; adaptive control Table of Contents
封面內頁 簽名頁 授權書 iii 中文摘要 v 英文摘要 vi 誌謝 vii 目錄 viii 圖目錄 x 表目錄 xii 附錄 xiii 符號說明 xiv 第一章 緒論 1.1研究動機 1 1.2研究目的 2 1.3文獻回顧 2 1.4本文內容簡介 4 第二章 倒單擺系統之介紹及分析 2.1動態方程式 5 2.2動態 方程式之線性化 8 2.3系統轉移函數 9 第三章 模糊控制系統 3.1模糊概念 13 3.2模糊邏輯控制器 14 3.3模糊邏輯系統輸入輸 出關係 20 3.4廣用型估測器 21 第四章 動態模糊控制系統之設計與分析 4.1非線性系統模型 23 4.2適應控制 27 4.3動態結構 模糊系統 32 第五章 控制器設計 5.1現代控制設計 35 5.1.1控制器增益K值之選定 36 5.2動態模糊控制器設計 37 第六章 模擬 6.1現代控制模擬 41 6.2動態模糊控制系統模擬 44 第七章 結論 7.1結論 62 7.2未來展望 62 參考文獻 63 附錄 A 66 REFERENCES
[1] L.X. Wang,“Adaptive fuzzy systems and control: Design and stability analysis,”Englewood Cliffs, NJ: Prentice-Hall, (1994) [2] Y.C. Chang,
”Adaptive fuzzy-based tracking control for nonlinear SISO systems via VSS and H-inf approaches,”IEEE Trans. On Fuzzy systems , pp.
278-292. (2001) [3] C.S. Chen and W.L. Chen, “Robust model reference adaptive c control of nonlinear systems using fuzzy systems,” I.J. of systems science, pp. 1435-1442. (1996) [4] C.Y. Su and Y. Stepanenko, “Adaptive control of a class of nonlinear systems with fuzzy logic, “IEEE Trans. On Fuzzy systems , vol.2,pp. 285-294. (1994).
[5] S. Tong and H.X. Li, “Fuzzy adaptive sliding-mode control for MIMO nonlinear systems, “IEEE Trans. On Fuzzy systems , vol.11,No.3,pp.
354-360. (2003).
[6] C. Panchapakesan, M. Palaniswami, D. Ralph, and C.Manzie, “Effects of moving the centers in an rbf network, “IEEE Trans. on Neural Networks,vol.13,No.6,pp. 1299-1307. (2002), [7] H. Han, C.Y. Su, and Y. Stepanenko, “Adaptive control of a class of nonlinear systems with nonlinearly parameterized fuzzy approximators, “IEEE Trans. On Fuzzy systems , vol.9,No.2,pp. 315-323. (2001) [8] M. Maeda and S.
Murakami, “A self-tuning fuzzy controller, “Fuzzy Sets and Systems, vol.51,pp.29-40. (1992) [9] Y.M. Park, U.C. Moon, and K.Y. Lee, “A self-organizing fuzzy logic controller for dynamic systems using a fuzzy auto-regressive moving average (FARMA) model, “IEEE Trans. On Fuzzy systems , vol.3,No.1,pp.75-82. (1995) [10] J.X. Xu and J. Xu, “A new fuzzy logic learning control scheme for repetitive trajectory tracking problems,“Fuzzy Sets and Systems, vol.133,pp.57-75. (2003) [11] L. Behera and K.K. Anand, “Guaranteed tracking and regulatory
performance of nonlinear dynamic systems using fuzzy neural networks,“IEE Proc.-Control Theory Appl. ,vol.146,pp.484-491. (1999) [12] C.J.
Chien, “A sampled-data iterative learning control using fuzzy network design, “Internat. J. Control,vol.73,pp.902-913. (2000) [13] C. T. Lin and C.S.G. Lee, “Neural network-based fuzzy logic control and decision system, “IEEE Trans. Comput,vol.40,pp. 1320-1336. (1991) [14] K.S.
Narendra and A.M. Annaswamy, “A new adaptive law for robust adaptation with persistent excitation, “IEEE Trans. On Automation control, vol.32,No.2,pp. 134-145. (1987) [15] S.Sastry and M.Bodson,“Adaptive control:stability, convergence and robustness “Englewood Cliffs, NJ:Prentice-Hall, (1989) [16] G.C. Goodwin and D.Q. Mayne, “A parameter estimation perspective of continuous time model reference adaptive control, “Automatica, vol.23,No.1,pp. 57-70. (1987) [17] G.P. Liu, V. Kadirkamanathan, and S.A. Billings, “Variable neural networks for adaptive control of nonlinear systems, “IEEE Trans. On systems, man, and cybernetics-Part C vol.29,No.1,pp. 34-43. (1999) [18] J.E. Slotine and W. Li,“Applied nonlinear control ,”Englewood Cliffs, NJ: Prentice-Hall, (1991) [19] L.X. wang and J.M. Mendel ,”Fuzzy basis function
,universal approximation , and orthogonal least squares learning”,IEEE Trans. Neural Networks,Vol.3,pp.807-814, (1992) [20] 楊仁達，”倒單 擺的平衡與位置控制”，碩士論文，動力機械工程研究所，(1995) [21] 陳昭雄、周晏鈴，”應用動態模糊系統於非線性不確定系統之分 析與控制”，2004中華民國自動控制研討會，(2001)
