臺灣博碩士論文加值系統

本論文研製二階動態系統之適應性順滑模態控制器，主要為改善傳統順滑模態控制設計時，必須事先掌握未知參數上限的缺點，結合適應性法則，以即時估測的方式取得系統的未知參數。在本論文中，根據系統特性的差異歸納出三種情況，分別提出不同的適應性順滑模態控制方式，以解決高增益輸入、外界干擾、估測誤差等問題，其中包括三個設計步驟，首先給定適當的參考模型，其次是選定順滑模態函數，並依據不同的系統特性設計里奧波諾夫函數，最後再求得適應性順滑模態控制法則。為了驗證適應性順滑模態控制器的可行性，以常見的二階MBK機械系統進行數值模擬，從模擬結果中可以看出系統的響應確實對外界干擾具有強健性，而且高增益輸入的問題也可獲得改善，至於系統的未知參數，也可經由適應性法則來降低其估測誤差。
關鍵字：順滑模態控制，適應控制

This thesis proposes an adaptive sliding mode controller design to deal with the limitation of traditional sliding mode control, which requires the upper bound of unknown parameters. Most importantly, with the adaptive law the unknown parameters can be estimated in real time. There are three approaches developed for three cases with different system parameters and disturbances. These approaches can solve the high gain problem, reject the external disturbances, and reduce the estimation error. Furthermore, three design steps are also included to set an appropriate reference model, to choose suitable sliding function, and to design the adaptive sliding mode control. To demonstrate the usefulness of the proposed scheme, numerical simulation is applied to a MBK system. From the simulation results, the adaptive sliding mode controller is indeed robust to the disturbances, faced no high gain problem, and available to estimate the unknown parameters with smaller estimation error.

Keywords：Sliding Mode Control，Adaptive Control

目錄　　　　　　
中文摘要…………………………………………………………… i
英文摘要…………………………………………………………… ii
誌謝 …………………………………………………………… iii
目錄 …………………………………………………………… iv
表目錄 …………………………………………………………… v
圖目錄 …………………………………………………………… vi
符號說明…………………………………………………………… viii
第一章 緒論………………………………………………………
1.1 研究背景………………………………………………… 1
1.2 研究動機………………………………………………… 1
1.3 研究方法與本文架構…………………………………… 2
第二章 二階動態系統之適應性順滑模態控制器設計…………
2.1 系統與問題描述………………………………………… 3
2.2 順滑模態控制理論……………………………………… 4
2.3 適應控制理論…………………………………………… 9
2.4 二階動態系統之適應性順滑模態控制器設計………… 15
第三章 二階動態系統之適應性順滑模態控制器應用與模擬…
3.1 二階動態系統描述與參數規格設計…………………… 21
3.2 Case-I：μ為未知且不知其上限，k 與d(t)之上限
dmax為已知的模擬…………………………… 22
3.3 Case-II：d(t)之常數部分d0為未知且不知其上限，
m、k與δ(t)之上限δmax為已知的模擬……… 41
3.4 Case-III：m與k為未知且不知其上限，d(t)之上限
dmax為已知的模擬…………………………… 45
3.5 模擬結果探討…………………………………………… 50
第四章 結論與未來展望…………………………………………
4.1 結論……………………………………………………… 51
4.2 未來展望………………………………………………… 53
參考文獻…………………………………………………………… 54
附錄 ……………………………………………………………57

參考文獻　　　　　　
[1] J. D. Wang, T. L. Lee and Y. T. Juang, “New Methods to Design an Integral Variable Structure Controller,” IEEE Transactions on Automatic Control, Vol. 41, pp. 140-143, 1996.
[2] D. Sbarbaro, “Application of Integral Variable Structure Controllers,” Proceedings of the 1996 IEEE International Conference on Control Applications, Dearborn, MI pp. 673-678, 1996.
[3] V. I. UtKin. Sliding Modes and Their Application in Variable Structure Systems, Moscow: MIR publishers, 1978.
[4] E. Baily and A. Arapostathis, “Simple Sliding Mode Control Scheme Applied to Robot Manipulator,” Int. J. Control, Vol. 45, pp. 1197-1209, 1987.
[5] S. V. Emelyanov, Variable Structure Control Systems, Nkuka, Moscow, 1967.
[6] V. I. UtKin, “Variable Structure Systems with Sliding Modes,” IEEE Transactions on Automatic Control, Vol. 22, pp. 212-222, 1977.
[7] J. Y. Hung, W. Gao and J. C. Hung, “Variable Structure Control: A survey,” IEEE Transactions on Automatic Control, Vol. 40, pp. 2-22, 1993.
[8] 陳永平、張浚林，可變結構控制設計，二版，全華科技圖書，台北，民國九十一年。
[9] W. Song, Y. Liu and L. Sun, “Model Reference Adaptive Integral-type Sliding Mode Control Design for a Class of Uncertain Systems,” Proceedings of the 6th World Congress on Intelligent Control and Automation, June 21-23, 2006, Dalian, Chain, pp. 2056-2060, 2006.
[10] K. K. Young “Asymptotic Stability of Model Reference Systems with Variable Structure Control,” IEEE Transactions on Automatic Control, Vol. 22, pp. 279-281, 1977.
[11] J. J. E. Slotine and S. S. Sastry, “Tracking Control of Nonlinear Systems Using Sliding Surfaces with Application to Robot Manipulators,” Int. J. Control, Vol. 38, pp. 465-492, 1983.
[12] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Prentice Hall, 1989.
[13] K. J. Astrom “Theory and Applications of Adaptive Control: A Survey,” IEEE Transactions on Automatic Control, Vol. 19, pp. 471-486, 1983.
[14] S. Sastry and M. Bodson, Adaptive Control Stability, Convergence and Robustness, Prentice Hall, 1989.
[15] D. E. Miller and E. J. Davison, “An Adaptive Controller which Provides Lyapunov Stability,” IEEE Transactions on Automatic Control, Vol. 34, pp. 599-609, 1989.
[16] D. E. Miller and E. J. Davison, “An Adaptive Controller which Provides an Arbitrarily Good Transient and Steady-State Response,” IEEE Transactions on Automatic Control, Vol. 36, pp. 68-81, 1991.
[17] J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs NJ, 1991.
[18] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Prentice Hall, 1989.
[19] L. Hsu, A. D. Ara?瀰o and R. R. Costa, “Analysis and Design of I/O Based Variable Structure Adaptive Control,” IEEE Transactions on Automatic Control, Vol. 39, pp. 4-21, 1994.
[20] L. Yan, L. Hsu, R. R. Costa and F. Lizarralde, “Variable Structure Model Reference Adaptive Control for Systems with Unknown High Frequency Gain1,” Proceedings of the 42th Conference on Decision and Control, Maui, Hawaii, pp. 3525-3530, 2003.
[21] L. Yan, L. Hsu and S.Xiuxia, “A Variable Structure MARC with Expected Transient and Steady-State Performance,” Automatic, In Press, 2006.
[22] L. Hsu, “Variable Structure Model Reference Adaptive Control Using only I/O Measurement: part Ⅱ,” Proceedings of the 27th Conference on Decision and Control, Austin, Texas, pp. 2396-2401, 1988.
[23] L. Hsu, F. Lizarralde and A. D. Ara?瀰o, “New Results on Output-Feedback Variable Structure Model-Reference Adaptive Control: Design and Stability Analysis,” IEEE Transactions on Automatic Control, Vol. 42, pp. 386-393, 1997.
[24] A. K. Mohammadi, “A Variable Structure Model Reference Adaptive Controller, for SIMO Systems,” Proceedings of the First International Conference on Innovative Computing, Information and Control, 2006.
[25] D. W. Repperger and J. H. Lilly, “A Study on a Class of MRAC Algorithms,” Proceedings of the 38th Conference on Decision and Control, Phoenix, Arizona USA, pp. 3321-3326, 1999.
[26] K. Nonaka, M. Yamakita and K. Furuta, “A Study on Model Reference Variable Structure Control with Adaptive Sliding Surface,” Proceedings of the 35th Conference on Decision and Control, Kobe, Japan, pp. 3504-3509, 1996.
[27] S. H. Huh and Z. Bien, “Robust Sliding Mode Control of A Robot Manipulator Based on Variable Structure-Model Reference Adaptive Control Approach,” IET Control Theory Applications, pp. 1355-1363, 2007.
[28] D. E. Miller, “A New Approach to Model Reference Adaptive Control,” IEEE Transactions on Automatic Control, Vol. 48, pp. 743-757, 2003.
[29] C. H. Chou and C. C. Cheng, “A Decentralized Model Reference Adaptive Variable Structure Controller for Large-Scale Time-Varying Delay Systems,” IEEE Transactions on Automatic Control, Vol. 48, pp. 1213-1217, 2003.
[30] A. C. Huang and Y. C. Chen, “Adaptive Sliding Control for Single-Link Flexible-Joint Robot with Mismatched Uncertainties,” IEEE Transactions Control System Technology, pp. 770-775, 2004.
[31] E. L. Mirkin, “Variable Structure Model Reference Adaptive Control with an Augmented Error Signal for Input-Delay Systems,” PhysCon 2005, St. Petersburg, Russia, pp. 573-577, 2005.
[32] E. Bertran and G. M. Lopez, “Adaptive VS-MRAC for Disturbance Cancellation, ”Electronics Letters, Vol. 31, pp. 142-144, 1995.
[33] E. L. Mirkin, “Combination of Sliding Mode and Reference Model Prediction Methods for Adaptive Control of Input-Delay Systems,” Proceeding of the 7th International Workshop on Variable Structure Systems, Sarajevo, pp. 153-162, 2002.
[34] 周建興，「針對不確定動態系統之參考模式調適可變結構控制器設計」，國立中山大學，博士論文，民國九十一年。
[35] Richard T. O'Brien, Jr. and Jamie M. Howe, “Optimal PID Controller Design using Standard Optimal Control Technique,” 2008 American Control Conference, pp. 4733-4738, Westin Seattle Hotel, Seattle, Washington, USA, 2008.
[36] C. Knospe, “PID Control,” IEEE Control Systems Magazine, Vol. 26, pp. 30-31, 2006.
[37] Jun ZHAO, Ping LI, and Xue-song WANG, “Intelligent PID Controller Design with Adaptive Criterion Adjustment via Least Squares Support Vector Machine,” 2009 Chinese Control and Decision Conference, pp. 7-12, China University of Mining and Technology, China, 2009.
[38] K. Zhou, J. C. Doyle and K. Glover, Robust and Optimal Control, Prentice Hall, Upper Saddle River, NJ, 1996.
[39] H. P. Whitaker, J. Yamron and A. Kezer, “Design of model reference adaptive control systems for aircraft,” Instrum. Lab., MIT Press, Cambridge, MA, Tech. Rep. R-164, 1958.