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研究生:詹景超
研究生(外文):Ching-Chao Chan
論文名稱:輸入式不確定系統之強健控制研究
論文名稱(外文):Robust Control Design of Uncertain System with Parameter Uncertainty in the Input Matrix
指導教授:黃正能
指導教授(外文):Cheng-Neng Huang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:系統及船舶機電工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:75
中文關鍵詞:強健不確定擴增系統
外文關鍵詞:riccatiltruncertaintyrobust
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  在本文中,我們將針對具有輸入式不確定的系統來設計一個可以追蹤參考輸入之H∞-強健控制器。輸入式不確定在於系統狀態空間方程式的輸入矩陣,其具有已知的上下限邊界,此不確定因素將使系統追蹤上產生不確定的擾動,還有可能造成系統的不穩定。

  H∞-控制系統的特色是可以使受控體在不確定的外擾及系統參數變動的情況下,仍可維持系統的穩定與強健性,透過設定權重函數來使擴增系統的靈敏度函數、互補靈敏度函數及控制能量函數的奇異值圖擁有良好的形狀。

  對於擴增系統使用黎卡迪方程式,求解出H∞-控制增益,所得的狀態回授控制要使系統在輸入式不確定的干擾下能達到H∞-控制的穩定與強健性。然後使用迴路函數整形的方法,來求得H∞-觀測增益,希望使輸出回授控制也擁有良好的性能。

  為了驗證以上的H∞-控制理論,在本文中將以直流無刷伺服馬達為系統進行模擬,設定輸入式不確定矩陣的大小,其使外加電壓產生干擾。以求解出的H∞-控制器做追蹤和性能的模擬。
 In this thesis, we are trying to design a robust H∞-controller being capable of tracking reference input for uncertain system with parameter uncertainty in the input matrix. The parameter uncertainties appearing in the input matrix of a system state-space equation have known upper and lower bounds and may cause the system unstable.

 The character of an H∞-control law is that it can ensure the closed-loop system stable while guaranteeing the system robustness to the uncertain exogenous inputs and the plant uncertainties. By selecting suitable weighting functions in the H∞-formulation, we can shape the system sensitivity, power transfer and the complementary sensitivity functions in the s-domain to ensure the system stability and robustness.

 The uncertainties in the system input matrix is assumed to be bounded in a specific form given in this research. The loop transfer recovery (LTR) technique is applied to the H∞-control problem containing the input matrix uncertainties to propose the H∞/LTR methodology in this thesis.

 To test the feasibility of the proposed H∞/LTR control law, a DC brushless motor with parameter uncertainty in the system input matrix is simulated under the interference voltage. Simulation results reveal that the desired system performance can be achieved by using the proposed control strategy while guaranteeing the closed-loop stability and robustness.
第一章 緒論
1.1 研究動機………………………………………………………1
1.2 文獻回顧………………………………………………………2
1.3 本文架構………………………………………………………3
第二章 控制理論
2.1 範數……………………………………………………………4
2.2 H∞控制理論……………………………………………………7
2.3 H∞控制問題……………………………………………………9
2.4 奇異值整形……………………………………………………16
2.5 擴增系統矩陣…………………………………………………25
第三章 追蹤問題
3.1 控制問題的擴增方法…………………………………………30
3.2 系統開迴路的規格問題………………………………………37
第四章 輸入式不確定系統的H∞/LTR設計
4.1 系統的H∞控制器設計………………………………………43
4.2 系統的H∞/LTR之設計………………………………………46
第五章 電腦模擬
5.1 無刷直流伺服馬達的系統……………………………………53
5.2 馬達的H∞控制器設計與模擬………………………………58
5.3 模擬結果討論…………………………………………………71
第六章 結論………………………………………………………………72
參考文獻…………………………………………………………………74
1.Alexander Weinmann," Uncertain Models and Robust Control", Springer-Verlag, Austria, 1991
2.Al-Mamun, A., and T.H. Lee, and T. S. Low, "Disk drive servo controller design using H∞-LTR," Proc. IEEE. JECON 21st international Conf. on Industrial Electronics, Control and Instrumentation, vol. 2, pp925-930, 1995.
3.Athans, M.," A tutorial on the LQG/LTR method," Proc. Am. Control Conf., June 1986, pp. 1289-1296.
4.Doyle, John C., and Gunter Stein," Multivariable feedback design: concepts for a classical/modern synthesis," IEEE Trans. Autom. Control, vol. AC-26, pp. 4-16, 1981.
5.Hwang, C.N.," Formulation of H2 and H∞ Optimal Control Problems- Variational Approach", Journal of the Chinese Institute of Engineerings, Vol. 16, No. 6, pp. 853-866, 1993.
6.I.R. Petersen," Stabilization of an uncertain linear system in which uncertain parameters enter into the input matrix", SIAM J. Control Optim. 26 (1998) 1257-1264
7.John C. Doyle, Gunter Stein," Robustness with Observers", IEEE Transactions on Automatic Control, Vol.24, No. 4, pp. 607-611,1979
8.John C. Doyle, Keith Glover, Pramod P. Khargoner and Bruce A. Francis," State-Space Solution to Standard H2 And H∞ Control Problem", IEEE Trans. Automatic Control, Vol. 34, No. 8, pp. 831-847, 1989
9.K. Zhou and P.P. Khargonekar," Robust stabilization of linear systems with norm-bounded time-varying uncertainty", Systems Control Lett. 10 (1998) 17-20
10.Kwitegetse, B. S.," Loop transfer recovery for H∞ synthesis," Proc. IEEE. Conf. on Decision and Control, vol.2, pp1718-1719, 1994.
11.Lihua Xie and Carlos E. de Souza," Robust H∞ control for linear time-invariant systems with norm-bounded uncertianty in the input matrix", Systems & Control Leters 14 pp. 389-396 1990.
12.P.P. Khargonekar, I.R. Petersen and K. Zhou," Robust stabilization of uncertain linear systems: quadratic stabilizability and H∞ control theory", IEEE Trans. Automat. Control, Issue: 3, Volume: 35, March 1999
13.Rawson, J. L., H. H. Yeh, and C. H. Hsu," H∞/LTR: A loop shaping method for output feedback problem compensator design," Proc. Am. Control Conf., 1991, pp. 2196-2201
14.Stein, Gunter, and Michael Athans," The LQG/LTR procedure for multivariable feedback control design," IEEE Transactions on Automatic Control, vol. AC-32, no. 2, Feb. 1987, pp. 105-114.
15.Stephen P.Boyd, Craig H. Barratt," Linear Controller Design", Prentice-Hall International Editions, USA, 1991
16.黃正能,陳冠良,"狀態空間H∞-控制器之迴路整形及其在船上的應用",國立成功大學造船暨船舶機械工程研究所碩士論文,1997。
17.黃正能,詹國琴,"非線性系統之H∞-控制器設計及迴路整型",國立成功大學造船暨船舶機械工程研究所碩士論文,1999。
18.楊憲東,葉方柏,"線性與非線性H∞控制理論",全華科技圖書,1997
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