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Digital Redesign and Robust Stabilization : an LMI Approach
|關鍵字:||Digital redesign;數位重新設計;linear matrix inequalities;asymptotical stability;sliding mode control;線性矩陣不等式;漸近穩定;順滑模態控制||出版社:||電機工程學系所||引用:|| B. C. Kuo, “Digital Control Systems,” 2nd edition, 1992.  J. Ackermann, “Robust control systems with uncertain physical parameters,” Springer-Verlag, 1993.  K. J. Astrom, and B. Wittenmark., “Computer controlled systems,” (Prentice-Hall, 1984).  W. M. Wonham, “Linear Multivariable Control : A Geometric Approach,” New York : Springer-Verlag,1974.  Emelyanov, S. V. : Variable structure control systems, Nauka, Moscow, 1967.  V. I. Utkin, “Sliding Mode and Their Applications in Variable Structure Systems,” Moscow : MIR, 1987.  Stephen Boyd, Laurent El Ghaoui, Eric Feron and Venkataramanan Balakrishnan, “Linear Matrix Inequalities in System and Control Theory,” Philadelphia, 1994.  Chang-Hua Lien, “Robust observer-based control of systems with state perturbations via LMI approach,” IEEE Trans. Automat. Contr., vol. 49, no. 8, AUGUST 2004.  Z. 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本文提出以線性矩陣不等式(linear matrix inequalities, LMIs)及李亞波諾夫穩定準則(Lyapunov stability criterion)為基礎，針對線性非時變離散時間系統而提出一些有關穩定度分析及控制法則的設計方法，所設計的數位系統，在設計程序中即已將穩定度考慮進去，並且予以有效的檢查。吾人考慮三個數位設計的問題，包括數位重新設計、狀態回授及基於觀測器的數位強健穩定控制與數位順滑模態控制器的設計，吾人將所有穩定的充份條件利用Schur complement轉換成線性矩陣不等式的表示方式，並且以套裝軟體的工具箱予以有效的求解。最後，吾人以數值範例來說明所提設計方法確屬有效。
Most physical control systems are described by continuous-time state equations for which many well-established analog control design methods are available. With the rapid and revolutionary advances in digital technology and microelectronics, it has made possible to implement such analog controllers using a digital controller for the sake of better reliability, more flexibility, low cost and high-performance control. There are many digital controller design methods reported in the literature. However, to guarantee the stabilizability of the control systems is the most important issue.
This thesis presents some stability analyses and controller design method for a class of linear uncertain discrete-time systems based on linear matrix inequalities (LMIs) techniques and Lyapunov stability criterion. With the developed LMI-based stability condition, the stability of the designed digital systems is effectively checked during the design procedure. Digital redesign approach, state feedback observer-based robust stabilization control and sliding mode control cases are considered; some sufficient stability and stabilization conditions are represented in terms of LMIs, which can be solved efficiently by using existing LMI software packages. Finally, numerical examples are given to illustrate the effectiveness of the proposed design methods.
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