Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/7450
標題: 數位重新設計與強健穩定 :線性矩陣不等式法
Digital Redesign and Robust Stabilization : an LMI Approach
作者: 閻正武
Yen, Cheng-Wu
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: [1] B. C. Kuo, “Digital Control Systems,” 2nd edition, 1992. [8] J. Ackermann, “Robust control systems with uncertain physical parameters,” Springer-Verlag, 1993. [20] K. J. Astrom, and B. Wittenmark., “Computer controlled systems,” (Prentice-Hall, 1984). [24] W. M. Wonham, “Linear Multivariable Control : A Geometric Approach,” New York : Springer-Verlag,1974. [32] Emelyanov, S. V. : Variable structure control systems, Nauka, Moscow, 1967. [35] V. I. Utkin, “Sliding Mode and Their Applications in Variable Structure Systems,” Moscow : MIR, 1987. [44] Stephen Boyd, Laurent El Ghaoui, Eric Feron and Venkataramanan Balakrishnan, “Linear Matrix Inequalities in System and Control Theory,” Philadelphia, 1994. [2] 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. [3] Z. Ji, L, Wang, G. Xie and F. Hao, “Linear matrix inequality approach to quadratic stabilization of switched systems,” IEE Proc.-Control Appl., vol. 151, no. 3, MAY 2004. [4] Han Ho Choi, “LMI-based sliding surface design for integral sliding mode control of mismatched uncertain systems,” IEEE Trans. Automatic. Contr., vol. 52, no. 4, APRIL 2007. [5] W. Chang, J. B. Park, H. J. Lee, and Y. H. Joo, “LMI approach to digital redesign of linear time-invariant systems,” Proc. IEE, Contr. Theory Appl,. vol. 149, no. 4, pp. 297-302, 2002. [6] A. Fujimori, “Optimization of static output feedback using substitutive LMI formulation,” IEEE Trans. Automat. Contr., vol. 49, no. 6, pp. 995-997, Jun.2004. [7] A. H. D. Markazi and N. Hori, “A new method with guaranteed stability for discretization of continuous- time control systems,” in Proc. Amer. Control Conf., Chicago, IL, pp. 1397-1402, 1992. [9] M. Chilali and P. Gahinet, “ Design with Pole Placement Constraints : an LMI Approach,” Proc. 33rd Conf. Decision and Control, pp. 553-558, Lake Buena Vista, Florida, 1994. [10] A. Trofino, “Parameter dependent Lyapunov functions for a class of uncertain linear systems : An LMI approach,” in Proc. 38th IEEE Conf. Decision and Control, Phoenix, AZ, pp. 2341-2346, 1999. [11] D. Ramos and P. Peres, “An LMI condition for the robust stability of uncertain continuous-time linear systems,” IEEE Trans. Autom. Control, vol. 47, no. 4, pp. 675-678, Apr. 2002. [12] L. S. Shieh, J. L. Zhang, and J. W. Sunkel, “A new approach to the digital redesign of continuous-time controllers,” Control Theory Adv. Technol., vol. 8, no. 1, pp. 37-57, 1992. [13] L. S. Shieh, Y. J. Wang, and J. W. Sunkel, “Hybrid state-space self-tuning control of uncertain linear systems”, Proc. Inst. Elect. Eng. D., vol. 140, no. 3, pp. 99-110, 1993. [14] L. S. Shieh, X. Zou, and N. P. Coleman, “Digital interval model conversion and simulation of continuous-time uncertain systems," Proc. Inst. Elect. Eng.-Control Theory Appl., vol. 142, pp. 315- 322, 1995. [15] L. S. Shieh, W. M. Wang, and J. W. Sunkel(1996), “Digital redesign of cascaded analogue controllers for sampled-data interval systems,” Proc. Inst. Elect. Eng., vol. 143, no. 11, pp. 489-498, 1996. [16] L. E. Sheen, J. S. H. Tsai, and L. S. Shieh, “Optimal digital redesign of continuous-time systems with input time delay and/or asynchronous sampling,” J. Franklin Inst., vol. 335B, no 4, pp. 605-616, 1996. [17] C. C. Hsu, K. M. Tse, and C. H. Wang, “Digital redesign of continuous systems with improved suitability using genetic algorithms-Electronics letters,” Electron . Lett., vol. 33, pp. 1345-1347, 1997. [18] N. Rafee, T. Chen, and O. P. Malik, “A technique for optimal digital redesign of analog controllers,” IEEE Trans. Control Syst. Technol., vol. 5, pp. 89- 99, 1997. [19] B. C. Kuo, “Digital control systems,” New York: Holt, Rinehart and Winston, pp. 321-338, 1980. [21] L. S. Shieh, J. L. Zhang and S. Ganesan., “Pseudo- continuous-time quadratic regulators with pole placement in a specific region,” IEE Proc. D, 137, (5), pp. 297-301, 1990. [22] J. S. H. Tsai., L. S. Shieh, and J. L. Zhang., “An improvement of the digital redesign method based on the block-pulse function approximation,” Circuits Syst. Signal Process., 12, (1), PP. 37-49, 1993. [23] D. Luenberger, “Observers for multivariable systems,” IEEE Trans. Control, vol 11, pp. 190-197, 1966. [25] D. C. Youla, J. J. Bongiorno, Jr., and C. N. Lu, “Single-loop feedback stabilization of linear multivariable dynamical plants,” Automatica, vol. 10, pp. 159-173, 1974. [26] A. B. Chammas and C. T. Leondes, “On the design of linear time-invariant systems by periodic output feedback : Part 1. Discrete-time pole assignment,” Int. J. Contr., vol. 27, pp. 885-894, 1978. [27] A. B. Chammas and C. T. Leondes, “On the finite time control of linear systems by piecewise constant output feedback,” Int. J. Contr., vol. 30, pp. 227- 234, 1979. [28] J. P. Greschak and G. C. Verghese, “Periodically varying compensation of time-invariant systems,” Syst. Contr. Lett., vol. 2, pp. 88-93, 1982. [29] P. P. Khargonekar, K. Poolla, and A. Tannenbaum, “Robust control of linear time-invariant plants using periodic compensation,” IEEE Trans. Automat. Contr., vol. AC-30, pp. 1088-1096, 1985. [30] T. Mita, B. C. Pang, and K.Z. Liu, “Design of optimal strongly stable digital control systems and application to output feedback control of mechanical systems,” Int. J. Contr., vol. 45, pp. 2071-2082, 1987. [31] V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Trans. Automat . Contr., vol. AC-22, pp. 212-222, 1977. [33] V. I. Utkin, “Variable structure systems : Present and Futures,” Automatic and Remote Control, vol. 44, Pt 1, pp. 1105-1119, 1983. [34] O. M. E. El-Ghezawi, S. A. Billings, and A. S. I. Zinober, “Variable Structure Systems and Systems Zeros,” IEE Proc., vol. 130, Pt.D, pp. 1-5, 1983. [36] B. S. Heck, “Sliding-mode Control for Singularly Peturbed Systems,” Int. J. Control, vol. 53, No. 4, pp.985-1001, 1991. [37] B. M. Diong, and J. V. Medanic, “Dynamic Output Feedback Variable Structure Control for System Stabilization,” Int. J. Control, vol. 56, No. 3, pp. 607-630, 1992. [38] V. I. Utkin, “Application Oriented Trends in Sliding Mode Control Theory,” Proc. of IEEE IECON'93, Maui, HW, USA., pp. 1937-1942, 1993. [39] K. Furuta, “Sliding-Mode Control of a Discrete System,” Systems & Letters, vol. 14, pp. 145-152, 1990. [40] C. Y. Chan, “Servo-Systems with Discrete-Variable Structure Control,” Systems & Letters, vol. 17, pp. 321-325, 1991. [41] C. L. Hwang, “Design of Servo Controller via the Sliding Mode Technique,” IEE Proc., Part D. vol. 139, pp. 439-446, 1992. [42] S. K. Spurgeon, “Hyperplane Design Techniques for Discrete-Time Variable Structure Control Systems,” Int. J. Control, vol. 55, pp. 445-456, 1992. [43] C. Y. Chan, “Robust Discrete-Time Sliding Mode Controller,” Systems & Letters, vol. 23, pp. 371- 374, 1994.
摘要: 
自然界,大部分的系統都是用連續時間系統的狀態方程式來描述。由於在數位技術及微電子學方面的快速進步,使得原本以類比設計的控制方法可以用數位控制器去實現,並且得到吾人所希望的提高可靠度、降低設計成本、更具設計上的彈性以及高性能的控制法則的設計目標。許多有關數位控制器的設計方法發表在文獻上,無論如何,保證控制系統的穩定度才是最重要的課題。
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.
URI: http://hdl.handle.net/11455/7450
其他識別: U0005-1008200711524900
Appears in Collections:電機工程學系所

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