基于鲁棒稳定性的多速率采样控制系统设计

摘要/Abstract

摘要：

提出了基于鲁棒稳定性的多速率采样控制系统设计方法.对于具有给定补偿F的系统，首先拓展Lyapunov上限法得出鲁棒稳定性判定新条件.当系统具有边界不定的不确定性时，定义最大可承受边界为鲁棒稳定半径（Robust Stability Radius，RSR）.通过对鲁棒稳定判定条件的分析，可将求解RSR的问题归结为求解一个复杂非线性方程,并利用数值计算方法求解该方程得到解析解.作为F的函数，通过一般优化方法即可实现F优化设计，使得系统RSR最大，而且在保证鲁棒稳定的同时可以承受不确定参数的变化范围最大.最后给出实例，说明了所提方法的可行性和有效性.

关键词: 鲁棒稳定性, 多速率采样控制系统, Lyapunov函数的上限

Abstract:

This paper concerned the optimal design of a multirate sampled-data control system based on robust stability. For a system with a given F, a new condition for robust stability test of uncertain system was developed by extending Lyapunov upper bound method. For a system with an unknown uncertainty bound, the robust stability radius (RSR) was defined. The RSR calculation problem could be converted to a mathematical process of solving an equation by analyzing the robust stability test condition proposed. The equation was solved using numerical mathematical methods to get the analytical solution as RSR. As a function of F, the F optimization design could be achieved by a general optimization method to get the biggest RSR. With this F, the system could remain stable with the uncertain parameters varying set being the largest. Finally, a simple example was provided to test the feasibility of the proposed method.

Key words: robust stability, multirate sampleddata control system, upper bound of Lyapunov function

中图分类号:

TP 13

李夏雨1,金惠良1,钟庆昌2. 基于鲁棒稳定性的多速率采样控制系统设计[J]. 上海交通大学学报（自然版）, 2013, 47(12): 1902-1906.

LI Xiayu1,JIN Huiliang1,ZHONG Qingchang2. Optimal Design of a Multirate Sampled-Data Control System Based on Robust Stability[J]. Journal of Shanghai Jiaotong University, 2013, 47(12): 1902-1906.

参考文献

［1］Zhang P, Ding S X ，Wang G Z. Fault detection in multirate sampleddata systems with timedelays［J］. International Journal of Control, 2002, 75(18): 14571471.

［2］Tomizuka M. Multirate control for motion control applications ［C］// 8th IEEE International Workshop on Advanced Motion Control. Kawasaki, Japan: IEEE, 2004: 2129.

［3］Fadali M S. Observerbased robust fault detection of multirate linear system using a lift reformulation ［J］. Computers and Electrical Engineering, 2003, 29(1): 235243.

［4］Ciefrri R, Longhi S. Decentralized control of multirate sampleddata systems ［C］//IEEE Control Systems Soeiety Proc of the 4lst IEEE Conf on Decision and Control. Novada, USA: IEEE, 2002: 584585.

［5］Wang J, Chen T, Huang B. Multirate sampleddata systems: Computing fastrate models ［J］. Journal of Process Control, 2004, 14(1): 7988.

［6］Polushin I G, Marquez H J. Multirate versions of sampleddata stabilization of nonlinear systems ［J］. Automatica, 2004, 40(6): 10351041.

［7］Davide Barcelli, Alberto Bemporad, Giulio Ripaccioli. Decentralized hierarchical multirate control of constrained linear systems ［C］//18th IFAC World Congress. Milan, Italy: IFAC， 2011: 277283.

［8］彭述清.基于模型估计的多采样率控制系统鲁棒稳定性［D］. 昆明：云南大学信息学院， 2010.

［9］Laila D S,Nesic D, Astolfi A. Advanced topics in control systems theory ［M］. London :Springer Verlag, 2006: 91137.

［10］Hetel L, Daafouz J, Richard J P, et al. Delaydependent sampleddata control based on delay estimates ［J］.Systems & Control Letters,2011, 60(2): 146150.

［11］Fridman Emilia, Blighovsky Anatoly. Robust sampleddata control of a class of semilinear parabolic systems ［J］. Automatica, 2012, 48(5): 826836.

［12］Su JuingHuei, Fong IKong. New robust stability bounds of linear discretetime systems with time varying uncertainties ［J］. Int J Control, 1993, 58(6): 14611467.

［13］Thompson P M, Dailey R L, Doyle J C. New conic sectors for sampleddata feedback systems ［J］. Systems & Control Letters, 1986, 7(5): 395404.

［14］Dullerud G, Glover K. Robust stabilization of sampleddata systems to structured LTI perturbation ［J］. IEEE Trans Automatic Contr,1993, 38(10): 728730.

［15］Bernstein D S, Hollot C V. Robust stability for sampleddata control system ［J］. Systems & Control Letters, 1989, 13(3): 217226.

［16］Jin Huiliang, Mirkin L, Palmor Z J. Robustness of sampleddata control system with generalized sampleddata hold functions ［J］. International Journal of Robust and Nonlinear Control, 2007, 17: 649673.

［17］陈根永.数值计算方法与MATLAB应用［M］.郑州：郑州大学出版社, 2010.

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