Explanation of reduced order controller for a class of H∞ singular control problem
-
摘要: 一类奇异H∞控制问题可以利用系统矩阵的结构特征通过线性矩阵不等式或2代数黎卡提方程方法直接显式构造得到降阶控制器.进而利用系统不稳定的不变零点可以构造出更低阶次的控制器.基于2代数黎卡提方程方法,特别是系统Hamilton矩阵的结构特点和系统可观测性理论,论述了不变零点在构造系统降阶控制器中所起的作用,即通过选择控制器的自由参量,使某些不稳定的不变零点关于虚轴对称的点构成系统控制器不可观的稳定极点,从而实现了控制器进一步降阶.Abstract: The structure character of system transfer matrices can be used to solve a class of singular H∞ control problem and a reduced order H∞ controller can be constructed in explicit form either by linear matrix inequations method or two algebra Riccati equation method. The order of the system H∞ controller can further be reduced by use of system unstable invariant zeros. Based on two algebra Riccati equation method especially the structure of the system Hamilton matrix and system observability theory, the role of invariant zeros in constructing system reduced order controllers was given. That is, by the suitable selection of free parameters of the system H∞ controller, some points which were symmetry with the unstable invariant zeros about the imaginary axis became the stable poles of the system controller which were not observable and could be reduced from the system, thus could get further reduced order controller.
-
Key words:
- control equipment /
- Riccati equations /
- H∞ control /
- observability
-
[1] Doyle J C, Glover K, Khargonekar P P, et al. State-space solutions to standard H2 and H∞ control problems[J]. IEEE Trans Auto Contr, 1989, AC-34(8):831~847 [2] Iwasaki T, Skelton R E. All controllers for the general H∞ control problem: LMI existence conditions and state space formulas [J]. Automatica, 1994, 30(8):1307~1317 [3] Xin X, Guo L, Feng C B. Reduced-order controllers for continuous and discrete-time singular H∞ control problems based on LMI[J] Automatica, 1996, 32(11):1581~1585 [4] 曾建平.基于LMI的H∞控制问题降阶控制器的存在性研究 . 北京:北京航空航天大学自动化科学与电气工程学院,2000 Zeng Jianping. Study on the existence of reduced-order controllers for general H∞ control problem LMI-based .Beijing:School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, 2000(in Chinese) [5] Takao Watanabe,Anton A Stoorvogel. Plant zero structure and further order reduction of a singular H∞ controller[J] Int J Robust Nonlinear Control, 2002,12:591~619 [6] Zhou Kemin, Doyle J C, Glover K. Robust and optimal control[M] Prentice-Hall Inc,1996.327~372 [7] 程 鹏.线性系统理论[M] 北京:北京航空航天大学出版社,1987.43~52 Cheng Peng. Linear system theory[M] Beijing:Beijing University of Aeronautics and Astronautics Press,1987. 43~52(in Chinese) -
点击查看大图
计量
- 文章访问数: 1676
- HTML全文浏览量: 11
- PDF下载量: 172
- 被引次数: 0
下载:
