一类奇异H_∞问题的降阶控制器的解释

Explanation of reduced order controller for a class of H_∞ singular control problem

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 。

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.