Simultaneous stabilization with near-optimal H∞ performance

被引:33
作者
Miller, DE [1 ]
Chen, TW
机构
[1] Univ Waterloo, Dept Elect & Comp Engn, Waterloo, ON N2L 3G1, Canada
[2] Univ Alberta, Dept Elect & Comp Engn, Edmonton, AB T6G 2G7, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
disturbance rejection; optimal control; sampled-data systems; simultaneous stabilization; time-varying control;
D O I
10.1109/TAC.2002.805687
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper, we consider the use of linear periodically time-varying (LPTV) controllers for simultaneous stabilization and disturbance rejection. Here, we consider the case in which the control signal u does not appear directly in the output to be controlled (z) and the disturbance w does not appear directly in the measured output y. we prove that for every finite set of such plants for which the high-frequency gains (from u to y) satisfy a linear independence condition, we can design an LPTV controller which provides not only closed-loop stability but also near-optimal disturbance rejection in the Hinfinity. sense. The approach works as follows. We first design a (near-optimal) linear time-invariant (LTI) controller for each possible model. We then propose the following periodic control mechanism: during the first part of every period, we (linearly) estimate what the control signal would be if we knew the plant and if the corresponding LTI controller were applied; during the last part of the period, we apply this (suitably scaled) estimate. We end up with a stable LPTV controller, parametrized by the period T, which will provide simultaneous stability for modest values of T, and which will recover the near-optimal performance as T --> 0.
引用
收藏
页码:1986 / 1998
页数:13
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