EXTENDED H∞ CONTROL WITH POLE PLACEMENT CONSTRAINTS VIA LMI APPROACH AND ITS APPLICATION

Abstract

As well known, extended H∞ control accepts unstable weighting functions which are included in a generalized plant, so it has wider availability than standard H∞ control. On the other hand, the root-clustering problem for H∞ control has been considered by Chilali and Gahinet and the solution is derived. But it is not so easy to apply the solution to extended H∞ control, because the formulation of the root-clustering controllers is discordant with that of extended H∞ controllers. Therefore, we can not simply combine the root-clustering conditions with extended H∞ control. In this paper, we propose a LMI based design method for this control problem by using modified formulation of controllers of the root-clustering problem derived by Chilali and Gahinet. These types of control problems appear in design problems of a vibration isolation controller which attenuates vibrations forced by narrow-band frequency disturbances. A controller for a simple vibration isolation experimental system is designed by the proposed method and performance of a designed controller is verified by experimental results.