Nonstationary robust control method taking account of nonstationary influence of uncertainty-its application to positioning control of flexible structures

Abstract

In positioning control problems, generally, the influence of uncertainty in a controlled object model increases at the terminal of positioning. That is, it possesses a nonstationary characteristic. For such a problem, this study presents a nonstationary robust control method (NRCM) taking account of the nonstationary influence of uncertainty. In this method, we define a frequency-shaped weight and a time-varying coefficient of unstructured uncertainty and introduce the generalized plant including them. The nonstationary controller is derived from the combination of the following two criteria. One of them is a time-varying game-type criterion function. The other one is the criterion function on the error between the responses of the nominal system and the uncertain system with the controller derived from the first one. Therefore, NRCM corresponds to the optimization problem based on the coupled criteria. From its application to a positioning control problem of a flexible structure, the usefulness of the method is verified numerically and experimentally.