Adaptive Nonstationary Control Using Solutions of Time-Varying Riccati Equations(Its Application to Positioning Control of Vibration Systems)

Abstract

The author's previous study proposed an efficient design method of time-varying gain type controller using the solutions of time-varying Riccati equations (TVREs) and its application to a positioning control problem of a vibration system. The responses of this method become similar to the responses of conventional nonstationary optimal regulators (NORs) which are effective controllers for positioning control problems of vibration systems. This method generates the solutions of TVREs and the responses of a controlled object simultaneously. Therefore, different from the use of NORs, the time-varying gains are obtained by real-time computations in actual implementations. This feature is convenient for the realization of some adaptive control. This study investigates the effectiveness of an adaptive nonstationary control method based on the feature of the previous study. The effectiveness of the method is verified theoretically and experimentally by applying the method to an actual positioning control problem for the experimental system consisting of an X-Y table and a flexible structure on the table.