Adaptive Nonstationary Control Using Solutions of Time-Varying Riccati Equations

Abstract

One of the authors has 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 time-invariant vibration system. The responses of this method become similar to the responses of conventional nonstationary optimal regulators (NORs) which are effective controllers for positioning of vibration systems. This method generates the solutions of a TVRE and the responses of a controlled object simultaneously. 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 applies an adaptive nonstationary control method based on the feature of the previous study to the positioning control of a time-varying vibration system whose natural frequency is time-varying. The effectiveness of the method is verified theoretically and experimentally.