Discrete-Time Adaptive Control for Linear Systems with Unknown Time-Varying Parameters

Abstract

A new design method of a discrete time adaptive control system is presented for a single-input, single-output, time-varying plant with known dead time. It is assumed that the plant has unknown time-varying parameters which are described by AR model. First, an indirect model reference adaptive controller is designed for the case where the parameters of the time-varying parameter dynamics are pre-assigned. In this method, the unknown time-varying parameters are estimated as the state variables of the AR model using Kaiman filter. The control input is calculated based on the future value of the plant output estimated by restricted complexity predictor. Next, the adaptive controller is extended for the case where the parameters of the time-varying parameter dynamics are unknown. In this case, the adaptive control is performed using two-stage method which alternates between recursive parameter estimation and Kaiman filtering. Finally, the results of computer simulation of adaptive control applied to the plant with sinusoidally varying parameters are included to illustrates the effectiveness of the proposed method.