Adaptive Repetitive Control Systems for Fast Rejection of Periodic Disturbances with Uncertain Multiple Periods

In this paper, a discrete-time repetitive control problem is considered for the cases where the disturbance consists of periodic signals with several different periods but the periods are uncertain. A new adaptive repetitive control system for such cases is proposed and consists of three elements; a stabilizing controller, a period estimator and an adaptive reduced order periodic signal generator. The controller not only assures the stability of the overall adaptive repetitive control system including the time-varying generator but also assigns all poles of the closed-loop system on the disk with a given radius. The design problem is reduced to a simple and feasible l1 norm minimization problem. The estimator estimates multiple periods of disturbance from the input/output data of the plant. The algorithm consists of the well-known recursive least squares method. In order to reject periodic disturbances with uncertain multiple periods, the adaptive generator is adjusted on-line by using the period estimated. The repetitive controller with the generator is implemented with much less memory elements than the previous ones. As a result, the degree of the controller is significantly reduced and much faster convergence of the controlled error to zero is provided. The effectiveness is demonstrated by simulations.