Abstract
In this paper, a new approach to reject quickly any periodic signals with unknown multiple periods is proposed and a useful adaptive repetitive control system with a recursive identification of the multiple periods is presented. The contributions are as follows: Firstly, an effective periodic generator for the case of multiple periods is proposed. The proposed repetitive controller is implemented with much less memory elements than the previous ones. As a result, the degree of the controller is highly reduced and much faster convergence of the controlled error to zero is provided. Secondly, the proposed controller assures the stability of the adaptive repetitive control system. The proposed controller is obtained by solving a simple linear programming problem. The design effort is very small independent of the periods. Thirdly, a simple period identification algorithm is proposed to estimate the multiple periods. The parametric model to be estimated consists of a simple FIR model and the algorithm is based on the well-known recursive least squares method. The effectiveness is demonstrated by simulations.
