Synthesis of repetitive control systems and its application

Abstract

A new control scheme named repetitive control is proposed, in which the controlled variables follow the periodic reference commands with high accuracy. The error convergence condition for linear plants is derived by applying the small gain theorem and a synthesis algorithm using the methods of Kalman Filter and the perfect regulation is presented. We also investigate the repetitive control for a class of nonlinear systems described by x(t)=Ax(t)+Bu(t)+f(x(t)) and y(t)=Cx(t)+Du(t). The stability condition is developed using the passivity theorem. The scheme is applied to the trajectory control for a three-link manipulator.