Overshootless repetitive control

Repetitive control (RC) is a widely used effective approach for periodic reference tracking and periodic disturbance rejection. In this paper, its use for periodic disturbance rejection and piecewise constant reference tracking is analyzed in a continuous-time framework. First, two previously proposed repetitive control structures, namely the basic repetitive controller and the current iteration repetitive controller, are studied. We first show that they do not provide a satisfying piecewise constant reference tracking performance, either because of a nonzero steady state error or because of large overshoots. Then a new structure, named the overshootless repetitive controller, is proposed to provide the same suitable periodic disturbance rejection capability as the current iteration repetitive controller while providing better transients.