Finite dimensional internal model-based repetitive control of nonlinear passive systems

In this paper a new class of globally stable finite dimensional repetitive controllers for nonlinear passive systems is proposed. The passivity-based design of the proposed repetitive controller avoids the problem of tight stability conditions and slow convergence of the conventional, internal model-based, repetitive controllers. The existing internal and external model-based repetitive controllers can be derived as the special cases of the proposed controller. Also, it is possible a simple extension of the basic algorithm by an adaptive notch filter which provide asymptotic tracking of periodic signal with unknown signal frequency. The simulation results on a two degrees of freedom planar elbow manipulator illustrate the controller performances.