MIMO multi-periodic repetitive control system: adaptive control schemes

This paper presents a simple feed forward adaptive multiperiodic repetitive control scheme for the ASPR (almost strictly positive real) or ASNR (almost strictly negative real) plant to asymptotically track/reject multiperiodic reference/disturbance signals. The Liapunov stability analysis is given and simulations are included. The extension of the Liapunov stability analysis to ASPR or ASNR plant under certain nonlinear perturbations and an exponential stability scheme are discussed as well. Finally an adaptive proportional plus multiperiodic repetitive control scheme is proposed.