Adaptive MIMO Multi-periodic Repetitive Control System: Liapunov Analysis

This paper presents a simple feed forward adaptive plus multi-periodic repetitive control scheme for the ASPR (Almost Strictly Positive Real) or ASNR (Almost Strictly Negative Real, see Appendix for definition) plant to asymptotically track or reject multi-periodic reference or disturbance signals. The Liapunov stability analysis is given. This is an extension work of the Liapunov stability analysis for multi-periodic repetitive control system under a positive real condition. A simulation is 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 MRC (multi-periodic repetitive control) scheme is proposed.