A discrete time repetitive control system for MIMO plants

This paper presents an analysis and design of a repetitive control (RC) system for discrete time MIMO plants. The structure of the proposed RC system does not require the a prior decoupling of the MIMO plant. With the use of non-causal terms, which are allowed in the design of RC systems, a matrix function called the phase cancellation inverse (PCI) is defined. The PCI operates on the open-loop matrix transfer function by cancelling the the phase lag in the diagonal elements and eliminating the off-diagonal elements. It is shown that the PCI always satisfies the stability condition for the MIMO repetitive controller. Using a factorization method, the design technique is expanded to include non-squared plants with more inputs than outputs. The repetitive controller is applied experimentally to a non-minimum phase MIMO system. The results show that the new design yields superior performance when compared to a single-input single-output repetitive controller design.