A Discrete-Time MIMO Repetitive Controller

A discete-time repetitive controller for tracking control of MIMO linear system subject to repetitive desired trajectories is presented. Within the framework of periodic functions, an explicit procedure for stably investing the plant dynamics is formulated. This procedure, which is also applicable to nonminimum phase plants, can be used to determine the exact feedforward input of the plant. A repetitive controller is then formated to automatically genrate this feedforward input without requiring a exact knowledge of the plant dynamics. The necessary and sufficient coditions for exponential stability of this repetitive controller is derived. This controller can also be applied for tracking control of a nonminimum phase plast. A simulation study of the application of the proposed controller for force control of a single axis positioning device is presented.