Parameterization of all multivariable ripple-free deadbeat tracking controllers

This paper presents an explicit parameterization of all ripple-free deadbeat tracking controllers for multi-input multi-output (MIMO) sampled-data control systems. The advantages over the previous results are the following. First, a useful necessary and sufficient condition to obtain a ripple-free deadbeat tracking response for MIMO sampled-data control systems is presented. Second, not only all ripple-free MIMO deadbeat tracking controllers but also all achievable deadbeat sequences and all control input ones are characterized by completely free parameters in an explicit form. Third, the design method is simple and straightforward. The computation consists of simple polynomial matrix equations without involving troublesome calculation such as the reduction to Smith–McMillan form. Fourth, the class of the reference inputs for which ripple-free deadbeat tracking responses are achieved is generalized. Finally, a numerical example demonstrates that the proposed parameterization makes it easy to clarify the relationship between the settling time and the free parameters and to find the minimum settling time ripple-free deadbeat controller.