Iterative learning control with advanced output data for nonminimum phase systems

This paper investigates iterative learning control of discrete time nonminimum phase systems. First, an iterative learning control scheme of linear maximum phase systems is briefly discussed. It is shown that the inverse mapping from desired output to input is stable for maximum phase systems with the proposed method. Next, the results are extended to nonminimum phase systems. The stability of the inverse mapping from the desired output to the input can be shown based on the results of maximum phase systems. The input should be updated with the output which is more advanced than the input by the sum of the relative degree of the system and the number of nonminimum phase zeros. Also, the results are extended to the nonlinear systems and the boundedness of the desired input is proven locally around the origin. An example is given to indicate the importance of proper advances of output in the input update law.