A Design Procedure for Repetitive Control Systems

The benefits of repetitive control in closed loop control applications involving periodic input signals of known period are well-known since such controllers employ high gains at and around the discrete signal frequencies in periodic signals to achieve high accuracy. The current paper describes, for the first time, a procedure for modifying a given repetitive controller design so as to achieve a specified level of nominal performance, subject to optimizing a measure of stability robustness. The form of the repetitive controller structure is, in effect, specified apriori. The nominal performance is specified here in the form of sensitivity function values at discrete signal frequencies of interest. The stability robustness is specified in the form of a weighting function on the complementary sensitivity function. The procedure has been demonstrated to be feasible, on the basis of simulation results, and to lead to implementable controllers. The procedure should be applicable to a variety of repetitive controller structures.