Discrete Time Linear Optimal Repetitive Control - A Low Order Controller Scheme

This paper proposes a new method to discrete time linear time invariant (LTI) repetitive control tracking problem when the reference signal includes a single period with an already known high period. Based on an earlier result in [1], as period gets high, dimension of the augmented state-space description there also gets very high. This in turn leads to higher order computation issues for designing the control law when optimality methodology is used. The low order controller designed in this paper is thus served for this purpose, where the computational problem is eased by using spectrum analysis of the reference signal. Application of this new low order repetitive controller to a non-minimum spring mass damper system demonstrates its effectiveness for tracking problems even if the periodic signal has a very high period.