Finite frequency control of discrete linear repetitive processes with application in iterative learning control

For systems that repeatedly perform a given task, iterative learning control makes it possible to update the control signal to the system during successive trials in order to improve the tracking performance. Iterative learning control has an inherent two-dimensional/repetitive system structure since dynamics involves in two independent directions, i.e. time and trials. In this paper, the repetitive process structure is exploited in a method that results in a one step synthesis both a stabilizing feedback controller in the time domain and a feedforward controller which guarantees convergence in the trial domain. Furthermore, with the aid of the Generalized Kalman-Yakubovich-Popov lemma the controller design is performed in finite frequency range to determine which frequencies have to be emphasized in the learning process. The advantage of a proposed design method lies in the fact that it is presented in terms of solutions to a set of linear matrix inequalities which requires a reasonable computational cost to solve them. The effectiveness of the theoretical developments will be validated by considering a pick-and-place robot system as a practical application.