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Design of robust iterative learning control schemes in a finite frequency range

Iterative learning control has been especially developed for systems defined over a finite duration that repeat the same task. Each execution is known as a trial, or pass, and the sequence of operations is that a trial is completed, the system is then reset to the starting location, and the next pass begins. The novel feature of this control law design method is to use information from the previous pass, or a finite number of previous passes, to update the control input applied on the next pass and thereby improve performance from pass-to-pass. Iterative learning control has an inherent two-dimensional systems structure since the dynamics evolve in two independent directions. In this paper, the repetitive process structure is exploited to develop a controller design algorithm that produces both a stabilizing feedback controller in the time domain and a feedforward controller that guarantees convergence in the pass-to-pass domain for all admissible uncertainties. Using the Generalized Kalman-Yakubovich-Popov lemma, controller design is performed over a finite frequency range. A major advantage of this new algorithm lies in the fact that it can be computed using linear matrix inequality software without incurring unacceptable computing cost.