A novel design strategy for iterative learning and repetitive controllers of systems with a high modal density: Theoretical background

This paper discusses the design and application of iterative learning control (ILC) and repetitive control (RC) for high modal density systems. Typical examples of these systems are structural and acoustical systems considered in active structural acoustic control (ASAC) and active noise control (ANC) applications. The application of traditional ILC and RC design techniques, which are based on a parametric system model, on systems with a high modal density has several important drawbacks: the design procedure is complex, the controllers require much computational power and the robustness of the controllers is low. This paper describes a novel strategy to design noncausal ILC and RC filters, which is especially suited for high modal density systems. Since it does not require a parametric system model, the novel strategy avoids several drawbacks of the traditional techniques: no cumbersome parametric model estimation is required; the ILC and RC controllers are robust to small changes of the poles and zeros of the controlled system; and the complexity of the ILC and RC control filters is restricted. A crucial element in the proposed strategy is the noncausal filtering in the ILC and RC controllers, which requires the availability of a trigger signal to announce a new ILC trial or RC period in advance. A numerical validation on a simulation model proves the potential of the developed strategy.