Repetitive processes are characterized by a~series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations which increase in amplitude in the pass to pass direction and cannot be controlled by standard control laws. Here we give new results on the design of physically based control laws for the sub-class of so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control. The main contribution is to show how control law design can be undertaken within the framework of a general robust filtering problem with guaranteed levels of performance. In particular, we develop algorithms for the design of an and l 2–l 8 dynamic output feedback controller and filter which guarantees that the resulting controlled (filtering error) process, respectively, is stable along the pass and has prescribed disturbance attenuation performance as measured by and l 2–l 8 norms.
Wu, L., Lam, J., Paszke, W., Galkowski, K., Rogers, E., & Kummert, A. (2009). Control and filtering for discrete linear repetitive processes with H∞ and ℓ2–ℓ∞ performance. Multidimensional Systems and Signal Processing, 20(3), 235-264. https://doi.org/10.1007/s11045-008-0061-4