Adaptive Multi-periodic Repetitive Control for a Class of Discrete-time Strictly Proper Systems

For LTI plant, SPR(Strictly Positive Real)/ASPR(Almost Strictly Positive Real) property was recently used to design a continuous-time (adaptive) multi-periodic repetitive control system that guarantees the Lyapunov stability of the whole system. However in discrete time, SPR/ASPR property requires the controlled plant to be proper and unfortunately in practice it is very rare to find a plant where the input u(k) has an immediate effect on the output y(k). Therefore, such existing repetitive control algorithm cannot be directly applied. To solve this problem, a new non-identifier-based adaptive repetitive control algorithm is proposed. Such algorithm does not need any plant parameter information, thus is highly robust. The algorithm also suggests that the form and success of the controller will depend crucially on the plant’s relative degree. Lyapunov method is used for stability analysis and simulation results are given.