Robustness analysis of a gradient-based repetitive algorithm for discrete-time systems

This paper investigates the possibility of using a truncated finite impulse response (FIR) model approximation to implement a well-known gradient type repetitive control algorithm. As a result it is in fact shown that the algorithm iteratively solves a model predictive control related cost function. Furthermore, it is shown how accurate the FIR approximation of the original system has to be in order for the algorithm to converge to zero tracking error. Under certain assumptions on the plant model it is shown that the algorithm results in monotonic convergence in the l_∞-norm. The algorithm is applied in real-time to a nonminimum mass-damper-spring system, and experimental results are compared to the theoretical results.