A Gradient-based Repetitive Control Algorithm Combining ILC and Pole Placement

Abstract

In this paper the application of a well-known adjoint iterative learning control algorithm to repetitive control (RC) problems is explored. It is found that due to the lack of resetting in RC, and the non-causal nature of the adjoint algorithm, the implementation requires a truncation procedure that can lead to instability. As a new result it is shown that the algorithm iteratively solves a model predictive control (MPC) related cost function. Furthermore, it is shown how accurate the finite impulse response 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. In order to avoid the truncation procedure it is proposed that pole placement be used to shorten the impulse response of the plant and thus guarantee convergence. A robust design procedure is formulated in order to select suitable pole locations. The proposed algorithm is validated using real-time experiments on a nonminimum phase spring-mass-damper system. The experimental results show fast convergence to near perfect tracking, demonstrating the applicability of the proposed algorithm to RC problems.