A Multistage Update Rule Framework for Iterative Learning Control Systems

The proportional type update rule (PTUR) is the most widely used iterative learning control (ILC) scheme. Recently, a fractional-power type update rule (FTUR) was proposed to accelerate PTUR. However, PTUR and FTUR converge slowly for small and large tracking errors, respectively. In this study, a multistage update rule (MSUR) is designed to accelerate PTUR and FTUR along the whole iteration axis. Under the proposed switching mechanism, PTUR and FTUR are adopted for large and small errors for fast convergence, and then PTUR is applied for zero-error tracking. The convergence of MSUR is proved by the analysis of a nonlinear recursion with perturbation. Moreover, for system information that is unknown, an extended MSUR is presented, and its zero-error convergence is proved. In addition, we discuss the influence of the parameters in MSUR on the convergence rate and propose a set of parameter selection rules to maximize the convergence rate of MSUR. Meanwhile, variable-gain and variable-power MSURs are designed to further accelerate the MSUR that only has a single gain and fractional power. Numerical simulations and experimental test verify the theoretical results.