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.
Note to Practitioners
—Many engineering systems, including high-speed trains, earth-orbiting satellites, and robotic arms, complete a given tracking task over a finite time interval repeatedly. Fast convergence rate and high tracking precision are key technical requirements in these applications. Iterative learning control (ILC) has been shown as an effective control method for these tasks. However, the widely-used proportional-type update rule (PTUR) and fractional-power type update rule (FTUR) in ILC cannot meet the abovementioned requirements well. PTUR converges fast for large tracking errors but slow for small tracking errors; in contrast, FTUR delivers fast convergence rate for small tracking errors but converges slow for large errors without achieving zero-error. Combining advantages of both PTUR and FTUR rules, a novel multistage update rule (MSUR) is proposed to adaptively switch between them to deliver fast convergence and zero tracking errors. The selection of parameters and their effect on control performance are detailed for engineering applications.