Iterative Learning Control of Iteration-Varying Systems via Robust Update Laws with Experimental Implementation. (May 2017) - Altın, Berk; Willems, Jeroen; Oomen, Tom; Barton, Kira
Abstract: Iterative learning control (ILC) is an efficient way of improving the tracking performance of repetitive systems. While ILC can offer significant improvement to the transient response of complex dynamical systems, the fundamental assumption of iteration invariance of the process limits potential applications. Utilizing abstract Banach spaces as our problem setting, we develop a general approach that is applicable to the various frameworks encountered in ILC. Our main result is that robust invariant update laws lead to stable behavior in ILC systems, where iteration-varying systems converge to bounded neighborhoods of their nominal counterparts when uncertainties are bounded. Furthermore, if the uncertainties are convergent along the iteration axis, convergence to the nominal case can be guaranteed. Abstract : Highlights: An abstract vector space approach is employed to study iterative learning control under uncertain iteration-varying effects. Bounded-input bounded-output and asymptotic stability is ensured by designing the first-order update law to be robust. Asymptotic performance and design trade-offs are discussed. An optimization approach is suggested to address inherent design trade-offs. Simulation examples and experimental implementation on a linear motion stage verify theoretical findings.