Robust PD-type iterative learning control for discrete systems with multiple time-delays subjected to polytopic uncertainty and restricted frequency-domain

Abstract

© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature. This paper proposes the PD-type iterative learning control (ILC) for multiple time-delays systems with polytopic parameter uncertainty. Based on repetitive process framework, the system under study is equivalently converted into a class of uncertain repetitive processes with multiple time-delays. This approach accounts for effective inclusion of both time and trial domain objectives and hence some requirements on transient dynamics and trial-to-trial error convergence are incorporated for robust design procedures. Additionally, this approach can easily avoid the need for computation with very large dimensioned matrices as it is required for the lifting approach. Also, the proposed controller is designed with the generalized Kalman-Yakubovich-Popov lemma to ensure the monotonic trial-to-trial error convergence in finite frequency domain. This allows us to reduce the conservatism inherent to entire frequency range approaches since the reference signal spectrum reside in a known frequency range. Moreover, the sufficient conditions for the convergence of the resulting scheme are expressed by linear matrix inequalities and hence they are amenable to effective algorithmic solution. Finally, numerical simulations of different scenarios are presented to illustrate the effectiveness of the proposed method. In particular, to highlight the potential interest in PD-type ILC the robust tracking performance is compared with the results for P and D types of ILC.