Sampling rate selection for multi‐loop cascade control systems in an optimal manner

Abstract

This article proposes an optimization‐based approach to selecting the sampling periods for classes of linear time‐invariant (LTI) regulators in a cascaded multi‐rate control structure, to account for practical implementation on numeric systems. Starting from the Shannon‐Nyquist sampling theorem, which proposes the minimum required sampling frequency for completely recovering the original analog signal from its discrete samples, the scope of the sampling process, viewed from a control perspective, is to ensure asymptotic stability of the closed‐loop system, with the smallest possible degradation of the initially‐proposed performance indices as possible according to a set of well‐picked criteria. As such, a configurable optimization‐based approach is proposed, solved with the mixed‐integer artificial bee colony (MI‐ABC) algorithm, for selecting the sampling periods by specifying the emphasis between closed‐loop fidelity and ease of implementation, with an intuitive visualization method. The proposed solution is illustrated on two case studies, with emphasis on the construction of the proposed functionals and their practical implications.