Abstract
This paper studies the anti-windup (AW) problem for a certain class of non-linear systems, in which the plant is globally quadratically stable and also partially linearisable by a suitably chosen non-linear feedback control law. Three types of AW compensators are proposed for this type of non-linear system: the first one is a non-linear extension of the popular linear internal model control (IMC) scheme; the second one has a similar structure to the IMC AW compensator yet is of reduced order and has entirely linear dynamics; and the third one is again a linear AW compensator, but can endow the closed-loop system with some sub-optimal performance properties. All three AW compensators are able to provide global exponential stability guarantees for the aforementioned class of systems. This work was inspired by a wave energy application whose dynamics fall into the class of systems studied in this study. Simulation results show the efficacy of the three AW compensators when applied to the wave energy application.
Highlights
Anti-windup (AW) compensation is a common approach of ensuring a system’s behaviour remains acceptable if the demanded control signal exceeds the control constraints present in the system
This paper proposes three AW compensators for this class of systems: The first two are nonlinear versions of so-called Internal Model Control (IMC) anti-windup, which is well known to be globally stabilising in the linear case
Three IMC-type compensators which guarantee global exponential stability have been proposed for a class of input-constrained partially linearisable nonlinear systems
Summary
Anti-windup (AW) compensation is a common approach of ensuring a system’s behaviour remains acceptable if the demanded control signal exceeds the control constraints present in the system. This paper proposes three AW compensators for this class of systems: The first two are nonlinear versions of so-called Internal Model Control (IMC) anti-windup, which is well known to be globally stabilising in the linear case. The third contains a free “state-feedback” matrix, which can be used to optimise performance and is one of the key advancements of this work over [29] This last compensator has a similar structure to that in [24], but its construction requires the solution of a Linear Matrix Inequality (LMI) rather than a nonlinear partial differential inequality as in [24]. The paper provides simulation results demonstrating the effectiveness of the techniques on the motivating WEC control problem
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