Global Model Recovery Anti-Windup Control With Prescribed Performance for Saturated Systems

In this paper, we investigate the problem of reference tracking for a class of linear systems subject to actuator saturation and propose a global model recovery anti-windup (MRAW) strategy with prescribed performance. We adopt the classic MRAW framework, where one of the outputs of the anti-windup compensator is regarded as the tracking error, reflecting the difference between the unconstrained system and the saturated system. Then, instead of employing the commonly used ${\mathcal {L}}_{2}$ gain, we present the prescribed performance functions (PPFs) to characterize the real-time tracking error such that the transient performance can be captured more specifically. In particular, to avoid singular issues arising from the occurrence of saturation, we modify the existing PPFs with an auxiliary system when saturation occurs. Based on these modified performance functions, we follow a modified performance control approach and design the remaining output that is injected into the anti-windup activation module. Such a design procedure is constructive, making it conducive to its extension to nonlinear systems. Theoretical results establish the boundedness of all signals in the closed-loop system. Simulation results verify the effectiveness of our design strategy. Note to Practitioners—This paper is motivated by the commonly encountered actuator saturation in practical systems. In this paper, under the prescribed performance control (PPC) framework, a novel model-recovery anti-windup design, combined with an auxiliary system, is proposed to handle adverse effects caused by actuator saturation. Its possible application to existing controllers makes such a strategy a popular choice with practitioners. Differently from the existing PPC-based works, most of which pertain to semi-global nature, the strategy presented in this paper eliminates the initial condition dependence restriction and renders global results. Unlike the Linear Matrix Inequality (LMI)-based anti-windup designs, the proposed design can be extended to a class of nonlinear systems, which encompass a fairly general class of practical systems such as aerospace and mechatronic systems.