Controller and anti‐windup co‐design for the output regulation of rational systems subject to control saturation

Abstract

This article presents a novel framework for the output regulation of rational nonlinear systems subject to input saturation, where the controller structure is composed by an internal model generator in series with an output feedback stabilizing stage. In order to address the effects of control saturation, we propose the use of an anti‐windup compensation loop into both internal model and stabilizing control stages. Given prior knowledge of the system zero‐error steady‐state condition and a proper internal model, we cast the regulation error dynamics in a differential‐algebraic form, which leads to matrix inequalities conditions that ensure closed‐loop stability and exponential transient performance. Optimization problems are then proposed to simultaneously compute the stabilizing controller and the anti‐windup gains such that a domain of attraction estimate is maximized.

Robust practical output regulation of rational nonlinear systems via numerical approximations to the regulator equations

“…In order to deal with nonlinear functions f z (z, w, v) and h z (z, w, v) using LMI-based conditions, we consider using the so-called differential-algebraic representation, which was previously used to develop an stabilization framework for the asymptotic output regulation. 30,31 In these previous works, however, it was considered the use of exact zero-error steady-state mappings x(w) and 𝝃(w) during the coordinate change procedure presented in (59), a special case where the relaxations 𝚫 f (w) and ẽ(w) are precisely equal to zero. The novelty of this article lies on the employment of the DAR approach into the practical output regulation context where the solutions to the regulator equations are possibly relaxed.…”

“…Recently, there have been efforts to also employ this DAR strategy in order to solve output regulation problems for rational nonlinear systems. 30,31 These works were however restricted to the asymptotic output regulation problem and thus require strict assumptions regarding the solution of the regulator equations and the a priori knowledge of a feasible internal model immersion.…”

“…The purpose of this article is to present further developments and stronger results upon the previously cited works 30,31 by considering the practical output regulation framework, allowing one to deal with systems where an exact solution to the regulator equations is unknown and when the required internal model order is too high or even infinite. Our article presents a systematic control design framework for the robust practical output regulation of rational nonlinear systems subject to harmonic exosystems.…”

Controle de ganho escalonado para rotação e translação de espaçonaves usando quatérnios e síntese por otimização convexa

“…É de grande importância assegurar que a convergência do sistema seja executada com uma taxa de decaimento aceitável, do contrário a manobra efetuada pela espaçonave pode ser finalizada em um período muito além do aceitável. Para tanto, utiliza-se o conceito de estabilidade exponencial (Castro et al, 2021):…”

“…Já as restrições LMI (Linear Matrix Inequalities, ou Desigualdades Matriciais Lineares) (Boyd et al, 1994) serão empregadas visando a resolução do problema de otimização convexa. Para analisar a estabilidade do sistema será utilizado o teorema de Lyapunov, e a convergência assintótica será garantida dentro de um tempo especificado pela utilização do decaimento exponencial (Castro et al, 2021).…”