文章基本信息

标题：Integral control of stable nonlinear systems based on singular perturbations ⁎
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作者：Pietro Lorenzetti ; George Weiss ; Vivek Natarajan 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2020
卷号：53
期号：2
页码：6157-6164
DOI：10.1016/j.ifacol.2020.12.1698
语种：English
出版社：Elsevier
摘要：AbstractOne of the main issues related to integral control is windup, which occurs when, possibly due to a fault, the input signaluof the plant reaches a value outside the allowed input rangeU.This paper presents an integral controller with anti-windup, called saturating integrator, for a single-input single-output nonlinear plant having a curve of locally exponentially stable equilibrium points that correspond to constant inputs inU.A closed-loop system is formed by connecting the saturating integrator in feedback with the plant. The control objective is to make the output signalyof the plant track a constant reference r, while not allowing its input signaluto leaveU.Using singular perturbation methods, we prove that, under reasonable assumptions, the equilibrium point of the closed-loop system is exponentially stable, with a “large” region of attraction. Moreover, when the state of the closed-loop system converges to this equilibrium point, then the tracking error tends to zero. A step-by-step procedure is presented to perform the closed-loop stability analysis, by finding separately a Lyapunov function for the reduced (slow) model and a Lyapunov function for the boundary-layer (fast) system. Afterwards, a Lyapunov function for the closed-loop system is built as a convex combination of the two previous ones, and an upper bound on the controller gain is found such that closed-loop stability is guaranteed. Finally, we show that if certain stronger conditions hold, then the domain of attraction of the stable equilibrium point of the closed-loop system can be made large by choosing a small controller gain.
关键词：Keywordsnonlinear systemsintegral controlsingular perturbation methodwindupLyapunov methods