Disturbance rejection in control systems with saturating actuators
type: Item
instance of: scholarly article
title: Disturbance rejection in control systems with saturating actuators
zbMATH Open document ID: 0971.93058
DOI: 10.1016/S0362-546X(00)85012-9
author: C. Gökçek
author: S. M. Meerkov
author: Pierre T. Kabamba
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-10-16T00:00:00Z
review text: The authors consider a control system such that plant \(P(s)\) and controller \(C(s)\) have the following state-space representations \[ \dot x_p= A_0 x_p + B_1 w + B_2 v, \qquad z= C_1 x_p,\qquad y= C_2 x_p, \] and \[ \dot x_c= M x_c + L y, \qquad u= K x_c, \] where \(x_p\) and \(x_c\) are the states of the plant and the controller respectively and \(u, v, w, y, z \in \mathbb{R}.\) The disturbance \(w\) is a standard white noise and the actuator characteristics is \(v =\phi(u)\) where \(\phi(u)\) is standard saturation function \[ \phi(u) = \begin{cases} +1, \quad u > +1 \\ u, \quad -1 \leq u \leq +1 \\ -1,\quad u < -1.\end{cases} \] Let \(\sigma_z^2\) and \(\sigma_u^2\) be (steady-state) variances of \(z\) and \(u\). The authors consider the following problem. Analysis problem: given \(P(s)\) and \(C(s)\), assuming that the controller \(C(z)\) stabilize the system when \(w \equiv 0\), determine the variance \(\sigma_z^2.\) Synthesis problem: given \(P(s)\) and \(\rho >0\), find a controller \(C(s)\) that stabilizes the system when \(w \equiv 0\) and minimizes \(J = \sigma_z^2 + \rho \sigma_u^2.\) The authors use the method of stochastic linearization. The solution involves nonlinear equations and simple bisection algorithms that can be used for the solution of these equations are provided.
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93B18
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1472215
zbMATH Keywords: control system
zbMATH Keywords: actuator saturation
zbMATH Keywords: stochastic linearization
zbMATH Keywords: disturbance rejection
zbMATH Keywords: white noise
reviewed by: Yu. V. Kozachenko
MaRDI profile type: Publication
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full work available at URL: s0362-546x(00)85012-9
OpenAlex ID: W2121920584
description: scientific article; zbMATH DE number 1472215