João Manoel Gomes da Silva

Anti-windup Design for Time-delay Systems Subject to Input Saturation An LMI-based Approach

This paper focuses on the study and the characterization of stability regions for linear systems with delayed states and subject to input saturation through anti-windup strategies. In particular, the synthesis of anti-windup gains in order to guarantee the stability of the closedloop system for a region of admissible initial states as large as possible is addressed. Based on the modeling of the closed-loop system, resulting from the controller plus the anti-windup loop, as a linear time-delay system with a deadzone nonlinearity, stability conditions in an LMI form are stated, for both the delay independent and delay dependent contexts, by using quadratic functionals and a modified sector condition. LMI-based optimization schemes for computing the anti-windup gains that lead to the maximization of the size of the region of stability associated to the closed-loop system are then proposed. The application of the technique and the trade-off between the size of the delay and the region of stability are illustrated by means of numerical examples.

Regional Stability Analysis of Discrete-Time Dynamic Output Feedback Under Aperiodic Sampling and Input Saturation

This technical note addresses the problem of regional stability analysis of a continuous-time plant controlled by a discrete-time dynamic output feedback control law with saturation constraints under aperiodic sampling. To cope with the aperiodic sampling problem, the proposed approach is based on an impulsive system modeling and the use of looped functionals. A generalized sector-based relation is applied to tackle the control saturation effects. From these ingredients, conditions to ensure regional asymptotic stability of the closed-loop system under aperiodic sampling are derived. Based on these conditions, LMI-based optimization problems are proposed to compute estimates of the region of attraction of the closed-loop system or to maximize the bound on the maximal admissible interval between two successive sampling instants, for which the regional stability can be ensured with respect to a given set of admissible states. A numerical example illustrates the application of the results.

Wave Equation With Cone-Bounded Control Laws

This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations.

Anti-windup design with guaranteed regions of stability for discrete-time linear systems with saturating controls

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be modeled by a linear system connected to a deadzone nonlinearity. From this model, stability conditions based on quadratic Lyapunov functions are stated. Algorithms based on LMI schemes are proposed for computing both the anti-windup gain and an associated stability region.

Síntese de controladores repetitivos chaveados : uma aplicação à fontes ininterruptas de energia (UPS)

This paper presents a methodology for the synthesis of repetitive switched controllers to ensure the reference tracking of sinusoidal signals and the disturbance rejection on Uninterruptible Power Supplies - UPS. To improve both transitory and steady-state behavior of the output signal, we consider a state-space realization of a switched repetitive controller aiming two distinct operation conditions: transitory response (to improve the recovery time when the load is changed) and steady-state (to reduce the total harmonic distortion of the output signal when subjected to nonlinear loads). Based on a state-space framework, a state feedback is introduced to ensure the stability of the closed-loop when it is subjected to an arbitrary switching function. From a Lyapunov-Krasovskii functional, LMI conditions are derived to compute the stabilizing feedback gain. The dynamic behavior of the proposed control scheme is presented through simulation of a real UPS model subjected to non-linear loads.

Well-posedness and stability of a 1D wave equation with saturating distributed input

In this paper, it is considered a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. The slope has a finite length and is attached at both boundaries. It is equipped with a distributed actuator subject to a saturation. By closing the loop with a saturating input proportional to the speed of the deformation, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups technics. The asymptotic stability of the closed-loop system, when the tuning parameter has a suitable sign, is proven by Lyapunov technics and a sector condition describing the saturating input.

Static anti-windup for systems with sector-bounded nonlinearities

This paper considers the problem of static anti-windup synthesis for a class of systems featuring both saturated control action and additional sector-bounded nonlinearities. Anti-windup algorithms are developed which ensure, in the first instance local stability and performance, and are then stated for the global case when this is possible. The static anti-windup gains are computed from the solutions of sets of linear matrix inequalities, making the synthesis procedure numerically tractable.

Estratégia de controle para o seguimento de referências em sistemas de tempo discreto com atuadores saturantes

Este trabalho aborda o problema de seguimento de referencias em sistemas lineares sujeitos a saturacao dos atuadores atraves de uma representacao no espaco de estados. O objetivo e garantir o seguimento de referencias constantes e a rejeicao de perturbacoes tambem constantes, em regime permanente, atraves da adicao de uma acao integral a uma malha de controle com realimentacao unitaria. Base-ado nesta estrutura, condicoes na forma de inequacoes matriciais sao propostas para o projeto simultâneo de uma realimentacao de estados estabilizante e de um controlador de anti-windup estatico. Estas condicoes garantem que as trajetorias do sistema em malha fechada sao limitadas em um conjunto invariante se as condicoes iniciais do sistema pertencerem a este conjunto e se as referencias/perturbacoes pertencerem a um certo conjunto admissivel. Problemas de otimizacao baseados em inequacoes matriciais lineares (LMIs) sao entao propostos para maximizar os conjuntos de referencias/perturbacoes e/ou condicoes iniciais admissiveis.

A framework for the nonlinear control of dual-stage systems

Abstract This paper presents a framework for the nonlinear control of dual-stage actuators (DSA). Motivated by various nonlinear controllers that make use of sector bounded and £ ∞ nonlinearities for the control of saturated linear systems, a methodology for integrating such nonlinear functions in order to improve the performance of DSA is presented. The stability of the closed-loop system is assessed by casting the nonlinearities in a mixed sector-bounded plus quasi-Linear Parameter Varying (LPV) framework, leading to a set of linear matrix inequalities (LMIs) to be satisfied by the controller parameters. Taking advantage of the developed framework, a new £ ∞ function is proposed to avoid the saturation of the secondary actuator. Simulation results illustrate the validity of the proposed framework and its potential for the performance improvement of DSA.

Linear Systems Subject to Control Saturation—Problems and Modeling

This chapter is dedicated to the statement of problems we are concerned with when controlling linear systems with saturating inputs. These problems are addressed in the book by different approaches and different models for the saturation term. With this aim in mind, we first present the system and the assumptions made. Then, the problems of stability analysis and stabilization are formally stated. These problems are formulated in the contexts of asymptotic stability as well as external stability (which arises when the system is subject to the action of external signals). An introduction is given to the anti-windup problem and different ways of modeling the saturation term are presented. These representations are particularly important when seeking numerical tractable conditions to the main problems considered.