Controle Robusto PID Para Sistemas Lineares Incertos Utilizando Desigualdades Matriciais Lineares

Abstract

This paper investigates the problem of PID (Proportional-Integral-Derivative) control design for uncertain linear systems. Starting from the definition of intervals for the gains of the controller, a state space realization of order 2 for the PID controller is employed for the feedback of SISO dynamic systems of arbitrary order with uncertain time-invariant parameters belonging to polytopes. Therefore, in closed-loop, one gets a linear uncertain system depending on uncertain parameters and on the controller gains belonging to known intervals. A procedure based on the iterative subdivision of the space of the controller parameters is applied and parameter-dependent Lyapunov functions are used to identify the stable regions and, then, to assure a guaranteed H∞ performance index for each region. Numerical examples, including comparisons with one method from the literature, are presented to illustrate the advantages of the proposed technique.