Estabilidade de sistemas de controle com atraso variável

Abstract

A robust stability analysis is presented for proportional-integral controlled closed-loop systems with time-varying delay. The two main purposes of the text are to answer which type of delay corresponds to the worst case in terms of stability: the constant delay or the sawtooth delay, and to analytically find a proportional-integral controller that guarantees stability for models with bounded time-varying time delays. Methods are presented for obtaining the solution of a system with time-delay, as well as a discussion about the state space of this type of system. Inconsistencies for systems with rate of change of the time-delay function greater than one are presented and an alternative state space for systems with variable delay is presented based on a topological equivalence with respect to systems with constant delay. After a brief presentation of the general stability concepts and also of the stability criteria for systems with constant delay and variable delay, results regarding the robust stability of systems with variable delay are demonstrated and simulation results are shown for a closed-loop system whose proportionalintegral controller derives from a rule proposed in the text.