The Invariance Property of Control Systems with Imperfect Relay Elements

摘要

We consider the problem of ensuring the invariance property for a linear stationary system with relay controls. In the case of perfect relays, wide-class exogenous disturbances are compensated theoretically on the basis of sliding mode theory. Existing imperfections of relay elements make it impossible to implement a perfect sliding mode; thus, the closed-loop system has dynamics in a zero neighborhood of the given variety. This causes undesirable oscillations in a steady-state mode ("chattering"), leading to missed invariance with respect to exogenous and parametric disturbances. This paper solves the problem of ensuring invariance under imperfect relay elements and involves two approaches. The first one allows for making the relay characteristic close to that of the perfect counterpart (by means of increasing the feedback amplification coefficient); consequently, the chattering problem is eliminated. The second approach proceeds from the high-frequency modulation principle and performs regularization of relay switchings; using the linearization effect for the relay characteristics, the second approach guarantees the invariance property.