Dynamical discontinuous feedback control of nonlinear systems

The problem of analyzing dynamical discontinuous feedback nonlinear controlled plants is addressed. The continuous feedback scheme is assumed to be constituted by a dynamical feedback plant, of nonlinear nature, and a controlled switch obeying a pulse-width-modulation (PWM)-type of switching strategy with sufficiently high sampling rate. It is found that the actual closed-loop controlled responses of the system exhibit chattering motions constituting nonideal sliding regimes which converge continuously toward certain average manifolds as the sampling frequency is increased. These manifolds are immersed in the regions of the composite state space where the duty ratio function is not acting under saturation conditions. The average system is simply obtained by an infinite sampling frequency assumption on the PWM process. A PWM feedback interconnection scheme, with general duty ratio function, is shown to be easily analyzable in terms of an average model which captures the essential features of the discontinuously feedback controlled system