Robust stabilization of nonlinear plants with uncertain hysteresis-like actuator nonlinearities

Abstract

This paper addresses the stabilization problem of an uncertain intrinsically nonlinear SISO plant containing non-smooth nonlinearities (dead-zone, backlash, hysteresis) in the actuator device. A unified framework for its solution is here proposed, assuming that the parameters of the nonlinearities are uncertain as well. To this purpose, the hysteresis model used in [8] has been modified into an “extended” one, and a robust control law ensuring asymptotic stabilization has been synthesized using it. The resulting controller has been shown to be a full generalization of previous results (it includes, as particular cases, control laws [3] previously developed for backlash and dead-zone), ensuring also that the inner “forbidden” part of nonlinearity characteristics is never entered, even in the presence of uncertainties. Theoretical results have been validated by simulation on a simple mechanical system.