A VSC approach for the robust stabilization of nonlinear plants with uncertain non-smooth actuator nonlinearities - a unified framework

This note addresses the stabilization problem of an uncertain intrinsically nonlinear single-input–single-output plant containing nonsmooth 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 a previous paper 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 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.