Global Asmptotic Stability for Systems with Friction and Input Backlash

Adaptive variable structure control (VSC) of a class of nonlinear dynamic systems with backlash hysteresis affecting the input is considered in this paper. Utilizing the solution properties of the nonlinear differential equation that models backlash hysteresis, a robust adaptive VSC controller is developed and used to achieve global asymptotic tracking without the need to use an adaptive backlash inverse controllers. Simulation studies utilizing the proposed controller on a one degree-of-freedom system suffering from input backlash elucidate the robustness and performance aspects of this approach