Adaptive control of systems with backlash hysteresis at the input

A new compact dynamical model for backlash inverse is presented. This model may be utilized for both backlash at the input or at the output. Two cases are considered: the case where the backlash spacing is known as well as the case of unknown backlash spacing. For the latter case, an adaptive update law is developed to compensate for the unknown spacing. The adaptive backlash inverse controller is a break-away from existing backlash compensators which are mostly implemented in discrete-time and utilize complex control algorithms. The advocated results are applied to a one degree-of-freedom system affected by backlash. The stability of the closed-loop system is shown using Lyapunov arguments. Simulation results show that the control methodology greatly improves tracking performance over a PD type controller.