Adaptive robust control for nonlinear system with input backlash or backlash-like hysteresis

An adaptive robust control (ARC) algorithm is developed for a class of uncertain dynamic nonlinear system with unknown input backlash or backlash-like hysteresis, parametric uncertainties and uncertain disturbances. Due to the non-smooth dynamic nonlinear nature of backlash, existing robust adaptive control methods mainly focus on using approximate inversion of backlash by on-line parameter adaptation. But experimental results show that a linear controller alone can perform better than a controller including the selected backlash inverter with a correctly estimated or overestimated backlash gap. Unlike many existing control schemes, the backlash inverse is not constructed in this paper. A new linearly parameterized model for backlash is presented. The backlash nonlinearity is linearly parameterized globally with bounded model error as backlash-like hysteresis. The adaptive robust control law is designed to ensure that all closed-loop signals are bounded and achieve the tracking within the desired precision. Simulations results illustrate the performance of the proposed ARC.