High performance adaptive robust control for nonlinear system with unknown input backlash

A high performance adaptive robust control (ARC) algorithm is developed for a class of nonlinear system with unknown input backlash, parametric uncertainties and uncertain nonlinearities disturbances. Due to the inherent dynamic nonlinear nature of backlash, existing robust adaptive control methods mainly focus on using on-line parameter adaptation for an approximate inversion of the unknown backlash. As a result, even in the absence of other uncertain nonlinearities and disturbance, asymptotic output tracking can never be achieved by continuous controller for the non-smooth characteristics of backlash. Experimental results also show that a linear controller alone performed 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 and the projection algorithm is used for parameters estimation. The proposed adaptive robust control law consists of three parts: model compensation term, the robust control term and robust feedback term. The ARC ensure that all closed-loop signals are bounded and achieves the tracking within the desired precision. Simulations results illustrate the performance of the ARC.