Continuous-time Adaptive Control of Systems with Unknown Backlash

This paper addresses one of the nondifferentiable nonlinearities which appear very often in industrial control applications: backlash. We first present a right inverse of backlash and then give one of its possible numerical implementations. Characteristics like backlash are seldom known, so an adaptive version of our backlash inverse is more suitable for applications. We develop an adaptive backlash inverse scheme and apply it to feedback control of a known linear plant with an unknown backlash at its input. We use simulation results to illustrate the achieved performance improvements.