Robust inverse compensation and control of a class of non-linear systems with unknown asymmetric backlash non-linearity

A robust control approach with the inverse backlash compensation is presented for a class of non-linear systems preceded by unknown asymmetric backlash non-linearity. Firstly, the analytical expressions of the inverse compensation error for an asymmetric backlash are obtained by introducing new indicator functions, which make it possible to design a corresponding controller for the asymmetric input backlash. With the developed compensation error expression, conventional robust control approaches can be utilised to deal with such a non-smooth non-linear system. As an illustration, a robust adaptive control strategy is applied to demonstrate the approach. The developed control laws ensure the robust inverse compensation and achieve tracking within a desired accuracy. Finally, simulations performed on an unstable and uncertain non-linear system illustrate and clarify the effectiveness of the developed approach.