I. Introduction
Backlash nonlinearity due to mechanical transmission via gears is not only inevitable in mechanical transmission but also one of the most important nonlinear factors that affect the dynamic performance and steady precision of controlled systems. It is quite challenging to compensate for the influence of backlash nonlinearity because of the nondifferentiable property of the conventional backlash model. If the impact of backlash nonlinearity cannot be alleviated or eliminated, the limit cycle may exacerbate the stability of the controlled systems. In addition, the collisions between the gears will produce serious concussion and noise. Since the 1940s, backlash nonlinearity has been one of the hot topics among the high-precision mechanical control community.