I. Introduction
BACKLASH characteristics are common in control systems such as servomechanisms, electronic relay circuits and electromagnetic devices with hysteresis. It is one of the most important nonlinearities that limit the performance of speed and position control in industrial, robotics, automotive, automation and other applications. The control of systems with backlash has been the subject of study since 1940s. Linear controllers have been investigated, including PID controllers, high-order linear controllers, state feedback controllers. For backlash nonlinearity, inverse compensation of backlash are designed widely both in a non-adaptive and an adaptive setting [1]. An adaptive inverse of backlash was construct to cancel the effect of backlash nonlinearity in [2], [3], but the initial condition should be strictly limited. A smooth inverse of backlash was developed to compensation the effect of backlash with back-stepping approach in [4], where the derivation of the control input was used to get the controller, which maybe unavailable. Backlash compensation using neural network[5], [6] or fuzzy logic [7], [8] has been used in feedback control system. For those intelligent compensation, neural networks or fuzzy logic were mainly used for cancellation of the inversion error for their excellent nonlinearity approximation ability. The common feature of the inverse schemes is that they rely on the construction of an inverse backlash to mitigate the effect of the backlash nonlinearity. Experiment by [9] shows that a linear controller alone performed better than a controller including the selected backlash inverter with a correctly estimated or overestimated backlash gap, the reason being that measurement noise induced chattering in the inverter. It was noted that the linear controller alone also traverses the backlash gap rapidly since only the motor moment of inertia (and not the load) is driven inside the backlash gap. As pointed out in the recent comprehensive survey paper with 96 references on controlling mechanical systems with backlash[1] that weak action in the backlash gap (i.e., by simply lowering the closed-loop system bandwidth when the gap is open) might be advantageous.