Backstepping Control for Gear Transmission Servo Systems With Backlash Nonlinearity

The output tracking problem of gear transmission servo (GTS) systems with backlash nonlinearity is studied in this paper. A new concept-“soft degree”-is proposed to overcome the nondifferentiable “hard” characteristic of the backlash nonlinearity. Furthermore, a detailed softening process-static softening is presented, where a backstepping control algorithm is developed to guarantee that the output of the controlled systems can track any given desired sufficiently smooth trajectory by arbitrary precision and the limit cycles that appear due to backlash nonlinearity can be avoided. Simulation results validate the effectiveness of the proposed controller.

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.