Backstepping Control Collaborative Shaft Torque Observer for Limit Cycle Oscillation Suppression of Fully Closed-Loop Gear Transmission Servo System

To address the problem of gear clearance causing the limit cycle oscillation at the positioning end, further deteriorating the positioning accuracy of the servo system, and even causing tooth breakage in severe cases, a backstepping control (BC) method based on shaft torque observer (STO) is proposed in this article for a fully closed-loop gear transmission servo system. First, a gear transmission servo control system model is established, which includes a permanent magnet synchronous motor model, a backlash model, and a gear transmission system model. Second, the description function method is utilized to analyze the limit cycle oscillation mechanism of nonlinear systems. Next, speed loop and current loop BC subsystems are proposed. To avoid the problem of limit cycle oscillation and decreased positioning accuracy caused by backlash nonlinearity in the fully closed-loop gear transmission servo system, a STO is proposed and real-time observation and online compensation of shaft torque are carried out, which effectively eliminates the limit cycle oscillation at positioning end. Ultimately, a 2.0-kW gear transmission servo system is used as a case study, the validity of the proposed BC-STO is tested via experimental results, the limit cycle oscillation is effectively eliminated, and the positioning accuracy is significantly improved.

I. Introduction

Usually, the position control structure that uses motor shaft end position signals to achieve position control is called “semi-closed-loop control” and the control structure that uses load end position signals to achieve position control is called “fully closed-loop control” [1]. With the development of technology and industry, high-performance fully closed-loop servo transmission systems have been extensively used in high-precision fields, for instance, CNC machine tools, numerical control robots, and medical equipment, due to their high dynamic response and positioning accuracy [2], [3]. In the gear servo transmission system, there must be a certain gear clearance between the gears, otherwise the gears will get stuck and break during operation, which will accelerate the wear of system components and ultimately lead to the system losing control. Backlash is one of the most common nonlinear factors in servo transmission, which seriously restricts the static and dynamic performance of servo transmission systems [4], [5]. In addition, backlash nonlinearity can also lead to limit cycle oscillations at the positioning end of the fully closed-loop servo transmission system, resulting in a decrease in positioning accuracy and even system instability in severe cases [6]. Therefore, eliminating the limit cycle oscillation created by backlash nonlinearity is of great significance for improving the positioning accuracy of the fully closed-loop servo system [7].