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.