Relay-Polynomial Second-Order Sliding-Mode Control Based on Backlash Compensation and Exact Differentiator for A PMSM Servo System

This paper investigates the control issue related to backlash nonlinearity in permanent magnet synchronous motor (PMSM) servo systems by introducing a relay-polynomial second-order sliding-mode control (SOSMC) method, which incorporates backlash compensation and an exact differentiator. Backlash, an inherent nonlinear phenomenon in mechanical transmissions, significantly influences the dynamic performance and control accuracy of servo systems. This paper proposes a method for online identification of backlash amplitude using a speed difference integration approach. Based on the identified model, backlash torque compensation is applied. Additionally, a finite-time exact differentiator (FTD) is employed to estimate speed errors and their derivatives, thereby enabling the construction of the SOSMC, with the finite-time stability of the closed-loop system proven through subsequent analysis. Compared to conventional sliding-mode control (SMC), the proposed SOSMC achieves finite-time convergence and improves tracking performance. The efficiency of the proposed control method is corroborated through simulations. Simulation results indicate that the SOSMC surpasses conventional methods in enhancing the performance of PMSM servo systems.