An adaptive second-order sliding-mode observer for permanent magnet synchronous motor with an improved phase-locked loop structure considering speed reverse

An adaptive second-order sliding-mode observer based on Super-Twisting Algorithm (STA-SMO) to estimate rotor position and speed of permanent magnet synchronous motor (PMSM) is proposed in this paper. The advantages of the proposed observer algorithm are reflected in small chattering, high tracking accuracy, good robustness to parameters change and external disturbance in wide positive and reversal speed range. The Lyapunov stability of the system is proved. A new perturbation term form is employed and according to the stable condition of STA-SMO, the adaptive sliding-mode coefficients related to absolute value of estimated speed are deduced to guarantee the performance mentioned above in wide positive and negative speed range. In order to extract rotor position and speed in both speed range from the adaptive STA-SMO, an improved conventional phase-locked loop (IPLL), which is more accurate, is studied and its non-linear dynamics are analyzed in detail to prove the effectiveness of the IPLL theoretically. In the end, the effectiveness of the adopted adaptive second-order sliding-mode observer with IPLL structure is verified through simulations. Simulation results show that the position error and chattering of the proposed adaptive observer are decreased more than 25% and 50% compared with conventional SMO and STA-SMO in wide positive and negative speed range. Meanwhile, the proposed system still has good estimation performance and strong robustness with torque and parameters variation.