In this article, a novel adaptive super-twisting nonlinear Fractional-order PID sliding mode control (ASTNLFOPIDSMC) strategy using extended state observer (ESO) for the speed operation of permanent magnet synchronous motor (PMSM) is proposed. Firstly, this paper proposes a novel nonlinear Fractional-order PID (NLFOPID) sliding surface with nonlinear proportion term, nonlinear integral term and nonlinear differential term. Secondly, the novel NLFOPID switching manifold and an adaptive supertwisting reaching law (ASTRL) are applied to obtain excellent control performance in the sliding mode phase and the reaching phase, respectively. The novel ASTNLFOPIDSMC strategy is constructed by the ASTRL and the NLFOPID sliding surface. Due to the utilization of NLFOPID switching manifold, the characteristics of fast convergence, good robustness and small steady state error can be ensured in the sliding mode phase. Due to the utilization of ASTRL, the chattering phenomenon can be weakened, and the characteristics of high accuracy and strong robustness can be obtained in the reaching phase. Further, an ESO is designed to achieve dynamic feedback compensation for external disturbance. Furthermore, Lyapunov stability theorem and Fractional calculus are used to prove the stability of the system. Finally, comparison results under different controllers demonstrate that the proposed control strategy not only achieves good stability and dynamic properties, but also is robust to external disturbance. INDEX TERMS Adaptive super-twisting nonlinear Fractional-order PID sliding mode control (ASTNL-FOPIDSMC) strategy, extended state observer (ESO), permanent magnet synchronous motor (PMSM), nonlinear Fractional-order PID (NLFOPID) sliding surface, adaptive super-twisting reaching law (ASTRL).

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An active magnetic bearing (AMB) is a kind of high-performance bearing that uses controllable electromagnetic force to levitate the rotor. Its control performance directly affects the operation characteristics of high-speed motors and other electromechanical products. The magnetic bearing control model is nonlinear and difficult to control. Sliding mode control algorithm can be used in the magnetic bearing control system, but the traditional sliding mode control has the problem of high-frequency chattering, which affects the operation stability of magnetic bearings. Based on the second-order sliding mode control algorithm, a new second-order sliding mode controller for active magnetic bearing control was designed, and the stability of the designed sliding mode control law was proven by Lyapunov criterion. On the basis of the established active magnetic bearing control model, the numerical analysis of the designed controller was carried out, and the control effect was compared with that obtained by the exponential reaching law for the sliding mode control algorithm. The experimental results show that the designed sliding mode controller has better dynamic performance and stability than the exponential reaching law for the sliding mode controller.

A novel sliding mode controller (SMC) with nonlinear fractional order PID sliding surface based on a novel extended state observer for the speed operation of a surface-mounted permanent magnet synchronous motor (SPMSM) is proposed in this paper. First, a new smooth and derivable nonlinear function with improved continuity and derivative is designed to replace the traditional nonderivable nonlinear function of the nonlinear state error feedback control law. Then, a nonlinear fractional order PID sliding mode controller is proposed on the basis of the fractional order PID sliding surface with the combination of the novel nonlinear state error feedback control law to improve dynamic performance, static performance, and robustness of the system. Furthermore, a novel extended state observer is designed based on the new nonlinear function to achieve dynamic feedback compensation for external disturbances. Stability of the system is proved based on the Lyapunov stability theorem. The corresponding comparative simulation results demonstrate that the proposed composite control algorithm displays good stability, dynamic properties, and strong robustness against external disturbances.