This paper presents a sliding mode observer (SMO) with new reaching law (NRL) for observing the real-time linear speed of a controllable excitation linear synchronous motor (CELSM). For the purpose of balancing the dilemma between the rapidity requirement of dynamic performance and the chattering reduction on sliding mode surface, the proposed SMO with NRL optimizes the reaching way of the conventional constant rate reaching law (CRRL) to the sliding mode surface by connecting the reaching process with system states and the sliding mode surface. The NRL is based on sigmoid function and power function, with proper options of exponential term and power term, the NRL is capable of eliminating the effect of chattering on accuracy of the angular position estimation and speed estimation. Compared with conventional CRRL, the SMO with NRL achieves suppressing the chattering phenomenon and tracking the transient process rapidly and accurately. The stability analysis is given to prove the convergence of the SMO through the Lyapunov stability theory. Simulation and experimental results show the effectiveness of the proposed NRL method.

Aiming to address the shortcomings of the single-point variable air gap permanent magnetic levitation system in terms of dynamic performance and anti-disturbance capabilities, an improved linear active disturbance rejection control (ILADRC) strategy is proposed. First, based on the system dynamics model, a conventional linear active disturbance rejection control (LADRC) controller is designed, with the total perturbation observed and compensated for in real time by a linear expanded state observer (LESO). Building upon this, the known part of the model is embedded into the LESO framework to enhance the accuracy of total perturbation observation, and the ILADRC controller is designed to further improve the system’s stability and perturbation resistance. The stability and tracking performance of the ILADRC are then verified through theoretical analysis. Finally, the ILADRC strategy is compared with proportional-integral-derivative (PID) control, traditional LADRC control, and auxiliary model-based linear active disturbance rejection control (AMLADRC) in both simulation and experimental settings. The results show that the ILADRC strategy outperforms the other three control strategies, significantly improving the system’s dynamic performance and disturbance resistance.

In order to improve the tracking accuracy of the linear maglev synchronous motor maglev system with non-linear, strongly coupled, and other uncertainty problems, a fixed-time fractional order terminal sliding mode control (FFTSMC) strategy based on adaptive fixed-time extended state observer (AFxESO) is proposed. Firstly, a fast AFxESO is constructed and an adaptive law is designed to dynamically adjust the gain to reduce the estimation error and measurement noise, which enables the observer to accurately estimate the perturbation of the unknown boundary in a fixed-time. Secondly, a new FFTSM controller is designed by applying the theory of fractional order calculus, which can speed up the system convergence and suppress the chattering problem in SMC. Then, using the Lyapunov stability theory, it is demonstrated that the proposed AFxESO-FFTSM control scheme can guarantee the global fixed-time convergence of the system to equilibrium and the convergence time is dependent on the selection of the controller parameters, which effectively overcomes the drawbacks of finite-time control. Finally, the feasibility and superiority of the proposed strategy are verified on the linear maglev synchronous motor system experiment platform.