Fractional order sliding mode control for linear maglev synchronous motor based on an adaptive fixed-time extended state observer

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.