Sliding mode control of magnetic levitation ball systems based on a high-gain disturbance observer

Using a high-gain disturbance observer（HGDO）, a self-adaptive nonsingular terminal sliding mode control (ANTSMC) approach is devised to solve the issue of control performance degradation in magnetic levitation ball systems caused by modeling errors and unknown disturbances. First, a model of the maglev ball system is developed and the model is linearized at the equilibrium point. Then, to weaken the chattering of the sliding mode controller and guarantee the finite-time convergence of tracking errors, an adaptive nonsingular terminal sliding mode controller is designed. To estimate the lumped disturbance, a high-gain disturbance observer is employed. Theoretical convergence findings demonstrate that the suggested high-gain disturbance observer may rapidly converge to an adjustable neighborhood of real disturbance values. Adaptive nonsingular terminal sliding mode control law with disturbance compensation is designed based on the disturbance estimation, the system is proven globally uniformly and ultimately bounded under the control law. According to simulation and quantitative analysis, the system's robustness under the same control method is improved when the controller with a high-gain disturbance observer lowers the integral time squared error（ITSE）value by 75% and the integral time absolute error（ITAE） value by 60% for the total disturbance observation error when compared to the controller with a generalized proportional-integral observer.