Aiming at the problems of low control precision and poor anti-disturbances ability of permanent magnet spherical actuator (PMSA), an active disturbance rejection trajectory tracking control method based on nonlinear extended state observer (NESO) is proposed in this paper. Firstly, the multivariable and strong coupling mathematical model of the PMSA is obtained by rigid body rotation coordinate transformation and the Lagrange dynamic equation. Then, the tracking differentiator is used to reduce the influence caused by the expected trajectory jump. In addition, NESO is designed to observe and calculate coupling of the system, external disturbance, and model error online. Finally, the nonlinear control law is used to compensate for the observed disturbance, and the stability is proved based on the Lyapunov equation. Simulation and experimental results show that the proposed control scheme can achieve decoupling and tracking control of the complex system in the presence of model error, random disturbance, and other uncertain factors, has good control accuracy and response speed, and has strong robustness to uncertain disturbances.

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In order to deal with the modeling of uncertainty and external environment disturbance in the trajectory tracking system of 3 degrees of freedom permanent-magnet spherical actuator, a nonsingular terminal sliding mode control method with sliding perturbation observer is proposed in this article. First, a sliding perturbation observer, which can estimate compound disturbance only by feedback position signals, is proposed to reduce the uncertainty caused by angular velocity observation. Then, based on the sliding perturbation observer, a nonsingular terminal sliding mode control method is designed to satisfy the requirements of system nonsingularity, robustness, and control accuracy. The stability of the controller is proved by the Lyapunov theory. Finally, simulation and experimental results show that the proposed control method has excellent anti-disturbance performance, which provides an important reference for the future applications of permanent-magnet spherical actuators in aerospace and other industrial fields.