Designing Active Disturbance Rejection Control of Permanent Magnetic Spherical Actuator Based on Nonlinear Extended State Observer

Abstract

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.

Nonsingular terminal sliding mode control with sliding perturbation observer for a permanent-magnet spherical actuator

“…The SPO applied in this article can reduce the inaccuracy caused by the velocity observation. 26 It is easy to deduce the estimation error dynamics equation (18) as follows…”

Symmetric Nonlinear Feedback Control and Machine Learning for Sustainable Spherical Motor Operation

“…Nicholas Minorsky's 1922 groundbreaking work on three-term or PID controllers and James Watt's introduction of the 16th century Ctrifugal Governor laid the foundations for modern feedback control techniques [22]. There are various control schemes for sphere engines, with joint and operational space control being prominent approaches, each addressing specific mechanical design aspects [23][24][25][26][27][28][29][30][31]. Joint space control focuses on the design of feedback controllers that closely align the actual movement and the desired movement, typically converting the desired movement into a joint variable and controlling each joint independently.…”