Robust dynamic decoupling control for permanent magnet spherical actuators based on extended state observer

This study presents a robust dynamic decoupling control strategy to solve the trajectory tracking problem for the permanent magnet spherical actuator (PMSA). The dynamic model of PMSA obtained by the Lagrange-Euler formalism is obviously a multi-variable non-linear system with strong cross-couplings. Furthermore, uncertainties such as model errors and external disturbances will also affect the precision of the control system. In the active disturbance rejection control (ADRC) framework, the decoupling problem can be reformulated as disturbance rejection by merging the cross channel interference into the lumped disturbance, which consists of internal dynamics and external disturbances. The lumped disturbance is then estimated using extended state observer (ESO) and canceled out in the control law. Herein, the linear active disturbance rejection control is selected for PMSAs, as the tuning process can be greatly simplified by making all the parameters of ESO or controller a function of bandwidth. Simulations and experiments are presented to corroborate the effectiveness and robustness of the proposed strategy, showing that the proposed control algorithm can decouple and linearise the system in the presence of model errors as well as the load and random disturbances. Meanwhile, the modified system has better static and dynamic performances with strong robustness to uncertainties.