Augmented PD control method for permanent magnet spherical actuators with 3D magnet array

A permanent magnet spherical actuator (PMSA) with 3D magnet array is proposed in this paper. The application of 3D magnet array improves the output torque significantly. However, as PMSA is a nonlinear and multivariable system, it is very complicate to realize accuracy control. Therefore, an augmented PD algorithm is proposed in this paper. Compared with the simple PD control method, a feedforward term is added into the proposed algorithm to improve the control performance. Euler angles are applied to describe the orientation of rotor. Lagrange equations are utilized to establish the dynamic model of the actuator. As the center of gravity does not coincide with the center of rotor sphere, gravity torque is taken into consideration to enhance the precision of dynamic model. The stability of this algorithm is validated with detailed derivation. Simulation model is formulated in Matlab/Simulink. It proves that the proposed algorithm can make the system track the continuous trajectories in high accuracy.