Design, Modelling, and Control Strategies of a Three Degrees-of-Freedom VR Spherical Motor Part II: Dynamic Modeling and Control

Abstract

This paper presents the dynamic modeling and the control strategy of an interesting three degrees-of-freedom (DOF) variable-reluctance (VR) spherical motor which presents some attractive possibilities by combining pitch, roll, and yaw motion in a single joint. Both the forward dynamics which determine the motion as a result of activating the electromagnetic coils and the inverse model which determines the coil excitations required to generate the desired torque are derived. The model represents the first detailed study on the inverse dynamics, and yet, permits a spectrum of design configurations to be analyzed. The solution to the forward dynamics of the spherical motor is unique but the inverse model may have multiple solutions and therefore an optimal choice is required. The multiple-coil excitations allows an optimal control vector to be chosen to minimize a specific cost function. This characteristic significantly differs from that of a popular three-consecutive-rotational-joint wrist based on the traditional single-axis motor or spherical motors of other types, which are typically characterized by having an unique solution to both the forward and inverse dynamics. The control strategy of a VR spherical motor consists of two parts; namely, the control of the rotor dynamic in terms of the actuating torque, and the determination of the optimal inputs for the required torque. An optimal choice is determined from an unconstrained optimization problem. The implementation issues in determining the optimal control input vector in real-time are also addressed.