Simulation of an Electromechanical Spin Motor System of a Control Moment Gyroscope

A two-phase brushless DC motor (BDCM) with pulse-width modulated (PWM) voltage drive is simulated to control the flywheel speed of a control moment gyroscope (CMG). An overview of a double-gimballed control moment gyroscope (DGCMG) assembly is presented along with the CMG torque effects on the spacecraft. The operating principles of a two-phase brushless DC motor are presented and the system's electro-mechanical equations of motion are developed for the root-mean-square (RMS) currents and wheel speed. It is shown that the system is an extremely "stiff" set of first-order equations for which an implicit Euler integrator is required for a stable solution. An adaptive proportional voltage controller is presented which adjusts the PWM voltages depending on several control modes for speed, current, and torque. The simulation results illustrate the interaction between the electrical system and the load dynamics and how these influence the overall performance of the system. As will be shown, the CMG spin motor model can directly provide electrical power use and thermal power output to spacecraft subsystems for effective (average) calculations of CMG power consumption.