Nonlinear Control Analysis of a Double-Gimbal Variable-Speed Control Moment Gyroscope

Abstract

A single double-gimbal variable-speed controlmoment gyroscope is considered as amethod for three-dimensional spacecraft attitude control. First, the system’s equations of motion are developed, where gimbal and wheel accelerations are prescribed as control inputs. The resulting necessary motor torques as well as system energy rates are computed for verification. Next, a novel control algorithm is developed from the stability constraint for reference trajectory tracking. In contrast with the control development for single-gimbal variable-speed gyros, a Newton–Raphson scheme is required to solve for the desired double-gimbal variable-speed control moment gyroscope control variables because they appear in cross product and quadratic form, preventing analytical solutions. Analysis of the control theory suggests that the same torque amplification effects exist as in a single-gimbal control moment gyro, but control by a single double-gimbal variable-speed control moment gyroscope device is not robust due to potential configurations that result in control singularities. When these singularities are avoided, a simulation with successful reference trajectory tracking is achieved. Allowing double-gimbal gyros to have variable wheel speeds provides additional torquing capabilities, which is significant if failure modes are considered. As will be shown, a single double-gimbal variable-speed control moment gyroscope device can provide limited threedimensional attitude control.