A Nonlinear Discrete-time Model for Controlled Moment Gyroscope

A controlled moment gyroscope (CMG) is usually used as an actuator to control the attitude of artificial satellites and spacecrafts by applying the gyro effect. To design and analyze a digital controller of the CMG, it requires a discrete-time model, which can be derived by discretizing a continuous-time model. Since the CMG is nonlinear and has an affine constrain for a nonholonomic system, its linear approximation becomes uncontrollable and unavailable for control design. This paper proposed a discrete-time model for the CMG system, which does not use the linear approximation of the continuous-time model, by using a method called continualized discretization proposed. Simulation results show that the proposed model yields better performances than the conventional forward difference model in reproducing the dynamical characteristic of the continuous-time model, even for a large sampling interval and fast dynamical response.