Analysis and Comparison of Linear, Feedback Linearized and Backstepping Controllers Based on Quaternion in Spacecraft Attitude Control

In this paper, the attitude control design and analysis of a spacecraft as a rigid body based on three controllers of linear, nonlinear based on feedback linearization and backstepping is presented. According to the global presentation of the attitude based on quaternion parameters, these parameters have been used to derive the dynamic equations. Global asymptotic stability of linear and backstepping controllers is proved based on the Lyapunov method. The closed-loop stability of the feedback linearized controller is also proved by showing there are no internal dynamics. The controller gains are determined in linear and backstepping controllers based on linearized dynamics, derived from the local linearization around the equilibrium point. While, in the feedback linearized controller, gains are determined based on the global linearized dynamic equation. The performance of these three controllers in different scenarios is compared to each other. The results show that the feedback linearized controller can satisfy accurately the desired rise time. Whereas, the maximum error in achieving the desired rise time is 17% and 22% for backstepping and linear controllers, respectively. Of course, the control effort for the feedback linearized and backstepping is 100% and 46% more than the linear controller, respectively.