Unwinding-Free Fast Finite-Time Sliding Mode Satellite Attitude Tracking Control

Abstract

A double-gimbal variable-speed control moment gyro (DGVSCMG) is considered for attitude control of a rigid satellite for track-to-track maneuver. Satellite attitude tracking control involves precision and time limit. In addition, satellite attitude control also faces rotation kinematic singularity, rotation unwinding, and control singularity associated with DGVSCMG. The rotation singularity and unwinding problems are solved using the body and shadow sets of the modified Rodrigues parameters. A nonlinear unwinding and kinematic singularity-free fast finite-time sliding mode tracking attitude control is proposed and designed for the satellite attitude control using a single unit of DGVSCMG. The issue of control singularity is addressed using constrained optimization to avoid gimbal lock. It is proved through five new propositions that the system states errors converge first to the sliding surface and then to the origin in fast finite-time with unwinding-free dynamics showing global stability of the system for the track-to-track maneuver. As a special case, it is shown that the proposed control is also applicable to rest-to-rest maneuver. Simulation results are presented and compared with a finite-time sliding control showing superiority of the proposed fast finite-time control in terms of time of convergence and unwinding and singularity-free angular motion.