Adaptive Smooth Control via Nonsingular Fast Terminal Sliding Modes for Distributed Space Telescope Demonstration Mission by CubeSat Formation Flying

Abstract

This article presents a nonsingular fast terminal sliding mode (TSM)-based adaptive smooth control methodology for a distributed space telescope (DST) demonstration mission. The DST has a flexible focal length that corresponds to the relative position in the formation flying concept. The limited specification of a CubeSat generally restricts the performance of actuators—most critically the degrees of freedom of controlled motion. This investigation leads to the development of an adaptive smooth control methodology via nonsingular fast TSMs. The adaptive smooth control algorithm that was developed for a single-input–single-output system is adopted and extended to the relative orbit and attitude control systems of the DST. The software simulation is conducted under a real mission, which means the real CubeSat structures, hardware specifications, and operational constraints. The proposed algorithm possesses only seven parameters that can be easily adjusted considering their physical meanings. Furthermore, the predesignated error bounds are analytically derived, which enhances the applicability of the algorithm to real missions. The simulation compares the efficiency of the adaptive smooth nonsingular fast TSM controller with the linear quadratic regulator and proportional derivative algorithms. The results verify that the adaptive smooth nonsingular fast TSM control algorithm shows better control performance in the perspective of the alignment time and the fuel consumption for the DST demonstration mission.