Time-Varying Non-Singular Terminal Sliding Mode Attitude Control of Satellites

Abstract

This paper proposes a novel time-varying nonsingular terminal sliding mode (TVNTSMC) control algorithm for the attitude control of a rigid spacecraft, which gives the user the ability to select convergence time in advance and also ensures global robustness to undesired external disturbances. The satellite dynamics are represented using minimal (three dimensional) Modified Rodrigues Parameters (MRP) description, which is then transformed into Lagrangian form and is used to formulate the state-space representation. A new non-linear sliding surface is designed in terms of the MRP parameters and a piecewise continuous time-varying function which is then used for expressing the attitude control algorithm. The expressions for settling time and convergence time to the origin of the system are calculated using Lyapunov theory. The design parameters of the time-varying function are derived from the user-specified convergence time, which ensures that the system states converge to the origin at the pre-specified time. The global finite-time stability of the overall system in the presence of external disturbances is shown using the Lyapunov method. The simulations are carried out for different user chosen convergence times to elucidate the efficacy of the proposed control.