Robust Nonsingular Terminal Sliding Mode Attitude Control of Satellites

Abstract

This paper proposes a time-varying nonsingular terminal sliding mode control (TVNTSMC) law to control the attitude of rigid spacecraft. It provides an advantage for users to stipulate convergence time beforehand, and the proposed control algorithm will ensure global robustness to uncertainties as well as to external disturbances. A minimal (three-dimensional) modified Rodrigues parameter (MRP) explanation is used to represent the dynamics of a rigid satellite; then, the state-space representation of the dynamics is developed by transforming the dynamics into Lagrangian form. MRPs are used to design a new nonlinear sliding surface. The attitude control algorithm is expressed by a piecewise continuous function with time-varying properties. The Lyapunov theory is used to calculate the convergence and settling time to reach the equilibrium point. The time-varying function parameters are derived from convergence time prespecified by the user, which will ensure the system trajectories converge to the origin within the time specified. The global finite-time stability of the overall system is presented using the Lyapunov theorem in the presence of external disturbance. The simulation results are presented for different convergence times as input by the user to show the efficacy of the proposed controller.