Finite time attitude control of double tethered satellites system in deep space

A finite time attitude control law incorporating a disturbance observer is proposed for double tethered satellites system (2-TSS) with a variable length tether in deep space. For each single tethered satellite, a disturbance observer combining with the theory of Extended State Observer (ESO) is firstly utilized to precisely estimate the synthesis of external bounded disturbances and parameter uncertainties. The stability of the observer is analyzed so that the observation errors are globally uniformly ultimately bounded and finally converge to a small neighborhood. Then to realize attitude control with high precision and fast response in finite time, a finite time attitude control law is proposed through designing a fast nonsingular sliding mode surface with a specific switching function. The Lyapunov stability analysis is performed to show that the system states are finite time stable and that the sliding mode surface can reach a small region of origin. Finally, numerical simulations demonstrate the effectiveness of proposed control schemes with disturbance observer.