To solve the stability and fast deployment problems of tethered satellite system (TSS) in elliptical orbits

a novel backstepping-like nonlinear control algorithm was proposed based on the traditional backstepping control method. Different from the traditional backstepping method which is only suitable for strict feedback systems

the proposed backstepping-like nonlinear control has a wider range of application that it can be applied to the control of non-strict feedback systems and can improve the control performance with effective use of the nonlinear model. First

the nonlinear dynamic model for the deployment of TSS in elliptical orbit was established based on the Lagrangian mechanics

and the dimensionless system model was further simplified with a new dimensionless transformation. Then

by utilizing the simplified model

a backstepping-like nonlinear control method was proposed to deal with the coupling characteristics of the system model

and the Lyapunov function was adopted to verify the asymptotic stability of the system states. Finally

simulation experiments of non-linear control and PID control for the deployment of TSS in elliptical orbit were carried out

and the effectiveness of the proposed backstepping-like nonlinear control was verified by comparison. Simulation results show that the proposed method deployed the tether satellite effectively and stably and achieved better performance than the classical PID controller.