Space tether satellites systems are one of the most promising directions in the modern space industry. Such systems consist of two or more spacecraft connected to each other by very long tethers. Great extension and variable configuration of the system in the orbital flight conditions provide some dynamic features, which are not typical of conventional spacecraft. The concept of the tethered satellite system (TSS) promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. The overarching theme of the paper is to show various control methods of the tethered satellites system (TSS) that have been undertaken recently, and also to emphasize on the importance of the TSS control method as an important aspect in the tether concepts, design, and missions. This review article presents the historical background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements. The paper introduces the strategies and methods applied in controlling the TSS not excluding their advantages and disadvantages during the tether satellite deployment, retrieval, and station keeping procedures. At the end of the paper, a conclusion is made about the effectiveness of the control methods in stabilizing the libration and vibration motions of the TSS.

The control of a tethered satellite system pendular motion is done by application of Hamiltonian equation of motion on a control design method known as planar H tracking. In this case, the reference motion is considered a natural planar motion. The control of the TSS is accomplished by using the inside plane control inputs as well as the outside plane control inputs. The designed control laws are able to drive the pendular motion to a natural planar trajectory with the required characteristics. The control inputs are analyzed using their magnitude ability. The numerical simulation results for each control inputs show that the inside of plane input not only has strongmagnitude, but also effectively controls the pendular motion of the tethered satellite system.