Real time control of tethered satellite systems to de-orbit space debris

Abstract Space debris has become a huge concern for orbital missions that makes remediation a critical and necessary action. Using Tethered Satellite System (TSS) to de-orbit debris is one active method to reduce the population of debris in Low Earth Orbits (LEO). We propose a TSS where a satellite is connected to a large space debris by an elastic tether. This system in LEO is subjected to many different disturbances such as aerodynamic drag, which necessitate a robust control method. Here, we present a robust optimal H 2 − H ∞ controller based on State-Dependant Riccati Equation (SDRE). The characterize of the optimal solution in the context of robustness to disturbance is our main goal. We show that the control law can be expressed in the form of traditional Riccati equation. The SDRE is a powerful method to control nonlinear systems, however, it can not be used as a real-time scheme. We overcome this drawback of SDRE by using an approximation approach based on Bellman's principle of optimality. This method is presented in terms of least squares techniques and can relieve the problem of high computational loads when using SDRE in real-time control systems. Also, we extend the approximation method for the H 2 − H ∞ control method. The performance of proposed controllers is evaluated by numerical simulations and the results show a convergence of the states to zero. Also, the control law forces the system to decrease the velocity of the debris in the orbit, thus the altitude of debris orbit decreases automatically so that atmospheric drag will cause the debris to burn out more rapidly by entering Earth's atmosphere.