Stability Research of a Triangular Tethered Satellite Formation: Dynamics, Filtering, and Control

This article investigates the stability of a triangular tethered satellite formation (TTSF) and the performance improvement by filtering and the virtual control of general force. The equation of motion is formulated by Lagrangian equation, and the state space equation (SSE) is derived with the second-order terms decoupled. Then the stability of SSE is discussed with the tethers nonstretched and stretched, respectively, where the existence of a stable orbit arounthe equilibrium is explored and the effect of initial conditions on the stability of the system around a stable orbit is discussed. To smooth the system response, a steepest descent-based state filter for TTSF system is designed, which provides the optimized state information. Moreover, to get the expected system response, a virtual control law is acted on the system with hysteresis relay property employed to strengthen its robustness. Finally, simulation results are shown to validate the theoretical analyses.