Proportional-derivative Control of Second-order Tethered Satellites System Based on Extended State Observer and Feed-forward Compensation

This paper researches the proportional-derivative (PD) feedback control with feed-forward compensations from input for a triangular tethered satellite system (TTSS), and the extended state observer (ESO) design which is further incorporated in control to estimate the structural uncertainties in system. By expanding Lagrangian equations under chosen variables, the dynamic equations of TTSS are derived which is the second-order nonlinear equation. Then the feedback control under typical feed-forward compensations is discussed as the nonlinear functions in system are counteracted, and the controlled outputs are computed by deriving the transfer functions of the transformed structures. Moreover, in case of the uncertain structures in system which may constrain the control effect, ESO-based PD control is further proposed, and the observed error and controlled accuracy are analyzed by Lyapunov functions. Simulation results on the designed controls are presented to validate the theoretic analyses.