Linear analysis and control of a tethered system with two rigid end bodies

Abstract

A model is proposed for studying the dynamics of a tethered satellite system with identical rigid end-masses, offset tether attachment points, and a massless tether. The equations of motion are developed and linearized for use within a linear control system. A Linear Quadratic Regulator (LQR) paired with a reduced-order closed loop estimator is designed to control the attitude of each end-mass individually using Reaction Wheel Assemblies (RWAs), assuming measured angular rates from gyroscopes on the end-masses and tether. Modal analysis shows the existence of a slow tether libration mode and two fast modes of end-mass oscillation. The oscillation is shown to be approximated by a rigid pendulum with an accelerating pivot point. Two control methodologies are investigated: one which aligns each end-mass with the nadir vector and the other which aligns each end-mass with the tether. Results suggest that both modes of operation are controllable by a system architecture which employs LQR control and reduced-order closed loop estimation with a wide range of required control effort.