Control of a rotating variable-length tethered system

Techniques are developed and illustrated to control the motion of a tethered satellite system (TSS) comprising n point masses and interconnected arbitrarily by m idealized tethers. In particular, the control problem of a triangular and symmetrical TSS with n = 3 point masses and m = 3 tethers is discussed. The equations of motion are derived by the use of Lagrange's equations. Several mission scenarios for a proposed NASA mission that consider the operation of an infrared telescope are introduced and asymptotic tracking laws based on input-state feedback linearization are developed. The effects of smoothness and nonsmoothness of desired mission trajectories on control performance are discussed. It is shown that required thrust levels can be significantly decreased by the use of additional tether length control to keep the TSS in a state corresponding to an instantaneous relative equilibrium at any point in time during the mission. In the final section, a mathematical model is proposed for the total required control impulse to facilitate a trade study that discusses the effects of the individual system parameters on the control input.