Abstract: The problem of H_∞ loop shaping attitude stabilization control for Tracking and Data Relay Satellite (TDRS) is investigated. The TDRS has lightly damped flexible modal frequencies and sloshing modal frequencies. The modal frequencies have large uncertainties, and so is the system gain. Firstly, the dynamic model of the satellite is established using the Lagrange Equation, and the structured model uncertainties are described, then the H_∞ loop shaping controller is designed. In the process of designing H_∞ loop shaping controller, the robust stabilization and robust performance specifications which need to be satisfied by the control system of the flexible satellite are brought forward in the first step. Subsequently the attitude stabilization controller of the flexible satellite is designed using the H_∞ loop shaping theory, then the order reduction of the controller designed before is done by the ν gap metric, and the robust stability and robust performance are analyzed. Finally, the mathematical simulation is conducted to demonstrate the validity of the H_∞ loop shaping controller.

Key words: Tracking and Data Relay Satellite(TDRS), H_∞ loop shaping, attitude, μ analysis, gap metric