TORQUE SHAPING USING TRIGONOMETRIC SERIES EXPANSION FOR SLEWING OF FLEXIBLE STRUCTURES

Optimal torque shaping based on a trigonometric series expansion of mo dified bang-bang input is obtained for simultaneous slewing and vibrat ion suppression of flexible structures using a reaction wheel. Vibrati on energy is analyzed vis-a-vis maneuver time, torque shaping paramete r, and number of terms to be used in a trigonometric series. Analytic expressions of performance indices and their derivatives are derived i n modal space. A gain set of a tracking controller adopting Lyapunov s tability theory is optimized to guarantee accurate targeting for the s ystems with/without external disturbances. Open-loop and closed-loop c ontrols are applied to the flexible single-axis structure with a centr al hub and four cantilevered appendages. It is verified through numeri cal simulation that the flexible structure shows good slewing capabili ty and excellent vibration suppression when adopting open loop torque shaping. Moreover, the Lyapunov tracking control law shows no performa nce degradation during/after the maneuver even in the presence of exte rnal disturbance.