Minimum Residual Vibrations for Flexible Satellites with Frequency Uncertainty

The resonant frequencies will be excited if satellites perform a rapidly maneuver, which will increase the vibration settling time. In order to reduce the maneuver time and the residual vibration after maneuver, a set of shaped angular acceleration profiles are presented, and their analytical solutions are derived by minimizing the time integral of the squared magnitude of the difference between angular acceleration and its mean value subject to that the magnitude of the residual vibrations at several frequencies surrounding the natural frequency are zero. Then, suitable frequency points, where the residual vibrations are constrained to be zero, are chosen to minimize the acceleration time subject to both the residual vibration magnitude limit and the angular acceleration magnitude limit. Finally, three sets of simulations are presented to demonstrate that the shaped angular acceleration profiles can reduce the residual vibration under the frequency uncertainty.