A time linear arrival approach to the control of flexible structures

While a bang-off-bang command is the time optimal command for maneuvering a rigid body, when implemented in a flexible structure significant residual vibration can result. To reduce residual vibration, an algorithm that has been used is to approach the destination linearly in the phase plane. While this significantly reduces vibration, the method results in an exponential time domain expression that can take a very long time. This paper presents an arrival algorithm that decreases linearly in the time domain. The result is a maneuver that takes longer than a bang-off-bang command, but is less aggressive. When compared to the phase linear arrival approach the time linear arrival is more aggressive, but can be completed in a specified amount of time.