Simultaneous optimization of input shaping and feedback control for slewing flexible spacecraft

This paper examines the problem of simultaneous optimization of feedforward and feedback control laws for minimum time slewing of flexible spacecraft with vibration suppression. For some initial results the problem is studied in the context of a spacecraft made up of a pack of hinge-connected hexagonal bodies that are initially stacked one upon another, and then are deployed to form a 40 m × 12 m × 0.2 m large, flexible structure. Each hexagonal body is fairly rigid and upon deployment and latch-up is intended to perform an independent task. The latch stiffness between the hexagonal units characterize the main flexibility of the overall structure. CMGs mounted on the bodies provide slewing torque. The dominant vibration modes are identified from the residues in the transfer function from the torque to an angular displacement. This paper shows an open loop, near minimum time slewing torque obtained by convolution of the three-impulse sequences of (Singer, N.C. and Seering, W.P., March 1990) for suppressing multiple modes of vibration with the bang-bang torque for minimum time control of a rigid body of equivalent inertia. Vibration suppression effected is shown, where a plot of vibrations occurring with the shaped bang-bang torque is overlaid for comparison.