A high-precision dynamic model of a flexible spacecraft installed with solar arrays, which are composed of honeycomb panels, is established based on the nonconstrained modes of flexible appendages (solar arrays), and an effective cooperative controller is designed for attitude maneuver and vibration suppression by integrating the proportional–derivative (PD) control and input shaping (IS) technique. The governing motion equations of the system and the corresponding boundary conditions are derived by using Hamiltonian Principle. Solving the linearized form of those equations with associated boundaries, the nonconstrained modes of solar arrays are obtained for deriving the discretized dynamic model. Applying this discretized model and combining the IS technique with the PD controller, a hybrid control scheme is designed to achieve the attitude maneuver of the spacecraft and vibration suppression of its flexible solar arrays. The numerical results reveal that the nonconstrained modes of the system are significantly influenced by the spacecraft flexibility and honeycomb panel parameters. Meanwhile, the differences between the nonconstrained modes and the constrained ones are growing as the spacecraft flexibility increases. Compared with the pure PD controller, the one integrating the PD control and IS technique performs much better, because it is more effective for suppressing the oscillation of attitude angular velocity and the vibration of solar array during the attitude maneuver, and reducing the residual vibration after the maneuver process.
Discrete-Time Implementation and Experimental Validation of a Fractional Order PD Controller for Vibration Suppression in Airplane Wings
