Fractional-Order Dynamics and Control of Rigid-Flexible Coupling Space Structures

摘要

Based on the fractional-order constitutive law of viscoelastic material, a generic fractional-order dynamics has been derived for general rigid-flexible coupling viscoelastic structures in a uniform framework, ranging from purely elastic solids to purely viscous fluids. A new fractional-order transfer function of the coupling structures has been derived by separating the dynamic responses of the rigid and flexible components in a distinguished and coupled form: the transfer function of the rigid component and the fractional-order transfer function of the flexible component. Based on the ideal Bode plot, it has been found that the resonant modes of the coupling structure depend only on the inertia ratio of the flexible component over the rigid component and the natural frequency of the flexible component. Finally, a new fractional-order lead-lag compensator design method is developed to suppress the residual vibration for a given frequency range instead of the error constant, gain crossover frequency, and phase margin. Numerical results show that the proposed fractional-order controller is effective and robust in achieving the control requirement.