Fractional-order dynamics and control of rigid-flexible coupling space structures

A two-parameter fractional-order model of viscoelastic material was proposed. The model is then used to derive the fractional-order dynamics of rigid-flexible coupling structures to simplify the modeling and controller design for residual vibration suppression. 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.