Stabilization of a rotating flexible structure subject to matched input disturbances

In this paper, we are concerned with nondissipative controllers design of a rotating flexible structure subject to boundary control matched disturbances. The active disturbance rejection control (ADRC) method is adopted to cancel the disturbances. Firstly, the time varying gain extend state observers (ESOs) are constructed to estimate the disturbances. Then, using estimates of uncertainties generated by ESOs, nondissipative torque control and shear control are designed for disk and beam respectively. Finally, when the angular velocity of the disk is less than the square root of the smallest natural frequency of the beam, we prove that the proposed controllers can ensure the stability of the closed-loop system in the sense that the disk can be rotated with the desired angular velocity and the beam can be stabilized. Moreover, simulation results are presented to illustrate the effectiveness of the control strategy.