Modal space vibration control of a beam by using the feedforward and feedback control loops

This paper introduces a vibration control method for a flexible beam subjected to arbitrary, unmeasurable disturbance forces. The concept of independent modal space control is adopted. Here, we choose the modal filters as the state estimator to obtain the modal coordinates and modal velocities for the modal space control. Because of the existence of the disturbance forces, applying only the state feedback to suppress the vibration usually cannot achieve the desired control performance. The modal space feedforward control is then introduced to cancel out the disturbance forces. In this paper, the feedforward and feedback control method is implemented to reduce the beam vibration. The disturbance force observer is established to observe the disturbance modal forces for the feedforward control. The control gains are derived from the extended optimal control algorithm, where the disturbance modal forces are treated as exogenous state variables. By combining the feedback, feedforward control laws and the disturbance force observer together, the vibration control performances are discussed.