Vibration control of a beam using the nearly optimal control algorithm with a disturbance force observer

Active vibration control of a flexible beam subjected to arbitrary, unmeasurable disturbance forces is investigated in this paper. The concept of independent modal space control is adopted. Both the feedforward and feedback control is implemented here to reduce the beam vibration. Because of the existence of the disturbance forces, the feedforward control is applied by employing the idea of force cancellation. A modal space disturbance force observer is then established in this paper to observe the disturbance modal forces for the feedforward control. For obtaining the feedforward and feedback control gains with the optimal sense, the nearly optimal control law is derived, where the modal disturbance forces are regarded as additional states. The vibration control performances and the asymptotic properties of the control law are discussed.