Robust vibration control of a beam using the H_∞-based controller with model error compensator

The vibration control of a flexible beam subjected to arbitrary, unmeasurable disturbance forces is investigated in this paper. The beam is analyzed by using modal expansion theorem. The independent modal space control is adopted for the active vibration control. Discrete sensors and actuators are used here. The modal filters are used as the state estimator to obtain the modal co-ordinates and modal velocities for the state feedback control. Because of the existence of the disturbance forces, the vibration control only with the state feedback control law cannot suppress the vibration well. The method of disturbance forces cancellation is then added in the feedback loop. In order to implement the disturbance forces cancellation, the unknown disturbance forces must be observed. The model error compensator is employed to observe the unknown disturbance modal forces for the direct cancellation. After the implementation of the disturbance modal forces cancellation, there are still some residual disturbance modal forces which excite the beam. The disturbance attenuation problem is of concern in the design of the state feedback control law. For ensuring that influence of the residual disturbance modal forces is reduced to an acceptable level, the robust static H_∞ state feedback controller is designed. The vibration control performances of the feedback control with the H_∞ controller and the disturbance forces cancellation are discussed.