Active linear quadratic Gaussian control of the vibration of a flexible beam with a time-varying mass

A linear quadratic Gaussian method for active vibration control of a flexible beam with a time-varying mass is studied in this article. As the time-varying mass can change the resonance frequencies of system and induce instability of system, the vibration control of time-varying mass systems using piezoelectric actuators has been the subject of recent interest. The equation of motion of a beam with a time-varying concentrated mass is obtained by using admissible functions and the principle of separation of variables. Then, active control using piezoelectric actuators is simulated for the time-varying mass system. The linear quadratic Gaussian control strategy is employed for the suppression of transverse vibration of the beam with time-varying mass under different conditions. The numerical results show that the proposed scheme can attenuate the vibration of the variable mass system effectively in the interested frequency range. The control method can be used for the beam with constant mass or time-varying mass.