State Observing Method and Active Vibration Control Based on Virtual Sensing

State feedback is mostly used in the active vibration control of structural systems. However, the most challenging problem is to achieve the whole state of the structure. Another issue in active vibration control is that, in many cases, only some particular modes need to be controlled, while the other modes can remain unchanged in order to save on the costs of the control. To solve the above issues, this paper proposes a state-observing method and conducts a non-spillover partial pole placement control using a multistep method. Using the finite element method, the electromechanical coupling equations of motion of the beam are formulated. The reduced finite element model is then obtained by using the system equivalent reduction expansion process method. Introducing the real measurements by sensors and applying the local corresponding principle, the modes of the structural system are corrected, which are then utilized to predict all the degrees of freedom without measuring by sensors. Then, the non-spillover partial pole placement based on the state feedback is conducted using the multistep method. The optimal locations of actuators are derived by the genetic algorithm to control the specific structural modes effectively. The numerical simulations and experimental studies are also carried out.