Dynamics and Control of a Flexible Hub-Beam System with Considering the Effect of Damping

In this paper, dynamics and control of a flexible hub-beam system is investigated with considering effect of damping. Dynamic expression with containing damping is presented. Active controller is designed using optimal tracking control theory. Three kind of damping are considered: structural damping, wind damping, and damping at bearing of the hub. In wind damping, viscous wind damping and square wind damping are considered. Since active controller is a function of mode coordinates, extraction method of modal coordinate from actual physical measurements is developed. Simulation results indicate that the simplified first-order approximation coupling model presented is valid for dynamic description of flexible hub-beam system and so is available for control study. Damping has important effect on dynamic characteristics of the system. In the case that angular velocity of large motion of the system is low, desired motion trajectory may be achieved by using optimal tracking controller and the vibration of the beam caused by the large motion may be suppressed by this controller at the same time.