Active Control of Parametric Vibrations in Coupled Rotor-Blade Systems

In rotor-blade systems basis as well as parametric vibration modes will appear due to the vibration coupling among flexible rotating blades and hub rigid body motion. Parametric vibration will typically occur when the hub operates at a constant angular velocity. Operating at constant velocity the model becomes periodic-variant. In order to reduce basis as well as parametric vibrations by means of active control in such systems a time-variant control strategy has to be adopted. This paper presents a methodology for designing an active controller to reduce vibrations in a coupled rotor-blade system. The main aim is to control blade as well as hub vibrations in such a system by means of active control with focus on reducing the parametric vibration. A periodic state feedback controller is designed by transforming the system into a linear time-invariant form. Using this a controller is designed and transformed into a time-periodic form by a reverse transformation. The modal matrices used for the transformation are periodic and consist of basis as well as parametric vibration modes of the rotating system. It means that the modal coordinates of the transformed system address both type of modes. The designed control scheme is applied to a coupled rotor-blade system and dynamic responses are numerically evaluated. Such responses show that the vibrations are efficiently reduced. Frequency response diagrams demonstrate that both basis and parametric vibration modes are significantly attenuated. Furthermore, the efficiency of applying the modal transformation method for time-varying systems, not only for the controller design but also for system analysis and to achieve optimal actuator placement, is discussed.