Modal Vibration Control in Periodic Time-Varying Structures with Focus on Rotor-Blade Systems

The demands for high efficiency machines initiate a demand for monitoring and active control of vibrations to improve machinery performance and to prolong machinery lifetime. Applying active control to reduce vibrations in flexible bladed rotor-systems imply that several difficulties have to be overcome. Among others it is necessary, that the control scheme is capable to cope with non-linear time-varying dynamical system behaviour. However, rotating at constant speed the mathematical model becomes periodic time-variant. In this framework the present paper gives a contribution to design procedures of active modal controllers. The main aim is to reduce vibrations in periodic time-varying structures. Special emphasis is given to vibration control of coupled bladed rotor systems. A state feedback modal control law is developed based on modal analysis in periodic time-varying structures. The first step in the procedure is a transformation of the model into a time-invariant modal form by applying the modal matrices, which are also periodic time-variant. Due to coupled rotor and blade motions complex vibration modes occur in the modal transformed state space model. This implies that the modal transformed model is reformulated using complex mode theory. Next, a linear constant gain controller for the reformulated system is designed by linear control technique. Finally, this constant gain controller is transformed to a time-periodic form by applying reverse modal transformation. The non-measurable states are estimated using a periodic time-varying state observer designed by a methodology similar to the controller design. Furthermore, the modal matrices are used to analyse the controllability of the system in order to determine optimal actuator placement in the system. For this the modal transform technique is a very effective tool. The control design methodology is applied to a coupled rotor-blade system to demonstrate the efficiency of such a procedure. A simulation model for the system is formulated and a time-periodic modal controller is designed using the described methodology. Simulation results are provided to demonstrate the applicability and effectiveness of the technique. The results obtained shows that the control design technique is capable to cope with the time periodicity of this class of systems.