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This work deals with the problem of modelling and analysis in rotordynamics as well as the active control of vibrations caused by unbalance in a rotor system. The system model was obtained by Finite Element Method taking into account the gyroscopic effects. The finite element model is used to get the Campbell diagram, the critical speeds, the modal shapes and to design the control scheme to attenuate the vibrations amplitude by an active suspension which uses linear electromechanical actuators. Due to the great number of states involved in the model, a state observer is necessary in order to apply a Linear Quadratic Regulator with full state feedback. The controller is applied considering the dynamics of actuators in the active suspension. Some numerical simulations to verify the controller-observer performance and experimental results on a novel test rig to prove the closed loop behavior are presented.