Active Vibration Isolation of a Flexible Rotor Being Subject to Unbalance Excitation and Gyroscopic Effect Using \({\boldsymbol{\mathcal{H}}}_{\boldsymbol{\infty}}\)-Optimal Control

This contribution deals with active vibration isolation of unbalance induced vibrations of a rotating shaft using \({\mathcal{H}}_{\infty }\)-optimal control and piezoelectric actuators. Controller design for the considered system is challenging and requires a high demand in robustness due to speed-dependent system behavior in consequence of the gyroscopic effect. Recent studies in the field of active control of rotor systems, especially at the Institute for Mechatronic Systems in Mechanical Engineering at TU Darmstadt, mainly focus on the attenuation of rotor displacements. For many applications, like aircraft engines, not only the rotor’s deformation itself is of high interest, but also its interaction with the environment. Former works on active vibration attenuation show that active reduction of rotor displacements can be attended by an undesirable increase of bearing forces. In addition to these works, this article deals with the decoupling of a rotating shaft from the surrounding structure, which is also known as vibration isolation. The investigations are based on a rotor test rig with a statically determined bearing configuration. One of the two bearing supports is active and consists of two piezoelectric stack actuators as well as two collocated piezoelectric load washers. The operating range of the test rig includes two unbalance induced resonances. Since the control performance strongly depends on the accuracy of the description of the system dynamics, a finite element model of the rotor is determined and extended by discrete piezoelectric elements. The obtained parametric model is capable of capturing the system’s speed-dependent dynamics. The \({\mathcal{H}}_{\infty }\)-optimal controller will be derived using the parametric finite element model. Finally, the feasibility of the described approach will be validated by testing the control performance by means of vibration isolation in simulation and experiment.