Unbalance and resonance elimination with active bearings on general rotors

In this work, we found a closed-form analytical solution for the elimination of unbalance-induced bearing forces on arbitrary, gyroscopic rotors. We demonstrate that the force-free condition is met for any unbalance distribution. Furthermore, we proved that up to two resonances can be fully eliminated. We found a new Lyapunov stability theorem to prove the controller's superior stability properties. The advantage of our approach is that different active bearing technologies are unified in a single, generalized theory. Our theory is not only limited to rotors, but applies to all systems with harmonic excitation that share the same general matrix structure. Finally, we provide evidence that our theoretic assumptions are also satisfied in reality: In an experiment we demonstrate that unbalance-induced bearing forces and rotor resonances can not only be eliminated in theory, but also in practice.