Unbalance compensation using generalized notch filters in the multivariable feedback of magnetic bearings

Unbalance of magnetically levitated rotors causes undesirable synchronous vibrations which may lead to saturation of the magnetic actuator. To avoid this problem we propose a generalized narrow-band notch filter which is inserted into the multivariable feedback without destabilizing the closed loop. The parameters of the generalized notch filter strongly depend on the inverse sensitivity matrix evaluated at rotational speed. This matrix is easily measured a priori and stored in a look-up table. It is shown that a decentralized notch is feasible for weakly gyroscopic rotors. The proposed notch filter approach has advantages in terms of run-time complexity and analytical verification of closed-loop stability. Results from the implementation of the proposed unbalance compensation in industrial magnetic bearing systems are included.