Frequency-Shaped Optimal Control of Unbalance Response in Active Magnetic Bearing System

Optimal control with frequency-shaped cost functional is applied to the control of unbalance response in active magnetic bearing system. The active magnetic bearing system is modeled as a symmetric rigid rotor supported by two anisotropic bearings. The cost functional is expressed in terms of frequency dependent weighting matrices defined in the frequency domain so that a penalty is given over the rotational speed of rotor. The control scheme consists of two closed loops: one for the stabilization of system and another for the control of unbalance response. The control method renders the varying optimal feedback gains, as the rotational speed changes. The performance of this control method is evaluated through simulations to check its applicability to suppression of unbalance response or force in active magnetic bearing system. Simulation work is carried out at three rotational speeds: below the first critical speed, between the first and second critical speeds, and above the second critical speed. It is robust in the sense that it does not require accurate estimation of unbalance, whereas it still guarantees the system stability.