Elimination of imbalance vibrations in magnetic bearing systems using discrete-time gain-scheduled Q-parametrization controllers

We propose a method to eliminate the imbalance vibrations in magnetic bearing systems using discrete-time gain-scheduled Q-parametrization controllers. Imbalance in rotating machines generates variable frequencies sinusoidal disturbance forces that cause the vibrations. Since the frequency of vibrations equals the rotational speed, the free parameter Q of the Q-parametrization controllers is scheduled as a function of the rotational speed to achieve rejection of the imbalance sinusoidal disturbance forces at all operating speeds. First, we present a mathematical model for the magnetic bearing in state space from which includes the effect of imbalance. Next, we explain the discrete-time Q-parametrization controller design for the magnetic bearing to achieve robust stability mid rejection of the variable frequencies sinusoidal disturbance forces. Finally, several simulation results are presented. The results showed that elimination of the imbalance vibrations are achieved at all operating speeds, and moreover robust stability is also achieved