Q-parameterization control of vibrations in a variable speed magnetic bearing

In this paper we propose a controller design methodology using the Q-parameterization theory for a variable speed magnetic bearing in order to achieve elimination of unbalance vibrations. Rotor unbalance usually generates sinusoidal disturbance forces, with frequency equals to the rotational speed. So in order to achieve asymptotic rejection of these disturbance forces, the Q-parameterization controller free parameter Q is chosen such that the controller has jw axis poles at the different speeds of rotation. First, we give a mathematical model for the magnetic bearing in state space form. Second, we explain the proposed Q-parameterization controller design methodology. The controller free parameter Q is assumed to be a proper stable transfer function whose order equals twice the number of operating speeds. Third, we showed that the controller free parameter which satisfies the design objectives can be obtained by simply solving a set of linear equations rather than solving a complicated optimization problem. We also showed that the controller order equals: Number of degrees of freedom x (order of Q + 3). Finally, several simulations were obtained to evaluate the proposed controller. The results obtained showed the effectiveness of the proposed controller in eliminating the unbalance vibrations at the different speeds.