Application of discrete-time gain-scheduled Q-parameterization controllers to magnetic bearing systems with imbalance

In this paper the problem of imbalance in magnetic bearings is solved using discrete-time gain-scheduled Q-parameterization controllers. Imbalance in rotating machines causes sinusoidal vibrations of variable frequencies. Since the frequency of vibrations equals the rotational speed the free parameter of the Q-parameterization controllers is scheduled as a function of the rotational speed to achieve rejection of the imbalance sinusoidal disturbance forces (which cause the vibrations) at all operating speeds. First we present a mathematical model for the magnetic bearing in state space from which includes the effect of imbalance. Second, we explain the discrete-time Q-parameterization controller design for the magnetic bearing to achieve robust stability and imbalance compensation. The free parameter is assumed to be a second order proper stable transfer function whose denominator parameters are fixed and the numerator parameters are scheduled as second order polynomial functions of the rotational speed such that rejection of the imbalance sinusoidal disturbance is achieved. Finally several simulation results are presented. The results showed that elimination of the imbalance vibrations are achieved at all operating speeds, moreover robust stability is also achieved