Adaptive unbalanced vibration control of magnetic bearing systems with rotational synchronizing and asynchronizing harmonic disturbance

In this study, we focus on the error in the estimated frequency of disturbance and present a new method of adaptive multiple frequency tracking and a new modification law after examining the relationship between the frequency error and output level in detail. We also develop a multiple frequency estimation algorithm which is insensitive to observation noise and theoretically prove the asymptotic stability for an adaptive nonlinear algorithm and adaptive frequency tracking method. The results of simulation show that when the frequency estimated by the difference equation method approaches the true value, the output error asymptotically converges to zero (or an equilibrium point). This corresponds to the asymptotic stability condition. The effectiveness of this method and the theoretical proof are verified by simulation. The experimental results show that the proposed algorithm is effective for achieving unbalanced vibration suppression.