Many practical problems in magnetic bearing control concern essentially the minimization (maximization) of the dynamic compliance (stiffness) of the rotor. In this paper, the problem of minimizing the peak compliance of a high speed machining (HSM) spindle's thrust axis is examined. Experimental results are presented which demonstrate that μ synthesis provides an excellent tool for tackling this problem. Both complex μ and mixed μ synthesis are used to design controllers. The performance of the μ controllers is compared to that of an optimized PID controller. Under μ control, the dynamic stiffness of the system was increased by more than a factor of two over that obtained with the optimal PID controller. Careful attention was given to developing an accurate system model and uncertainty description, especially related to the transfer function of the magnetic actuators with solid stators and thrust disk.
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Fittro et al. (2003) studied this question.