OPTIMAL-CONTROL OF A MAGNETIC BEARING WITHOUT BIAS FLUX USING FINITE VOLTAGE

Conventional active magnetic bearings (AMB) are operated using a bias current (or flux) to achieve greater linearity and dynamic capability. Bias, however, results in undesirable rotating losses and consequent rotor heating. While control without bias flux is an attractive altern ative, it is considerably more complex due to both force slew rate lim itations and actuator non-linearity. in this paper, optimal control of a magnetic bearing without bias is investigated. A single-degree-of-f reedom system consisting of a mass and two opposing electromagnets is considered. The optimal control problem is examined for a cost functio n that penalizes both poor regulation and rotational energy lost. Thou gh a standard optimization procedure does not directly yield an analyt ical solution, it does show that the optimal control is always bang-ba ng including possibly a singular are. First, the minimum time problem is solved for a simple switching law in three dimensional state space. A non-standard, physics-based approach is then employed to obtain an optimal solution for the general problem. The final result is an optim al variable structure feedback controller. This result provides a benc hmark which can be used for evaluation of the performance of a practic al feedback controller designed via other methods. The practical contr oller will be designed to support a flexible rotor and achieve robustn ess and optimally reject disturbance. This result may also be applied to many other applications which contain opposing quadratic actuators. (C) 1998 John Wiley & Sons Ltd.