Optimal control of a magnetic bearing without bias flux

Conventional active magnetic bearings are operated using a bias current (or flux) to achieve greater linearity and dynamic capability. Bias results in undesirable rotating losses and consequent rotor heating. In this paper, optimal control of a magnetic bearing without bias is investigated. A single degree-of-freedom system consisting of a mass and two opposing electromagnets is considered. The optimal control problem is examined for a cost function that penalizes both poor regulation and rotational energy lost. Although a standard optimization procedure does not directly yield an analytical solution, it does show that the optimal control is always bang-bang with possibly a singular arc. 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 optimal variable structure feedback controller