The nature of coupling in the heteropolar magnetic bearings permits other remaining active coils in the stator to assume actions of the failed coils to produce the same force resultants. This fault-tolerant control usually reduces load capacity because the redistribution of the magnetic flux which compensates for the failed coils leads to premature saturation in the stator or journal. Distribution matrix of voltages which consists of redefined biasing voltage vector and two control voltage vectors can be optimized in the manner that peak flux density is minimized. An elegant optimization method using Lagrange Multiplier is presented in this paper. The redistribution matrices calculated with Lagrange Multiplier method were compared with Maslen and Meeker’s solutions, local minima are guaranteed and also the global minimum can be obtained if an effective global minimum searching algorithm is used. The linearized control forces can be realized up to certain combination of 5 poles failed for the 8 pole magnetic bearing. Position stiffness and voltage stiffness are calculated for the fault-tolerant magnetic bearings. Simulations show that fault-tolerant control of the multiple poles failed magnetic bearings with a horizontal flexible rotor can be stabilized with reduced load capacity.

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