Fault Tolerant, Decoupling Control of Magnetic Bearings Including Material Path Reluctances

An equivalent magnetic circuit of 8-pole heteropolar magnetic bearing including path reluctances is developed with non-dimensional forms of flux, flux density, and magnetic force equations. The results show that fluxes and magnetic forces are considerably reduced for the magnetic circuit including relatively large path reluctances. A Lagrange Multiplier optimization method is used to determine current distribution matrices for the magnetic bearing including large path reluctances. Optimizing this cost function yields distribution matrices calculated for certain combination of 5 poles failed out of 8 poles. Control gains are determined based on the conditions that the closed loop dynamic properties of a failed magnetic bearing should be the same as those of an unfailed magnetic bearing. The cross coupled stiffnesses due to uneven flux distribution in case of a failed magnetic bearing are effectively canceled out by use of the cross feedback control.