Raising Power Loss Equalizing Degree of Coil Array by Convex Quadratic Optimization Commutation for Magnetic Levitation Planar Motors

This paper proposes a convex quadratic optimization commutation method to raise the equalization degree of power loss distribution of coil array for magnetic levitation planar motors. Starting with the modeling of electromagnetic forces/torques and commutation of coil array, the global power loss and the local power losses of coil array are analyzed, and the power loss equalizing degree is defined to evaluate the power loss distribution of coil array being commutated dynamically. Then, in consideration of the fact that the global power loss is the quadratic function of commutated coil currents, the convex quadratic function optimization with equality constraint and boundary constraints is applied to commutate the coil array, and the power loss equalizing degree is raised by decreasing the boundary constraints of optimization. Taking the magnetically levitated planar motor under investigation as examples and using quadprog routine in Matlab Optimization Toolbox, which is a dedicated quadratic optimization routine, it is verified that the power loss equalizing the degree of coil array is raised gradually and the power loss distribution of coil array becomes more uniform along with decrease of the boundary constraints. The convex quadratic optimization commutation is verified experimentally on a constructed multi-dimension force/torque measurement platform. Using the convex quadratic optimization commutation can not only improve the power loss distribution of coil array of magnetically levitated planar motors, but also make it possible to select lower capacity power amplifiers to produce the identical desired electromagnetic forces and torques.