Abstract: It is essential to decouple the multi- degrees-of-freedom dynamics for controlling a multi-degrees-of-freedom magnetically levitated stage with moving-coils. Decoupling the multi- degrees-of-freedom dynamics needs to decompose forces and torques acting on translator of the stage to their corresponding degrees-of-freedom. Force/torque decomposing can only be validated by real-time commutating the coil array because of the quasi-static magnetic field of the permanent magnet array. Firstly, the force/torque decomposing model is build by using the planar integration of Lorentz force law. Then, the coil array real-time commutation law of the multi-degrees-of-freedom magnetically levitated stage with moving-coils is established based on the force/torque decomposing model and the principle of minimal coil array heat-loss. Lastly, the numerical stability of the law and its error influence on corresponding force/torque are analyzed. Theoretical analysis and case research indicate that this law is of high numerical stability, it can calculate coil array currents accurately and reliably and the error of force/torque actuated by the law-commutated currents is quite small. This coil array real-time commutation law can be used to commutate the coil array, decompose the forces and torques, so as to control the multi- degrees-of-freedom magnetically levitated stage with moving-coils.

Key words: Coil array Real-time commutation law, Condition number, Force/torque decomposing, Magnetically levitated stage with moving-coils, Numerical stability