Coil Array Real-time Commutation Law for Magnetically Levitated Stage with Moving-coils

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.