Nonlinear Modeling And Vector Control Of The Dual-flux-modulated Magnetic Gear Machine

Field-modulated machine(FMM)has attracted more and more attention in the field of direct drive due to its high torque density and low rated speed.In this paper,the development status of the FMM is introduced,and then the research work of the DualFlux-Modulated Magnetic Gear Machine(DFM-MGM)is carried out as follows.Firstly,the operation principle of the DFM-MGM is studied.Combined with the mechanical structure and magnetic circuit structure of the DFM-MGM,this paper introduces the magnetic field modulation mechanism and operation principle of the DFM-MGM,and discusses the influence of the introduction of auxiliary modulation ring on the magnetic circuit and performance of the motor by analyzing the magnetic density distribution and harmonic content in the three-layer air gap.Secondly,the nonlinear mathematical model of the DFM-MGM is established.Because winding inductance will be affected by the salient pole effect of the outer rotor.273 sample points are selected by the full analysis factor test method,and the finite element simulation model of the DFM-MGM is built.The relationship between winding flux and inductance,winding current and outer rotor angle is obtained.Combined with polynomial regression model and Fourier series,the nonlinear mathematical model of inductance and dual rotor permanent magnet flux is established,and the influence of polynomial order and Fourier series on the mathematical model is analyzed The accuracy and complexity of the model are compromised to select the appropriate order of polynomial regression model.Then,the electromagnetic torque of inner and outer rotors is decoupled.The magnetic fields of the two rotors have the same rotation speed and constant phase difference when the motor runs stably.By using double d-q rotating coordinate system,the permanent flux linkage of the inner and outer rotors of the motor is superimposed into the combined permanent flux linkage of the two rotors.The electromagnetic relationship similar to that of the traditional permanent magnet synchronous motor is obtained,and the nonlinear electromagnetic equation of the DFM-MGM is written according to the practice of permanent magnet synchronous motor.Finally,according to the magnetic circuit and dual rotor motion characteristics of the DFM-MGM,the motion equations of inner and outer rotors are written.The simulation model of the DFM-MGM is established by MATLAB.The steady and dynamic characteristics of the DFM-MGM working in two modes of motor and magnetic gear are analyzed,and the torque and speed responses of inner and outer rotors under different working conditions are calculated.The amplitude of the resultant flux linkage of two rotor’s PM flux linkage will change under different phase differences,which will indirectly affect the amplitude of the back EMF.Combining with the cosine theorem,the relationship between the amplitude of the back EMF and the phase difference of the inner and outer rotor magnetic fields is obtained.The correctness of the dual d-q rotation equivalent model is proved by the combination of simulation and experiment.The research in this paper provides a complete set of reference scheme for nonlinear modeling and control of field modulated permanent magnet motor.In the dual d-q coordination system,the decoupling process of the electromagnetic and mechanical equations of the inner and outer rotors is also suitable for other types of field modulated motors and multi port motors,which has important reference value for the modeling and control research of other FMM.