Research On Control Strategy For Torque Ripple Suppression Of The Permanent Magnet Motor With Auxiliary Stator

Permanent magnet motors have been widely used in aerospace,rail transportation,new energy vehicles,and high-speed equipment due to their high torque density,efficiency,and reliability.However,the increasing prices and limited supply of rare earth materials have led to a growing interest in non-rare earth or rare earth-free permanent magnet motors.Among them,the use of non-rare earth ferrites with a concentrated-flux structure is considered a good design solution for permanent magnet motors with good electromagnetic performance.However,the concentrated-flux structure produces high torque ripple while improving electromagnetic performance.To supress the torque ripple of the concentrated-flux permanent magnet synchronous motor with auxiliary stator(referred to as permanent magnet motor with auxiliary stator),a torque ripple suppression control strategy using harmonic current drive is designed in this paper.This control strategy effectively reduces torque ripple while also addressing the issue of reduced torque density due to harmonic current.The paper systematically conducts mathematical modeling of the motor,designs and verifies the torque ripple suppression control strategy through finite element analysis,simulates the control system,and experimentally validates the control strategy.The main research include the following aspects:(1)The magnet flux linkage shift phenomenon caused by the asymmetric structure of motor auxiliary stator is studied,and two sets of dq-axis coordinates are used to orient the noload magnetic field and the armature reaction magnetic field,respectively.The difference between the magnet flux linkage and the inductance is introduced as the electric angle θs,and the magnet flux linkage equation,voltage equation,and torque equation are derived to obtain the motor’s mathematical model considering magnet flux linkage shift(referred to as the magnet flux linkage shift model).Through finite element simulation verification,the magnet flux linkage shift model has higher torque average accuracy than the conventional model.To further reflect the motor’s torque ripple,the motor’s voltage equation and torque equation,taking into account magnetic saturation,cross-coupling effects,and magnetic field harmonics,are derived.By exploring the characteristics of cubic spline interpolation and combining the rules of motor torque waveform,four sampling points are selected to construct the motor torque lookup table model,which is proved to reflect the motor’s torque ripple and lay the foundation for the design of torque ripple suppression control strategy.(2)Using the minimum copper loss principle to identify the dq-axis current working point of the motor,the instantaneous maximum torque per ampere(MTPA)curve of the torque response lookup table model and the constant MTPA curve of the magnet flux linkage shift model(corresponding to the constant MTPA control strategy)are obtained.Furthermore,using cubic spline interpolation to connect the points on each instantaneous MTPA curve that correspond to equal torque values,the four-sampling-point constant torque ripple suppression control strategy(referred to as the four-sampling-point control strategy)is obtained.The circular current trajectory of the four-sampling-point control strategy is transformed into a three-phase coordinate system to obtain three-phase currents.Then,finite element simulation is used to show that compared with the constant MTPA control strategy driven by a sine wave,the torque ripple of the four-sampling-point control strategy driven by harmonic current is significantly reduced.Based on the torque ripple deviation,it is suggested that increasing the number of sampling points can further reduce torque ripple.Therefore,a seven-sampling-point control strategy is developed by adding three more sampling points.Finite element simulation results show that the seven-sampling-point control strategy further reduces torque ripple,and the deviation rate of the torque average value response decreases.The torque deviation analysis shows that torque ripple can be further reduced by increasing the number of sampling points.(3)The seven-sampling-point control strategy reduces torque ripple while also reducing torque density.To address the issue of reduced torque density caused by harmonic currents,a control strategy that increases motor torque density is sought,namely,one that seeks a higher average torque current ratio.The mathematical relationship formula for the instantaneous average maximum torque per ampere(IA-MTPA)curve(corresponding to the IA-MTPA control strategy)is derived,and the IA-MTPA curve is obtained as the contour of the ?Te/?i2 graph.Finite element simulations verify that the torque density of the IA-MTPA control strategy is higher than that of the seven-sampling-point control strategy,and that the copper loss is reduced when the average torque output is the same.However,torque ripple increases.To ensure the effectiveness of torque ripple suppression,an intermediate control strategy between the IA-MTPA and seven-sampling-point control strategies is designed.By deriving that the IAMTPA curve is also the contour of the graph,and combining it with the copper loss lookup table,a formula that satisfies the intermediate control strategy is derived,and the threephase current is obtained by transformation.Finite element simulations show that this control strategy can simultaneously increase torque density and reduce torque ripple at rated current.The torque ripple value is the same as that of the constant MTPA control strategy at the intersection with the seven-sampling-point control strategy rated torque part,which is the torque ripple suppression control strategy tending towards IA-MTPA(TIA-MTPA).Simulation results show that the torque density of the TIA-MTPA control strategy is higher than that of the constant MTPA control strategy.The seven-sampling-point control strategy and TIA-MTPA control strategy are combined to form the designed torque ripple suppression control strategy.(4)A motor simulation module that can reflect motor torque ripple is obtained through theoretical derivation.The key step of using the dq-axis magnet flux linkages to find the dqaxis current was achieved by reversing magnet flux linkage table.A PIR controller was used to better track the given harmonic current.The given torque was converted into given current using a lookup table module.An inverter module was added to simulate the actual system behavior.The control system simulation showed that the seven-sampling-point control strategy had the smallest torque ripple,and the TIA-MTPA control strategy had a higher torque density than the constant MTPA control strategy.The above results demonstrate the effectiveness of the designed control strategy.(5)An experimental platform is built based on the rated data of the permanent magnet motor with auxiliary stator,and experimental equipment was assembled.C code is generated based on the model-based design scheme using Simulink.The experimental results show that the seven-sampling-point control strategy can effectively suppress torque ripple,and the torque density of the TIA-MTPA control strategy was higher than that of the constant MTPA control strategy,thus validating the effectiveness of the control strategy.