MATLAB Simulation Research on Permanent Magnet Synchronous Motor Vector Control Wei Hanpei 1*, Wei Haifeng 1,2, Zhang Yi 1,2 1 School of Electrical an Information, Jiangsu University of Science an Technology, Zhenjiang, 212003, China; 2 Jiangsu Provincial Key Laboratory of Pulp an Paper Science an Technology Nanjing Forestry University Nanjing, 210037, China E-mail:1506089882@qq.com Abstract Accoring to the mathematical moel of PMSM (permanent magnet synchronous motor) an vector control metho, PMSM FOC (vector control) simulation moel is built on the basis of MATLAB/Simulink environment. The system aopts the rotor fiel oriente vector control metho of i 0 to realize PMSM ecoupling control. The spee regulator an current regulator uses the conventional PI control algorithm, an the inverter aopts SVPWM moulation strategies. The simulation results prove the feasibility of the control metho, which provies a goo theoretical basis for the parameters of PMSM control system harware settings. At the same time, builing simulation moel PMSM FOC SPWM moulation strategy on the basis of FOC SPVWM simulation, making FFT (spectrum analysis) comparison between which an the SVPWM moulation's single phase current. The result that the output harmonic of SVPWM moulation is far less than SPWM moulation proves the avantages of SVPWM moulation strategies. Keywors: PMSM, vector control, SVPWM, MATLAB/Simulink. 1. Introuction Permanent Magnet Synchronous Motor (PMSM), as a new type motor, the operation reliability of which is relatively high without the electrical brush as well as the commutator. The stuies on PSMS have significant social an economic benefits, with the rapi evelopment of it as well as the high efficiency, low loss, small volume an some other excellent properties, which have important implications for energy saving an environment protection. The control moe of the traitional U/F (constant voltage frequency ratio)is not suitable for the riving system, which has higher requirement on spee, with low spee, little torque an low static stability of spee[4]. In this context, the actual spee of alternating current ynamo can not 1
be controlle accurately[3]. In some occasions with higher requirements, the square wave (brushless irect current motor) an the SPWM (silent pulse with moulation) moulation strategy are impossible to meet the eman of high precision an low noise, because of the influence of the torque ripple, such as the raar servo control system, robot, numerically-controlle machine tool an etc. The vector control has become the important irection of moern AC variable spee[5][6]. Base on the rotor fiel oriente vector control, this text has presente theoretical analysis an stuy an establishe the simulation moel of PMSM system with the help of MATLAB/Simulink thus to make stuy on control simulation. The result inicates that this control moe is consistent with the theoretical analysis an has a goo ynamic performance. 2. PMSM Mathematical Moel The mathematical moel of Permanent Magnet Synchronous Motor (PMSM), as a strong coupling linear system, is use to analyze the performance of motor an realize theoretical basis of torque an rotational spee control[7][8]. It can transform the motor form three-phase static coorinate system into two-phase rotating coorinate system in orer to realize ecoupling of torque an flux linkage. The mathematical moel of -q coorinate system as follows: The voltage moel of -q coorinate system: u ri L i we Liq t (1) iq uq riq Lq we ( Li f ) t (2) The stator wining of the electromagnetic torque expression is: 3 3 Te N ( L ) p Lq iiq N piq f 2 2 (3) The motor motion equation is: 3 wm Te TL N p( iq i q ) TL J 2 t (4) in this equation: u respectively are irect-axis voltage, quarature-axis voltage; u q respectively are irect-axis current, quarature-axis current; inuctance, quarature-axis inuctance; L L q i i respectively are irect-axis f is the flux linkage given by rotor; Te is motor output q electromagnetic torque; TL is loa torque; N p is motor pole logarithmic; w e w m respectively are 2
electrical angular velocity an angular velocity of rotation. Can be obtaine by mathematical expressions: using the control moe of i=0, the PMSM is equivalent to a separately excite c machine from the motor pot. At the same time, the three-phase stator current only inclues the part of torque current an the stator flux linkage vector is orthogonal in the permanent magnet flux linkage space vector. In this way, motor s output torque is just connecte with i q, an in irect proportion to i q ( T 1.5N i ). e p q f 3. PMSM control strategy 3.1 FOC control thoughts PMSM is a nonlinear, multivariable an strong couple system. It is very ifficult to control it irectly an accurately. Thus realizing the torque an flux of ecoupling an simplifying the magnetic chain relationship is necessary. The following figure 2 raws a physical moel of the seconary c motor[9][10]. q Ia O If Ic Figure 1: physical moel of the seconary c motor As shown in the figure 1, the fiel wining f an the compensation wining c are both on the stator, an only the armature wining a is on the rotor. The f axis is calle irect axis or axis, an the irection of the main flux along the axis; the axis of a an c will become quarature axis or q axis. The armature reaction can be counteracte by compensation wining, so the main flux of c motor is mainly an only etermine by fiel current of fiel wining. The current 3
which controls the armature wining can also control torque, an there is no interference between fiel an torque. That s why the control is so simple. Therefore, the analysis an control will be simplifie greatly[10] accoring to the principle that ifferent coorinate system will generate the same magnetomotive force. The PMSM physical moel an the c electromotor moel are regare as an equivalent through the Clark transform an Park transform. The total magnetic flux rotor of PMSM is the equivalent c motor excitation flux through control. At this moment, i can be equivalent to fiel current of c motor, an iq is equivalent to the armature wining current. Because the rotor permanent magnet can prouce excitation, the flux will be realize constant if i can be controlle as zero. Torque can be controlle by controlling the size of i q. That s the best avantage of the control moe of i 0. 3.2 FOC system construction The basic thought in vector control technology of PMSM is set up on the equation of transformation of coorinates an the electromagnetic torque of the machine. The control on torque an rotate spee can be realize by ajusting the quarature axis current in the thought, with the transformation of PMSM from three-phase stationary coorinate system to -q coorinate system. Its system structure frame is shown as figure n* n i*=0 i PI regulator 2 PI regulator 1 iq* iq PI regulator 3 u* uq* Park inverse transformation uα* uβ* SVPWM prouce moule pwm1 pwm3 pwm5 Threephase brige type inverter PMSM θ ia ib ic optical encoer θ n 3. iq i Park transform θ iα iβ Clark transform Figure 2: PMSM FOC system structure frame As is shown as figure 2 above, i*, the current signal of axis, is set 0, an i q*, the current signal of q axis, is set by the given rotate spee an actual rotate spee through a spee regulator. The actual current i a b i c i which collecte by electric current transucer will 4
become the equivalent current i i q of rotating coorinate system (-q coorinate system) through Clark an Park transformation. The fixe quantity an feeback quantity output the given voltage signal u * an u q*, u * an through reversing the Park transformation, it can get given quantity u q* of -q axis through current regulator. An u * an u of two-phase static coorinate system ( coorinate system), then loa into SVPWM thus to generate moel, an finally output PWM wave which can be use to control the voltage source pressure transucer an funamental current amplitue an ajustable frequency ac voltage. 4. The realization of PMSM FOC system s MATLAB/Simulink Figure 3: PMSM FOC MATLAB/Simulink simulation structure chart As shown in figure 3, it is a simulation structure chart of permanent magnet synchronous motor vector control simulation structure chart which base on MATLABS/Simulink. It can be ivie into a rotation spee link, two current links, SVPWM generator moule, voltage type inverter moule an motor style moule. Besies, the rotation spee link an current link both aopt the traitional PI control algorithm. The resultant vector an voltage sector ecie simulation chart uses inverse Park transformation an inverse Clark transformation to change the voltage of rotary coorinate 5
system to three-phrase stationary frame. In this way, the section of composite voltage vector can be confirme an lots of operations of anti-trigonometric function can be avoie. As a result much time can be save. The action time of ajacent voltage vector computational simulation chart: to get composite voltage vector in fixe section, the size an irection of composite voltage vector must be ascertaine by calculating the action time of ajacent voltage vector. In orer to reuce torque ripple, more voltage vector must be compoune, which leas to magnetic linkage that keep very close to roun. Then the perio of PWM an sampling time can be highly reuce. But limite by the switching frequency of power tube, the rate of PMW is 20KHz. The motor moule, which is built accoring to mathematics moel of permanent magnet synchronous motor. D-axis inuctance an electromagnetic torque given both are 8.5mh. Stator resistance given is 2.873 ῼ, an the given rotor flux control is 0.175Wb. 5. Simulation results The simulation time was set as 0.4s. In orer to valiate the given rev of motor, irection an the impact of given loa torque to stator three phase, the simulation spee must be set from 1000rpm to -2000rpm, with 1000rpm before 0.25s, an -2000rpm after 0.25s; at the same time, the given loa torque is set from 1nm to 4nm, with 1nm before 0.4s an 4nm after 0.4s; meanwhile, the initial position is set to 0 in the PMSM. Figure 4: simulating waveform of a single-phase voltage 6
Figure 5: simulating waveform of line voltage Figure 4 shows the single-phase voltage simulation waveforms of the PMSM. If the three-phase brige inverter is given 300V DC voltage Uc, then the above voltage will change into 100V, 200V, 100V, 100V, - 200V, 100V, namely 1/3Uc, 2/3Uc, 1/3Uc, -1/3Uc, -2/3Uc, -1/3Uc. Also, when the spee is 0.25s an the change is given, the frequency changes significantly. We can conclue that simulation results are in accor with theory. Figure 5 is the line voltage simulation waveform of PMSM. Given that the three-phase brige inverter DC voltage Uc is 300V,an the above output line voltage is 300V, then SVPWM moulation output voltage utilization rate is 100%. It proves one of the avantages of the SVPWM moulation. Figure 6:stator three-phase current waveform 7
Figure 7:irect-axis current simulation simulation waveform Figure 6 is the stator three-phase current simulation waveform of the PMSM. As is shown in the picture, at 0.1s when the given loa torque changes from 1n.m to 4n.m, the stator three-phase current amplitue increases to 4 times of the original with the frequency remaining invariant; at 0.25s when the given spee changes from 1000rpm to -2000rpm, the stator three-phase current frequency increases to 2 times of the original with the amplitue unchange an phase sequence change. This verifies that the electromagnetic torque of the motor output is only proportional to the three-phase stator current amplitue an irrelevant to frequency; the spee is proportional to frequency an irrelevant to current amplitue; irection is relate to phase sequence. Figure 7 is the irect-axis current simulation waveform of the PMSM. The figure shows that given that the current is zero an the air-gap flux is fixe, the actual ID value is influence by the given loa torque, spee an irection. Figure 8:q-axis current simulation waveform 8
Figure 9:output electromagnetic torque simulation waveform Figure 8 is the q-axis current simulation waveform of the PMSM. As is shown in the figure, at 0.1s when the given loa torque changes from 1n.m to 4n.m, the q-axis current value increases to four times of the original; at 0.25s when the given spee varies from 1000rpm to -2000rpm, it quickly comes back to the initial value after a series of pulsating, thus verifying that the q-axis current value is only affecte by a given loa torque an irrelevant to spee an irection. Figure 9 is the output electromagnetic torque simulation waveform of the PMSM. The figure shows that the waveform is consistent with that of the above-mentione q-axis current (torque current). Therefore, it verifies that while the air-gap flux maintains constant, electromagnetic torque is proportional to the q-axis current, that is, the electromagnetic torque of the motor output can be change by changing the q-axis current value. 9
Figure 10: the motor spee simulation waveform The figure 10 is the actual spee simulation waveform of permanent magnet synchronous motor, it shows that the actual spee follows the given spee strictly an response quickly, an the stabilization error can be controlle between -1rmp to 1rmp. To some extent, it proves the avantages of vector control. At the same time, in orer to prove the avantages of SVPWM s moulation strategy, on the basis of FOC SVPWM Delta-Sigma an then buil the open loop control moel of PMSM FOC SPWM, apply the moel to the three stator current polarity. From the two moels of stator current A, carry out the analysis of FFT, which funamental frequency is 50 HZ an the perio is eight weeks. The frequency spectrum analysis of the them are as follow: Figure 11 all-igital fuzzy stator current Figure 12 all-igital fuzzy stator current base on SPWM waveform an FFT base on SVPWM waveform an FFT analysis analysis The image shows that the moel's total harmonic istortion is 1.52%, which is establishe by SPWM. With establishe uner the control of PMSM by SVPWM, the other moel s total harmonic istortion is 0.23%, which is smaller than the former one. So we shoul choose the SVPWM moulation strategy. 6. Conclusions This paper introuces the origin of permanent magnet synchronous motor s vector control ieas as well as the construction of control system. Then making comparison between the moulation simulation moel of PMSM FOC SVPWM mae by MATLAB/Simulink an 10
SPWM open loop control. The result proves the methos of vector control's feasibility an the avantages of moulation strategy. Acknowlegment. This work was financially supporte by National Natural Science Founation of China (61503161), Open Fun Project of Jiangsu Provincial Key Lab of Pulp an Paper Science an Technology (201302), an A Project Fune by the Priority Acaemic Program Development of Jiangsu Higher Eucation Institution (PAPD). REFERENCES [1] Wang Qinglong, Zhangxing, Zhang Chongwei. Permanent magnet synchronous motor vector control spee ouble sliing moel reference aaptive system ientification[j].proceeings of the CSEE, 2014,06(2):84-89. [2] Wang Chunming, Ji Yanju, Luan Hui.MATLAB /SIMULINK permanent magnet synchronous moter vector control system simulation[j]. Journal of jilin university (information science eition),2009,01(4):12-15. [3] Wang Yongxing, Wen Xuhui, Zhaofeng.Multi-imensional optimization of multiphase permanent magnet synchronous motor vector control[j].proceeings of the CSEE,2015,10(5):123-127. [4] Ding Shuo, Cui Zongze, Wu Qinghui al. Permanent magnet synchronous motor base on SVPWM vector control simulation stuy[j]. Foreign Electronic Measurement Technology, 2014,06(3):40-47. [5] An Quntao, Sun Li, Sun Li Zhi al. The new openwining permanent magnet synchronous motor vector control system research[j]. Proceeings of the CSEE,2015,22 (10):87-91. [6] Ding Wen, Gao Lin, Liang Deliang al. The moe Ling an simulation of permanent magnet synchronous motor vector control system[j]. Micro-machine,2010,12(7):123-129. [7] Hou Yanting, Luo Hui, Wu Jiawei. Research an implementation of three-level SVPWM algorithm base on DSP[J]. Servo Control,2015,Z3(11):57-65. [8] Chen Zhen, LiuZhenxing, Fei Guirong. The application of fuzzy PI control in permanent magnet synchronous motor[j]. Fujian Computer,2016,01(11):156-170. [9] Zhang Chaoyang, Feng Xiaoyun, Xu Junfeng. Permanent magnet synchronous motor operation weak magnetic control strategy research[j]. Electric Drive,2014,05(6):201-208. [10] Wang Lin. Vector control an irect torque control technology[j]. Value Engineering,2014/28(4) :201-208. 11