A Comparative Study On Field Oriented Control And Direct .
256JOURNAL OF COMPUTERS, VOL. 8, NO. 1, JANUARY 2013A Comparative Study on Field Oriented Controland Direct Torque Control for Permanent MagnetLinear Synchronous MotorJun ZhuSchool of Electrical Engineering and Automation, Henan polytechnic University, Jiao Zuo, ChinaControl Engineering Open Lab. of Key Subjects of Henan, Henan polytechnic University, Jiao Zuo, ChinaEmail: zhujun@hpu.edu.cn1Xudong Wang1, Baoyu Xu2, Haichao Feng1 and Xiaozhuo Xu1School of Electrical Engineering and Automation, Henan polytechnic University, Jiao Zuo, China2School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, ChinaEmail: {wangxd ,xubaoyu, fhc, xxz}@hpu.edu.cnAbstract—Although the permanent magnet linearsynchronous motor has been used in industry gradually, ithas some drawbacks to restrict the using region. In order toovercome the disadvantages, the advanced control strategieswere adopted to improve the performance of PMLSM. Inthe paper, the field oriented control and direct torquecontrol strategies were researched, their control model wasestablished respectively, so that their simulation results weregiven to rectify the control effects. Though the comparativeanalysis, it is showed that the FOC has quickly dynamicresponse to track the system performance although itsmathematic model is more complex, the DTC also hasquickly dynamic response, but its torque and flux linkagehave more obvious pulsation.Index Terms—comparative, field oriented control, directtorque control, permanent magnet linear synchronousmotor.I. INTRODUCTIONAs a kind of special electrical motor, the permanentmagnet linear synchronous motor (PMLSM) can be seenas a permanent magnet rotating synchronous motor(PMRSM) cut along the radial and stretched the linearstyle, its mainly feature is direct driver function. PMLSMcan connect the load and motor’s mover directlyconstructed an integrated structure. The PMLSM directdriver system can convert the electrical energy directlyinto mechanical energy without any other intermediatedrive gearing, so that it can eliminate the advance effectsof PMRSM connected through link bar, such as backlash,high friction and high inertia etc. Because of its simpleand high stiffness structure and direct driver model, thePMLSM can obtain more high speed and accelerate thanthe traditional PMRSM. It has a lot of advantages, suchManuscript received November 10, 2011; revised December 8,2011; accepted March 25, 2012.This work was supported in part by a grant Dr. foundation of henanpolytechnic university under grand (B2011-104), Control engineeringopen Lab. of key subjects of henan(KG2011-12) ， Science andtechnology research key project of education department of henanprovince (12A470004) and outstanding talent plan in hennaprovince(104200510021).zhujun@hpu.edu.cn 2013 ACADEMY PUBLISHERdoi:10.4304/jcp.8.1.256-263as high force density, lower inertia, high positioningprecision and accuracy, high dynamic performance,unlimited travel and so on. In recent years, PMLSM hasbeen widely used in electromechanical servo system, highspeed and high precision digital control system, precisioninstrument, precision machining, horizontal and verticaltransportation system, and other industry applicationregion[1-3].Meanwhile, the PMLSM drive system also have somedrawbacks, its direct driver model without intermediatedrive transmission make the PMLSM sensitive to internalsystem perturbation and external disturbances. It hassome disadvantage, such as the end effect, nonlinearmodel and parameter uncertainty to bring the thrust ripple,slot and end effects, which can reduce the servoperformance of PMLSM. The disadvantages of PMLSMmake the system control more difficult, so the more highrequirement was proposed to design the controller toimprove the system performance of PMLSM[4-7].The direct torque control (DTC) algorithm wasproposed in 1971 in the IEEE, which were firstly appliedin the mid 1980s, and then it was extended to the weakmagnetic speed range. The control strategy can achieve avery quick and precise torque control response withoutusing of complex algorithms.In this algorithm the instantaneous values of the statorflux and torque are calculated according to the primaryvariables (stator currents and voltages). They can becontrolled directly by selecting an optimum inverterswitching table, which are used to determine the optimumvoltage vector of the inverter to obtain the fastest torquecontrol. It does not need coordinate transformation andany current regulator, the resulting DTC structure isparticularly simplistic and therefore, becomes its majoradvantage and thus can be considered as highperformance vector controllers based on the decouplingof flux and torque.DTC has shown to be the simplest torque control ofpermanent magnet synchronous motor for industrialapplications where torque control is highly desirable．It
JOURNAL OF COMPUTERS, VOL. 8, NO. 1, JANUARY 2013requires few sensors and does not depend heavily onmotor parameter estimation[8].The first asynchronous motor high-end inverter basedon direct torque control was advent in the ABB companyin 1995. In recent years, the direct torque control strategywas used in electric locomotive traction system, verticallift system and some high power AC variable speedapplications. It is reported that the tram cars and electriclocomotives based on DTC had reached 1000 inABB.DTC has been widely attention and research,because it novel control ideas, clear and concise systemarchitecture and excellent dynamic performance.Nowadays, Germany, Japanese and American aredeveloping the DTC technology, then pushed outasynchronous motor variable frequency speed regulationdevice. In China, Tsinghua University, NanjingUniversity of Aeronautics and Astronautics and CSRhave made great achievements[9-10].Now, DTC has existed for two decades, it still hassome disadvantages. The slow transient response to thestep changes in torque during start-up is one of thedisadvantages, which can exist in conventional DTC. Themost serious disadvantage of conventional DTC is theripple, which exists in the torque and flux variables. Thisundesirable ripple is of higher value when the selectedstate of the inverter remains unchanged for severalsampling periods, which accordingly implies that theswitching frequency of the inverter is not constant.The maintaining of the inverter switching frequencyconstant is of course particularly important so far as theoptimized design of the converter is concerned. Severaltechniques have been proposed to overcome this problem.These include Space Vector Modulation (SVM)[11],multilevel inverter[12], predictive control[13] andartificial intelligence technique[14-15]. But thesetechniques make the control scheme more complex andremove the basic advantage of DTC-simplicity[16].The field oriented control (FOC) was proposed byF.Blaschke in the Siemens company in 1970s. FOC hastwo kinds of models, they are field oriented vectorcontrol based on rotor magnetic field and stator magneticfield. The field oriented control based on stator magneticfield was proposed in 1980s, it has two basic controlideas, the direct torque self-control theme by professorM.Depenbrock in Germany, another one is direct torqueand flux linkage control theme by professor I.Takahashiin Japan The coordinates transformation is adopted inFOC, it makes the three phase transform to two phaseperpendicular for the AC motor, so that we can controlthe AC motor according to the DC motor ’ s controlrules ， which can control the flux linkage and torquerespectively[17].In order to overcome the shortcomings to improve theservo performance of PMLSM, we can improve thestructure design of PMLSM, or adopt some advancecontrol strategies, such as the field oriented control anddirect torque control. The field oriented control (FOC) isa kind of usual control method for AC servo motor. It isbeing used in PMLSM controlling. According to themultivariable, nonlinearity and strong coupling of 2013 ACADEMY PUBLISHER257PMLSM, the field oriented control converts the statorcurrent of PMLSM into rotor synchronous current byusing vector conversion technology. That separates theflux linkage and torque currents so as to linearly controlthe output torque of PMLSM, so that the thrust ripple andend effect can be reduced, and the servo performance wasimproved for the PMLSM servo system. The directtorque control (DTC) is also a kind of advance controlstrategies for AC servo motor after the vector control. Itis being used in PMLSM controlling. According to themultivariable, nonlinearity, strong coupling of PMLSMand avoiding the complex coordination convert of vectorcontrol, the direct torque control can direct control thetorque of motor through stator flux orientation technique,converts the stator current of PMLSM into rotorsynchronous current by using vector conversiontechnology so that the end effect and torque ripple can bereduced and the control performance can be improved ofPMLSM[18-22].The permanent magnet linear synchronous motorusually can be divided into sine wave driving permanentmagnet linear synchronous motor and the square-wavedriving permanent magnet Brushless DC motor. In thepaper, the two control strategies FOC and DTC wereresearched for PMLSM driven by three phase sine wave.II. THE MATHEMATICAL MODEL OF PMLSMIn order to establishing the accurate mathematic ofPMLSM, the assumptions were given as follow [23]:a. the primary has Symmetrical three-phase windingconnected with Y, which have the same number ofturns, resistance and other parameters;b. the rotor has not damper winding, the conductivityratio is zero for the permanent magnet materials, themagnetic circuit is linear and the effects can be ignoredof hysteresis, eddy current and magnetic saturation on themotor;c. the fundamental magnetic potential is considered,which is produced by permanent and stator winding;d. ignored the cogging, not considering the effects onmotor parameters of the temperature and frequencychanging.The space vector coordination for PMLSM is as Fig.1.Figure 1. The space vector axis of PMLSM
258JOURNAL OF COMPUTERS, VOL. 8, NO. 1, JANUARY 2013In the Fig.1, the abc is three-phase static coordinates,a-axis points to the actual stator phase A axis, αβ is twophase static coordinates. xy is stator rotor coordinate, thepositive direction of x axis is the direction of stator fluxlinkage of ψ s . The torque angle δ is the angle between xaxis and d axis. dq is two-phase rotating coordinate onthe rotor, the positive direction of d axis is the directionof rotor flux linkageψ f , θ is the angle between d axisJ(1)uq Rs iq pψ q ωrψ d .(2)In the eq.(1) and eq.(2), p is differential operator, Rs isarmature winding resistance, ωr is rotor angular velocity.They show d and q components of the stator voltage inthe rotor synchronous dq0 axis.The flux linkage equations are:ψ d Ld id ψ f .(3)ψ q Lq iq .(4)In the eq.(3) and eq.(4), ψ f is flux linkage constant ofpermanent magnet, Ld and Lq are dq coil self-inductance.The electromagnetic torque equation is: ψ f iq Te pn (ψ d iq ψ q id ) pn .22 ( Ld Lq )id iq (5)Theon33electromagneticαβ coordinates is:torqueequation3pn (ψ α iβ ψ β iα )2.1 pn ψ sψ f sin δLsTe (6)In the eq.(5)and eq.(6), Te is electromagnetic torque, pnis motor pole pairs. ψ α andψ β are αβ axis componentsof the stator flux linkage. δ is the torque angle betweenψ s andψ f .The mechanical motion equation is: 2013 ACADEMY PUBLISHER Te TL Bωr .dt(7)The variable J is moment inertia, B is frictioncoefficient.In the static two phase αβ axis, the voltage, fluxlinkage and torque are as follow: uα Rs pLa u pLαβ β and a axis. When the load is constant, xy and dqcoordinates are synchronization, that means δ is constant,conversely, δ is a variable [24].According the assumptions and space vectorcoordinates, the mathematic model can be obtained basedon rotor rotating dq coordinates system.The equations of voltage, flux linkage, torque andmotion for PMLSM are as follow:The voltage equations are:u d Rs id pψ d ω rψ q .ωr iα ωrψ fRs pLβ iβ pLαβ sin θ .(8) cos θ ψ α ( uα Rs iα )dt .(9)ψ β ( u β Rs iβ )dt .(10)Te 32pn (ψ α iβ ψ β iα ) .(11)In the eq.(8), (9), (10) and (11), uα and uβ are αβ axiscomponents of the stator voltage.current αβ axis components.iα and iβ are the statorψαand ψ β are αβ axiscomponents of the stator flux linkage.For the vector control of PMLSM, three kinds ofcoordinate change are used, they are stator three phaseabc coordinate, stator two phase static αβ coordinate andtwo phase dq coordinate based on the rotating magneticfield of rotor. They have the following conversionrelationship. Fd F q 23 cos θ sin θ ( ) ( ) ( ) ( ) cos θ sin θ 2πcos θ 2π332π2πsin θ 33Fa Fb . (12) Fc 1 1 1 F a 2 Fα 22 Fb . F 3 3 β 0 3 Fc 22 Fd cos θ F sin θ q sin θ Fα .cos θ Fβ (13)(14)In the eq(12),(13) and (14), F can be expressed voltage,current and flux linkage respectively.III. THE CONTROL MODELOF PMLSM.A. The Principle of Field Oriented Control.The field oriented control can reduce the torque ripple,end effect and improve the dynamic responseperformance for the torque control research. The field
JOURNAL OF COMPUTERS, VOL. 8, NO. 1, JANUARY 2013oriented strategy of PMLSM is same as PMRSM. Thereare some mainly control methods:a. id 0 control method, b. maximum torque-currentratio control method, c. cos δ 1 and constant fluxlinkage control methods, etc.The id 0 control method is a simple and high efficientcurrent control scheme, it doesn’t have demagnetizingeffect without d axis demagnetizing component for thearmature reflect. The performance of PMLSM will not bedeterioration for the demagnetizing phenomenon, so thatthe electromagnetic torque is proportional to the armaturecurrent. It is Te pnψ f iq , in the paper, the systemprinciple of FOC for PMLSM based on id 0 as Fig.2.259forecasted through the current regulator, the PWM signaldrive the inverter to provide the voltage to PMLSM, sothat we can obtain the high efficient control method forPMLSM.B. The Simulation Model of Field Oriented Control forPMLSM.According to the vector control principle, the PMLSMvector control model was established based on PWM, itcontains PMLSM module, the coordinate transformationand inverse transformation from stationary coordinate tosynchronous rotating coordinate, speed regulator loop andcurrent regulator loop, then a dual closed loop vectorcontrol system is built for PMLSM based on PWMcontrol. Its simulation model as Fig.3C. The Principle of Direct Torque ControlThe classical bang-bang control was adopted for thePMLSM direct torque control, as Fig.4. The stator fluxFigure 2. id 0 FOC principle of PMLSMThe control scheme mainly contains several controlmodules. They are stator current detection, rotor positionand speed detection, speed loop regulator, ormation, and voltage PWM control modules. It isrealized as the following procedures, the rotor spaceposition is detected by using sensor, the rotor speed andelectrical angle are calculated, the q axis reference iq* ofstator current is output from the PI speed regulator. Thestator phase current is detected through current sensor. Itis decomposed to obtain the dq axis component id and iq.The space vector voltage dq axis component ud and uq areFigure 4. Direct torque bang-bang hysteresis loop control principlelinkage and torque observe model were established forPMLSM. According to the stator voltage us and rotorposition signal δ sr , the electromagnetic torque Te andFigure 3. The field oriented control simulation model of PMLSM. 2013 ACADEMY PUBLISHER
260JOURNAL OF COMPUTERS, VOL. 8, NO. 1, JANUARY 2013Figure 5 Note how the caption is centered in the column.stator flux linkageψson the static coordinates wereestimated. The controller is contained the stator fluxlinkage, motor torque and speed variable, the settingspeed and stator flux linkage amplitude. The directcontrol was realized through the flux and torque controlsignal and the real position signal of torque angle.According to the flux, torque variable quantity and torqueangle, the proper switch signal was inquired to control theinverter to drive the PMLSM.process, their response state respectively as Fig.6, Fig.7,Fig.8 and Fig.9.Although the simulation experience results have someovershoot, the response of speed and torque are veryquickly, they can recover the setting variety in time andreduce the ripple successfully when the PMLSM isstarting and changing the load. It is showed that thevector control can provide greatly dynamic performancefor PMLSM in Fig.6 and Fig.7.654Speed(m/s)D. The Experiment Simulation of Direct Torque ControlAccording to the vector control principle, the PMLSMvector control model was established based on PWM, itcontains PMLSM module, the coordinate transformationand inverse transformation from stationary coordinate tosynchronous rotating coordinate, speed regulator loop andcurrent regulator loop, then a dual closed loop vectorcontrol system is built for PMLSM based on PWMcontrol. Its simulation model as Fig.52100IV. THE SIMULATION EXPERIMENT OF PMLSM.inductance Ld is 13.91mh, q axis inductance Lq is13.91mh, viscous friction coefficient B is 0.1N · s/m,rotor mass is 96kg, pole pitch τ is 39mm.In the experiment, the given load torque was1000N·M and velocity was 3.0m/s, at 0.2s the loadtorque was changed as 1000N · M, after 0.5s, then thevariable state of speed, torque, stator abc axis current anddq axis current can be obtained along the whole loading 2013 ACADEMY )Figure 6. Speed response of PMLSM.300020001000· m)Torque(NA. The Simulation Experiment of Field Oriented Controlfor PMLSMThe field oriented control of PMLSM based on PWMcan be verified through the experiment simulation. Thesystem simulation parameters are given as follows:Number of pole pairs is 3, flux of permanent magnetψ f is 0.2324Wb, rotor resistance Rs is 1 Ω , d Time(s)Figure 7. Torque response of PMLSM.0.450.5
JOURNAL OF COMPUTERS, VOL. 8, NO. 1, JANUARY 2013261In Fig.8 and Fig.9, we can see the stator current atstaticabccoordinationandsynchronousrotating αβ coordination respectively. It is showed that theq axis current component can separate successfully, sothat we can control the speed and torque directly andobtain perfectly dynamic performance for the PMLSMthrough vector control.40302010( )Current(A)0Figure 10. The flux linkage of DTC for 0.5Time(s)Figure 8. Stator abc axis currentFrom the Fig.11 and Fig.12, although the response hasa certain overshoot, it shows that the speed and torqueresponse are very quickly. At 0.2s, the load was changedsuddenly, it has some ripple, the response can track thesetting variable in time, and the ripple of torque is verylittle.0.30.2· .30.350.40.450.5Time(s)Figure 9. Stator dq axis.currrentFigure 11. Speed response of PMLSMB. The Simulation Experiment of Direct Torque ControlThe direct torque control of PMLSM based on bangbang control can be verified through the experimentsimulation. The system simulation parameters are givenas parameters in simulation A.In the experiment, the given load torque was1000N·M and speed was 3.0m/s, at 0.2s the load torquewas changed as 1000N·M, after 0.5s, then the variablestate of flux linkage, speed and torque can be obtainedalong the whole loading process, their response staterespectively as Fig.10, Fig.11 and Fig.12.In the Fig.10, it showed that the state flux trajectory ofDTC for PMLSM is almost circle although it has someperiod fluctuation, it is mean that the ideal state fluxlinkage trajectory can be obtained
The permanent magnet linear synchronous motor usually can be divided into sine wave driving permanent magnet linear synchronous motor and the square-wave driving permanent magnet Brushless DC motor. In the paper, the two control strategies FOC and DTC were researched for PMLSM driven by three phase sine wave. II. THE MATHEMATICAL MODEL OF PMLSM
1.1 Definition, Meaning, Nature and Scope of Comparative Politics 1.2 Development of Comparative Politics 1.3 Comparative Politics and Comparative Government 1.4 Summary 1.5 Key-Words 1.6 Review Questions 1.7 Further Readings Objectives After studying this unit students will be able to: Explain the definition of Comparative Politics.
"essence" of politics. 3 Comparative studies then is much more than simply a subject of study—it is also a means of study. It employs what is known as the comparative method. Through the use of the comparative method we seek to describe, identify,and explain trends—in some cases, even predict human behavior. Those who adopt
akuntansi musyarakah (sak no 106) Ayat tentang Musyarakah (Q.S. 39; 29) لًََّز ãَ åِاَ óِ îَخظَْ ó Þَْ ë Þٍجُزَِ ß ا äًَّ àَط لًَّجُرَ íَ åَ îظُِ Ûاَش
Collectively make tawbah to Allāh S so that you may acquire falāḥ [of this world and the Hereafter]. (24:31) The one who repents also becomes the beloved of Allāh S, Âَْ Èِﺑاﻮَّﺘﻟاَّﺐُّ ßُِ çﻪَّٰﻠﻟانَّاِ Verily, Allāh S loves those who are most repenting. (2:22
On the other hand, Jean Blondel noted that a primary object of comparative politics is public policy or outcomes of political action. Why we need to study comparative politics? According to Sodaro (2008: 28–29) the main purposes of studying comparative politics are as follows:
the_Olive_Tree for a review. Prof. Paczkowski (Rutgers University) Comparative Economic Systems (362:01) Reading List September 3, 2008 9 / 41. Comparative Economic Systems . A Dictionary of Economics, edited by J. Eatwell, M. Milgate and P. Newman (in Alexander Library reference section). Ledyard, J. O.
is presented in section four. Static and dynamic comparative advantage analysis for India and China individually and within a comparative framework is undertaken in section five. Factor intensity analysis of the comparative advantage of the two economies is presented in section six. Section seven presents the main findings and conclusions.
examinées dans le cadre de l'analyse comparative. 2. Analyse comparative : l'analyse comparative s'est intéressée aux matières sélectionnées du PEI et du GCSE du point de vue de leur cadre d'évaluation et de leurs exigences cognitives. En s'appuyant sur le cadre de référence CRAS (Pollitt et al 2007)1,
