Control System of Permanent Magnet Synchronous Motor for

9 49 49 49 49 4 QR of RTRI, Vol. 41, No. 2, Jun. 2000

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Control System of Permanent Magnet Synchronous Motor forControl System of Permanent Magnet Synchronous Motor forControl System of Permanent Magnet Synchronous Motor forControl System of Permanent Magnet Synchronous Motor forControl System of Permanent Magnet Synchronous Motor for Railway V Railway V Railway V Railway V Railway Vehicle Tehicle Tehicle Tehicle Tehicle Traction.raction.raction.raction.raction.

Keiichiro KONDOKeiichiro KONDOKeiichiro KONDOKeiichiro KONDOKeiichiro KONDOEngineer, Electric Drive Systems G.,Vehicle Technology Development Div.,

Technological Development Dept.

Koichi MAKoichi MAKoichi MAKoichi MAKoichi MATSUOKATSUOKATSUOKATSUOKATSUOKAChief Engineer, Electric Drive Systems G.,

Vehicle Technology Development Div.,Technological Development Dept.

Abstract: We have been studying the application of a permanent magnet synchronousmotor (PMSM) for railway vehicle traction in order to reduce the weight and size of directdrive traction motors. As a part of this study, it is required to establish a current controlsystem of PMSM suitable for railway vehicle traction. In this paper, we discuss the currentcontrol system mentioned above and suggest a method which is available under the conditionof railway vehicle traction. Next we investigate how to decide the current response timeconstant Td and reach a conclusion that about 10ms is appropriate under some assumedconditions. Then we check this current control system, when used for railway vehicle traction,through experiments and studies on influence of parameter changing and sudden changes inthe line voltage. Finally we can conclude that the current control system has satisfactoryperformance for railway vehicle traction.

keyword:keyword:keyword:keyword:keyword: permanent magnee synchronous motor, vector control, vehicle traction

1. Introduction1. Introduction1. Introduction1. Introduction1. Introduction

The electrical motor traction force is usually trans-mitted to wheels via reduction gears in the electrical rail-way traction system. The reduction gears reduce the re-quired traction motor torque and enable down-sizing ofthe traction motor , though they cause noise and necessi-tate maintenance and a complicated truck construction.To solve this problem, the authors have studied a wheelmounted motor which can transmit traction force to wheelswithout using reduction gears1) 2) 3). On the other hand,the direct drive motor tends to become larger in mass andsize because it is required to have more torque than thetraction motor with gears. So we decided to apply a highefficiency permanent magnet synchronous motor to thewheel mounted traction motor and eventually intend toreduce its mass and size. Nobody has ever experiencedpermanent magnet synchronous motor traction for rail-way vehicles and consequently there is a difficult prob-lem to be solved, which is to establish a permanent mag-net synchronous motor control system for railway vehicletraction.

In this paper, first we will discuss an appropriatemain traction circuit system from the viewpoint of powerconversion. Then we will suggest and examine a currentregulation system (ACR) which is capable of high perfor-mance current control even with a much lower performancetraction inverter than an inverter for general use. In ad-dition, we will show that the suggested traction controlsystem is sufficient in practical use through an analysisof operation status under the condition of actual railwayvehicle traction, for instance, parameter changing in thetraction motor as a control object or sudden changes inthe line voltage.

2. Construction of main tract ion c ircuit and2. Construction of main tract ion c ircuit and2. Construction of main tract ion c ircuit and2. Construction of main tract ion c ircuit and2. Construction of main tract ion c ircuit andcontrol system.control system.control system.control system.control system.

2.1 Main traction circuit study2.1 Main traction circuit study2.1 Main traction circuit study2.1 Main traction circuit study2.1 Main traction circuit study

Table 1 shows the candidates for the power conver-sion method and their features, which would be useful forpermanent magnet synchronous motor traction. A cur-rent source inverter4) or cycroconverter5), both of whichconsist of thyristers , are utilized for the synchronousmotor drive before large-scale switching devices, for in-stance GTO or IGBT which turns off by itself, were devel-oped. We currently use GTO or IGBT and the inverterswhich consist of those devices are utilized broadly for in-duction motor drive. As is shown in Table 1, from theviewpoint of down sizing and mass product effect, we con-sider that voltage source inverters (VSI) would suit thePMSM drive for railway vehicle traction.

2.2 Control system study2.2 Control system study2.2 Control system study2.2 Control system study2.2 Control system study

For railway vehicle traction, motor drive system re-quirements are:

- Accurate and rapid torque (de-facto current) control.- Stability for sudden changes in the line voltage andwheel slip/skid.- Easiness to manage the harmonic line current causedby PWM.

On the other hand, there will be two control methodsfor the AC motor drive with VSI, as shown in Fig.1. Oneis the field orientation control with de-coupling compen-sation on the dq coordinate system which synchronizeswith the field flux. The other is a method in which theswitching pattern is decided directly to reduce the errorof current. In the former method, the inverter outputs avoltage vector, which is obtained as a result of current

9 59 59 59 59 5QR of RTRI, Vol. 41, No. 2, Jun. 2000

regulation, by means of sinusoidal and triangle carriercomparison PWM. This control method is easy to designand tune because of the linear control system and facili-tates the estimation of harmonic currents because thePWM control of inverters is basically independent of thecurrent regulation. Although the latter method could besimpler than the former, on the other hand, the PWM isintegrated into the current regulation system and it makesthe estimation of harmonic currents difficult.

Through the study mentioned above, we consequentlyreached a conclusion to adopt the field orientation controlmethod with the feed back current error and feed forwardcompensator.

2.3 Detection of rotor angle2.3 Detection of rotor angle2.3 Detection of rotor angle2.3 Detection of rotor angle2.3 Detection of rotor angle

The field flux direction has to be detected as a ro-tor angle in the field orientation control in PMSM. Forthis purpose, an optical or magnetic encorder and a wind-ing type resolver have been applied. But they don’t suitmounting on railway vehicles for which anti-vibration andall-weather operation is required. To meet the require-ments, we have developed a down-sized VR resolver, whichhas no windings on the rotor. The VR resolver detectsrotor angles by the changes in the reactance between theexciting and output windings according to the rotor angle.

2.4 Structure of control system2.4 Structure of control system2.4 Structure of control system2.4 Structure of control system2.4 Structure of control system

The structure of PMSM control system which is ob-tained through the study mentioned above is shown inFig.2. This is an individual drive system, where eachinverter drives each PMSM, to control PMSM in synchro-nization with the rotor frequency. Therefore, a three-levelIGBT inverter is suitable for the PMSM drive from the

1) Self commutated type voltage source inverter Advantages are : - Adaptive voltage and adaptive frequency by itself. - Small size commutated circuit - rich technical experience for induction traction motor drive. Disadvantages are : - Rather complicated construction of circuit. - Expense of semiconductor device and its driver circuit

2) DC chopper or Rectifier and current source4) inverter commutated by e.m.f Advantages are : - Simplified main circuit. - No need for main commutation circuit. - Low cost in semiconductor device and its driver circuit. - An experience in TGV-At in France. Disadvantages are : - Requirement of two power converters. - Requirement of large scale reactor as a current source. - Requirement of auxiliary commutation circuit. - No experience in domestic railway operator.

3) Cycro converter5)

Advantages are : - No need for main commutation circuit. - An experimental experience in Japan National Railways. Disadvantages are : - Complicated main circuit, which includes two sets of rectifier con-nected by a reactor.

TTTTTable 1 Candidates of power conversion methodable 1 Candidates of power conversion methodable 1 Candidates of power conversion methodable 1 Candidates of power conversion methodable 1 Candidates of power conversion methodand thei r featuresand thei r featuresand thei r featuresand thei r featuresand thei r features

Fig. 1 Candidates of current control systemFig. 1 Candidates of current control systemFig. 1 Candidates of current control systemFig. 1 Candidates of current control systemFig. 1 Candidates of current control system

(b) Current error compensat ion method wi th de-(b) Current error compensat ion method wi th de-(b) Current error compensat ion method wi th de-(b) Current error compensat ion method wi th de-(b) Current error compensat ion method wi th de-coupl ing compensatorcoupl ing compensatorcoupl ing compensatorcoupl ing compensatorcoupl ing compensator

(a) Direct switching control method(a) Direct switching control method(a) Direct switching control method(a) Direct switching control method(a) Direct switching control method

Fig. 2 A construction of control systemFig. 2 A construction of control systemFig. 2 A construction of control systemFig. 2 A construction of control systemFig. 2 A construction of control system


Fig. 3 ACR with command current de-coupl ingFig. 3 ACR with command current de-coupl ingFig. 3 ACR with command current de-coupl ingFig. 3 ACR with command current de-coupl ingFig. 3 ACR with command current de-coupl ing

Fig. 4 Components of voltage vector (Fig. 4 Components of voltage vector (Fig. 4 Components of voltage vector (Fig. 4 Components of voltage vector (Fig. 4 Components of voltage vector (id = 0 A rating rating rating rating ratingp o i n t )p o i n t )p o i n t )p o i n t )p o i n t )

viewpoint of the current capacity of semiconductor devices.The rotor angle which is detected by the VR resolver isconverted into a digital angular signal by the R/D con-verter to be utilized for coordinate transformation be-tween dq coordinates and three phases and for calcula-tion of rotating velocity. It is the traction motor torque Tmand terminal voltage Vm in the high speed range thatconsequently have to be controlled for railway vehicle trac-tion. At the current command production part, generatedare a torque current command iq

*, which makes the torquecommand Tq

* follow the actual torque Tm and a flux cur-rent command id

*, which makes the terminal voltage com-mand Vm

* follow the actual terminal voltage Vm , which arebased on the operation command from the cab. At thecurrent regulation part, a de-coupling is performed by theirfeed forward control and the current errors are regulatedby this feed back in order for actual currents id and iq tofollow the current commands id

* and iq*. In the voltage

vector as an output of ACR part, the amplitude of voltagevector is used for producing a modulation issue with thefilter capacitor voltage and converted into signal wavesfor PWM control. As a result of PWM control, gate pulsesare generated to control the ON-OFF status of each in-verter.

3. Construction of ACR3. Construction of ACR3. Construction of ACR3. Construction of ACR3. Construction of ACR

3.1 Construction of ACR3.1 Construction of ACR3.1 Construction of ACR3.1 Construction of ACR3.1 Construction of ACR

The construction of ACR, which is obtained in chap-ter 2, is shown in Fig. 3. As the eq.(1) indicates, an inter-ference is caused between d axis and q axis by an arma-ture reaction in PMSM.

Eq. (2) expresses that id and iq need to be regulatedindependently, precisely and rapidly without any inter-ference so that Tm is controlled precisely and rapidly. Torealize the independence of the currents, the de-couplingcontrol is performed.

0d m d q d

q d m q q f

v r sL L iv L r sL i

ωω ωΦ+ −

= + + ○ ○ ○ ○ (1)

{ ( ) }m f d q d qT p L L i iΦ= + − ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ (2)

wherevd: Voltage d axis component.vq: Voltage q axis component.

id: Current d axis component.iq: Voltage q axis component.ω: Electrical angular velocity.rm : Armature winding resistance.Ld: D axis inductance.Lq: Q axis inductance.φf: PMSM emf. constant.p: Pole pair.s: Differencial operator.

At the inverter for railway vehicle traction, 1-pulsemode, in which a rectangular wave comes at about a halfof each fundamental wave period, is introduced, so thatthe voltage efficiency is improved; switching loss is re-duced and consequently a down-sized drive system isachieved. The digital control period for ACR is longerthan several hundred micro seconds so that both high con-trol performance and low cost are realized.

On the other hand, as shown in Fig.4, most of voltagevector elements consist of de-coupling control components.For this reason, in the de- coupling control with actualcurrent in the 1-pulse mode range, a delay caused by thecurrent calculation and a harmonic current due to the 1-pulse mode may degrade the control performance andsometimes trigger off an unstable phenomenon on thecurrent regulation.

To cope with this problem, we suggest and introduce ade-coupling control method with a current command in-stead of actual currents where a current regulation delayGp(s) is taken into account.

3.2 ACR Designing method3.2 ACR Designing method3.2 ACR Designing method3.2 ACR Designing method3.2 ACR Designing method6)6)6)6)6)

From Fig. 3, the output voltage vector of the ACR [vdvq] is given by the following equations.

* *

* *

( )( ) ( ) 0

( ) ( )( )d PId d d q p q

q fd p d PIq q q

v G s i i L G s iv L G s i G s i i

ωωΦω

− − = +

− (3)

where GPId(s) = Kpd+Kid / s GPIq(s) = bKpq+Kiq / s Gp(s) = 1/(1+sTd) expresses a current control response.Consequently, the a following equation is obtained.

*

*

( ) 00 ( )

d p d

q p q

i G s ii G s i

=

○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ (4)

The following GPId(s) and GPIq(s) are introduced fromthe eq.(1), eq.(3) and eq.(4).


( ) ( )( )

1 ( )p md

PIdp

G s Z sG s

G s=

− ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ (5)

( ) ( )( )

1 ( )p mq

PIqp

G s Z sG s

G s=

− ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ (6)

Eq.(5) and eq.(6) indicate that the current control re-sponse is Gp(s), if the compensator GPId(s) and GPIq(s) aredesigned to satisfy eq.(5) and eq.(6). Here Gp(s) is givenas a control specification by the designer. In consider-ation of the convenience in designing a major control loop,which will be mentioned in the next paragraph, and in theanalysis of its characteristics, a torque control systemwould be better as a one-order delay system with a timeconstant Td. If Gp(s) is a one-order delay system with atime constant, compensators on ACR would be PI com-pensators in eq.(7) and eq.(8) which consist of motor con-stants and Td , given by the following formulas.

id

PId pdKG Ks

= +○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ (7)

iqPIq pq

KG K

s= +

○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ (8)

Where

/pd d dK L T= /id m dK r T= /pq q dK L T= /iq m dK r T=

According to the above discussion, if the ACR is con-structed as shown in Fig.3, the current control responsecan be one order delayed with a time constant Td , evenwhen an inverter with long control period is used and acurrent with much harmonics drives the motor.

3.3 Designing method to decide the current control3.3 Designing method to decide the current control3.3 Designing method to decide the current control3.3 Designing method to decide the current control3.3 Designing method to decide the current controlresponse time constant response time constant response time constant response time constant response time constant TTTTTddddd

The current control response should be decided in con-sideration of the following major control system charac-teristics.

(a) Slip and re-adhesion control loop(b) Regenerating brake control under a light consum-ing load condition.(c) Depressing instability at sudden line voltagechanges.

Because the response time constant for the above (a)and (b) is about several hundred miliseconds, 10ms areenough for Td even in consideration of the above (c).

On the other hand, when Td gets smaller, we have topay attention to the following.

(a) Switching frequency for PWM.(b) Control operating period(c) A voltage margin for current control in the weaken-ing flux control range.

Because of (a) and (b) among the restrictions, Td needsto be longer than a few mili seconds. In addition, Td mustbe longer than 8 ms to secure a voltage margin for currentcontrol under the condition of DC 1500 V inverter voltage.

In consideration of the above required control perfor-mance and restrictions, Td =10ms is appropriate for de-signing the time constant for ACR.

4. Characteristics analysis on suggested control4. Characteristics analysis on suggested control4. Characteristics analysis on suggested control4. Characteristics analysis on suggested control4. Characteristics analysis on suggested controls y s t e ms y s t e ms y s t e ms y s t e ms y s t e m

4.1 A study of parameter changing4.1 A study of parameter changing4.1 A study of parameter changing4.1 A study of parameter changing4.1 A study of parameter changing

ACR shown in Fig. 3 includes rm, Ld and Lq at respec-tive gains. On the other hand, motor constants havechanged by its temperature or flux. Thus it is necessaryto study the effect of ACR for different parameter values.A roots (p1~p6) and zeros (z1~z5) locus of ACR system isshown in Fig.5 in the case where rm changes between 0.5and 1.5 time the nominal rm. At the nominal condition, allpoles except the pole 0.01+j0.0 which expresses one-orderdelay response with Td=10ms overlap zeros and one orderdelay response on ACR is realized by a zero pole cancella-tion. When rm changes, zeros move and can’t depress poles,which consequently cause a reduction of control perfor-mance in ACR. However, as is shown by Fig. 5, the changeof rm barely affects the current control response.

Fig. 6 shows roots and zeros locus of ACR system inthe case where Ld and Lq change between 0.5 and 1.5 timesthe nominal Ld and Lq. According to this result, the induc-tance changes due to magnetic saturation highly influ-ence the current control because the values of inductanceare used for de-coupling control. To cope with this prob-lem, we can apply a method to compensate the valuesused for controller according to the motor current.

Fig. 5 Root and zero locus in changing Fig. 5 Root and zero locus in changing Fig. 5 Root and zero locus in changing Fig. 5 Root and zero locus in changing Fig. 5 Root and zero locus in changing rm

Fig. 6 Root and zero locus in changing Fig. 6 Root and zero locus in changing Fig. 6 Root and zero locus in changing Fig. 6 Root and zero locus in changing Fig. 6 Root and zero locus in changing Ld and and and and and Lq


TTTTTable 2 Specif icat ion for stat ic testable 2 Specif icat ion for stat ic testable 2 Specif icat ion for stat ic testable 2 Specif icat ion for stat ic testable 2 Specif icat ion for stat ic test

Fig. 8 A test result of current step responseFig. 8 A test result of current step responseFig. 8 A test result of current step responseFig. 8 A test result of current step responseFig. 8 A test result of current step response(at 25% rat ing speed, asynchronous PWM mode)(at 25% rat ing speed, asynchronous PWM mode)(at 25% rat ing speed, asynchronous PWM mode)(at 25% rat ing speed, asynchronous PWM mode)(at 25% rat ing speed, asynchronous PWM mode)

4.2 Stability against line voltage sudden changes4.2 Stability against line voltage sudden changes4.2 Stability against line voltage sudden changes4.2 Stability against line voltage sudden changes4.2 Stability against line voltage sudden changes

Fig. 7 shows the root locus of the drive system includ-ing the controller for line voltage sudden change while thetrain speed is increased to 150km/h. In any speed range,all poles are on the left side of the imaginary axis on thecomplex plane. This means that the suggested controlsystem can depress the unstable behavior without mak-ing the main traction circuit unstable even in case theline voltage suddenly changes.

In addition to the above mentioned test results, wechecked whether the field flux e.m.f can be depressed bythe feed forward compensation even in the range of 1´-pulse mode.

From the above mentioned results we verified thesuggested control system and the designing method.

5.2 5.2 5.2 5.2 5.2 Practical test for vehicle drive characteristics.Practical test for vehicle drive characteristics.Practical test for vehicle drive characteristics.Practical test for vehicle drive characteristics.Practical test for vehicle drive characteristics.

To verify the actual vehicle drive characteristics, twoPMSMs for one bogie are equipped on 3-car test vehiclesand a running test is performed at speeds up to 80km/hunder DC 1500V feeding condition. 70kW outer roter typePMSMs are used on the test bogie and a DC motor are onthe other traction bogies.

Fig. 10 shows the result of powering and regeneratingtests together with the traction of DC motors originallyequipped on the other bogies. Smooth acceleration anddeceleration can be seen and the actual acceleration valuesatisfies the specified value.

In addition to the test result mentioned above, testswere performed, including a light consumption load re-generative brake control test and a starting test in thebackward moving condition for some functions specifiedto railway vehicle traction, and we obtained satisfactorytest results.

6. Conclusions6. Conclusions6. Conclusions6. Conclusions6. Conclusions

We made it clear that the permanent magnet syn-chronous motor drive system which is obtained through

Fig. 7 Root locus for l ine voltage sudden changeFig. 7 Root locus for l ine voltage sudden changeFig. 7 Root locus for l ine voltage sudden changeFig. 7 Root locus for l ine voltage sudden changeFig. 7 Root locus for l ine voltage sudden change

(Traction motor)Formula : wheel mounted type permanent mganet synchronous motorType : RMT3Rating : 900V-60A-50Hz-750rpm-80kW-8poleConstant rm = 0.1 ohm Ld = Lq = 10.3 mH(Load equipment)Load : 425 kW DC generatorPower consuming : load resistance(Inverter)Formula : IGBT 3 step PWM VSIMax. rating : 210kVA-1100V-200APWM : asynchronous PWM carrier 500Hz synchronous 1´-pulse(Control system)Control operation period Ts = 1.0msCurrent response time constant Td = 1.0ms

5. Practical test for the suggested control system5. Practical test for the suggested control system5. Practical test for the suggested control system5. Practical test for the suggested control system5. Practical test for the suggested control system

5.1 Practical test for the suggested current5.1 Practical test for the suggested current5.1 Practical test for the suggested current5.1 Practical test for the suggested current5.1 Practical test for the suggested currentcontrol systemcontrol systemcontrol systemcontrol systemcontrol system 7)7)7)7)7)

We carried out tests to verify the designing methodfor the suggested ACR which is discussed in chapter 2with the equipment shown in Table 2. Fig. 8 shows thetest result of current step response from 100% rating ofthe q axis current to 125% at 25% of the rating revolutionspeed. As a result, a one-order delay current responsewith Td=10ms is realized without any interference to thed axis current, as is designed. In Fig. 9, even in the 1-pulse mode, the current response as designed can also beseen.


ReferencesReferencesReferencesReferencesReferences

1) Koichi Matsuoka, et al: “Development of Direct DriveMotor for Next Generation Commuter Train (OuterRotor PMSM)(in Japanese)”, Proceedings of RotaryMachinery Study Meetings of IEEJ, RM-97-127,pp.111-116, 1997

2) Koichi Matsuoka: “F-Development of Wheel mountedType Traction Motor -A Novel Drive System withoutReduction Gears”, RRR, Vol.56, No.2, pp.16-21, 1999

3) Koichi Matsuoka: “F-Development of Wheel mountedType Traction Motor for Railway Vehicle Traction(inJapanese)”, Proceedings of Traffics and Electrical Rail-ways Study Meetings of IEEJ, TER95-103, 1995

4) Lacote: “The New generation of SNCF high-speed roll-ing stock Atlantic TGV rollong stock(in Japanese)”,REVUE GÉNÉRALE DE CHEMINS DE FER 106e

ANNEE, GAUTHIER-VILLARS, pp.61-72, 19875) Takuji Sasaki: “Development of AC Traction Motor -

A Memory of the running test with actual vehicle anddevelopment of Brashless Motor(in Japanese)”, Rail-way Pictorial, No.551, 1991

6) Keiichiro Kondo, et al: “A Designing Method in Con-trol System of Permanent Magnet Synchronous Mo-tor for Railway Vehicle Traction(in Japanese)”, Trans.of IEEJ A Publication of Industry Applications Soci-ety, Vol.118-D, No.7/8, pp.900-907, 1998

7) Keiichiro Kondo, et al: “Stability Analysis of Perma-nent Magnet Synchronous Motor Drive System forRailway Vehicle Traction under Line VoltageChange(in Japanese)”, Trans. of IEEJ A Publicationof Industry Applications Society, Vol.118-D, No.7/8,pp.900-907, 1998

Fig. 9 A test result of current step responseFig. 9 A test result of current step responseFig. 9 A test result of current step responseFig. 9 A test result of current step responseFig. 9 A test result of current step response(at 100% rat ing speed, 1´-pulse mode)(at 100% rat ing speed, 1´-pulse mode)(at 100% rat ing speed, 1´-pulse mode)(at 100% rat ing speed, 1´-pulse mode)(at 100% rat ing speed, 1´-pulse mode)

Fig. 10 A test result of traction test with an actualFig. 10 A test result of traction test with an actualFig. 10 A test result of traction test with an actualFig. 10 A test result of traction test with an actualFig. 10 A test result of traction test with an actualtes t veh ic letes t veh ic letes t veh ic letes t veh ic letes t veh ic le

the above discussions has appropriate performance forrailway vehicle traction. A summary of the results of thisstudy is as follows.

(1) It is clear that the vector control with a voltagesource inverter has various advantages as a railwayvehicle drive system of permanent magnet synchronousmotor.(2) We suggested ACR with de-coupling compensatorwhich consists of current commands and one-order de-lay element, and a designing method to apply it to ve-hicle traction.(3) We analyzed the influence of the suggested controlsystem for different parameter values and line voltagesudden changes and analyzed its characteristics.(4) We made practical tests of the suggested system ona test plant and on an actual vehicle to verify that thesuggested system performed as designed.

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Control System of Permanent Magnet Synchronous Motor for