THE 7th STUDENT SYMPOSIUM ON MECHANICAL AND MANUFACTURING ENGINEERING

Control and implementation of a Permanent Magnet Synchronous

Motor in a CowBrush unit

E. Olesen, R. Starup-Hansen, K. Labata

Department of Materials and Production, Aalborg UniversityFibigerstraede 16, DK-9220 Aalborg East, DenmarkEmail: eolese15, rstaru18, klabat18@student.aau.dk,

Web page: http://www.mechman.mp.aau.dk/

AbstractIn this project a study of a previous model of a Cowbrush has been studied in order to optimize its mechanical designand upgrade it so it can be run by a Permanent Magnet Synchronous Motor instead of the previous single phase ACmotor. Besides this, the drive train has also been changed from a worm gear to a 4.5:1 belt drive. This modificationsentail changes in both the electrical part of the system, for which a new inverter had to be designed, and control part,which uses a Digital Signal Processor and Field Oriented Control to control the electromechanical system.

Keywords: Cowbrush, PCB, PMSM, Field Oriented Control, Inverter design

1. IntroductionA recent law in Denmark [1] requires dairy cattle farmsto provide at least one automatic Cowbrush unit per 50cows. The supposed reason for this change is stated inthe article from [2], where a scientific study has showna 30% reduction in mastitis, which is an udder infection.Besides this, it also shows an attractive increase in themilk production, where the best study shows an increaseof one liter of milk per cow per day. On the other handone of the disadvantages of the Cowbrushes is the riskfor the cow to get its tail entangled in the brush andtorn off.

A Danish company called GEA Farm TechnologiesMullerup A/S, provides two different Brush units,namely an E and M-brush. The drive train of GEA’sBrushes has been studied in an earlier semester projectat AAU, where it was found that the drive trainwas inefficient (21%) due to a single phase inductionmachine coupled with a wormgear [3]. The conceptstudy was done for a physical E-brush, that was givento AAU, and can be seen at Fig.1.

Therefore GEA is interested in a new updated Cowbrushversion, where the drive train is replaced with amore efficient concept. Besides the efficiency, a desiredcontrol of the brush also needs to be taken into account.This has lead to the following wishes and requirementsfrom GEA.

Fig. 1 Example of an E-brush already implemented in a farm.

Requirements

• A simple transmission solution with a motor andgear integrated in one unit.

• An improved efficiency.• Voltage- and frequency-independent solution with

a grid connection of 90-265V AC and 50/60Hz.• Universal application.

Wishes

• A transmission system which is not self locking,which allows the cows to disentangle their tails sothey do not get torn off.

• An electrical control that activates the brush when

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the housing is rotated more than 5°, and maintainsa constant brush speed of around 35Rpm.

• A control structure that changes the direction ofrotation at a desired sequence to get an evenly wearof the brush bristles.

• An economically attractive solution that matchesor reduces the original transmission costs.

The article will, in section 2, describe how a mechanicaldrive train is developed whose structure is built such thatit is universal and can be integrated into different units.

In section 3 it will describe how a electrical circuit isdesigned to control a Permanent Magnet SynchronousMotor that drives the mechanical transmission.

In section 4 it will describe how the electromechanicalpower transmission is modelled and how the systemparameters is identified.

In section 5 it will describe how the electromechanicalsystem is controlled, by the use of Field OrientatedControl.

Finally in section 6 a conclusion summarizes theachieved results from the work.

2. Mechanical Concept Design

The concept design is based on a simple functionalanalysis, which is limited to concern a chain/belt trans-mission because of their high efficiency performances[4].

2.1 Transmission principleIn the analysis three different concepts are compared,which are shown at Fig.2.

MM

Brush

MMM

Brush

A) B)

MM

Brush

C)

M

Fig. 2 Transmission principles A, B and C.

On the Fig.2 the M denotes the motor and pulley whichare integrated in one unit. Brush denotes the pulley

that is attached to the brush shaft and thereby rotatesthe brush when the motor rotates.

Of the three principles, the A principle is chosenbecause of the simplicity and number of elements. Here,the tension of the belt/chain can be done with a linearor torsional spring.

2.2 Selection of the beltIt is chosen to use a belt drive instead of a chain drivefor the following reasons: The belt drive is easier tomaintain, does not require the same safety attention,does not need lubricants and can be adjusted to slipif overload is applied to protect the PMSM.

A disadvantage of the belt drive compared to the chainis a better life time and more compact design.

There exist a variety of standard belts which couldbe utilized for the transmission. Here a polyvee beltis chosen, because it has one of the smallest possiblepulley dimensions together with the flat belt and timingbelt. Besides this, it has a higher capacity than a flatbelt and the pulley is easier to manufacture than a gearfor a timing belt.

2.3 Structural ConstructionCAD drawings are developed for the transmissionprinciple, and implemented in the existing housing,which is shown in Fig. 3.

Fig. 3 A close-up of the Cow-housing CAD-drawing withthe mechanical concept implemented

The principle is constructed with a support plateconsisting of a shaft for the motor arm and a tension

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feature where the linear spring can be attached andelongated to a desired tension of the belt.

The motor arm is a simple profile with two tubes ineach end which can be mounted on the shaft from thesupport plate and attached to the PMSM shaft.

Finally, a brush and motor pulley are constructed, wherethe motor pulley is screwed onto the rotor of the PMSM,which is possible since the motor type is an outrunnerwith a stationary shaft in the middle.

The constructed transmission has a gearing ratio of 4.5.

3. Printed Circuit Board Design

The electrical circuit to supply and control the PMSMis designed based on a general inverter, which throughinversion transforms a DC voltage into three sinusoidalvoltages for the PMSM. A general schematic of aninverter is shown at Fig. 4.

A B C

+

-

qA

qA

qB

qB

qC

qC

Fig. 4 A general inverter design for a three phase motor.

It is chosen to design a PCB with the inverter; besidesthis, some extra peripherals for the PCB are needed tobe able to utilize a feedback control of the PMSM. Theoverall functions of the PCB are:

• Position feedback for PMSM by Hall or encodersensors

• Gate drivers for the six external transistors• Acceleration feedback for activation of PMSM

with Gyroscope• Current feedback for the three motor phases for the

FOC control• Plug-in system for DSP to control the different

peripherals

For the design it is chosen to use a chip, which hasthe following functions: it can drive the gates of thetransistors with an input from the DSP, it can providecurrent feedback from the three motor phases and it can

supply the DSP with an integrated buck regulator. Thechip is from Texas Instruments, and has the model nameDRV8353RH [5].

For the half bridges, MOSFETs are used with theTO220 housing to make cooling easy. The half bridgesare placed close to two relatively large (10000uF)capacitors, which are used as a DC-BUS to ensure aripple free potential when fast switching is done. Therest of the components and configurations for the chipcan be found in the project [6]. The complete PCBdesign is shown at Fig. 5.

Fig. 5 A picture of the PCB where the DSP can be pluggedin on the other side.

The STM32F446RE micro-processor is chosen as DSPto control the system. The processor has two advancedcontrol timers which can produce 6 PWM signalsto control the motor, 3 regular and 3 inverted. Theadvanced control timers can also read inputs fromhall sensors. Other functionalities include ADC’s and180MHz clock speed providing good computationalpower.

4. Time Domain Model

To be able to simulate the dynamic and steadystate response of the electro-mechanical system amathematical time domain model has to be established.It begins with a model of the PMSM, which includesa transformation from the physical three phase circuitto a complex space vector orientation. After this, ittranslates the electrical torque from the PMSM into themechanical system, where the PMSM is geared throughthe belt to the brush. The transformations are done withreference to the frame shown at Fig. 6.

3

A

B

C

α

β

θe

dq

Fig. 6 The reference frame for the model of the PMSM.

The three axes A, B and C in figure 6 describe theorientation of the electrical phases for the PMSM,where each phase can be described with the equivalentelectrical circuit shown in Fig. 7.

- +

i ava Ra Laea

- +

i bvb RbLb eb

- +i cvc Rc

Lc ec

n

Lm

Lm

Fig. 7 An electrical schematic of the simplified circuit, withresistors, inductors and emf’s all connected in the star pointn.

To simplify the electric equivalent circuit some assump-tions have been made: The windings resistance, induc-tance and mutual inductance are equal and consideredconstant, the small airgaps between the magnets areneglected, magnetic saturation, reluctance torque andtemperature sensitivity are neglected and the back emfis considered sinusoidal. The voltage equations for eachphase are expressed with (1) to (3).

vAn = RA iA + LAdiAdt

+ Lm (diBdt

+diCdt

)

+ λd

dtcos θe (1)

vBn = RB iB + LBdiBdt

+ Lm (diAdt

+diCdt

)

+ λd

dtcos θe −

2π

3(2)

vCn = RC iC + LCdiCdt

+ Lm (diAdt

+diBdt

)

+ λd

dtcos θe −

4π

3(3)

Where (R) is the resistance, (L) the inductance, (e)the back-emf, (λ) the flux linkage and (θe) the rotorposition.

4.1 Clarke TransformationThe Clarke transformation transforms the referenceframe (A,B,C) into the stator fixed reference frame(α,β). This is accomplished by using the matrix inequation (4).[

kαkβ

]=

2

3

[1 −1

2 −12

0√32 −

√32

] kAkBkC

(4)

Here k is an arbitrary constant such as voltage orcurrent. The Clark transformation can be utilized toreduce the voltage expressions (1) to (3) into a moresimplified notation expressed with (5)

~vαβ = R ~iαβ + (LABC − Lm)d ~iαβdt

+ λ j ωe ejθe (5)

Here LABC and R defines the individual phase resis-tance and inductance. In the next section this expressionis transformed into the rotating reference frame (d,q).

4.2 Park TransformThe Park transformation transform a rotating spacevector in the (α,β) reference frame into a space vector inthe rotating (d,q) frame. The advantage of this is that anyposition dependencies in the equations are cancelled out.The (d,q) frame is rotating with the electrical velocity(ωe). To perform the Park transformation, the rotationmatrix equation (6) is used.[

kdkq

]=

[cos θe sin θe− cos θe sin θe

] [kαkβ

](6)

By applying the transformation to the equation 5 thesimple expression (7) emerges.

~vdq = R ~idq + Ldq(d ~idqdt

+ j ωe ~idq) + j ωe λ

= R ~idq + Ldqd ~idqdt

+ j ωe (Ldq ~idq + λ) (7)

4

This can be expanded to the individual axes of dand q with equation (7) which defines two simpleelectrical circuits with DC signals for the motorsdynamic behavior.

ud = <udq = R id + Lddiddt− ωe L iq (8)

uq = =udq = R iq + Lqdiqdt

+ ωe (L id + λ)

From these electrical circuits a corresponding electro-magnetic torque τe can be described for the PMSM withequation (9).

τe =3λ zp iq

4(9)

This torque is transferred into the mechanical systemwhich will be described in next section.

4.3 Mechanical SystemThe mechanical system consists of the PMSM, thegearing and the brush. The system is described withreference to the motor side of the gearing, so if a loadtorque is applied to the brush it is transferred throughthe gearing to the motor. The resulting moment actingon the mechanical system is modelled as the electricaltorque subtracted from friction losses and a load torquewith equation (10).

dωmdt

Jeq = τe −B ωm + sgn(ωm) τdf −1

Nτload

(10)

Here (B) is the viscous damping coefficient, Jeq isthe equivalent inertia of the system, (τdf ) is the staticfriction of the system, (τload) is a load torque and (ωm)the mechanical velocity.

4.4 Nonlinear and Linear systemsThe model of the electromechanical system can bedescribed with the three differential equations (11) to(13).

dωmdt

=1

Jeq(τe −B ωm + sgn(ωm) τdf ) (11)

diddt

=1

Ldvd −

R

Ldid +

zp2ωm iq (12)

diqdt

=1

Lqvq −

R

Lqiq −

zp2ωm id −

zp2ωm

λ

Lq(13)

By neglecting the nonlinear terms of the equations,a linear model can be obtained which then can betransformed into transfer function with the use of

the Laplace transform. The linear representation isexpressed with (14) to (16).

ωm(s)

iq(s)=

3λ zp4

J s+B(14)

id(s)

vd(s)=

1

Ld s+R(15)

iq(s)

vq(s)=

1

Lq s+R− ωm(s)

vq(s)

zp λ

2Lq(16)

4.5 Parameter IdentificationThe unknown parameters needed to be identified forthe model are: Phase resistance (R), synchronous in-ductance (Ld, Lq), flux linkage amplitude (λ), momentof inertia (J) and friction coefficients (B, τdf ).

4.5.1 Phase resistanceThe phase resistance is determined with a DC source,where the line to line resistance is assumed to be linear.A set of different voltages and currents is collectedand shown at Fig. 8. A proportional regression is thenutilized to indicate the slope, where the phase resistanceis equal to half of the slope which gives 0.22Ω.

0 1 2 3Current (A)

0

0.5

1

1.5

Vol

tage

(V

)

Line ABLine BCLine CAR

m = 0.4346

R2 = 1

Fig. 8 Collected resistans measurements with a proportionalregression.

4.5.2 Synchronous inductanceThe inductances are measured with an AC steady-state impedance method with reference to [7] thatconsist in aligning the PMSM to the q or d-axisand then lock the rotor mechanically. Hereafter, anAC voltage is applied, where two of the phases areconnected to the negative potential and one phase tothe positive. The inductance will consist of 1.5 timesthe phase inductance. By knowing R from the previous

5

experiment and calculating the impedance (Z) with therms values of voltage and current the reactance (X) canbe calculated with equation (17).

X =√Z2 −R2 =

√V 2

I2−R2 (17)

Knowing X and the frequency of the AC signal f theinductance is calculated with equation (18).

L =2

3

X

2π f(18)

The collected measurements for the voltage, current andinductance for the q-axis are shown at Fig. 9 and Fig.10.

0 5 10 15Time 104

-30

-20

-10

0

10

20

30

AC

Vol

tage

(V

)

v1

v2

v3

v4

v5

0 5 10 15Time 104

-5

0

5

AC

Cur

rent

(A)

i1

i2

i3

i4

i5

Fig. 9 Collected measurements for different AC signals with100Hz for the q-axis.

From Fig. 10 it is seen that the tendencies for theinductance are constant. The resulting inductances forboth the d and q-axis are listed in Tab.I.

Frequency Ld Lq Unit100Hz 6.23 6.63 mH500Hz 4.05 4.77 mH

Tab. I The mean inductance for two frequencies and axes.

0 1 2 3 4Rms Current (A)

6

7

8

Indu

ctan

ce (

mH

)

Lq

Fig. 10 Collected measurements for synchronous inductancein the q-axis with 100Hz

4.5.3 Flux Linkage AmplitudeThe flux linkage amplitude λ can be theoreticallycalculated by the peak amplitude (epeak) divided by theelectrical velocity (ωe) as in equation (19).

λ =epeakωe

(19)

It can also be measured by a test where the rotor isrotated with a drill machine, at a constant velocity,where the PMSM is not electrical connected. Therebythe induced voltage from the flux linkage can bemeasured with an oscilloscope, where the inducedphase back emf will be shown if the oscilloscope isconnected to one of the phases and the neutral point.The experimental value found is equal to λ=0.0213Wb.

4.5.4 Moment of inertiaThe equivalent moment of inertia is calculated by theconservation of kinetic energy, where the inertia ofthe structural components is estimated with the CADdrawings. The equivalent inertia for the system is Jeq=0.14kgm2.

4.5.5 Friction coefficientsA run out test is performed for determining the frictioncoefficients. The test is performed by driving theCowbrush with an initial constant angular velocity andthen suddenly turning off the motor, causing the systemto decelerate due to the friction in the system. Bymeasuring the decelerating velocity over time, it ispossible to fit a friction model. The deceleration iscollected for different initial velocities, and comparedto see if the parameters are constant or how much they

6

vary. The values obtained are B = 0.0273NmRad/sand τdf = 0.03Nm.

An example of two velocity profiles and the fitted curvesis shown at Fig. 11.

0 0.1 0.2 0.3Time (s)

0

10

20

30

40

Vel

ocity

(ra

d/s)

fit1V1fit3V3

Fig. 11 Collected velocity measurements for two test withthe corresponding fits.

5. Control Stratey

The control strategy for the system is a Field OrientatedControl (FOC), where a torque control of the motor willbe designed. The torque control is chosen to utilize asmooth operation of the brush even though the loadsfrom the cow are expected to be very irregular.

A block diagram describing the FOC strategy for thesystem is shown at Fig. 12.

PIidref

iqref

M

PI

+-

+-

ed

eq

vd

vq

vα

vβ

SV-PWM

PCB Inver-

ter

A B C

Park

iA

iC

iB

Hall sensors

iα

iβClarke

id

iq

θeωm

Inve-rsePark

Fig. 12 Field Oriented Control structure

Two PI controllers are chosen for the system, which willprovide a constant voltage at steady state and thereby aconstant velocity of the brush.

The torque reference for the PMSM is chosen to belike the original single phase induction machine, where

the torque speed characteristic is approximated with twolinear lines. This is shown at Fig.13.

Te

ωm

OperationRegionRated values

Desired PMSM behaivor

Fig. 13 An illustration of the desired torque speed character-istic for the PMSM.

The operating region for the motor is chosen basedon the wishes from GEA, where a brush operatingvelocity of 35Rpm was desired. Therefore it seemssensible to control the motor with an operating regionof 30-40Rpm for the Brush which geared gives a motorvelocity of 130-180Rpm. Besides this the motor haveto be able to deal with a load of 25Nm in the region,which is a load postulated from the earlier concept study[3]. This has lead to the determination of a maximumoperation torque of 26.4Nm at 30Rpm, which for themotor is equal to 5.88Nm at 130Rpm.

By converting the desired torque speed curve into acurrent speed curve instead, a reference is establishedfor the current controller in the q-axis. This reference isshown at Fig. 14.

Iq

ωm

OperationRegion

15A 11.4A

135 Rpm

180 Rpm

Fig. 14 An illustration of the desired current reference of theq-axis controller depending on the motor speed.

The requirements for the PI controllers are categorizedwith stability and loads. For the stability it is requiredthat the controller is stable but also relatively stablewith a phase margin beyond 45° and a gain margin of

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minimum 8 dB. For the load case, it is required that thecontroller can handle step loads of maximum 26.4Nm,with a maximum percentage error of 5%.

5.1 PI designThe controller is designed for the linear transferfunctions derived in section 4. Here it is chosen to usethe same controller parameters for both the d and q-system. The controllers are tested with an implementedlinear system in SIMULINK which is shown at Fig. 15.

idref

iqref

+-

+-

ed

eq

kp

ki1s

++

vd 1Ls + R

id

kp

ki1s

++

vq 1Ls + R

iq kT1

Js + B

Te+

-

TLoad

ωm

Fig. 15 Block diagram of the linear system.

The general PI controller is expressed with the transferfunction in equation (20) where kp is the proportionalgain and ki is the integral gain.

Gc(s) = kp +Ki

s(20)

The optimal design will be to place the zero upon thepole from the plant and thereby achieve a pure integratorresponse. But this can be difficult to obtain because itmight need a large energy source.

Therefore it is chosen to investigate the largest deceler-ation of the system if a cow applies 26.4Nm modelledas a step. This would give a deceleration of 42s−2. Thisindicates the slope of the change in torque, which needsto be handled by the controller to ensure a track of thereference. Here the initial gains were chosen as 80%of the value for the proportional gain and 20% for theintegral gain which were normalized with respect to theDC gain of the system.

After tuning with the linear model a final set of valueswhere obtained for the controllers, kp = 8.32 and ki=3.75, which simulated results are shown at Fig. 16.

The ki could be increased more, to achieve a smallererror faster, but the controller is capable of tracking thereference within the percentage requirements already soit is left as it is.

0 2 4 6 8 10Time (s)

0

2

4

6

8

10

Tor

que

(Nm

)T

e

TLoad

0 2 4 6 8 10Time (s)

0

5

10

15

Cur

rent

(A)

iq

Ref

Fig. 16 Simulation of final controller parameters; Top: Plotof the iq current and the reference. Bottom: the developedelectromechanical torque and applied load step.

5.2 Discrete SystemThe continuous system needs to be transformed into adiscrete system, because the DSP cannot handle con-tinuous time signals. The discrete system is developedwith the method of emulation, where the continuouscontroller and plant is mapped into the z-domain. Herethe important parameter is the sampling time (Ts),because this time can make a s-stable controller z-unstable. The sampling time for the system will bechosen with a rule of thumb, that says that the samplingfrequency should be ten times faster than the bandwidth.In this case it will require a sampling frequency of 2kHz.The discrete open loop transfer function for the systemis expressed with equation (21).

G(z) =

(kp +

T ki (z + 1)

2 z − 2

)kDC

1− e−T

z − e−RL T

(21)

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5.2.1 Difference equationsThe z-domain controller needs to be described as adifference equation to be able to implement it on theDSP. The controller pulse transfer function for thecontroller is expressed with equation (22).

M(z)

E(z)= kp 2 z − 2 kp + T ki z + T ki (22)

By rearranging the expression and division with z it canbe transformed into a difference equation like equation(23).

m(kT ) = kp e(kT )− kp e(kT − 1) +1

2ki e(kT )

(23)

+1

2T ki e(kT − 1) +m(kT − 1)

The expression is used for both the d and q axiscontroller in the DSP, where Ts = 0.0005s. Besides thisa saturation limit is also used in the DSP to ensure thatthe integrator part does not windup.

6. Conclusion

The conclusion is based on the workload for the projectwhich is referred to with [6].

The original E-brush power transmission was found tobe inefficient due to the single phase induction motorwhich was coupled with a worm gear. Therefore a newconcept design had to be developed.

A simple functional analysis was performed, which wasbased on a belt/chain driven drive train. Here, a conceptdesign with a polyvee belt drive was developed, witha tension mechanism. The chosen belt gearing wasdesigned to exploit the housing in the best possible way,which lead to a gearing ratio of 4.5. The performanceof the polyvee belt has an efficiency of almost 100%.Finally, the concept was constructed such that thePMSM and the belt drive could be mounted on a supportplate which is universal for other Cowbrush units asdesired.

An already existing converter was utilized to convertthe grid line voltage into a DC supply voltage for theelectrical circuit.

It can be concluded that a Printed Circuit Board (PCB)was developed, which theoretically can invert a DCsource of 10 to 100V with a variable frequency upto 20kHz. It can also be concluded that the PCB canobtain feedback signals from a PMSM, for both current

measurements of each phase and position measurementsfrom a hall/ encoder sensor. The PCB was designedto fit together with a DSP from STM, which couldcontrol the peripherals of the PCB, consisting of the gatedrivers for the external MOSFETs, the Gyroscope forthe activation, the current and position feedback signalsand the FOC control strategy for the PMSM.

It can be concluded that a nonlinear model of theCowbrush unit was established, which included anelectrical model of the PMSM and a mechanical modelof the drive train.

It can be concluded that the electrical model transformthe three phase circuit into a rotor fixed circuit of twocomponents instead. This transformation is done with aClarke and a Park transformation.

It can be concluded that the nonlinear model parametersare obtained through laboratory test, to be able tosimulate the dynamic and steady state responses ofthe system. With the experimental tests the parameterswhere found which is listed in Tab. II.

Parameters ValuesR 0.22ΩL 4 - 6.3mHλ 0.0216WbJ 0.14 kg m2

B 0.0273 Nm Rad/sτdf 0.03Nm

Tab. II Model parameters obtained through experimentaltest.

The nonlinear model was transferred into linear transferfunctions by neglecting the nonlinear couplings. Thetransfer functions where studied, where it was foundthat they both where stable. Besides this the sensitivityof the electrical system was investigated, which showedthat the variation in the resistance could be neglectedand that the variation in the inductance could changethe system significantly.

It can be concluded that a FOC control strategywas developed for the model, where two linear PIcontollers are designed. The resulting parameters forthe controllers was a proportional gain of 8.32 and aintegral gain of 3.75. These parameters was tested in thenonlinear and linear models, where it can be concludedthat they meet the requirements.

AcknowledgementThe authors of this work gratefully acknowledge

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Grundfos for sponsoring the 7th MechMan symposium.

References[1] Dyrlæger og ko, Lov om hold af malkekvæg -

hvilke nye regler træder i kraft pr. 1. juli 2016?Dyrlæger og ko, 2019. Visited 2019-11-04.

[2] Eric Metzger, Making the case for cow brushes.Progressive Dairyman, 2019. Visited 2019-11-04.

[3] F. C. A. L. A. T. S. Borup, M. Brandt, “Conceptstudy of pm synchronous motor drive system incow brush application,” Mechman, April 2019.

[4] P. R. N. Childs, Mechanical design engineeringhandbook. Elsevier Science and Technology, 2013.

[5] TEXAS INSTRUMENTS, DRV835x 100-VThree-Phase Smart Gate Driver, 2019.

[6] K. L. E. Olesen, R. Starup-Hansen, “Control andimplementation of a permanent magnetsynchronous motor in cowbrush unit,” Mechman,May 2019.

[7] W. L. Soong, “Inductance measurements forsynchronous machines,” Power EngineeringBriefing Note Series, April 2019.

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