1

Simulation of A

PMSM Motor Control System

for EPS Controllers

July 23, 2003

by

Guang Liu

Alex Kurnia

Ronan De Larminat

2

OUTLINE

1. Introduction

2. System block diagram

3. Simulink models of system elements

4. Simulation and experimental results

5. Conclusion

3

1. INTRODUCTION

4

1. INTRODUCTION

Simplified Block Diagram of An EPS System

EPS

Steering
mechanism

5

2. SYSTEM BLOCK

DIAGRAM

6

2. SYSTEM BLOCK DIAGRAM

7

3. SIMULINK MODELS OF SYSTEM ELEMENTS

3. SIMULINK MODELS OF

SYSTEM ELEMENTS

8

3. SIMULINK MODELS OF SYSTEM ELEMENTS

Permanent Magnet Synchronous Motor (PMSM) Model

9

q

dt

d

e

q

d

dt

d

d

d

s

d

i

L

i

L

i

R

v

ω

−

+

=

)]

3

4

cos(

)

3

2

cos(

cos

[

3

2

π

θ

π

θ

θ

−

+

−

+

=

c

b

a

d

v

v

v

v

)]

3

4

sin(

)

3

2

(

sin

sin

[

3

2

π

θ

π

θ

θ

−

−

−

−

−

=

c

b

a

q

v

s

v

v

v

PM

e

d

dt

d

e

d

q

dt

d

q

q

s

q

i

L

i

L

i

R

v

λ

ω

ω

+

+

+

=

]

)

(

[

2

3

q

d

q

d

q

PM

e

i

i

L

L

i

P

T

−

+

=

λ

m

m

f

L

e

dt

d

J

K

T

T

ω

ω

+

+

=

θ

θ

sin

cos

q

d

a

i

i

i

−

=

)

3

2

sin(

)

3

2

cos(

π

θ

π

θ

−

−

−

=

q

d

b

i

i

i

)

3

4

sin(

)

3

4

cos(

π

θ

π

θ

−

−

−

=

q

d

c

i

i

i

3. SIMULINK MODELS OF SYSTEM ELEMENTS

Permanent Magnet Synchronous Motor (PMSM) Equations

D-Q axis electric circuit equations

Park transformation equations

Torque equations

Inverse Park transformation equations

10

3. SIMULINK MODELS OF SYSTEM ELEMENTS

Motor Position Sensor Model

Complete Sensor:

Error generator:

11

3. SIMULINK MODELS OF SYSTEM ELEMENTS

Current Sensing Model

V

αβ

V_A

V_B

V_C

V1

V2

V3

(3)

(1)

(5)

(4)

(6)

(2)

12

3. SIMULINK MODELS OF SYSTEM ELEMENTS

PI Controller Model

13

3. SIMULINK MODELS OF SYSTEM ELEMENTS

Inverse Park and SVM Model

14

4. SIMULATION & EXPERIMENTAL RESULTS

4. SIMULATION AND

EXPERIMENTAL RESUTLS

15

4. SIMULATION & EXPERIMENTAL RESULTS

0

0.5

1

1.5

2

2.5

3

3.5

4

0

0.5

1

1.5

T

o

rque

(N

.m

.)

Time (Sec.)

Resolution = 6 count per rev.

0

0.5

1

1.5

2

2.5

3

3.5

4

-30

-20

-10

0

10

20

30

P

h

a

s

e

c

u

rre

n

t (A

)

Time (Sec.)

Simulated torque ripple with 6-count resolution

Torque ripple = 1 N.m., current becomes square wave.

16

4. SIMULATION & EXPERIMENTAL RESULTS

Simulated torque ripple with 48-count resolution

0.5

1

1.5

2

2.5

3

3.5

4

0.985

0.99

0.995

1

1.005

T

o

rque(N

.m

.)

Time (Sec.)

Resolution = 48 count per rev.

0

0.5

1

1.5

2

2.5

3

3.5

4

-30

-20

-10

0

10

20

30

P

h

a

s

e c

u

rrent

(A

)

Time (Sec.)

Torque ripple = 0.012 N.m.

17

0.5

1

1.5

2

2.5

3

3.5

4

0.996

0.998

1

1.002

To

rq

u

e

(N

.m

.)

Time (Sec.)

Resolution = 4096 count per rev.

0

0.5

1

1.5

2

2.5

3

3.5

4

-30

-20

-10

0

10

20

30

P

h

as

e c

u

rr

ent

(A

)

Time (Sec.)

4. SIMULATION & EXPERIMENTAL RESULTS

Simulated torque ripple with 4096-count resolution

Torque ripple = 0.006 N.m.

18

4. SIMULATION & EXPERIMENTAL RESULTS

Measured torque ripple with 48-count resolution

Phase A current is 10A/div. Average torque = 1.05 N.m.
Torque ripple = 0.023 N.m. (peak to peak)

19

0.5

1

1.5

2

2.5

3

3.5

4

0.435

0.44

0.445

0.45

0.455

0.46

0.465

T

o

rque(

N

.m

.)

Time (Sec.)

Current sense error = 0.15 (A)

0

0.5

1

1.5

2

2.5

3

3.5

4

-15

-10

-5

0

5

10

15

M

o

to

r c

u

rr

e

n

t (A

)

Time (Sec.)

4. SIMULATION & EXPERIMENTAL RESULTS

Simulated current sensing with 0.15A error

3-per-rev torque ripple is about 0.017 N.m

20

4. SIMULATION & EXPERIMENTAL RESULTS

Measured torque ripple with current sense error

3-per-rev torque ripple is about 0.020 N.m
Phase A current is 10A/div.

21

4. SIMULATION & EXPERIMENTAL RESULTS

Measured torque ripple with current error eliminated

3-per-rev torque ripple is eliminated
Phase A current is 10A/div.

22

4. SIMULATION & EXPERIMENTAL RESULTS

Simulated d-axis step response

Rise time is about 2 ms.
There is no overshoot.

23

Measured d-axis step response

Rise time is 1.8 ms.
There is no overshoot.

4. SIMULATION & EXPERIMENTAL RESULTS

24

5. CONCLUSION

CONCLUSION

• A complete PMSM drive model has been

presented.

• Experimental results are provided to validate the

simulation models.

• The effect of position sensor resolution and

current measurement errors are simulated and
validated.

• The current loop step response is simulated and

validated.

• The simulation work helps reduce product cost

and development time.