1
Simulation of A
PMSM Motor Control System
for EPS Controllers
July 23, 2003
by
Guang Liu
Alex Kurnia
Ronan De Larminat
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.