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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 APMSM Motor Control System
for EPS ControllersJuly 23, 2003
by
Guang LiuAlex Kurnia
Ronan De Larminat
2
OUTLINE
1. Introduction2. System block diagram3. Simulink models of system elements4. Simulation and experimental results5. 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
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3. SIMULINK MODELS OF SYSTEM ELEMENTS
3. SIMULINK MODELS OF SYSTEM ELEMENTS
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3. SIMULINK MODELS OF SYSTEM ELEMENTS
Permanent Magnet Synchronous Motor (PMSM) Model
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qdtd
eqddtd
ddsd iLiLiRv ω−+=)]3
4cos()3
2cos(cos[32 πθπθθ −+−+= cbad vvvv
)]3
4sin()3
2(sinsin[32 πθπθθ −−−−−= cbaq vsvvv PMeddt
dedqdt
dqqsq iLiLiRv λωω +++=
])([23
qdqdqPMe iiLLiPT −+= λ
mmfLe dtdJKTT ωω ++=
θθ sincos qda iii −=
)3
2sin()3
2cos( πθπθ −−−= qdb iii
)3
4sin()3
4cos( πθπθ −−−= qdc iii
3. SIMULINK MODELS OF SYSTEM ELEMENTS
Permanent Magnet Synchronous Motor (PMSM) Equations
D-Q axis electric circuit equationsPark transformation equations
Torque equationsInverse Park transformation equations
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3. SIMULINK MODELS OF SYSTEM ELEMENTS
Motor Position Sensor Model
Complete Sensor:
Error generator:
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3. SIMULINK MODELS OF SYSTEM ELEMENTS
Current Sensing Model
VαβV_A
V_B
V_C
V1
V2V3
(3)
(1)
(5)
(4) (6) (2)
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3. SIMULINK MODELS OF SYSTEM ELEMENTS
PI Controller Model
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3. SIMULINK MODELS OF SYSTEM ELEMENTS
Inverse Park and SVM Model
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4. SIMULATION & EXPERIMENTAL RESULTS
4. SIMULATION AND EXPERIMENTAL RESUTLS
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4. SIMULATION & EXPERIMENTAL RESULTS
0 0.5 1 1.5 2 2.5 3 3.5 40
0.5
1
1.5
Torq
ue(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
Pha
se c
urre
nt (A
)
Time (Sec.)
Simulated torque ripple with 6-count resolutionTorque ripple = 1 N.m., current becomes square wave.
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4. SIMULATION & EXPERIMENTAL RESULTS
Simulated torque ripple with 48-count resolution
0.5 1 1.5 2 2.5 3 3.5 40.985
0.99
0.995
1
1.005To
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
Pha
se c
urre
nt (A
)
Time (Sec.)
Torque ripple = 0.012 N.m.
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0.5 1 1.5 2 2.5 3 3.5 4
0.996
0.998
1
1.002
Torq
ue(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
Pha
se c
urre
nt (A
)
Time (Sec.)
4. SIMULATION & EXPERIMENTAL RESULTS
Simulated torque ripple with 4096-count resolution
Torque ripple = 0.006 N.m.
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4. SIMULATION & EXPERIMENTAL RESULTS
Measured torque ripple with 48-count resolutionPhase A current is 10A/div. Average torque = 1.05 N.m.Torque ripple = 0.023 N.m. (peak to peak)
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0.5 1 1.5 2 2.5 3 3.5 4
0.435
0.44
0.445
0.45
0.455
0.46
0.465To
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
Mot
or c
urre
nt (A
)
Time (Sec.)
4. SIMULATION & EXPERIMENTAL RESULTS
Simulated current sensing with 0.15A error3-per-rev torque ripple is about 0.017 N.m
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4. SIMULATION & EXPERIMENTAL RESULTS
Measured torque ripple with current sense error3-per-rev torque ripple is about 0.020 N.mPhase A current is 10A/div.
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4. SIMULATION & EXPERIMENTAL RESULTS
Measured torque ripple with current error eliminated3-per-rev torque ripple is eliminatedPhase A current is 10A/div.
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4. SIMULATION & EXPERIMENTAL RESULTS
Simulated d-axis step responseRise time is about 2 ms.There is no overshoot.
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Measured d-axis step responseRise time is 1.8 ms.There is no overshoot.
4. SIMULATION & EXPERIMENTAL RESULTS
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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.
