The document describes a simulation of a PMSM motor control system for electric power steering controllers. It includes: 1) A system block diagram showing the main components of an EPS system including a PMSM motor, steering mechanism, and EPS control unit. 2) Simulink models of the key system elements - the PMSM motor, position sensor, current sensing, PI controller, and inverse Park and space vector modulation models. 3) Simulation and experimental results showing the effects of position sensor resolution and current sensing errors on torque ripple, and validating the simulated d-axis step response with experimental measurements. 4) A conclusion that the complete PMSM drive model and experimental validation can

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

2. OUTLINE
1. Introduction
2. System block diagram
3. Simulink models of system elements
4. Simulation and experimental results
5. Conclusion
2

3. 1. INTRODUCTION
3

4. 1. INTRODUCTION
Simplified Block Diagram of An EPS System
EPS
Steering
mechanism
4

5. 2. SYSTEM BLOCK
DIAGRAM
5

6. 2. SYSTEM BLOCK DIAGRAM
6

7. 3. SIMULINK MODELS OF SYSTEM ELEMENTS
3. SIMULINK MODELS OF
SYSTEM ELEMENTS
7

8. 3. SIMULINK MODELS OF SYSTEM ELEMENTS
Permanent Magnet Synchronous Motor (PMSM) Model
8

9. 3. SIMULINK MODELS OF SYSTEM ELEMENTS
Permanent Magnet Synchronous Motor (PMSM) Equations
Park transformation equations D-Q axis electric circuit equations
2π 4π
2
vd = [va cos θ + vb cos(θ −
3 3
) + vc cos(θ −
3
)] vd = Rs id + Ld d
i − Lqω e dt iq
dt d
d
2π 4π
2
vq = [−va sin θ − vb sin s (θ −
3 3
) − vc sin(θ −
3
)] vq = Rs iq + Lq dt iq + Ldω e dt id + ω e λPM
d d
Inverse Park transformation equations
Torque equations
ia = id cosθ − iq sin θ
3
Te = P[λ PM iq + ( Ld − Lq )id iq ] 2π 2π
2 ib = id cos(θ − ) − iq sin(θ − )
3 3
d
Te = TL + K f ω m + J ωm 4π 4π
dt ic = id cos(θ − ) − iq sin(θ − )
3 3
9

10. 3. SIMULINK MODELS OF SYSTEM ELEMENTS
Motor Position Sensor Model
Complete Sensor:
Error generator:
10

11. 3. SIMULINK MODELS OF SYSTEM ELEMENTS
Current Sensing Model
V_B
(1) V1
(5) (3)
Vαβ
V_A
V3 V2
(4) (6) (2)
V_C
11

12. 3. SIMULINK MODELS OF SYSTEM ELEMENTS
PI Controller Model
12

13. 3. SIMULINK MODELS OF SYSTEM ELEMENTS
Inverse Park and SVM Model
13

14. 4. SIMULATION & EXPERIMENTAL RESULTS
4. SIMULATION AND
EXPERIMENTAL RESUTLS
14

15. 4. SIMULATION & EXPERIMENTAL RESULTS
Simulated torque ripple with 6-count resolution
Torque ripple = 1 N.m., current becomes square wave.
Resolution = 6 count per rev.
1.5
1
Torque(N.m.)
0.5
0
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (Sec.)
30
20
Phase current (A)
10
0
-10
-20
-30
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (Sec.)
15

16. 4. SIMULATION & EXPERIMENTAL RESULTS
Simulated torque ripple with 48-count resolution
Torque ripple = 0.012 N.m.
Resolution = 48 count per rev.
1.005
Torque(N.m.)
1
0.995
0.99
0.985
0.5 1 1.5 2 2.5 3 3.5 4
Time (Sec.)
30
20
Phase current (A)
10
0
-10
-20
-30
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (Sec.)
16

17. 4. SIMULATION & EXPERIMENTAL RESULTS
Simulated torque ripple with 4096-count resolution
Torque ripple = 0.006 N.m.
Resolution = 4096 count per rev.
1.002
Torque(N.m.)
1
0.998
0.996
0.5 1 1.5 2 2.5 3 3.5 4
Time (Sec.)
30
20
Phase current (A)
10
0
-10
-20
-30
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (Sec.)
17

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)
18

19. 4. SIMULATION & EXPERIMENTAL RESULTS
Simulated current sensing with 0.15A error
3-per-rev torque ripple is about 0.017 N.m
Current sense error = 0.15 (A)
0.465
0.46
Torque(N.m.)
0.455
0.45
0.445
0.44
0.435
0.5 1 1.5 2 2.5 3 3.5 4
Time (Sec.)
15
10
Motor current (A)
5
0
-5
-10
-15
0 0.5 1 1.5 2 2.5 3 3.5 4
Time (Sec.)
19

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.
20

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.
21

22. 4. SIMULATION & EXPERIMENTAL RESULTS
Simulated d-axis step response
Rise time is about 2 ms.
There is no overshoot.
22

23. 4. SIMULATION & EXPERIMENTAL RESULTS
Measured d-axis step response
Rise time is 1.8 ms.
There is no overshoot.
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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.
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