Simulationpmsm Motor Control System

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

OUTLINE 1. 2. 3. 4. 5.

Introduction System block diagram Simulink models of system elements Simulation and experimental results Conclusion

2

1. INTRODUCTION

3

1. INTRODUCTION

Simplified Block Diagram of An EPS System

EPS

Steering mechanism

4

2. SYSTEM BLOCK DIAGRAM

5

2. SYSTEM BLOCK DIAGRAM

6

3. SIMULINK MODELS OF SYSTEM ELEMENTS

3. SIMULINK MODELS OF SYSTEM ELEMENTS

7

3. SIMULINK MODELS OF SYSTEM ELEMENTS

Permanent Magnet Synchronous Motor (PMSM) Model

8

3. SIMULINK MODELS OF SYSTEM ELEMENTS

Permanent Magnet Synchronous Motor (PMSM) Equations

Park transformation equations

D-Q axis electric circuit equations

2 2π 4π vd = [va cos θ + vb cos(θ − ) + vc cos(θ − )] 3 3 3

vd = Rs id + Ld

2 2π 4π ) − vc sin(θ − vq = [−va sin θ − vb sin s (θ − )] 3 3 3

vq = Rs iq + Lq dtd iq + Ldω e dtd id + ω e λPM

i − Lqω e dtd iq

d dt d

Inverse Park transformation equations Torque equations Te =

3 P[λ PM iq + ( Ld − Lq )id iq ] 2

Te = TL + K f ω m + J

d ωm dt

ia = id cosθ − iq sin θ ib = id cos(θ − ic = id cos(θ −

2π 2π ) − iq sin(θ − ) 3 3

4π 4π ) − iq sin(θ − ) 3 3 9

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

V_B (1)

V1 (3)

(5)

Vαβ

V3 (4)

V_A

V2 (6)

(2)

V_C

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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

Simulated torque ripple with 6-count resolution Torque ripple = 1 N.m., current becomes square wave. Resolution = 6 count per rev.

Torque(N.m.)

1.5

1

0.5

0

0

0.5

1

1.5

2 Time (Sec.)

2.5

3

3.5

4

0

0.5

1

1.5

2 Time (Sec.)

2.5

3

3.5

4

30

Phase current (A)

20 10 0 -10 -20 -30

15

4. SIMULATION & EXPERIMENTAL RESULTS

Simulated torque ripple with 48-count resolution Torque ripple = 0.012 N.m. Resolution = 48 count per rev.

1 0.995 0.99 0.985 0.5

1

1.5

2 Time (Sec.)

2.5

3

3.5

4

0.5

1

1.5

2 Time (Sec.)

2.5

3

3.5

4

30 20 Phase current (A)

Torque(N.m.)

1.005

10 0 -10 -20 -30

0

16

4. SIMULATION & EXPERIMENTAL RESULTS

Simulated torque ripple with 4096-count resolution Torque ripple = 0.006 N.m. Resolution = 4096 count per rev.

1

0.998

0.996 0.5

1

1.5

2 Time (Sec.)

2.5

3

3.5

4

0.5

1

1.5

2 Time (Sec.)

2.5

3

3.5

4

30 20 Phase current (A)

Torque(N.m.)

1.002

10 0 -10 -20 -30

0

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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)

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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

0.455 0.45 0.445 0.44 0.435 0.5

1

1.5

2 Time (Sec.)

2.5

3

3.5

4

0.5

1

1.5

2 Time (Sec.)

2.5

3

3.5

4

15 10 Motor current (A)

Torque(N.m.)

0.46

5 0 -5 -10 -15

0

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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.

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4. SIMULATION & EXPERIMENTAL RESULTS

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

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4. SIMULATION & EXPERIMENTAL RESULTS

Simulated d-axis step response Rise time is about 2 ms. There is no overshoot.

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4. SIMULATION & EXPERIMENTAL RESULTS

Measured d-axis step response Rise time is 1.8 ms. There is no overshoot.

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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. 24