Motor Control

Prof. Wonhee Kim

Energy System Engineering, Chung-Ang University

2

3 Phase Permanent Magnet Synchronous Motor (PMSM)

3

3 Phase Permanent Magnet Synchronous Motor (PMSM)

4

3 Phase PMSM Modeling

1 2 2sin sin sin3 3

1 sin

1 2sin3

1 2sin3

m a b c l

a a n a a e

b b n b b e

c c n c c e

K p i p i p i BJ

i v v R i K pL

i v v R i K pL

i v v R i K pL

where va, vb, vc and ia, ib, ic are the voltages and currents inphases A, B, and C, respectively. ω is the rotor (angular)velocity, θ is the rotor (angular) position, B is the viscousfriction coefficient, J is the inertia of the motor, Km is the motortorque constant, Ke is the back-emf constant, R is the phasewinding resistance, L is the phase winding inductance, and p isthe number of pole pair. τl is the load torque perturbation.

5

PMSM with Clarke Transformation

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PMSM Modeling with Clarke Transformation

1 sin cos

1 sin

1 cos

m l

e

e

K i p i p BJ

i v R i K pL

i v R i K pL

1 2 2sin sin sin3 3

1 sin

1 2sin3

1 2sin3

m a b c l

a a n a a e

b b n b b e

c c n c c e

K i p i p i p BJ

i v v R i K pL

i v v R i K pL

i v v R i K pL

7

PMSM with DQ (Park) Transformation

1 sin cos

1 sin

1 cos

m l

e

e

K i p i p BJ

i v R i K pL

i v R i K pL

cos sinsin cos

cos sinsin cos

d

q

d

q

i ip pi ip p

v vp pv vp p

1

1

1

m q l

d d d d q

q q q q d e

K i BJ

i v R i pL iL

i v R i pL i KL

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DC Motor

1

1

1

m q l

q q q q d e

d d d d q

K i BJ

i v R i pL i KL

i v R i pL iL

1

1

m l

e

K i BJ

i v Ri KL

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DC Motor Control

DC motorPI

dqi

d- -

v

i

PI

eK

1

1

m l

e

K i BJ

i v Ri KL

10

PMSM Control

cos

2cos32cos3

d

d

d

p

p

p

cos

sin

d

d

p

p

11

PMSM Control

12

PMSM Control

PMSM

DQ/Clarke Transform-

ation

InverseDQ/Clarke Transform-

ation

PI

PIddi

dqi

d- -

-

qv

dv

avbv

aibi

qi

dici

PI

eK

cv

1

1

1

m q l

q q q q d e

d d d d q

K i BJ

i v R i pL i KL

i v R i pL iL

• Desired current to generate the torque

cos sinsin cos

cos sinsin cos

d

q

d

q

i ip pi ip p

v vp pv vp p

cos , sind dd ms q msi I p p i I p p

1 [ sin cos ]m m lK i p K i p BJ

d

d dm qK i

cos,

sin

d dmsd d

d qm ms m

p pi i

K p p K

sin

dd

m ms

IK p p

cos , sind dms msi I p i I p

Desired Direct Current for PMSM Control

• Field oriented control: zero direct current for torque maximization

cos,

sin

d dmsd d

d qm ms m

p pi i

K p p K

0,d

d dd q

m

i iK

0.5rms

r

NN

sin , cosd d

d da r b r

m m

i N i NK K

Desired Direct Current for PMSM Control

• Field weakening control: negative direct current to avoid the input saturation

1

1

1

m q

d d d q

q q q d e

K i BJ

i v Ri pL iL

i v Ri pL i KL

Back-emf cancellation using negative ide

dKipL

Desired Direct Current for PMSM Control

• Field weakening control: negative direct current to avoid the input saturation

cos,

sin

d dmsd d

d qm ms m

p pi i

K p p K

tan ,d d

d dd l q

m m

i iK K

0.5 lms

pp

sin , coscos cos

d dd d

l r lm l m l

i p i pK K

2 2

2 22 2, atand e

d l d

pLK pLKeiR p L R p L

Desired Direct Current for PMSM Control

• Comparison of open-loop, FOC, and FWC

(a) Open-loop (b) FOC (c) FWC

Desired Direct Current for PMSM Control

PMSM Control

Inverter

Inverter

Carrier-based PWM

Carrier-based PWM

Carrier-based PWM