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VECTOR CONTROLLED

RELUCTANCE SYNCHRONOUSMOTOR DRIVES WITH

PRESCRIBED CLOSED-LOOPSPEED DYNAMICS

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Model of Reluctance SynchronousMotor

Non-linear differential equations formulated in rotor-

fixed d,q co-ordinate system describe the reluctance

synchronous motor and form the basis of the control

system development.

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Control Structure for ReluctanceSynchronous Motor

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Master Control Law

Linearising function

1 1

15T J c L L i id r d q d q L

Demanded dynamic behavior

d

d t T

rd r

1

1

Dynamic torque equation

ddt J c L L i ir

d q d q L 1 5

Vector control condition

for maximum torquea) per unit stator current

b) for a given stator flux

baser

r

basedKd

baserdKd

forii

forii

tanLLc

T

J

i qd5

Lrd1

d

i

J

Tc i

cq dem

d r L q dK

d

1

5

5

*

*

a) b)

i i sign Tq dem d dem d

tan

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SET OF OBSERVERS

FOR STATE ESTIMATION

AND FILTERING

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Pseudo-Sliding Mode Observer for Rotor

Speed

i d 1

s

Ksm

i d*

ud

1

Ld

R

L

s

d

v d eq

Ksm

R

L

s

q

1

s

1

Lq

i q uqiq

*

vq eq

d

d t

i

i

R

L

R

L

i

i

L

L

u

u

v

vd

q

s

d

s

q

d

q

d

q

d

q

d eq

q eq

*

*

*

*

0

0

10

01

d

d t

i

i

R

Lp

L

L

pL

L

R

L

i

i

L

L

u

ud

q

s

dr

q

d

rd

q

s

q

d

q

d

q

d

q

10

01

a)

*

*

d d d

q q q

i i

i i

d d d

q q q

i i

i i

*

*

Motor equations

Model system

definition of error

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The Filtering Observer

r

L

1

s

1

s

K K

r

1 5~ ~ ~ ~J

c L L i id q d q

VJ

where design of:

needs adjustment of the

one parameter only or astwo different poles:

k J Ts 9 0~

k J Ts 81 4 02~

k J ~

1 2 k J ~

1 2

Electrical torque of

SRM is treated as an

external model input

Filtered values of and are produced by the

observer based on Kalman filter

r

e

Jc L L i i k e

k e

r

r d q d q L

L

~

15

L

Load torque is modeled

as a state variable

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Original control structure of speed

controlled RSM

q

rotor

position

sensor

external load

torque L

r

UqUd

I2- I 3I q

I d

Id dem

demanded d_q

stator currentsdemanded three-

phase voltages

vd_eq

Iq dem

U 1

U2

U3

I 1

Reluctance

Synchronous

Motor

Master

Control

Law

Angular

velocity

extractor

Power

electronic

drive

circuit

a_b &

d_q

transf.

Rotor flux

calculator

demanded

rotor speed

Sliding-mode

observer

Slave

control law

Filteringobserver

r

I dUdI q

d_q

&

a,b,c

transf

Switching

table

s

r

d

T

Udc

Measured variables:

rotor position,

stator current,

DC circuit voltage

Uq

d

vq_eq

q

L

r

q r q r

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Reference Model

(of closed-loop system)

Inner & Middle Loop

(real system)

correction

loop

mrK

Ts

Kd

1

Ts1

1

d

rd

id

Model TF

r

d

s

s sT

1

1

Parameter mismatch

increases a correction

Kmr r id

Ts

KK

sT

K

Ts

K

s

s

d

mr

mr

d

d

r

11

1

1

11

Masons rule

Kmr

r

d

s

s sT

1

1

MRACouter loop

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Simulation results

a1) id=const without MRAC

0 0. 05 0. 1 0. 15 0. 2 0. 25 0. 3 0. 35 0. 40

0.5

1

1.5

2

2.5

3

3.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0. 05 0. 1 0. 15 0.2 0. 25 0. 3 0. 35 0. 40

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

10

20

30

40

50

60

70

80

90

100

0 0. 05 0. 1 0. 15 0. 2 0. 25 0 .3 0. 35 0 .4-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-20

0

20

40

60

80

100

a) id,iq = f(t) b) d, q = f(t) c) Ld= f(t)

d) id, est = f(t) e) L, Lest = f(t) f) id, r = f(t)

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Simulation results

a2) id=const with MRAC

0 0. 05 0. 1 0. 15 0. 2 0. 25 0 .3 0. 35 0 .4-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.05 0.1 0. 15 0. 2 0. 25 0.3 0.35 0.40

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

10

20

30

40

50

60

70

80

90

100

0 0. 05 0. 1 0. 15 0. 2 0. 25 0. 3 0. 35 0. 4-1

0

1

2

3

4

5

0 0. 05 0. 1 0. 15 0. 2 0. 25 0.3 0. 35 0.4-20

0

20

40

60

80

100

120

a) id,iq = f(t) b) d, q = f(t) c) Ld= f(t)

d) id, est = f(t) e) L, Lest = f(t) f) id, r = f(t)

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Simulation results (without MRAC)

b1) dq-current angle control

0 0. 05 0. 1 0. 15 0. 2 0. 25 0 .3 0. 35 0 .4-0.5

0

0.5

1

1.5

2

2.5

0 0. 05 0.1 0. 15 0.2 0.25 0. 3 0.35 0.4-0.2

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0. 15 0. 2 0. 25 0. 3 0. 35 0.40

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0. 05 0. 1 0.15 0. 2 0. 25 0 .3 0.35 0. 4-0.5

0

0.5

1

1.5

22.5

3

3.5

4

4.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-20

0

20

40

60

80

100

120

0 0.05 0. 1 0. 15 0.2 0.25 0. 3 0. 35 0.40

10

20

30

40

50

60

70

80

90

100

a) id,iq = f(t) b) d, q = f(t) c) Ld= f(t)

d)id

,est

= f(t) e)L

,Lest

= f(t) f)id

,r

= f(t)

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Simulation results (with MRAC)

b2) dq-current angle control

0 0. 05 0. 1 0. 15 0. 2 0. 25 0 .3 0. 35 0 .40

0.5

1

1.5

2

2.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-20

0

20

40

60

80

100

120

0 0. 05 0. 1 0. 15 0. 2 0. 25 0. 3 0. 35 0. 40

10

20

30

40

50

60

70

80

90

100

0 0.05 0.1 0. 15 0. 2 0. 25 0.3 0. 35 0. 4-1

0

1

2

3

4

5

6

a) id,iq = f(t) b) d, q = f(t) c) Ld= f(t)

d)id

,est

= f(t) e)L,

Lest= f(t) f)

id,

r= f(t)

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Effect of MRAC on Various

Types of Prescribed Dynamics

a) constant torque

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-50

0

50

100

150

200

250Ideal, Estim. & Real Speed

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-50

0

50

100

150

200

250Ideal, Estim. & Real Speed

b) first order dyn.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-50

0

50

100

150

200

250Ideal, Estim. & Real Speed

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-50

0

50

100

150

200

250Ideal, Estim. & Real Speed

c) second ord. dyn

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-50

0

50

100

150

200

250Ideal, Estim. & Real Speed

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-50

0

50

100

150

200

250Ideal, Estim. & Real Speed

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Conclusions and Recommendations

The simulation results of the proposed new controlmethod for electric drives employing SRM show a

good agreement with the theoretical predictions.

The only departure of the system performance

from the ideal is the transient influence of the

external load torque on the rotor speed.

This effect is substantially reduced if MRAC outer

loop is applied. It is highly desirable to employ suggested control

strategy experimentally.