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Transcript of 04_01eng
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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.