vector controlled reluctance synchronous motor drives with prescribed closed-loop speed dynamics
DESCRIPTION
VECTOR CONTROLLED RELUCTANCE SYNCHRONOUS MOTOR DRIVES WITH PRESCRIBED CLOSED-LOOP SPEED DYNAMICS. Model of Reluctance Synchronous Motor. - PowerPoint PPT PresentationTRANSCRIPT
VECTOR CONTROLLED RELUCTANCE SYNCHRONOUS
MOTOR DRIVES WITH PRESCRIBED CLOSED-LOOP
SPEED DYNAMICS
Model of Reluctance Synchronous Motor
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.
Control Structure for Reluctance Control Structure for Reluctance Synchronous MotorSynchronous Motor
Master Control Law 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 Tr
d r
1
1
Dynamic torque equation
d
dt Jc L L i ir
d q d q L
1
5
Vector control condition for maximum torque
a) per unit stator current
b) for a given stator flux
baserr
basedKd
baserdKd
forii
forii
tanLLc
T
J
iqd5
Lrd1
d
i
J
Tc i
cq dem
d r L q dK
d
15
5
*
*
a) b)
i i sign Tq dem d dem d tan
SET OF OBSERVERS FOR STATE ESTIMATION
AND FILTERING
Pseudo-Sliding Mode Observer for Rotor Speed
id 1
s
Ksm
id*
ud
1
Ld
R
Ls
d
vd eq
Ksm
R
Ls
q
1
s
1
Lq
iq uq
iq*
vq eq
d
d t
i
i
R
LR
L
i
i
L
L
uu
v
vd
q
s
d
s
q
d
q
d
q
d
q
d eq
q eq
*
*
*
*
0
0
10
01
d
d t
ii
R
Lp
L
L
pL
L
R
L
ii
L
L
uu
d
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
Angular velocity extractor
d
q
s
d
s
q
d
q
q
d
d
q
d
q
d eq
q eq
R
LR
L
L
LL
L
ii
v
v
0
0
0
0
Error system
v V sign i i
v V sign i i
d eq d d
q eq q q
max*
max*
( )
( )
0
Condition for Sliding Motion
Sliding-Mode Observer
v
v
L
LL
L
ii
d eq
q eq
q
d
d
q
d
q
0
0
Pseudo-SMC Observerv K i i
v K i i
d eq sm d d
q eq sm q q
( )
( )
*
*
Estimate of rotor speedEquivalent variables
rq q eq
d d
L v
pL i*
The Filtering ObserverThe Filtering Observer
r
L
1
s
1
s
K K
r
15~
~ ~ ~
Jc L L i id q d q
VJ
where design of:
needs adjustment of the one parameter only or as two different poles:
k J Ts 9 0
~k J Ts 81 4 0
2~
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
Original control structure of speed Original control structure of speed controlled RSMcontrolled RSM
q
rotorpositionsensor
external loadtorque L
r
UqUd
I2- I 3
I q
I d
Id dem
demanded d_qstator currents
demanded three-phase voltages
vd_eq
Iq dem
U 1
U2
U3
I 1
ReluctanceSynchronous
Motor
MasterControl
Law
Angularvelocityextractor
Powerelectronic
drivecircuit
d_q
transf.
Rotor fluxcalculator
demandedrotor speed
Sliding-modeobserver
Slavecontrol law
Filteringobserver
r
I dUdI q
d_q&
a,b,ctransf
Switchingtable
sr
d
Udc
Measured variables:rotor position,stator current,DC circuit voltage
Uq
d
vq_eq
L
r
r r
Reference Model (of closed-loop system)
Inner & Middle Loop(real system)
correction loop
mrK
Ts
Kd1
Ts1
1
dr̂d
id
Model TF
r
d
s
s sT
1
1
Parameter mismatch increases a correction
Kmr r id
Ts
KK
sTK
Ts
K
s
s
dmr
mrd
d
r
11
11
11ˆ
Mason’s rule
Kmr
r
d
s
s sT
1
1
MRAC outer loop
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)
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 0.4010
20
304050
60
7080
90100
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)
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
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
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)
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 0.40102030405060708090
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)
Effect of MRAC on Various Types of Prescribed Dynamics
a) constant torquea) 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
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.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
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
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
Conclusions and Recommendations
The simulation results of the proposed new control method 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.