SENSORLESS INDUCTION MOTOR DRIVE

ugliestmysticΤεχνίτη Νοημοσύνη και Ρομποτική

14 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

48 εμφανίσεις

Stephen J. DODDS, University of East London

Viktor A. UTKIN, Institute of Control Sciencies,


Russian Academy of Sciences, Moscow

Jan VITTEK, University of Transport and
Communications, Zilina

SENSORLESS
INDUCTION MOTOR

DRIVE

CONTROL S
YSTEM W
ITH

PRESCRIBED


CLOSED
-
LOOP
ROTOR MAGNETIC

FLUX AND SPEED
DYNAMICS

BASIC PRINCIPLE

nonlinear plant




,
y
f
y
u


y
A
y
B
1
1
1
1
1


y
r

y
A
y
B
m
m
m
m
m
r
y


i.e.,

specified

closed
-
loop system

u



y
A
y
B
y


c
l
c
l
r
y
r
y

y

MOTION

SEPARATION



f
y
u
A
y
B
y
,


c
l
c
l
r
LINEARISING FUNCTION

nonlinear


plant




,
y
f
y
u

u

y

nonlinear

control


law



u
g
y
y

,
r
y
r
linear and de
-
coupled


closed
-
loop system

with prescribed dynamics

EXTENSION TO INDIRECTLY CONTROLLED VARIABLES

nonlinear plant

i.e.,

specified

closed
-
loop system

u


z

z

LINEARISING FUNCTION

nonlinear


plant

u

z

nonlinear

control


law


z
A
z
B
1
1
1
1
1


z
r

z
A
z
B
m
m
m
m
m
r
z


available

measurements

controlled

variables




,
x
f
x
u



z
h
x


z
A
z
B
z


c
l
c
l
r
observer

z
r



,
x
f
x
u



y
g
x



z
h
x

y



u
g
x
z


,
r

x


y
p
x




,
z
q
x
u





q
x
u
A
h
x
B
z
,



c
l
c
l
r
Z
r
MODEL OF MOTOR AND LOAD






,


r
L
T
T
L
L
J
J
c





1
1
0
5





T
I







P
I

r
c

4





I
P
I
U


c
c
a
r
1
2
1





P



r
r
r
c
p
p
c








3
3
T








0
1
1
0

T











rotor magnetic flux linkage


T
I
I









stator currents

U
T
U
U









stator voltages


motor torque


r
rotor speed



c
L
L
L
L
r
s
r
m
1
2


/
c
L
L
m
r
2

c
R
L
T
r
r
r
3
1


c
L
T
m
r
4



a
R
L
L
R
s
m
r
r
1
2
2


L
s
L
r
L
m
stator, rotor and mutual inductances

R
s
R
r
stator and rotor resistances

expressed in

stator
-
fixed

frame



c
pL
L
m
r
5
3
2

CONTROL
LAW

DESIGN

1.
SIMPLIFICATION OF CONTROL PROBLEM BY


INNER/OUTER CONTROL LOOP STRUCTURE






I
P
I
U


c
c
a
r
1
2
1



inner
-
loop sub
-
plant








P
I

r
c

4
outer
-
loop sub
-
plant





r
T
T
L
J
c


1
5

T
I

master

control

law

slave

control

law

observers

I

inner

loop

outer

loop

U

d



r



d



d







r

I


Two options are
considered
:


A High Gain Proportional
Control Law with Saturation
Limits


Bang
-
Bang Control Law
Operating in the Sliding Mode


Automatic Start Algorithm
bypasses Slave Control Law

with simple algorithm,

which applies maximum voltage

to one phase until magnetic flux

has grown sufficiently
.



U
sgn
I
I


U
d
max




U
sat
I
I
U


G
I
d
,
max

min



U
U



max
U


0
If

then

2. Slave Control Law

3. MASTER CONTROL LAW

independently

controls rotor speed and magnetic flux norm with
first order dynamics and time constants, T1 and T2





r
T
T
L
J
c


1
5

T
I







r
d
r
T


1
1







P
I

r
c

4









2
3
4
c
c
T
I








1
2
T
d



T
T
d
r
L
c
J
T
T
I











1
5
1









T
d
c
c
c
T
I



3
4
4
2
1
2
mastercontrol law

linearising functions

motor equation

motor equation

desired closed
-
loop equation

desired closed
-
loop equation





I
d
d
r
L
d
c
J
T
c
c
c
T




































1
1
1
2
5
1
3
4
4
2





~
~


~
~

~


















*
~
~
Q
I









1
1
2
c
c
3.
STATE ESTIMATION AND FILTERING

3.1.
Rotor Flux Estimator





c
a
c
c
c
c
4
1
2
2
1
2
1
1



























I
U
I







P
I

r
c

4





I
P
I
U


c
c
a
r
1
2
1



based on

motor equations



P

r



c
a
c
c
dt
c
c
4
1
2
2
1
2
1
1




































I
U
I



sgn
*
~
~
~
~
Q
Q
I
U



































1
2
1
1
1
4
1
2
2
T
c
a
c
c
q
d



flux component estimates are limited on the basis that

they have zero long
-
term averages with




t
dt



0
0
eliminate

flux estimate then

given by:
-

ROTOR FLUX ESTIMATION ALGORITHM by numerical integration

slope

K
I

3.2. Pseudo
-
Sliding Mode Observer and Angular Velocity Extractor




~
~
*
*
I
I
U
v




c
a
1
1


v
v
sgn
I
I



max
*


v
K
I
I



I
*





I
P
I
U


c
c
a
r
1
2
1



motor equation



1
0
0
1
s


c
a
1
1
1
0
0
1
U

I



c
c
r
1
2
P



1
0
0
1
s
I
*
(not

used

directly)

-
v


U
max

U
max
For
classical

sliding

-
mode observer:
-

For
pseudo
sliding

-
mode observer:
-

K
I


,

,

K
I




lim
~
~
K
c
c
I
r












v
P
1
2


angular velocity
extractor



~
~
c
a
1
1
1
0
0
1

r
eq
T
c
c
p


















v
T


~
~
1
2
3.3 Filtering Observers



e
J
c
k
e
k
e
r
r
r
T
T
L
L
























~
~



1
2

T
I











~







P
I
K


r
c




4
Rotor angular velocity

and load torque observer

Rotor magnetic flux observer

1
s
1
s


1
2
~
~
J
c
T
T


T
I
k

k



r

r




L


1
0
0
1
s






P


r
~
c
4
I




P



r
k

1
0
0
1
OVERALL CONTROL SYSTEM BLOCK DIAGRAM

U







d

U



3/2

transform

I

2

-
I

3

I



measured

stator

currents

I
















rotor

speed



r

I

d



demanded





stator currents

demanded 3
-

phase voltages

















r





d

v



eq

v



q





I

d



U

1

U

2

U

3

I

1

Induction

motor

Master

control

law

Angular

velocity

extractor

Filtering

observers

external load

torque



L

Power

electronic

drive

circuit

 

trans

-
formation

2/3

trans

-
form

Rotor flux

estimator



d

demanded

rotor speed

Sliding
-
mode

observer

high gain

/signum



r



Slave control law


Simulation Results for High
-
Gain Slave Control Law

Simulation Results for Sliding Mode Slave Control Law

Comparison of Simulated System Behaviour with Ideal Transfer
Function for High Gain Proportional CL

Comparison of Simulated System Behaviour with Ideal
Transfer Function for Bang
-
Bang Slave CL

Experiments with Induction Motor

Experimental
Bench


of East London
University, UK

January 2000

-
50

0

50

-
40

-
20

0

20

40

Voltages Ualpha v. Ubeta

[V]

[V]

-
1

-
0.5

0

0.5

1

-
1

-
0.5

0

0.5

1

Currents Ialpha v. Ibeta

[A]

[A]

-
0.1

-
0.05

0

0.05

0.1

-
0.1

-
0.05

0

0.05

0.1

Flux Links PSIalpha v. PSIbeta

[Vs]

[Vs]

0

0.5

1

1.5

2

-
200

-
100

0

100

200

Ang. Velocities & Torque v. time

[rad/s], [Nm]

time [s]

Experiments with Induction Motor,

d
=
200 rad/s, T
1
=
0.5 s

0
0.01
0.02
0.03
0.04
0.05
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
1.765
1.77
1.775
1.78
1.785
1.79
1.795
1.8
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0
0.5
1
1.5
2
-1200
-1000
-800
-600
-400
-200
0
200
400
0
0.5
1
1.5
2
-150
-100
-50
0
50
100
150
200
250
0
0.5
1
1.5
2
-50
0
50
100
150
200
250
a1) speed up

b) Estimated variables
from observers

c) Real and ideal
rotor speed

a) stator currents and
rotor flux

a2) steady state

0
0.5
1
1.5
2
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
b1) estim. rotor flux
norm and load torque

b2) estim. rotor speed
and load torque

c1) estim. rotor
speed, SM observer

c2) real and ideal
rotor speed

Conclusions and
Recommendations


Forced Dynamic Control introduces a new approach to
the control of el. drives with induction motors, when
behaviour of the rotor magnetic flux and rotor speed
dynamics are precisely defined.


The experimental results show good agreement with
the theoretical predictions.


Further improvement of the Forced Dynamics Control
can be done with MRAC or SMC based outer control
loop.