A MOTION SEPARATION METHOD FOR THE CONTROL OF …
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Transcript A MOTION SEPARATION METHOD FOR THE CONTROL OF …
SENSORLESS INDUCTION MOTOR DRIVE
CONTROL SYSTEM WITH PRESCRIBED
CLOSED-LOOP ROTOR MAGNETIC
FLUX AND SPEED DYNAMICS
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
BASIC PRINCIPLE
u
nonlinear plant
y
LINEARISING FUNCTION
f y, u A y B y
y f y, u
cl
y
specified
closed-loop system
y A y B y
y
cl
r
cl r
i.e.,
y
r
nonlinear
control
law
u g y, y
r
cl r
u nonlinear
plant
y f y, u
y A y B y
1
y
m
1 1
1 1r
y
B y
A
m m
m mr
MOTION
SEPARATION
linear and de-coupled
closed-loop system
with prescribed dynamics
y
EXTENSION TO INDIRECTLY CONTROLLED VARIABLES
z qx, u
nonlinear plant
u x f x, u
z hx controlled
y px
z
r
variables
available
measurements
z
cl
1
z
1 1
1 1r
m
A z B z
m m
m mr
nonlinear
control
law
Zr
specified
closed-loop system
z A z B z
cl
cl r
i.e.,
z A z B z
LINEARISING FUNCTION
qx, u A hx B z
u g x , z
z
r
x
observer
u
cl r
nonlinear
plant
x f x, u
z hx
y gx
z
y
r
MODEL OF MOTOR AND LOAD
1
1
c TTT I , 0
L
L
L
J
J 5
I c c P a I U
P c I
r
1
2
T
T I
4
r
I
1
P
expressed in
stator-fixed
frame
r
0 1
T
1
0
motor torque
rotor magnetic flux linkage
r
rotor speed
stator currents
U
r
c L
stator voltages
R s R stator and rotor resistances
r
2
c 3pL
5
m
L L r L m stator, rotor and mutual inductances
s
c L / L L L2
1
U T U
p r
c
3
c3
p
r
2 L
L
m
r
m
c L
4
m
T
r
c 3 R r L r 1 Tr
r
a R L2
1
s r
s
m
L2 R
r
r
CONTROL LAW DESIGN
1. SIMPLIFICATION OF CONTROL PROBLEM BY
INNER/OUTER CONTROL LOOP STRUCTURE
r
outer-loop sub-plant
d
P c I
r
d
master
control
law
Id
outer
loop
r
observers
slave
control
law
r
4
1
c TTT I
L
J 5
U
inner-loop sub-plant
inner
loop
I c c P a I U
1
2
r
1
I
2. Slave Control Law
Two
sgn I I
U sat G I I , U
I
UU
If
d
max
then
max
d
U U
min
options are
considered:
U 0
max
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.
3. MASTER CONTROL LAW
independently controls rotor speed and magnetic flux norm with
first order dynamics and time constants, T1 and T2
motor equation
r
1
c TTT I
L
J 5
desired closed-loop equation
r
1
d r
T
1
I
T
P c I
r
linearising functions
1 J
T T
T I
r
L
c5 T1 d
c3
c4
1
2c4 T2
d
4
motor equation
2 c c T I
3
4
desired closed-loop equation
1
d
T
2
mastercontrol law
1
Id
1 ~
J
d r L
~
c5 T1
~
c
3
1
d
~
c
2~
c4T2
4
3. STATE ESTIMATION AND FILTERING
3.1. Rotor Flux Estimator
based on
motor equations
eliminate
P
r
P c I
r
4
I c c P a I U
1
2
r
1
1
1
a1
c I U
I
4 c
c
c c
1 2
2
2
1
1
a
1
I
c I U dt
4
c
c
c c
2
2
1 2
ROTOR FLUX ESTIMATION ALGORITHM by numerical integration
~
1
a
1
*
1
~
Q
1 sgn 1 d Q c4 ~ I ~ U
2T
c
c
flux estimate then
given by:-
flux component estimates are limited on the basis that
they have zero long-term averages with t dt 0
1
*
Q~ ~ I
c c
1 2
q
2
0
2
3.2. Pseudo-Sliding Mode Observer and Angular Velocity Extractor
cc P
1 2
motor equation
I c c P a I U
1
2
*
r
1
U
1
1
I
For pseudo sliding
-mode observer:-
v K I I I *
0
0
1
1 1
-v
0 1
Umax
Umax
1
0
0
1
s
, KI
I
1 0
ca
For classical sliding
-mode observer:v v sgn I I* ,K
max
1
s
I ~
c ~
a I U v
*
r
~c ~a
slope
1 1
KI
I* (not
used
directly)
1 0
0 1
angular velocity
T
~
~
~
~
v c c P
v
T
c
c
p
extractor
1 2
r
K
r
eq
1 2
I
lim
3.3 Filtering Observers
Rotor angular velocity
and load torque observer
e
r
Rotor magnetic flux observer
r
T T
1 ~
~ c T I k e
r
L
J 2
k e
4
~
P
c IK
r
L
r
P k
k
k
1
s
1~
c
~ 2
J
r
1
s
~
c4 I
r
T
L
TT I
1 0
0 1
1
0
0
1
s
P
r
OVERALL CONTROL SYSTEM BLOCK DIAGRAM
demanded
rotor speed
demanded
stator currents
d
Id
Master
control
law
Slave control law
2/3
high gain
trans
/signum
-form
Id
d
U
U
I trans
I
Induction
motor
rotor
speed
-formation
I1
I2-I3
v q
Rotor flux
estimator
r
U1
U2 Power
electronic
U3
drive
3/2
transform
r
Filtering
observers
external load
torque L
circuit
d
demanded 3phase voltages
Sliding-mode
v eq
observer
Angular
velocity
extractor
r
measured
stator
currents
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
Voltages Ualpha v. Ubeta
Currents Ialpha v. Ibeta
40
1
[A]
[V]
20
0.5
0
0
-20
-0.5
[A]
[V]
-40
-50
0
50
-1
-1
Flux Links PSIalpha v. PSIbeta
0.1
-0.5
0
0.5
1
Ang. Velocities & Torque v. time
200
[Vs]
[rad/s], [Nm]
0.05
100
0
0
-0.05
-100
[Vs]
-0.1
-0.1
-0.05
0
0.05
time [s]
0.1
-200
0
0.5
1
1.5
2
Experiments with Induction Motor,
d=200 rad/s, T1=0.5 s
0.09
2
a1) speed up
1.5
1
0.08
0.07
0.06
400
b1) estim. rotor flux
norm and load torque
200
0
0.5
0.05
-200
0
0.04
-400
0.03
-0.5
-600
0.02
-1
-1.5
-2
-800
0.01
0
0.01
0.02
0.03
0.04
0.05
-0.01
0
a) stator currents and
rotor flux
0.5
1
1.5
2
a2) steady state
150
0.2
100
0
50
-0.2
0
-0.4
-50
-0.6
-100
1.77
1.775
1.78
1.785
1.79
1.795
1.8
-150
1
1.5
2
250
200
0.4
0.5
c) Real and ideal
rotor speed
250
0.6
-1200
0
b) Estimated variables
from observers
0.8
-0.8
1.765
-1000
0
c1) estim. rotor
speed, SM observer
200
150
100
50
b2) estim. rotor speed
and load torque
0
0.5
1
1.5
c2) real and ideal
rotor speed
0
2
-50
0
0.5
1
1.5
2
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.