Stephen J. DODDS, University of East LondonStephen J. DODDS, University of East London
Viktor A. UTKIN, Institute of Control Sciencies,Viktor A. UTKIN, Institute of Control Sciencies,
Russian Academy of Sciences, MoscowRussian Academy of Sciences, Moscow
Jan VITTEK, University of Transport and Jan VITTEK, University of Transport and Communications, ZilinaCommunications, Zilina
SENSORLESS INDUCTION MOTOR DRIVE CONTROL SYSTEM WITH PRESCRIBED
CLOSED-LOOP ROTOR MAGNETICFLUX AND SPEED DYNAMICS
BASIC PRINCIPLEBASIC PRINCIPLE
nonlinear plant
,y f y u
y A y B1 1 1 1 1 y
r
y A y Bm m m m mr
y
i.e.,
specifiedclosed-loop system
uu
y A y B y cl cl ry
r
yy
yy
MOTIONMOTIONSEPARATIONSEPARATION
f y u A y B y, cl cl r
LINEARISING FUNCTIONLINEARISING FUNCTION
nonlinear plant
,y f y u
uu yynonlinearcontrol
law
u g y y ,r
yr
linear and de-coupled closed-loop system
with prescribed dynamics
EXTENSION TO INDIRECTLY CONTROLLED VARIABLESEXTENSION TO INDIRECTLY CONTROLLED VARIABLES
nonlinear plant
i.e.,
specifiedclosed-loop system
uu
zz
zz
LINEARISING FUNCTIONLINEARISING FUNCTION
nonlinear plantuu
zznonlinearcontrol
law
z A z B1 1 1 1 1 z
r
z A z Bm m m m mr
z
availablemeasurements
controlledvariables
,x f x u
z h x
z A z B z cl cl r
observer
zr
,x f x u
y g x z h x yy u g x z ,
r
x
y p x
,z q x u
q x u A h x B z, cl cl r
Zr
MODEL OF MOTOR AND MODEL OF MOTOR AND LOADLOAD ,
r LT T
L LJ Jc
1 10
5 T I
P Ir
c4
I P I U c c ar1 2 1
P
rr
r
c p
p c
3
3
T
0 1
1 0
T
rotor magnetic flux linkage
T I I
stator currents
UT U U
stator voltages
motor torque
r rotor speed
c L L L Lr s r m1
2 /
c L Lm r2
c R L Tr r r3
1
c L Tm r4
a R L L Rs m r r1
2 2 Ls
Lr
Lm
stator, rotor and mutual inductances
Rs
Rr stator and rotor resistances
expressed instator-fixedframe
c pL Lm r5
3 2
CONTROL LAW DESIGN
1. SIMPLIFICATION OF CONTROL PROBLEM BY INNER/OUTER CONTROL LOOP STRUCTURE
I P I U c c ar1 2 1
inner-loop sub-plant
P Ir
c4
outer-loop sub-plant
r
T TLJ
c 1
5 T I master
controllaw
slavecontrol
law
observers
I
innerloop
outerloop
U
d
r
d
d
r
I
Two options are Two options are consideredconsidered::
A High Gain Proportional A High Gain Proportional Control Law with Saturation Control Law with Saturation LimitsLimits
Bang-Bang Control Law Bang-Bang Control Law Operating in the Sliding Mode Operating in the Sliding Mode
Automatic Start Algorithm Automatic Start Algorithm bypasses Slave Control Law bypasses Slave Control Law with simple algorithm,with simple algorithm,which applies maximum voltage which applies maximum voltage to one phase until magnetic flux to one phase until magnetic flux has grown sufficientlyhas grown sufficiently..
U sgn I I Udmax
U sat I I U GI d
,max
min
U U
max
U0
If then
2. Slave Control Law
3. MASTER CONTROL LAWindependently controls rotor speed and magnetic flux norm with
first order dynamics and time constants, T1 and T2
r
T TLJ
c 1
5 T I
r d rT
1
1
P Ir
c4
2
3 4c c TI
1
2T d
T Td r Lc
J
TT I
1
5 1
Td
c
c c TI 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 2c c
3. STATE ESTIMATION AND FILTERING3.1. Rotor Flux Estimator
ca
c c c c41
2 2 1 2
1 1
I U I P I
rc
4
I P I U c c ar1 2 1
based onmotor equations P
r
ca
c cdt
c c41
2 2 1 2
1 1
I U I
sgn * ~~
~ ~Q Q I U
1
21 1
14
1
2 2T
ca
c cq
d
flux component estimates are limited on the basis thatthey have zero long-term averages with t dt
00
eliminate
flux estimate thengiven by:-
ROTOR FLUX ESTIMATION ALGORITHM by numerical integration
slope KI
3.2. Pseudo-Sliding Mode Observer and Angular Velocity Extractor
~ ~* *I I U v c a1 1
v v sgn I I max
*
v K I I I*
I P I U c c ar1 2 1
motor equation 1 0
0 1
s
c a1 1
1 0
0 1
U I
c cr1 2
P
1 0
0 1
s
I* (not
useddirectly)
-v Umax
Umax
For classical sliding-mode observer:-
For pseudo sliding-mode observer:-
KI,
, KI
lim
~ ~K
c cI
r
v P1 2
angular velocity
extractor
~ ~c a1 1
1 0
0 1
r eq
Tc c p
v T ~ ~
1 2
3.3 Filtering Observers
e
Jc k e
k e
r r
r
T TL
L
~~
12 T I
~ P I Kr
c 4
Rotor angular velocityand load torque observer
Rotor magnetic flux observer
1
s
1
s
12~
~J
cT T T I
kk
r
r
L
1 0
0 1
s
P r
~c4I
P r
k 1 0
0 1
OVERALL CONTROL SYSTEM BLOCK DIAGRAM
U
d U
3/2transform
I2-I3I
measuredstatorcurrents
I
rotorspeed
r
Id
demanded stator currents demanded 3-
phase voltages
rd
veq
vq
Id
U1
U2
U3
I1
Inductionmotor
Mastercontrol
law
Angularvelocityextractor
Filteringobservers
external load
torque L
Powerelectronic
drivecircuit
trans-formation
2/3trans-form
Rotor fluxestimator
d
demandedrotor speed
Sliding-modeobserver
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 Experiments with Induction Motor
Experimental Bench
of East London University, UKJanuary 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, T1=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 Conclusions and RecommendationsRecommendations
Forced Dynamic Control introduces a new approach to Forced Dynamic Control introduces a new approach to the control of el. drives with induction motors, when the control of el. drives with induction motors, when behaviour of the rotor magnetic flux and rotor speed behaviour of the rotor magnetic flux and rotor speed dynamics are precisely defined.dynamics are precisely defined.
The experimental results show good agreement with The experimental results show good agreement with the theoretical predictions. the theoretical predictions.
Further improvement of the Forced Dynamics Control Further improvement of the Forced Dynamics Control can be done with MRAC or SMC based outer control can be done with MRAC or SMC based outer control loop.loop.