stephen j. dodds, university of east london viktor a. utkin, institute of control sciencies, russian...

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.