Prof. Ján VITTEK & Dr. Juraj ALTUS University of Žilina, SK

Prof. Ján VITTEK & Dr. Juraj ALTUSProf. Ján VITTEK & Dr. Juraj ALTUS University of Žilina, SKUniversity of Žilina, SK

Department of Electric Traction and EnergeticsDepartment of Electric Traction and EnergeticsProf. Stephen J. DODDS & Dr. Roy PerrymanProf. Stephen J. DODDS & Dr. Roy Perryman

University of East London, UKUniversity of East London, UKSchool of Electrical and Manufacturing EngineeringSchool of Electrical and Manufacturing Engineering

Prof. Ján VITTEK & Dr. Juraj ALTUSProf. Ján VITTEK & Dr. Juraj ALTUS University of Žilina, SKUniversity of Žilina, SK

Department of Electric Traction and EnergeticsDepartment of Electric Traction and EnergeticsProf. Stephen J. DODDS & Dr. Roy PerrymanProf. Stephen J. DODDS & Dr. Roy Perryman

University of East London, UKUniversity of East London, UKSchool of Electrical and Manufacturing EngineeringSchool of Electrical and Manufacturing Engineering

FORCED DYNAMICS FORCED DYNAMICS CONTROL OF CONTROL OF INDUCTION INDUCTION

MOTOR WITHMOTOR WITH SELECTABLE SELECTABLE DYNAMICSDYNAMICS

FORCED DYNAMICS FORCED DYNAMICS CONTROL OF CONTROL OF INDUCTION INDUCTION

MOTOR WITHMOTOR WITH SELECTABLE SELECTABLE DYNAMICSDYNAMICS

University of East London1999

FORCED DYNAMICS SPEED CONTROL FORCED DYNAMICS SPEED CONTROL of EL. DRIVES with Induction Motorsof EL. DRIVES with Induction Motors

FORCED DYNAMICS SPEED CONTROL FORCED DYNAMICS SPEED CONTROL of EL. DRIVES with Induction Motorsof EL. DRIVES with Induction Motors

Application of:Application of: block control principle linearising function pseudo-sliding mode observers for angular

speed estimation filtering observer including load torque

estimation

Achievements:Achievements: speed control without shaft sensor closed-loop dynamics for speed control

chosen to suit particular drive application enhanced reliability of whole electric drive

Application of:Application of: block control principle linearising function pseudo-sliding mode observers for angular

speed estimation filtering observer including load torque

estimation

Achievements:Achievements: speed control without shaft sensor closed-loop dynamics for speed control

chosen to suit particular drive application enhanced reliability of whole electric drive

Research CO-ORDINATIONProf. Stephen J. DODDSUniversity of East LondonSchool of Electrical and Manufacturing EngineeringDepartment of Electrical & Electronic EngineeringLongbridge RoadDAGENHAM, RM8 2ASUnited Kingdom

BASIC PRINCIPLEBASIC PRINCIPLE

nonlinear plant

,y f y u

y A y B1 1 1 1 1

yr

y A y Bm m m m mr

y

i.e.,

specifiedclosed-loop system

uu

y A y B y c l c l ry

r

yy

yy

MOTIONMOTIONSEPARATIONSEPARATION

f y u A y B y, cl c l 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

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 SIMPLIFICATION OF CONTROL PROBLEM BY INNER/OUTER CONTROL LOOP STRUCTURE

r

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

d

d

r

I

Rotor speed and rotor magnetic flux norm are demanded values

MASTER CONTROL LAWindependently controls rotor speed and magnetic flux norm with first order

dynamics and time constants, T1 and T2

T Td r Lc

J

TT I

1

5 1

Td

c

c c TI 3

4 4 2

1

2

linearising functions r

T TLJ

c 1

5 T I

r d rT

1

1

motor equation

desired closed-loop equation

master control law

I

d

d r L

d

c

J

T

c

c c T

1

1

1

2

5 1

3

4 4 2

~

~

~

~

~

P Ir

c4

23 4

c c T I

1

2T d

motor equation

desired closed-loop equation

Acceleration Demands for Acceleration Demands for Three Various Dynamics

1. Constant Acceleration

3. Second Order Dynamic

rd1

d T

1a

1

dd T

a

ndd

dnrd2ndnd

aa

ha2aa

_

_ *ˆ

dyn d d rJ a sign * *

dyn d rJ

T

1*

2. First Order Dynamic

dyn dJ a *

nat

settl1

n1*5.1T

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-100

-50

0

50

100

150

200 r

obs

id

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

250

id

U a

r

U a

obs

U a

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-100

-50

0

50

100

150

200

r

obs

id

SET OF OBSRVERS FOR STATE ESTIMATION AND FILTERING

P Ir

c4

I P I U c c ar1 2 1

is based onmotor equations P

r

eliminate

Drift Corrections algorithm is used forfinal magnetic flux

filtering

ca

c cdt

c c41

2 2 1 2

1 1

I U I

ca

c c c c41

2 2 1 2

1 1

I U I

1.Rotor Flux Estimator1.Rotor Flux Estimator

Pseudo-Sliding Mode Observer andAngular Velocity Extractor

slope KI

~ ~* *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

P r21cc

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. Filtering Observer

e

Jc k e

k e

r r

r

T TL

L

~~

12

T I

Rotor angular velocityand load torque observer

12~

~J

cT T T I

1

s

1

s

kk

r

r

L

Overall Control Systems StructureOverall Control Systems Structure

r

U

UT3 2

transform

I2-I3I

measuredstatorcurrents

I

rotorspeed

r

Id

demanded stator currents

demanded three-phase voltages

rl

veq

vq

Id

U1

U2

U3

I1

Inductionmotor

Mastercontrol

law

Angular

velocity

extractor

Filteringobservers

external loadtorque L

Powerelectronic

drivecircuit

trans-formation

T2 3trans-form

Rotor fluxestimator

d

demandedrotor speed

Sliding-modeobserver

hysteresis/ signum slave CL

Slave control law

r

Comparison of Control System Comparison of Control System Response and Demanded ResponseResponse and Demanded Response

The actual system response is compared with the simulated output of the ideal speed response of prescribed dynamics .

The actual system response is compared with the simulated output of the ideal speed response of prescribed dynamics .

theor

Ud

Uqdem

Ud dem

Control

Laws Power Electronics

Induction Motor and Load

I Id q

,

U Ud q

,

dem r

1

1 1 s T

Ideal closed-loop system behaviour

Uq

1sT2sT

1

022

0

2

1

Ks

K)s(F

Experimental Results for Induction Motor DriveExperimental Results for Induction Motor DriveDriven by First Order DynamicsDriven by First Order Dynamics

-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]

Experimental Bench of East London University, Results:Daniel Vysoudil, AD Developments, Milton Keynes, UK

Experimental Results for Constant Acceleration

1.76 1.765 1.77 1.775 1.78 1.785 1.79 1.795

-60

-40

-20

0

20

40

60

u

U a

i

U a

U a

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

250

id

U a

r

U a

obs

U a

Experimental Results for First Order Dynamics

1.76 1.765 1.77 1.775 1.78 1.785 1.79 1.795

-60

-40

-20

0

20

40

60

u

i

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-100

-50

0

50

100

150

200

r

obs

id

Experimental Results for Second Order Dynamics

1.76 1.765 1.77 1.775 1.78 1.785 1.79 1.795

-80

-60

-40

-20

0

20

40

60

ui

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-100

-50

0

50

100

150

200 r

obs

id

Second Order Dynamics and Various Damping Factor

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


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-50

0

50

100

150


underdumpedsystem =0.5

overdumpedsystem =1.5

critically dumpedsystem =1

a) b) c)

Various Prescribed Dynamicsincluding MRAC

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


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


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


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


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


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


a) constant torque b) first order dyn. c) second ord. dyn.

Conclusions and RecommendationsConclusions and Recommendations A new approach to the control of electric drives with A new approach to the control of electric drives with

induction motors, based on feedback linearisation has induction motors, based on feedback linearisation has been developed and experimentally proven.been developed and experimentally proven.

Three various prescribed dynamics to speed demands Three various prescribed dynamics to speed demands were achieved.were achieved.

Further research will focus on the application of the Further research will focus on the application of the new approach to: new approach to:

a) high power electric drives, including magnetic a) high power electric drives, including magnetic saturation and high speed applications, andsaturation and high speed applications, and

b) enhancement of control system for outer loop based b) enhancement of control system for outer loop based on MRAC or SMC to improve precision of control.on MRAC or SMC to improve precision of control.

Prof. Ján VITTEK & Dr. Juraj ALTUS University of Žilina, SK

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