SLIDING MODE BASED OUTER

CONTROL LOOP FOR INDUCTION MOTOR DRIVES WITH FORCED

DYNAMICS

SLIDING MODE BASED OUTER

CONTROL LOOP FOR INDUCTION MOTOR DRIVES WITH FORCED

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

r

mastercontrol

law

slavecontrol

law

observers

I

innerloop

outerloop

U

d

d

d

I P I U c c ar1 2 1

inner-loop sub-plant

P Ir

c4

r

T TLJ

c 1

5 T I

r

I

Rotor speed and rotor magnetic flux norm are demanded values

MASTER CONTROL LAW

r

T TLJ

c 1

5 T I

r d rT

1

1

motor equation

desired closed-loop equation

P Ir

c4

23 4

c c T I

1

2T d

motor equation

desired closed-loop equation

T Td r Lc

J

TT I

1

5 1

Td

c

c c TI 3

4 4 2

1

2

linearising functions

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

~

~

~

~

~

SET OF THREE OSERVERS FOR STATE ESTIMATION

AND FILTERINGFOR IM

P Ir

c4

I P I U c c ar1 2 1

is based onmotor equations P

r

eliminate

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

Drift Corrections algorithm is used forfinal magnetic flux

filtering

1.Rotor Flux Estimator1.Rotor Flux Estimator

2. Pseudo-Sliding Mode Observer

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

~ ~* *I I U v c a1 1

v v sgn I I max

*

v K I I I

*

For classical sliding-mode observer:-

For pseudo sliding-mode observer:-

,

, KI

-v

I* (not

useddirectly)

slope KI 1 0

0 1

s

Umax

~ ~c a1 1

1 0

0 1

lim

~ ~K

c cI

r

v P1 2

angular velocity

extractor r eq

Tc c p

v T ~ ~

1 2

Umax

r1

s

K K

r

Filtered values of and are produced by the observer based on Kalman filter

3. Filtering Observer3. Filtering Observer

Electrical torque of SM is treated as an external input to the model

where design of:

needs adjustment of the one parameter only or as two different poles:

k J Ts 9 0

~k J Ts 81 4 0

2~

k J ~ 1 2 k J ~1 2

rL

e

Jc k e

k e

r r

r

T TL

L

~~

12 T I

Load torque is modeled as

a state variable

1

s

L

12~

~J

cT T T I

Original Control Systems StructureOriginal 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

rotor speed

Sliding-modeobserver

/signum

slave CL

Slave control law

r

demanded

Overall Control System StructureOverall Control System Structure

L r

Induction motor

Power Electronics

Inner Loop

Controller

Power Supply

Middle Loop

Controller

Outer Loop

Controller

SMCouter loop

Middle loop

Inner loopr̂

ddadi

bdi

cdi

c

b

u

u

c

b

i

i

as

bs

cs

ai

bi

ci

Original Control System Completed with SMC Based Outer Control Loop

- u’ m

+ u’ m

KSM

S

u’ Real System

K

sT

d

1 '

1

s

T s

d ’ d u’

r

r

-

S

S Td r r dtω̂Tω̂ωK

dtSKω

rωrdSM

SMd

]ω̂Tdtω̂ω[Kω' rωrdSMd

Original Control System Completedwith SMC Based Outer Control Loop

(Continued)

Derivation of is eliminated.rω̂

KSM

Implemented Inner/Middle Control Loop with nominal

transfer function 1

1sT

1

s

T

- -

d ‘d

r

r

r̂

S

Inner & middle loop

Slope, K

s

1

T

Ts

Kd1

mu

mu

u

d r̂S

s

d u

&

, &

' '

'

r

d

d

d

s

s

K

sT

K

T T

1

0 1

0

Switching boundary equation:

r̂

dr ˆ

drr T

ˆ

1̂

Ssignuu m

K T T

s

s sT

d

r

d

1

1

1

&

'

SMC based

outer loop

rrd TS ̂ˆ

Experimental Verification

Parameters of the IM:

Pn=1100 W; n=297,9 rad/s; Tn=3,7 Nm

Equivalent Circuit Parameters:RS=7,15 ; RR=7,15 ;LM=0,474 H; LR=0,482 H; LS=0,482 H

Parameters of IGBT Semikron 6MBI-060 are as follows: nominal voltage: 1000 [V] , nominal current: 6x10 [A].Current sensors are as follows: LEM LTA 50P/SPI.

Experimental results for Inner and Middle Loops Alone, 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

0 0.5 1 1.5 2-100

-50

0

50

100

150

200

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 2-50

0

50

100

150

200

a) stator currents b) estim. speeds c) rotor speed

0 0.5 1 1.5 2-600

-400

-200

0

200

400

600

0 0.5 1 1.5 2-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

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 2-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

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

a) stator currents b) estim.speeds c) rotor speed

Experimental results with SM basedOuter Loop, d=200 rad/s, T1=0.5 s

0 0.01 0.02 0.03 0.04 0.05-1

-0.5

0

0.5

1

1.5

2

0 0.5 1 1.5 2-20

0

20

40

60

80

100

120

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 2-20

0

20

40

60

80

100

120

a) stator currents b) estim.speeds c) rotor speed

0 0.5 1 1.5 2-150

-100

-50

0

50

100

150

200

250

0 0.5 1 1.5 2-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

Experimental results with SM basedOuter Loop, d=100 rad/s, T1=0.5 s

Experimental results for d=15 rad/s, T1=0.5 s

1.7 1.72 1.74 1.76 1.78 1.8-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1.7 1.72 1.74 1.76 1.78 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 2-5

0

5

10

15

20

0 0.5 1 1.5 2-40

-30

-20

-10

0

10

20

30

a) statorcurrentsin steady

state

b) rotorspeed

1. Inner and Middle Loop Alone 2. Together with Outer Loop

Conclusions and RecommendationsConclusions and Recommendations

A new approach to the control of el. drives with induction motors, when original forced dynamic system was completed for outer control loop based on SMC has been developed and experimentally proven.

Further improvement can continue via application of the vector control and space vector modulation.

Precise comparison of the effects of MRAC and SMC based outer control loop is also desirable.