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8/12/2019 DTC Controller Design for IM with wavelet Noise Reduction European journal of scientific research_2013

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DTC Controller Design for IM with wavelet Noise Reduction

Khalaf Salloum Gaeid

IEEE Member

Electrical Engineering Department ,Tikrit University ,Iraq

E-Mail: salimhazim2010gmail!c"m

bstract! The alg"rithm "# the $irect t"rq%e c"ntr"l &DT'( inv"lves a $ec"%pling "# )"th t"rq%e

an$ #l%* thr"%gh a t+" c"ntr"l l""ps! In this alg"rithm, the inverter s+itching a)ility is c"mpletely

%se$ as a res%lt impr"ves the "verall system per#"rmance! tat"r #l%* an$ t"rq%e estimati"n )ase$ "n

v"ltage m"$el an$ l"+ pass #ilter is %se$ t" "verc"me the sat%rati"n an$ D' $ri#t! e+ meth"$ "#DT' %sing +avelet impr"ves the in$%cti"n m"t"r "perati"n, s%ch as minimizing the n"ise in the inner

an$ "%ter "perati"n cl"se$ l""p system! The sim%lati"n res%lts pr"ve that the pr"p"se$ c"ntr"l

alg"rithm is e##icient an$ r")%st in )"th transient an$ stea$y state regi"ns!

Ke"words! DT'. In$%cti"n M"t"r. pee$ '"ntr"ller, /l%* an$ T"rq%e Estimati"n, avelet

#$ Introduction

The c"nversi"n "# electrical energy int" a mechanical energy is the principle "# any electrical

m"t"r! T+" in$epen$ent c"ntr"l l""ps can )e %tilize$ t" per#"rm the $ec"%pling "# )"th #l%* an$

t"rq%e "# in$%cti"n m"t"r $rive +hen the DT' appr"ach is %se$ 1! The $ynamic per#"rmance

speci#icati"ns "# the in$%cti"n m"t"r $rive an$ hence the stea$y state are cl"sely relate$ t" the acc%rate

veri#icati"n "# $ec"%pling pr"cess! The v"ltage m"$el )ase$ is +ell-kn"+n meth"$s t" estimate the

#l%* an$ t"rq%e parameters 2, )esi$e the c%rrent m"$el )ase$! ensing "# )"th c%rrent an$ v"ltage

are %se$ as a t""l t" per#"rm the estimati"n! /irstly the DT' +as patente$ )y the invent"r Man#re$ D!

ith t+" patents ,"ne in U an$ in 3ermany4,5! Direct sel#-c"ntr"l &D'( +as the ")6ect "# the

)"th patents! imilar techniq%e, $escri)e$ )y 7apanese invent"rs Takahashi an$ "g%chi terme$ $irect

t"rq%e c"ntr"l &DT'( 8,9!The merits "# DT' c"mpare$ t" the tra$iti"nal ' $rive techn"l"gy are in the #"ll"+ing aspects,

t"rq%e resp"nse, t"rq%e c"ntr"l at l"+ #req%encies, t"rq%e repeata)ility, m"t"r static spee$ acc%racy

an$ $ynamic spee$ acc%racy ;:

The a$vantages "# +avelet trans#"rm is l"calize$ in )"th time an$ #req%ency $"mains, res%lting

+avelet c"e##icients at $i##erent levels an$ scales! cc"r$ing t" that, the +avelet trans#"rm &T(

)ecame s" imp"rtant in the analysis "# signals +ith l"calize$ stea$y state an$ transient c"mp"nents!

+avelet ne%ral net+"rk &( e##ective scheme "# parameter i$enti#icati"n is presente$ #"r

impr"ving $ynamic per#"rmance "# DT' system has )een ma$e )y <! In the c"nventi"nal DT' "#in$%cti"n m"t"r, the stat"r c%rrent l"+ "r$er harm"nic c"mp"nent is very high at l"+ spee$! It yiel$s

mailto:[email protected]

mailto:[email protected]



high m"t"r t"rq%e ripple at l"+ spee$ =! +avelet ne%ral net+"rks &( are applie$ t" DT an$

#l%* c"ntr"l #"r the IM $rives! The c"ntr"ller +ith the str%ct%re "# n"nlinear a%t"regressive

m"ving average &>M( )ase$ ne%ral net+"rk is %tilize$ as spee$ c"ntr"ller t" c"ntr"l the

t"rq%e10! ?ase$ "n the c"nventi"nal DT' meth"$, the t"rq%e an$ #l%* m"$els have )een estimate$

an$ analyze$! The c"ntri)%ti"n "# this paper, a ne+ c"ntr"l meth"$ has )een pr"p"se$ t" s"lve spee$

harm"nic c"mp"nent at l"+ spee$! T" #%rther impr"ve the t"rq%e resp"nse an$ re$%ce the t"rq%e

ripple, +avelet n"ise re$%cti"n c"ncept has )een intr"$%ce$ int" the t"rq%e an$ #l%* m"$els!

The paper is "rganize$ as #"ll"+s! In ecti"n 2, +e present the DT' "perati"n, an$ then +e ")tain

the spee$ c"ntr"ller in ecti"n 4! In ecti"n 5, +e present +avelet n"ise re$%cti"n, an$ the res%lt an$

$isc%ssi"n "# the pr"p"se$ appr"ach is ill%strate$ in ecti"n 8, an$ the paper en$s +ith s"me

c"ncl%$ing remarks in ecti"n 9!

%$ DTC &'eration

There are t+" general c"ntr"l meth"$s in varia)le #req%ency $rive &@/D( ,vect"r c"ntr"l an$ scalarc"ntr"l! Direct t"rq%e c"ntr"l &DT'( is c"nsi$ere$ as a "ne types "# the vect"r c"ntr"l +hich is

%se$ t" c"ntr"l )"th in$%cti"n m"t"r t"rq%e an$ spee$! Meas%rement "# )"th v"ltage an$ c%rrent "#

the m"t"r is %se$ t" estimate the t"rq%e an$ #l%* 11! The estimati"n "# stat"r #l%* linkage has )een

per#"rme$ )y integrating the )"th $irect an$ q%a$rat%re stat"r v"ltages! The estimati"n "# the t"rq%e

+ill )e ")taine$ )y pr"$%ct "# estimate$ m"t"rAs stat"r #l%* an$ c%rrent vect"rs! '"mparis"n estimate$

#l%* magnit%$e +ith the re#erence #l%* an$ the estimate$ t"rq%e +ith re#erence val%e is the ne*t step

in the generati"n "# c"ntr"l signal pr"cess as can )e seen in /ig!1!/l%* hysteresis an$ t"rq%e hysteresis

c"ntr"llers #i*e$ +ith certain all"+e$ t"lerance #"r each "# them! I# the $i##erence )et+een estimate$

t"rq%e "r #l%* an$ their re#erences m"re than all"+e$ t"lerance, the I3?T s+itches "# the @/D are

t%rne$ "## an$ the err"rs "# the #l%* an$ t"rq%e +ill remain at l"+ levels! The a)"ve c"mparis"n "#

)"th t"rq%e an$ #l%* +ith their re#erences +ill c"ntr"l the v"ltages "# the inverter 12! The s+itching

is a ran$"m pr"cess )eca%se "# the hysteresis )ehavi"r c"ntr"l!

(ig$#$ DT' principle pr"cess

The DT' can )e $ivi$e$ int" t+" types, either $irect sel# c"ntr"l&D'( "r space vect"r

m"$%lati"n&@M(14! The s+itching ta)le in DT' all"+s selecting the vect"r p"siti"n t" apply t"

the inverter acc"r$ing t" the D' "# the stat"r #l%* an$ the electr"magnetic t"rq%e 15 as can )e

sh"+n in ta)le 1! /r"m ta)le1, "ne can n"tice that the s+itching #req%ency "# the I3?Ts %se$ in this

scheme is n"t c"nstant! I# +e c"ntr"l the t"lerance )an$s, the average s+itching #req%ency can )e kept

at its re#erence val%e, hence the c%rrent an$ t"rq%e ripple +ill )e minimize$!

http://en.wikipedia.org/wiki/Voltage


http://en.wikipedia.org/wiki/Electric_current






Ta)le 1!+itching Ta)le "# DT'

ect"r

1 2 4 5 8 9

1+=φ d

1+=dT 2u 4

u5

u 8u

9u

1u

0=dT 0u

;u

0u

;u

0u

;u

1−=dT 9u

1u

2u 4

u5

u 8u

1−=φ d

1+=dT 4u

5u 8

u9

u1

u2

u

0=dT ;u

0u

;u

0u

;u

0u

1−=dT 8u

9u

1u

2u 4

u5

u

hen the in$%cti"n m"t"r r%n +ith higher spee$s, there are n" sensitive parameters )%t at l"+spee$s the stat"r #l%* estimati"n )ec"mes s" imp"rtant an$ critical $%e t" err"r in stat"r resistance

pr"perty 18191;

2.1. Torque and Flux Estimation

M"re attenti"n has )een pai$ t" the v"ltage m"$el #l%* estimat"r rather than the c%rrent m"$el )ase$

in its clear c"ncept an$ simple signal pr"cessing! The initial err"r val%e an$ D' "##set inp%t, in l"+

spee$ stage, cann"t )e s%ppresse$ )y the l"+ pass #ilter &BC/(, as +ell as , the BC/ )rings stea$y-

state err"rs in )"th amplit%$e an$ phase 1<!

The $q $ynamic m"$el "# a sq%irrel cage in$%cti"n m"t"r +ith a re#erence #rame #i*e$ t" the stat"r is

given )y 1=:

s s

s

s s s M j

dt

d

i RV φ ω φ

++= &1(

r r sr r r M

dt

r d

i RV φ ω ω φ

(& −++= &2(

The #l%* "n the q-a*is +hich is the real part "# the stat"r #l%* can )e ")taine$ as in &4(

∫ −= sqsqsqs Rivφ &4(

The #l%* "n the q-a*is +hich is the Imaginary part "# the stat"r #l%* can )e ")taine$ as in &5(

∫ −= sdsdsds Rivφ &5(

The estimate$ stat"r #l%* can )e ")taine$ as in &8(

dsqs s jφ φ φ += &8(

The magnit%$e "# the #l%* is:

dsqs s φ φ φ += &9(

The phase shi#t +ill )e as:

real

img a tan=ϑ &;(

The electr"magnetic t"rq%e is #"%n$ as:

(&4

2qr dsdr qs

r

me iiii

L

pLT −= &<(



(sin&DDDD δ φ φ σ

r s

r s

m

e L L

pLT = &=(

δ is angle )et+een the r s φ φ E vect"rs

r s

m

L L

L2

1−=σ &10(

here σ is the leakage #l%*

The t"rq%e an$ #l%* estimati"n circ%it can )e sh"+n in the /ig!2

3angle

2Flux

1Torque

K Ts

z-1

phi_q

K Ts

z-1phi_d

Re

Im-1

3/2*p

Rs

Rs

|u|

u

Ids

3

Iqs

2!d

1

!q

i_qs

i_qs

i_ds

i_ds

(ig$% $ Tor)ue and flu* estimation

ItAs ")vi"%s #r"m &=( that an increase in t"rq%e can )e ")taine$ )y increasing the phase angle δ

)et+een stat"r an$ r"t"r #l%* vect"r& r s φ φ E (! Divi$ing the vect"r ∆ int" h"riz"ntal an$ vertical

c"mp"nents, the vertical c"mp"nent "# ∆ )eing resp"nsi)le #"r t"rq%e c"ntr"l & sq ( an$ the

h"riz"ntal c"mp"nent & s

d

( c"ntr"ls the #l%* as sh"+n in /ig!4!

ds

qs Torque increase

flux increase

Lamda(r)

Lamda(s)

(ig$+$ DT' $rive c"ntr"l "# )"th #l%* an$ t"rq%e

T+" schemes "# DT' c"ntr"l +as implemente$, "ne +ith"%t %sing +avelet techniq%es as can )e

sh"+n in /ig5! an$ the "ther "ne +ith +avelet n"ise re$%cti"n as +ill )e seen later!



2

"ag#

1

$a%es

Flux sele&%ion

'(F

%orque (I

Torque and )lux e s%ima%or

PWM generation

)lux (I

+ %o ,# %rans

.

!_a&

I_a

3

Flux*

2

Torque*

1

!d& us

/ig!5 ! im%link implementati"n "# the DT' +ith"%t avelet

+$ S'eed Controller

The $irect t"rq%e an$ #l%* c"ntr"l &DT/'( %ses a select"r s+itches statements "# the v"ltage inverter

c"mp"nents %sing ne%ral net+"rk $"ne )y 20! s can )e seen in /ig!8, DT' %ses l""k%p ta)les t"

select the s+itching pr"cess acc"r$ing t" the inverter states! 21!cc%rate kn"+le$ge "# )"th

magnit%$e an$ p"siti"n "# c"ntr"lle$ #l%* sh"%l$ )e kn"+n t" get e##icient DT' c"ntr"l in the

in$%cti"n m"t"rs!

The meas%re$ stat"r v"ltages an$ c%rrents are %se$ t" ")tain the #l%* acc"r$ing t" the stat"r v"ltage

m"$el as menti"ne$ )e#"re in /ig!2 !This meth"$, %ses the "pen l""p trapez"i$al integrati"n !The

c"ntr"l alg"rithm %ses the CM meth"$ are )ase$ "n average val%es an$ the s+itching signals #"r

the inverter 22! Cr"p"rti"nal pl%s Integral &CI( c"ntr"ller an$ the CM is %se$ t" minimize the

t"rq%e ripples an$ make inverter have )etter e##iciency!

2

Torque*

1

Flux*

Saturated Multi switch

ZIC Rate limitter

LPF

lookup table

PI3

"ag#

2

re) speed0*

1

a&%ual speed0

/ig! 8 ! im%link implementati"n "# the spee$ c"ntr"ller

,$ Circuit Im'lementation

The e##ectiveness "# the pr"p"se$ DT' )ase$ "n +avelet n"ise re$%cti"n )l"ck $iagram is $epicte$ in

/ig!9!

In this circ%it sampling time is 2e-8 ec %se$ t" )e very #ast in "r$er t" prevent the #l%* an$ t"rq%e

$eviati"n #r"m the all"+e$ t"lerance! I# the c"ntr"l alg"rithm has 18- 40 Fsec e*ec%ti"n time "r less it

+ill give g""$ res%lts as +ell as it +ill )e a simplicity in$icati"n "# the alg"rithm!



-C-

wref

powergui

1/z

1/z

VabcA

B

C

a

b

c

IabcIab

*

s% )lux

re) Flux*

Torq re)*

4peed #on%roller

Tm

Signal Build

mwm

is_abc

Tm

measurA

B

C

IM

Induction Motor

Pulses

A

B

C

IGBT Inverter

F28335 eZdsp

Flux*

Torque*

I_a

!_a&

s% )lux

$a%es

T#

RT

RT

RT

actual speed

/ig!9 ! im%link implementati"n "# the pr"p"se$ alg"rithm

In this circ%it there are many ")servati"ns +hich give the DT' c"ntr"l its p"+er#%l s%ch as, there is

n" nee$ #"r c""r$inate trans#"rms )l"cks )eca%se the in$%cti"n m"t"r is +ith stati"nary re#erence

#rame! CI c%rrent c"ntr"llers are eliminate$ #r"m the inner l""p ,hence n" t%ning an$ #aster time "#

implementati"n! /inally, the D' ripple is re$%ce$ t" l"+est level $%e t" the r")%st DT' scheme!

-$ .avelet Noise Reduction

The meanings "# the +avelets are little +ave "r ripple +ith small time $%rati"n, the pr"perties "# the

+avelet that $i##erentiates it #r"m the "ther signal pr"cessing techniq%es an$ make it )etter than the

"thers! The +avelet either "rth"g"nal "r n"n "rth"g"nal24 ! The +avelet $ilati"n an$ translati"n are

%se$ t" trans#"rm the "riginal t" ne+ signal +ith smaller scales acc"r$ing t" high #req%ency

c"mp"nents!

The scaling #%ncti"n $etermine$ )y the B?/ s" that is ass"ciate$ +ith the appr"*imati"ns "# the

+avelet $ec"mp"siti"n, the +avelet #%ncti"n $etermine$ )y the G?/ s" that is ass"ciate$ +ith the

$etails "# the +avelet $ec"mp"siti"n!

The "ise >e$%cti"n s%)system sh"+s +avelet )%t +ith a s"#t thresh"l$ applie$ t" the

trans#"rme$ signal )an$s!The pr"p"se$ t"rq%e an$ #l%* +avelet n"ise re$%cti"n reg%lat"rs are $evel"pe$ )y %sing +avelet

$)10 +ith < levels $ec"mp"siti"n as can )e seen in /ig!;!



2

$a%es

1

"ag#

Torque (I

Flux and %orque es%

Noise reduction wavelet

Noise reduction wavelet

Flux Selector

LPF

PWM Generation

)lux (I

+ %o ,#

.

!_a&

I_a

3

!d& us

2

Torque*

1

Flux*

/ig! ; ! im%link implementati"n "# the DT' +ith avelet

?y atten%ating the higher #req%ency )an$s, the high #req%ency n"ise is re$%ce$ an$ the thresh"l$levels can )e a$6%ste$ t" see the e##ects "# atten%ati"n "n the $en"ising characteristics "# the system!

ne+ c"ntin%"%s +avelet eq%ati"n +as $evel"pe$ this circ%it as in &11(!

(<H(50&&I2(42H50&& −+−= t F t F W &11(

here F is the #l%* #%ncti"n as can )e seen in the /ig!< an$ /ig!= #"r r%nning signal that %se$

a$aptive &$)10 (+avelet !

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

n egra = .

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

Pattern and Adapted Wavelet

/ig!< ! In$%cti"n m"t"r act%al #l%*&a)"ve( +ith a$apte$ +avelet #l%* "%tp%t

0 20 40 60 800

1

2

Running SignalF((t-40)/32) + 2 F((t-40)/8)

Pattern Detection using Adapted Wavelet

0 20 40 60 80

8

32

64

/ig!= ! In$%cti"n m"t"r r%nning signal &a)"ve( an$ pattern $etecti"n +ith a$apte$&$)10( +avelet



Using Matla)Him%link t" #in$ the percentage "# energy c"rresp"n$ing t" the appr"*imati"n

in#"rmati"n &Ea(, an$ the percentages "# energy c"rresp"n$ing t" the $etail in#"rmati"n & E $ ( as can )e

sh"+n in ta)le 2 +hich is acc"r$ing t" Eq!12 investigati"n!

(,&2, LC energ! E E "a = &12(

here &C#L( is the stat"r c%rrent &Ia( $ec"mp"siti"n at each level

Ta)le 2! Energy percentage "# $etails an$ appr"*imati"n +ith 11 levels &$)10( +avelet

Energ"

/ercentage

00$012+ 00$0132 00$0100 00$03#

#

00$03#

,

00$03,

0

00$003

,

00$000

+

00$000

0

#44$44 #44$44

Ea 00$0-00 00$012+ 00$0131 00$010

0

00$03#

4

00$03#

-

00$03,

0

00$003

,

00$000

1

#44$44 #44$44

Ed 4$4#2, 4$44%+ 4$44#% 4$44#% 4$444, 4$44+, 4$4#+- 4$44#+ 4$444% 4$444

4

4$4444

The "ptimal $ec"mp"siti"n +ith respect t" a c"nvenient criteri"n can )e ")taine$ )y an e##icient

alg"rithm! The entr"py & E ( #%ncti"ns is a criteri"n that veri#ying an a$$itive-type pr"perty are +ell

s%ite$ #"r this )eca%se E &0( J 0 an$ there is n" in#"rmati"n l"ss25! cc"r$ing t" the entr"py & l"genergy( type ,the )est level is 9 as can )e sh"+n in /ig!10!

(0,0)

(1,0) (1,1)

(2,0) (2,1)

(3,0) (3,1)

(4,0) (4,1) (4,2) (4,3)

(5,0) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (5,7)

(6,0) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) (6, 7) (6,8) (6,9) (6,10)(6,11)(6,12)(6,13)(6,14)(6,15)

2000 4000 6000 8000 10000 12000 14000-0.05

0

.

/ig!10!?est level $ec"mp"siti"n, )est tree&le#t( an$ $ata #"r n"$e&9,18(

2$ Results and Discussion

T" veri#y the pr"p"se$ alg"rithm, a sim%lati"n has )een carrie$ "%t )y %sing Matla)H im%link! The

starting c%rrent is re$%ce$ #r"m &9!8-2!8( mp +ith"%t m%ch $ist"rti"n! The stat"r c%rrent $%ring

varia)le re#erence spee$ is $epicte$ in /ig!11!



0 4 8 12

2.5-

0

2.5

5

Time(sec)

C

u r r e n t ( A m p )

/ig!11! In$%cti"n m"t"r c%rrent

The stea$y state resp"nses at spee$ 2000 >CM %n$er #%ll l"a$ t"rq%e &4!8!m( an$ at spee$

4000>CM %n$er l"a$ t"rq%e &2!m( "perating c"n$iti"n are ill%strate$ in /ig!12! It is n"tice$ that

the presente$ scheme $elivers a stea$y state per#"rmance at spee$ 2000>CM an$ ;0 >CM transient

spee$ resp"nse +ithin a minimal time "# 0!4 ec!

0 4 8 120

400

800

1200

1600

2000

2400

2800

3200

Time(sec)

S p e e d ( R P M )

/ig!12! In$%cti"n m"t"r spee$ re#erence an$ act%al spee$

The 19!99 K t"rq%e "versh""t is re$%ce$ t" <!8;15K in the case "# pr"p"se$ +avelet n"ise

re$%cti"n meth"$ as $epicte$ in /ig!14! It is n"tice$ that the +avelet pr"p"se$ scheme pr"vi$es a

sm""th stea$y state per#"rmance in terms "# t"rq%e t" impr"ve$ "verall system per#"rmance!

!

0 4 8 12

4-

2-

0

2

4

Time(sec)

T o r q u e ( N . m

)

/ig!14 ! In$%cti"n m"t"r t"rq%e +ith +avelet &re$( an$ +ith"%t +avelet &green(



The t"rq%e err"r )et+een +avelet n"ise re$%cti"n t"rq%e an$ t"rq%e estimati"n in pr"p"se$ meth"$

is l"+ an$ eq%al t" L0!4!m as can )e sh"+n in /ig!15!

1 2 3 4 5 6 7 7 9 100.4-

0.3-

0.2-

0.1-

0

0.1

0.2

0.3

0.4

Time(sec)

T o r q u e ( N . m

)

/ig!15 ! T"rq%e err"r )et+een +avelet n"ise re$%cti"n t"rq%e an$ t"rq%e estimati"n

The D' v"ltage $elivere$ t" the circ%it can )e $epicte$ as in /ig!18!

0 4 8 12500

550

600

650

700

750

Time(sec)

D C v o l t a g e a p p l i e d ( v o l t )

/ig! 18 ! In$%cti"n m"t"r D' v"ltage

The stat"r #l%* estimati"n +ith an$ +ith"%t +avelet can )e sh"+n in /ig! 19!

0 1 2 3 4 5 6 7 8 9 100

0.10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time(sec)

F l u x ( W b )

flux estimation without wavelet

flux estimation with wavelet

/ig!19 ! In$%cti"n m"t"r #l%*

The parameters "# in$%cti"n m"t"r that are %se$ in this sim%lati"n are sh"+n in ta)le 4!

Ta)le4!In$%cti"n m"t"r parameters



M"t"r speci#icati"n Unit @al%e

C"+er + 1

'%rrent mpere 2!8

@"ltage &$elta( @"lt 500

>ate$ spee$ 2<00 >CM

"! "# C"le 2

M"ment "# inertia g!m2 4!8e-5tat"r resist! N 20!=

>"t"r resist! N 1=!8

tat"r in$%ct! Genry 80e-4

>"t"r in$%ct! Genry 80e-4

2$ Conclusions

This paper has presente$ a m"$i#ie$ DT' )ase$ "n +avelet net+"rk as n"ise re$%cti"n in )"th inner

an$ "%ter cl"se l""p system "# stat"r #l%* an$ t"rq%e estimati"n #"r impr"ve all system per#"rmance!

?est "perati"n ")taine$ +ith the +avelet t" minimize t"rq%e an$ hence spee$ err"r )et+een re#erence

an$ act%al val%es! Gigh e##iciency l"+ l"sses )eca%se the I3?Ts %se$ as s+itches +"rks +hen it

is nee$e$ t" keep t"rq%e an$ #l%* +ithin all"+e$ t"lerant )an$s "# hysteresis c"ntr"llers!

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