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Abstract

This purpose of this research is to

develop a hIgh efficient temperature

estimation system for induction furnace in

the Somboon Malleable Iron Industrial Co,Ltd.

The mam obstruction of temperature

measurement is that the thermocouple

cannot be used to measure temperature

continuously because of the high temperature

of molten steel. Therefore, the comparly wants

to develop all efficient temperature estimation

system. The temperature is estimated

indirectly from the power input, the coolant

temperature, and the flow rate of the coolant

in order to find a mathematical model of the

induction furnace. In this research, the

recursive parameter estimation usmg Kalman

Filter is proposed for state estimation of the

linear dynamics in finding its parameters in

order to estlmate the molten steel m the

inductlOn furnace.

Key word : Induction Furnace,

Temperature Estimation. Recursive Parameter

Estimation, Kalman Filter

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~U~~ bd ~1'Vl~Bru'lll.n~~~~ 19l'l'l~B~nl'j , " . b'VlJI16i'lll~~~lubb:Ubb'iJ'iJ 0,500 B~Al-

b'll6H'iitlEil)

bUUBru'lllilj]tll b'lll~nlu bd6nf1tJj~~lru1(P)' , 'II

..J . 'l'lb'd~1 1

Tii-1) bUu~ru'llldJj]tllb'lll~nlu b'd 6ilf1tJj~~lru 1(P)'

f1b1~1 i-1

PIr/i) ~~~'~nu1~~liJBUb'l11 (kW)

A1w (i) erl9ljlmj1'V11il'llB~tll'l1l~tJbiJU(kg/hr)

tlT,y (i) t:J~~I\l~ru'llldJ~'1lB\lthlll~miJu(K)

bUU Fhf1~un'iJ 1011 t'ldl ~~fl'dl~1BU~1 b~l~. bb~~~d 6i'1JeNJ11~'lIl~

buulOilf1~Un'iJlOilt'ldl~~t'ldl~1"BU~1 b'Vn~

'1lB~tll'l1l~B biJU '1lB\lj~U'iJ b'llltiHdl111~~'l

bUuFh'Vi6J1un'iJn1j 6'lru b~ tl t'lJ'l~1€lU'lleN" ~

J'll~'lIl~

~. a:>nSDVmSRU1U (Kalma~..filter)

Kalman Filter [5.6,7.8] buum::'iJ'du­

mjdu.Jl'llB~'l1B~~f1~::'Vhn1jtJj~~lru6'l bl9lI?l'1l B~ 'lJ

j~'iJU~~F1'l6'l19l1 b'1l~ b~uf1ii~t1Jb!JlrujUmU <E~1u mjtJj~~IRWbl9lI?l'1l€l~ Kalman Filter ~~b'l11fi~

tJ~ ~lruf11(P)'~1 nn1jll?l'llB~j:-;'iJuf1ii t'lJl~ ~~~UJ5

b'B~b~UnU6'lbl9ll9lbb1il:-;~mtJmu(P)'dtl~t1Jt1Jlruj'iJm'U

11?ltl Kalman Filter ~~~hdJumjn'iJ'VJn 1 m~lfIJ

f11l9l1#)~lm:-;'iJtJ~\ltJ~~lru'Vil1911~m.h~ bb:U'U til

bb1il:-;tJ1~lruf111?l1~1:u bb:U'U til bV;BVhmjtJj~~lru

Eil bl9l191'llB ~j~'iJU 1l9l tl~:-;1i~ ~~H1(P)'~1 m~'iJtJj'd ~1tJ 'lJ

n~ b'll'U b'1lf:d ~t1JQJlrujtJm'U~lnmjll?lbb~:-;'VJn 1

"l1mJ~1'Umjr11'l1l'Ul9lFll'llB\l6'l bl9ll?lck\l~'U'1JtJ'lj:-;U'iJ "

~I?l b~~~'U'lIl~nm&'1lB~ "Kalman Filter" , z;.. ""'" IV I £::>.~ Q QJ

U'U~I~ln'lll1illn'VI1il1 tl'Vlt)'ltt]t'lJl ~~ b'll'U dUm 1il~

6'l€l~1!tJtlf16'l1?l (Least squares), 115FllbliJ~t1r11~~• 6W\ltJmJf1~1?l (Least mean squares), 'Vlt)'lt~

t'l'dl~'t.h~:-;btJ'U (Probability theory), &~'iJumj

~~'V11~ 6'lfr&i (Stochastics systems) <E~'Vlt)'lt~

bb1il:;fl'dl~1b'lll~ldii bUU~U~I'U1un1jtJBnbbtJ'iJ 'lJ oJ

Kalman Filter

TI~'ljrulj:-;U'iJ bb'iJU~I1iltJ\l~ ~F116'll9l4 bbtJU

1:u~mtJtJ~

x(k) = Cl>(k - J)x(k -1) + r(k - J)u(k. --1) + w(k -I)

(12)

y(k) = H(k)x(k) + v(k) (13)

11?ltlvi w(k-l) FiB ~t1Jt1Jlruj'iJm'U'llB~

m:-;tJ'd'Unlj (Process nOIse), v(k) FiB ~QJb!Jlru

~f1JnSSU(llS un

jUmU~lnmjl~ (Measurement noise) bl,61:; bbiil:;l,xiifOilml~ bb1.h1Jj1U~1~ (cova­

l,x~ill illlru~-:I ~ B-:I bUU ~ill illlru bbUU 1:l~ (random riance) dJ'Ul1J~I~-nml1V1'U ~~-:ld ~~ ~~ q

sequence) ~i1rilbQ~m1J'UfI'U~ Aa ...

E{w(k)w(k)T} = R ' E(v(k)v(k)T) == Rw v

E{w(k)) = E{v(k)) == 0

~ln~~mjvl (12), (13) lrhJfl-:l~1ma~

~-:I~QJ(j,jlru~-:I Sla-:ll~ilml~~~rr'Ui5n'U f111 61~I'U~:; ~11-:11:;UU~'Vh mj1J1:;~1 ru~ b~ ~

'Vll-:1 b1iillV1~B b~tml1 b1J'U~QJtlll ru1um'U~'lJl1 ~fl-:lJ:;UUb~~1~8l~fOil~6'l~I-:1J:;Vl11-:1nljl~~~-:I

(White noise) FiB (y(k)) bbiil:::"llnm1t!J:::tnru (YCklk)) ulm

1J1'U\~lJ'l'll'UltJm~~ i(kjk)) '1l-:lbbr;;1~\l~\lm~~ 4

E {w(i)wU) T} == E (v(i)v(j)T) = 0 ~1 i :F j

I w(k -1) v(k) ,

x(k) r ­u(k-I) ! /~ , ~ y(k) r(k -1) i--- ~ }------- _. --' --1 H(k)

L \..J­"-- ../, ---!I ..

, ----- ,r--l:I I x(k -- 1J. __, i ! '----1 <I>(k - J) ~ oj z-t 1­

___JI , J.L --------, -------------------------------------------------------l-----­

i ,~-.- ---1 ,/- i(klk - I) ,--'--- y(kjk)/'\ --j I (k -I) I ~ )------ -----'1 H(Ir.) r ._----.-\.)

~'Hl'HNftl{(l:lJl~-__ ..-J i - [ x(k-l[k-l) I

r------l r--l If- -----J e(klk -I)

1$(k -I) ------1 z-' J~J~ L(k) r-----·~ ,_. ..J L--i(k!k) ---'

63 Dn 21 8UJ18U 2550 UU18U 2551

';;:n nJll'V'lvl 4 'Vii rn"J ~ 11~ 6UJn 11 (9)1

1J"J~mrumWl~ x(k) 1~~~D

(9)11J1~~lrurif)tJm!1 (Priori estimate):

x(klk -1) '" C1>(k - l)x(k - Ilk -I) + r(k - t)u(k -I)

(1.4)

~11J"J:;~lruWll~'lIl~~ (Postenori estimate):

i(klk) = i(k\k -1) + L(k)[y(k) -- H(k)i(klk -1)]

(15)

o I ..c:ti , q.,

nlVltJ~A1A11~A~I~bF1~BtJnBtJVltJl

(Priori error) bb~:;fh Adl~A~I(Yl bl'l~BWrn~Vl~~

(Postenori error) 1~djtJ11Jm~6'1~rn1v1 (16) bb~:;

(17) AB

(16)e(klk -1) =x(k) - x(k!k -1)

(17)e(klk) = x(k) - i(klk)

bb~~nTVltJ~lVfrilA11~F1~1l91bl'l~mJ bbwilil::

(9)1lVfiJAl A11~F1 ~l~ bF1~m.J"l.IB~A1F1dl~bbU 1­

U11tJi1~ (error covariance) IYll~~~nTJyj (18)

bW:; (19) AB

F111~l'I~l~ bl'l ~€1'U"l.JB~ filF111~ bbU"JU"J1tJ

11~rimJ'llltrl (Priori error covariance):

p(klk -1) == E{e(klk -l)eT (klk -1)}

(18)

:5 f) J n s s u Ci I S

l'Idl~F1~I~ bl'l~€I'U"l.leNfhfrJl~bb1J11hdtJ

id~Wll~'lIl~~ (Posteriori error covariance):

p(klk) == E~(klk)eT (klk)}

(19)

1~t1v1 E(·} bbV1tJfhF111~F11~Wr~ bb~~

~nn6'1~rn1v1 (15), (17) bb~:; (19) G'lim"JflVll

F111~l'I~l~bF1~BtJ"l.If)~A1F1dl~bb1J1U11tJid~Wll~

Vl~~ P(klk) 1~~~D

p(klk) == (I - L(k)H(k))p(klk -1)(1 - L(k)

H(k)Y + L(k)R,C (k) (20)

fil L(k) vlrhlVffil~~wil~nl~~~B~

E{er (klk)e(klk)} = fE{e: (klk)}= trP(klk) i=,j

yjbd~1 iJfiltrBtlyj~(Yl ~lm1nVll1~~t1

8tr(P(klk))---'---=0

oL(k)

~ < otr(ABA T

) 1"'onmBn~m;-ru = 2AB 'Ol:: ~

aA Fh L(k) (9)l~~~m1v1 (21)

L(k) '" p(klk - t)H T (k)(H(k)P(kik .- I)HT

(k) + R, t (21)

b~ml1~~m1v1 (21) bbV1'U6NltJSl~m1'Y\

(20) ~~1~

p(klk) =(1- L(k)H(k))P(klk - J)

(22)

'Olln1i1~m1v1 (18) 6'11~11fl'llllrnl~A~I(Yl

--- - -- --

LA~BU~B~~lAl1~U~~~11U~1~ri8UM~1

~k 1k-) 1li1Ael

p(klk -1) == <])(k -1)P(k - Ilk -1)<I>(k - 1/ + R",

(23)

~l n fll~~ ~~U"l!1~lPiumm11~'1'Vl~ t'l'1Jel'l

li11mB'IAT~6'lmUbbl.i'lbUU 2 ~1~bJWI li1~.a

1. G'l~m1 iihM11J fll~tJ~'JJ~lvl~Wl.'U b1 sn (Time update):

i(klk ·-1) == flI(k -l)i(k - tlk -1) + r(k -' J)Il(k -1)

p(klk -1):::: <lJ(k np(k - 11k _I)~r(k -1) + ~

2.~~n11~lM~'JJn11tJ~uAlvl~Un1Jnl~1t'l

(Measurement update):

L(k) == p(kik - 1(.)(H(k)P(klk -IIH (k) + R JI P(k!k) == (I - L(k)Hlk»)P(kjk t)

x(klk) == i(klk -1) + L(k)(y(k) _. H(k)x(k!k -1»

~~b!lml16l~fll~vY'I 2 tJ1~bJW1"l!1'llPium

l-klU n11rllU1 ru n1 ~'JJ1U n11"lJ eJ~ li11 n1el'l

rn16'l~lU [9] ~~iJ,ffu~e:Juli1'1.a

1. nlVlU~Alb1~~U x.(0 10), P(O I0)

2. A1UltlJrh P(k Ik-1) 1t'l~l-k P(k-11 k­

1), k-1) bb6'l:: :i:-<'w

3. A1UltlJFll L(k) 'O:jln P(k Ik-1), H(k)

bb6'l~ I\. 4. A1U1ruAl P(k Ik) 'O:jln~l L(k) bb6'l::

P(k Ik-1)

5. A1U1ruMlli11~~~~ltlJ i(k Ik) ~lnFh

L(k), bb6'l:; y(k)

6. 1'll'lhk~ bb(?\-5WneJ1Jvi 21~~un~.ffut'leluvi

5 bb6'l:;'O:j:;'O:jum:;U1Ufll~btJB1'l1.Jln'lril k V11li1

nlVlUt'lH

4. mSrJ~C11t1t.f:mSDumS8Ululunuu

rilROOJCTllf8oofa - uu,ndEJ:JUl1WM

'W'O:jl~rulbbUU~l6'lB~b(nl'Vl6'lf.l~1~M:; bb1J1J

bVld~1thlvJthlu~~m~vi (3) b116il~1~fl~t'l1~ '"

1Vi'B ~lu1tJ'lJ8~ bb'JJ'JJ~l6'le:J~ m11t'l'lJB~li11mB'l " '"

A11~~lU (y(k) == H(k)8(k)+v(k)) 'lli1li1~.a (bUU

b16'llvilottufll~M~f.nJ1~'Vl:;)

a (k)'!

e,(k) \+v(k)I:,(k) == [~,,(k) - M" (k)M;, (k) -1 T (I< _ 1)"/ f ; .11 (I, (k) \

LB,(I<).

(24)

LL6'l::: v(k) Ael ~rurulru11Jm'W~lnm11t'l1t'l~iJ

bbUU~l6'le:J'I"f'j ~f11~ (n1 bLUU1:l.i ~mii8~ li1~.a

e(k) = <D(k -1)6(k-l)

(25)

1(n~vi (1J( -1) A8 b~'Vl~n'1lbeJn~n~ru

(Identity matrix) 'lJ'Wl~ 4x4

"","VI ~.d,/ I

'O:jln'l1'W1~~neJ'WM'Wl'W6il~11flVllAl

'V'l1~liibt'le:J11t'l~1-k1fjb'O:jI,'W~n86'lnel~'Vi~ (Genetic

Algorithm) 'li'l1li1t:-J~lP1~dAf) 81=0.0005, 62 ==

0.027, 83 == 0.0915 84 = 1 u~lu1Fl1'1'11'W1~l:J.a

~::1i n 1 ~ ~ 1:: ~Jl ru Al'V'l111 ii bt'l 81 bbU1J 1'W.Jl

(Recursive Parameter EstimatIOn) li11~li11

\ . LJun -63 0r121 Sl1:11rlu -?550 . OU1PiU :.1551 I

mfNF\T1~:lJ1U (Kalman FIlter) 1UnI';jVl1fOh

'ji11111iJb\nB1 e1,82,e3,84 b~B'vhm';j1.h:;:l.nru

~ru'llllJiJ'lJB~J11~'lIl:; (Ts(k)) 1W\n1'l1l61B:IJ1~'lIl:;

bbU'lJ b'lllfl VJtl11'V'lvh

5. Qtlnsnilla.:5sms

h1u1bbFl1:IJ LabVIEW 'Yib'1lB:lJt9iBflu

FieldPoint Module (FP- 2000, FP-AIO-600, FP­

Al-lll) 1Unl1 bn'lJ'lJB:lJ6'l'vl1~1~~1Fl bm'lll~€:I:IJ "

1~mhu'Vl-:i1'Lliilii\nb\9l€:l1 (Transmitter) br:j8

bbU61-.:J~Ww1rubtJum:;bb1.'l1'V'lf:j1:IJ1\9l1~1'Ll 4-20 rnA Q..' 1l...; ojL.<i

1\9ltJ~:: b1:IJ'Vh n11 bn1J'1J€:I:IJ 1.'1 b~ €:I b'lIl ~ nrl mlt'Ll" "

6'tfn1::rl'lll61B:lJ6'l:: 6nmtJ'Ll'lJ€:I~ b'lll6'l1 bb~1 .:E~'1Je:J:lJ6'l "

rl'V\'1m11\9l~e:J f)\9l11n111'l1l1.'l'lJe:J~J1'l1l~m~U (Flow

meter:400 l/min) e:Jru'lllilii'lJ€:I~J1'l1l6'im~'Ll'lJ1b'l11-, " '1J1Be:Jn (Thermocouple TYPe K) bb6'l:::€:Iru'lllil~ , " U1F1l\9l1'l1l6'le:J:IJ (Thermocouple TYPe R) sh'Ll

'jill ~~~1'Ll1'V'lf:j1iJe:JU b'1J1 b\9l1'l1l 1.'l€:l:IJ b~e:J b'lIl ~ n rt n "

'lIl6'le:J:IJ~:;1.'I1mb~1'~:;iiri1'ji11l,hn'LlA-.:JVilo'ie:J 1.1 00 kW

1i1U1bbF11:IJ MATLAB t11'l1€:1:IJ1.'l~1~1u'V\'1 "

bb'lJ'lJ ~11.'1 e:J-.:J €:Iru 'lIlil ii'lJ e:J-;J b\9l1'l1l 6'l €:I:IJ16'!'lIl:: 1?11 tJ1f5 , " b~bU~nf)6'1F1e:J~Vi:IJ (GA) br:jB61:IJ:IJ~1vfbtlu

e:Jru'llliliJ'lJe:J-.:JJ111.'l'lll:;1u bvnrl1\9l1I91mh~t9ie:J bfl8~ , " 'lIl~-;J'~nmr'Ll'V\'1n1J'lIl1fih'jill111iJ b\9le:J1 81, e2,83, 84

1~t11i~1m€:l~F\11mJ1'U (Kalman Filter) b~e:J'lIl1

bb'lJ'lJ~16'l e:J~e:Jru'llliliJ'lJ€:I~ b\9l1'l1l 6'1 €:I:IJ11.'l'lll :;~';wfih b~:IJ q "

l11U'lJe:J~'jiII111~b\ne:J1 81,e2,e3,e4 ~iifiht9i1-;J 6"J t1U

6. W8mSnaaDIJ118~5,nsni

doC:: ~ "":0 <Vall Q./

b:IJe:J'Vl1n11 bn'lJ'lJe:J:IJ~'Vl'Vl1n111~ Ae:Je:J\9l11 "

m11'l1l1.'l'lJe:J-.:JJ1'l1lr;:im~'Ll, Bru'lllil~'lJe:J-.:JJ1'l1lr;:im~'Ll , " 'lJ1b'ih -'lJ1e:Je:Jn, 'jill ~-;J-.:J1'Ll1 'V'lfhiJe:J'LIb'll1 b\9l1'l1l 6'1B:IJ

fl1~~ 6 Bumru FieldPoint ~~e:J~A1'lJA:lJ1i1u. , n11 bn'lJ-ll€:l:IJ6'l'lJe:J~b\9l1'l1l1.'1 B:IJ11.'l'lll:;

"

5flJnSSUC1lS un

-- ----

fl1't''-,l 7 f11jb~m.J~El~~f1jrubbSl~b'1l'Ub'1lf)1(;]1-':) "1

1'Uf11J-.r~ bf1U-nfJ:lJ6l'1Jf)-.:) b\7i1Vl6lEl:lJ16iVl~ [1]"

e. 0.001

e 0.0031, e, 0.5005

e 0.9980 ~_.-

€lruVl.IJjjii'Vhrrnlwl'~1"l

qruVl.IJi1"'11nmd1.h:::lnrul'l'JtIl"'1 b'W\ii nil'<lnD1VhJ

'QruVl3Jjj,,"nmJl.!d:;lJ1ru~'1iJfj·hndB"lrI1~61lJ1'W

..... .~--_._---

(1,100kW) bb6l~fJruVlll~hJ1m\7i1Vl6lfJ:lJ 'lI1~~,;;;)ln , " ~hl'VhnTJVl1Fil'V\lJliJ b\9H.d 1~~ li~1nJfJ~

If ~ I':::: 2.0' C>, If d~.

mJ6l:lJl'Um~A1bj:lJ(Pl'W'1JfJ~'V\THlJbl91m 'Vl:lJAl

~l~ "1 n'U~~';;;)d~~Slf11j'Vl~6l€l~~~1911Jl~'Vl 2 AeJ

b~fJli~dnjfJ~A116l:lJ1'U~ln1J~j~:lJlru

Vl1Fil'V\ljlribl91f)11~~~1911jl~vi 2 bb~d Vl~~~ln

~'U'll1Fil'V\lJ1ri bl91fJ11~ bb'Vl'W1'Wi;UJf11J bbUU-;;fl6ifJ~

b1911 Vl Sl eJ:lJ16l 'lI1 ~ bbU'UbVl d~1'l1l1 'rl th byj mhnl J

~J ~:lJ1fl.J ElruVlJliJ'1JfJ~J116lVl~1'W bl911Vl 6l El:lJ']j~ ~ Sl q "

00007 0.0006 0.0008 0.0006

0.0031 0.0031 0.0031 0.0031

0.1000 0.0500 02009 0.0091

1.0000 0.9990 0.9990 1.0000 .,,,,--_._­

--~~---~----'-"'"

1374.0 1419.0 1453.0 1487.0 1521.0

1374.0 1418.0 1453.4 1487.7 1520.5

1374.0 1420.7 1457.3 1491.9 1525.0

-----­ ---­ ----­

63 Dn 21 6U'"'Ilnu 2550 - OU1FlU 2551

:JF1JnSSUii lS un ------­ -­ --­ -~ ----_._. -

8. ncr6nssuus::mn

1. ~II_ ·UOI~O~U= __ __ _

~lIlnld~~ ~ f)\l~ln\l1'U1~udbb~~\j1~ bili'U

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f11111l:lJl'Wl'UnldVllAl'1"l111~b\P101"lJB\lb\P11Vl~tl:lJ

l'U~1\jb~~~'W'11B\jnl1Vlli1tl:lJl~Vl::;'V1iinldl~

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l.b:;:lJ1rutlruVlil~'11tl-(Jtll bVl ~nl~tllfj b~ b'U~mrlll-, "

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f) ruVlil~hjIi11:lJldtl~11~O/('Urio'U~~~'I'hrnd b~Jl , " bVl ~ n i>'l\l1 'U bb~~~Yi<JJ\j1BmJtJd:;:lJ1ru Al~lJl-

v

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[5J Adly A. GirgIs, R Grover Brown,

"Application of Kalman Filtering in

Computer Relaying", IEEE Transactions

on Power Apparatus and Systems, Vol

PAS-l00, NO.7 July 1981.

[6] Gene F. Franklin, J. David Powell,

Michael Workman, "DigItal Control of

Dynamic Systems", Optimal Estimation,

1997, page: 382-393.

[7] Greg Welch, Gary Bishop, "An Intro­

duction to the Kalman Filter", Depart­

ment of Computer SCIence UniversIty

of North Carolina at Chapel Hill, 2006.

[8] Rudy Negenbom, "Robot Localization

and Kalman Filters", Thesis Utrecht

Umversity, 2003, page: 33-57.

[9] Sanchal Leaspisitthagoorn, "Deve­

lopment of Kalman FIlter into Scada",

Thesis (M.Eng. (Chemical Engineering))

Kasetsart University, 2003, page:

11-20.

•

, aLJun '63 Uri 21 BU)lFiU 2550 - U'1P:U 2551