Computer Control System for Continuous Reheating Furnace

. furnacc-Fnll nr.d sla~-surface te!'1peraturcs anr. on flm.]. (8) ~or ti~e inte~ratinn, exnlicit ir.tc~ra­ ti on . conRistinr: of such c.Cl!'1nnne<'ts ns ~J.aJ-­ tef,'pcrn t1lre 1.n 1 ftlrnaCC-H ,~ 11 tenpera ture aJone W8S adopted to ensure readv calculation. . (0) !!ea t 105<; of furn ace :'otlv 'vas ado;>ted as the control ,,?rar.ctcr to E'stabl is~ i 1entification be t l,.'een t he act'tal fllrnacE' 3n(: [;1ooel. Awon~

Pi

f (

~l Vk,

( k*l Vp

2621

T - , T ) + V,AlI - f Gi l Gi ~ T(a' TGi+l)

-U~~{~Sii

Ssj {(T

+ 273)4 -

Gi

+ 273)4}

(T .

s~

~rpwi

Swi { (T Gi + 273) 4 - (T wi

+273)4}_g

(5)

where, 8: Feat loss f, the heat quantity that flows from i-I to the i-th block, is adopted as heat emission between the exhaust gas and gas. f(

\:;1

1-=1'71:,

Tr,i-l +

T~i_l' TGi ) =

Sgi_l

Cl' .

'-1

~l "'k .

\. (Tr,i-l + 273)4 - (T Gi

+ 273)4 \

(6)

This formula, which is set up for each block, enahles calculation of T - T that will make 11 1 - J! zero. As thrk for~nla adopts the form o¥ ,on-linear simultaneous equations it must loe solved by repeatin g calculations ' accordin g to the '!ewton' s me thod. In other words, it is a method in "'hich the followino:> formula is used to obtain tft~lnext more ' accurate gas temperature TG from the approximate value Tg kof the k-th oas tempe'.' rature. (T \{) -lE k G

11

(7)

=( ~l )

(8)

n

lfuere J is a ,Jacoh ian matrix. Since, in this case, it can he formed i nto a tridiago nal ma trix such as shown be 1010" th e formul .1. ] ends its e lf to ready solution. furtlterr.lOre, as the ,1il'lension is equivalent to the nU'1lher of gas blocks, which is normally in t he order of 4 to 5, the time require d for calculRtion is small. (9)

mAT

I

G2

m2~TG2 01l/clT!!}

-"_" Cl'! n ~TG n- 1

n

'OlIn _l.aT~nj ' Hn It]' Gn

ii) Slab temperature calculation of Premise (7) The i-th mesh temrerature of the k-th slal, is obta'ne<1 with reference to TSki in the followin3 manner. (10) (T

(11)

ski tilC'

abov(' nren isp.s, those that nay :' iv c

reise to pro') 1 ercs are closely s tu,'iC' ,' in 2 . 1. ~

.

2.1.1. Rel.:nions 11ip fOrl'111l:1 of ~Cld" 1 i) ~as teMperature calculation far Premise (n) rnha] "nce Fi in the hea t l1alanc.e 0 f the i-th ~a s hlock may he written as eST 5 _ F

2.1.2. Comparison with actual furnace Figure 3 shows a typical example of comparison made hetween Olctual data and simulated

2622

M. Kamata, S. Murakami a nd H. Wakasuki

data of temperature of each zone, by feeding i".to the si r'lulator actual operation da ta concerning the slah size, discharged tiMe and flow. The dimensions of the Model is m= 4 and n=5, whi le~t = O.02h r and for heat loss, a fixed value was fed in. Even with the use of such a crude model, it r'ay be said that sufficient accuracy can he assured for control. The closely study the rationalit y of the premises given in 2.1, the effects were exaMined by varying the various parameters. The studies revealed the following matters. i) As for Premise (1) that the r,as te~pera­ ture of the zones will be uniforM, influence was minimized by ena~lin~ smooth vari1tion of the form of emissivity ~ .. hetween the ~as and s1.ab. In a steady f~~nace operating condition, no particular problem ~ad arisen. POlo/ever, w11en the fur na ce had been s hut down for a 10nR period of hours , teMPerature variation c;).usecl by the slab position was found to he large depending on the form of ~ .. ' This point, t he re fore , calls for fut~i:-J studies. ii) As for Premise (3) that it is of a one
the output of the predictor, an optimum flow pattern includin g that for the future has been adopted, and this initial value is taken as t'le current set flow. This sub-optimiz<1tion filter adopts a calculation system as descrihed below. (1) l'sing the degree of temperature uniformity as t:le basis, the object flow and the inlet temperature of the soakinE zone are obtainer1 • (2) FIOl~ distrihl1tion includin1Y, that for the future is set hy rougnly calculating the ahovemen tione,j oh' ect value for the soaking zone ilnd the total flow for other zones, anr i then distributinR flow so thnt the it will beCOMe close to t he fu r nace 's upper limit from upstream. (3) 8y performin~ simulation includin g that fo r the future, deviation in discharged slab t emperat ures el(t) and deviation with re ga rd to the inlet temperature of the soaking zone stated in (1) e (t) are obtained. 2 (4) Through integration by multiplication with weighted functions h (t), h (t), and h1 2 (t), aiming at minimizin g variance in temperature deviation, orimary correction amounts vl(t), v (t) and v~(t) are calculated respectively tor the soaRing zone , No . 2 heating zone and ~lo. I heating zone. VI (t)

r

el(S)hl(S-t)ds

(12)

1 e 2 (S)h 2 (S-t)ds

(13)

t

V2 (t)

t

S e 3 (S)h 3 (S-t)dS

(14) t (5) Provided that there is some allowance in the flow of the "lo. 2 heating zone, flow distribution for the ~o. I & No. 2 heating zones are changed for an amount of 0\ so as to obtain the furnace's upper limit, aimin?; at improvin g heat efficiency. V3 (t)

V* ( t) 2

"'2 (t) +

0(

)~

V ( t) 3

V (t) 3

0(

(15) (16)

(h) After correcting the flow incl~ding that for the future by using V1 (t) , ~r~(t) and

V * (t), the operation is brought back to 1 (3) •

The values hl(t), h (t) and h (t) have been 2 3 composed based on tne concept underlying feed fo rward of the linear system, and has been found to be sufficiently useful for this control system. 3.

ApD ICATIO'1 TO REAL PROCESS

3.1. Control system The control system described in Chapter 3 has been introduced as the computer based control system for the ~o. 2 Not Strip Hill of NKK 's Fukuyama Horks. To reduce the amount of working memory and to shorten calculation time, the dimension of the simulation morel used inside the predictor employed in actual control (ri~. 11) has been brought claim to the lowest limit. (m=l, e=2, n=5.) Even with

Computer Control System for Continuous Reheating Furnace such minimum dimensions for the simulation model, we have a satistactory result concerning the accuracy of prediction control. 3.2. Control results Figure 5 shows a typical example of effects obtained with the present computer-base~ control system. Ordinarily, in hot rollin?, lines, the discharge temperature is controlled at the exit-side of the rougher mill in consideration of temperature drop in the rougher mill. The present control system has exibited an extremely high hit ratio, that is, the exit-side temperature of the rougher mill was concrolled to within + 15 degree. In addition to this, it has improved heat efficiency and has resulted in r educ in~ fuel consumption by more than 10, nOm:cal/ ton.

Heat transfer coefficient of steel Specific heat of steel Specific heat of gas Volume ratio of gas to fuel Heating value OF fuel including sensible heat of air Mesh interval of slab Time interval Number of slabs in furnace ~umber of meshes of slab Number of meshes furnace wall Number of blocks of gas Mass of steel in one mesh

K

f r:

p

LlH

h i

A~

n

i

2623

s

m n

I-lki

r.O'lCLUSION In the foregoing papers, we have descrihed the new control syste~ for slab reheating furnaces based on the use of a heat conduction model and a heat balance model. Differing from conventional systems which focus on slab temperature control, the present system is a ne,. attempt that aims at realizing minimum energy consumption and slab temperature control. In b uilc1in~ the system, simplified models obtained after makin~ various omissions have been adopted in consideration of use for on-line control. Largely satisfactory results have been obtained. The present system, although still incomplete, is the first attempt ever made in ,.hich a heat halance model has been adopted. The authors shall be more than happy if the concept underlying the present system should serve as an aid in developing future control systems for slab reheating furnaces. REFERENCE Macedo, F.X., R.D. Glatt, Il. Brown , and A.V. Simpson (1976). Operating experience with a computer-based reheat furnace control system. In Int e rnational meeting on iron and steel making. Vol 2a , Verein Deutsher Eisenhuttenleute, Dusseldovf. ppl-9 ~orisue, T. (1970). Computer aided optimal control of a continuous slab heating furnace. In Preprints for IFAC Kyoto symposium, pp.58-63. Ogawa, S. (1975). A new mathenatical model for computer control of distrihuted parameters system. In preprints for IFAC n-th world congress, Vol 2c. pp.1-5. NOMENCLATURE Gas temperature Slab temperature Wall temperature Fuel flow rate Emissivity between slab and gas Emissivity between wall and gas Sectional area of slab (width x length) Area of furnace wall Sectional area of furnace Stefam - Boltzmann's constant

Sl Ot! ,rll<; k"eu

,, "zoo mm

,, " 2!)Omm

n.

2~Omm

o o

;;;

'270 _~Co" ,

: .~ ---: ..

r~c:. i>

1260 -

0 '200 . __

-__ _

.,

_

1240

I

2

I

.... 1

3

..

I

.4

~ _

-

_-

-

-

:>

~

.... "j

TI me

6.

[1'1,]

1230 -

E

,".

No 2

Heotlno

lone

10000 -

, \ , \,

,

~

E z

,

.'

~o

I

..-/ '

Sook '"101 lone

~,

/ 1'

~

e

/

"

"

o Time [hr]

Fig. 1. Variation of temperature of discharged slab VS. fuel flow

M. Kamata, S. Murakami and H. Wakasuki

2624

Ou ts ide of wo lf

x

TWlm-1

x T Wi2 l

In SIde of wa it

TWII

"'W ,

Gas

f

TG I -I

Vi

Vi

V I -I

To,

+,

¥

f ;

TSJ

I

Surface of slab Dlschar9in9

side

~ .

~"".;,:.

)( TS j 2 TS j 3

,

..

6.=d

)( TSJI- I

Center ot slob

Fig. 2.

~

~

l300

l Sookino zone

~ ..... 1280 r

Simulation mod e l

c,.1 'v· ' •

i~ 1260 ~

11

~ 1240 ~'-

,

I

1260l

:::l

i~ 1240 -

1

Reheating

I'-----_

11

_ _ __ __ ----...JI

g~ 1220-_TIme

I:

1, 1

,

!i

Ob •• r .... r

L~

I,

Heat conduction

1

model in .'ob

I I

HeOI ba lance

I

k: d

1

m o del

c:: ---'

Chr]

, ,

L--i,

!

i '

No.2 Heof inlJ zone

Gas tempert"ure TB

'urnoce

mode l

1220~

:

'---'----J I

rnnI

-----

real

X

l

: Est lmoted slob temperofu re

,.

-

To

t Heat 10$$

i'. 1 •

-.J

-T ime ( hr]

No 2 Heal ing .lone

,c E

z

2'

'0000

Fig. 4.

Soaking lone

Control block diagram

~

NO.I He ating zone Compu •• r <0", ' 1"0 '

-

oE ~.s

~ ~ 250 i:'~

5 .~

~----_

('')O -

B£

( _ 0 01.. ,

~-J

I~06

E1300''-'~--~

1 ~"'t

[ .••" J - TIme Chr]

..

,-

::::::" :::..: IlTfl'ITTTTTT11Tn mTi

~ § 1200-

r ..., _ _ ...

t'O · I(~ " ' .ftl

l";

1000 --

.~

900 -

0

Compute' con".'

Fig. 3.

" "

rTnll ! , i j : , ! 11r , . _ _ .... _ - " ' -

_,......., ... ," '''Cl =::, . . ._.......... ._ ...... 5_",_

i ; 1100 o

I

,.e

28 0 '

Result of Simulation Fig. 5.

Result of comput e r contro l

For Discussion see page 2631