ISIJ Internatlonai Vol 39 (1999) No 10, pp. 1053-1060

Mold Level Control in Continuous Caster by Neural NetworkModel

Toshihiko WATANABE.Kayako OMURA.MasamiKONISHl. Shozo WATANABE1)andFURUKAWA2)

Process Technology Resea!ch Laboratory, KobeSteel, Ltd., Takatsukadai, Nishi-ku, Kobe, 651 -2271 Japan.

1)KakogawaWorks. KobeSteel, Ltd., Kanazawa-cho.Kakogawa,675-0137 Japan.2) KobeWorks, KobeSteel, Ltd., Nadahama-higashi-machi. Nada-ku, Kobe, 657-0863 Japan.

(Received on February 19, l999., accepted in final form on Alpril 14. 1999)

Kazuhiro

In continuous billet casting, keeping the mold level steady is one of the most important technologies for

maintaining steel quality. Using conventional methods, it is difficult to attain precise control of the moldlevel because of the nonlinear characteristics of the process. Wehave developed a contro[ system using aneural network model to overcomethis problem, In this paper, control problems of a continuous caster areintroduced first, Next, the structure of the control system is proposed, In our proposed system, the neural

network model recognizes the temporal patterns of inlet flow and controls the stopper stroke for a maincontrol loop with a PI controller. The problems involved in construction of a valid neural network modelthat has good generalization and robust properties, are discussed from the viewpoint of optimizing the

numberof hidden layer units by the information criterion. Finall ysomeresults of its application are described.

KEYWORDS:continuous casting; billet casting; mold level control; neural network; AIC; expert system.

l. Introduction

The linear control theory is quite effective for control

of various processes, while its operational range remainswithin linear process characteristics. Furthermore, the

characteristics do not change over time. However, in

actual processes, there exist numerousdifficulties pre-venting these assumptions from being held and there

are also restrictions in terms of economy, safety, anddemandsfor product quality. Various applicable tech-

nologies have been proposed to control the processeswith nonlinear or time varying characteristics, such asadaptive controll) and the variable structure system.2)

Recently, from another point of view, newtechnologies

have been applied to various processes. The ExpertSystem is mainly applied to the declsion makingprob-

lem in a plant by using humanoperators' expertise.3)

Fuzzy Control was a]so applied to nonlinear processesthat cannot be modeled mathematically but are easily

handled by humanexperts.4) As for Neural Networkapplications,5) robotics control problems6) and patternrecognition problems were successfully solved.

It is needless to mention that the demandsfor higherindustrial product quality and lower costs becomeeverstricter year by year. In order to meet these demands,the control system should be improved by unifying the

technologies described above to reflect the formerlyneglected properties of the process.

Wedeveloped a control system for the mold level in

a continuous billet caster, using AI technologies andlinear controller. In our developed control system, aNeural NetworkModelrecognlzes temporal patterns and

1053

works In cooperation with a main control loop with aPI controller. The Neural Network can describe thearbitrary nonlinear relations as a general approximator.In this paper, the problems involved in the construc-tion of a valid Neural Network Model that has goodgeneralization and robust properties are discussed,

optimizing the numberof neurons by the informationcriterion. The results from application to actual plants,

accompaniedby a large reduction in mold level varia-

tions, are also shown.

2. Mold Level Control in Continuous Billet Caster

2.1. An Outline of a Continuous Casting Process andMold Level Control

Thecontinuous casting machinecontinuously solidifies

molten steel refined by a converter or ladle furnaces andproduces billets efficlently. Themolten steel from a ladle

is poured into a water cooled mold via a tundish. Thesteel strands of which the surface has solidified in the

mold are withdrawn at a predetermined speed. After the

strand is cooled in the secondary cooling equipment, they

are cut into billets. Figure I showsthe continuous billet

casting machine as well as the mold level controller.

Since the mold level variation is closely related to the

billet surface quality, the mold level must be controlled

stably and precisely to improve the quality. It is as-

sumedthat as level variation increases, inclusions such as

powders on the molten steel surface are entrapped andinduce surface defects or cracks after ro]ling.

In order to stabilize the mold level, two actuators areapplicable for the control. Oneis a stopper actuator that

@1999 ISIJ

ISIJ international. Vol, 39 (1999), No. 10

Tundish $Stopper

$Molten

Steel

Stopper Stroke

Change

Nozzle LeVel sensor Mold Level

Mold_

Controller """"~>Level

Mold _ Mold

Drawing ~!) \ 1~'

:~/~~:\rd::

Speed

Roll

~)

,

,~~~1~; "'~;~~~~

~~) '~ '

Fig. l' Mold level control in continuous caster.

~$~O~~~OF$

~sieO~

~i

H

,*' ~:>,,*

! Fluctuation of the

characteristics duringoperation

Stopper poSition

Fig. 2. Conceptual figure of nonlinear characteristics of the

stopper.

can regulate the inlet flow to the mold with a short timeconstant, and the other is drawing rolls that can regulatethe drawing speed (outlet flow from the mold). Eachofthe control methods using these actuators has bothadvantages and disadvantages. In the case where the

stopper is used to stabilize the mold level, the moldlevel control feature can easily be changedby erosion ofthe stopper or nozzle clogglng. Changing the controlfeature increases the mold levei variation. As a result,

the product quality often worsens. In the case of controlby the drawing speed, the operational range is limited to acertain range so as to be properly solidified.7) The de-tailed features of these two actuators are described below.

2.2. Control by Stopper Actuator

In our plant, the stopper actuator can respond swiftly

to the mold variation with a time constant of 0.1 sec. Its

operational range is from a closed to an openstatus. Theflow characteristic is nonlinear itself in the operational

range as depicted by the solid line in Fig. 2. This figure

shows a conceptual drawing of the actuator property.Whensteel containing a high percentage of aluminumis

cast, the control feature caneasily be changedby blocking

up at the nozzle part. It wasalso found that the stopperitself gradually becomesmolten. These changes of the

top shape of the stopper lead to a change in flowcharacteristics as depicted by the dotted line in Fig. 2.

Furthermore, a gain of the inlet flow depends on the

constituents of the steel and on the various environ-ments of the process such as the temperature of thesteel and the amount of molten steel in the tundish.Thesealso affect the flow property as well as the changeof the top shape. Hysteresls such as minor backlash orstick slip of the stopper is likely to cause unstablephenomena.Mold level variation is due to these factors.

2.3. Control by Drawing Rolls

Thedrawing rolls can control the drawing speedwhilereferring to the deviation of the mold level. In this controlloop, depicted by the dotted line in Fig. I ,

it can linear-ly manipulate the mold level by changing the drawingspeed under every condition of the process. So, the moldlevel variatlon controlled by the drawing speed actuator

can be suppressed within a comparatively small range.Consequently, the quality of products is always good.Moreover, the operationai range is limited to ~3o/o froma set value that is decided according to the type of caststeel, so as to be properly cooled or to maintain theproductivity. For the samereason, the time constant ofthis actuator is set at around 2.0sec. These restrictions

result in someundesirable situations. For example, thedrawing speed variation can reach its lower limitation

by the drawing speed control, because of disturbance.

2.4. Conventional Control MethodsIn continuous billet casting, that a smal] section mold

is used for, the mold level is controlled by the drawlngspeed for producing products that are made to less

stringent quality standards. On the other hand, the

mold leve] is generally controlled by a stopper or a slid-

ing nozzle actuator in order to produce steel of highquality. However, it must be pointed out that someproblems exist in using control by regulating inlet flow

as described above. In order to improve the performanceof the mold level control, several methodsare proposed.

A method was proposed that uses an optimal controllaw based on the state space method.8) In this ap-proach, it is necessary to deal with the changing inlet flowcharacteristics described above. In order to overcomethese difficulties, a method was also proposed thatidentifies response characteristics from the mold level,

the position of the sliding nozzle and the drawing speed.It can adapt the gains of the controller from an identifiedmodel.9) However, the identification cannot work wellin the case of the stopper, because the characteristics ofthe inlet flow are basically nonlinear and can easily bechangedas described above.

Our approach is to use both actuators simultaneouslyfor the mold level control to utilize each good propertyand also to compensatefor the disadvantages of each,in order to keep the cast quality high for every casting.

3. ANewMold Level Control System

3.1. Basic Conceptsand Strategies ofthe Control Design

Our basic idea is to use the drawing speed actuatormainly when the process condition is comparativelystable. The stopper is used for preventing mold level

variation caused by a sudden change of the processcharacteristics, i.e. a large disturbance. The supervisor

C 1999 ISIJ 1054

ISIJ International, Vol. 39 (1 999), No. 10

realized as Expert System watches the process condi-tion from measured process variables to decide the

appropriate control action. However, in order to usethe drawing speed actuator effectively, weshould over-

comethe restriction, i,e. ~3o/o limitation from the set

value, and restrain the disturbances that the drawingspeed actuator cannot cope with by itself. It is also

necessary to limit the interference of these two actuators,non]inear phenomenaof the stopper and the stoppererosion as discussed in Sec. 2. If the inlet flow canmaintain an almost equal value of the outlet fiow, i.e.

drawing speed, by the manipulation of the stopper, the

mold level control by the drawing speed actuator can besuccessful for a longer period than the control only bythe drawing speed actuator. In order to realize these

concepts, the controller should detect the tendency ofthe inlet flow to reach its limitation, andmovethe stopperto keep the inlet flow equal to the predetermined outlet

flow. Furthermore, it is desirable that the stoppermanipulation which cooperates with the main control

100p of the drawing speed actuator is small, so as not toactivate the nonlinear behavior of the sto pper andpreventerosion. Thesestrategies of the control design cannot berealized by a linear controller or traditional simple signal

processing.In order to realize these functions, a neural network

model is used to recognize the tendency of the inlet flowcalculated from the mold level and the drawing speed,

and is manipulated by an up-and-downmotion of the

stopper from the recognized results. Figure 3shows the

conceptual configuration of the main control systemwhereby the mold level is controlled mainly by the

drawing speed cooperation with the neural networkmodel to manipulate the proper stopper control actionsupervised by the Expert System. In the following, the

neural network modeland expert system will be describ-

ed in detail.

4. Recognition of Temporal Patterns by a Neural Net-

work Model

4.1. Roles of the Neural Network ModelThere exist two approaches for recognition of tem-

poral data by the neural network model.10) Oneis the

"Context Model" such as the recurrent type neural

network that recognizes dynamicsby context layers, andthe other is the "Buffer Model" whose input data aretemporal patterns of the process data. In the "Buffer

Model" approach, the modelcan easily be tuned becausethe influences of past states can be expressed easily asthe numberof input neurons. However, the total numberof units in the "Buffer Model" is generally more thanthe numberin the "Context Model". Manypatterns ofteaching data are indispensable for the "Buffer Model".Every piece of temporal pattern data cannot be actually

collected, and furthermore each data includes noise andambiguity. Therefore, the network must have features ofvalid generalization for unknownpatterns androbustnesswith regard to noise. This problem is sameas the "Orderdecision" problem in system identification. In this sec-tion, the decision of the numberof hidden layer units

Tundish

Stopper

~)~

~~)~Drawing

Roll A~)

Fig.

Inlet FlowError[m/min]0.05

o

-0.05

Input

Layer

Fig.

-40 i

Z- l

HiddenLayer

3.

ExpertSystem

,~~•~)~~

Neuro-Controller

PI Controller

SpeedChange

Anewmold level control system.

-30 ; -20 :

E~=

Neuron

Unit delay ~

-lOj

OutputLayer

~Close Hold Open

4. Neural network model for stopperrecognition of the temporal data.

Z- l

OTime[sec]

control via

in the "Buffer Model" is discussed using the teaching

patterns of our billet casting data.

The neural network that weuse has three layers andis feedforwardly connected as shownin Fig. 4. Input data

are temporal data of the inlet flow error e, that is

calculated as an estimation value from a mold level anddrawing speed as follows:

e=P* +v- vo •••••••••'(1)

WhereP* denotes the differential value of the mold level,

v is the current drawing speed, and vo is the set value ofthe drawing speed. Output data are instructions for the'stopper actuator; output open pulse, output close pulse,

andoutput nothing (hold) to amotor to drive the stopper.There are ten neurons in the input layer, so as to processpast 45 sec. Thetendency of process data is checkedevery

1055 @1999 ISIJ

ISIJ International, Vol, 39 (1 999), No. IO

5sec. This range and the sampling period are determinedaccording to the frequency of the empirical]y observeddisturbances, suggestion by simulatlon results, and re-sults of the experiments in the actual casting.

4.2. Determination of the Numberof Hidden LayerUnits

In the neural network modeling approach, the accuracyof identificatlon Is almost always improved by increasingthe numberof the hidden layer units. Onthe other hand,

a modelcomposedof redundant neurons deteriorates the

accuracy of p.rediction. This prob]em Is well knownasthe "Over fitting problem". Amodel of the appropriatetmit size should be selected for the appllcation to theactual plant.

Thoughseveral methodshavebeenproposed to decidethe numberof hidden layer unlts in a multilayer feed-

forward neural network, in practice It depends uponthe optimality of learning, that is to decide the synapseweights to minlmize the squared error objective function.In other words, as nonlinear optlmization such as the

learning of a neural network model is not necessarily

solved, a learning algorithm is quite important in orderto decide the valid numberof hidden layer units.

As the information criterion for estimation of theprobabilistic function, AIC (Akaike's Information Cri-terion)11) and MDLP(Minimum Descriptlon LengthPrinciple)12) are proposed. In this section, wediscuss the

optimlzation methodof the numberof hidden layer units

by AIC. A teaching signal to the output layer unit is

assumedto be {O, I}. Thenumberof parameters (synapseweights) is assumedto be P. Then AIC is defined asfollows:

AIC= - 2(maximumlogarithm likelihood) +2p .....(2)

A neural network model for pattern recognition canbe thought to be expressed as the a posteriori probabilis-tic function that the teaching signal is equal to lcorresponding to certain input. Assuming that thetralning data is independent of the output from the

model, the logarithm likelihood L can be calculated as:

N K N KL=- ~ ~Oik(1-tik)- ~ ~Iog(1+exp( O,k))

i=1 k=1 i*1 k=1*(3)

where Oik denotes the input value to the k-th outputneuron of the i-th training data, Ndenotes the numberof the tralning data, and K is the numberof outputneurons. As the activation function in each neuron, thefollowlng slgmoid function is used:

1f(x) =~ •ex~t[lx) ~""'"""~"(4)

4.3. ALearning Methodby Maximizing Likelihood

From Eq. (3) the maximumlogarithm likelihood is

approximately calculated from synapse weights trained

by meansof BP(error back-propagation) algorithms. 13)

In this paper, we use another learning a]gorlthml4'15)

that is derived from maximizing L in Eq. (3). Thealgorithm Is almost the sameas the BPalgorithm, besides

@1999 ISIJ 1056

START

Set the numberof iterations,M

:~ o

i := O

Select the i-th training data and input to the NN

Calculate the output of the NN

Correctlon of the synapse weights by eq.(5)

i := i+ l

j~N NOYES

j := j + 1

NOj;~M

YES(Endof the learning)

Calculate the logarithm likelihood Lof the trained NNby e .(3)

Calculate the AIC value by eq~2)

E~)

Fig. 5-.

Algorithm of the learnin_g and evaluating the AICvalue.

the error signal ~is used as:

~=tik-yik........

..........(5)

for changing the weights from the hidden layer units tothe output layer units. Whereyik denotes the output valuefrom the k-th output neuron of the i-th training data.

This algorithm (below called ML: MaximizingLike]ihood) is equivaient to the algorithm derived fromminimizing the objective function of Kullback di-

vergence,15) as maximumlikelihood mlnimizes theKullback divergence in this case.

Furthermore, in order to improve the performance ofthe algorithm, wecan a]so emp]oy the various existing

methodssuch as noise adding methods.This algorithm described aboveas a flow chart diagram

is shownin Fig. 5.

4.4. Numerical Experiments of Learning and Unit Se-lection

Before constructing a neural network model for

recognizing the temporal flow data and controlling the

mold level, simple numerical experiments are madetoconfirm the validation of the algorithm described above.Theactual process data or collected data, such as humanoperational data through their judgement and expertise,

often include necessary measurednoise or ambiguity. Asa trained network should have robust features withregard to these uncertainties, the learning algorithmneeds to have robust and stable characteristics of con-vergence.

Asimple pattern classification problem for evaiuatingthe performance of the algorithms is to decide either

category from two-dimensional input data. 121 training

patterns are prepared for the experiments assumedthat

ISIJ International, Voi. 39 (1999). No. 10

AIC250

200

150

1oo

50

o

CL

"r:..

1 2 3 4 5 6 7 8 9 10

Numberof hidden units

Fig. 6. Learning Results ofNumerical Experiments.

ldeal(~ R'utp"t ~)7

O ~~

O R

In putO pattern O1O I~F

-1

.45 o (o9)(5~\~)2

time (sec) ~)

t(o 9)

O

G)(O,9)

~)

R

R

(o g)

R(o g)

(o 7)

r~LL~J

Rr~~d ~ILt~~~

o Inputpattern

1o

-1

o.45(~~~\L)2

time (sec)

(i)

~)

O

(i)

(~

~~

~~

~

(~

(i) R

R R

(i)(o g)

R~

~)(o g)

(o g)

R

(o 8)

Orl~cr

(O g)

Fig. 7.

AIC600

500

400

300

200

1oo

o

~~

R~~LJ

(O,9)

(O 9)

~) OpenOZero~~ OIOSe

Fig. 9. Evaluation ofconstructed neural network.

O R

R ~~ OPen

O OZero~Ur CIOSe

Data patterns for training'

1 93 75Numberof hidden units

Fig. 8. Learning results by using casting process data

these are measureddata adding artificial noise underthe true decision boundary. TheMLalgorithm and the

conventional BP algorithm are employed for training

neural networks that have a different numberof hiddenlayer units. The numberof each training iterations is

RULEI IF PV OI ANDVc OI ANDdev = = STPTHENdev = VEL; RUN;

RULE2: IF (IPVj > 2.0 ORIVcl > 3.0) ANDdev = = VELTHENdev = STP; RUN;

RULE3: IF PV> 0.9 ANDPV' > OAANDdev = = VELTHENdev = STP; RUN;

RULE4: IF IPVI 1.0 ANDIPV'I 0.1 ANDVcl 0.1

ANDdev = = STPTHENdev = VEL; RUN;

PV : mold level deviation

Vc : drawing speedPV': differential value of PV

' [: sign of abso]ute va]ue

STP : PI controller by the stopper

VEL: NNcontroller with PI controller

by the drawing speed

Fig, lO. Examplesof shifting rules in expert system.

lOOOOO.This is sufficient iteration for synapse weightsto converge to the certain values.

Theresults of the hidden layer units selection are shownin Fig. 6. Eachvalue of AIC is showncorresponding tothe numberof the hidden layer units. The model of 4hidden iayer units is selected as the mlnimumvalue of

AIC Iearned by the MLalgorithm, while the model of

6hidden layer units is selected by the BPalgorithm. Asimple structure model, which is expected to have better

performance of generalization androbustness in this case,

can be constructed by meansof the MLalgorithm fromthese results.

4.5. Construction of Neural NetworkIn order to accumulate the training data, experi-

mentsin which the stopper opening Is operated by humanoperators were repeated. This was done to refine the

1057 @1999 ISIJ

ISIJ International, Voi. 39 (1999), No. IO

_sp_e~d_~la_b_il_i~~L~-1

l VcoVo A l [ +

G2 l

l+T2S B+ l +[

l

G3 speedcompensator

l lPY + G! + l+D l+TIS s +c s

stoppercontroller

hydraulic servo stopper mold

Fig, Il. Drawing speed compensator,

neural network judgment capability by adding training

data if erroneous judgement of neural network com-pared with humanjudgement wasmade.As a result, 144training data were finally accumulated. Figure 7showsthe typical 17 input/output data set used for training.

In the figure, the abscissa stands for the time and the

ordinate is the temporal data of the normalized inlet

flow error calculated by Eq. (1). Symbolsshownon theright side of patterns indicate the teaching data, i.e.,

the upwardarrow showsthe output to open the stopper,the downwardarrow showsthat to close it, and the circle

showstake no action. For complicated patterns such asthose of No. 14 and 15, it is difficult to process themwith an algorithm such as the conventional PID com-putation but with the neural network teaching easily

takes place by simply adding the patterns.

The results of learning by meansof the MLalgorithm

are shown in Fig. 8 as well as the results by the BPalgorithm. The 100OOOiterations are made for thetraining of the network. The value of AIC attained bythe MLalgorithm is mostly smaller than that by the BPalgorithm. In other words, the neural network modelobtained by the MLalgorithm as the probabilistic modelof the pattern recognition seemsappropriate from the

viewpoint of the likelihood. Basedon these results, the

neural network model of 3hidden layer units is select-

ed for recognizing the temporal pattern in the control

system.After the model construction, the performance of the

model is confirmed through the experiments comparedwith humanoperation in terms of critical condition such

as rapid change of process characteristics. By using theconstructed network, the stopper is manipulated based

on the output neuron value whenits va]ue exceeds 0.8.

Several examples of the evaluation are shownin Fig. 9.

In the figure, symbols on the right side of the patternsdenote the judgement by the neural network as well asthe output value of the activated output neuron. Fromthese results, appropriate judgements can be madebythe constructed neural network.

5. Supervisor Selecting a Controller

5.1. Expert Systemas the Supervisor of the Control

Asmentionedabove, the neural network modeldecidesthe action at intervals of 5.0sec for control of theinlet flow. Consequently, not all frequency classes of

@1999 ISIJ 1058

" 5~= o.~ ~~ ~ -5'"E

J~ 4,0

~"**~s 3'o1;;1;;

o.o1~

E

-~.>E~2 -5.0

0.0 15050 1OOtime (sec)

(a) Result without compensator

~~5"~.~; * o~ " -5~~="~~ 4,0

"~=". ~~ 3,0

o.o~E

-~.>E~2 *5.0

0,0 50 1OO 150time (sec)

(b) Result with compensatorFig. 12. Simulation results of compensator,

disturbance can be restrained, that is, from design con-cepts as described in Sec. 3. The expert system alwayssupervises the behavior of the process and shifts thecontrol loop frorn drawing speed PI control with theneural network model to PI control only by the stopperactuator. The expert system watches the mold level,

drawing speed, molten steel weights in the tundish andso on. It selects the control loop (Logic) decided totally

from these p,rocess values. The expert system is a typeof "productron system" Thls system written in Clanguage, infers a selection every 0,Isec. Figure 10showsexamples of production rules.

5.2. Shifting a Controller

Whenthe expert system decides to shift the con-troller from the one by the drawing speed actuator to

the other only by the stopper, the mold level is usually

awayfrom the set value. At that time, the drawing speedvalue is also awayfrom the set value. In order to control

ISIJ International. Vol, 39 (1999), No. 10

rT~ITIInput

Steel weightin tundish

Mold level

Drawingspeed

ComputerSystemfor MoldLevel Control

Controller mainly by the drawing speed:

r~~T~ITlOutput

t Drawingspeed manipulation by PIDrawingspeed

correction+

Stopper manipulation by NNExpert ~lsystem

Controller mainly by the stopper: +Stopper manipulation by Pl + Motor ulse

+ + to the stopper

Drawingspeed compensator

Drawingspeedstabilizer

Fig. 13. Systemconfiguration.

~oocL

o>o~2oEco(U

co>

value

i 2mmT

upperlimit

setvalue

lowerlimit

_ _ _ __---\~o_p pulse~r_____

__LL__)r~r~1________

- -/- - -fl--ctose pulse

O 1 2 3time (min)

Fig. 14. Effect ofneural network controller.

Thenumberof casting

30

25

20

15

10

5

sto pper

o

the number of sample

f = :~: 2.7mm

a =2 9mm

1:,

= 109

1:,(Dq)'~Q)

oQ)::

~

drawing speed control control drawing speed control

I2mm

301Q

155

>(D~!oEco~a:f

~c::

>~'~oG)coooO IO 20 30 40 50 60

time (sec)

Fig. 15. Shifting situation by Expert system.

70

O 4 6 8 102Mold level variation x [mm]

(a) Results by the Conventional Control System

Thenumberof casting

30

25

20

15

10

5

o

the number

f = :!:1.5mm

a =0.9 mm

of sample~l= 67

the entire conditions of this process successfully, weshould pull back the drawing speed to the set value. If

we pull back the drawing speed to the set value in-

stantaneously, It gives rise to variation of the moldlevel. To avoid this, weconstruct a feedback controller

with first order delay and design a feedforward control-ler to restrain the disturbance caused by changing the

drawing speed. This control logic for shifting the con-troller is shownin Fig. Il. The feedforward controller,

as shownby the "speed compensator" in the figure, is

O 4 6 8 102Mold level variation x [mrn]

(b) Results by the DevelopedControl System

Fig. 16. Applied resultsofreductioninmoldlevel variations.

designed to be equal to the dynamic characteristics of

A-B-C to A-D-C. The feedback controller which slowly

resets the drawing speed is shownas the "speed stabilizer"

in the figure. Wehave checked the performance of the

feedforward controller through a computer simulation

and confirmed that it can change the speed withoutvarlation of the mold level. In other words, we canshift a controller without mold level variation. Thesimulation results are shownin Fig, 12.

6. Process Application and Results

6.1. Configuration of the Controller

Wedeveloped the control system using a personal

1059 @1999 ISIJ

ISIJ International, Vol. 39 (1999), No. 10

eJ)F~

(,)

C~O

~HO~)~O~::,

F~

e)~

6000

5000

4000

3000

2000

1ooo

o1.7 1.75 1.91.8 1.85

Drawingspeedv [m/min]

Fig. 17. Drawing speed manipulation by newapplied control

system.

v o = 1.8 m /Inin

n = IeoO

r * I .79 [m / min]

a * O.012 [m / min]

computer. The configuration is shown In Fig. 13. Theinput data used for calculating the manipulation value

are mold level, set value of drawing speed and tundishweight. The position of the stopper and the drawingspeed are also input. The motor pulse to the stopperactuator and the correction value of drawing speed areoutput.

6.2. Applied Results

Weapplied this control system to our continuous billet

caster. Figure 14 shows a commandfrom the neuralnetwork modelcorresponding to the mold level and the

drawing speed. Changing the inlet flow by the distur-

bance, the neural network model decides to outputthe close pulse, and the changeof inlet fiow is restrained

to a small range and thus the variation of the mold level

is small. Figure 15 shows the situation of shifting thecontroller. At about 35 sec and 48 sec, the controller is

shifted according to the judgementby the Expert System.It can be seen that changing the controller can be donewithout a large variation of the mold level. Figure 16showsa histogram of the mold level variation range bythe newcontrol system comparedwith the conventionalcontrol system, that is PI controller only by the stopperactuator, in actual operations. It can be seen that the

meanvalue of the mold level is improved, and thestandard deviation of the mold level is also decreased.

The variation of the drawing speed which is set to

1.8m/min is also shownin Fig. 17. Fromthese results,

the variation of the drawing speed is sufficiently small,

that is far less than 3o/o of the set value. Both the inter-

nal and surface quality wasactually inspected and werefound to be good enough.

7. Conclusion

In this paper, a mold level control system using theneural network model was described. A unit selection

method is considered to be effective in constructing theneural network model for application to the actual

process. Two different control methods, i,e., thecontroller by the stopper and the linear controller bythe drawing speed using the neural network model tomanipulate the stopper opening, are combined by thesupervisor realized by the expert system. This systemhas actually been applied to a continuous billet casterin our process. Through this application, the effective-

ness of the system has been checked and confirmed.Themold level variation has been greatly reduced com-pared with the conventional control system. Thereforethe quality of the products has been remarkablyimproved. In the future, we are going to apply theidea of this kind of intelligent system to other iron andsteel making processes.

1)

2)

3)

4)

5)

6)

7)

8)

9)

lO)

l l)

l2)

13)

14)

15)

REFERENCESK. J. Astr6m and B. Wittenmark: Adaptive Control, Addison-Wesley Publishing Company,Mass, (1989), 163.

V. I. Utkin: IEEE T,'ans, on Automatic Conn'o!, AC-22 (1977),

No. 2, 212.

M, Funabashi and S. Masvi: T,'ans. of'lPSJ, 28 (1987), No. 2, 197.

O. Yagishita, O. Itoh and M. Sugeno: System,s and Conl"o!, 28(1984), No, lO, 597.

D. E. Rumelhart and J. L. McClelland: Parallel DistributedProcessing, MITPress, Mass, (1988), 318.

M. Kawato, K. Furukawaand R. Suzuki: Bio!ogica/ Cybe,',1etics,

57 (1987), 169.

K. Omura.T. Watanabeand M. Konishi: Proc. IFACWorkshopon ComputerSoftware Structure Integrating AI/KBSSystemsin

Process Control, The Norwegian Society of Automatic Control,Norway, (1991), 229.

K. Hanazaki. T. Yamada.T. Murakami. J. Mitani and K.Hamada:CAMP-ISIJ, 5(1992), 353.

Y. Sasabe. S. Kubota, A. Koyamaand H. Miki: ISIJ Int., 30(1990), No. 2, 136.

M. Ishikawa: T.IEEE Jpn., 109-D (1989). No. 4, 225,

H. Akaike: IEEET,'ans. Automatic Control, AC-19(1974), No.6, 716.J. Rissanen: The Annals of Statistics, 14 (1986), No. 3, 1080.T. Kurita: T,'ans. IEICE. J73-D-2 (1990), No. I l, 1872.

T. Kurita: IEICE Technical Report, NC91-36, (1991).

Y. Tan, Y. Kato. T. Ejima: Trans. IEICE, J73-D-2 (1990), No.12, 2022.

C 1999 ISIJ 1060