Multivariable Control of Hot Strip Mill Looper

CONTROL OF HOT STRIP MILL

Copyright © IFAC Control Science and Technology (8th Triennial World Congress) Kyoto, Japan , 1981

MUL TIV ARIABLE CONTROL OF HOT STRIP MILL LOOPER Y. Kotera and F. Watanabe Central Research Laboratory, Mitsubishi Electric Corporatz'on, Amagasaki 661 , japan

Abstract, The design and application of a multivariable control in the hot strip mill looper is mentioned in the paper. Basic equations of looper motion are derived in connection with rolling conditions. Optimized multivariable control, decoupling the mutual interactions in the looper, is demonstrated on the actual production mill. The performance is much superior to those with conventional methods. Under the ordinary rolling conditions the looper position variation is reduced to 1-2 degree and the interstand tension variation is negligibly small. The feasibility of supplement compensation of derivative action is investigated, simulation study proved further possibilities of the looper control. Keyword, Steel industry; rolling mills; looper models; dynamic control; multivariable control systems; interaction decoupling

interstand strip tension. And the optim ized multivari-

INTRODUCTION

able control is designed. The experimental roiling on an actual production mill proved the remarkable improve-

In the hot strip mill, the loopers establish a low and constant level of interstand strip tension, and secure a

ment of this new control compared with the con-

successful operation of tandem rolling. Loopers prevent

ventional method. The possibility of further progress in

the outbreak of high tensions on the strip and absorb

this function is investigated employing an additional

the excess amount of stored strip loop, even when

compensation of derivative action .

metal-flow rate on each stand is out of equilibrium. The loopers also serve the isolation of the rolling actions on each stand, enabl ing the better performance

FUNDAMENTAL MODELS OF THE LOOPER

of the automatic gauge control and, hence, the higher

MOTION

grade of finished products. A looper is located in the middle of two adjacent Proper functioning of the looper is considered

in-

stands of multistand tandem hot strip mill , as shown

dispensable to the efficient operation of modern hot

in Fig. 1. The looper roll is set at the top of the arm,

strip mills. Recent mill operation is headed toward the

which pivots on the drive axis. Loopers can be driven

low temperature heating on the material and high speed

electrically, hydrau I ically or pneumatically.

rolling for energy saving, but increases the disturbance to the looper. The greater amount of disturbances and

The looper is raised above the pass line making con-

higher grade of products require much more of the

tact with the strip,

looper control performance.

strip. The loop length can be adjusted by the pivot

The special feature of this looper control exists in

motion are described in the following;

and forms a loop of the stored

motion of the looper. Basic relations of the looper that, the looper includes an oscillatory mechanism and

1)

The stored strip length between the two ad -

dynamic characteristic is closely related to the rolling

jacent stands is given as the time intergration

conditions employed on the stand.

of the difference in the strip velocities between the preceding and the following stands,

I n this paper, the mathematical model of a looper

2)

drive is presented, and the static and dynamic character-

The interstand strip tension a is determined by the strech of the interstand strip that is

istics are studied. A new type of looper system is

the difference between the stored strip length

demonstrated, which is equipped with the detector of

and the loop length formed in the two stands

2471

Y. Kotera and F. Watanabe

2472

An under dumped oscillatory loop exists from the

by the looper. 3)

The looper drive applies torque g to support

interstand tension to the looper position, of which the

the interstand tension, the strip weight, the

natural frequency is reciprocal to the inertia moment

weight of the looper itself and the torque

M, and proportional to the value KgB . The KgB value

Acceleration or

is determined by the area of strip corss section and the

deceleration torque is also required, due to the

looper operating point. The state of stability depends

inertia moment of the mechanism when the

on the rate of frictional loss on the ax is f.

required to bend the strip.

looper position is varied . Quantities

In

the

above

phyical

relations depend

not only on the looper mechanism but also on the

A direct looper drive with a low inertia motor is desirable for the faster response.

state of roll ing on the stand, wh ich is ; a)

Dimension of the looper mechanism

b)

Dominant disturbances to the looper are the changes

looper arm length

in the stirp velocity at the entry or the exit in the

looper weight

adjacent stands.

Divot point location to the pass line and to the rolling stands

As is described above, the steady state and the dynamic

inertia moment of the looper, including the looper drive

characteristics of the looper depend so much on the

Rolling conditions

rolling conditions and metallurgicals of the material.

rolling action. Special attension should be paid to the

stri p size rolling temperature rolling speed

DYNAMIC CHARACTERISTIC OF THE LOOPER

interstand tension Changes in the interstand t ension cause the deviation A linearlized mathematical model around a nominal

in thi ckness and width on the strip, and also introduces

operating point is given as in Fig. 2. The characteristic

instability of rolling operation. Th e looper position

features of this looper model are as follows;

whereas, must be kept as close as possible to its nominal point in order to absorb the loop length change.

The transfer function

from

the difference in strip

speed v to the interstand tension a becomes a first

Most co nvent ional loopers suffered dy namic instabil ity

order lag, the time constant of which is derived to be ;

of looper position and l or th e transient tension variations, mainly due to the insufficient control systems,

T

-

1

a - Kv a K a Q

(1)

where only the looper posit ion is detected . It is used for the control of both looper position and strip tension .

KaQ =

El L 1 + K Qa El L

(2)

For the success of the looper operation, detectors are equipped for the looper position and the interstand

where the constant K Qa represents the effect of tension

tension, and th e torque of the looper drive and the

to the change in the strip loop length . This effect is

rolling velocity on the stand are adopted as the control

introduced assuming that the interstand ·strip is a beam

inputs.

under tensila stress bounded at the two rolling stands. In this case, the loop length changes by itself in proportion to the applied tension .

Fig . 3 is the equivalent transformation of Fig. 2. and mathematical model is given as

While a tension free loop of the interstand strip forms two sides of the triangle from the looper roll to the

a = e (m

roll bites in both stand s, and the effect of K Qa ex -

ri

=

tinguishes. Accounting this effect of K Qa , the time

Ii

= n

constant Ta b2comes 3-7 times as long as that of a triangular model (Price, 1973) . This improved modelling brings good agreements with the experimental evidence. The constant K Qa is roughly proportional to the looper operating point and inversely proportional to the strip

e

Kv a ·a

(-Kga·a - f·n - KgO·O + g )

(3)

(4) (5)

El L

(6)

1 + K Qa El L

=llM Kvn = K QO

m

+ Kvn · n + v )

(7)

(8)

tension. The steady state gain of tension due to the 1 difference in strip velocity v is - K-va - . The constant

I nput variables shou Id be selected as to get faster

Kva depends mainly on the rolling variables, e.g. pro-

responces, and so that the mutual interaction of one

portional to the thickn ess reduction and the rolling

control to the other output should be minimized. The

speed on the stand .

frequency response matrix is derived as follows ;

Multivariable Control of Hot Strip Mill Looper

o(S )] = ~ [v,(S)) [o(s) d(s) g,(s)

(9)

fp"

looper position with input gr. I n this su itable selection (10)

(S)]

of the input variables, however, the change in the looper torque still affects the interstand tension, and

(s) P'2 lP21 (s) P22 (s)

the change in the rolling speed has a little effect on the looper position.

- e(S2 + fmS + mKgo)( 1 + T gS) [

According to these understandings, the main control loop for interstand tension is closed with input vr , and

d(s) = (1 + TvS) (1+ T g S){(S2 + fmS + mKgo) . (S + eKvo) + emKgoKvnS} P(s) =

2473

emKga( l + TgS) emK vn S(l+T vS) ] m(S + eKva)( 1 + T vS)

( 11)

T v is the time constant of the roll speed regulator SR and T g is of the torque regulator TR.

The

application of a precompensator (Rosenbrock,

1974) is effective to this type of control for the sepa-

Some inner compensations are thought to be effective to improve the looper dynamics. The torque compensation relating to looper motion adjusts variably the rate of damping, the looper torque is also adjusted in relation with the

NONINTERACTION CONTROL OF THE LOOPER

ration of the mutual coupling of two variables. I n the transfer function of this case, shown in Eqn. (9), with (12) and (13), the steady state response of output and n, which is equal to

looper position in order to give

constant tension on the strip at any operating point.

0 [

Ii,

0

is given as ;

(0))

n(O)

(Kvo+Cva)(f + Cf + KgO T g) + KgaKvn

The rolling speed compensation, in relation with interstand tention, reduces the level of tension variation

[

from disturbance.

Kvn ] . [v, (O) ] - (f+Cf+KgOTg) Kga Kva + Cva g,(O)

( 14)

In this matrix of steady state gains, all the looper Taking into account the torque compensation, with

constants are positive and the inverse exists surely. The

CgO and Cf' and the roll speed compensation, with

precompensator [C(s)] , therefore, can be determined as;

Cva , the transfer function is to be transformed as ; C(S) -

d(s) = [Tg S3 + (1 + fmTg)S2 + m(f + Cf + KgoTg)S + m(Kgo - CgO)]

Kvn CI l (S)C I2 (S)] = [- (Kva+Cva) [ C (s) C (s) Kga f+Cf+ KgoT g 21 22

J (15)

As the result of this precompensation the total transfer

.[T vS2+(1 +eKvaTv)S+e(Kva+Cva)]

function Q(s) from U's to the outputs, as in Fig. 5,

+ (1 +Tg S)(l +TvS) emKgaKvnS

can be modified as in eqn. (16) ;

(12)

PII(s)= - e{Tg S3 +(1 +fmTg )S2 +m(f+Cf+KgOTg)S +m(Kgo -Cgo)} PI2(s)=emK vn S(1 +TvS)

(16)

P21 (s)= emKga( 1 + T gS) P22 (s) = m {TvS2 + (1 + eKva Tv)S + e(K va + Cva)} (13)

The expression (16) is plotted in frequency region in Fig. 6. Compared with the frequency response in Fig. 4, the mutual interactions are reduced considerably in the

The frequency characteristic from the control inputs (v"

g ,) is shown in Fig. 4, where the compensation

low

frequency

range up to the intermediate. The

characteristics of the main control response are scarcely

CgO is selected equal to KgO and typical values of an

influenced. The index A of mutual interaction is also

actual looper are applied. I n this figure the dynamics

shown in the figure, which represents the normalized

of the regulators, SR and TR, are also cosidered.

ratio of the mutual interactions to the main control responese ;

The followings can be understood from this figure; 1)

As the control input for the tension a, the

A= 1

q'2 (s) q21 (S)I qll (s) q22 (s)

(17)

roll ing speed refference v, has a wider frequency band of gain and smaller phase lag than the 2) 3)

4)

looper torque reference g,.

For most of the disturbances in the actual rolling fall

The i nterstand tension control with v, has less

on this frequency range, this compensation is considered

effect on the looper position.

to work sufficiently. Only a small effect remains on the

As the control input for the looper position

looper position 0 from the tension control, and almost

0, the reference g, realizes faster response than

no change in the interstand tension a from position

the reference vr •

control, and by far the faster responses are expected

The looper position control with g, causes less

for both the looper position and the interstand tension

interaction to the tension.

control.

Y. Kotera and F. Watanabe

2474

The new multivariable control is implemented on the

This form of the precompensator roughly satisfies the

actual production mill, the performance chart is shown

relation in eqns. (20) and (21) but not completely .

in Fig. 7. It is evident that the looper position and the interstand tension are controlled within the narrow

As the result of this derivative compensation, the

band of deviations. A typical resu Its with a conventional

frequency response of the object,

control method , on the same material under the same

as is shown by the solid lines in the Fig. 8. Compared

rolling schedule, are shown in the figure .

with the result of the constant gain compensation in

~e and ~e is

improved

eqn. (15) which is plotted in the dotted lines, it is In order to get a further improvement, an additional compensation of deri vative action in the precompensator

obvious that the amount of the mutual interaction

~e is reduced on the whole frequency range . While

~a

the response

can be probabl y adopted .

~a

and

are qu ite identical with

the case of the constant gain compensation. In additon Th e complete diagonalization of this process on the

to this improvement in the mutual interaction, con·

w hole f requenc y range can

siderable improvement is made for the main response

be accompl ished, as is

obvious in Eqn. (16) , w hen all elements of the precom pensator and the transfer function of the looper

~o in the high frequency range . The index A of the mutual interaction is also improved as in th is figure.

are in the followin g relations c 21 (s) -

c " (s)

The

p" (s) p" (s)

(18)

effectiveness

precompensation

of

the

derivative action in the

is examined on the time domain

simulation . The response of the interstand tension a p " (s)

c " (s)

c,;Tsj

(19)

p " (s)

and

the

looper

disturbance

Vd

position

0

under the strip speed

is shown in the Fig. 9. Resultant curves

shown in the dotted lines are for th e case of constant Refering to the eqn . (13), and for the case Cgo is

gain compensation and the solid lines for the case with

eq ua l to KgO, eq ns. (18) and (19) are reduced as follows;

the derivative action .

c,, (s) _

eK ga (l+Tg S)

~ - - T vS 2 + (1+eK'-v-a= T'---v-")S =--"--+- e-o(c-K:-v-a- + --=co-v-a"7) c" (s) c " (s)=

TgS

2

-i- T1

(20)

The redu ced amount of mutual interactions and the

mK v/J ( 1 + T vS) +-fmTg-'c)S-=-+- m- (C-::f-+- C=--J'-+---C-:K-go---:T=-g---C) (21 )

two outer feedbacks. The control performance, hence,

improved characteristic enable the higher gains of the attains much improvement, especially on the looper position control.

It is unreal , I-]owever, to get procompensator which satisfi es th e relations of eq ns. (20) and (21) completely,

CONCLUSION

becuase of the parameter inaccuracies or pole-zero cancellation. As is shown in Fig. 5, the input signal to the precomp ensator elements c , , (s) and c, th e

interstand

ten sion,

and

I

(s) relates

th e observation noise

Fundamental equations for the hot mill looper are described.

pre vents th e fu ll realization of this function in the high

Th e static and dynam ic characteristics are explained

frequenc y ran ge. the constants e and Kv a in eqn . (20)

with

depend strongl y on the rolling conditions, because of

mechanical dimensions of the looper.

regard

to

the

rolling conditions and to the

these uncertainti es the supplement of the dyanmic can cellation to c, , (s) and c, , (s) is thought unfeasible.

A multivariable control of the interstand tension and

Therefor e c,

the looper operating position is investigated. For the

I

an d c, '

are designed the same with

tho se in eqn. ( 15).

mutual interactions, we derived precompensators giving independent control of the two.

On th e oth er hand , d y namic compensation in c,

2

(s)

and c" (s) are li kely to be real . In eqn. (21), we can assum e l » actual

f.m .T g and f +Cr»

loopers, and

this paper is being implemented on the actual pro-

th ey can be easily determined

duction mill . Under the ordinary rolling schedules, the

regardless of the rolling conditions. The time derivative of looper position

The looper control based on the developments of

Kgo ·Tg , for any case of

e corresponds

looper angle variation is reduced to 1-2 degree (peak to

to the looper rotation

peak) and the tension variation is negligibly small.

n, which is observed through the detector of rotation

The results are much superior to those of the con-

on the looper axis. The rotation signal is to be applied

ventional looper control.

for the derivative action in the precompensator. Th e precomp ensator with derivative action is expressed as ;

- (K va + C Va ) K V/J + K V/J T vS ) C(S) = [ Kga f + Cr + Kge T g+(~ + fT g)S

The feasibility of supplement compensations of derivative action is investigated , the result of simulation

(22)

study

proved

performance.

the

further

progress of this control

Multivariable Control of Hot Strip Mill Looper

2475

REFERENCES Price, J.C. (1973). The hot strip mill looper. _ SR

IEEE Trans. Ind. Appl., Vol. 1A-9, No.5, pp.556·562 Rosenbrock, H. H.

---'1'"

(1974). Computer Aided Control

c

System Design. Academic Press, London

m=

--,

-

_

ius-". .~--t{.J

~

I

M

KI.' o L

,

, . "1 "~,~, E L-

a

n

looper rotation (deg/sl

8

looper position (degl

. . -'-

/4, ... ,. -

'

1" T ... S-,

"

.....'.

m

v

strip speed difference (mm /s i looper torque (kg.m)

L

nominal loop length (mm)

C,

" 5

modulus of strip elasticity (kg/mm 2 ) M : inertia moment of looper (deg /s 2 )/ (kg.m)

V:

fl :

strip speed

Fig. 3

Kga: torque constant (kg.m)/(kg/ mm 2 ) Kg8 : torque constant (kg.m) / (deg)

K,' rJ ..

g r : torque reference

looper rotation

Ur : speed reference

Kva: slip constant (mm/s)/(kg/mm 2 )

~

•

g: drive torque

: friction loss rate (kg .m) / (deg /s)

-51

•

~

E

.l ...... :

/1

r

g

f

Kill

TR

strip tension (kg/ mm 2 1

~

,

.-'

Kt'll= KW

List of symbols

u .

"LT ; . . ~

•

e

looper position

Vd

disturbance

a:

strip tension

Block diagram of looper including inner compensations

40r-~------------~---------------------------.

KQa: loop storage constant (mm) / (kg/ mm2)

striP tens ion (kg/mml)

Q

loaper pos iti on (deg)

KQ8 : loop storage constant (mm) / (deg)

Vr:

speed re ference (mm/s)

gr :

torque reference (kg.m)

o UN.

IJ l g,

" v.

rolling stand Vi

(J I g,

.. 80 I I

I

I

~

~

0'

Fig. 4

0: looper posi tion

a: strip tension Vo

SR

exit velocity

TR

g: drive torque

torque regulator u'

Fig. 1

Frequency response of loo per including inner compensations

entry velocity

Vi :

speed regu lator

'0.0

'0 FREQUENCY (rad/sec)

.'

f

Looper mechanism

Pi a

Ua • "' c , (S /f '~' ..... l"

..

5R

c

g U1

g

'"';;; " z-

" c Isl • •

::;;

)0

'

D!:} · H

-.. L

I

-

5- - "

... - . -

~

0 · ...

•

. . j,

Pl O -

Isl - •

t'.' .

OH ; (5) _ + ..'

un

CC

l!dl

TR

g,

'""-0 '3

L

__ 1. _

K\., L

,

.J

-

Kl.' n "

v: strip speed difference

g: drive torque

a: strip tension

8: looper position

Plo: tension controller

Pl O: position controller

a

strip tension

a'

tension reference

0

loop position

O·

position reference

Ua

tension controller output

U8 : position controller output

11: looper rotation

Fig. 2

Linearized modei of looper

Fig. 5

Multivariable control of looper

Y. Ko t e ra and F . Wat anabe

24 76

40 r------------------r------------------------------- , strip tenSion (kg / mm:

40'r--r--------r---a--s-t~ r ip-t-en s~io -n~(~ kg-/~m-m -.,7)----'

I

looper positi on (d eg )

looper posi t ion (deg) Uu:

tension cont ro ller output (mm i s)

_ ___...::::,_=------":...'.::U.::"---,U:.:O:...:...!p::o:.:s;:.:t':.:o.::n~controller output (kg.m)

O/ Uo

o

o

-40

- 40

Uo : te nsio n con troller out put Imm!s ) Uo: posi t ion co n t roll er ou t put (kg .m)

- ----------~~~--------~~~~-

- - - - consta nt gain precompensator

a;

a;

:s

~

<{

:s

~

'"

o/UO

'"

<{

- 80

- 80 ·0 ,

Index o f Interac ti on

120

·00

01

10

100

REOUENCY

~

(rdel

100.0

- 120 0.1

1.0 10.0 FREQU ENCY I,.d/sl

sI

Fig. 6 Frequency response of looper with precompensator (constant gain)

Fig.8 Frequency response of lcoper with precompensat or (derivative)

i- - -t- .

~~~~~ r

positIOn ! 20

~

. 1O ~ '_ • ...1

, strilJ ten sio n Ikg .' mm !)

,

[2.51- . · 0 -;--,--+J-:

~ -t loope r pusl t lon ~ 20

Idegl

, ' 10

i

t-

r-r -'c. i

stnp tenSion (kg / mm:)

?51 LO-r----T'

Li

.1

l...

Fig. 7 Performance of looper control

ldeg l l kg . m m : 5.0 0.5 -

/

2.5

0.25

o

o

I

(i

loope r pOSi t ion

---

precompensator with derlvatlye

-2.5 - --- constant gaIn precompensator

- 5.0

0.2

OA

0.6

0.8

1.0

TIME Iseel

Fig. 9 Simulation results

100.0

For Discussion see page 2513