Automatic Profile and Flatness Control for Steckel Mill

Copyright @ IFAC Automation in Mining, Mineral and Metal Processing, Tokyo, Japan , 2001

AUTOMATIC PROFILE AND FLATNESS CONTROL FOR STECKEL MILL - Self-tuning Mechanism and Interactive Bender Setup Ken Kuribayashi, Masahiro Kayama, Yutaka Saitou, and Yoshihiko Iida

Hitachi. Ltd.

Abstract: In this paper, several new technologies of Automatic Profile and Flatness Control (APFC) developed for Steckel mill are proposed to improve crown accuracy and shape flatness . First adjustment of the mechanical APFC model using multiple regression technique is described to make it be more suited to the actual mill behavior. Then the online self-tuning mechanism of the controller is represented in detail to adapt it to the current rolling condition. Also setup logic determining appropriate combination of bender references is discussed. Namely determined bender references for former passes are calculated again to obtain desired crown which may be deteriorated by bending of the last several passes. Finally the developed methods are applied to the actual Steckel Mill and demonstrated their effectiveness. Copyright@ 20011FAC Keywords: Hot strip mill, Profile and flatness control, Model-based control, Adaptive control, Multiple regression analysis

1. INTRODUCTION

2. STECKEL MILL

In this paper, several new technologies of Automatic Profile and Flatness Control (APFC) developed for the Steckel mill are described. Since stableness of rolling of the Steckel mill is lower than the Tandem mill in addition to its rolling environments such as a work roll condition is varied easily, it is very hard to improve crown accuracy and shape flatness.{Wang et al., 1998) For this the APFC model based setup control is introduced with adaptation function and setup logic for determining acceptable bender references for crown and shape.(Guerrero et al., 1999; Kuribayashi et al., 2000) First adjustment of the mechanical APFC model using multiple regression analysis is described to make it be more suited to the actual mill behavior. Then the online self-tuning mechanism of the controller is represented in detail to adapt it to the current rolling condition. Namely, desired crown target is modified with the linear addition of control and model errors evaluated after rolling of the previous coils. Interactive setup logic, which determines the optimal combination of bender reference for each pass, is also described to keep constant crown ratio at the final pass for the shape flatness considering to minimize the deterioration of crown accuracy. Finally the developed system is applied to the actual Steckel mill plant, and effectiveness is demonstrated with obtained crown and shape results.

Fig. 1. indicates the construction of Steckel mill consisting of a single stand and two furnace coilers, where a transfer bar from the roughing mill is rolled into a hot coil. Since it includes profile meters at the entry and delivery sides of the mill as well as a shape meter at the delivery side of mill, crown can be measured at each pass, while shape is obtained only at a final pass. Rolling with the same work roll is done by 3 - 7 times for each coil by changing the rolling direction, while about ten coils are rolled between work roll exchange. It is hard to keep stable rolling condition because of thermal expansion and wear of work roll, temperature decrease of strip, and so on. Therefore control of Steckel mill is not so easy compared with it of Tandem hot mill. 3-7 times (passes) to roll ~ •

Transfer bar from Rougher Mill

Furnace Coiler ... Down

~Q:QJ}~-~r . ~. .\

Profile gauge

Fig. 1.

149

Single stand mill

\8;

Shape meter

Construction of Steckel Mill in this paper

3. TECHNOLOGIES FOR IMPROVING CROWN

(B 4"C Rw), is an independent variable, X I, X2, X3, and X4, respectively, while E h is a dependent variable Y, and neglect other items, which have just small contribution to E h. By multiple regression analysis with accumulated data sets of (XI, X2, X3, X4, Y) obtained from entry and delivery side profile meters and other detectors, multiple regression equation is obtairied as equation (2).

ACCURACY AND FLATNESS

3.1

Adjustment o/the mechanical APFC model

The mechanical APFC model used in this system is described below, where output crown ratio is represented by a linear combination of input crown ratio and other several related items.

Y

=

al"(XI) + a2"(X2) + a3"(X3) + ~"(X4) +
E

h

= BI"

H + B 2"P + B3" F + B4" CRW B + B 5 "CR + B6

Where E h EH P F CRW CRB B 1' " B6: CH Ch H h

(2)

E

(1)

Where

Output crown ratio ( = Ch / h) Input crown ratio ( = CH / H) Rolling force Bending force : Work roll crown Back up roll crown Coefficients determined by mechanical analysis Input crown Output crown Entry thickness Delivery thickness

al"'~

: Multiple regression coefficients

By using equation (2), equation (1) can be modified to equation (3). = al"(B 1 " EH) + a2"(B 2"P) + a3"(B3"F) + ~"(B4" (CR W + L\ C R w)) (3)

Eh

Where L\ CRw: Constant item corresponding to the work roll crown prediction error. By using equation (3) instead of equation (1), the APFC model was better suited to the actual mill, which is expected to yield more proper bender set up to improve crown accuracy and shape flatness .

The equation (1) represents the formulation of the conventional mathematical APFC model obtained by strict two dimensional elastic and plastic simulation results, in which several coefficients are modified experimentally to extend two dimensional model to three dimensional one. However since it has been mainly tuned for Tandem mill, namely not so proper for Steckel mill, it is necessary to make it more suited to Steckel mill.

3.2

Self tuning mechanism a/the controller

Because of unstable rolling condition mentioned above, model error cannot be avoided even though it is minimized statistically. Since the APFC model is already adapted to the consistent mill behavior, how to compensate control error caused by current unstable rolling condition is discussed in the section. According to the analytic knowledge that the APFC model errors of neighboring coils are correlated strongly, the adaptive control is introduced, where the target crown is modified by 6. at the setup turung. 6. is represented by a linear combination of control error of the previous coil and model errors at the several previous coils, which is the essential point of the APFC. As shown in the Fig. 2., model error is calculated precisely by subtracting estimated crown from detected crown. The estimated crown is obtained by calculation using the APFC model with actual control data such as bending and rolling forces as well as calculated data such as work roll condition corresponding to the detected crown. The APFC target and modified value 6. are determined as follows .

As mentioned in the Chapter 2, from a view point of control, a benefit of this Steckel mill is that both of entry and delivery crowns can be detected with prepared proftle meters. Therefore the crown information of every pass can be utilized except for rougher plate crown, which cannot be detected because profile meter and side guide are interacted to each other. (Kuribayashi et al., 2000) As mentioned in the previous papers, the reliability of detected crown of each pass was analyzed based on the statistical theory. Accordingly the detected crown is statistically used for model adaptation in advance and also is used for the online adaptive control only final pass crown. In this section, the former technique is described in detail, while the latter one is discussed in the section 3.2.

(4)

To improve the APFC model accuracy taking account of the unique or specific behaviors of actual plant, the multiple regression analysis is applied using actual data obtained from the plant. Suppose that each input item, (B 1 " EH), (B 2"P), (B 3"F), and

Where C*

150

Modified target crown used for control Target Crown

D. Where

= Cl • £"-1 + C2 • £"-2 + C3 •

£"-1

£.2

Ec. Cha Chm

Eco

Where (n) : Final Pass number (n-l) : (Final-I) Pass number EI Shape compensation coefficients

(5)

APFC model error of the previous coil. ( = Cha - Chm) APFC model error of the second previous coil Control error of the previous coil ( = Cha - ChI) Actual Crown Estimated crown with the APFCmodel

If F(n_l) > Fmax, F(n_l) = F max, while if F(n-I) < F min , after F(n_l) = F min , the F(n) is determined again with equation (7).

F(n)

3.3. Interactive setup for comparative control of crown and shape

In the APFC, two values (crown and shape) have to be controlled with just one actuator (bender). Therefore crown is mainly controlled at the former passes, while the last two passes are prepared to control shape to be flat. Conventionally after the bending force for the former passes are decided to realize target crown ratio, that for the last two passes are determined considering shape flatness by maintaImng constant crown ratio. For the flat shape, the shape priority logic is developed applying to the final two passes to obtain flat shape by keeping constant crown ratio at the final pass. Since it modifies bending forces for the last two passes compulsory when the bender saturates at it maximum or minimum value, namely when constant crown ratio cannot be satisfied. Equation (6) indicates rolling and bending force balance at the last two passes.

• p(n)

+ El) / B 2(o)

Where (i) (n) Fo FLM Ch'

(6)

Actual data (benders, WR condition .....)

Pass number (except for final 2 passes) Final Pass number Original calculated bending force Bending limit value (Max. or Min value) Calculated crown using bender limit (FLM) Original calculated crown

F2

. - ; ; - - (1) original bending setup

F3 For shape

Estimated crown

APFC """""

Detected crown

'---------

-1

(7)

F(i) = Fo(i) - I Fo(n) - FLM } • (Chl(n) - Cho(n)} / I Ch' (i) - Cho(i) } (8)

Cho

~

(B 3(n-l) • P(n-I) + B2(n-1) • F(n_l)

When the bending forces of the last two passes are saturated, they are modified appropriately by solving the above balance equation. However once the shape logic is applied, the calculated crown is not satisfied for original target. The interactive setup algorithm covers this situation to aim the correct target crown. If the original target crown is not obtained under the calculation with shape logic, this technique will be applied to obtain correct target crown with keeping the shape stability by modifying the bending setup for former bending setup except for final 2 passes. In the algorithm, after setup execution, predicted crown is estimated again with the APFC model to check whether the C· is obtained or not. When not, the bender value of the former passes is modified to reduce the difference between the predicted crown and C·. Fig. 3. describes the schematic illustration of the interactive setup execution, where the original bending setup values are modified based on the following equation.

In this method, model and control errors are compensated easily by just modifying the target crown. The compensated values are neither stored in the controller, nor used in model training to avoid that large control error caused by exceptional unstable rolling deteriorates model accuracy.

F(o-I) = (B 3(n) • Pto) + B2(o) • F(n) - B3(n-l) • P(n-I) - El) / B2(n-l)

=

- B 3(n)

For crown

r

~ JIL. \

(2) Shape priority logic

Mod<1 'm><

+ ~Of------'. (3) APFC interactive setup logic

Fig. 2.

Schematic diagram for calculating model error

Fig. 3.

151

Bending setup with interactive setup

4. EVALUATION RESULTS IN THEACfUAL STECKEL MILL

The result shows the developed self-tuning mechanism works well. Table 2 and Table 3 show the synthetic evaluation of crown and shape. These tables show the comparison between Conventional and Developed APFCs applied new functions. The results show the accuracy of crown is improved with keeping shape.

The mechanical APFC model is adjusted by multiple regression analysis using actual data obtained from the plant. Effects of input crown ratio, aJ, and bending force, al , were larger than 1.0, while effect of rolling force, a2, was less than 1.0. Effect of work roll crown, a. was rather small, which indicated that estimation model of work roll condition was not suited enough to the actual Steckel mill. These adjusted parameters and actual data have about 80% of correlation according to the result of the multiple regression analysis. The work roll condition item was compensated again with fl CRw of equation (3) to be more suited to the actual behavior. By the above operations, accuracy of the mechanical APFC model could be improved enough to be used for the setup calculation. For Cl, c2, and Cl of the equation (5), we also determined experimentally. Table 1 indicates the linear correlation of model error between neighboring coils evaluated with the below equations. (correl), = (Cov(C, C ,,)/ a C

j '

a C;.,}

Table 1 Correlation of Model Error between Neighboring Coils Correlation (Correl») 0.63 0.39 (Correlh Table 2 Crown Deviation from Target Value Width Conventional Developed Avg. Std. Avg. Std. 3f -8.5 31.9 2.3 19.9 4f -12.4 32.0 -1.9 17.0 5f -6.2 34.8 -8.4 21.4 [tLm]

(9)

Width 3f 4f 5f

n

Cov(X,Y)

=

(1/n) .L (Xj - X)(Yj - Y)

(11)

J- l

According to Table 1, C, and C2 are determined, as 0.7 and 0.0, respectively. Then C3 is tuned to 0.7 regarding to the actual rolling results. Fig. 4. shows an example of control results of coils between work roll exchange. According to the figure, difference between target and actual crowns is less than about 10 tL m, while shape is less than 100 I-unit. Also the APFC target, C·, which is the modified crown target for control, is demonstrated to work effectively to decrease the deviation of actual and target crowns. 1-<>- APFC Tarl'e.... Actual CrownO- Tarl'et

5. CONCLUSIONS Automatic Profile and Flatness Control (APFC) with several new technologies are described in this paper. In future, the long span learning method will be investigated for the APFC model to avoid the decrease of control accuracy caused by time variant effects.

Crownt\- Actual Sbapk

REFERENCES

500

80

70 r--------y.~~r_----------~400 60

r-------~----1-----------~

200

::

U

30

--'0:'===- - - 1

20

r-------~~~~----------~

Guerrero J., Kinose R and Matsui Y. (1999) New Installation and Operation of a Steckel Mill in North American Stainless. 1999 AlSE Annual convention Kuribayashi, K. (2000) Automatic Profile and Flatness Control for Steckel Mill (in Japanese) (MID-OO-29). Annual Report of Metal Industries Division, The Institute of Electrical Engineers of Japan Wang Z. (1998) Application of Self-Adaptive Strip Shape Control for UC Mill Based on Neurak Network Prediction ModeL Steel Rolling '99

300

e50 r-------+-~~~----------~ IOO 2~40 r-~---::1'--::------\~--fr--==-=--~ 0

'7J

'§

4'c.:

-lOO tl - 200

-300 10 r-------------------------~ -400 0

L---~--~----~--~--~--~ -500

0

2

4

6 8 Coil Sequence

[Crown] Avg. 2.7um [Shape] Avg. 49.3 I-unit

10

Table 3 Flatness of Shape Conventional Developed Avg. Std. Avg. Std. 20.2 76.9 8.4 42.3 -35.5 138.4 6.3 93.3 -129.5 199.5 14.5 149.1 [I-unit]

12

Std.dev.6.8um Std.dev. 45.4 I-unit

Fig. 4. Control result for Crown and Shape

152