- Email: [email protected]
Flatness and Profile Integration Control Model for Tandem Cold Mills
Available online at www.sciencedirect.com
ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNmIONAL. 2012, 19(3): 31-37
Flatness and Profile Integration Control Model for Tandem Cold Mills S H A N X i ~ - y i n g ' . ' , ~ , LIU Hong-min'*2,
JIA Chun-yu'.'
,
SUN Jian-liang"'
(1. Engineering Research Center of Rolling Equipment and Complete Technology of Ministry of Education, Yanshan University, Qinhuangdao 066004. Hebei, China; 2. State Key Laboratory of Metastable Materials Science and 3. Hot Tandem Rolling Factory, Technology, Yanshan University, Qinhuangdao 066004, Hebei, China; Jinan Iron and Steel Co Ltd. Jinan 250101, Shandong, China)
Abstract: Using the effective matrix methods of flatness and profile control synthetically, the flatness and profile integration control scheme for tandem cold mills is built in order to increase flatness and profile control precision of tandem cold mills. Corresponding control strategies are adopted for various control objectives of different stands and the coordination control strategies of various stands are given, which makes the on-line flatness control cooperate with on-line profile control and implements the parallel control of different stands. According to the measured flatness and profile data of some 1550 mm tandem cold mills, the control scheme is verified and the result indicates that the scheme has high flatness and profile control precision with steady and reliable control process. A new way and method is supplied for researching shape control of tandem cold mills. Key words: flatness; profile; shape; effective matrix; tandem cold mill
Steel strips are the main steel products and are used widely and weightily in industries of automobile, shipbuilding, bridge, architecture, instrument, electron, food packing and household appliances, etc['-']. Shape is an important quality indicator of steel strips. It influences the lumber recovery of steel products, the quality of subsequently deeply processed products and the good performance of the deep processing directly and it is also the most strict and difficult indicator among the performance indicators (including mechanical property, thickness precision, shape and surface quality) of cold-rolled strip
product^^^-^^. Shape control system of strip mills mainly includes the pre-set control and the closed loop feedback ~ o n t r o l ~ ~ T - ~h e' . pre-set control can control all stands and its common implementation methods are variation method, finite-element method, boundary element method and strip element method, etc. T h e pre-set control is a kind of "cursory" control because it can not consider various interference factors and some parameters only adopt their average values. In order to implement precise control, the on-line con-
trol model must be used for on-line regulation on the basis of the set values, making these set values be suitable for the practical rolling process. T h e closed loop control can calculate control quantity quickly to cont'rol shape and its common implementation methods are effective function method, regression method and intelligent method, etc. T h e shape meter is usually equipped in the outlet of the last stand and shape on-line control is implemented only at the last stand. For the front stands without shape meter, they are not controlled any longer after pre-set, which puts the task of on-line correcting shape deviation on the last stand. If the on-line shape deviation is big enough to exceed the regulation ability of the last stand, the shape quality of finished products will be influenced. If other stands all participate in shape control, the load of regulating shape at the last stand can be lightened and the ability of correcting shape deviation of the whole tandem cold mills can be strengthened and the shape quality of finished products can be controlled. Flatness and profile are two major quality indicators of shape and they are interactional and closely
Foundation Item: Item Sponsored by National High-Tech Research and Development Project of China (2009AA042143) ; Hebei Provincial Great Natural Science Foundation of China (E2006001038) ; Hebei Provincial Science and Technology Project of China (10212101D) E-mail: rnublueskyBqq. corn; Received Date: January 18, 2011 BiographyiSHAN Xiu-ying(l982-), Male, Doctor;
Journal of Iron and Steel Research, International
32
relatedC7-". Using the effective matrix methods of flatness and profile control synthetically and adopting different control objectives by the characteristics of various stands, the flatness and profile integration control scheme for tandem cold mills is built in order to increase flatness and profile control precision, which makes the on-line flatness control cooperate with the on-line profile control and implements the parallel control of different stands. T h e result of industry verification indicates that the scheme has high flatness and profile control precision with steady and reliable control process and can upgrade the control ability of tandem cold mills with much significance for improving product quality.
1 Whole Structure of Flatness and Profile Integration Control Scheme Modern strip mills are mostly tandem cold mills. The closed loop shape control is usually at the last stand and the p r e s e t shape control is usually at other stands for the restriction of shape detection means. So the shape control ability of tandem cold mills is not brought into play. In order to upgrade the on-line shape control ability and precision of tandem cold mills, the flatness and profile integration control scheme is built for some 1550 mm five-stand tandem cold mills, which makes all stands participate in the on-line shape control. Each stand of the tandem cold mills is a UCMW mill with strong shape control ability. The tilting roll, the bending work roll, the bending intermediate roll and the axial shifting intermediate roll are taken as flatness and profile regulating means. T h e built flatness and profile integration control scheme for tandem cold mills is shown in Fig. 1 where PMC (Profile Matrix Control) expresses the profile control matrix model and FMC (Flatness Matrix Control) expresses the flatness control matrix model. In the scheme, the front four stands are controlled by the profile control matrix model with profile as the objective and the fifth stand is controlled by the flatness control matrix model with flatness as
F1
Fig. 1
F2
F3
F4
P F6
Flatness and profile integration control scheme
VOl. 19
the objective, making various stands participate in the on-line shape control and implement the parallel control of various stands, which can adequately use the regulating ability of various stands and upgrade the on-line control ability of flatness and profile for tandem cold mills on the whole.
2
1
Building of Flatness Control Matrix Model
The effective matrix method for flatness regulation is a simple and practical explicit coptrol by which the relation between various regulating means and various order flatness components can be built according to an effective matrix and the parallel control of various regulating means can be implemented. It is suitable for the on-line flatness control with fast calculating speed. Therefore, the effective matrix method for flatness control is adopted to build the on-line flatness control model, 2.1
Effective matrix method for flatness control T h e effective functions of various regulating means on flatness are as follows: fl
(Y) =
au,h
l
c11
p4 (y) AOZ f2(y)=-'ClZpl Auz
Pl (Y)
+
c21
P2 (Y)
+
C31
+
p3 ( Y 1
(1)
c4l
(y)+cZZpZ
(y>+c32$3
(y)+
(2)
c42p4 ( y ) f3
(Y) =
b
3
-C13 P1 (Y)
C43P4(Y) f4
(Y)
A04 =--c14
-
Au4
c44
Pa (Y)
+C23
P2 (Y)
+c33
p3 (Y)
+
(3)
+
Pl (Y) +c24pz ( y ) +c34p3 (y>
(4)
where, fi ( y ) , f 2 (y) , f 3 ( y ) and f 4 ( y ) are the effective functions of the tilting roll, the bending work roll, the bending intermediate roll and the axial shifting intermediate roll, respectively; Au, , n u z , Au3 and Au4 are the variations of the tilting roll quantity, the work roll bending force, the intermediate roll bending force and the intermediate roll axial shifting quantity, respectively; hl, b 2 ,h3and b4are the variations brought by the tilting roll, the bending work roll, the bending intermediate roll and the axial shifting intermediate roll, respectively; p1(y) , p2 (y) 9 P3 ( y ) and p4( y ) are the linear, quadratic, cubic and biquadratic Legendre orthogonal polynomials, respectively; and cB (i, j = 1 , 2 , 3 , 4) are effective coefficients. The flatness variation brought by the four regu-' lating means is as follows:
Issue 3
Flatness and Profile Integration Control Model for Tandem Cold Mills
33 '
4) If the maximum of Aei is less than
A u = A U ~ + A U ~ + A O ~ + A O ~f = l(y)Aui+
Ef,
return
~ Z ( Y ) A U ~ + ~ ~ ( Y ) A U ~ ~ ~ ~(5) ( Y ) AtoU2); ~ According to Eqn. (1) to Eqn. ( 5 ) , the relation between the flatness variation and the various regulating variations can be obtained as follows:
5) According to the current flatness control equation, the regulation quantity AU, of flatness control means is calculated to control flatness; 6) Return to 2) and repeat these operations. matrix model
where, Ae, , Ae2, Ae3 and Ae4 are the variations of the linear flatness component e l , the quadratic flatness component e2 , the cubic flatness component e3 and the biquadratic flatness component e 4 , respectively. Let
Lc4l c42 c43 c44] there is AE=CAU (7) where C is the effective matrix for flatness control and the matrix element ci, is an effective coefficient whose physical meaning is the variation of the i t h flatness component brought by the unit variation of the j t h regulation parameter u, ; AE is the variation of flatness component parameters; AU is the variation of flatness regulating means. If the measured flatness deviation is a E , according to the effective matrix C for flatness control, the flatness control equation can be obtained as AU=C-'AE (8) T h e aim of flatness control is to eliminate flatness deviation and the actual flatness regulating quantity is -AU. It is obvious that if the effective matrix for flatness control is given, the flatness control quantity can bf; easily calculated by the flatness deviation. T h e effective matrix for flatness control can be calculated by the flatness prediction model or the measured dataC6'.
Implementing of flatness control matrix model Fig. 2 shows the structure of the flatness control matrix model FMC. When the model works, the detailed calculation flow is as follows: 1) Give the standard flatness curve Rf and the minimum flatness control error E f ; 2 ) Collect the current flatness data and obtain Yf by pattern recognition; 3 1 Calculate the flatness deviation coefficient
Ydk) Fig. 2
3
Structure of flatness control matrix model
Building of Profile Control Matrix Model
T h e effective matrix method for profile control is similar with the effective matrix method for flatness control and it is also a simple and practical explicit control model. It is suitable for on-line profile control with fast calculating speed. Therefore, the effective matrix method for profile control is also adopted to build the on-line profile control model. 3. 1
Effective matrix method for profile control T h e transverse distribution of strip exit thickness can be expressed by polynomials and usually biquadratic polynomials can meet the precision hl ( y ) = a O + a l p ~ ( y ) + a 2 ~ 2 ( y ) + a 3 ~ 3 ( y ) + a ~ p( y ~) (9) where, a. is concerned with the average thickness of the strip; and al , a 2 , a3 and a4 are concerned with the profile of the strip. Therefore, al , a 2 , a3 and a4 can be called profile coefficients. T h e effective functions of various regulativg means on profile are as follows:
2.2
aE=Rf-Yf;
:J
\Y/
au3
au3y1'y
34 '
VOl. 19
Journal of Iron and Steel Research, International
where, fcl ( y ) , fez ( y ) , f c 3 ( y ) and fc4 ( y ) are the effective functions of the tilting roll, the bending work roll, the bending intermediate roll and the axial shifting intermediate roll on profile, respectively. T h e profile variation brought by the variations AUI 9 Auz , Au3 and Au4 of the tilting roll quantity u1, the work roll bending force u 2 ,the intermediate roll bending force u3 and the intermediate roll axial shifting quantity u4 is as follows
is given, the profile control quantity can be easily calculated by the profile deviation. T h e effective matrix for the profile control can be calculated by the profile prediction model or the measured data.
Implementing of profile control matrix model Fig. 3 shows the structure of the profile control matrix model. When the model works, the detailed calculation flow is as follows: the standard profile curve R, and the A ~ I ( Y ) = ~ , I ( ~ > A u , + ~ ~ ~ ( Y > A u ~ + ~ ~ ~ ( Y ) A 1) u ~ Give + minimum profile control error ee ; fc4 (y)Au4 (11) 2) Collect the current profile data and obtain Y, Substitute Eqn. (10) into Eqn. (111, then there is by pattern recognition; Ah1 ( y ) = A a , p ~ ( y ) + A a ~ p ~ ( y ) + A a ~ p ~ ( y ) + 3 Calculate the profile deviation coefficient nA = Aa4 P4 (Y) (12) where R, -Y, ; 4 ) If the maximum of Aai is less than ec , return aa, aa, aa, aa, to 2 ) ; 5) According to the profile control matrix equation, the regulation quantity AW, of profile control (13) means is calculated to control profile; 6 ) Return to 2) and refieat these operations. 3.2
1
Let
i-
IYdk)
Fig. 3
I
I
I Pattern recomition L
Structure of profile control matrix model
4 Calculation Flow of Flatness and Profile Integration Control Scheme aa4 _ aa, _ aa4 _ aa4 _
au, auz au3 au4 then Eqn. (13) can be abbreviated as AA=MAU (15) where, AA is profile variation; AU is the variation of profile control means; and M is the effective matrix for profile control. For the problem of profile control, set the current profile as A = [ a l , a 2 , a 3 , all' and give it an increment AA, making the profile reach the control objective A, = a,, , aoz , aO3, ad]', i. e. , A 4-AA = A,, then there is AA=A, -A (16) According to Eqn. ( 15 ) , the required control quantity making the profile change AA is obtained AW=M-'AA=M-'(A,-A) (17) where M-I is profile control matrix. Eqn. (17) is the profile control equation. It is obvious that if the effective matrix for profile control
In order to implement the parallel control of various stands of tandem cold mills, the coordination control strategy of various stands need to be built. Here the timeslice-rotation method is adopted to coordinate the control actions of various stands. Beginning with the first stand, the first stand executes control actions and the other stands have not any control action at the moment. In succession, coming to the second stand, the second stand executes control actions and the other stands have not any control action. T h e rest may be deduced by analogy and the third stand, the fourth stand and the fifth stand execute control actions respectively. After the fifth stand executes control actions, the control power returns to the first stand and then various stands execute control actions one by one according to stand sequence. In this way, these operations are repeated and the coordination control of various stands can be implemented. T h e calculation flow chart of implementing the method is shown in Fig. 4.
Issue 3
. z Flatness and Profile Integration Control Model for Tandem Cold Mills
35
&, (i=1,2,3,4)andstandard flatness curveRf Give minimum control errors .cr and EI
Give maximum control number k-max and let k=l,n=l
N
t
1
n=n+l
Collect(predict)currentprofile
Collect@rerlict)currentflatness data of stand 5
Calculate profile deviation Aa, (i=1,2,3,4)by R,
Calculate flatness deviation
1"
IN
Aa, and PMC model to control
Fig. 4
I
Calculate control quantity AUrby Ae, and FMC model to control flatness of stand 5
Flow chart of flatness and profile control
5 Simulation Experiment of Synthetical Control Scheme In order to do the simulation experiment of flatness and profile control, the simulators of flatness and profile must be built, i. e. , the prediction models of flatness and profile are built as the virtual control objectives or detecting instruments of flatness and profile and their prediction values are Y f and Y,respectively. Here BP network is adopted to build the prediction models of flatness and profile respectively. T h e input parameters of the flatness prediction model are strip width, various order components of entry flatness, entry thickness, exit thickness, deformation resistance, elasticity modulus, forward tension, backward tension, rolling force, tilting roll quantity, work roll bending force, intermediate roll bending force and intermediate roll axial shifting quantity, and the output parameters are various order components of exit flatness. T h e
input parameters of the profile prediction model are strip width, various order coefficients of entry profile, entry thickness, exit thickness, deformation resistance, elasticity modulus, forward tension, backward tension, rolling force, tilting roll quantity, work roll bending force, intermediate roll bending force and intermediate roll axial shifting quantity, and the output parameters are various order coefficients of exit profile. In order to validate the built flatness and profile prediction models, the measured data of some 1550 mm five-stand tandem cold mills are adopted to validate the two models. T h e tandem cold mills have shape meter for measuring flatness and thickness meter for measuring profile, and then the measured flatness and profile data are discrete values. Twenty examples are done and here the validation results of two examples are given. Fig. 5 and Fig. 6 show the prediction results of flatness and profile respectively. It can be seen that the predicted result and the measured
VOl. 19
Journal of Iron and Steel Research, International
36
,.
7
. . . . Measuredvalue
-Predicted value
-200
-600
Fig. 5
0
In order to validate the built flatness and profile integration control scheme, the simulation experiment is done by the measured data of some 1550 mm fivestand tandem cold mills. T h e neural network prediction models of flatness and profile are trained with the measured flatness and profile data as samples and the simulators of flatness and profile are obtained as the control objectives of flatness and profile. Flatness and profile prediction networks adopt the same learning parameters with the learning efficiency of 0.01, the momentum factor of 0.8, the learning efficiency diminution factor of 0. 98 and the learning efficiency accretion factor of 1. 05. Entry profile is proportionally allocated by exit thicknesses of various stands as the control objectives of various stands and the standard flatness curve of the fifth stand is the null curve. In the simulation experiment, the strip parameters are: entry width 928 mm, entry thickness 2.53 mm and exit thickness 0. 512 mm. Fig. 7 shows the profile control effects of the first stand, the second stand, the third stand and the fourth stand respectively, where the actual values mean the profile control results of various stands by the built shape control model. Fig. 8 shows the flatness control effect of the fifth stand, where the flatness control result means the flatness control result by the built shape control model. It can
I
600
200
Widthlmm
Flatness prediction result
- Measured value -Predicted value *
35
-5
$-lo
-600
-200
Fig. 6
0
Widthmun
600
200
Profile prediction result
result of flatness and profile anastomose as well, which indicates that the built flatness and profile prediction models have high precision and they can supply the exact control objectives for research on flatness and profile control. 10
0
5 -lo B‘a -20
0 Actual section configuration
$ -30
2 8
e5
10 0
* -10 -20
-30 -400
-200
0
200
400
-400
-200
0
200
400
Widthmun (a) Stand 1;
(b) Stand 21 ( c ) Stand 3; Fig. 7 Profile control result
be seen from Fig. 7 that the actual profiles of the front four stands anastomose with the objective values well. And it can be seen from Fig. 8 that the flatness control process of the fifth stand is steady with short response time, fast regulating speed and wee steady error and the flatness control effect is
(d) Stand 4.
rather good.
6
Conclusions
1) T h e industrial validations indicate the built flatness and profile prediction models have high precise prediction results and they can supply the exact
Flatness a n d Profile Integration Control Model for T a n d e m Cold Mills
Issue 3
Fig. 8 Flatness control result of stand 5
control objectives for researching on flatness and profile control. 2 ) The simulation experiments indicate that the built flatness and profile integration control scheme for tandem cold mills has high flatness and profile control precision with steady and reliable control process. 3 ) The paper supplies a new method for researching on shape control of tandem cold mills. References: [l]
ZHAI Bo, SUN Rongsheng, SUN Jian-lin. Application of Sheet Shape Control Technology on Continuous Rolling Mills in Angang CJ]. Angang Technology, 2009, (1): 49 (in Chinese).
37
ZHANG Jing, QIN Jiu-lian. Calculation and Control of Plate Shape on Hot Strip [J]. Control Engineering of China, 2008, 15(S): 21 (in Chinese). XU Jian-yong. High Precision Thickness and Shape Control Technology for Thin Strip Rolling [J]. Iron and Steel, 2002, 37(1): 73 (in Chinese). SUN Tie-kai, ZHAO Yong-he. Research on Profile Controlling Characteristics of WRS Mill [J]. Journal of Yanshan University, 1991, 15(2): 139 (in Chinese). PENG Yan. Theoretical Studies and Engineering Application of Shape Preset Control for HC Cold Mill Based on Strip Element Method [D]. Qinhuangdao: Yanshan University, 2000 (in Chinese). H E Hai-tao. Research on Flatness On-Line Intelligent Control for the Wide Strip Steel Cold Mill [D]. Qinhuangdao: Yanshan University, 2008 (in Chinese). PENG Yan, ZHENG Zhen-zhong, WANG Jian-guo. Influence and Compensating Means of Profile in Strip Flatness Measuring and Controlling of Reversible Rolled Strip Profile [J]. Journal of Yanshan University, 1999, 23(1) : 76 (in Chinese). GUO Jian-bo, LIAN Jia-chuang, T U Yuehong. The Calculation of Work Roll's Temperature Field and Thermal Crown in Hot Strip Mills [J]. Journal of Yanshan University, 1998, 22 (3) : 255 (in Chinese). LIU Yu-li, H U Xi-zeng, ZHAO Yong-he. Theory and Experiment Study on the Shape Control Function of HC Mill [J]. Journal of Yanshan University, 1990, 14(2): 1 (in Chinese). ZHANG Xiu-ling, LIU Hong-min. Transfer Matrix Method of Flatness Control [J]. Chinese Journal of Mechanical Engineering, 2003, 39(11): 100 (in Chinese).
ScienceDirect JOURNAL OF IRON AND STEEL RESEARCH, INTERNmIONAL. 2012, 19(3): 31-37
Flatness and Profile Integration Control Model for Tandem Cold Mills S H A N X i ~ - y i n g ' . ' , ~ , LIU Hong-min'*2,
JIA Chun-yu'.'
,
SUN Jian-liang"'
(1. Engineering Research Center of Rolling Equipment and Complete Technology of Ministry of Education, Yanshan University, Qinhuangdao 066004. Hebei, China; 2. State Key Laboratory of Metastable Materials Science and 3. Hot Tandem Rolling Factory, Technology, Yanshan University, Qinhuangdao 066004, Hebei, China; Jinan Iron and Steel Co Ltd. Jinan 250101, Shandong, China)
Abstract: Using the effective matrix methods of flatness and profile control synthetically, the flatness and profile integration control scheme for tandem cold mills is built in order to increase flatness and profile control precision of tandem cold mills. Corresponding control strategies are adopted for various control objectives of different stands and the coordination control strategies of various stands are given, which makes the on-line flatness control cooperate with on-line profile control and implements the parallel control of different stands. According to the measured flatness and profile data of some 1550 mm tandem cold mills, the control scheme is verified and the result indicates that the scheme has high flatness and profile control precision with steady and reliable control process. A new way and method is supplied for researching shape control of tandem cold mills. Key words: flatness; profile; shape; effective matrix; tandem cold mill
Steel strips are the main steel products and are used widely and weightily in industries of automobile, shipbuilding, bridge, architecture, instrument, electron, food packing and household appliances, etc['-']. Shape is an important quality indicator of steel strips. It influences the lumber recovery of steel products, the quality of subsequently deeply processed products and the good performance of the deep processing directly and it is also the most strict and difficult indicator among the performance indicators (including mechanical property, thickness precision, shape and surface quality) of cold-rolled strip
product^^^-^^. Shape control system of strip mills mainly includes the pre-set control and the closed loop feedback ~ o n t r o l ~ ~ T - ~h e' . pre-set control can control all stands and its common implementation methods are variation method, finite-element method, boundary element method and strip element method, etc. T h e pre-set control is a kind of "cursory" control because it can not consider various interference factors and some parameters only adopt their average values. In order to implement precise control, the on-line con-
trol model must be used for on-line regulation on the basis of the set values, making these set values be suitable for the practical rolling process. T h e closed loop control can calculate control quantity quickly to cont'rol shape and its common implementation methods are effective function method, regression method and intelligent method, etc. T h e shape meter is usually equipped in the outlet of the last stand and shape on-line control is implemented only at the last stand. For the front stands without shape meter, they are not controlled any longer after pre-set, which puts the task of on-line correcting shape deviation on the last stand. If the on-line shape deviation is big enough to exceed the regulation ability of the last stand, the shape quality of finished products will be influenced. If other stands all participate in shape control, the load of regulating shape at the last stand can be lightened and the ability of correcting shape deviation of the whole tandem cold mills can be strengthened and the shape quality of finished products can be controlled. Flatness and profile are two major quality indicators of shape and they are interactional and closely
Foundation Item: Item Sponsored by National High-Tech Research and Development Project of China (2009AA042143) ; Hebei Provincial Great Natural Science Foundation of China (E2006001038) ; Hebei Provincial Science and Technology Project of China (10212101D) E-mail: rnublueskyBqq. corn; Received Date: January 18, 2011 BiographyiSHAN Xiu-ying(l982-), Male, Doctor;
Journal of Iron and Steel Research, International
32
relatedC7-". Using the effective matrix methods of flatness and profile control synthetically and adopting different control objectives by the characteristics of various stands, the flatness and profile integration control scheme for tandem cold mills is built in order to increase flatness and profile control precision, which makes the on-line flatness control cooperate with the on-line profile control and implements the parallel control of different stands. T h e result of industry verification indicates that the scheme has high flatness and profile control precision with steady and reliable control process and can upgrade the control ability of tandem cold mills with much significance for improving product quality.
1 Whole Structure of Flatness and Profile Integration Control Scheme Modern strip mills are mostly tandem cold mills. The closed loop shape control is usually at the last stand and the p r e s e t shape control is usually at other stands for the restriction of shape detection means. So the shape control ability of tandem cold mills is not brought into play. In order to upgrade the on-line shape control ability and precision of tandem cold mills, the flatness and profile integration control scheme is built for some 1550 mm five-stand tandem cold mills, which makes all stands participate in the on-line shape control. Each stand of the tandem cold mills is a UCMW mill with strong shape control ability. The tilting roll, the bending work roll, the bending intermediate roll and the axial shifting intermediate roll are taken as flatness and profile regulating means. T h e built flatness and profile integration control scheme for tandem cold mills is shown in Fig. 1 where PMC (Profile Matrix Control) expresses the profile control matrix model and FMC (Flatness Matrix Control) expresses the flatness control matrix model. In the scheme, the front four stands are controlled by the profile control matrix model with profile as the objective and the fifth stand is controlled by the flatness control matrix model with flatness as
F1
Fig. 1
F2
F3
F4
P F6
Flatness and profile integration control scheme
VOl. 19
the objective, making various stands participate in the on-line shape control and implement the parallel control of various stands, which can adequately use the regulating ability of various stands and upgrade the on-line control ability of flatness and profile for tandem cold mills on the whole.
2
1
Building of Flatness Control Matrix Model
The effective matrix method for flatness regulation is a simple and practical explicit coptrol by which the relation between various regulating means and various order flatness components can be built according to an effective matrix and the parallel control of various regulating means can be implemented. It is suitable for the on-line flatness control with fast calculating speed. Therefore, the effective matrix method for flatness control is adopted to build the on-line flatness control model, 2.1
Effective matrix method for flatness control T h e effective functions of various regulating means on flatness are as follows: fl
(Y) =
au,h
l
c11
p4 (y) AOZ f2(y)=-'ClZpl Auz
Pl (Y)
+
c21
P2 (Y)
+
C31
+
p3 ( Y 1
(1)
c4l
(y)+cZZpZ
(y>+c32$3
(y)+
(2)
c42p4 ( y ) f3
(Y) =
b
3
-C13 P1 (Y)
C43P4(Y) f4
(Y)
A04 =--c14
-
Au4
c44
Pa (Y)
+C23
P2 (Y)
+c33
p3 (Y)
+
(3)
+
Pl (Y) +c24pz ( y ) +c34p3 (y>
(4)
where, fi ( y ) , f 2 (y) , f 3 ( y ) and f 4 ( y ) are the effective functions of the tilting roll, the bending work roll, the bending intermediate roll and the axial shifting intermediate roll, respectively; Au, , n u z , Au3 and Au4 are the variations of the tilting roll quantity, the work roll bending force, the intermediate roll bending force and the intermediate roll axial shifting quantity, respectively; hl, b 2 ,h3and b4are the variations brought by the tilting roll, the bending work roll, the bending intermediate roll and the axial shifting intermediate roll, respectively; p1(y) , p2 (y) 9 P3 ( y ) and p4( y ) are the linear, quadratic, cubic and biquadratic Legendre orthogonal polynomials, respectively; and cB (i, j = 1 , 2 , 3 , 4) are effective coefficients. The flatness variation brought by the four regu-' lating means is as follows:
Issue 3
Flatness and Profile Integration Control Model for Tandem Cold Mills
33 '
4) If the maximum of Aei is less than
A u = A U ~ + A U ~ + A O ~ + A O ~f = l(y)Aui+
Ef,
return
~ Z ( Y ) A U ~ + ~ ~ ( Y ) A U ~ ~ ~ ~(5) ( Y ) AtoU2); ~ According to Eqn. (1) to Eqn. ( 5 ) , the relation between the flatness variation and the various regulating variations can be obtained as follows:
5) According to the current flatness control equation, the regulation quantity AU, of flatness control means is calculated to control flatness; 6) Return to 2) and repeat these operations. matrix model
where, Ae, , Ae2, Ae3 and Ae4 are the variations of the linear flatness component e l , the quadratic flatness component e2 , the cubic flatness component e3 and the biquadratic flatness component e 4 , respectively. Let
Lc4l c42 c43 c44] there is AE=CAU (7) where C is the effective matrix for flatness control and the matrix element ci, is an effective coefficient whose physical meaning is the variation of the i t h flatness component brought by the unit variation of the j t h regulation parameter u, ; AE is the variation of flatness component parameters; AU is the variation of flatness regulating means. If the measured flatness deviation is a E , according to the effective matrix C for flatness control, the flatness control equation can be obtained as AU=C-'AE (8) T h e aim of flatness control is to eliminate flatness deviation and the actual flatness regulating quantity is -AU. It is obvious that if the effective matrix for flatness control is given, the flatness control quantity can bf; easily calculated by the flatness deviation. T h e effective matrix for flatness control can be calculated by the flatness prediction model or the measured dataC6'.
Implementing of flatness control matrix model Fig. 2 shows the structure of the flatness control matrix model FMC. When the model works, the detailed calculation flow is as follows: 1) Give the standard flatness curve Rf and the minimum flatness control error E f ; 2 ) Collect the current flatness data and obtain Yf by pattern recognition; 3 1 Calculate the flatness deviation coefficient
Ydk) Fig. 2
3
Structure of flatness control matrix model
Building of Profile Control Matrix Model
T h e effective matrix method for profile control is similar with the effective matrix method for flatness control and it is also a simple and practical explicit control model. It is suitable for on-line profile control with fast calculating speed. Therefore, the effective matrix method for profile control is also adopted to build the on-line profile control model. 3. 1
Effective matrix method for profile control T h e transverse distribution of strip exit thickness can be expressed by polynomials and usually biquadratic polynomials can meet the precision hl ( y ) = a O + a l p ~ ( y ) + a 2 ~ 2 ( y ) + a 3 ~ 3 ( y ) + a ~ p( y ~) (9) where, a. is concerned with the average thickness of the strip; and al , a 2 , a3 and a4 are concerned with the profile of the strip. Therefore, al , a 2 , a3 and a4 can be called profile coefficients. T h e effective functions of various regulativg means on profile are as follows:
2.2
aE=Rf-Yf;
:J
\Y/
au3
au3y1'y
34 '
VOl. 19
Journal of Iron and Steel Research, International
where, fcl ( y ) , fez ( y ) , f c 3 ( y ) and fc4 ( y ) are the effective functions of the tilting roll, the bending work roll, the bending intermediate roll and the axial shifting intermediate roll on profile, respectively. T h e profile variation brought by the variations AUI 9 Auz , Au3 and Au4 of the tilting roll quantity u1, the work roll bending force u 2 ,the intermediate roll bending force u3 and the intermediate roll axial shifting quantity u4 is as follows
is given, the profile control quantity can be easily calculated by the profile deviation. T h e effective matrix for the profile control can be calculated by the profile prediction model or the measured data.
Implementing of profile control matrix model Fig. 3 shows the structure of the profile control matrix model. When the model works, the detailed calculation flow is as follows: the standard profile curve R, and the A ~ I ( Y ) = ~ , I ( ~ > A u , + ~ ~ ~ ( Y > A u ~ + ~ ~ ~ ( Y ) A 1) u ~ Give + minimum profile control error ee ; fc4 (y)Au4 (11) 2) Collect the current profile data and obtain Y, Substitute Eqn. (10) into Eqn. (111, then there is by pattern recognition; Ah1 ( y ) = A a , p ~ ( y ) + A a ~ p ~ ( y ) + A a ~ p ~ ( y ) + 3 Calculate the profile deviation coefficient nA = Aa4 P4 (Y) (12) where R, -Y, ; 4 ) If the maximum of Aai is less than ec , return aa, aa, aa, aa, to 2 ) ; 5) According to the profile control matrix equation, the regulation quantity AW, of profile control (13) means is calculated to control profile; 6 ) Return to 2) and refieat these operations. 3.2
1
Let
i-
IYdk)
Fig. 3
I
I
I Pattern recomition L
Structure of profile control matrix model
4 Calculation Flow of Flatness and Profile Integration Control Scheme aa4 _ aa, _ aa4 _ aa4 _
au, auz au3 au4 then Eqn. (13) can be abbreviated as AA=MAU (15) where, AA is profile variation; AU is the variation of profile control means; and M is the effective matrix for profile control. For the problem of profile control, set the current profile as A = [ a l , a 2 , a 3 , all' and give it an increment AA, making the profile reach the control objective A, = a,, , aoz , aO3, ad]', i. e. , A 4-AA = A,, then there is AA=A, -A (16) According to Eqn. ( 15 ) , the required control quantity making the profile change AA is obtained AW=M-'AA=M-'(A,-A) (17) where M-I is profile control matrix. Eqn. (17) is the profile control equation. It is obvious that if the effective matrix for profile control
In order to implement the parallel control of various stands of tandem cold mills, the coordination control strategy of various stands need to be built. Here the timeslice-rotation method is adopted to coordinate the control actions of various stands. Beginning with the first stand, the first stand executes control actions and the other stands have not any control action at the moment. In succession, coming to the second stand, the second stand executes control actions and the other stands have not any control action. T h e rest may be deduced by analogy and the third stand, the fourth stand and the fifth stand execute control actions respectively. After the fifth stand executes control actions, the control power returns to the first stand and then various stands execute control actions one by one according to stand sequence. In this way, these operations are repeated and the coordination control of various stands can be implemented. T h e calculation flow chart of implementing the method is shown in Fig. 4.
Issue 3
. z Flatness and Profile Integration Control Model for Tandem Cold Mills
35
&, (i=1,2,3,4)andstandard flatness curveRf Give minimum control errors .cr and EI
Give maximum control number k-max and let k=l,n=l
N
t
1
n=n+l
Collect(predict)currentprofile
Collect@rerlict)currentflatness data of stand 5
Calculate profile deviation Aa, (i=1,2,3,4)by R,
Calculate flatness deviation
1"
IN
Aa, and PMC model to control
Fig. 4
I
Calculate control quantity AUrby Ae, and FMC model to control flatness of stand 5
Flow chart of flatness and profile control
5 Simulation Experiment of Synthetical Control Scheme In order to do the simulation experiment of flatness and profile control, the simulators of flatness and profile must be built, i. e. , the prediction models of flatness and profile are built as the virtual control objectives or detecting instruments of flatness and profile and their prediction values are Y f and Y,respectively. Here BP network is adopted to build the prediction models of flatness and profile respectively. T h e input parameters of the flatness prediction model are strip width, various order components of entry flatness, entry thickness, exit thickness, deformation resistance, elasticity modulus, forward tension, backward tension, rolling force, tilting roll quantity, work roll bending force, intermediate roll bending force and intermediate roll axial shifting quantity, and the output parameters are various order components of exit flatness. T h e
input parameters of the profile prediction model are strip width, various order coefficients of entry profile, entry thickness, exit thickness, deformation resistance, elasticity modulus, forward tension, backward tension, rolling force, tilting roll quantity, work roll bending force, intermediate roll bending force and intermediate roll axial shifting quantity, and the output parameters are various order coefficients of exit profile. In order to validate the built flatness and profile prediction models, the measured data of some 1550 mm five-stand tandem cold mills are adopted to validate the two models. T h e tandem cold mills have shape meter for measuring flatness and thickness meter for measuring profile, and then the measured flatness and profile data are discrete values. Twenty examples are done and here the validation results of two examples are given. Fig. 5 and Fig. 6 show the prediction results of flatness and profile respectively. It can be seen that the predicted result and the measured
VOl. 19
Journal of Iron and Steel Research, International
36
,.
7
. . . . Measuredvalue
-Predicted value
-200
-600
Fig. 5
0
In order to validate the built flatness and profile integration control scheme, the simulation experiment is done by the measured data of some 1550 mm fivestand tandem cold mills. T h e neural network prediction models of flatness and profile are trained with the measured flatness and profile data as samples and the simulators of flatness and profile are obtained as the control objectives of flatness and profile. Flatness and profile prediction networks adopt the same learning parameters with the learning efficiency of 0.01, the momentum factor of 0.8, the learning efficiency diminution factor of 0. 98 and the learning efficiency accretion factor of 1. 05. Entry profile is proportionally allocated by exit thicknesses of various stands as the control objectives of various stands and the standard flatness curve of the fifth stand is the null curve. In the simulation experiment, the strip parameters are: entry width 928 mm, entry thickness 2.53 mm and exit thickness 0. 512 mm. Fig. 7 shows the profile control effects of the first stand, the second stand, the third stand and the fourth stand respectively, where the actual values mean the profile control results of various stands by the built shape control model. Fig. 8 shows the flatness control effect of the fifth stand, where the flatness control result means the flatness control result by the built shape control model. It can
I
600
200
Widthlmm
Flatness prediction result
- Measured value -Predicted value *
35
-5
$-lo
-600
-200
Fig. 6
0
Widthmun
600
200
Profile prediction result
result of flatness and profile anastomose as well, which indicates that the built flatness and profile prediction models have high precision and they can supply the exact control objectives for research on flatness and profile control. 10
0
5 -lo B‘a -20
0 Actual section configuration
$ -30
2 8
e5
10 0
* -10 -20
-30 -400
-200
0
200
400
-400
-200
0
200
400
Widthmun (a) Stand 1;
(b) Stand 21 ( c ) Stand 3; Fig. 7 Profile control result
be seen from Fig. 7 that the actual profiles of the front four stands anastomose with the objective values well. And it can be seen from Fig. 8 that the flatness control process of the fifth stand is steady with short response time, fast regulating speed and wee steady error and the flatness control effect is
(d) Stand 4.
rather good.
6
Conclusions
1) T h e industrial validations indicate the built flatness and profile prediction models have high precise prediction results and they can supply the exact
Flatness a n d Profile Integration Control Model for T a n d e m Cold Mills
Issue 3
Fig. 8 Flatness control result of stand 5
control objectives for researching on flatness and profile control. 2 ) The simulation experiments indicate that the built flatness and profile integration control scheme for tandem cold mills has high flatness and profile control precision with steady and reliable control process. 3 ) The paper supplies a new method for researching on shape control of tandem cold mills. References: [l]
ZHAI Bo, SUN Rongsheng, SUN Jian-lin. Application of Sheet Shape Control Technology on Continuous Rolling Mills in Angang CJ]. Angang Technology, 2009, (1): 49 (in Chinese).
37
ZHANG Jing, QIN Jiu-lian. Calculation and Control of Plate Shape on Hot Strip [J]. Control Engineering of China, 2008, 15(S): 21 (in Chinese). XU Jian-yong. High Precision Thickness and Shape Control Technology for Thin Strip Rolling [J]. Iron and Steel, 2002, 37(1): 73 (in Chinese). SUN Tie-kai, ZHAO Yong-he. Research on Profile Controlling Characteristics of WRS Mill [J]. Journal of Yanshan University, 1991, 15(2): 139 (in Chinese). PENG Yan. Theoretical Studies and Engineering Application of Shape Preset Control for HC Cold Mill Based on Strip Element Method [D]. Qinhuangdao: Yanshan University, 2000 (in Chinese). H E Hai-tao. Research on Flatness On-Line Intelligent Control for the Wide Strip Steel Cold Mill [D]. Qinhuangdao: Yanshan University, 2008 (in Chinese). PENG Yan, ZHENG Zhen-zhong, WANG Jian-guo. Influence and Compensating Means of Profile in Strip Flatness Measuring and Controlling of Reversible Rolled Strip Profile [J]. Journal of Yanshan University, 1999, 23(1) : 76 (in Chinese). GUO Jian-bo, LIAN Jia-chuang, T U Yuehong. The Calculation of Work Roll's Temperature Field and Thermal Crown in Hot Strip Mills [J]. Journal of Yanshan University, 1998, 22 (3) : 255 (in Chinese). LIU Yu-li, H U Xi-zeng, ZHAO Yong-he. Theory and Experiment Study on the Shape Control Function of HC Mill [J]. Journal of Yanshan University, 1990, 14(2): 1 (in Chinese). ZHANG Xiu-ling, LIU Hong-min. Transfer Matrix Method of Flatness Control [J]. Chinese Journal of Mechanical Engineering, 2003, 39(11): 100 (in Chinese).