JP2000140920A - Method for controlling looperless rolling - Google Patents

Abstract

PROBLEM TO BE SOLVED: To stably pass a sheet through even when the model of a controlled system is varied and to realize highly accurate thickness/width control. SOLUTION: In a rolling process in which a tensiometer 20 is equipped and means for measuring or estimating each thickness between stands is provided, at the time of determining a compensator based on a μ-synthesis, by taking at least one or more of the amount of variation ΔAp, ΔBp1, ΔBp2, ΔCp1, ΔCp2, ΔDp11, ΔDp12, ΔDp21, ΔDp22 of matrices, Ap, Bp1, Bp2, Cp1, Cp2, Dp11, Dp12, Dp21, Dp22 into consideration, the correcting values ΔSrefi, ΔSrefi+1 of the screw-down location of a stand and correcting value ΔVrefi of the circumferential speed of the roll of the stand are calculated with a compensator and by correcting the screw-down location and circumferential speed of the roll by calculated values, even when the controlled system is varied, control performance is held at high grade.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a looperless rolling control method and, more particularly, to a thickness deviation control for minimizing a roll thickness deviation as much as possible.

[0002]

2. Description of the Related Art The history of the looperless rolling, particularly the hot rolling process, is still short. Notable technologies include, for example, “Iron and Steel”, Vol. 66, No. 4 (1980), p. 301 “looperless rolling system in hot rolling tandem finishing mill”; “Iron and Steel”, Vol. 69 , No.13 (1983) p.1126 “Tension control system IV for hot strip mill finishing mill”;
"Hitachi Review" Vol.65, No.2 (1983) p.141-p.146 "Looperless control system in hot strip mill";
“Iron and Steel”, Vol. 70, No. 5 (1984) pp. 428-429, “New Tension Control Methods I and II for Hot Rolling Finishing Mills”; “Kawasaki Steel Technical Report”, Vol. 16, No. 3 ( 1984) pp.173-180 “Tension control system for hot strip mill finishing mill”; “Nippon Kokan Giho” No.107 (1985) p.12-20 “Development of new tension control system for hot rolling finishing mill” ; “Iron and Steel”, Vol. 72, No. 2 (1986), pp. 57-60
“Development of a new tension control method for hot rolling finishing mills”; “Materials Research Group of the Institute of Electrical Engineers of Japan”, Vol.MID-93, No.1-5 (1993) p.13-
20 “Tension control of hot rolling finishing mill”.

At the time, there was no technique for directly measuring the tension between stands at the time, so that the tension between stands was changed by the torque G of the mill motor, the torque arm coefficient a,
The following formula G = a * F + b * T _b +, which is called a torque arm formula, which is established with respect to the rolling reaction force F, the forward tension (total tension) _Tf and its coefficient c, and the back tension (total tension) _Tb and its coefficient b
Emphasis has been placed on the development of a technique for estimating the forward tension _Tf when the backward tension _Tb is known based on c * _Tf .

[0004] Thus, the rear tension T _b is 0 [ton] a is F1 tension control between the (multi-stage stand of the first stage) finishing mill and F2 finishing mill, and F2 finishing mill and the F3 finish rolling mill It was limited to the tension control between stands in the preceding stage between the two. Further, it is extremely difficult in actual operation to accurately estimate the torque arm coefficient a, and there is naturally a limit in control performance and accuracy.

However, in recent years, the total tension between the stands is measured by measuring the weight of the steel sheet with a looper, and the unit tension between the stands is measured from the thickness and the width of the rolled steel sheet. Technology has been put to practical use. This not only eliminates the necessity of estimating the tension from the conventional torque arm system, but also increases the accuracy of the measured tension.

In recent years, with regard to motors for driving rolling mills and the like, large-capacity AC motors have come into wide use, and the performance (especially responsiveness) of control operating terminals has been improved. It was possible to correct the non-uniformity of the mass flow. Therefore, by utilizing the design of the control system, it has come to an era where rolling without a looper is also possible.

On the other hand, the present inventors have recognized that the following three are major disturbances in the hot rolling process. (1) Change in plasticity coefficient (ΔQ [kgW / mm]): A slab generated mainly because the skid that supports the slab in the heating furnace generates uneven temperature having a period equal to the distance between the skids in the slab longitudinal direction. This is a bias of the deformation resistance with respect to the longitudinal direction having a period equal to the distance between the skids. this is,
Induces large deviation in the thickness of the exit side of the rolling mill. This is commonly referred to as a skid mark. The skid mark is 0.
It is a disturbance of 2 [Hz] to 1.0 [Hz].

(2) Roll eccentricity (ΔS _d [mm]): Rolling load fluctuation caused by roll eccentricity caused by a keyway of a bearing portion of a backup roll of a rolling mill is a rolling position deviation. Thickness deviation that occurs to cause
This is called roll eccentricity. Roll eccentricity is 4.0 [Hz]
It is a disturbance of about 10.0 [Hz]. (3) Rolling mill entry side thickness deviation (ΔH [mm]): In a rolling mill equipped in tandem, a thickness deviation caused by a skid mark (ΔQ) or a roll eccentricity (ΔS _d ) in a preceding rolling mill is: In the rolling by the rolling mill at the next stage, the entry side sheet thickness deviation becomes.

[0009] Under such recognition, the inventors of the present invention disclosed in Japanese Patent Application Laid-Open No. Hei 7-164028, in consideration of the fact that the behavior of the sheet thickness and the sheet width may interfere with each other even in the looperless rolling, and the sheet width deviation may be reduced. A method is disclosed in which a control system is set and controlled by applying the H と し て theory for the purpose of simultaneously and sufficiently removing the influence of the three main disturbances on the plate thickness even when the thickness fluctuates. The compensator calculated according to the invention disclosed in Japanese Patent Application Laid-Open No. 7-164028 corresponds to the deviation control device 21 in FIG. 1 for explaining the framework of the present invention.
Further, a transfer function K _a (s) of _a compensator disclosed in Japanese Patent Application Laid-Open No. 7-164028 and an enlargement system (Genera
lized Plant) transfer function G _a (s) is shown in FIG.
It becomes what is shown in.

Here, regarding the transfer function G _zw (s) from the disturbance input w _a to the control amount z _a , applying the H∞ theory,

[0011]

(Equation 1)

A transfer function K (s) is obtained and set. When the H∞ theory is used, the transfer function K _a (s) of the compensator satisfying the condition is given by a matrix of state variable expressions. That is, the system matrix (A _cp , B _cp , C _cp , D _cp ) of the compensator is given as the solution.
This state of the compensator and x _c, as input observed variables y _a, means a compensator for calculating a control input u _a.
In particular,

[0013]

(Equation 2)

Since these are dynamic compensators represented by the following formula, the Laplace operator s

[0015]

(Equation 3)

Can be expressed as The H∞ theory and μ synthesis described later are detailed in Shokodo “H∞ control”; Asakura Shoten, the system control information library “control system design”, etc., and these books are referred for detailed description. I want to.

[0017]

However, the method disclosed in Japanese Patent Application Laid-Open No. Hei 7-164028 has the following problems.

(Problem 1) Non-Consideration of Variation of Controlled Object The temperature of a rolled steel sheet varies from one steel sheet to another due to skid marks and the like, as a matter of course. Therefore, it is theoretically necessary to grasp the temperature of each steel plate and use a compensator corresponding to the temperature. This is because even a compensator that provides an optimum rolling means for a steel sheet at a certain temperature may perform inappropriate rolling for a steel sheet having a different temperature. However, it is not realistic to set the different compensators by grasping the temperature for each steel plate. Therefore, it is necessary to design a control system that appropriately rolls the control object that fluctuates in this way with one compensator, and set the control system in the control computer. However, JP-A-7-164
In the method disclosed in Japanese Patent No. 028, H 公報 theory is used only for the matrix of the nominal plant in designing the control system, and the above-described fluctuation of the control target is not considered. For this reason, when the control object has some fluctuation, predetermined characteristics cannot be achieved.

Similarly, the size of the steel plate to be rolled (the target thickness,
Each matrix (row) can be selected according to the target plate width)
Column) varies greatly, so each time
Cousin A _p, B_p1, B_p2, C_p2, D_p21And recreate this
Design an optimal compensator corresponding to the
Need to be prepared and controlled. However, rolled steel sheet
(Target thickness, target width), temperature, threading speed, etc.
Design compensators for all cases accordingly and
Setting a computer for a rolling mill to execute control is
Always cumbersome and unrealistic. So in this case
Is also desired to be realized with a single compensator.
In the method disclosed in JP-A-164028,
I couldn't do it.

(Problem 2) Insufficient accuracy of the transfer model In addition, in the method disclosed in the above-mentioned Japanese Patent Application Laid-Open No. 7-164028, the sheet thickness deviation, the sheet width deviation and the deformation resistance deviation measured at the exit side of the former rolling stand. Is transferred to the next rolling stand and used as the thickness deviation and the sheet width deviation on the entrance side of the next rolling stand. However, since this is a transfer model using the first-order pade approximation, The accuracy of the transfer model is poor, and there is a limit to achieving high-precision control.

In designing the control system of the rolling control, without using the transfer model, the deviation of the thickness of the entrance side, the deviation of the entrance side width, the deviation of the deformation resistance (or the deviation of the temperature of the rolled steel sheet) of each stand.
Regardless of whether the overall system model is configured by treating the system as a deterministic disturbance applied to the stand, or the overall system model is configured using the transfer model, there is no significant difference in the control system constructed as a result. I know from experience.

The order of the controlled object (state x of the controlled object)
_p ), the order of the compensator (state x of the compensator)
It is well known that the smaller the number of element variables of _c ), the faster the control system design and adjustment can be made. However, when the transfer model is used as in the invention described in Japanese Patent Application Laid-Open No. 7-164028, a variable relating to the transfer is: ΔHt ₆ : Transfer plate thickness deviation between F5-F6 stands ΔHt ₇ : Transfer between F6-F7 stands Plate thickness deviation ΔBt ₆ : Transfer plate width deviation between F5-F6 stands ΔBt ₇ : Transfer plate width deviation between F6-F7 stands ΔKt ₆ : Transfer plate temperature deviation between F5-F6 stands ΔKt ₇ : Transfer plate temperature between F6-F7 stands Since the deviation has to be added to the state quantity, the order of the controlled object increases, and as a result, the order of the compensator also increases. Therefore, configuring the entire system without using the transfer model has an advantage that the order can be reduced.

[0023] (Problem 3) is a way of taking the observed quantity y _p takes how observation quantity y _p elements variables, JP 7-164028
In the case where the transfer model described in (Problem 2) is used as in the invention described in Japanese Patent Application Laid-Open Publication No. H10-209, the values obtained by transferring the output plate thickness deviation and the output plate width deviation of the preceding stage by the model are used as the input plate pressure deviation of the next stage. Therefore, it is appropriate to take these deviations on the observation side as observation quantities.However, when the transfer model is not used, it is necessary to take the exit side sheet thickness deviation and exit side sheet width deviation into the observation quantities. There is.

(Problem 4) How to take an element variable of the control amount z _{p As} in the invention described in Japanese Patent Application Laid-Open No. 7-164028, the control amount z _a does not include the stand-to-stand tension deviation Δσ _i , In the case of including the element variables related to the sheet thickness and the sheet width, the transfer function K (s) of the compensator that gives a satisfactory result as shown in FIG. 11 is obtained for the sheet thickness and the sheet width. As shown in FIG. 12, there is a case where a behavior that should be determined to be impossible to roll is exhibited. Therefore, in order to obtain a rollable result, it is necessary to always include the element variables related to the tension.

Therefore, the present invention relates to a method disclosed in
SUMMARY OF THE INVENTION It is an object of the present invention to solve the above-described problems of the invention described in Japanese Patent Application Publication No. JP-A-2006-133, and to provide a more accurate looperless rolling control method.

[0026]

SUMMARY OF THE INVENTION The looperless pressure of the present invention
The rolling control method has n (i = 1, ... n, n ≧ 2) rolling stands.
And equipped with a tension meter between each stand,
One, the exit side of each stand, directly under the roll bite of each stand
Or measure the thickness and width of each stand
In a rolling process having a means for estimating,
I-stand on the upstream side and i + 1 stand on the immediate downstream
Of a tandem rolling mill rolling at multiple stands including
Tand exit side thickness deviation Δh_i, I + 1 stand exit side plate thickness deviation
Difference Δh_{i + 1}, I stand exit side plate width deviation Δb_i, I + 1
Tund exit side plate width deviation Δb_{i + 1}, I stand rolling reaction force deviation
Δp_i, I + 1 stand rolling reaction force deviation Δp_{i + 1}And i
/ I + 1 stand-to-stand tension deviation Δσ_iAt least one of
Observation amount y above_pAnd i / i + 1
Tend tension deviation Δσ_iIn addition, i-stand outlet side plate thickness deviation
Difference Δh_i, I + 1 stand exit side thickness deviation Δh_{i + 1}, Is
Tund exit side plate width deviation Δb_i, I + 1 stand exit side plate width deviation
Difference Δb_{i + 1}, I stand pressure reduction position correction amount ΔSref_i, I +
One stand pressure reduction position correction amount ΔSref_{i + 1}And i stand
Roll peripheral speed correction amount ΔVref _iMust have at least one
Control amount z as required_pSelected as element variables of
圧 Sref_i, I + 1 stand down position
Correction amount ΔSref_{i + 1}And i stand roll peripheral speed correction amount
ΔVref_iIs the control input u_pAnd i stand to i + 1
Roll eccentricity ΔSd_i, ΔSd_{i + 1}, I stand to i + 1
Stand entry side thickness deviation ΔH_i, ΔH_{i + 1}, I stand ~
i + 1 Stand entry side width deviation ΔB _i, ΔB_{i + 1}And i
Stand to i + 1 stand
Temperature deviation ΔTd_i, ΔTd_{i + 1}Disturbance of at least one of
Input w_pSelected as element variables of the rolling process
State quantity x_pThe element variables of i stand to i + 1
Stand-down position deviation ΔS_i, ΔS_{i + 1}, I / i + 1 star
Tension deviation Δσ_i, I stand to i + 1 stand
Standing speed deviation ΔVn_i, ΔVn_{i + 1}, And i stand to i
+1 stand neutral point speed reference deviation ΔVref_i,
ΔVref_{i + 1}And neutral point speed deviation ΔVn_i, ΔVn_{i + 1} The difference between
Integral ΔVc_i, ΔVc_{i + 1}Select at least one or more of
The following equation of state dx describing the dynamics of the rolling process_p/ dt = A_px_p+ B_p1w_p + B_p2u_p z_p = C_p1x_p+ D_p11w_p+ D_p12u_p y_p = C_p2x_p+ D_p21w_p+ D_p22u_p And its disturbance input w_pThe dynamic characteristics of the element variables of
State variable x of element variable_wControl input of disturbance and disturbance input element variables
Force u_wThe next state equation dx described using_w/ dt = A_wx_w+ B_wu_w w_p = C_wx_w+ D_wu_w From the state quantity x of the rolling process_pAnd disturbance input w_pEssence of
State x of elementary variable_wIs the state quantity x_aBy
Equation of state of generalized plant synthesized by dx_a/ dt = A_ax_a+ B_a1w_a + B_a2u_a z_a = C_a1x_a+ D_a11w_a+ D_a12u_a y_a = C_a2x_a+ D_a21w_a+ D_a22u_a Of the disturbance input w_aControl amount z_aTransfer characteristic G up to_zwa
Observable y that minimizes the maximum singular value of_aControl input u_a
Transfer function K leading to_a(s)
Matrix A describing the control target of the_p, B_p1, B_p2,
C_p1, C_p2, D_p11, D_P12 , D_P21, D_P22Fluctuation amount
ΔA_p, ΔB_P1, ΔB_P2, ΔC_P1, ΔC_P2, ΔD_P11,
ΔD_P12, ΔD_P21, ΔD_P22At least one of
The next state equation dx_x/ dt = A_xx_x+ B_x1w_x+ B_x2u_x z_x = C_x1x_x+ D_x11w_x+ D_x12u_x y_x = C_x2x_x+ D_x21w_x+ D_x22u_x Of the disturbance input w_xControl amount z_xTransfer characteristic G up to_zwx
Observable y that minimizes the maximum singular value of_xControl input u_x
Transfer function K leading to_x(s) is calculated by H∞ theory,
Transfer function K_xbased on (s)_xControl input from
Force u_xIs set in the deviation control means, and the deviation control means
I, stand side exit thickness deviation Δh_i, I + 1 stand out
Side plate thickness deviation Δh_{i + 1}, I stand exit side plate width deviation Δb_i,
i + 1 stand exit side plate width deviation Δb_{i + 1}, I stand rolling
Reaction force deviation Δp_i, I + 1 stand rolling reaction force deviation Δp_{i + 1} 
And i / i + 1 stand-to-stand tension deviation Δσ_iAt least
And one or more of the above transfer functions K_xCompensator represented by (s)
To the i-stand rolling position correction amount ΔSref_i, I + 1
Stand pressure reduction position correction amount ΔSref_{i + 1}And i standro
Wheel peripheral speed correction amount ΔVref_iCalculate at least one of
To correct the partial pressure reduction position and the roll peripheral speed.
It is characterized by the following.

In another embodiment of the present invention, n (i = 1,.
n, n ≧ 3) rolling stands and between each stand
Equipped with a tension meter, and the output side of each stand,
Just under the roll bite of each stand or between each stand
Pressure with means for measuring or estimating thickness and width
In the rolling process, the rolled material is placed on an i-stand, i + 1
And tandem rolling in this order at the i + 2 stand
Outer thickness deviation Δ of stand i to i + 2 stand of rolling mill
h_i, Δh_{i + 1}, Δh_{i + 2}, IStand-i + 2 Stan
Door exit side width deviation Δb_i, Δb_{i + 1}, Δb_{i + 2}, Istan
De-i + 2 stand rolling reaction force deviation Δp_i, Δp_{i + 1}, Δ
p_{i + 2}And between i / i + 1 stand and i + 1 / i + 2 switch
Tend tension deviation Δσ_i, Δσ _{i + 1}At least one of
Observation amount y above_pAnd i / i + 1
Between stand and i + 1 / i + 2 tension deviation Δσ between stands_i,
Δσ_{i + 1}In addition, i-stand to i + 2 stand exit side plate thickness
Deviation Δh_i, Δh_{i + 1}, Δh_{i + 2}, I stand-i + 2
Stand exit side width deviation Δb_i, Δb_{i + 1}, Δb_{i + 2}, I
Stand to i + 2 stand down position correction amount ΔSref_i, Δ
Sref_{i + 1}, ΔSref_{i + 2}And i stand to i + 1 stun
Droll peripheral speed correction amount ΔVref_i, ΔVref_{i + 1}At least
Control quantity z if necessary._pAs an element variable of
Select the i-stand to i + 2 stand depression position correction amount Δ
Sref_i, ΔSref_{i + 1}, ΔSref_{i + Two}And i stand to i
+1 Stand roll peripheral speed correction amount ΔVref_i, ΔVref_{i + 1}
Is the control input u_pAnd i stand to i + 2 stand low
Eccentricity ΔSd_i, ΔSd_{i + 1}, ΔSd_{i + 2}, IStand to i +
2 stand entry side thickness deviation ΔH_i, ΔH_{i + 1} , ΔH _{i + 2},
i-stand to i + 2 stand entrance side plate width deviation ΔB_i, ΔB
_{i + 1} , ΔB_{i + 2}And i stand to i + 2 stand plate temperature
Degree deviation ΔTd_i, ΔTd_{i + 1} , ΔTd_{i + 2}At least one of
Disturbance input w above_pAnd rolling as
Process state quantity x_pAs an element variable of
i + 2 stand down position deviation ΔS_i, ΔS_{i + 1} , ΔS
_{i + 2}, I / i + 1 to i + 1 / i + 2 tension deviation between stands
Δσ_i, Δσ_{i + 1}, I stand-i + 2 stand neutral point
Speed deviation ΔVn_i, ΔVn_{i + 1}, ΔVn_{i + 2}And i stand
To i + 2 stand neutral point speed reference deviation ΔVref
_i, ΔVref_{i + 1}, ΔVref_{i + 2}And neutral point speed deviation ΔVn_i,
ΔVn_{i + 1} , ΔVn_{i + 2}Integral ΔVc_i, ΔVc_{i + 1} , Δ
Vc_{i + 2}At least one or more of the rolling process
The next state equation dx describing the dynamic characteristics_p/ dt = A_px_p+ B_p1w_p + B_p2u_p z_p = C_p1x_p+ D_p11w_p+ D_p12u_p y_p = C_p2x_p+ D_p21w_p+ D_p22u_p And its disturbance input w_pThe dynamic characteristics of the element variables of
State variable x of element variable_wControl input of disturbance and disturbance input element variables
Force u_wThe next state equation dx described using_w/ dt = A_wx_w+ B_wu_w w_p = C_wx_w+ D_wu_w From the state quantity x of the rolling process_pAnd disturbance input w_pEssence of
State x of elementary variable_wIs the state quantity x_aBy
Equation of state of generalized plant synthesized by dx_a/ dt = A_ax_a+ B_a1w_a + B_a2u_a z_a = C_a1x_a+ D_a11w_a+ D_a12u_a y_a = C_a2x_a+ D_a21w_a+ D_a22u_a Of the disturbance input w_aControl amount z_aTransfer characteristic G up to_zwa
Observable y that minimizes the maximum singular value of_aControl input u_a
Transfer function K leading to_a(s)
Matrix A describing the control target of the_p, B_p1, B_p2,
C_p1, C_p2, D_p11, D_P12, D_P21, D_P22Fluctuation amount
ΔA_p, ΔB_P1, ΔB_P2, ΔC_P1, ΔC_P2, ΔD_P11,
ΔD_P12, ΔD_P21, ΔD_P22At least one of
The next state equation dx_x/ dt = A_xx_x+ B_x1w_x + B_x2u_x z_x = C_x1x_x+ D_x11w_x+ D_x12u_x y_x = C_x2x_x+ D_x21w_x+ D_x22u_x Of the disturbance input w_xControl amount z_xTransfer characteristic G up to_zwx
Observable y that minimizes the maximum singular value of_xControl input u_x
Transfer function K leading to_x(s) is calculated by H∞ theory,
Transfer function K_xbased on (s)_xControl input from
Force u_xIs set in the deviation control means, and the deviation control means
, I-stand to i + 2 stand exit side thickness deviation Δh_i,
Δh_{i + 1}, Δh_{i + 2}, I stand to i + 2 stand out side
Sheet width deviation Δb_i, Δb_{i + 1} , Δb_{i + 2}, I stand ~ i
+2 stand rolling reaction force deviation Δp_i, Δp_{i + 1}, Δp_{i + 2} 
And between i / i + 1 stand to i + 1 / i + 2 stand
Tension deviation Δσ_i, Δσ_{i + 1}Above at least one of
Notation transfer function K_xgiven to the compensator represented by (s),
Stand to i + 2 stand down position correction amount ΔSref_i, ΔSr
ef_{i + 1}, ΔSref_{i + 2}And i stand to i + 1 stand
Roll peripheral speed correction amount ΔVref_i, ΔVref_{i + 1}At least
Calculate one or more pieces and calculate their partial pressure reduction position and roll peripheral speed
Is modified.

Further, in another aspect of the present invention,
The next state equation dx constructed in 1 or 2_x/ dt = A_xx_x+ B_x1w_x + B_x2u_x z_x = C_x1x_x+ D_x11w_x+ D_x12u_x y_x = C_x2x_x+ D_x21w_x+ D_x22u_x Of the disturbance input w_xControl amount z_xTransfer characteristic G up to_zwof
Observable y that minimizes the maximum singular value_xControl input u_xTo
Transfer function K_x(s) is calculated by H∞ theory.
Thus, the generalized plant described by the above equation of state is represented by G
_x(s), defines the variation of the considered matrix as Δ,
(1) When i = 1, G₁(s) = G_x(s), D₁= I (unit line
Column) and (2) disturbance input w_xControl amount z_xBiography leading to
Arrival characteristics G_zwObservable y that minimizes the maximum singular value of_xFrom
Input u_xTransfer function K leading to_xiFind (s) and (3) change
For the quantity Δ, D_i(jω) G_i(jω) D_i ^-1matrix D that minimizes the maximum singular value of (jω)_i(jω), and
(4) If D_i(jω) G_i(jω) D_i ^-1the maximum of (jω)
If the singular value is less than 1, K _xi(s)
Finish the control system design as a number, (5)_i(jω)
G_i(jω) D_i ^-1If the maximum singular value of (jω) is 1 or more,
In the expansion system, a disturbance input w_xD before input
_i ^-1(s) in front of the control variable z_xD after the output of
_i(s) is added afterwards, and the newly expanded system dx_xi/ dt = A_xix_xi + B_xi1w_xi+ B_xi2u_xi z_xi = C_xi1x_xi+ D_xi11w_xi+ D_xi12u_xi y_xi = C_xi2x_xi+ D_xi21w_xi+ D_xi22u_xi And construct a disturbance input w_xiControl amount z_xiTransmission characteristics leading to
Sex G_zwiObservable y that minimizes the maximum singular value of_xiControl from
Input u_xiTransfer function K leading to_xi(s) is calculated by H∞ theory
In the method of returning to the processing of (3) above,
Transfer function K_xithe order of (s) to a lower order of higher availability
D to hold down_i(s) with respect to the Laplace operator s
Select from matrices that have only real numbers
It is characterized in that it is applied.

[0029]

DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the present invention will be described below with reference to the drawings. In the following description, the superscript T
Represents the transposed matrix, and | F | ∞ represents the H∞ norm of the matrix F. The H∞ norm is the maximum singular value of the matrix F. The “deviation” used in the present embodiment means a deviation from a reference value. For example, the deviation Delta] p _i from the reference value of the rolling reaction force p _i, the deviation from the rolling reaction force reference value p _0i at the operating reference point, ie Δp _i = p _i - p
_It means _0i .

Hereinafter, the problems dealt with in this embodiment will be quantitatively determined.
State it. For example, the state quantity of the rolling process is x_p, Observation
The amount is y_pAnd the control amount is z_pAnd the control input_p, The disturbance input
w_p, The matrix describing the control target is A_p, B_p1, B
_p2, C_p1, C_p2, D_p11, D _p12, D_p21, D_p22age
(The subscript p means a plant to be controlled.
Suffix w to indicate a disturbance, meaning an extended system including the disturbance
Subscript a and augmentation system for μ synthesis
x), and the dynamic characteristics of the rolling process are dx_p/ dt = A_px_p+ B_p1w_p + B_p2u_p z_p = C_p1x_p+ D_p11w_p+ D_p12u_p y_p = C_p2x_p+ D_p21w_p+ D_p22u_p It is necessary to perform linearization in order to express with a state equation like
There is.

For example, the variables p _i representing the rolling reaction force of the i-stand are the entry thickness H _i , the exit thickness h _i , the entry width B _i , the front unit tension σ _i , and the rear unit tension σ _{i of the} i-stand. _-1 ,
When a physical quantity calculated by the rolled steel sheet temperature Td _i, deviation Delta] p _i from the reference value of the rolling reaction force p _i is thickness at entrance side deviation [Delta] H _i, delivery side thickness deviation Delta] h _i, entry side width deviation ΔB _i , front unit tension deviation Δσ _i , rear unit tension deviation Δ
Using σ _i-1 and the temperature deviation ΔTd _i of the steel sheet to be rolled, Δp _i = (∂p _i / ∂H _i ) ΔH _i + (∂p _i / ∂
h _i ) Δh _i + (∂p _i / ∂B _i ) ΔB _i + (∂p _i / ∂
_{σ i) Δσ i + (∂p} i / ∂σ i-1) Δσ i-1 + (∂p i /
Performing linearization using can be described as ∂Td _i) ΔTd _i.

Here, for example, (∂p_i/ ∂H_i) Is i
Stand side thickness H_iWhen the rolling reaction force p
_iIs called the coefficient of influence that determines how much
It is. FIG. 6 illustrates the concept of the influence coefficient.
You. These influence coefficients are calculated based on the rolling model and
Matrix A of the state equation of interest_p, B_p1, B_p2, C
_p1, C_p2, D_p11, D_P12, D_P21, D_P22Ask for
It is. However, this influence coefficient depends on the temperature of the rolled steel sheet Td._i
It will fluctuate greatly.

Hereinafter, this problem will be described in detail with reference to elements of a matrix of a state equation. In the following [Equation 4] to [Equation 8], the size (target plate thickness, target plate width), specific temperature, and specific temperature of a specific rolled steel plate used for designing the control target in the case of three stands Matrix A _p , B _p1 , B _p2 , C _p2 , D _p21 (hereinafter referred to as “matrix of the nominal plant”) regarding the threading speed of
Is expressed using the influence coefficient. In these equations, the value of the element in which the number 0 is described is 0, and the value of the element in which the influence coefficient is described is the value of the influence coefficient.

[0034]

(Equation 4)

[0035]

(Equation 5)

[0036]

(Equation 6)

[0037]

(Equation 7)

[0038]

(Equation 8)

In the following [Equation 9] to [Equation 13], 3
In the case of a stand, an example of a matrix value at a certain operating point and an example of its maximum variation are shown.

[0040]

(Equation 9)

[0041]

(Equation 10)

[0042]

[Equation 11]

[0043]

(Equation 12)

[0044]

(Equation 13)

In calculating the maximum variation examples shown in [Equation 9] to [Equation 13], the influence coefficient (∂p _i / ∂H _i ) and the (∂
In addition to calculating a matrix when the value of p _i / ∂h _i is multiplied by 10, the influence coefficients (∂p _i / ∂H _i ) and (∂p _i / ∂h _i ) are further calculated as shown in the following [Equation 15]. ) To 1/1
The matrix in the case of 0 was calculated and obtained.

[0046]

[Equation 14]

[0047]

(Equation 15)

[0048] As will now be seen, for example, the matrix A (4, 2) component of _p is that the a 109.39 if nominal, influence coefficient fluctuates rolled steel sheet temperature Td _i (∂p _i / When .differential.H _i) and (∂p _i / ∂h _i) is 10-fold, (4,2) component of the matrix a _p is 11.6725
become. On the other hand, the influence coefficients (∂p _i / ∂H _i ) and (∂
When p _i / ∂h _i) is 1/10, (4,2) component of the matrix A _p will become one 671.773.

Hereinafter, the rolling control method according to the present embodiment, in which one compensator can cope with such a change in the controlled object, will be described in detail. Since the procedure for the two stands and the procedure for the three stands are almost the same, the procedure for the two stands will be discussed first for the sake of simplicity, and then the procedure for the two stands will be described. Here are some points to keep in mind when applying in cases.

(1) In the case of two stands: The F6 and F7 stands, which are the latter two stands of the seven rolling mills, will be described in detail. At this time, state equations representing the dynamic characteristic, the state of the rolling process x _p, disturbance input quantities w _p, the observed quantity y _p, the control input u _p to x _p = [ΔS ₆ respectively, [Delta] S _7, .DELTA..sigma _6, ΔVn ₆ , ΔVn ₇ , ΔVc ₆ , ΔVc ₇ ]
^T w _p = [ΔSd ₆ , ΔSd ₇ , ΔH ₆ , ΔH ₇ , ΔTd ₆ , ΔTd ₇ , ΔB ₆ ,
^{_{ΔB 7] T y p = [}} Δh 6, Δh 7, Δb 6, Δb 7, Δσ 6, Δp 6, Δp 7]
^{_{T u p = [ΔSref 6,}} ΔSref 7, ΔVref 6] when defined as ^T (each element will be described later), a state equation describing the rolling _{phenomenon, dx p / dt = A p} x p + B p1 w _p + B _p2 referred to as _{u p y p = C p2 x} p + D p21 w p. At this time, each matrix A _p , B _p1 , B _p2 ,
C _p2 and D _p21 are as described in [ _Equation 16] or [Equation 17].

[0051]

(Equation 16)

[0052]

[Equation 17]

Each of these matrices A _p , B _p1 , B _p2 , C
_p2 each component, D _p21, as in the previous example, vary the temperature of the rolled steel sheet is large, the influence coefficient (∂p _i / ∂
H _i ) and (∂p _i / ∂h _i ) are 10 times or 1 /
When it becomes 10, the matrix described in the above [Equation 17] fluctuates greatly as described in the following [Equation 18]. The numbers described in [Equation 18] represent the variation of each component of the matrix in%. For example, the matrix A _p (3,
The (1) element fluctuates by 514%, while the (1,1) element fluctuates by 0% (no fluctuation).

[0054]

(Equation 18)

The variable element variables (candidates) for describing the case where the control is performed using the two stands F6 and F7 are as follows.

Element variables (candidates) of state quantity x _p ΔS ₆ : F6 stand rolling position deviation ΔS ₇ : F7 stand rolling position deviation Δσ ₆ : F6 / F7 stand unit tension deviation ΔVn ₆ : F6 stand neutral point speed deviation ΔVn _7: F7 stand neutral point speed deviation [Delta] Vc _6: F6 integral d of the difference between the neutral point speed reference deviation stand the neutral point speed deviation _{(ΔVc i) / dt = ΔVref} i - ΔVn i ΔVc 7: F7 neutral point of the stand integrating d of the difference between the speed reference deviation and the neutral point speed deviation _{(ΔVc i + 1) / dt} = ΔVref i + 1 - ΔVn i + 1

Element variable (candidate) of control amount z _p Δh ₆ : F6 stand exit side thickness deviation Δh ₇ : F7 stand exit side thickness deviation Δb ₆ : F6 stand exit side plate width deviation Δb ₇ : F7 stand exit side plate width deviation Δσ ₆ : Unit tension deviation between F6 / F7 stand ΔSref ₆ : F6 stand rolling reference change amount ΔSref ₇ : F7 stand rolling reference change amount ΔVref ₆ : F6 stand roll peripheral speed reference changing amount

[0058] observed quantity y _p of the element variable (candidate) Δh _6: F6 stand delivery side thickness deviation Δh _7: F7 stand delivery side thickness deviation Δb _6: F6 stand delivery side width deviation Δb _7: F7 stand delivery side width deviation Δσ ₆ : F6 / F7 stand unit tension deviation Δp ₆ : F6 stand rolling reaction force deviation Δp ₇ : F7 stand rolling reaction force deviation

[0059] The control input quantity u _p of the element variable (candidate) ΔSref _6: F6 stand pressure reference change amount ΔSref _7: F7 stand pressure reference change amount ΔVref _6: F6 stand roll peripheral speed reference change amount

Element variable (candidate) of disturbance input amount w _p ΔSd ₆ : F6 stand roll eccentric disturbance ΔSd ₇ : F7 stand roll eccentric disturbance ΔH ₆ : F6 stand entrance side thickness deviation ΔH ₇ : F7 stand entrance side thickness deviation ΔTd ₆ : F6 stand rolled steel plate temperature deviation (corresponding to skid mark) ΔTd ₇ : F7 stand rolled steel plate temperature deviation (corresponding to skid mark) ΔB ₆ : F6 stand entrance width deviation ΔB ₇ : F7 stand entrance width deviation

The characteristics of the disturbance input amount w _p include the following disturbance-free disturbance state amount x _w , assumed disturbance control input amount u _w ,
Using the deemed disturbance observable y _w (by convention, the word “observation” is used, but not actually observed), and the system matrices A _w , B _w , C _w , and D _w , dx _w / dt = A _w x _{It is given by w} + B _{w w} w _p = C _w x _w + D _w u _w = y _w .

[0062] considered disturbance state amount x _w of the element variable (candidate) ΔSd _s6: ΔSd ₆ state variable of ΔSd _s7: ΔSd ₇ of the state variable ΔH _s6: ΔH ₆ of the state variable ΔH _s7: ΔH ₇ of the state variable ΔTd _s6: state variable ΔTd of ΔTd _{6 s7:} ΔTd ₇ of the state variable ΔB _s6: state variable ΔB of ΔB _{6 s7:} ΔB ₇ of the state variable

Element variables (candidates) of the assumed disturbance input amount w _p ΔSd ₆ : F6 stand roll eccentric disturbance ΔSd ₇ : F7 stand roll eccentric disturbance ΔH ₆ : F6 stand entry side thickness deviation ΔH ₇ : F7 stand entry side thickness Deviation ΔTd ₆ : F6 stand rolled steel plate temperature deviation (corresponding to skid mark) ΔTd ₇ : F7 stand rolled steel plate temperature deviation (corresponding to skid mark) ΔB ₆ : F6 stand entrance width deviation ΔB ₇ : F7 stand entrance width deviation

Element variable (candidate) of assumed disturbance control input amount u _w ΔSd _u6 : input variable of ΔSd ₆ ΔSd _u7 : input variable of ΔSd ₇ ΔH _u6 : input variable of ΔH ₆ ΔH _u7 : input variable of ΔH ₇ ΔTd _u6 : Input variable of ΔTd ₆ ΔTd _u7 : Input variable of ΔTd ₇ ΔB _u6 : Input variable of ΔB ₆ ΔB _u7 : Input variable of ΔB ₇

Here, the system matrices A _w , B _w ,
C _w and D _w are constructed by approximating the dynamic characteristics of the disturbance in, for example, a primary system as follows. For example, when the roll eccentric disturbance of the F6 stand is remarkable in a frequency band of 4 [rad / s] or more as shown in FIG. 7, the frequency characteristic is represented by G _sd6 = (s + 1) / (s + 4) = [ -3 / (s + 4)] + 1 and a constant gain of 0 [d / d] above 4 [rad / s]
B] represented by a transfer function having, which is further, as in _{d (ΔSd s6) / dt =} -4ΔSd s6 + ΔSd u6 ΔSd s6 = -3ΔSd s6 + ΔSd u6, expressed in the form of a state equation.

As described above, the remaining variables ΔSd _s7 , Δ
When the frequency characteristics including H _s6 , ΔH _s7 , ΔT _s6 , ΔT _s7 , ΔB _s6 , and ΔB _s7 are given, for example, as shown in [ _Equation 19],

[0067]

[Equation 19]

These variables ΔSd _s6 , ΔSd _s7 , ΔH _s6 , Δ
H _s7 , ΔTd _s6 , ΔTd _s7 , ΔB _s6 , and ΔB _s7 are expressed in a similar state variable expression. A state equation describing the dynamic characteristics of the disturbance can be constructed by forming a matrix of a system in which all of these are summed up, for example, as in the following [Equation 20].

[0069]

(Equation 20)

Further, a state equation of an expanded system (generalized plant) combining the disturbance characteristic state equation shown in [Equation 20] and the state equation of the rolling process described above is created. 〕become that way.

[0071]

(Equation 21)

[0072] However, in the [equation 21], and the state variables of the magnification system of x _a and z _a a magnification system evaluation variable (control variable), a w _a a disturbance input, and the observed variable y _a,
Let u _{a be a} control input. At this time, the system matrix is as shown in [Equation 22].

[0073]

(Equation 22)

Next, a generalized plant G _x (s) for control system design based on μ synthesis and a compensator K _x (s) configured when designing a control system using a technique called μ synthesis. 2 is shown in FIG. A control system design method called μ synthesis is a method in which the variation Δ is | Δ
A compensator that maintains the stability of the control system and minimizes the maximum singular value of the transfer characteristic G _zw from the disturbance input amount w _x to the control amount z _x even if it fluctuates arbitrarily in the range of | ∞ ≦ 1. Of the transfer function K _x (s) is obtained. Where | Δ | ∞ is Δ
H∞ norm.

Control system based on μ synthesis shown in FIG.
The generalized plant for the design has a state quantity x_xAs H
一般 Generalized plan built during control system design using theory
G (expansion system) state quantity x_aAnd the frequency added to this
Number weight function (w in FIG. 3) _T, w_sX)
_addAnd merge with. Also, the control amount z_xAs H∞ 理
Plant constructed during control system design using theory
(Enlarged system) control amount z_aOr the control amount z_aSelected
The amount of the linear combination of the selected element variables and the variation of the control
Part of output element variables related to Δ representing minute (in FIG. 3,
z_Ap, z_Cp2And the merger with Further
, Y_x= y_a u_x= u_a Dx defined as_x/ dt = A_xx_x+ B_x1w_x + B_x2u_x z_x = C_x1x_x+ D_x11w_x+ D_x12u_x y_x = C_x2x_x+ D_x21w_x+ D_x22u_x This is described by a state equation such as

[0076] Therefore, with respect to Δ represents the variation of the transfer function K _x (s) and the control target of the compensator satisfies _{u x = K x (s)} y x w x = Δz x. Further, the variation Δ satisfies | Δ | ∞ ≦ 1. In order to use the technique called μ-synthesis, the configuration must be as shown in FIG. 2 (or FIG. 3).

Next, the block diagram shown in FIG.
The dynamic characteristics of the two stands F6 and F7, which are the latter two stands of the rolling mill, are expressed as dx _p / dt = (A _p + ΔA _p ) x _p + (B _p1 + ΔB _p1 ).
_{w p + B p2 u p y} p = (C p2 + ΔC p2) x p + (D p21 + ΔD p21) w
_This is a representation of the state equation described by _p , including its variation. Further, this is transformed into the form of FIG. 2 necessary for using a method called μ synthesis,
FIG. 4 is a block diagram shown in FIG. 3. Hereinafter, a method for deriving the block diagram of FIG. 3 based on the block diagram of FIG. 4 will be described.

(Example) Attention is paid to the main variable elements of the matrices A _p and C _{p2, and} an example of a design method in the case of considering the fluctuations of ΔA _p , ΔB _p1 , ΔC _p2 and ΔD _p21 : Now, for example, δ ₁ : A _The normalized variation of the (3,1) component of the _p matrix δ ₂ : A The normalized variation of the (3,2) component of the _p matrix δ ₃ : The (3,3) component of the Ap matrix normalized variation [delta] _4: C _p2 matrix (1,1) component of normalized variation [delta] _5: C _p2 matrix (2,2) defined as a normalized variation of the component (- 1 <δ _i <1) them _{if, Δ A = diag [δ 1} , δ 2, δ 3] Δ B = diag [δ 4, δ 5] matrix is determined by the delta _Ap, delta _Cp is, | Δ _Ap | ∞ ≦ 1 | Δ _Cp2 | ∞ ≦ 1.

[0079] Furthermore, | delta | By using the '∞ ≦ 1 and becomes Δ', Δ = diag [Δ A, Δ B, Δ '] is delta configuration as, | delta | satisfies ∞ ≦ 1 I have. However, diag [a, b, c] means a matrix having matrices a, b, c on diagonal elements.

Further, as shown in the following [Equation 23], the hat B
₂ , the hat C ₂ , the hat D ₁₂ , and the hat D ₂₁

[0081]

(Equation 23)

It can be confirmed by a simple matrix calculation that the equation described as the following [Equation 24] holds.

[0083]

(Equation 24)

[0084] Further, as an evaluation variable z _a, the addition defines a _{z a = w s (C p1} x p + D p11 w p) + w T u p, the block diagram of FIG. 3 can be constructed. In FIG. 3, as the dynamic characteristic of the disturbance, describes _{dx w / dt = A x x} w + B W u w w p = C w x w + D W u w as in the following [Equation 25] I have.

[0085]

(Equation 25)

According to the above procedure, the block diagram of FIG. 3 has a form equivalent to that of FIG. 2, and thus the μ synthesis method has been formulated. At this time, the following state equation _{dx x / dt = A x x} x + B x1 w x + B x2 u x z x = C x1 x x + D x11 w x + D x12 u x y x = C x2 x x + D matrix involved in _x21 w _x + D _x22 u _x is given as [Equation 26].

[0087]

(Equation 26)

As described above, in the matrix representing the control object, attention is paid to the component having large fluctuation, and the control system is designed by newly constructing an enlarged system in consideration of the fluctuation of the component. This is a feature of the looperless rolling control method according to the present invention. Which component to focus on is determined based on the design specifications.

Now, if the configuration as shown in FIG. 4 can be made and the matrix as shown in [Equation 26] can be formed, H
Reducing the theory, the transfer function K _x (s) of the compensator is obtained. The transfer function K _x (s) is obtained by a DK iterative calculation method described below, making full use of a commercially available control system design CAD.

In the above example, the matrices A _p , C
_Although the control system is configured by focusing on the main variable element of _p2 , there is also a method of configuring by focusing on other main variable elements. Hereinafter, (a) μ and (b) the DK iterative calculation method will be described.

(A) μ The maximum singular value of the transfer characteristic from the disturbance input to the control amount is determined based on the state equation composed of the state equation describing only the behavior of the control object and the frequency characteristic of the disturbance. Although the method of finding the minimum compensator by H∞ theory is different from the method of finding the compensator by μ synthesis,
Closely related to each other. μ is an evaluation criterion used in control system design and corresponds to H∞ norm in H∞ theory.

(B) DK Iterative Calculation Method Originally, the transfer function K _x (s) of the compensator minimizing μ
Should be calculated. However, since a method of systematically calculating this as in the H∞ theory has not been developed, today, the problem of minimizing the μ value is reduced to the problem of minimizing the H∞ norm to obtain a compensator. -ing

[0093] _{Specifically, dx x / dt = A x} x x + B x1 w x + B x2 u x z x = C x1 x x + D x11 w x + D x12 u x y x = C x2 x _x + D _x21 w _x + D _x22 u _{x In the} state equation of _x + D _x21 w _x + D _x22 u _x , the maximum singular value of the transfer characteristic G _zw from the disturbance input w _x to the control amount z _x is from the observation amount y _x to the control input u _x The transfer function K _x (s) is obtained by the H∞ theory. The compensator calculates D _i (jω) G _{i for the} variation Δ
(jω) Matrix D _i that minimizes the maximum singular value of D _i ^-1 (jω)
(jω) and D _i (jω) G _i (j
If the maximum singular value of (ω) D _i ^-1 (jω) is less than 1, the fact that it is close to a compensator that minimizes the μ value is used.

Therefore, the DK iterative calculation method is
Let G be a generalized plant described by the equation of state_x(s)
Is defined as Δ, and (1) i = 1
And G₁(s) = G_x(s), D₁= I (identity matrix),
(2) Disturbance input w_xControl amount z_xTransfer characteristic G up to_zw
Observable y that minimizes the maximum singular value of_xControl input u_x
Transfer function K leading to_xi(s) is calculated, and (3) the variation Δ
D_i(jω) G_i(jω) D_i ^-1matrix D that minimizes the maximum singular value of (jω)_i(jω), and
(4) If D_i(jω) G_i(jω) D_i ^-1the maximum of (jω)
If the singular value is less than 1, K _xi(s)
And the control system design is completed. (5) If D_i(j
ω) G_i(jω) D_i ^-1The maximum singular value of (jω) is 1 or more
In the enlarged system, as shown in FIG.
w_xD before input_i ^-1(s) in front of the control variable z
_xD after the output of_i(s) is added afterwards, and the newly expanded system dx_xi/ dt = A_xix_xi + B_xi1w_xi+ B_xi2u_xi z_xi = C_xi1x_xi+ D_xi11w_xi+ D_xi12u_xi y_xi = C_xi2x_xi+ D_xi21w_xi+ D_xi22u_xi And construct a disturbance input w_xiControl amount z_xiTransmission characteristics leading to
Sex G_zwiObservable y that minimizes the maximum singular value of_xiControl from
Input u_xiTransfer function K leading to_xi(s) is calculated by H∞ theory
To return to the process of (3).

Further, in the method of the present invention, in order to keep the order of the transfer function K _xi (s) of the compensator to a low order that is highly available, D _i (s) is set to a real number that is not related to the Laplace operator s. We choose from matrices that have only elements. This is understood from the fact that when a compensator is obtained based on the H∞ theory, the compensator has the same order as the order of the expansion system. It is empirically known that the above-described DK iterative calculation method can calculate a compensator that is preferably performed only at most twice.

The processing after the transfer function K _x (s) of the compensator is set in the control computer will be described with reference to FIG. In Figure 1, thickness gauge 4, the plate width meter 6, the side plate out i stand by rolling reaction force measuring device 10 thickness deviation Delta] h _i, i stand delivery side width deviation [Delta] b _i, i stand rolling reaction force error Delta] p _i is measured You. The thickness gauge 5, the width gauge 7, and the rolling reaction force measuring device 11 measure the i + 1 stand exit side sheet thickness deviation Δh _{i + 1} , the i + 1 stand exit side sheet width deviation Δb _{i + 1} , and the i + 1 stand rolling reaction force deviation Δp _{i +. 1} is measured. Further, the tension meter 20 measures i / i + 1 the tension deviation σ _i between stands.

These measured values are all input to the deviation control device 21 provided in the control computer, and based on the transfer function K _x (s), the rolling position operation commands ΔSref _i , ΔSref _{i + 1} , i stand roll peripheral speed command ΔVref _i is calculated. i stand to i + 1
The stand rolling position operation commands ΔSref _i and ΔSref _{i + 1} are respectively applied to the rolling position drive devices 12 and 13, and the i stand roll peripheral speed command ΔVref _i is applied to the rolling motor drive rotation speed control device 16.

(2) In the case of three stands: In the case of three stands, a control system that can achieve the object can be designed by the method disclosed in the case of two stands. At this time, the element variables (candidates) of the variables when describing the case where the control is performed using the three stands F5, F6, and F7 only increase as follows.

Element variables (candidates) of state quantity x _p ΔS ₅ : F5 stand rolling position deviation ΔS ₆ : F6 stand rolling position deviation ΔS ₇ : F7 stand rolling position deviation Δσ ₅ : F5 / F6 stand unit tension deviation Δσ ₆ : F6 / F7 stand unit tension deviation ΔVn ₅ : F5 stand neutral point velocity deviation ΔVn ₆ : F6 stand neutral point velocity deviation ΔVn ₇ : F7 stand neutral point velocity deviation ΔVc ₅ : F5 stand neutral point velocity reference deviation and neutral point integrating d of the difference between the speed deviation _{(ΔVc i) / dt = ΔVref} i - ΔVn i ΔVc 6: F6 integral d of the difference between the neutral point speed reference deviation stand the neutral point speed deviation (ΔVc _{i + 1)} / dt _{= ΔVref i + 1 - ΔVn i} + 1 ΔVc 7: F7 integral d of the difference between the neutral point speed reference deviation stand the neutral point speed deviation _{(ΔVc i + 2) / dt} = ΔVref i + 2 - ΔVn i + 2

[0100] control variable z _p of elements variable (candidate) Δh _5: F5 stand delivery side thickness deviation Delta] h _6: F6 stand delivery side thickness deviation Delta] h _7: F7 stand delivery side thickness deviation [Delta] b _5: F5 stand delivery side width deviation [Delta] b ₆ : F6 stand exit side plate width deviation Δb ₇ : F7 stand exit side plate width deviation Δσ ₅ : F5 / F6 stand unit tension deviation Δσ ₆ : F6 / F7 stand unit tension deviation ΔSref ₅ : F5 stand pressure reduction reference change amount ΔSref ₆ : F6 stand roll reference change amount ΔSref ₇ : F7 stand roll reference change amount ΔVref ₅ : F5 stand roll circumferential speed reference change amount ΔVref ₆ : F6 stand roll circumferential speed reference change amount

[0101] observed variables y _p of the element variable (candidate) Δh _5: F5 stand delivery side thickness deviation Δh _6: F6 stand delivery side thickness deviation Δh _7: F7 stand delivery side thickness deviation Δb _5: F5 stand delivery side width deviation Δb ₆ : F6 stand exit side plate width deviation Δb ₇ : F7 stand exit side plate width deviation Δσ ₅ : F5 / F6 stand unit tension deviation Δσ ₆ : F6 / F7 stand unit tension deviation Δp ₅ : F5 stand rolling reaction force deviation Δp ₆ : F6 stand rolling reaction force deviation Δp ₇ : F7 stand rolling reaction force deviation

[0102] The control input quantity u _p element variable of (candidate) ΔSref _5: F5 stand pressure reference change amount ΔSref _6: F6 stand pressure reference change amount ΔSref _7: F7 stand pressure reference change amount ΔVref _5: F5 stand roll peripheral speed reference Change amount ΔVref ₆ : F6 stand roll peripheral speed reference change amount

Element variable (candidate) of disturbance input amount w _p ΔSd ₅ : F5 stand roll eccentric disturbance ΔSd ₆ : F6 stand roll eccentric disturbance ΔSd ₇ : F7 stand roll eccentric disturbance ΔH ₅ : F5 stand entry side plate thickness deviation ΔH ₆ : Thickness deviation of F6 stand entrance side ΔH ₇ : F7 stand entrance side thickness deviation ΔTd ₅ : F5 stand rolled steel plate temperature deviation (corresponding to skid mark) ΔTd ₆ : F6 stand rolled steel plate temperature deviation (corresponding to skid mark) ΔTd ₇ : F7 stand rolled steel plate temperature deviation (corresponding to skid mark) ΔB ₅ : F5 stand entrance side plate width deviation ΔB ₆ : F6 stand entrance plate width deviation ΔB ₇ : F7 stand entrance plate width deviation

The other points are the same as those in the case of the two stands, and the description is omitted. As shown in FIG. 8, as is clear from the comparison of the thickness accuracy at the exit side of the final rolling mill,
Using a compensator using μ-synthesis achieves better plate thickness accuracy. Further, as shown in FIG. 9, comparing the tension control performance between the last rolling mill and the second rolling mill counted from the last rolling mill, it is clear that the use of the compensator using μ-synthesis is clearer. Good tension control accuracy has been achieved.

That is, in the present embodiment, the state equation is reconstructed in consideration of the variation of the control object, and the transfer function obtained based on the equation is set in the compensator to perform the rolling control. With only one compensator, high-precision control can be realized in response to the fluctuation of the control target. In addition, since the inter-stand tension deviation is always included as a control amount of the rolling process, high-precision control can be realized not only for the plate thickness and the plate width but also for the tension.

In the present embodiment, the rolling control is performed without using the transfer model by using the sheet thickness deviation and the sheet width deviation on the exit side of each stand as the amount of observation of the rolling process.
Highly accurate control can be realized. In addition, since the order of the control target and the order of the compensator can be reduced as much as possible, there is an advantage that the design and adjustment of the control system can be easily performed.

The above-described rolling control method according to the present embodiment is actually realized by a microcomputer system including a CPU, a ROM, a RAM, and the like, and a program for realizing the above functions is stored in the ROM. You. In addition, it is also possible to externally supply the program to the computer system.

In this case, means for supplying the program, for example, a recording medium storing the program constitutes the present invention. As a recording medium for storing the above program, in addition to the ROM, for example, a floppy disk, a (registered trademark) hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a CD-I, a CD-R, a CD-ROM
RW, DVD, zip, magnetic tape, nonvolatile memory card, and the like can be used.

The functions of the above-described embodiments are not only realized by the computer executing the supplied program, but also the OS (operating system) or other application software running on the computer. When the functions of the above-described embodiment are realized in cooperation with the computer, or when all or a part of the processing of the supplied program is performed by a function expansion board or a function expansion unit of a computer, the functions of the above-described embodiment are realized. Such a program is also included in the embodiment of the present invention.

[0110]

As described above in detail, according to the present invention, it is possible to construct a control system capable of maintaining high-quality control performance even when the control object fluctuates. In addition, the thickness control and the width control can be maintained with high accuracy irrespective of the variation of the control object.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration example of a rolling control system that implements the present invention.

FIG. 2 is a block diagram showing a typical enlarged system when a compensator is designed using the μ synthesis theory of the present embodiment.

FIG. 3 is a block diagram illustrating a configuration example when a compensator is designed using the μ synthesis theory of the embodiment.

FIG. 4 is a block diagram showing dynamic characteristics of a controlled object having an additive variation.

FIG. 5 is a block diagram for explaining the concept of conversion by D (s) in the DK iterative calculation.

FIG. 6 is a characteristic diagram illustrating a concept of an influence coefficient.

FIG. 7 is a diagram showing a gain frequency characteristic of G _sd6 (s) = (s + 1) / (s + 4).

FIG. 8 is a characteristic diagram showing a comparative example of the thickness accuracy on the exit side of the last rolling mill.

FIG. 9 is a characteristic diagram showing a comparative example of tension control performance between a last rolling mill and a second rolling mill counted from the last rolling mill.

FIG. 10 is a block diagram illustrating a typical magnification system when designing a compensator using H∞ theory.

FIG. 11 is a characteristic diagram illustrating a sheet thickness behavior when _a control variable z _a does not include an element variable related to tension.

FIG. 12 is a characteristic diagram showing a tension behavior when _a control variable z _a does not include an element variable relating to tension.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Rolled steel plate 2 i stand rolling machine 3 i + 1 stand rolling machine 4 thickness gauge 5 thickness gauge 6 width gauge 7 thickness gauge 8 Roll roll rotation speed measuring device 9 Roll roll rotation speed measuring device 10 Rolling reaction force measuring device REFERENCE SIGNS LIST 11 Rolling reaction force measuring device 12 Rolling position driving device 13 Rolling position driving device 14 Rolling roll motor 15 Rolling roll motor 16 Rolling roll motor rotation speed control device 17 Rolling roll motor rotation speed control device 18 Rolling roll motor rotation speed measuring device 19 Rolling Roll motor rotation speed measuring device 20 Tensiometer 21 Deviation control device

Claims (3)

[Claims] (1) There are n (i = 1, ... n, n ≧ 2) rolling stands
And equipped with a tension meter between each stand,
One, the exit side of each stand, directly under the roll bite of each stand
Or measure the thickness and width of each stand
In a rolling process having a means for estimating, a rolled material is placed on an upstream i-stand and an i + 1 immediately downstream thereof.
A tandem rolling mill that rolls on multiple stands, including stands
Of the stand thickness deviation Δh_i, I + 1 stand out
Side plate thickness deviation Δh_{i + 1}, I stand exit side plate width deviation Δb_i,
i + 1 stand exit side plate width deviation Δb_{i + 1}, I stand rolling
Reaction force deviation Δp_i, I + 1 stand rolling reaction force deviation Δp_{i + 1}
And i / i + 1 stand-to-stand tension deviation Δσ_iAt least
Also one or more observations y_pI / i + 1 tension deviation between stands Δσ_iBesides istan
Door side thickness deviation Δh_i, I + 1 stand exit side thickness deviation Δ
h_{i + 1}, I stand exit side plate width deviation Δb_i, I + 1 stun
Door exit side width deviation Δb_{i + 1}, I stand rolling position correction amount Δ
Sref_i, I + 1 stand pressure reduction position correction amount ΔSref_{i + 1}And
And i stand roll peripheral speed correction amount ΔVref _iAt least
One or more control amount z as required_pSelected as element variables of
Select the i stand pressure reduction position correction amount ΔSref_i, I + 1 stand pressure
Lower position correction amount ΔSref_{i + 1}And i stand roll peripheral speed
Correction amount ΔVref_iIs the control input u_pAnd i stand to i +
One stand roll eccentricity ΔSd_i, ΔSd_{i + 1}, I stand ~
i + 1 Stand entry side thickness deviation ΔH_i, ΔH_{i + 1}, Ista
To i + 1 stand entry side plate width deviation ΔB _i, ΔB_{i + 1}You
And the pressure rolled at each of the i stand to the i + 1 stand
Temperature deviation ΔTd of rolled material_i, ΔTd_{i + 1}At least one of
Is the disturbance input w_pAnd the state variable x of the rolling process_pAs an element variable of
Stand to i + 1 stand pressure reduction position deviation ΔS_i, ΔS
_{i + 1}, I / i + 1 stand-to-stand tension deviation Δσ_i, Istan
To i + 1 stand neutral point speed deviation ΔVn_i, ΔVn_{i + 1},
And i-stand to i + 1 stand neutral point speed reference
Lens deviation ΔVref_i, ΔVref_{i + 1}And neutral point speed deviation ΔVn
_i, ΔVn_{i + 1} Integral ΔVc_i, ΔVc_{i + 1}At least
The following equation of state dx describing the dynamic characteristics of the rolling process_p/ dt = A_px_p+ B_p1w_p + B_p2u_p z_p = C_p1x_p+ D_p11w_p+ D_p12u_p y_p = C_p2x_p+ D_p21w_p+ D_p22u_p And its disturbance input w_pThe dynamic characteristics of the element variables of
State variable x of element variable_wControl input of disturbance and disturbance input element variables
Force u_wThe next state equation dx described using_w/ dt = A_wx_w+ B_wu_w w_p = C_wx_w+ D_wu_w From the state quantity x of the rolling process_pAnd disturbance input w_pEssence of
State x of elementary variable_wIs the state quantity x_aBy
Equation of state of generalized plant synthesized by dx_a/ dt = A_ax_a+ B_a1w_a + B_a2u_a z_a = C_a1x_a+ D_a11w_a+ D_a12u_a y_a = C_a2x_a+ D_a21w_a+ D_a22u_a Of the disturbance input w_aControl amount z_aTransfer characteristic G up to_zwa
Observable y that minimizes the maximum singular value of_aControl input u_a
Transfer function K leading to_aIn obtaining (s), a matrix A describing the control target of the rolling process_p, B
_p1, B_p2, C_p1, C_p2, D_p11, D_P12 , D_P21, D
_P22Fluctuation amount ΔA_p, ΔB_P1, ΔB_P2, ΔC_P1, ΔC_P2,
 ΔD_P11, ΔD_P12, ΔD_P21, ΔD_P22At least
Is the next state equation dx reconstructed considering one or more_x/ dt = A_xx_x+ B_x1w_x+ B_x2u_x z_x = C_x1x_x+ D_x11w_x+ D_x12u_x y_x = C_x2x_x+ D_x21w_x+ D_x22u_x Of the disturbance input w_xControl amount z_xTransfer characteristic G up to_zwx
Observable y that minimizes the maximum singular value of_xControl input u_x
Transfer function K leading to_x(s) is obtained by the H∞ theory, and the obtained transfer function K_xbased on (s)_xFrom
Control input u_xIs set in the deviation control means, and the deviation thickness means Δh on the exit side of the i-stand is set by the deviation control means.
_i, I + 1 stand exit side thickness deviation Δh_{i + 1}, I stand
Exit side plate width deviation Δb_i, I + 1 stand exit side plate width deviation Δb
_{i + 1}, I stand rolling reaction force deviation Δp_i, I + 1 stand
Rolling reaction force deviation Δp_{i + 1} And i / i + 1 tension between stands
Deviation Δσ_iAt least one of the transfer functions K
_xgiven to the compensator represented by (s)
Correction amount ΔSref_i, I + 1 stand pressure reduction position correction amount ΔSr
ef_{i + 1}And i stand roll peripheral speed correction amount ΔVref_iof
Calculate at least one or more, and determine the partial pressure reduction position and
The peripheral speed of the wheel
Parless rolling control method. 2. The apparatus has n (i = 1,..., N ≧ 3) rolling stands.
And equipped with a tension meter between each stand,
One, the exit side of each stand, directly under the roll bite of each stand
Or measure the thickness and width of each stand
In a rolling process having a means for estimating, a rolled material is divided into an i-stand, an i + 1 stand and an i + 2 star.
Stand of a tandem rolling mill rolling in this order
~ I + 2 stand exit side thickness deviation Δh_i, Δh_{i + 1}, Δh
_{i + 2}, I stand to i + 2 stand exit side plate width deviation Δ
b_i, Δb_{i + 1}, Δb_{i + 2}, IStand-i + 2 Stan
De-rolling reaction force deviation Δp_i, Δp_{i + 1}, Δp_{i + 2}And i /
Tension deviation between i + 1 stand to i + 1 / i + 2 stand
Δσ_i, Δσ _{i + 1}At least one of the observations y_pof
Select as an element variable, tension between i / i + 1 stand to i + 1 / i + 2 stand
Deviation Δσ_i, Δσ_{i + 1}In addition, i-stand to i + 2 studio
Output side sheet thickness deviation Δh_i, Δh_{i + 1}, Δh_{i + 2}, Ista
To i + 2 stand exit side plate width deviation Δb_i, Δb_{i + 1},
Δb_{i + 2}, I-stand to i + 2 stand pressing position correction amount
ΔSref_i, ΔSref_{i + 1}, ΔSref_{i + 2}And i stand ~
i + 1 stand roll peripheral speed correction amount ΔVref_i, ΔVref
_{i + 1}At least one of the control amounts z_pof
Select as an element variable, i-stand to i + 2 stand rolling position correction amount ΔSref_i,
ΔSref_{i + 1}, ΔSref_{i + Two}And i stand to i + 1 star
Roll peripheral speed correction amount ΔVref_i, ΔVref_{i + 1}Control input
Force u_pAnd i-stand to i + 2 stand roll eccentricity Δ
Sd_i, ΔSd_{i + 1}, ΔSd_{i + 2}, IStand-i + 2 Stan
Entry side plate thickness deviation ΔH_i, ΔH_{i + 1} , ΔH _{i + 2}, Istan
Do ~ i + 2 Stand entry side width deviation ΔB_i, ΔB_{i + 1} , Δ
B_{i + 2}And i stand to i + 2 stand plate temperature deviation Δ
Td_i, ΔTd_{i + 1} , ΔTd_{i + 2}Disturbance of at least one of
Input w_pAnd the state variable x of the rolling process_pAs an element variable of
Stand to i + 2 stand down position deviation ΔS_i, ΔS
_{i + 1} , ΔS_{i + 2}, I / i + 1 to i + 1 / i + 2 stand
Tension deviation Δσ_i, Δσ_{i + 1}, I stand-i + 2 studio
Command neutral point speed deviation ΔVn_i, ΔVn_{i + 1}, ΔVn_{i + 2}and
Neutral point speed reference from i stand to i + 2 stand
Deviation ΔVref_i, ΔVref_{i + 1}, ΔVref_{i + 2}And neutral speed deviation
Difference ΔVn_i, ΔVn_{i + 1} , ΔVn_{i + 2}Integral ΔVc_i, Δ
Vc_{i + 1} , ΔVc_{i + 2}At least one of the following equations, and the following equation of state dx describing the dynamic characteristics of the rolling process_p/ dt = A_px_p+ B_p1w_p + B_p2u_p z_p = C_p1x_p+ D_p11w_p+ D_p12u_p y_p = C_p2x_p+ D_p21w_p+ D_p22u_p And its disturbance input w_pThe dynamic characteristics of the element variables of
State variable x of element variable_wControl input of disturbance and disturbance input element variables
Force u_wThe next state equation dx described using_w/ dt = A_wx_w+ B_wu_w w_p = C_wx_w+ D_wu_w From the state quantity x of the rolling process_pAnd disturbance input w_pEssence of
State x of elementary variable_wIs the state quantity x_aBy
Equation of state of generalized plant synthesized by dx_a/ dt = A_ax_a+ B_a1w_a + B_a2u_a z_a = C_a1x_a+ D_a11w_a+ D_a12u_a y_a = C_a2x_a+ D_a21w_a+ D_a22u_a Of the disturbance input w_aControl amount z_aTransfer characteristic G up to_zwa
Observable y that minimizes the maximum singular value of_aControl input u_a
Transfer function K leading to_aIn obtaining (s), a matrix A describing the control target of the rolling process_p, B
_p1, B_p2, C_p1, C_p2, D_p11, D_P12, D_P21, D
_P22Fluctuation amount ΔA_p, ΔB_P1, ΔB_P2, ΔC_P1, Δ
C_P2, ΔD_P11, ΔD_P12, ΔD_P21, ΔD_P22Few
At least one of the following state equations dx reconstructed considering dx_x/ dt = A_xx_x+ B_x1w_x + B_x2u_x z_x = C_x1x_x+ D_x11w_x+ D_x12u_x y_x = C_x2x_x+ D_x21w_x+ D_x22u_x Of the disturbance input w_xControl amount z_xTransfer characteristic G up to_zwx
Observable y that minimizes the maximum singular value of_xControl input u_x
Transfer function K leading to_x(s) is obtained by the H∞ theory, and the obtained transfer function K_xbased on (s)_xFrom
Control input u_xIs set in the deviation control means, and the deviation control means sets i-stand to i + 2 stand.
Discharge thickness deviation Δh_i, Δh_{i + 1}, Δh_{i + 2}, I stand
~ I + 2 stand exit side plate width deviation Δb_i, Δb_{i + 1} , Δb
_{i + 2}, I stand to i + 2 stand rolling reaction force deviation Δ
p_i, Δp_{i + 1}, Δp_{i + 2} And between i / i + 1 stand
~ I + 1 / i + 2 tension deviation between stands Δσ_i, Δσ_{i + 1}
At least one of the transfer functions K_x(s)
To the compensator to reduce i stand to i + 2 stand
Position correction amount ΔSref_i, ΔSref_{i + 1}, ΔSref_{i + 2}And i
Stand to i + 1 stand roll peripheral speed correction amount ΔVre
f_i, ΔVref_{i + 1}Calculate at least one or more of
The partial pressure reduction position and the roll peripheral speed have been corrected.
And a looperless rolling control method. 3. The following constituted in claim 1 or 2
State equation dx_x/ dt = A_xx_x+ B_x1w_x + B_x2u_x z_x = C_x1x_x+ D_x11w_x+ D_x12u_x y_x = C_x2x_x+ D_x21w_x+ D_x22u_x Of the disturbance input w_xControl amount z_xTransfer characteristic G up to_zwof
Observable y that minimizes the maximum singular value_xControl input u_xTo
Transfer function K_x(s) is calculated by H∞ theory.
Thus, the generalized plant described by the above equation of state is G_x(s)
 , The variation of the considered matrix is defined as Δ, and (1)
i = 1, G₁(s) = G_x(s), D₁= I (identity matrix) and
And (2) disturbance input w_xControl amount z_xTransfer characteristics up to
G_zwObservable y that minimizes the maximum singular value of_xControl input from
u_xTransfer function K leading to_xi(s) is calculated, and (3) the variation Δ
D_i(jω) G_i(jω) D_i ^-1matrix D that minimizes the maximum singular value of (jω)_i(jω), and
(4) If D_i(jω) G_i(jω) D_i ^-1the maximum of (jω)
If the singular value is less than 1, K _xi(s)
Finish the control system design as a number, (5)_i(jω)
G_i(jω) D_i ^-1If the maximum singular value of (jω) is 1 or more,
In the expansion system, a disturbance input w_xD before input
_i ^-1(s) in front of the control variable z_xD after the output of
_i(s) is added afterwards, and the newly expanded system dx_xi/ dt = A_xix_xi + B_xi1w_xi+ B_xi2u_xi z_xi = C_xi1x_xi+ D_xi11w_xi+ D_xi12u_xi y_xi = C_xi2x_xi+ D_xi21w_xi+ D_xi22u_xi And construct a disturbance input w_xiControl amount z_xiTransmission characteristics leading to
Sex G_zwiObservable y that minimizes the maximum singular value of_xiControl from
Input u_xiTransfer function K leading to_xi(s) is calculated by H∞ theory
In the method of returning to the processing of (3) above,
Transfer function K_xithe order of (s) to a lower order of higher availability
D to hold down_i(s) with respect to the Laplace operator s
Select from matrices that have only real numbers
3. The method according to claim 1, wherein
A method for controlling looperless rolling as described in the above.