JP2602370B2 - Dimension control method for bar and wire rod rolling - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

This invention relates to at least two downstream
The present invention relates to a dimensional control method in continuous rolling of a bar or a wire having a stand formed by a three-roll rolling mill.

[0002]

2. Description of the Related Art Conventionally, there is the following prior art regarding a dimensional control method in continuous rolling of a steel bar or a wire rod in which at least two stands on the downstream side are constituted by a three-roll rolling mill.

As a first example, Japanese Patent Laid-Open No. 59-39401 is disclosed.
As disclosed in Japanese Unexamined Patent Publication, there is a technique for controlling the tension of a material between a three-roll type rolling mill and a preceding and succeeding rolling mill without tension. As a second example, Japanese Patent Application Laid-Open No. Sho 62-230
As disclosed in Japanese Patent No. 413, at least one of a rolling roll rotation speed and a rolling roll gap is used as an operation amount.
There is a technique for measuring the tension generated in the rolled material and the cross-sectional profile of the rolled material by a profile meter installed on the exit side of the last stand of the rolling mill row to control the tension and the dimension of the final stand exit side. However, Japanese Patent Application Laid-Open No. 59-39401 does not disclose a specific method of setting a gain, and the control performance of this technique is unknown. In the latter technique, feedback control is performed by actually measuring a dimensional deviation by a rolled material cross-sectional profile meter at the stand exit side, and the control operation is delayed by a dead time due to a distance from the finishing stand to the rolled material cross-sectional profile meter.

[0004]

SUMMARY OF THE INVENTION The present invention relates to a continuous rolling of bar and wire rods in which at least two stands on the downstream side are formed by a three-roll type rolling mill, and a cross section of the rolled material at the exit of the last stand of the rolling mill row. It is an object of the present invention to provide a dimensional control method in bar and wire rod rolling in which a settling time is short and an offset is zero, and a multivariable control with good control performance is performed when controlling a height dimension and a width dimension.

[0005]

SUMMARY OF THE INVENTION The present invention provides a method for transforming, loading,
Rolling speed and roll clearance operation amount using the rolling state equation consisting of rolling and temperature, and the output of each stand taking into account the loop height between each stand of the rolling mill group and monitor compensation. A dimension control method in wire rod and bar rolling, characterized in that the calculated height of a side gage meter is controlled by feedback of a control deviation and a state vector based on an optimum regulator theory.

That is, the present invention relates to Japanese Patent Application Laid-Open No. 62-23041.
As shown in No. 3, the control operation delay caused by the distance from the finishing stand to the rolled material cross-sectional dimension meter, which is a problem in the method of controlling the cross-sectional shape and dimensions of the rolled material, is released from the final finishing stand. As a means for measuring the cross-sectional dimension of a rolled material, a value obtained by using a gage meter method widely used in the field of sheet rolling is used to increase the response speed of feedback, thereby solving the problem. is there.

[0007]

According to the present invention, the evaluation function J

[0008]

The optimum control input u (k) that minimizes J = Σ [e _T (j) Q · e (j) + v _T (j) Rv (j)] is equal to the control deviation e.
(k) and feedback of partial state vector xs (k)

[0009]

U (k) = − F ₁ e (k−1) −F ₂ [e (k) −e (k−1)] −F ₃ [xs (k) −xs (k−1)] Since a plurality of inputs are simultaneously obtained as + u (k-1), a control system having good control performance can be designed relatively easily.

[0010]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described below in detail based on embodiments. As the dynamics of the mill drive system, the rolling roll versus gap control system is approximated by a first-order lag system, and the rolling roll rotation speed control system is approximated by a secondary system. The symbols are shown in Table 1 below.

[0011]

[Table 1]

In Table 1, those with a symbol Δ indicate changes from the reference state (dimensional quantities), and those with a symbol * indicate the dimensionless quantities obtained by dividing the values by the physical quantities in the reference state. Show,
Subscripts i and j indicate stand numbers.

The non-linear rolling model is linearized and dimensionless around a reference state (Table 2) and displayed as a state space model.
Further, the following state equation is obtained by discretization at the control period Δt. Here, Δx is defined as a variation from the pass schedule value x ₀ , Δx * ≡Δx / x ₀ (however, ΔS * ≡Δs
/ H, Δt _f * ≡Δt _f / k _fm ). Also, delta x * is gate - dimethyl - a deviation from the lock-on value [Delta] x _L * in data calculation.

[0014]

X ′ (k + 1) = A′x (k) + B′u (k) + E′w (k) (1) y ′ (k) = C′x ′ (k) + F 'w (k) (2) where state vector x, output y, input u, and disturbance w
Is as follows.

[0015]

[Number 4] _{x '= (Δ S i *} , Δt fj *, ΔN ii *, ΔN ii *') T ··· (3) y '= (Δ h i *, Δt fj *) T ··· (4) u = (Δ S ref, i *, ΔN ref, ii *) T ··· (5) w = (ΔT mi *, ΔH i *, ΔB i *) T ··· (6) i = .., N ii = 1, 2,..., N−1 j = 1, 2,..., N−1 n: number of stands k: number of samples (integer) A ′, B ', C', E ', F': Matrix having partial differential coefficients of rolling characteristics and driving system dynamic characteristic parameters as elements Here, deviation of roll rotation speed and its time differential value ΔN in equation (3) _ii *, ΔN _ii * ′, the stand No. of the deviation ΔN _{ref, ii} * of the roll speed target value in equation (5). Subscript ii representing ii
= 1, 2,..., N−1, in this embodiment,
This is because the i = n (final) stand is used as the reference stand for fixing the number of roll rotations. The above equations (1) and (2) are discrete-time state equations composed of a linear unsteady rolling model and a mill drive system model using analysis results based on loop elasticity theory.

The material transfer delay formula between stands is as follows:

[0017]

ΔTm _{i + 1} * (k) = α _i · ΔT _mi * (k−li) (7) ΔH _{i + 1} * (k) = Δb _i * (k−li) (8) ΔB _{i + 1} * (k) = Δh _i * (k−li) (9) Here, l _i is No. i stand ~ N
o. Represents the material transfer time between i + 1 stands (discrete time system). The coefficient α _i representing the temperature change of the material is obtained by computer simulation using a non-linear rolling model. The coefficient α _i is a positive number close to 1 and can be approximately set to 1. In bar and wire rod rolling, the width of the exit side is considerably larger than the dimension of the entrance because the width is relatively large. The target values of the delivery side dimensions of the rolling mill rows (coarse rows, intermediate rows, finishing rows) are such that the height dimension and the width dimension are the same or almost the same. Therefore, no. The widened part (width dimension part) of the i-stand (one upstream stand) is No. The rolls are arranged so that the rolling direction changes by 90 ° for 2Hi rolls and 60 ° for 3 rolls, and the rolls are inserted in each stand so that the rolling-down portion (height portion) is at the i + 1 stand. Rolling while maintaining the posture of the material by the side guide (however, in the case of a 2Hi rolling mill composed of only a horizontal roll arrangement, the No. i stand outgoing side material is 90 ° by the No. i + 1 stand incoming side guide).
° torsion and rolling). As a result, no. No. i. At the (i + 1) -th stand, it is a widened portion (width-sized portion). Therefore, in equations (8) and (9), N at time k-li
o. The stand-side exit width dimension and the exit side height dimension are respectively the No. at time k. i + 1 stand entrance side height dimension and entrance side width dimension.

When there is a loop between the stands and the roll speed can be controlled independently (see FIG. 1), (1) the relationship between the bending moment acting on the loop and the curvature in the theory of elasticity. , And (2) From Hooke's law, the relationship between the tension t _fi and the loop length lsi is:

[0019]

T _fi −t _f0i = C _1i (lsi−lsoi) / lsoi (10) where subscript o: represents a reference state, C _1i : constant, loop height y _hi and loop The relationship of length lsi is

[0020]

(Y _hi −y _hoi ) / y _hoi = C _2i (lsi−lsoi) / lsoi (11) C _2i : constant The above formulas (10) and (11) and the definition formula of tension deviation [Δt _fi * = (t _fi −t _foi ) / k _fmi ]

[0021]

Δy _hj * (k) = (C _2j / C _1j ) k _fm0j · Δt _fj * (k) (12)

Therefore, in the system equations (1) to (6),
When the tension Δt _fj * is replaced by Δy _hj * using the relation of the equation (12) between the 2Hi mill and the 2Hi mill and the 3 roll mill where the loop exists, the discrete systems (1), (2) )ceremony,

[0023]

X (k + 1) = Ax (k) + Bu (k) + Ew (k) (13) y (k) = Cx (k) + Fw (k) (14) x = _{(Δ S i *, Δy h} , j *, Δt fl *, ΔN ii *, ΔN ii * ') T ·· (15) y = (Δ h i *, Δy h, j *, Δt fl *) T ·· (16) u = (Δ S ref, i *, ΔN ref, ii *) T ··· (17) w = (ΔT mi *, ΔH i *, ΔB i *) T ··· (18) i = 1 to n ii = 1 to n-1 j = 1 to m-1 l = m to n-1 n: the number of stands. X, y, A, B, C, E, and F in these equations are:
X ′, y ′, A ′, B ′, C ′, E ′, and F ′ in equations (1) and (2), but the element of the part where Δt _fj * is converted to Δy _hj * different. Stand No. Since a loop is set on the output side of 1, 2,..., M−1, a height deviation Δy _hj * is used as a state vector and an output vector instead of the tension deviation Δt _fj *. On the output side of the m-1,..., n-1 stands, the deviation Δt _fj * of the tension is designed as a state vector and an output vector because of looplessness. No. 1,
No. 2 stand is 2Hi mill, No. Nos. 3 and 4 are 3 roll mills. There is a loop between 1-2 and between 2-3,
No. Between 3 and 4, the values of the matrices A to C in the standard state of the rolling of Table 2 in the four-stand mill of Rupress are as shown in Table 3. The values of the matrices A to C are obtained by first obtaining the equations (10) and (11), then obtaining the state equations of the equations (1) to (6) using Table 2, and obtaining the equations (1) to (6) )), Δt _fj * is replaced by Δy _hj * in equation (12) to derive equations (13) to (18). The values of the matrices E and F are omitted because they are unnecessary for the control system design described below.

[0024]

[Table 2]

[0025]

[Table 3]

[0026]

[Table 4]

[0027]

[Table 5]

[0028]

[Table 6]

A discrete-time optimal control system was designed by applying the optimal control theory to this system. That is, assuming that the disturbance w is step-shaped, the evaluation function

[0030]

J = Σ [e _T (j + 1) Q · e (j + 1) + v _T (j) R · v (j)] (j = 0 to infinity) (19) The control input u (k) to be minimized is, according to the optimal regulator theory,

[0031]

U (k) = − F ₁ e (k−1) −F ₂ [e (k) −e (k−1)] −F ₃ [xs (k) −xs (k−1)] + U (k-1) (20) Here, the control deviation e, the partial state xs, and the first order difference v of the input u are:

[0032]

E (k) = r (k) −y (k) (r (k) ≡0: target value) (21) xs (k) = (ΔN _ii *, ΔN _ii * ′) _T (22) v (k) = u (k) -u (k-1) (23) That is, the evaluation function J is a control amount Δ
The weight matrix Q is the square of the deviation from the target value of h _i * and Δy _{h, j} *.
And ΔS _{ref, i} * and ΔN _{ref, ii}
This is the sum of the square of the difference between the value at time k in * and the value at time k−1 one sampling period before, multiplied by the weight matrix R.
The optimal gain matrix F = [F ₁ : F ₂ : F ₃ ] is obtained from the solution P of the following Riccati equation (25).

[0033]

F = ((R + G _T PG) −1) G _T PΦ (24) P = Φ _T PΦ−Φ _T PG (R + G _T PG) G _T PΦ + H _T QH (25) ) Where the −1 power of the matrix in equation (24) represents the inverse matrix, and the matrix Φ,
G and H are error systems of systems (13) and (14)

[0034]

X (k + 1) = ΦX (k) + Gv (k) (26) e (k) = HX (k) (27) X (k) = [e _T (k−1) ), E _T (k) −e _T (k−1), xs _T (k) −xs _T (k−1)] _T (28), which are obtained from matrices A to C . Subscript T
Indicates a transposed matrix. Here, the optimal control system of the discrete time system is derived, but if the rolling state equations (1) and (2) are given in the continuous time system, the optimal control of the continuous time system can be configured in the same manner.

By applying this optimum control law, an optimum control system as shown in FIG. 2 for wire rod and bar rolling is constructed. FIG. 2 shows an embodiment of a four-stand mill. Control computer 14, Le - flop height [Delta] y _{h, j} * a rolling Russia - deviation Le rpm .DELTA.N _ii * and its differential value .DELTA.N _ii * ', b - Le versus gap delta S _i *, rolling load delta P _i *, * finishing stand exit side height due to dimensional gauge 13 delta] h _4, samples the output side width [delta] b ₄ *, the delivery side gate each stand - dimethyl - seeking data calculated height Δ h _i *, the input shown And the optimal control input u (k) given by equation (20)
Was calculated, Russia - le gap setting value delta S _{ref, i} *, b - Le rotational speed setting value .DELTA.N _{ref, ii} * each B - Le clearance control system, Russia -
Output to the control system.

Here, the gage meter calculation height Δ h _i * of the cross-section height of the rolled material at each stand exit side is:

[0037]

[Number 15] _{Δ h i * = Δ S i} * + α i · ΔP i * / M i * + Δh M, is calculated by _i * ··· (29). M _i * is a dimensionless mill constant (M _i * ≡
h _{0, i} · M _i / P _{0, i} ) and α _i are scale factors. The first and second terms on the right side of the equation (29) are known gage meter equations, and Δh _{M, i} * in the third term on the right side is monitor compensation for providing absolute dimensional accuracy. It is.

Here, the monitor means monitoring of a deviation from a target dimension value by actually measuring a finished height and a width dimension of a rolled material with a mill exit side dimension meter. That is, in the gage meter control, generally, the deviation from the lock-on value of the material height on the delivery side is set to zero, but in precision rolling, absolute value control for setting the finishing height and width to target values is required. Become. Therefore, the finishing height and width are actually measured by the delivery dimension meter, and the gage meter calculation height is corrected so that the deviation from the target value becomes zero. This is monitor compensation.

The control system of loop height control + gauge meter AGC + monitor AGC compensation is shown separately in FIGS.
In this control system, the same parts as those in the control system of FIG. 2 are denoted by the same reference numerals.

The monitor compensation Δh _{M, i} * is obtained by the following procedure. Finishing stand exit side height Δh ₄ *, exit side width Δ of dimension meter 5
From the sample value of b ₄ *, the leader stand and the finishing stand (No. 3, No. 4 stand in this embodiment)
The output side height monitor correction amounts Δh _{x, 3} * and Δh _{x, 4} * of

[0041]

Δh _{x, 3} * = (K ₂ · Δh ₄ * −Δb ₄ *) / K ₁ (30) Calculated by Δh _{x, 4} * = Δh ₄ * (31) However, the coefficients K ₁ and K ₂ are calculated by using the influence coefficient.

[0042]

K ₁ = (∂Δb ₄ * / ∂ΔS ₃ *) · ((∂Δh ₃ * / ∂ΔS ₃ *) to the −1 power) (32) K ₂ = (∂Δb ₄ * / ∂ΔS ₄ *) · ((∂Δh ₄ * / ∂ΔS ₄ *) to the −1 power) (33)

Next, the monitor compensation amount Δh _{M, i} * (k) is calculated as follows:
D, finishing stand exit height monitor correction amount h _{x, 3} *, Δh
_{x, 4} *

[0044]

Δh _{M, i} * (k) = 0 (when i = 1, 2) Δh _{M, i} * (k) = Δh _{M, i} * (k-1) + 1 / T _i · K _{M, i} · Δh _{x, i} * (k) (when i = 3, 4) (34) _Ti is No. Material (rolled material) transfer time (sec) from one stand to the exit dimension meter
K _{M, i} is a monitor compensation integral gain. The weight matrices Q and R in the equations (24) and (25) and the monitor compensation gain K _{M, i} in the equation (34) are determined by repeating the simulation.

No. 1 and 2 stands are 2Hi type rolling mill,
No. No. 3 and 4 stands are 4-stand mills composed of 3-roll type rolling mills. The material average temperature, entrance height, and input width at the entrance of one stand are ΔT _{m, 1} * = − 0.
[028] The case where the step change was performed by ΔH _i * = ΔB _i * = 0.007 was examined.

The rolling conditions are as shown in Table 2, and the matrices A to C
Are as shown in Tables 3, 4, 5 and 6. Control cycle Δt
Is 100 msec, and the disturbance is the next step disturbance with the first stand entrance average material temperature ΔT _{m, 1} *, entrance height ΔH _i *, entrance width ΔB _i *.

At time k <30 (= 3 seconds) ΔT _{m, 1} * (k) = 0, ΔH ₁ * (k) = 0, ΔB ₁ * (k) = 0 Time k ≧ 30 (= 3 seconds) )) ΔT _{m, 1} * (k) = − 0.028, ΔH ₁ * (k) = 0.007, ΔB ₁ * (k) = 0.007 The step response without control is shown in FIGS. 5, 6 and 7. That is, FIGS. 5 to 7 show that the changes in the average temperature of the inlet material, the height of the inlet material, and the width of the inlet material are ΔT _{m, 1} * = − 0.02 _, respectively.
8, without control by ΔH ₁ * = ΔB ₁ * = 0.007, the height Δh ₄ * of the cross section of the rolled material on the exit side of the finishing stand, the width Δb ₄ * of the rolled material on the exit side, the loop height Δy _{h, j} *, tension Δt
It is an illustration figure of the step response of _fl *. Here, when the material temperature and the dimensional change are no. The time when one stand is reached is assumed to be time t = 3 seconds.

FIG. 8, FIG. 9, FIG. 10, FIG. 11, and FIG. 8 to 12
Is the output side height Δh ₄ * and the output side width Δb by ΔT _{m, 1} * = − 0.028, ΔH ₁ * = ΔB ₁ * = 0.007 in the case of control (looper control + all four stands AGC). ₄ *, loop height Δy
_{h, j} *, tension Δt _fl *, roll rotation speed ΔN _ii *, and roll response ΔS _i *. At this time, the monitor compensation is not performed, and Δh _{M, i} * is set to zero in Expression (29). The weight matrices Q and R are

[0049]

## EQU19 ## Q = diag (1,1,1,1,0.001,0.002,0.005) (35) R = diag (10,10,10,10,1,1.2,1.5) ... (35) 36). It can be seen that the tension, the outlet height, and the outlet width are controlled.

Next, in order to verify the effectiveness of the monitor compensation, the disturbance of the material temperature and the cross-sectional dimension of the material is changed by Δ
The case where only T _{m, 1} * = − 0.028 and ΔH ₁ * = ΔB ₁ * = 0.007 was added was examined.

FIGS. 13, 14 and 15 show the output side height Δh ₄ *, output side width Δb ₄ *, loop height Δy _{h, j} *, and tension Δt _fl * without monitor compensation. Is shown.

Since the lock-on value in the gage meter calculation deviates from the reference state, offsets occur in the height and width of the exit of the finishing stand. Here, No.
The time when the material tip reaches one stand is set to t = 0.2 seconds.

FIGS. 16, 17 and 18 show the output side height Δh ₄ *, the output side width Δb ₄ *, and the output side width when the monitor control is performed (loop control + tension control + all four stands AGC). −Step height Δ
The response example of _{yh , j} * and tension (DELTA) _tfl * is shown. Here, the monitor compensation integral gain is K _{M, 3} = 0.025, K _{M, 4} = 0.0
I put it as 10. It can be seen that no offset occurs in the height and width of the finishing stand.

In this embodiment, continuous rolling in which a side loop is provided between stands (negative weight is negligible) has been described. However, even when there is an apple loop or down loop between stands, the material has its own weight. If the state equation is formed using the relational expression between the loop height and the rolled material tension in consideration of the above, the dimensional control can be performed in the same manner as in the above embodiment.

According to the present invention, in continuous rolling of wire rods and bars by a rolling mill train, a loop exists between 2Hi mills on the upstream side and between 2Hi mills and 3 roll mills, and a 3 roll mill on the downstream side. In the meantime, for the case of the loop press, the nonlinear unsteady rolling model of the loop rolling is linearized in the reference state of the rolling by using the analysis result of the loop based on the elasticity developed by the present inventor, and is linearized. derives a rolling model, the same consists of the mill drive system model, the state vector and the output vector in Le - using a linear state equations comprising up height, exit side material height deviation delta h _i * (out i-th stand side material high rate of change from the lock-on value h _L of h _i) and Le - flop height Δy _{h, j} *
(Change rate of the j-th stand exit loop height yh _{, j from} the reference value), tension Δt _fl * (l-th stand exit tension t _fl
And a control amount composed of ΔS
_{ref, i} * (i-th stand setting roll gap target value S _{ref, i}
Change rate from the lock-on value _{SL, i} ) and ΔNref _{, ii} * (i
i-th stand b - Le rotational speed target value N _{ref, ii} of Pasusukeju - time k and the manipulated variable constituted by the difference between the value in one sampling period before time k-1 of the change rate) from Le value N _ii ( The rolling mill by controlling the material height and the loop height at each stand exit by optimal control such that the evaluation function defined by the quadratic form of the input vector) is minimized over the entire control time. A control method characterized by controlling a height dimension and a width dimension of a rolled material discharged from a row last stand, and an optimal control using a state equation (rolling model) including a loop height. It is significantly different from the prior art that the gain is obtained and that the dimensional control method for controlling the height and width of the material at the end of the final stand by controlling the material height and the loop height of each stand at the outlet. Is different.

[0056]

As described above, it has been clarified from the embodiment that the optimum regulator control according to the present invention has excellent control performance as follows.

(1) Tension control and each stand exit side gate
In the height control of the digital calculation, the settling time is short, and the offset can be controlled to zero.

(2) The finishing stand exit side height and exit side width can be controlled so that the offset is zero.

[Brief description of the drawings]

FIG. 1 is a front view showing a structure of a looper between stands.

FIG. 2 is a block diagram schematically showing a control system according to the embodiment.

FIG. 3 is a block diagram showing a part of a control system of the embodiment in detail.

FIG. 4 is a block diagram showing the remaining portion of the control system of the embodiment in detail.

FIG. 5 is a graph showing a step response without control.

FIG. 6 is a graph showing a step response without control.

FIG. 7 is a graph showing a step response without control.

FIG. 8 is a graph showing a step response when control is performed (without monitor compensation).

FIG. 9 is a graph showing a step response when control is performed (without monitor compensation).

FIG. 10 is a graph showing a step response when control is performed (without monitor compensation).

FIG. 11 is a graph showing a step response when control is performed (without monitor compensation).

FIG. 12 is a graph showing a step response when control is performed (without monitor compensation).

FIG. 13 is a graph showing a step response without monitor compensation when the lock-on value is shifted.

FIG. 14 is a graph showing a step response without monitor compensation when the lock-on value is shifted.

FIG. 15 is a graph showing a step response without monitor compensation when the lock-on value is shifted.

FIG. 16 is a graph showing a step response when monitor compensation is performed.

FIG. 17 is a graph showing a step response when monitor compensation is performed.

FIG. 18 is a graph showing a step response when monitor compensation is performed.

[Explanation of symbols]

1: No. i stand roll 2: No. i + 1
Stand roll 3, 4: Guide roll 5: Eject roll 6: Loop height detector 7: Pass line 8, 15: Material 9: Horizontal roll of 2Hi type rolling mill 10: 2Hi Vertical roll of die rolling mill 11, 12: Roll of 3-roll type rolling mill 13: Outer dimension gauge 14: Calculator for control

Claims (1)

(57) [Claims] At least two stands on the downstream side in the rolling direction are constituted by a three-roll type rolling mill, and the upstream side thereof is constituted by a 2Hi type rolling mill, between the stands of the 2Hi type rolling mill and between the 2Hi type rolling mill and the three rolls. In a dimensional control method in continuous rolling of a bar and a wire rod by a rolling mill row in which a loop exists between stands of a rolling mill, a deviation of a roll gap [(((measured value) S _i ) − (reference value S _{0, i} ))
/ (Reference value h _{0, i} ) of the height of the cross section of the rolled material at the stand exit side) (i = 1, 2,..., N) is ΔSi *, and the deviation of the target value of the roll gap [(( Target value S _ref , _i ) − (target value reference value S
_{ref, 0, i)) /} ( to the reference value h ₀ in the height dimension of the strip cross-section at the stand exit _{side, i)] (i = 1,2} , ···, n) and [Delta] S _ref, and _i *, Deviation of forward tension of rolled material [((actual measured value t _fj )-(reference value t _{f0, j} )) / (reference value k _fmj of average deformation resistance)] (j = m, ...,
n−1) is Δt _fj *, and the deviation of the roll rotation speed [(actual measurement N
_ii ) / (reference value N _{0, ii} ) -1] (ii = 1,2,3,..., n) and their time differentials are ΔN _ii *, ΔN _ii * ' and the value of the deviation [(target value n _{ref, ii)} / (target value reference value _{n ref, 0, ii) -1} ] (ii = 1,2, ···, n) and .DELTA.N _ref, and _ii *, Deviation of rolling load [(actual value P _i ) / (reference value P _{0, i} ) -1]
(i = 0, 1, 2,..., n) is defined as ΔP _i *, and the deviation of the cross-section height of the rolled material at the exit side [(actual value h _i ) / (reference value h _{0, i} ) −1 ] (I =
0, 1, 2,..., N) is Δh _i *, where the actually measured value h _i is a gage meter formula. , And the lock-on values of the roll gap, rolling load, and cross-sectional height of the rolled material are S _{L, i} , P _{L, i} and h _{L, i} , respectively, and their deviations are ΔS _{L, i} * _, respectively. , ΔP _{L, i} * and Δh _{L, i} *, And then, the deviation Delta] h of the lock-on value of the strip section height in stand delivery side _{L, i} * the distance to the monitor compensation amount Delta] h _M, a _i * the amount delta h _i * plus, delta h _i * = delta S _i * + α _i · Δ P _i * / M _i + Δ h _{M, i} * The monitor compensation amount Δh _{M, i} * is calculated from the measured values of the deviation of the cross-section height and width of the rolled material by the rolled material cross-sectional dimension meter provided on the exit side of the stand. Based on the coefficient of influence on the height and width of the cross-sectional dimension, the value is obtained by distributing and integrating each stand, and the average temperature of the material on the entrance side of each stand, the cross-sectional height of the rolled material, and the width Each deviation [(actual value) / (reference value) -1] is calculated as ΔT _mi *, ΔH _i * and ΔB _i * (where i =
1, 2,..., N) and the deviation of the loop height of the rolled material [(actual measurement value) / (reference value) -1] is Δy _hj * (where j = 1, 2,.・, M-1
Is a stand with a loop on its exit side, l = m, ...,
n-1 the output side Le - press stand, m 3 b - the most upstream stand Le rolling mill), and the state vector _{x, x = (Δ S i} *, Δy h, j *, Δt fl *, ΔN _ii *, the ΔN _ii * ') _{T (T} denotes a transposed matrix) output vectors _{y, y = (Δ h i} *, Δy h, j *, a delta] t _fl *) _T input vector u, _{u = (Δ S ref, i} *, ΔN ref, ii *) the _T disturbance w, Heights H _i , h _i (subscript i) of the rolled material on the entrance and exit sides of each stand
= 1, 2,... N: stand NO.) Are the dimensions in the material reduction direction on the entry side and the exit side, and the widths B _i and b _i of the rolled material on the entrance side and the exit side of each stand are the entry side.
The dimension in the material width spreading direction on the exit side (for 2Hi rolls,
The dimension in the direction forming an angle of 90 ° with the rolling direction, in the case of three rolls, the dimension in the direction forming an angle of 60 ° with the rolling direction), the equation of state of rolling x (k + 1) = Ax (k) + Bu ( k) y (k) = Cx (k) k: Sample number (integer) representing time in discrete time system A, B, C: Partial differential coefficient of rolling characteristics and drive system characteristic parameters in loop rolling Using a coefficient matrix as an element, the evaluation function J The control input _{u = (Δ S ref, i} *, ΔN ref, ii *) stand number in _T i, ii is, i = 0 to n, and as it can take any combination in a range of ii = 0 to n, When i = 0, b
Control gap and the optimal input of state vector feedback to minimize the final stand (the n-th stand) in the rolling mill row. A) controlling the height and width of the rolled material discharged from the step (b).