JP2904438B2 - Tension estimation and dimensional control method for bar and wire rod rolling - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a dimensional control method by estimating and controlling a tension deviation in continuous rolling of a bar or a wire.

[Conventional technology]

2. Description of the Related Art Conventionally, there is the following example as a method of estimating and controlling the tension of a bar or a wire.

As the first example, "Kobe Steel Engineering Report" Vol 35, No.2 (1985
As shown in -4), by using a torque lever (rolling torque / rolling load) memory method, the torque lever is approximated to be constant, and the initial setting of the stand is performed until the tip of the rolled material bites into the next stand. There is a tip tension control in which the number of rotations is corrected and the tension is controlled to be zero.

As a second example, as shown in the above-mentioned document, the torque lever (rolling torque / rolling load) memory method is used to approximate the torque lever to a constant value so that the leading end of the rolled material is applied to all the stands in the rolling mill row. After biting, there is a full-length tension control in which the tension is sequentially estimated from the upstream side by a torque formula, and non-interference control is performed so that each stand roll rotational speed is operated without any tension as an operation amount.

As a third example, as shown in the above-mentioned reference and Japanese Patent Application Laid-Open No. 60-121015, a deviation from a target tension is calculated using a measured value of the width of the rear surface of a rolling row and an influence coefficient of the tension on the width. There is a residual tension correction method of estimating the roll tension or the roll gap as an operation amount and controlling the target tension.

As a fourth example, the present inventors previously proposed in Japanese Patent Application Laid-Open No. 1-71512, added the stand tension deviation at the time of lock-out on each stand side for each lock-on, and estimated the absolute tension value. , There is a way to control.

In the method of the first example, the calculation error of the loss torque, the disturbance (input material temperature and dimensional fluctuation) or the operation amount (roll gap)
Is large, the tension estimation accuracy is reduced by approximating the torque arm length to a constant value.

In the method of the second example, the accuracy of estimating the tension is reduced due to the above-mentioned reason and the error of the coefficient indicating the relationship between the tension torque and the front and rear tensions. In addition, since the estimation is performed sequentially from the upstream stand to the downstream stand, the estimation error increases in the downstream stand.

In the method of the third example, the estimation accuracy is higher as the tension between the downstream stands has a greater influence on the product size, and it is considered to be effective as an aid to the method of the second example.

In the method of the fourth example, a tension estimation error is sequentially added from an upstream stand lock-on to a downstream stand lock-on due to an error of an influence coefficient of the tension on a rolling load and a rolling torque, and the like. The estimation accuracy may be insufficient due to the accumulation of the tension estimation error.

[Problems to be solved by the invention]

The present invention relates to continuous rolling of steel bars and wire rods. (1) Accurately estimating the tension deviation between each stand from the time of lock-on at the exit of each stand, and (2) the final stand exit height, It is an object of the present invention to perform multivariable control with good controllability with a short settling time and zero offset for the outlet side width.

[Means for solving the problem]

The present invention provides: (1) differentiating the rolling torque formula, taking into account the rolling load, the influence coefficient of the tension on the rolling torque, and the change in the torque arm length; , Material width), and a tension deviation estimating method characterized in that each stand tension deviation from each stand lock-on is calculated using actually measured values for the influence coefficient of the roll gap, and (2) the tension of (1) Using the rolling state equation consisting of deformation, load, and temperature using the estimated values, the number of roll rotations and the distance between rolls are used as operation amounts, and each stand taking into account the tension between monitors and monitor compensation of the target rolling mill group. Based on the optimal regulator theory, calculate the outlet gauge height
A dimensional control method in bar and wire rod rolling, wherein the control is performed by feedback of a control deviation and a state vector.

That is, the contents of claim (1) are described in "Kobe Steel Engineering Reports" Vol 35, No. 2 (1985-4).
Example, a problem in the tension estimation method of the second example, a calculation error of the loss torque, an error of approximating the torque arm length to a constant value, and a tension due to an error of a coefficient representing a relationship between the tension torque and the front tension and the rear tension. Accumulation of the estimation error and the estimation error at the downstream stand by sequentially calculating the tension estimation value from the upstream stand to the downstream stand, and the tension due to the error of the coefficient of influence of the tension on the rolling load and the rolling torque in the tension estimation method of the fourth example. Accumulation of the estimation error after the downstream stand lock-on by sequentially adding the estimation error from the upstream stand lock-on to the downstream stand lock-on is obtained from a minute physical quantity deviation from the lock-on when the rolling load is applied. Estimating only a small tension deviation from lock-on, taking into account changes in torque arm length, Minimized by the tension estimation error was partitioned entire stand by square method, in which so as to increase the tension estimation accuracy.

The content of claim (2) is based on the control method proposed by the inventors in Japanese Patent Application No. 61-15207 using the estimated tension value obtained by the method described in (1). As a result, the settling time for the final stand exit side height and exit side width is short,
Multi-variable control with good control performance with zero offset is performed.

In this case, the average value of the absolute value of the tension in the billet is set to no tension by the tensionless setup by correcting the number of roll rotations between billets.

Therefore, the tension control method of the present invention in which the estimated value of the tension deviation from lock-on is controlled to 0 has an effect of AGC (dynamic control for operating the roll gap during rolling) and a finish width control effect on the input side dimension disturbance.

[Action]

In the item (1) of the present invention, the differential type of the rolling torque formula is used. Assuming that the matrix expression AX = B and the weight matrix is W, the estimated value of the tension deviation from the lock-on value on the exit side of the No.n stand by the solution of the least squares method X = (A ^T WA) ^-1 A ^T WB Δ fi ^* Alternatively, the tension deviation estimated value ΔfL ^* j, i from the lock-on value on the exit side of the No.j stand when the tip of the material is engaged with the No.j stand is obtained. The tension deviation estimated value Δf ^* i at the time of trailing edge removal of the material is similarly obtained.

(Here, Δf ^* i = ΔfL ^* j, ii = 1 to n−1), it is possible to realize a highly accurate tension deviation estimation from the time of biting the front end of the material to the time of pulling out the rear end of the material.

In the second aspect of the present invention, the evaluation function Control input u (k) that minimizes
(K) and feedback of partial state vector xs (k) u (k) = − F ₁ e (k−1) −F ₂ [e (k) −e (k−
1)] − F ₃ [xs (k) −xs (k−1)] + u (k−1) Since a plurality of inputs are obtained at the same time, a control system having good control performance can be designed relatively easily.

〔Example〕

Hereinafter, details of the present invention will be described in detail based on examples. The symbols used in the basic formula of tension deviation estimation / control + AGC are shown below. FIG. 1 shows a schematic diagram of four-stand continuous rolling.

Symbol Hi, hi: Stand entry side, exit side material height mm Bi, bi: Stand exit side, exit side material width mm Ai, ai: Stand entrance side, exit side material cross section mm ² Tmi: Stand entrance side, entrance Average side material temperature ℃ Si, Sref, i: Set roll gap, set roll gap target value mm Ni, Nref, i: Roll rotation speed, roll rotation target value rpm t fi: Forward tension kg / mm ² k fmi: Average Deformation resistance kg / mm ² Pi: Rolling load ton Gi: Rolling torque ton ・ m Ki: Mill stiffness ton / mm αi: Scale factor Subscript i: Stand No. ₀ : Standard condition L: Lock-on value
Using 4) as an example, the following three stages will be described: (1) when the front end of the material is caught, (2) when the entire intermediate portion of the stand is caught, and (3) when the rear end of the material is pulled out.

The estimation of the tension deviation at the time of biting of the material tip is as follows. In FIG. 2, the time indicates the lock-on time on the exit side of the No. 1 stand. The lock-on values of the rolling load and rolling torque of the No. 1 stand are PL ₁ , ₁ , GL ₁ , ₁ . No.1 stand forward tension at time Is obtained by equation (1).

Estimated value Δf of No.1 stand tension deviation at time
₁ ^* is a solution obtained from equation (2) using only one stand equation or a solution obtained from equation (3) using weighted least squares method. It is.

Ie In the matrix A, B, X Weight matrix (diagonal matrix) From the equation (1), AX = B (two equations) ... (3) In contrast, two equations are given. To solve this, either solve from the physical quantity of the No. 1 stand alone, or
Solve so that the expected value of the square of the error by the multiplicative method is minimized. In the least-squares method, X = (A ^T WA) ⁻¹ A ^T WB (4) Therefore, the estimated value Δf of the No. 1 stand tension deviation
₁ ^{* _{is, Δ f 1 * = Δ fL}} 2, * 1 ... (5) Similarly, the estimated value of No.i stand tension deviation time delta f
i ^* is as shown in equation (6).

Next, the estimation of the tension when the entire intermediate portion of the stand is caught is as follows. The estimated value of No.i stand tension deviation at the time Δ fi ^* is tension deviation from the time Δ fL ₄ ^*, i (≡
Δfi ^* ). The estimated value Δ fi ^* of the tension deviation is obtained from Expression (7), and Expression (8) obtained by solving the matrix expression (7 ′) by the least square method.

When expressed in a matrix, AX = B (n equations) (7 ′) X = (A ^T WA) ⁻¹ A ^T WB (8) where W: weight matrix Subscript T: transpose of matrix −1: inverse matrix Δf ₁ ^* = ΔfLn ^* , i (9) (i = 1 to n−1) Next, the estimation of the tension at the time of the rear end removal of the material from time to time is as follows. When the rear end of the material has passed through the butt of No. j stand, the tension in front of No. 1 to j stand is Δt fi ^* = 0.
Since (i = 1 to j), No.j + 1 to n-1 stand front tension may be estimated. No.i (i = j + 1 to n-
1) The estimated value Δfi ^* of the stand tension deviation is a tension deviation ΔfL ^* from the time similarly to the estimation of the tension of the intermediate material ^.
₄ , i (≡Δfi ^* ). The tension value deviation Δfi ^* is obtained as follows. In this case, the physical strengths such as the rolling load and the rolling torque also have j + 1 to n-1 stands.
The matrix of equation (7) is a matrix composed of some elements A (l, m), X (m, 1), B (l, 1), W (l, l) l = j + 1 to n, m = j + 1 .About.n-1, j = 1.about.n-2, and the equation (7 ') is nm equations. The estimated value Δ of the tension deviation is obtained by the equation (8) solved by the least square method.
fi ^* is found. Therefore, the estimated value of the tension deviation is Δfi ^* = ΔfL ^* n, i (10) (i = j + 1 to n−1, j = 1 to n−2) ΔTmi ^* , Is an actually measured value or a calculated value in consideration of a material transfer delay between stands. The average temperature on the i-stand entry side at the time k is ΔTmi ^* (k) = βi ΔTmi ^* −1 (k−li−1) (11) where βi: correction coefficient li−1: i−1 to i-i transfer between stands Delay The entry side height is However, if there is no dimension measuring device between the stands, Is unknown and set to 0.

The entry width is Is determined from the gauge meter calculated height. Also, rolling load,
Table 1 shows the measured values of the influence coefficient of the tension on the rolling torque.

Table 2 shows the measured values of the influence coefficient of the disturbance and the roll gap on the torque arm length.

Next, a description will be given of a tension deviation estimation control + gauge meter AGC control system based on the optimal regulator theory using the tension deviation estimation value. As a mill driving system dynamic characteristic, a roll gap control system is approximated by a first-order system, and a roll rotation speed control system is approximated by a secondary system (symbols are as described above).

When the non-linear rolling model is linearized and dimensionless around the reference state (Table 3) and displayed as a state space model, and further discretized at the control period Δt, the following state equation is obtained. Here, Δx is a variation from the path schedule value x ₀ , Where Also, Is the deviation from the lock-on value ΔxL ^* in the gauge meter calculation.

x (k + 1) = Ax (k) + Bu (k) + Ew (k) (14) y (k) = Cx (k) + Pw (k) (15) where the state vector x, output y, and disturbance w are It is like. Here, Δfj ^* is a tension deviation estimated value.

i = 1 to n, j = 1 to n, n: number of stands A discrete-time optimal control system was designed by applying optimal control theory to this system. That is, assuming that the disturbance w is step-shaped, the evaluation function Is the control input u (k) is u (k) = − F ₁ e (k−1) −F ₂ [e (k) −e (k−
1)] − F ₃ [xs (k) −xs (k−1) + u (k−1) (21) Here, the control deviation e, the partial state xs, and the first order difference v of the input u are And the optimal gain matrix F = [F ₁ : F ₂ : F ₃ ] is obtained from the following Riccati equation:

F = (R + G ^T PG) ^-1 G ^T PΦ (25) P = Φ ^T PΦ−Φ ^T PG (R + G ^T PG) G ^T PΦ + H ^T QH (26) where the matrices Φ, G and H are System (14), (15)
X (k + 1) = ΦX (k) + Gv (k) (27) e (k) = Hx (k) (28) X (k) = [e ^T (k−1), e ^{T (k) -e T (k} -1), xs
^T (k) −xs ^T (k−1)] ^T (29) The coefficient matrix is obtained from the matrices A to C. Here, the optimal control system of the discrete time system is derived, but if the rolling state equations (14) and (15) are given in the continuous time system, the optimal control system 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. 3 for wire rod and bar rolling is constructed. FIG. 3 shows an embodiment of a final four-stand mill among all n stands. The control computer 6 Rolling torque Finishing stand exit height Δh ₄ ^* , exit side width Δ by dimension gauge 5
b ^* ₄ , No.1 stand entrance height by mill entrance thermometer 8 The sample is calculated for each stand exit gauge meter height The tension deviation estimated value Δfj ^* is obtained, the optimum control input u (k) given by the equation (21) is calculated, and the roll clearance set value Δ
ref ^* , i and the roll rotation speed setting value Δ gap ref ^* , j are output to the roll clearance control system and the roll rotation speed control system, respectively.

Here, the calculated height of the gauge at the outlet of each stand Is Is calculated by However, Is the dimensionless mill constant αi scale factor. The first term on the right side of equation (30)
The second term is a known gauge meter type, and the third term on the right side is ΔhM
^* , I is monitor compensation to give absolute dimensional accuracy.

The monitor compensation ΔhM ^* , i is obtained by the following procedure. Size five finishing stand delivery side height Delta] h ^* _4, from the sample values of the outgoing side width [Delta] b ₄ ^*, the reader stands and finishing stands (in the present embodiment No.3, No.4 stand) exit side height monitor Correction amounts Δhx, ₃ ^* , Δhx, ^* ₄ Is calculated by However, the coefficients K ₁ and K ₂ are calculated using the influence coefficient. Given by Next, the monitor compensation ΔhM, ^* i (k) is the correction amount Δhx,
^* ₃ (k), Δhx, ^* ₄ (k) More required. Here, Ti is the material transfer time (second) from the No. 1 stand to the exit dimension meter, and KM, i is the monitor compensation integral gain.

The weights Q and R in equations (25) and (26) and the monitor compensation integral gain KM, i in equation (35) were determined by repeating the simulation.

Next, as an example of the tension estimation / control + AGC, a description will be given of loopless rolling of a final four stands of a steel bar mill finishing size of 80φ.

In this case, the # 4 and # 5 stands are empty passes, and the finishing stand is # 10 stand.

Table 4 shows the control conditions. The control system was divided into subsystems for every four stands in order to prevent a decrease in the accuracy of the simulation when designing the controller and to shorten the online calculation time.

In the case of 80φ, the range of the tension control is the # 6 to # 9 stand front tension. The range of AGC is the last two stands.

 The procedure of the control input calculation is as follows.

1) The optimal gain matrix is stored in the computer.

2) The optimum input calculated from the calculated value, the estimated value of the output vector, the measured value of the partial state vector and the gain is output from the program controller to the programmable controller.

The control law includes a proportional / integral operation regarding a control deviation and a proportional operation regarding a partial state.

The response of the material temperature to the periodic disturbance was measured for the 80φ loopless rolling of a steel bar mill without and with control. In addition, the relationship between finish material temperature fluctuation and finish width fluctuation was grasped.

The response without control to the finished (# 10) material temperature fluctuation ΔT ₁₀ = 48 ° C. is shown in FIGS. 4 to 6. FIG. 4 shows the finishing material temperature T ₁₀ , and FIG. 5 shows No. 7 to No. 9 stand front tension deviation estimated value Δf _7.
^{* To} Δf ₉ ^* , and FIG. 6 is an illustration of the finish height Δh ₁₀ and finish width Δb ₁₀ . The variation of the height on the exit side of the finishing stand was Δh ₁₀ = 0.13 mm, and the variation of the exit side width was Δb ₁₀ = 0.30 mm. The response of the tension-free setup + # 6 # 9 forward tension Estimation and Control + Last 2 stand gauge meter AGC for finishing material temperature T ₁₀ = 49 ° C. from Figure 7 are shown in 12 FIG.

FIG. 7 shows the finish material temperature T ₁₀ , and FIG. 8 shows No. 7 to No. 9 stand front tension deviation estimated value Δf _7.
^{* To} Δf ₉ ^* , Fig. 9 shows the finish height Δh ₁₀ , finish width Δb ₁₀ , Fig. 10 shows the roll rotation N _{7 to} N of the No. 7 to No. 9 stands
₉ and FIG. 11 show the roll gaps ΔS ₉ and ΔS of the No. ₉ to No. 10 stands.
S _10, the rolling load P ₆ in FIG. 12 No.6~No.10 stand, P _7, P _8, P
₉ is an illustration of a P _10.

Although a step disturbance was assumed when designing the control system, it can sufficiently follow a sine disturbance. The variation of the height on the exit side of the finishing stand was Δh ₁₀ = 0.07 mm, and the variation of the exit side width was Δb ₁₀ = 0.20 mm. Further, in the front and tail portions of the material, the variation in the finishing width is reduced by the tensionless setup. Estimation of tension deviation
By the control + final two stand gauge meter AGC, the fluctuations of the height and width of the exit of the finishing stand can be controlled to Δh ₁₀ ≦ 0.10 mm and Δb ₁₀ ≦ 0.25 mm even when the material temperature varies greatly.

FIG. 13 shows the relationship between the variation in the finishing material temperature and the variation in the finishing width. In the case of only tensionless setup between billets, the finish width variation is 0.3 to 0.4 mm when the temperature variation is 50 to 55 ° C, but tensionless setup + tension estimation and control in billet + AGC
The variation of the finishing width is 0.2 to 0.2 when the temperature variation is 50 to 55 ° C.
It can be seen that precision rolling can be realized even if the temperature fluctuation is large, reduced to 0.25 mm.

The measurement results of the above responses confirmed the effectiveness of this control method in bar and bar rolling.

〔The invention's effect〕

As described above, in the case of this embodiment according to the present invention, it has been clarified that the control by the optimal regulator using the estimated value of the tension deviation has excellent estimation / control performance as follows.

(1) Tension deviation estimation accuracy is good.

(2) The tension control using the estimated value of the tension deviation and the height control of each stand exit side gauge meter can be controlled with high response.

(3) Fluctuation of the height and width of the outlet on the finishing stand can be controlled to 0.2 mm or less in the normal operation range (finishing temperature fluctuation 40 ° C or less).

In this embodiment, the estimation and control of the tension deviation at the time of removing the buttocks of the material intermediate portion and the rear end of the material + the gauge meter AGC are described. By using the estimated value and setting the operation amount of the stand where the material is not rolled to 0 in the above-mentioned optimum control input {Equation (21)} applied to the material intermediate portion, similarly, tension estimation / control + gauge meter Size control by AGC is possible.

In this embodiment, the loopless continuous rolling is described. However, even when there is a loop between stands, if a state equation is formed using a relational expression between the loop height and the rolled material tension, the loop of the present invention can be formed. Estimation of tension deviation
Control + AGC is possible. As another method, dimensional control can be performed by a method of measuring and controlling a loop height corresponding to a tension in the embodiment of Japanese Patent Application No. 61-87706 filed by the present inventors.

The tension estimation / control method of the present invention can be applied to a hot plate rolling, a cold plate rolling, and a shaped steel in the same manner.

[Brief description of the drawings]

FIG. 1 is a schematic diagram of four-stand continuous rolling, FIG. 2 is a schematic diagram showing a tension estimating method at each time, FIG. 3 is a configuration diagram showing an embodiment of the present invention, FIG. 4, FIG. 6 Figure finishing material temperature T ₁₀ in the case without control, Nanba7～nanba9 stand forward tension deviation estimate Δ
f ₇ ^* ~Δf ₉ ^*, illustration of the response of a finished height Delta] h _10, the finishing width [Delta] b _10, FIGS. 7, FIG. 8, FIG. 9, FIG. 10, FIG. 11 and FIG. 12, No .6~No.9 finishing material temperature T ₁₀ in the case of the stand front tension deviation estimation and control + gauge meter AGC, No.7~No.9 stand forward tension deviation estimate Δf ₇ ^* ~Δf ₉ ^*, finish height Δh ₁₀ , finishing width Δb ₁₀ , No. _{7 to} No. ₉ stand roll rotation speeds N _{7 to} N ₉ , No. ₉ to No. 10 stand roll gaps ΔS ₉ , ΔS
_{10, No.6~No.10} stand rolling load _{P 6, P 7, P 8} , P 9, P 10
FIG. 9 is a view for showing an example of the response. FIG. 13 is a graph showing a relationship between a change in finish material temperature and a change in finish width. 1,3: Horizontal roll, 2, 4: Vertical roll 5: Inlet dimension gauge, 6: Control computer 7: Material, 8: Inlet thermometer 9: Inlet dimension gauge

Claims (2)

(57) [Claims] In a continuous rolling of a bar and a wire rod by a rolling mill row, a deviation of a roll interval at each of the stands constituting the rolling mill row [(actual measured value Si) − (reference value S ₀ , i)] / (stand out). The reference value h ₀ , i) of the height dimension of the cross section of the rolled material on the side i = 1,2, ..., n, where n is the number of stands in the rolling mill row, and the deviation of the forward tension of the rolled material (stand exit side tension) [(forward tension t fi)-(reference value tf ₀ , i) ] / (Reference value k fmi of average deformation resistance) is defined as Δt fi ^*, and deviation of back tension (stand side entrance tension) of the rolled material [(back tension t bi) − (reference value tb ₀ , i)] / (Reference value k fmi of average deformation resistance) is defined as Δt bi ^*, and the deviation of rolling load [(actual load Pi) / (reference value P ₀ , i) −
1] is defined as ΔPi ^*, and deviation of rolling torque (actual value Gi) / (reference value G ₀ , i) −1
Is defined as ΔGi ^*, and the deviation [(actual measured value hi) / (reference value h ₀ , i) −1] of the cross-sectional height of the rolled material on the exit side is defined as Δhi ^*. Hcal, i + Si + αiPi / Mi Hcal, i: Caliber depth Si: Roll interval αi: Scale factor Pi: Rolling load Mi: Mill stiffness The lock-on value of variable xi is xL, i, and its deviation is ΔxL, i ^{* =} [(lock-on value xL, i) / (reference value x _0, i) -
1], and the deviation of the variable xi from the lock-on value xL, i is Δi ^* = Δ
xi ^* −ΔxL, i ^* , where the physical quantities of the variable xi are as follows: xi = (t fi, Gi, Pi, Tmi, Hi, Bi, Si) t fi: forward tension Tmi: input material Average temperature Hi: Inlet material height Bi: Inlet material width Average temperature Tmi of material at each stand entry side, deviation of rolled material cross-sectional height dimension Hi, width dimension Bi ΔTmi ^* , ΔHi ^* , ΔBi ^*
Is the actual measured surface temperature Ts1 of the thermometer installed on the entrance side of the NO.1 stand + the calculated value of the difference between the average temperature and the surface temperature ΔT1 (= Tm1-
Ts1), a relational expression representing the material transfer delay between stands in which the measured values H1, B1 of the dimension meter and the material height and the material width are alternately changed for each stand ΔTmi + 1 ^* (k) = αiΔTmi ^* (k-li) ΔHi + 1 ^* (K) = Δbi ^* (k-li) ΔBi + 1 ^* (k) = Δhi ^* (k-li) k: time of discrete time system li: No.i to i + 1 of discrete time system Material transfer time between stands αi: Calculated value obtained from the calculated value of the material temperature change between the roll bite and the stand Δbi ^* : deviation of the material width on the outlet side = [(calculated value bi) / (reference value)
bo, i) -1] Δhi ^* : Deviation of the material height on the delivery side = [(calculated value hi) / (reference value ho, i) -1], which is the value calculated from rolling load Pi and rolling torque Gi. The influence coefficients of the forward tension t fi and the rear tension t bi And the influence coefficient of the input material average temperature Tmi, the input material height Hi, the input material width Bi, and the roll gap Si with respect to the torque arm length li, And the differential form of the rolling torque formula In the matrix A, B, X, And the weight matrix (diagonal matrix) is Where x = A ^-1 B or the solution of the least squares method x = (A ^T WA) ^-1 A ^T WB, where (-1 is the inverse matrix and T is the transposed matrix) ), And in the method of obtaining the estimated value of the tension deviation Δ fi ^* , when the tip of the material bites,
Before No.j + 1 stand lock-on, the sub-matrices A (l, m), x (m, 1), B (l, 1), W (l, l), l of the matrices A, x, B, W = 1
From i, m = 1 to j−1, j = 2 to n−1, an estimated value Δfi ^* of the tension deviation is obtained as follows: ΔfLj, i ^* is output from the No.j stand. Assuming that the estimated value of the No. i stand tension deviation from the side lock-on time is Δfi ^* = ΔfLj, i ^* (i = 1 to j, j = 1 to n−1), the matrix A ( n, n-1), x (n-1,1), B (n, 1), W
When ΔfLn, i ^* from (n, n) is the estimated value of the No.i stand tension deviation from the lock-on on the exit side of the No.n stand during continuous rolling of all stands in the middle of the material, Δ fi ^* = .DELTA.fLn, i ^* (i = 1 to n-1). When the rear end of the material is removed, the sub-matrix A (l, m), x (m, 1), B (l, 1), W
(L, l) l = j + 1-n, m = j + 1-n-1, j = 1-n-
From equation (2), when ΔfLn, i ^* is the estimated value of the No.i stand tension deviation from the time when the No.n stand exit side lock-on is performed, Δfi ^* = ΔfLn, i ^* (i = j + 1 to n−1, j = 1
n-2) A method for estimating a tension deviation in a rolling of a steel bar and a wire rod, wherein the estimated value of the tension deviation Δfi ^{* is obtained} by: 2. Using the tension deviation was determined by the method of claim 1 estimate delta fi ^*, the state vector ^{x, x = (Δi *,} Δ fj *, ΔNi
^* , Δi ^* ) ^T , output y = (Δi ^* , Δfi ^* ) ^T input u = (Δref, i ^* , ΔNref, j ^* ) ^T disturbance w = (ΔTmi ^* , ΔHi ^* , ΔBi ^* ) ^T roll interval , Rolling load, and lock-on value of the rolled material cross-section height, respectively, are SL, i; PL, i; hL, i, and their deviations are, respectively, ΔSL, i ^* ; ΔPL, i ^* ; Δh
^{L, i *, ΔSL, i} * = (SL, i-S 0, i) / h 0, i ΔPL, i * = (PL, i-P 0, i) / P 0, i ΔhL, i * = _{(hL, i-h 0,} i) / h 0, i hL, i = Hcal, i + SL, i + αiPL, and i / Mi, the deviation of the strip section height in stand delivery side .DELTA.hi ^*,
Deviation Δh of lock-on value of cross section height of rolled material on exit side
The amount Δ obtained by adding the monitor compensation amount ΔhM, i ^* to the distance of L, i ^*
the ^{i *, Δi * = Δi *} + αiΔi * / Mi * + ΔhM, i * Δi * = ΔSi * -ΔSL, i * Δi * = ΔPi * -ΔPL, i * Mi * = h 0, i · Mi / P 0 , i, where the monitor compensation amount 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, the amount of reduction at each stand is calculated as Based on the coefficient of influence on the width dimension, values obtained by distributing and integrating to each stand, ΔNi ^* , Δi ^* : deviation of roll rotation speed [(actual value Ni)
/ (Reference value N ₀ , i) -1] and its derivative i = 1,2, ..., n j = 1,2, ..., n-1 where n is the number of stands in the rolling mill row. Equation of state x (k + 1) = Ax (k) + Bu (k), y (k) = Cx (k), k:
Using the sample number (integer), the following evaluation coefficient J, The height and width of the rolled material discharged from the last stand (the nth stand) in the rolling mill train are controlled by the control deviation and the optimal input of the state vector feedback that minimize the following. Do
Dimension control method in rolling of steel bars and wire rods: Here, when the front end of the material is bitten or the rear end of the material is pulled out, the operation amount of the stand where the material is not rolled is set to 0.
The stand number i, j in the control input u = (Δref, i ^* , ΔNref, j ^* ) can be any combination within the range of i ≧ 0 to n, j ≧ 0 to n. When ≧ 0,
The roll gap is not used as an operation amount, and when j ≧ 0, the roll rotation speed is not used as an operation amount.