JPH0794045B2 - Dimension control method in wire rod and bar rolling - Google Patents

Description

TECHNICAL FIELD The present invention relates to a dimensional control method in continuous rolling of wire rods and bars.

[Conventional technology]

Conventionally, there are the following prior arts regarding a dimension control method in continuous rolling of a wire rod and a steel bar.

As a first example, for example, “Plasticity and Machining” vol.20, No.22
4 (1979.9), the tension of the material in the steel bar rolling mill is directly detected, and the deviation of this detected value from the target value is calculated to determine the material tension between rolling mills in the continuous rolling mill train. In consideration of the influence, there is a technology for performing proportional / integral control of material tension with the operation number of the rolling roll.

As a second example, as disclosed in, for example, Japanese Patent Application Laid-Open No. 54-128469, a common drive block mill for finish rolling of wire rods is used by using the coefficient of influence of the reduction amount of a rolling roll on the product width dimension. Deviation from the target value of the measured value of the cross-sectional dimension of the product, which is the vertical dimension of the product with the rolling amount of the rolling roll in the final stand as the operating amount, and the product width dimension with the rolling amount of the rolling roll in the first stand as the operating amount. There is a technology for proportional control.

As a third example, as disclosed in, for example, JP-A-57-88908, between No. 1 stand and No. 2 stand-No. N stand in a common drive block mill for finish rolling of wire rods. By changing the relative speed of the material at No.1 to No.2 stand, the material width is measured at the stand exit side of any of No.2 to No.n stands. There is a technique for controlling the product width according to the deviation of the value from the target value.

As a fourth example, using the rolling equation of state consisting of material deformation in rolling, rolling load, and material temperature proposed by the inventors in Japanese Patent Application No. 59-218111 (Japanese Patent Publication No. 2-59002). There is a technology that controls the cross-sectional height and width of the rolled material on the exit side of the last stand of the rolling mill train by the feedback of the state vector based on the optimal regulator logic, using the rolling roll speed and the rolling roll gap as the manipulated variables. .

However, these prior arts have the following problems.

In the technique described in the first example, the determination of the gain in control is made by trial and error, and its optimization is limited.

In the technique described in the second example, the influence coefficient of the reduction amount of the rolling roll on the product width dimension is used as the proportional gain, but the control performance is unknown.

In the technique described in the third example, the specific gain determination method is not disclosed in Japanese Patent Laid-Open No. 57-88908, and the control performance is unknown.

The technology described in the fourth example is a control for feeding back a state vector based on an actual measurement value of the cross-sectional dimension of the rolled material by a dimension gauge provided on the final stand exit side of the rolling mill train. The control operation is delayed by the dead time due to the distance to.

[Problems to be Solved by the Invention]

INDUSTRIAL APPLICABILITY The present invention, in continuous rolling of wire rod and bar steel, has a short settling time and good control performance with zero offset when controlling the height dimension and width dimension of the rolled material cross section on the final stand exit side of the rolling mill train. It is an object of the present invention to provide a dimension control method in wire rod / bar steel rolling that performs multivariable control.

[Means for Solving the Problems]

A feature of the present invention is that in continuous rolling of a wire rod / bar steel by a rolling mill train, deviations between rolling rolls and gaps in each stand constituting the rolling mill train are ΔS _i ^* , ΔS _i ^* = (S _i − S _{o, i} ) / h _{o, i} i = 1,2, ..., n where, S _i : Rolling roll measured in the i-th stand versus gap S _{o, i} : Rolling roll in the i-th stand Reference value of clearance gap h _{o, i} : Reference value of height dimension of rolled material cross section on the exit side of the i-th stand The deviation of the forward tension of the rolled material is Δt _fj ^* , Δt _fj ^* = (t _fj −t _{fo, j} ) / K _{fmo, j} j = 1,2, ..., n-1 where t _fj : actual measured value of the forward tension of the rolled material at the j-th stand exit side t _{fo, j} : j-th stand exit side The standard (target) value of the forward tension of the rolled material at k _{fmo, j} : The standard value of the deformation resistance of the rolled material at the j-th stand. The deviation of the rolling speed of the rolling roll is ΔN _j ^* , and its time derivative is Δ _j ^* , ΔN _j ^* = (N _j / N _{o, j} ) −1 j = 1,2, ..., n−1 where N _{j is} the measured value of the rolling speed of the rolling roll at the j-th stand N _{o, j} : Standard value of rolling roll speed at j-th stand The deviation of rolling load is ΔP _i ^* , ΔP _i ^* = (P _i / P _{o, i} ) −1 i = 1,2, ..., n Here, P _i : Measured value of rolling load at the i-th stand P _{o, i} : Reference (target) value of rolling load at the i-th stand The deviation of the rolled material cross-sectional height dimension at the stand-out side of each stand is Δ.
h _i ^* , Δh _i ^* = (h _i / h _{o, i} ) −1 i = 1,2, ..., n where, h _i : Actual measurement of rolled material cross-section height dimension on the exit side of the i-th stand Value, h _{o, i} : Reference value of the height dimension of the cross section of the rolled material on the exit side of the i-th stand (where h _i is the gauge meter formula h _i = H _{cal, i} + S _i + α _i · P _i / M a value obtained by _i, H _{cal, i:} caliber of i-th rolling rolls in stands (grooved) depth S _i: measured value of the rolling roll pair gap in the i-th stand alpha _i: i-th stand Scale factor P _i : Actual measurement of rolling load at the i-th stand M _i : Mill rigidity at the i-th stand Roll roll gap at the i-th stand, rolling load and rolled material cross section at the exit side of the i-th stand The lock-on values of the height dimension are S _{L, i} , P _{L, i} and h, respectively.
_{L, i} (h _{L, i} = H _{cal, i} + S _{L, i} + (α _i · P _{L, i} ) / M _i ),
The deviations of the gap between the rolling roll in the i-th stand, the rolling load, and the lock-on value of the cross-sectional height dimension of the rolled material on the exit side of the i-th stand are ΔS _{L, i} ^* , ΔP _{L, i} ^*, and Δh _{L. , i} ^* , ΔS _{L, i} ^* = (S _{L, i} −S _{o, i} ) / S _{o, i} ΔP _{L, i} ^* = (P _{L, i} −P _{o, i} ) / P _{o, i} Δh _{L , i} ^* = (h _{L, i} −h _{o, i} ) / h _{o, i} Deviation Δh _{i of} cross-sectional height dimension of rolled material on the stand-out side of each stand
^* And the deviation Delta] h L of the lock-on value of the strip cross-sectional height in each stand outlet _{side, i} ^* monitor compensation amount on the distance in from Delta] h _M, the amount was added ^{_{i * Δ i *, Δ i}} * = Δh _i ^* −Δh _{L, i} ^* = Δ _i ^* + α _i · Δ _i ^* M _i ^* + Δh _{M, i} ^* i = 1,2, ..., n where Δ _i ^* = ΔS _i ^* −ΔS _{L ^{, i * Δ i * = ΔP}} i * -ΔP L, i * M i * = h o, i · M i / P o, i monitor compensation amount Δh _M, ^{i *:} provided on the delivery side of the rolling mill train From the measured deviations of the height and width dimensions of the rolled material measured by the rolled material cross-sectional dimension meter, the amount of reduction at each stand in the rolling mill train is determined by the height and width dimensions of the rolled material cross-section on the exit side of the finishing stand. Based on the influence coefficient on
Value obtained by distributing to each stand and integrating, the average temperature of the material on the entrance side of each stand, the deviation of the height dimension and the width dimension of the rolled material cross section, ΔT _mi ^* , ΔH _i ^* and ΔB _i ^* , ΔT _mi ^* = ΔT _mi / T _{mO, i} ΔH _i ^* = ΔH _i / H _{o, i} ΔB _i ^* = ΔB _i / B _{o, i} i = 1,2, ..., n State vector x, output vector y, input Let the vector u be x = (Δ _i ^* , Δt _fj ^* , ΔN _j ^* , Δ _j ^* ) ^T, where T means the transposed matrix.

y = (Δ _i ^* , Δt _fj ^* ) ^T u = (Δ _{ref, i} ^* , ΔN _{ref, j} ^* ) ^T i = 1,2, ..., n j = 1,2, ..., n-1 Here, ΔS _{ref, i} ^* : Target value of set rolling roll-gap in the i-th stand ΔN _{ref, j} ^* : As the target value of the set roll speed in the j-th stand, the control input is determined when designing the control system. Rolling state equation x (k + 1) = Ax (k) + Bu (k) y (k) = Cx (k) Here, k is an evaluation function J using a step number (integer) that represents the time of a discrete time system. The height and width dimensions of the rolled material discharged from the last stand (nth stand) in the rolling mill train are controlled by the optimum input consisting of the output vector (control deviation) and the feedback of the state vector that minimize Dimension control method in rolling rod and bar steel characterized in that Here, Q, R: weight matrix e (k) = r (k) -y (k), r (k) = O: target value, v (k) = u (k) -u (k-1) the control input ^{_{u = (Δ ref, i *}} , ΔN ref, j *) stand number i, j in ^T is, i = O~n, take any combination within the range of j = O~n-1 If i = O, the roll gap is not the manipulated variable, and if j = O, the roll gap is not the manipulated variable.

Hereinafter, the present invention will be described in detail.

INDUSTRIAL APPLICABILITY In the continuous rolling of wire rods and bar steels, the present invention uses a state equation consisting of deformation of the rolled material, load of the rolled material, and temperature of the rolled material, and the rolling speed of the rolling roll and the roll gap as the manipulated variables. Based on the optimal regulator theory, the calculated values of the cross-sectional height dimension of the rolled material at the outlet side of each stand in consideration of the rolling material tension between each stand in the machine train and monitor compensation are fed back of the control deviation and the state vector based on the optimal regulator theory. It is characterized by the point that it is controlled by. That is, the present invention, the present inventors have proposed in Japanese Patent Application No. 59-218111, rolled material cross-sectional shape, the problem in the control method of the dimension, the distance from the finishing stand to the rolled material cross-sectional dimension meter By replacing the control operation delay caused by the above with the calculated value by the gauge meter method used in the strip rolling field as a means to measure the cross-sectional dimension of the rolled material released from the finishing stand, the response speed of feedback can be improved. It is a solution that is raised.

In the present invention, the evaluation function The optimum control input u (k) that minimizes
In the feedback process of (k) and the 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)] + at the same time because a plurality of input is determined as u (k-1), can be relatively easily designed to better control system control performance it can.

In the control based on the optimal control theory, a multivariable controlled variable is controlled to an optimal state from all states by a multivariable manipulated variable. Therefore, a mathematical model (state equation) representing all states in the rolling process is required. In addition, in order to express the optimum state mathematically, an evaluation function is used to analytically obtain a control law that minimizes it, and the system is operated by this control law to perform control so that the optimum state is achieved. . In the optimal regulator theory, which is a typical control theory in the optimal control theory, a quadratic form evaluation function is used. This is because when the mathematical model (model) is linear and the evaluation function is a quadratic form, the control law is feedback control, and stable control can be realized in which the controlled variable is reliably brought close to the target value.

The quadratic evaluation function is obtained by multiplying the square of the deviation of the control amount by the weight matrix Q, and the difference between the value at a certain time and the value one sampling time before the operation amount from the reference value. The evaluation function is such that the control that minimizes the value obtained by adding the sum of the powers multiplied by the weighting matrix R over all controlled times is the optimum control. When the control system is designed by this evaluation function, high responsiveness that minimizes the sum of the square area (absolute value) of the deviation of the control amount over the entire time and the square area of the difference of the deviation of the manipulated variable is obtained. A control with a short settling time can be realized with an appropriate operation amount.

At that time, the reason why the difference of the manipulated variable is included in the evaluation function is that the manipulated variable becomes infinite in order to speed up the response when the manipulated variable is not entered, but in reality, due to equipment restrictions. This is because the rate of change of the manipulated variable is finite and it is impossible to change the manipulated variable at high speed as described above. Here, the weighting matrix Q that depends on the deviation of the control amount of the multi-variable manipulated variable is the control amount that is required to have a high responsiveness and a small deviation. Increase the size of the element. In addition, the weight matrix R that depends on the deviation of the manipulated variable is the same as the weight matrix R that depends on the manipulated variable as the response speed required for the control amount controlled by the manipulated variable is higher among the manipulated variables of the multivariable. Reduce the size of the element. However, regarding the magnitudes of the weighting matrices Q and R, between elements having the same physical quantity, for example, the rotational speed (rotation speed) of the rolling roll, the size relation of the elements is the change in the control quantity response speed or the corresponding manipulated variable. Corresponds to speed relationship.
There is no correspondence between different physical quantities.

Further, the weighting matrices Q and R are determined by trial and error until it is determined that the control result obtained by the computer simulation is a control result that should be satisfied by the designer of the control system.

Hereinafter, the present invention will be described in more detail based on its embodiments.

As the dynamic characteristics of the rolling mill drive system, the rolling roll-gap control system is approximated with a temporary delay, and the rolling roll speed control system is approximated with a secondary system.

The symbols are shown in Table 1.

The non-linear rolling model is linearized and dimensionlessized around the reference state (Table 2) and displayed as a state space model.
When discretized with the control period Δt, the following equation of state is obtained.

x (k + 1) = Ax (k) + Bu (k) + Ew (k) ... (1) y (k) = Cx (k) + Fw (k) (2) However, state vector x, output y, input u, The disturbance w is
It is as follows.

x = (Δ _i ^* , Δt _fj ^* , ΔN _j ^* , Δ _j ^* ) ^T ...
(3) y = (Δ _i ^* , Δt _fj ^* ) ^T (4) u = (Δ _{ref, i} ^* , ΔN _{ref, j} ^* ) ^T (5) w = (ΔT _mi ^* , ΔH _i ^* , ΔB _i ^* ) ^T (6) i = 1,2, ... n, j = 1,2, ..., n-1 n: number of stands where k: step number representing time in discrete time system ( Integer) Δ _i ^* : Deviation from lock-on value ΔS _Li ^* = ΔS _i ^* -
ΔS _{L, i} ^* ΔS _i ^* = (S _i −S _{o, i} ) / h _{o, i} S _i : Measured value of rolling roll-gap in the i-th rolling mill S _{o, i} : In the i-th rolling mill Reference value of rolling roll-to-gap _{ho, i} : Reference value of height dimension of rolled material cross section at the i-th rolling mill exit side Δt _fj ^* = (t _fj −t _{fo, i} ) / K _{fmo, j} t _fj : Forward tension of rolled material in j-th rolling mill t _{fo, j} : Standard (target) value of forward tension of rolled material in i-th rolling mill K _{fmo, j} : Average deformation of rolled material in j-th rolling mill Reference value of resistance ΔN _j ^* = (N _j / N _{o, j} ) −1 N _j : Measured value of rolling roll rotation speed in j-th rolling mill N _{o, j} : Rolling roll rotation speed in j-th rolling mill reference value T of the measured values: delta means a transposed matrix _{i ^*:} deviation = delta] h from the lock-on value ^{_{Δh Li * i * -Δh Li *}} Δh i * = h i of the reference value h _o, changes from _i Rate = Δh _i / h _{o, i} = (h _i / h _{o, i} ) -1 h _i : i th Of the height dimension of the cross section of the rolled material on the exit side of the rolling mill (dimension in the rolling direction) h _{o, i} : Reference value of the height dimension of the cross section of the rolled material on the exit side of the i-th rolling mill Δ _{ref, i} ^* : Set rolling roll-to-gap target value for i-th rolling mill ΔN _{ref, i} ^* : Set rolling roll rotation speed target value for j-th rolling mill ΔT _mi ^* : From reference (target) value T _{mO, i of} T _mi Rate of change = ΔT
_mi / T _{mO, i} ΔT _mi : Deviation from the reference value of the actual measured value of the rolling material average temperature at the i-th rolling mill entrance side T _{mO, i} : The standard value of the rolling material temperature at the i-th rolling mill entrance side ΔH _i ^* : deviation of the height dimension of the cross section of the rolled material on the entrance side of the i-th rolling mill ΔH _i ^* = ΔH _i / H _{o, i} = (H _i / H _{o, i} ) -1 H _i : i-th rolling Actual measurement of height of cross section of rolled material on machine side Ho _{, i} : Reference value of height of cross section of rolled material on machine side of i-th rolling mill ΔB _i ^* : Rolling on machine side of i-th rolling machine Deviation of width dimension of material cross section ΔB _i ^* = ΔB _i / B _{o, i} = (B _i / B _{o, i} ) -1 B _i : Measured width dimension of rolled material cross section at the i-th rolling mill entrance side Value (dimension in the direction perpendicular to the reduction) B _{o, j} : Reference value of the width dimension of the cross section of the rolled material on the i-th rolling mill entry side. The coefficient matrices A to F are the rolling characteristics and the dynamic characteristics of the rolling mill drive system. This is a matrix whose elements are partial differential coefficients.

Details of the linear rolling model are described in publicly known documents (1984 1993 Plastic Working Spring Lecture p533-536 “Equation of state of wire rod rolling”).

Table 3 shows the values of the matrices A to C in the standard rolling condition shown in Table 2 in the rolling mill train having four stands. The values of the matrices E and F are omitted because they are not necessary for designing the optimum control system described below. The matrix A is 13 rows and 13 columns,
The matrix B has 13 rows and 7 columns, and the matrix C has 7 rows and 13 columns. Further, among the elements of the matrix, D and − are symbols defined in the grammar of JIS FORTRAN multiple precision real number type arithmetic expressions. For example, it is a double precision real number type constant representing xDy: = x × 10 ^y .

In continuous rolling of wire rod and bar steel, it is necessary to control the height and width dimensions of the cross section of the rolled material discharged from the final stand of the rolling mill train to target values.

When the inventors have previously proposed the control system proposed in Japanese Patent Application No. 59-218111 to control the height and width dimensions of the cross section of the rolled material on the exit side of the rolling stand, When feedback control is performed from the provided dimensional gauge for measuring the cross-sectional dimension of the rolled material, a time delay occurs by the rolling material running time from the final stand to the dimensional gauge.

Therefore, in the present invention, the height dimension of the cross section of the rolled material on the exit side of the last several stands is measured by the gauge meter method calculated from the change of the rolling load and the rolling roll-to-gap, and the lock-on is performed. Control as a value. In this way the time delay is resolved.

On the other hand, if only the height dimension of the rolled material cross section on the exit side of the last few stands is controlled, the tension of the rolled material between the stands changes and the width dimension of the rolled material cross section is hardly controlled. In order to solve this problem as well, it is necessary to carry out multi-variable control for simultaneously controlling the tension of the rolled material between the last several stands. At that time, if the stand for controlling the height dimension of the rolled material section on the delivery side of the rolling mill is the final two stands, the width dimension of the rolled material section on the delivery side of the final stand is
An offset is generated from the target value. If the number of stands that control the height dimension of the rolled material cross section on the rolling mill exit side is four or more final stands, the width dimension of the rolled material cross section on the final stand exit side can be controlled so that the offset from the target value is almost zero. it can.

As described above, in a complex control system in which both control variables and manipulated variables are multivariable, a linear rolling model that considers mutual effects of variables is used and based on the optimal regulator theory that minimizes the quadratic evaluation function. By configuring the control system, it is possible to finely control all the control amounts with high responsiveness.

In the present invention, the optimal regulator theory is applied to design the discrete-time optimal control system. That is, assuming that the disturbance w is stepwise, the evaluation function The control input u (k) that minimizes u (k) = − F ₁ e (k−1) −F ₂ [e (k) −e (k−
_{1)] -F 3 [xs (} k) -xs (k-1)] + u (k-1) ...
It is given in (8).

In the present invention, the optimum gain value obtained in the design of the discrete time control system can be used as it is in the discrete time in the digital process computer. Even if the optimum gain obtained in the design of continuous time control is used,
When controlling discrete time with a digital computer,
If the gain is converted appropriately, optimum control can be realized in the same manner as the gain obtained in the design of the discrete time control system. In order to optimize the rolling control system, a scale that quantitatively determines that it is optimal is necessary. In that case, the requirements imposed on the control system, the front tension t of the strip rate of change from the lock-on value of the height dimension of the cross section delta _i ^* and the rolled material at the delivery side of the rolling mill is a control amount as the evaluation function
_The quadratic form of e (k + 1), which is a generalization of the square of the deviation (area = absolute value) of the change rate Δ _fi ^* from the target value of _fi ,
It is appropriate to use the first term on the right side of the equation (7). However, if the evaluation function is only this term, the acceleration v of the manipulated variable u (k), that is, the set rolling roll-to-gap target value _{Δref, i} ^* (k) and the set roll rotational speed target value ΔNref _{, j} ^* (k) _{, is} calculated. (K)
= U (k) -u (k-1) should be given as large as possible, which is not realistic. Therefore,
Constraints on the cost required for control or the magnitude of v (k) must be incorporated into the evaluation function. Therefore,
A quadratic form for v (k) is introduced in the second term on the right side of the equation (7). In this case, the rate of change Δ _i ^* from the lock-on value h _{L, i} of the height dimension h _i of the rolled material cross section at the i-th stand exit side, which is the controlled variable (output vector) over the entire control time ^. And a squared area of the deviation of the change rate Δt _fj ^* from the reference value of the forward tension t _fj of the rolled material at the i-th stand from the target value multiplied by a weight matrix Q,
The change rate _{Δref, i} ^* from the lock-on value S _{L, i of the} rolling roll-to-gap target value S _{ref, i} , which is the operation amount (input vector), and the setting at the j-th stand. A weighting matrix for the square area of the difference between the value k of the change rate ΔN _{ref, j} ^* of the rolling roll rotational speed target value N _{ref, j from} the reference value N _{o, j} and the value of time k−1 one sampling cycle before. The product of R and the sum should be minimized. That is,
This is an optimal control in which the deviation of the control (output vector) is settled to the target value in a short time with a manipulated variable (control input) of a finite size, and the weighting matrices Q and R are the deviation e and the input of the output vector y, respectively. It is a matrix whose elements are weighting factors applied to the difference v of the vector u, and is determined by trial and error to obtain a desired control result by computer simulation.

In equations (7) and (8), the first-order difference v of the control deviation e, the partial state vector xs, and the control input (manipulation amount) u is e (k) = r (k) −y (k) (r ( k) = O: target value) (9) xs (k) = (ΔN _j ^* , Δ _j ^* ) ^T (10) v (k) = u (k) -u (k-1) (11) ) Is defined as Is obtained from the following Riccati equation.

F = (R + G ^T PG) ⁻¹ G ^T PΦ (12) P = Φ ^T PΦ−Φ ^T PG (R + G ^T PG) ⁻¹ G ^T PΦ + H ^T QH… (13) Here, the formula (13) is steady. The Riccati equation in the state, P on the left side is P (k + 1), and P on the right side is P (k), but in the steady state, P (k + 1) on the left side is P (k) on the right side.
Since it is equal to (k), P (k + 1) = P (k) = P
And

However, the matrices Φ, G, and H are error systems of the system represented by the formulas (1) and (2) X (k + 1) = ΦX (K) + Gv (k) (14) e (k) = HX (k ) ... (15) X (k ) = [e T (k-1), e T (k) -e T (k-1), xs
^T (k) −xs ^T (k−1)] ^T (16), which is a coefficient matrix and is obtained from matrices A to C. Here, assuming that the disturbance w is stepwise, in a steady state, the change w of the disturbance w appearing in the rolling state equations (1) and (2).
(K)-(k-1) = 0. Therefore, the state equations (14) and (15) used when designing the control system that determines the control input that minimizes the evaluation function of equation (7) are the original rolling state equations (1) and (2). Due to the differential form of, the disturbance is canceled so that it is not used for control system statistics and control. Although the optimum control of the discrete time system is derived here, if the state equations (1) and (2) of rolling are given in the continuous time system, the optimum control of the continuous time system can be configured by the same method.

Here, the relationship between the evaluation function (7) and the above expressions (8) to (16) will be described. The optimum regulator is usually composed of state vector feedback. In the present invention, it is necessary to control the deviation of the height dimension of the cross section of the rolled material on the delivery side of the rolling mill, that is, the output vector. Further, the deviation of the rolling material tension between rolling mills is both a state vector and an output vector. Therefore, in order to realize the feedback control of these output vectors, the deviation of the height dimension of the cross section of the rolled material at the rolling mill exit side in the original system (1) and (2) and the rolled material between rolling mills It is necessary to change the system equation so that the output vector of the deviation of tension becomes the state vector in the new system equation.

That is, a system formula of proportional / integral control of the output vector of the deviation of the height dimension of the rolled material cross section on the delivery side of the rolling mill and the deviation of the rolled material tension between rolling mills and a secondary system approximation formula of the mill drive system is configured. It suffices to configure feedback proportional control of the partial state vector consisting of the rolling roll speed and its time derivative. To this end, the error (deviation of output vector from O) with a minus sign in Eqs. (1) and (2), the error difference and the partial state vector difference are calculated as shown in Eq. (16). Formula (14), (15)
The state vector in Where (14),
The coefficients φ, G and H in the equation (15) are obtained from the matrixes A to C from the original system equations (1) and (2).

At this time, the control input u that minimizes the evaluation function (7) expression
(K) is given by equation (8) from the optimal regulator theory. Here, the control deviation e (k) and the partial state vector xs
(K) and the first-order difference v (k) are defined by the equations (9) to (11), and are obtained from the Riccati equations of the optimal gain matrices (12) and (13).

By applying the optimum control law that minimizes the evaluation function (7), an optimum control system in wire rod and bar rolling as shown in FIG. 1 is constructed.

FIG. 1 (a) shows a rolling control system when the present invention is carried out.

The control computer 6 calculates the deviation Δ of the front tension t _fi of the rolled material.
t _fj ^* , rolling roll speed deviation ΔN _j ^* and its derivative Δ
and _j ^*, the deviation delta _{i *} from the lock-on value of the rolling roll pair gap in the i-th ^stand, the deviation delta _{i *} from the lock-on value of the rolling ^load, the rolling material at the delivery side of the stand finishing due to dimensional five The deviation Δh ₄ ^* from the lock-on value of the cross-sectional height dimension and the deviation Δb ₄ ^* from the lock-on value of the cross-sectional width dimension of the rolled material on the finishing stand exit side measured by the dimension meter 5 are sampled and sampled on each stand exit side. The calculated value Δ _i ^* of the cross-section height dimension of the rolled material by the gauge meter method is calculated, the optimum control input u (k) given by the equation (8) is calculated, and the set value Δ of the rolling roll-gap at each stand is set.
_{The ref, i} ^* and the rolling roll rotational speed setting value ΔN _{ref, j} ^* are output to the rolling roll-to-gap control system and the rolling roll rotational speed control system, respectively. Here, the value calculated by the gauge meter method of the cross-sectional height dimension of the rolled material at the stand exit side is Δ
_i ^{* _{is, Δ i * = Δ i *}} + α i · Δ i * / M i * + Δh M, i *
… Calculated by (17). Mi ^* is a dimensionless Mill constant (M _i ^* =
h _{o, i} · M _i / P _{o, i} ), α _i is a scale factor.

The right side of the equation (17), the first term and the second term, are calculation equations by a known gauge meter method, and the third term Δh _{M, i} ^*
Is monitor compensation to provide absolute dimensional accuracy.

The monitor compensation Δh _{M, i} ^* is obtained by the following procedure.

From the sample values of the deviation Δh ₄ ^* of the height dimension and the deviation Δb ₄ ^* of the width dimension of the cross section of the rolled material on the exit side of the final (finishing) stand by the dimension meter 5, the leader stand and finishing stand (in this embodiment, No. .3, No. 4 stand) The monitor correction amount Δh _{x, 3} ^* and Δh _{x, 4} ^* of the height dimension of the rolled material cross section on the exit side is expressed as Δh _{x, 3} ^* =-(K ₂ · Δh ₄ ^* −Δb ₄ ^* ) / K ₁ (18) Calculated according to Δh _{x, 4} ^* = Δh ₄ ^* (19). However, the coefficients K ₁ and K ₂ are K ₁ = (∂Δb ₄ ^* / ∂ΔS ₃ ^* ) · (∂Δh ₃ ^* / ∂ΔS ₃ ^* )
^-1 … (20) K ₂ = (∂Δb ₄ ^* / ∂ΔS ₄ ^* ) · (∂Δh ₄ ^* / ∂ΔS ₄ ^* )
^-1 is given by (21).

Next, the monitor compensation amount Δh _{M, i} ^* (k) is obtained by integrating the monitor correction amounts Δh _{x, 3} ^* and Δh _{x, 4} ^* of the height dimension of the rolled material section on the exit side of the leader stand and finishing stand. hand Required by. T _i is the material (rolling material) running time (seconds) from the No. 1 stand to the dimension meter on the exit side of the final (finishing) stand, and K _{M, i} is the monitor compensation integral gain. The weighting matrices Q and R in the equations (12) and (13) and the monitor compensation integral gain K _{M, i} in the equation (22) were determined by trial and error by repeating computer simulation.

On a 4-stand mill, the average material temperature on the entry side of the No. 1 stand and the height and width dimensions of the material cross section are stepped by deviations ΔT _{m, i} ^* = -0.091, ΔH ₁ ^* = ΔB ₁ ^* = 0.033, respectively. It was examined about the case where the shape changed.

The step response without control is shown in FIGS. 2 and 3.

As is clear from FIGS. 2 and 3, the final (finishing)
The deviations Δh ₄ ^* and Δb ₄ ^* of the height and width of the cross section of the rolled material on the stand exit side fluctuate greatly.

The above N, which is the premise of the results shown in FIGS. 2 and 3.
o.1 Deviations of the material average temperature, material cross-sectional height dimension and width dimension on the entrance side of the stand are at the time when 4,5 seconds have passed since the tip of the material reached the No. 1 stand.

Next, the step response in the case of control is shown in FIGS.
Shown in the figure.

Figures 4 to 7 show that the average material temperature on the No. 1 stand entry side, the height dimension of the material cross section, and the width dimension have deviations Δ, respectively.
T _{M, 1} ^{* =} _-0.091, the ^{_{ΔH 1 * = ΔB 1 * =}} 0.033 only when changes stepwise, the control has a case (AGC controlled by tension control + all stands of the rolled material between stands), Deviation of height and width of the cross section of the rolled material on the exit side of the final stand Δh ₄ ^* = Δb ₄ ^* , deviation of the forward tension of the rolled material at each stand Δt _fj ^* , deviation of the rolling speed ΔN _j ^* , rolling The step response of the roll-to-gap deviation ΔS _j ^* is shown. At this time, monitor compensation is not performed,
Δh _{M, i} ^* in equation (17) is set to zero. The weight matrices Q and R are Q = diag (1,1,1,1,0.1,0.1,0.1) (23) R = diag (10,10,10,10,1,1.2,1.5) (24) ) Is.

As is clear from FIGS. 4 to 7, when the control is performed, the deviation of the height dimension and width dimension of the rolled material cross section on the exit side of the final stand and the deviation of the front tension of the rolled material at each stand are extremely small. Therefore, precise rolling control is possible.

Next, in order to verify the effectiveness of the monitor compensation, the disturbance of the material temperature and the material cross-sectional dimension is ΔT _{m, 1} ^* = − from the material tip.
We examined the case where only 0.091 and ΔH ₁ ^* = ΔB ₁ ^* = 0.033 were added.

Figures 8 to 10 show the deviation Δh ₄ ^* = Δb ₄ ^* of the height dimension and width dimension of the rolled material cross section at the exit side of the final stand and the forward tension of the rolled material at each stand without monitor compensation. The response of the deviation Δt _fj ^* is shown. Since the calculated value (lock-on value) of the height dimension of the rolled material cross section by the gauge meter method deviates from the standard state, the height and width dimensions of the rolled material cross section on the exit side of the final stand are offset. There is.

The above N, which is the premise of the results shown in FIGS.
o.1 Deviations of average material temperature, height and width of material cross section on the stand entry side are No. 1 at the material tip.
This is at the time when 1.0 seconds has passed after reaching the stand.

Figures 11 to 13 show the deviations of the height and width dimensions of the cross section of the rolled material on the exit side of the final stand when monitor control is applied (tension control of rolled material between stands + AGC in all stands). The response results of Δh ₄ ^* = Δb ₄ ^* and the deviation Δt _fj ^* of the forward tension of the rolled material at each stand are shown. At this time, the monitor compensation integral gain is set to K _{M, 3} = K _{M, 4} = 0.05.

As is clear from FIGS. 11 to 13, when the monitor control is performed, there is no offset in the height dimension and width dimension of the rolled material cross section on the exit side of the final stand.

Here, the control system of the present invention will be described collectively.

Fig. 1 (b) shows tension control + gauge meter AGC + monitor A.
The details of the control system for GC compensation are shown below. The deviation Δh _i ^* of the height dimension of the cross section of the rolled material on the stand-out side of each stand is obtained by the calculation formula (17) using the gauge meter method. The first term and the second term on the right side of the equation (17) are known gauge meter equations.

The gauge meter control is generally a deviation control that makes the deviation of the height dimension of the rolled material section on the delivery side of the rolling mill from the lock-on value 0, but in order to realize precision rolling, the height of the rolled product section should be controlled. Absolute value control is required to control the height and width dimensions to the target values. Therefore, it is considered to realize the absolute value control in the control of the height dimension of the rolled material cross section on the outlet side of each stand, which is obtained by the tension control and the calculation formula (17) by the gauge meter method. Here, rolling by a rolling mill train including four stands will be described as an example. If the deviations of the height and width dimensions of the rolled product cross section from the target values are Δh ₄ ^* (k) and Δb ₄ ^* (k), the rolling on the stand-out side of each stand, which is calculated by the gauge meter method (17) To control the height of the cross section of the strip to absolute value control, the third dimension of equation (17) that indicates the height of the cross section of the rolled strip in the pre-finishing (leader) stand and finishing stand is used.
Item monitor compensation amount Δh _{M, 3} ^* (k), Δh _{M, 4} ^* (k)
Is calculated by the following procedure. Sample value Δh of the deviation from the target value of the height dimension and width dimension of the rolled product cross section measured by the dimension gauge installed on the rolling mill output side
Monitor correction amount Δh from ₄ ^* (k), Δb ₄ ^* (k)
_{x, 3} ^* (k) and Δh _{x, 4} ^* (k) are calculated by the equations (18) and (19). Here, k ₁ is the coefficient of influence that the calculated value by the gauge meter method of the height dimension of the rolled material cross section on the leader stand exit side when the rolled material tension between rolling mills is controlled affects the width dimension of the rolled product cross section. The coefficient of influence of the rolling roll pair gap in the leader stand on the width dimension of the rolled product cross section is divided by the influence coefficient of the rolling roll pair gap in the leader stand on the height dimension of the rolled material cross section on the leader stand exit side. As a quotient, (2
It is shown by the equation (0). k ₁ is obtained by computer simulation or actual measurement. k ₂ is an influence coefficient that the calculated value by the gauge meter method of the height dimension of the rolled material cross section on the exit side of the finishing stand when the tension of the rolled material between rolling mills is controlled, As the quotient of the coefficient of influence of the rolling roll pair gap in the finishing stand on the width dimension of the rolled product cross section divided by the influence coefficient of the rolling roll pair gap in the finishing stand on the height dimension of the rolled material section at the exit side of the finishing stand, 2
It is shown by the formula 1). k ₂ is obtained by computer simulation or actual measurement.

The monitor compensation amounts Δh _{M, 3} (k) and Δh _{M, 4} (k) are the monitor correction amounts Δh calculated by the equations (18) and (19), respectively.
_{x, 3} (k), Δh _{x, 4} (k) are multiplied by the integral gain to obtain the integral, which is obtained from the equation (22). Here, when the proportional control acts like the control by the calculated value by the gauge meter method of the height dimension of the rolled material cross section obtained from the rolling load and the gap between the rolling rolls, the rolling material running time from the final stand to the dimension gauge Therefore, there is a risk that the height dimension and the width dimension of the cross section of the rolled product will be largely deviated from the target values. Therefore, in the present invention, the height dimension and the width dimension of the rolled product cross section are set to the target values by integrating the monitor correction amount.

〔The invention's effect〕

As explained above, in the case of this embodiment of the present invention,
It has been clarified that the control by the optimal regulator has excellent control performance as follows.

(1) The tension control and height control of the gauge meter on the stand-out side of each stand can be controlled to offset = 0 with a short settling time.

(2) Offset of finishing stand exit side height and exit side width = 0
Controllable.

In this example, the looperless continuous rolling is shown, but even when there is a looper between the stands, if the state equation is configured by using the relational expression between the looper height and the rolled material tension, the same as in the above example. Dimension control is possible by the method.

[Brief description of drawings]

1 (a) and 1 (b) are configuration diagrams showing an embodiment of the present invention,
2 to 3 are examples of the step response of the exit side height Δh ₄ ^* , the exit side width Δb ₄ ^* , and the tension Δt _fj ^* without control, and FIGS. 4 to 7 are with control ( Example of step response of output side height Δh ₄ ^* , output side width Δb ₄ ^* , tension Δt _fj ^* , roll speed ΔN _j ^* , roll gap ΔS _i ^* in the case of (without monitor compensation), FIG. Fig. 10 shows an example of the response of the outlet height Δh _i ^* , outlet width Δb _i ^* , and tension Δt _fj ^* when there is no monitor compensation when the lock-on value of gauge meter calculation deviates from the standard state. FIG. 11 to FIG. 13 are illustrations of the response of the outlet height Δh _i ^* , the outlet width Δb _i ^* , and the tension Δt _fj ^* with monitor compensation. 1,3: Horizontal roll, 2,4: Vertical roll 5: Dimension meter, 6: Control calculator, 7: Material

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Harutoshi Ogai 1618 Ida, Nakahara-ku, Kawasaki-shi, Kanagawa Inside Nippon Steel Co., Ltd. 1st Technical Research Institute (72) Takao Kawanami Inami, Etsumitsu, Hachiman-ku, Kitakyushu, Fukuoka 1-1-1 Nippon Steel Co., Ltd. 3rd Technical Research Laboratory (72) Inventor Yoichi Naganuma 1618 Ida, Nakahara-ku, Kawasaki-shi, Kanagawa Nippon Steel Co., Ltd. 1st Technical Research Laboratory (72) Inventor Oka Toshihiro, 12 Nakamachi, Muroran City, Hokkaido Inside Nippon Steel Co., Ltd. Muroran Works (72) Inventor Naoki Tanaka 12 Nakamachi, Muroran City, Hokkaido Shin Nippon Steel Co., Ltd. Muroran Works

Claims (1)

[Claims] 1. In the continuous rolling of a wire rod / bar steel by a rolling mill train, deviations ΔS _i ^* , ΔS _i ^* = (S _i −S _{o, i} ) of rolling roll-to-gap at each stand constituting the rolling mill train. / h _{o, i} i = 1,2, ..., n where S _i : Measured value of rolling roll-gap at the i-th stand S _{o, i} : Reference value of rolling roll-gap at the i-th stand h _{o, i} : Reference value of the height of the cross section of the rolled material on the exit side of the i-th stand The deviation of the forward tension of the rolled material is Δt _fj ^* , Δt _fj ^* = (t _fj −t _{fo, j} ) / k _{fmo , j} j = 1,2, ..., n−1 where t _fj : actual measured value of the forward tension of the rolled material on the j-th stand exit side t _{fo, j} : of the rolled material on the j-th stand exit side Reference (target) value of forward tension k _{fmo, j} : Reference value of deformation resistance of rolled material at the j-th stand The deviation of the rotation speed of the rolling roll is ΔN _j ^* , and its time derivative is Δ _j ^* , ΔN _j ^* = (N _j / N _{o, j} ) −1 j = 1,2, ..., n−1 where N _j : measured value of rolling roll rotational speed at the j-th stand N _{o, j} : j The standard value of the rolling speed of the rolling roll at the th stand The deviation of the rolling load is ΔP _i ^* , ΔP _i ^* = (P _i / P _{o, i} ) −1 i = 1,2, ..., n where P _i : Measured value of rolling load at the i-th stand P _{o, i} : Reference (target) value of rolling load at the i-th stand The deviation of the rolled material cross-sectional height dimension on the stand-out side of each stand is Δ.
h _i ^* , Δh _i ^* = (h _i / h _{o, i} ) −1 i = 1,2, ..., n where, h _i : Actual measurement of rolled material cross-section height dimension on the exit side of the i-th stand Value, h _{o, i} : Reference value of the height dimension of the rolled material cross section on the exit side of the i-th stand (where h _i is the gauge meter formula h _i = H _{Cal, i} + S _i + α _i · P _i / M a value obtained by _i, H _{Cal, i:} caliber of i-th rolling rolls in stands (grooved) depth S _i: measured value of the rolling roll pair gap in the i-th stand alpha _i: i-th stand Scale factor P _i : Actual measurement of rolling load at the i-th stand M _i : Mill rigidity at the i-th stand) Roll roll gap at the i-th stand, rolling load, and rolled material at the i-th stand exit side The lock-on value of the cross-sectional height is S _{L, i} , P _{L, i} and h _{L, respectively.
i} (h _{L, i} = H _{Cal, i} + S _{L, i} + (α _i · P _{L, i} ) / M _i ),
The deviations of the gap between the rolling roll in the i-th stand, the rolling load, and the lock-on value of the cross-sectional height dimension of the rolled material on the exit side of the i-th stand are ΔS _{L, i} ^* , ΔP _{L, i} ^*, and Δh _{L. , i} ^* , ΔS _{L, i} ^* = (S _{L, i} −S _{o, i} ) / S _{o, i} ΔP _{L, i} ^* = (P _{L, i} −P _{o, i} ) / P _{o, i} Δh _{L , i} ^* = (h _{L, i} −h _{o, i} ) / h _{o, i} Deviation Δh _{i of} cross-sectional height dimension of rolled material on the stand-out side of each stand
^* And the deviation from the lock-on value deviation Δh _{L, i} ^{* of the} cross-sectional height dimension of the rolled material on the exit side of each stand, plus the monitor compensation amount Δh _{M, i} ^* , Δ _i ^* , Δ _i ^* = Δh _i ^* −Δh _{L, i} ^* = Δ _i ^* + α _i · Δ _i ^* / M _i ^* + Δh _{M, i} ^* i = 1,2, ..., n where Δ _i ^* = ΔS _i ^* −ΔS ^{_{L, i * Δ i * =}} ΔP i * -ΔP L, i * M i * = h o, i · M i / P o, i monitor compensation amount Δh _M, ^{i *:} provided on the delivery side of the rolling mill train From the measured values of the deviation of the height and width dimensions of the rolled material measured by the rolled material cross-sectional dimension meter, the amount of reduction at each stand in the rolling mill train is determined by the height and width of the rolled material cross-section at the exit side of the finishing stand. Value obtained by distributing to each stand and integrating based on the coefficient of influence on the size.The average temperature of the material on the entrance side of each stand, the deviation of the height and width of the cross section of the rolled material. The difference is expressed as ΔT _mi ^* , ΔH _i ^* and ΔB _i ^* , ΔT _mi ^* = Δ _mi / T _{mo, i} ΔH _i ^* = ΔH _i / H _{o, i} ΔB _i ^* = ΔB _i / B _{o, i} i = 1,2, ..., n State vector x, output vector y, input vector u, x = (Δ _i ^* , Δt _fj ^* , ΔN _j ^* , Δ _j ^* ) ^T where T means transposed matrix To do. y = (Δ _i ^* , Δt _fj ^* ) ^T u = (Δ _{ref, i} ^* , ΔN _{ref, j} ^* ) ^T i = 1,2, ..., n j = 1,2, ..., n-1 Here, ΔS _{ref, i} ^* : Target value of set rolling roll-gap in the i-th stand ΔN _{ref, j} ^* : As the target value of the set roll speed in the j-th stand, the control input is determined when designing the control system. Rolling state equation x (k + 1) = Ax (k) + Bu (k) y (k) = Cx (k) Here, k is an evaluation function J using a step number (integer) that represents the time of a discrete time system. The height and width dimensions of the rolled material discharged from the last stand (nth stand) in the rolling mill train are controlled by the optimum input consisting of the output vector (control deviation) and the feedback of the state vector that minimize Dimension control method in rolling rod and bar steel characterized in that Here, Q, R: weight matrix e (k) = r (k) -y (k), r (k) = O: target value, v (k) = u (k) -u (k-1) the control input ^{_{u = (Δ ref, i *}} , ΔN ref, j *) stand number i, j in ^T is, i = O~n, take any combination within the range of j = O~n-1 If i = O, the roll gap is not the manipulated variable, and if j = O, the roll gap is not the manipulated variable.