JPH0777648B2 - Dimension control method in wire rod and bar rolling - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention comprises a wire rod or a rod member, which comprises a multi-stage stand. (1) A loopless independent drive type mill (2) A common drive type block mill (3) The present invention relates to a method for accurately controlling the size of a wire rod or bar to be rolled when rolling by each type of mill of an independently driven mill with a loop. [Prior Art] Conventionally, the following examples have been given as the dimension control method for wire rods and steel bars. As a first example, "Plasticity and processing" Vol20, No.224, P841-849
As shown in (1979-9), the deviation of the measured value of the tension from the target value is obtained by the direct tension detection of the steel bar mill, and the roll rotation speed is controlled by considering the mutual influence between the stands. The proportional and integral control of the tension is performed. As a second example, as shown in Japanese Patent Laid-Open No. 54-128469, using the coefficient of influence of reduction on the product width dimension,
The vertical dimension of the product is controlled by rolling down the final stand of the common drive block mill for wire rod, the product width dimension is controlled by rolling down the first stand, and proportional control is performed by the deviation of the measured dimension from the target value. As a third example, as shown in JP-A-57-88908, No. 1 stand and No. 2 of finishing block mill for wire rods are used.
No. by changing the relative speed between ~ stand.
By changing the tension between No. 1 to No. 2 stands, the product width is controlled according to the deviation of the measured value of the outlet width of any one of No. 2 to n stands from the target value. As a fourth example, Japanese Patent Application No. 59-218111 filed by the present inventors
As shown in No. 6, using the rolling equation of state consisting of deformation, load, and temperature, the roll speed and roll gap are used as the manipulated variables, and the height of rolled material at the final stand exit side of the target rolling mill group is set. The width and width are controlled by state vector feedback based on the multivariable control theory. However, the control methods of the first to fourth examples have the following problems. That is, in the method of the first example, the gain is determined by trial and error, and there is a limit to the optimization. Also, because of feedback control, there is a limit in response speed, and it is difficult to cope with dimensional control of high speed rolling. In the method of the second example, the reciprocal of the influence coefficient of the reduction on the product size is used as the gain of proportional control, but the control performance is unknown. Also, because of feedback control, there is a limit in response speed, and it is difficult to cope with dimensional control of high speed rolling. In the method of the third example, no specific method for determining the gain is shown, and the control performance is unknown. Also, because of feedback control, the response speed is limited, and it is difficult to respond to the size control of high speed rolling. The method of the fourth example has relatively high performance according to the feedback multivariable control theory, but like the first to third examples, the control operation is performed only for the dead time due to the distance to the rolled material cross-section dimension meter on the stand exit side. However, it is difficult to cope with the size control of high speed rolling. [Problems to be solved by the invention] (1) Loopless independent drive system mill (2) Common drive system block mill (3) Loop independent drive system mill When rolling wire rods or bars, the rolling speed of the independent drive type mill of (1) and (3) is around 10m / s at the maximum, and the finishing rolling velocity of the wire block mill (2) is around 100m / s at the maximum. However, in feedback control, the response is slow, and the material on the outlet side of the mill passes through several meters and several tens of meters before the control is performed, and fine control is impossible. Also, on the entry side of the wire rod finishing block mill, the dimensions and temperature fluctuate greatly in a short time (for example, the 0.1 mm entry side dimension fluctuates in 0.1 s), so the dynamic operation is determined by trial and error. Fine control is difficult with conventional feedforward control. [Means for Solving the Problem] In the present invention, in the rolling of wire rods and rods by each type of mill including a multi-stage stand, the dynamic phenomenon of continuous rolling is analyzed by using a nonlinear unsteady model of wire rolling as a reference state of rolling. It is derived by linearizing around. The dynamic change of tension (state vector) (in the continuous time system, the time derivative of the tension (state vector) at time t, in the discrete time system, the value of the tension (state vector) at time k + 1) is In the discrete time system at time t, the state vector at time k,
It is represented by a rolling state equation consisting of a dynamic model expressed using the values of the input vector and the disturbance vector, and an output equation expressing the static relationship between the output vector and the state vector, and the disturbance vector. Compile the mill drive system model of roll gap and roll speed to create the state equation of the whole system of each stand,
Furthermore, for dimensions and temperature, create material transfer equations between each stand and substitute them into the equation of state of the entire system, and according to the mill type and its control method, Constituting the equation of state and satisfying it, in the common drive type block mill, the deviation of the mill output side from the target value is the control amount, and in the loopless independent drive type mill, the deviation of the tension and that is controlled amount. , In the independently driven mill with a loop, the deviation of the loop height from that is controlled, in the common driven block mill, the problem of the roll gap between the first stand and the last stand is manipulated, and in the independently driven mill. , The roll gap and roll speed of each stand are manipulated variables, and the amount obtained by multiplying each of them by the weight matrix is added or integrated over the entire control time. To, by finding the optimum manipulated variables to minimize it analytically, derives a multivariable control theory consists feed forward control + feedback control, it was calculated feedforward optimal gain and feedback optimal gain. Here, the mill drive system model is a model that represents the relationship between the time delay of the measured value and the target value of the control device (roll reduction system, roll rotation system). The material transfer type means that when the material is transferred from the No.i stand on the upstream side to the No.i + 1 stand on the downstream side, the average material temperature at the No.i + 1 stand entrance side, the material height at the entrance side, the width and the No. i This is a model showing the relationship between the average material temperature on the stand-in side, the material height on the stand-out side, and the width. In an actual process, the above optimum gain is stored in an online control computer (hereinafter abbreviated as "procon"), and the dimension control is performed online using the procon. Here, the measurement cycle of dimensions and temperature and the control cycle of roll operation are about 0.05 to 0.5 s, and the shorter the cycle, the finer the control becomes possible. [Operation] The present invention is a dimension control method for controlling a dimension of a rolled material discharged from a final stand to a target value with high response in rolling a wire rod / bar material by a mill including a multi-stage stand. The features are as follows. Is. First, as the offline calculation processing, 1) a dynamic model of rolling is derived by linearizing a dynamic phenomenon of rolling around a non-stationary rolling model around a reference state of rolling, It is represented by a rolling state equation composed of tension output equations, and a mill driving system model that expresses the dynamic phenomenon of the roll driving system is integrated. The state equation of each stand of the entire system, and the material size and temperature of the stand memory are also included. Of the multi-variable control theory composed of feedforward control + feedback control using the modeling that creates the equation of state to be used when designing the control system obtained by substituting the material transfer equation that represents the transfer delay of Based on this, the control system is designed to calculate the feedforward optimum gain and the feedback optimum gain. Secondly, in the actual process, the following dimension control is performed online using a programming computer. Online calculation is performed from the feedforward optimum gain and feedback optimum gain calculated off-line in advance, and the disturbance vector and state vector actually measured online, and as a result, (1) Loopless independent drive block mill (2) Block mill of common drive system (3) The size (output vector) of the rolled material discharged from the final stand of each type of mill of independent drive system with loop is controlled to a target value. This allows the finishing height and finishing width dimensions to be controlled with high response by feedforward control and with high precision to the target value by feedback control, even when the dimensions and temperature of the mill fluctuate greatly in a short time. The symbols used for the explanation are shown in Table 1 and defined as follows. In addition, each vector composed of multiple variables is defined as follows. Here, the subscript i, j that represents the stand number takes the value of i = 1,2, …………, n, j = 1,2, …………, n−1 (n: final stand No.). , The usage of the subscripts i and j that represent the stand No.
It is as follows. A variable whose value at the last stand No. n is always 0, for example,
Roll rotation speed target value deviation ΔN _{ref, j} ^* (k), measured value deviation ΔN _j ^* (k), stand tension deviation t _fj (k),
J is used as a subscript of the loop height deviation Δy _hj ^* (k). A variable whose value at the final stand No. n is a value other than 0, for example, i is used as a subscript of the deviation ΔS _{ref, i} ^* (k) of the roll gap target value. Below, the time is displayed in a discrete time system. 1) Δs _i ^* (k): Deviation of the rolling roll gap in each stand of the mill at time k in the discrete time system, that is, [{(measured value s _i (k)) − (reference value s _0i (k) )} /
{Reference value h _0i (k)} of the height dimension of the rolled material cross section on the No.i stand exit side] Here, the reference value is a pass schedule value (design value).

2) Δt_fj ^*(K): At each stand of the mill at time k in the discrete time system
Deviation of tension, that is, [{(actual measurement t_fj(K))-(reference value t_f0i(K))}
/ {Standard of average deformation resistance of rolled material in No.j stand
Value k_fm0j(K)}] 3) Δy_hj ^*(K): At each stand of the mill at time k in the discrete time system
Deviation of loop height, that is, [{(actual measurement y_hj(K))-(reference value y_h0i(K))}
/{No.j Reference value y of loop height at stand exit side
_h0j(K)}] 4) Δs_{ref, i} ^*(K): Deviation of roll gap target value at No.i stand, that is,
Then, [{(target value s_{ref, i}(K))-(reference value s
_{0, i}(K))} / {No.i Rolling material break on stand exit side
Reference value h of surface height_0i(K)}] 5) ΔN_{ref, j} ^*(K): Deviation of roll gap target value at No.j stand, that is,
Then, [{(target value N_{ref, j}(K))-(reference value N
_{0, j}(K))} / {Rot rotation speed in No.j stand
Reference value N_0j(K)}] where 4) and 5) are input vectors, and their target values and
Is the manipulated variable given as an input vector,
This is the command value output from the to the controller. 6) Δh_n ^*(K), Δb_n ^*(K): Rolled material on the exit side of the final stand (n-th stand)
Deviation of cross-sectional height and deviation of rolled material width, ie, {(actual measurement h_n(K)) / (target value h₀n (k))-1, (measured value b_n(K)) / (target value b₀n (k))-1} Here, the target value of the output vector is the target value
Is a value controlled by. 7) ΔT_{m, 1} ^*(K), ΔH₁ ^*(K), Δ^*B₁(K): Material average temperature and material cross-section height on the entrance side of the first-stage stand
And deviation of material cross-section width {(measured value T_{m, 1}(K)) /
(Reference value T_m0,1(K))-1, (measured value H₁(K)) /
(Reference value H_0,1(K))-1, (measured value B₁(K)) / (group
Quasi value B_0,1(K))-1} 8) Δ_n ^*(K), Δ_n ^*(K): Rolled material on the exit side of the final stand (n-th stand)
Integral value of cross-section height deviation and rolling material width deviation j: Discrete time time Δt: Control cycle 9) Δ_fj ^*(K): Integral of deviation of tension between stands at No.j stand exit side
value  j: time in discrete time system Δt: control cycle 10) y_hj ^*(K): Integral value of the deviation of the loop height at the No.j stand exit side j: time in discrete time system Δt: control cycle 11) (k): Shows the state vector and determines the basic state of the process.
Physical quantity. Here, we measured the roll gap of each stand and estimated the tension.
Reference value of fixed value or measured value, measured value of loop height
From the measured value, the measured value of the material size on the delivery side of the rolling mill, and the tension
Measured value or estimated value of, target value of measured value of loop height
Select from the integral value of the deviations from according to the mill type. Where roll gap, tension or loop height
The reason why the value at the time is also included is the dynamics of the reduction device.
Cus (mechanical operation of rolling down device and computer, controlling rolling down
Of the roll gap due to the electrical delay of the operating device.
(Represented by time delay between measured value and measured value) and material transfer delay in mill
This is because it is taken into consideration. The reason for including the integrated values of finishing height / width and tension is
Finishing height by state vector feedback integral control
Control the deviation (offset) of the width and tension from the target value to 0
This is because 12) (k): Shows the output vector and targets the value of each element of the vector
Physical quantity controlled as a value. Here, the dimensional deviation of the material on the delivery side of the rolling mill, the tension, and the loop
Selected according to mill type from height and deviation of their integrated value
Do. 13) (k): A physical quantity that represents the input vector and is the manipulated variable. Here, the roll gap of each stand and the roll speed
Select from the deviation obtained from the standard value and the standard value according to the mill type.
Set. 14) (k): An object that shows the disturbance vector and affects the process from the outside.
Reason. Here, from the reference value of the measured value of the dimension and temperature on the mill entrance side,
It is composed of the deviation of. In general, disturbances are often unknown, and conventional feedback
(C) Not considered in multivariable control theory. In the present invention, the disturbance is measured on the mill entrance side, and the disturbance is measured by the control system.
It is taken into consideration during timekeeping and online control. That is, the dynamic phenomenon of rolling is changed to the dynamic change of tension.
Dynamic model, output vector, and state vector
Output method that expresses the static relationship between
A state equation used when designing a control system
, And the feedback calculated from the multivariable control theory
Forward optimal gain and feedback Optimal gain and disturbance
Disturbance vector using measured values of vector and state vector
Feedforward control + state vector feedbar
The feature is multi-variable control by clock control. Hereinafter, the details of the present invention will be described by taking a 4-stand mill (n = 4) as an example.
explain. Figure 1 shows the structure of the loop between the stands. Numbers 1 and 2 indicate No.i and No.i + 1 stand rolls, respectively. 3 and 4 are guide rolls, and 5 is a kick roll. 6 is the loop height detector, 7 is the pass line, and 8 is the material.
I will. Fig. 2 shows the target 4-stand mill and the control system of the present invention.
System. 9 to 12 are No. 1 stand (first stand) to No. 4
Shows the roll of the mill (final stand).
Thermometers for measuring material temperature, 14 and 15 are the mill input side and output side respectively
Shown are the input and output size gauges for measuring the dimensions of
17 is a process computer for control. FIG. 3 shows an off-line calculation process and an operation of the control method of the present invention.
The flowchart of online control is shown below. The offline processing is as follows: 1) Modeling (in this specification, the model
Creating a module is called modeling) and 2) from control system design
Composed. 1) The outline of modeling is as follows. The dynamic phenomenon of continuous rolling of wire rods, the dynamic change of tension
Dynamic model, output vector, and state vector
Output method that expresses the static relationship between
It is expressed by the equation of state of rolling, which is composed of equations, and the control
Comprehensive drive system models that represent the dynamic phenomena of equipment,
The equation of state of
Create a material transfer formula for each stand and
Substituting into the overall state equation, Mill form and its control method
Create a state equation to be used when designing the control system according to
The 2) The control system design is as follows. State process during control system design created by the above modeling
Using the formula and the control theory invented by the present inventor,
Design a control system for word control + feedback control. Through this process, the feed forwarder that determines the optimum manipulated variable
Optimal gain and feedback control optimal gain are determined
Be done. Online processing is the collection of measured data, offline
Storage of calculated optimum gain, optimum using measured data
From operation amount calculation and output of the optimum operation amount to the operation end
It is constructed and calculated by the process computer. Next, the contents of offline calculation processing and online calculation processing
I will describe. First, each item of offline calculation processing is explained. Here, the numbers outside the margin of the flowchart shown in FIG.
It is No. To achieve optimal multivariable control, all possible pressures are
In order to determine the optimum condition from the rolled state, rolling phenomenon
Mathematical model that represents all feasible states of the controller and controller
(State equation) is required. Here, since the multivariable control theory is linear, the mathematical model
Also needs to be expressed linearly. For the subject of the present invention, the modeling is as follows. Modeling of control devices (roll reduction system, roll rotation system)
(Step 1): (mill drive system model) When the roll reduction control system is approximated by a first-order lag system, Δs_i ^*(S) = Δs_{ref, i} ^*(S) / (1 + T_as) Here, the stand No.i that controls the rolling reduction is based on the mill type.
The influence that the rolling reduction has on the finishing dimension is large.
Therefore, the following selection was made. (1) In the case of a loopless independent drive system mill i = 3,4 (2) In the case of a common drive system block mill i = 1,4 (i = 4: final stand) (3) Independent drive system with a loop In case of mill i = 3,4 T_a: Time constant where s: corresponds to time t of continuous time system by Laplace transform.
Putting variable s as d / dt and expressing in continuous time system, dΔs_i ^*(T) / dt = -Δs_i ^*(T) / T_a + Δs_{ref, i} ^*(T) / T_a When expressed in a discrete time system discretized with the control period Δt,
At time k, Δs_i ^*(K + 1) = a_aiΔs_i ^*(K) + b_aiΔs_{ref, i} ^*
(K) (1) where k in () is a positive integer in the discrete time system.
Time, k + 1 is the time after the control cycle Δt from k. Well
A_ai, b_aiIs the coefficient determined by the time constant T and the discretization
Represent. Furthermore, in the independently driven mill of the mill type (1), (3)
The roll rotation control system is added as a manipulated variable,
If it is approximated by a first-order lag system like the lower system, ΔN_i ^*(S) = ΔN_{ref, i} ^*(S) / (1 + T_Ns) where, i: stand No., T_N: Time constant, last stun
Operate by using the stand (i = 4) as the pivot (fixed) stand.
The stand numbers to be used are i = 1 to 3. When expressed in a discrete time system, ΔN at time k_i ^*(K + 1) = a_NiΔN_i ^*(K) + b_NiΔN_{ref, i} ^*
(K) (2) a_Ni, b_NiIs the time constant T_NAnd the coefficient determined by the discretization
Represent. Dynamic modeling of rolling phenomenon and state of the whole system
Formula (Step 2): The wire rolling phenomenon is the material on the inlet side, temperature change (disturbance) and reduction operation.
Due to the dynamic change of the work, further in the independent drive type mill,
The dynamic change of roll rotation operation is added,
The inter-tension and the height and width of the material on the outlet side dynamically change.
Is transmitted to the downstream stand after the material transfer time.
It is a rough dynamic phenomenon. Rolling speed of independently driven mills of mill types (1) and (3)
Degree, mill type (2) common drive wire rod block mill
The maximum rolling speeds are around 10m / s and 100m / s, respectively.
In feedback control, the response is slow and the feedback
The material on the outlet side passes through several meters and several tens of meters, and
Kana control is impossible. Therefore, fine precision
In order to realize the control of
You will need it. Since the control is operated by the model,
An accuracy model is needed. The dynamic phenomena of rolling at each stand are analyzed by
Non-linear continuous rolling model composed of
Linearization and dimensionlessization of Dell around the reference state (Table 2)
Of the tension, which is derived by
Dynamic models and dimensions that represent dynamic changes,
Control amount of tension (output vector), state vector, disturbance vector
Consists of output equations that represent the static relationship of Kuttle
Represents the linear equation of state of rolling. For details of this linear rolling model, refer to
Processing Spring Workshop p533-536) "State of wire rod rolling
Equation ”). It is discretized with the control period Δt, and the above equations (1) and (2) are used.
When combined with the mill drive system of, the equation of state of the entire system is
Is obtained as. x (k + 1) = Ax (k) + Bu (k) + Ew (k) (3) y (k) = Cx (k) + Fw (k) (4) where, state vector x, output vector y, input vector u ,
The disturbance vector w is as follows. x (k) = [Δs_i ^*(K), Δt_fj ^*(K), ΔN
_j ^*(K)]^T (5) y (k) = [Δh_n ^*(K), Δb_n ^*(K), Δt
_fj ^*(K)]^T (6) u (k) = [Δs_{ref, i} ^*(K), ΔN_{ref, j} ^*(K)]^T 
(7) w (k) = [ΔT_mi ^*(K), ΔH_i ^*(K), ΔB
_i ^*(K)]^T (8) where subscripts i = 1, ..., n, j = 1, ..., n−1, n: Stan
Number, superscript T: transpose of matrix vector Note that the subscripts i and j of the variables have their terms as elements of the vector.
It is shown to be repeated. Coefficient matrices A to F are partial differential coefficients of rolling characteristics and drive system characteristics.
Here is a matrix with elements. In addition, material transfer from No.i stand to No.i + 1 stand
Sending time t_diThe approximate number of steps of_i(L_iIs t_di≒ l_i・
0 or a positive integer such that Δt,
The material transfer delay equation between the ends is given as follows. ΔT_{mi + 1} ^*(K) = α_iΔT_mi ^*(Kl_i) (9) ΔH_{i + 1} ^*(K) = Δb_i ^*(Kl_i) (10) ΔB_{i + 1} ^*(K) = Δh_i ^*(Kl_i) (11) i = 1,2, ..., n−1 where No.i + 1 is the average material temperature at the stand entrance side.
The average temperature of the material on the tund entry side was adjusted by rolling with the No.i stand.
Temperature change in roll bite due to machining and No.i stand ~ No.i
Radiation, air cooling, water between stands between +1 stands
The temperature added with the temperature change due to convection heat transfer due to cooling is
T in continuous time system_d.Number of steps l in discrete time system₁Only time
Transferred late. In the case of wire rod and bar rolling,
The height and width directions change by 90 ° for each stand and alternate
Rolling No.i + 1 material height on the entry side of the stand because it is replaced
The material width and material width are the material width and material on the No.i stand exit side, respectively.
Height is t in continuous time system_d.Number of steps l in discrete time system₁
Coefficient α_iIs the temperature change of the material
A computer system using a non-linear rolling model with a coefficient
It is calculated by simulation. For the standard condition of rolling in Table 2 for 4-stand mill
Parameter α_i, l_iAre shown in Table 3. Modeling during control system design (state equation during control system design)
(Step 3): In Equations (3) and (4), material transfer between stands
As a disturbance to the next stand after a dead time due to delay
The effect is not considered. As a method to consider it, here (9) to (11)
Substitute equation for transfer delay into equations (3) and (4)
The temperature, material height, and width of each stand, and
We adopted a method of sequentially erasing from the elements of the code. That conclusion
As a result, the state vector includes past values of roll gap and tension.
And the order increases. On the other hand, the disturbance vector is
No. 1 Stand-side material average temperature, material height, width only
Will be configured. In addition, tension between each stand and offset of finishing height and width
Integral termTo the state vector of equation (5) and the output vector of equation (6)
Add. Then, the state equation used when designing the control system is as follows.
Is led to. (K + 1) = (k) + (k) + (k)
 (13) (k) = (k) + (k) (14) where, state vector, output vector, input vector
Elements and the contents of the coefficient matrix differ depending on the mill format.
Become. The contents of the elements of each vector are explained in the examples.
Reveal. However, the elements of the disturbance vector are common regardless of the Mill format
And is as follows. (K) = [[w₁(Km)]^T (15)₁ (K) = [ΔT_m1 ^*(K), ΔH₁ ^*(K), ΔB
₁ ^*(K)]^T (16) Control system design (Step 4): The conventional multivariable control theory is only feedback control theory.
Met. That is, in the conventional multivariable control theory, the state equation (1
Removed the disturbance vector (k) from Eqs. 3 and 14
Optimal input by minimizing the evaluation function using an expression
vector_optAs (k), the state vector (k)
feedback,_opt(K) =-^*Derive (k)
And the theory of controlling by it. However, in this control system, dimensional control in high-speed rolling is used.
Elephant and high response control, therefore feed
Forward control is required. Therefore, the inventor uses the feedforward control to increase the
The variable control theory was extended. That is, equations of state (13), (1
4) Minimize the evaluation function using the equation. By the way, as a time domain of control theory,
There is a time system. Below is a description of a discrete-time system that is easy to adjust in the actual process.
The multivariable control theory is explained. That is, for the state equations (13) and (14), the evaluation functionOptimal control input that minimizes^*(K) ((31)
We tried to derive (formula). This control theory does not satisfy the equations of state (13) and (14).
Is to minimize the above evaluation function.
Result in the minimization problem. A large number to minimize
There is a scientific method, but here, a typical method,
Grange's undetermined multiplier method was applied. Let Lagrange's undetermined multiplier vector be λ (j), and
The evaluation function L below is minimized.To do this, we use Eq. (18) as a minimum in the range from j = 0 to m.
Then, the limit value with m → ∞ can be obtained. Therefore, ∂λ / ∂ (m + 1) =^TQ (m + 1) +^TQ
・ (M + 1) −λ (m + 1) = 0 (1
9) ∂λ / ∂∂ (j) ＝^TQ (j) +^TQ
(J) +^Tλ (j + 1) −λ (j) = 0 (j = 1 to m) (20) ∂L / ∂ (j) = R (j) +^Tλ (j + 1) = 0 (j = 0 to m) (21) is a necessary condition for optimal manufacturing. The weight matrix R is such that | R | ≠ 0 from R> 0, so equation (21)
Than (j) = R^{-1 T}λ (j + 1) (22) Here, the superscript -1 represents the inverse matrix. In addition, the optimal regulator theory (feedback multivariable system
Theorem) to λ (j) a symmetric matrix P, a vector q
It is assumed that λ (j) = P (j) + q (j) (23) using (j). Analyzing equations (19), (20), (21), (22), and (23)
Solving, m → ∞, the optimal input u_opt(K) isIs. Where the gain matrix^*，_j ^*Is^* = [R +^TP]^{-1 T}P (25)Is given by. However, the matrix P is P =^TQ +^TP-^TP [R +^TP]^-1・
^TThis is the solution of the Riccati equation shown by P (27). By the way, at time k, predictable (15), (16)
The time range of the disturbance defined by the formula is No.n at time k.
From the disturbance (k) reaching the (final) stand, time k
The disturbance that is reached and measured by the inlet side size gauge and thermometer
(K + 1 + l₀) Up to the following time
The external disturbance is unknown. Where l₀: Starting from the dimension meter / thermometer on the mill entrance side
Material transfer time t_do= L₀.Of the discrete time system of Δt
On the other hand, the number of steps_j ^*Examining the properties of the matrix of,
[(-^*)^T]^j-1Contains the term. by the way,
Only state vector feedback, which is the conventional control theory
The system considering is as follows: (k + 1) = (k) + (k) = (-^*) (K) (28), and it is known that Eq. (28) is asymptotically stable.
The That is, when K → ∞, (k) → 0. Therefore, some finite j = l + l₀Then, [(-^*)^T]^j-1≒ 0 That is, j = l + l₀so,_j ^*Repeat the simulation of the weighting matrices Q and R so that ≒ 0
Can be determined by Determination of optimum control gain (step 5): In equation (24), j ≧ l + 1₀= L₀When,_j ^*≒ 0
When the weight matrix Q, R is determined, the right-hand side of Eq. (24)
Approximately two terms, j = 0 to L₀Hit in a finite time until
It can be turned off, and its control system is called a suboptimal control system. At that time, the suboptimal control input u^*(K) is the maximum of (24)
Appropriate control input u_optApproximately from (k)become. Where L₀= L + l₀ It is given by (30). Gain matrix^*，_j ^*Is^* = [R +^TP]^{-1 T}P (25)Becomes. At this time, the disturbance (k + j), j = 0 to L in equation (29)
₀Arrives at the No.n (final) stand at the current time k.
From the reached disturbance (k), at the time k, the size of the mill entrance side
Disturbances measured by a law meter and a thermometer (k + l + l₀) =
(K + L₀) Is measured at each time
, They are all predictable. The first term on the right side of Eq. (29) is feedback control, and the first term on the right side is
The second term is feedforward control. Also, in equation (25)^*, Of (31)_j ^*Is the optimum
Feedback gain, optimum feedforward gain
And, during online processing, the process computer
It is embedded and memorized. Next, the online calculation process is explained. This process is executed by the process computer. Obtained by offline processing and stored in the process computer
Optimal feedback gain and optimal feed forward
Dogain and the state vector measured online
The optimum control input is calculated using the disturbance vector, and its value
Is output to the control device as a manipulated variable
ON in the same way as the online processing of multi-variable control.
Executes line control. This publicly-known online process is performed, for example, in the well-known document: Showa.
60th Plastic Working Spring Lecture p101-104
Variable control (2) (Study on rolling characteristics of wire rod 9
Report) ”(see especially Chapter 3 and Table 3)
It is a thing. [Embodiment] In Fig. 1, between the stands of the independently driven mill of the mill type (3).
Here is the structure of a loop. Fig. 2 shows the target 4-stand mill and the control system of the present invention.
System. The actual results for the mill types of (1), (2), and (3) above
An example is shown below. (1) In the case of a loopless independent drive type mill, the roll gap of the final two stands and the final stamp are used as the operating ends.
Stand as a pivot stand.
Select the number of rotations. In addition, as the controlled variable,
Select the height / width, tension between each stand, and their integrated value.
Bu. The roll gap is selected as one set of horizontal and vertical rolls.
It is possible to use any combination of
When tension control is performed to avoid an increase in stem order
The last two stands, which have the highest dimensional control effect, are used as the operating end.
It was. State method used when designing the control system explained in action
State vector, output vector, input vector, and outside in equations (13) and (14)
The contents of the random vector elements are as follows. (K) = [Δs_i ^*(Kk_i), Δt_fj ^*(K-
k_j), ΔN_j ^*(K), Δ_n ^*(K), Δ_n ^*(K), Δ_fj ^*
(K)]^T (32) (k) = [Δh_n ^*(K), Δb_n ^*(K), Δt
_fj ^*(K), ￣Δh_n ^*k), Δb_n ^*k), Δt_fj ^*(K)]^T (3
3) (k) = [Δs_{ref, i} ^*(K), ΔN_{ref, j} ^*(K)]^T 
(34) (k) = [[w₁(Km)]^T]^T (15)₁ (K) = [ΔT_m1 ^*(K), ΔH₁ ^*(K), ΔB
₁ ^*(K)]^T (16) i = 1, ..., n j = 1, ..., n-1 k_i= 0,1, ..., l_n-1+ ... + 1_i(1≤i≤n-1), k_n= 0 m = 0, l₁, l₁+1₂，…, L₁+1₂+ ... + 1_n-1 k_i: From current time k to No.i stand to last stand
(No.n stand) Separates before the material transfer time in the mill
Each time (k, k−1, ………, k−k)_i) Time k
Time difference between them. Superscript T: Transpose of matrix vector where subscripts i and j for stand No. and subscript for time
Letter k_i, m, the term is repeated as an element of each vector
Is shown. The No. 1 star mill with the 4-stand mill under the rolling conditions shown in Table 2
Input side material average temperature, input side material height / width is ΔT_m1 ^*=
−0.091, ΔH₁ ^*= ΔB₁ ^*Change in steps by 0.033
We examined the case. Tension without control Δt_fj ^*, Outlet height Δh_i ^*， Outside
Width Δb^* _iThe step response of is shown in Figs. Here, the material temperature and material dimensional fluctuations are measured by the
The time when the side dimension meter is reached is t = 0 seconds. Figures 7 to 11 show tension control + final two-stand AGC
Tension Δt with control_fj ^*, Outlet height Δh_i ^*， Outside
Width Δb_i ^*, Roll speed ΔN_i ^*And roll gap Δs_i ^*
FIG. 6 is an exemplary diagram of a step response of. At this time, the operating end is Δs₃ ^*, Δs_Four ^*, ΔN₁ ^*, ΔN₂ ^*，
ΔN₃ ^*And the weight matrices Q and R are Q = diag (100,100,100,100,100,50,50,1,1,1) R = diag (1, 10, 0.2, 0.5, 0.8). Where diag represents the diagonal elements of the matrix. Tension, finishing stand Exit side height / width is short.
It can be seen that the Husset = 0 is controlled. (2) In case of common drive system and block mill Select the roll gap of No.1 and No.4 stand as the operation end,
The control amount is the height / width of the final stand and the integrated value.
The State method used when designing the control system explained in action
State vector and output vector in equations (13) and (14)
Toru, input vector, disturbance vector element contents
Is as follows. (K) = [Δs₁ ^*(Kk₁), Δs_n ^*(K), Δt_fj ^*(Kk_j), Δ_n ^*(K), Δ_n ^*(K)]^T 
(35) (k) = [Δh_n ^*(K), Δb_n ^*(K), Δ_n ^*(K), Δ_n ^*(K)]^T (36) (k) = [Δs_{ref, i} ^*(K), Δs_{ref, n} ^*(K)]^T 
(37) (k) = [[w₁(Km)]^T]^T (15)₁ (K) = [ΔT_m1 ^*(K), ΔH₁ ^*(K), ΔB
₁ ^*(K)]^T (16) i = 1, ..., n j = 1, ..., n-1 k_i= 0,1, ..., l_n-1+ ... + 1_i(1≤i≤n-1), k_n= 0 m = 0, l₁, l₁+1₂，…, L₁+1₂+ ... + 1_n-1 Similar to the mill of (1), the 4-star rolling conditions shown in Table 2
No.1 stand, the material height and the material width of the
ΔH₁ ^*= ΔB₁ ^*= 0.033 when changed in steps
Was examined. Tension without control Δt_fj ^*, Outlet material height Δh_i ^*，
Δb_i ^*The step response of is shown in Figs. here
The time when the material dimension variation reaches the entry side dimension gauge is t = 0 seconds
did. Figures 15 to 18 show No. 1 (start) and No. n (final) stands
Tension Δt with control by AGC of_fj ^*， Outside material height
Δh_i ^*, Output material width Δb_i ^*, Roll gap Δs_i ^*The
FIG. 6 is an exemplary diagram of a response of a top. In this case, the weighting matrices Q and R are Q = diag (100,100,100,100) R = diag (1,10). Finishing stand exit side height Δh_Four ^*, Output side width Δb_Four ^*Is offset
Is controlled to 0. (3) In case of independently driven mill with loop
Stand as a pivot stand.
Select the number of rotations. In addition, as the controlled variable,
Height / width and loop height between stands and their integrals
Choose a value. In addition, the selection of roll gap is independent of loopless.
The final 2 star with the highest dimensional control effect as well as the vertical drive mill
As the operating end. Here, the state vector of equation (32) and the output vector of equation (33)
Convert tortle element tension to loop height by:
(See FIG. 1). 1) In bending theory, the bending moment acting on the loop and
From the relationship of curvature and 2) Hooke's law, the tension t_fiAnd Lou
Length l_aiRelationship is t_fi-T_f0i= C_1i(L_ai-L_a0i) / L_a0i (38) where subscript 0: reference state, C_1i: Constant loop height y_hiAnd loop length l_aiThe geometric relation of is (y_hi-Y_h0i) / Y_h0i= (L_ai-L_a0i) / L_a0i (39) where C_2i: Constant From equations (38) and (39), tension Δt_fj ^*(K) and loop height
Δy_hj ^*The relationship of (k) is Δy_hj ^*(K) = C_2i/ C_1i・ K_fm0j・ Δt_fj ^*(K) (4
It is given by 0). Therefore, using the relationship of Eq. (40), (3
Convert the tension of the elements in 2) and (33) to the loop height
Then, equations (41) and (42) are obtained, respectively.

The elements of the state vector, output vector, input vector, and disturbance vector in the state equations (13) and (14) used when designing the control system described in the operation are as follows. (K) = [Δs _i ^* (k−k _i ), Δy _hj ^* (k−
k _j ), ΔN _j ^* (k), Δ _n ^* (k), Δ _n ^* (k), Δ _hj ^*
(K)] ^T (41) (k) = [Δh _n ^* (k), Δb _n ^* (k), Δy
^{_{hj * (k), Δ n}} * (k), Δ n * (k), Δ hj * (k)] T (42) (k) = [Δs ref, i * (k), ΔN ref, j * ] ^T (43) (k) = [[w ₁ (km)] ^T ] ^T (15) ₁ (k) = [ΔT _m1 ^* (k), ΔH ₁ ^* (k), ΔB
₁ ^* (k)] ^T (16) i = 1, ..., n j = 1, ..., n-1 k _i = 0,1, ..., l _n-1 + ... + l _i (1 ≦ i ≦ n− 1), k _n = 0 m = 0, l ₁ , l ₁ ＋ l ₂ ,…, l ₁ ＋ l ₂ ＋ ・ ・ ・ ＋ l _n-1 4 stand mill with rolling conditions shown in Table 4, No. 1 stand entry side Material average temperature, inlet material height, inlet material width is ΔT
_m1 ^* = -0.028, was studied for the case where a change in ^{_{ΔH 1 * = ΔB 1 * =}} 0.007 by the step-like. Figures 19 to 21 show the loop height Δ without control.
FIG. 6 is an exemplary diagram of y _hj ^* , outgoing material height Δh _i ^* , outgoing material width Δb _i ^* step response. Here, the time at which the material temperature and material dimension fluctuations reach the entrance side dimension gauge is t = 0 seconds. 22 to 26 show loop height control + final 2 stand AGC
Loop height Δy _hj ^* , _output material height Δh _i ^* , output material width Δb _i ^* , roll speed ΔN _i ^* ,
FIG. 6 is an exemplary diagram of a step response of a roll gap Δs _i ^* . In this case, the operating end is set to Δs ₃ ^* , Δs ₄ ^* , ΔN ₁ ^* , ΔN ₂ ^* ,
ΔN ₃ ^* , and the weighting matrices Q and R are Q = diag (100,100,200,200,200,100,100,10,10,10) R = diag (1, 5, 0.5, 0.8, 1). The loop height, finishing stand exit side material height, and exit side material width are controlled to offset = 0 in a short settling time. In this embodiment, the dimensional control method of the wire / bar material in the two-roll mill shown in FIG. 2 is shown, but the three-roll mill, in which three and four rolls are installed per stand, respectively.
Also in the dimension control in the roll mill, if the values of the coefficient matrices A to F of the equation of state are replaced with the values of the mill, it is possible to control to the target value with high response and accuracy by the method of the present invention. Further, also in the dimension control of the shaped steel mill, the steel pipe mill, the hot strip mill, and the cold strip mill, if the values of the coefficient matrices A to F of the equation of state are replaced with the values of the mill, the dimension control of the present invention is performed. The method can control the target value with high response and high accuracy. In this embodiment, the quadratic form is used as the form of the number of evaluations used when designing the control system. However, it is defined in a function of another form and multivariables of feedforward control + feedback control are used in the same manner. If the control system is constructed and the optimum gain is calculated, online dimension control is possible as in the present embodiment. [Effects of the Invention] As described above, in the case of this embodiment according to the present invention, the optimum gain, the dimension on the mill entrance side, the temperature, and the mill determined based on the multivariable control theory extended by the feedforward control. Dimension on the outlet side Further, for the loopless / independently driven mill of the mill type (1), the actual measured value or measured value of the tension on each stand outlet side, and for the loop of the mill type (3) / Independently driven mill, the loop on the outlet side of each stand By using the time-series measurement value of the actual measurement value of the
In the independently driven mills of the mill types (1) and (3), reduction of the final two stands and roll rotation speed of each stand except the pivot stand (the final stand in this embodiment), common drive / block mill of the mill type (2) In order to operate the No. 1 (starting stand) and No. n (final stand) reductions in a short cycle time series, the maximum speed of the following mill types (1) and (3) is around 10 m / s, In the high speed rolling of the mill type (2) with a maximum speed of around 100 m / s, the final stand exit side (finishing) dimension is offset (with the target value) with a short settling time (high response) in response to high-speed varying inlet side dimension. Deviation) = 0 (high accuracy), which gives an excellent control result.

[Brief description of drawings]

FIG. 1 is a diagram showing the structure of a loop between stands, and FIG. 2 is a configuration diagram showing an embodiment of the present invention. FIG. 3 shows a flowchart composed of off-line calculation processing and on-line control showing from modeling of the present invention to determination of optimum feedback control gain and optimum feedforward control gain based on multivariable control theory extended by feedforward control. It is a figure. Step response of loopless / independent drive mill
Shown in Fig. 11. 4 to 6 are illustrations of the step response of the tension Δt _fj ^* , the output material height Δh _i ^* , and the output material width Δb _i ^* without control, and FIGS. 7 to 11 are the tensions. Control + final two-stand tension with control by AGC Δt _fj ^* , output material height Δh _i ^* ,
It is an illustration figure of the step response of the delivery side material width Δb _i ^* , the roll speed ΔN _i ^*, and the roll gap Δs _i ^* . Step response of common drive / block mill is shown in Figs.
Shown in the figure. 12 to 14 are examples of step response of tension Δt _fj ^* , output material height Δh _i ^* , and output material width Δb _i ^* without control, and FIGS. 15 to 18 are No. .1 (starting stand) + No.n (final stand) with AGC control tension Δt _fj ^* , delivery side material height Δh _i ^* , delivery side material width Δb _i ^* and roll gap Δs _i ^* It is an illustration of a step response. The step response of the loop / independent drive mill is shown in Figs. 19 to 21 show the loop height Δy _j ^* without control,
Illustration of step response of exit side height Δh _i ^* and exit side width Δb _i ^* , Figures 22 to 26 show loop height control + final two-stand AGC
FIG. 7 is an exemplary diagram of a step response of a loop height Δy _j ^* , a delivery side material height Δh _i ^* , a delivery side material width Δb _i ^* , a roll rotational speed ΔN _i ^*, and a roll gap Δs _i ^{* in} the case where there is control by ． The numbers in Figure 1 are as follows. 1: No.i stand roll 2: No.i + 1 stand roll 3, 4: Guide roll 5: Kick-out roll, 6: Loop height detector, 7: Pass line,
8: Materials The numbers in Figure 2 are as follows. 9,11: Horizontal rolls 10, 12: Vertical rolls 13: Inlet thermometer, 14: Inlet dimension gauge, 15: Outlet dimension gauge, 16: Control calculator, 17: Material

 ─────────────────────────────────────────────────── ─── Continuation of front page (72) Inventor Toru Yamaguchi 23-15 Suzuko-cho, Kamaishi-shi, Iwate Nippon Steel Co., Ltd.Kamaishi Steel Co., Ltd. Muroran Works (56) References JP 62-244508 (JP, A) JP 62-244509 (JP, A)

Claims (3)

[Claims] 1. When rolling a wire rod or a bar rod by a loopless independent drive type mill consisting of multi-stage stands, a mill drive system linear model of roll gap and roll speed is created, The deviation (disturbance vector) is calculated from the measured value of the temperature and the reference value, the dimension deviation from the measured value of the material size on the rolling mill exit side and the target value, and the measured value of the roll gap and roll speed of each stand, Calculate the deviation from the estimated or measured value of tension and each reference value,
The rolling state quantity (state vector) is constructed, and the control quantity (output vector) is constructed from the deviation of the mill exit side dimension and tension from the target value and their integrated value, and the target of the roll gap and roll speed of each stand The manipulated variable (input vector) is constructed from the deviation obtained from the value and the reference value, and the dynamic phenomenon of continuous rolling is
The dynamic change of tension (state vector) (in the continuous time system, the time derivative of the tension (state vector) at time t, in the discrete time system, the value of the tension (state vector) at time k + 1) is In the discrete-time system at time t, the dynamic model and output vector and state vector represented by using the values of the state vector, input vector, and disturbance vector at time k,
It is represented by a rolling state equation consisting of output equations that express the static relationship of the disturbance vector, and by combining it with the mill drive system model and the material transfer equation between each stand regarding dimensions and temperature, the state equation of the entire system is obtained. Create an equation of state for the entire system to be used when designing a control system according to the mill control method, and introduce an evaluation function consisting of an output vector representing the controlled variable and an input vector representing the manipulated variable. Determine the manipulated variable (input vector) of the multi-variable control system consisting of feedforward control and feedback control that minimizes the value of, and control the dimension of the rolled material released from the final stand of the mill (output vector) to the target value. A dimension control method characterized by the above. Here, the mill drive system model is a model that represents the relationship between the time delay of the measured value and the target value of the control device (roll reduction system, roll rotation system). Further, the material transfer type means that when the material is transferred from the No.i stand on the upstream side to the No.i + 1 stand on the downstream side, the material average temperature of the No.i + 1 stand entrance side, the material height of the entrance side, and the width No.i This is a model showing the relationship between the average material temperature on the entrance side of the stand, the material height on the exit side, and the width. 2. When rolling a wire rod or bar material by a common drive type block mill consisting of multi-stage stands, a mill drive system linear model of the roll gap is created, and the measured values of the material size and temperature on the rolling mill entrance side are The deviation (disturbance vector) is calculated from the reference value, and the dimension deviation from the measured value and the target value of the material dimension on the rolling mill exit side, the measured value of the roll gap of each stand, the estimated value of tension, or the standard of the measured value The deviation is calculated from the value, the rolling state quantity (state vector) is constructed, the control quantity (output vector) is constructed from the deviation of the mill exit side dimension from the target value and its integrated value, and the roll of the first stand and the last stand The manipulated variable (input vector) is constructed from the deviation obtained from the target value of the gap and the reference value, and the dynamic phenomenon of continuous rolling is determined by the dynamic change of tension (state vector) (at time t in continuous time system). It takes time differential value of the tension (state vector), the discrete-time system, the continuous-time system value) of tension (state vector) at time k + 1, time t
In the discrete-time system, a rolling model consisting of a dynamic model expressed using the values of the state vector, input vector, and disturbance vector at time k, and an output equation expressing the static relationship between the output vector and the state vector, disturbance vector The state equation of the whole system is created by combining it with the above-mentioned mill drive system model and the material transfer equation between each stand concerning dimensions and temperature.
According to the control method of the mill, the state equation of the entire system used when designing the control system is constructed, and an evaluation function consisting of an output vector representing the controlled variable and an input vector representing the manipulated variable is introduced.
The manipulated variable (input vector) of the multivariable control system consisting of feedforward control and feedback control that minimizes the value of the evaluation function is obtained, and the dimension of the rolled material (output vector) released from the final stand of the mill is set as the target value. A dimension control method characterized in that it is controlled to. Here, the mill drive system model is a model that represents the relationship between the time delay of the measured value and the target value of the control device (roll reduction system, roll rotation system). Further, the material transfer type means that when the material is transferred from the No.i stand on the upstream side to the No.i + 1 stand on the downstream side, the material average temperature of the No.i + 1 stand entrance side, the material height of the entrance side, and the width No.i This is a model showing the relationship between the average material temperature on the entrance side of the stand, the material height on the exit side, and the width. 3. A mill drive system linear model of roll gap and roll speed is prepared when rolling a wire rod or a bar rod by an independently driven mill having a loop consisting of multi-stage stands, and the material size on the inlet side of the rolling mill is prepared. , The deviation (disturbance vector) is obtained from the measured value of the temperature and the reference value, and the dimension deviation is calculated from the measured value of the material size on the delivery side of the rolling mill and the target value, and the measured value of the roll gap of each stand and the loop height. The deviation is calculated from the actual measurement value of the mill and each reference value to form the rolling state quantity (state vector). From the deviation of the mill exit side dimension and the loop height from the target value and their integrated values, the control quantity (output vector) is calculated. ), The operation amount (input vector) is constructed from the deviation of the roll gap of each stand and the target value of the roll speed and the reference value, and the dynamic phenomenon of continuous rolling is defined by the loop height (state vector). Die Mick changes (in the continuous-time system, the time derivative of the loop height (state vector) at time t, in the discrete-time system, the loop height (state vector) value at the time k + 1) in continuous-time system. In the discrete-time system, a rolling model consisting of a dynamic model expressed using the values of the state vector, input vector, and disturbance vector at time k, and an output equation expressing the static relationship between the output vector and the state vector, disturbance vector The state equation of the entire system is created by combining it with the mill drive system model and the material transfer equations for each stand related to dimensions and temperature, which is used when designing the control system according to the mill control method. Form an equation of state for the entire system and derive an evaluation function consisting of an output vector that represents the controlled variable and an input vector that represents the manipulated variable. Then, the manipulated variable (input vector) of the multivariable control system consisting of feedforward control and feedback control that minimizes the value of the evaluation function is obtained, and the dimension (output vector) of the rolled material discharged from the final stand of the mill is calculated. A dimension control method characterized by controlling to a target value. Here, the mill drive system model is a model that represents the relationship between the time delay of the measured value and the target value of the control device (roll reduction system, roll rotation system). Further, the material transfer type means that when the material is transferred from the No.i stand on the upstream side to the No.i + 1 stand on the downstream side, the material average temperature of the No.i + 1 stand entrance side, the material height of the entrance side, and the width No.i This is a model showing the relationship between the average material temperature on the entrance side of the stand, the material height on the exit side, and the width.