JP2649370B2 - Control method using evaluation function - Google Patents

Description

Description: BACKGROUND OF THE INVENTION The present invention relates to a control method using an evaluation function, and in particular, to match a plurality of control amounts to a predetermined target value by changing a plurality of operation amounts. Control method that can be performed.

[Conventional technology]

In the case of controlling a plurality of control variables using a plurality of control variables so as to minimize an evaluation function in which the term of the square of the deviation between the target value and the actual value is one element, generally, the control variable M There is a relationship expressed by the following equation between _i (i = 1 to _m ) and the control amount C _j (j = 1 to n).

Here, G _ij is the transfer function relating to the control amount C _i and the operation amount M _j. Is generally G _ij ≠ 0, when it changes the certain operation amount M _i, represents that all of the control amount C _{i (i} = 1~n) is changed accordingly.

In order to bring the above-described control amount close to a certain target value, an evaluation function having a factor of the sum of squares of the deviation between the control amount and the target value is used, and the value of this evaluation function is maximum or minimum. A control method is known (for example, JP-A-59-168502).

However, the technique of the above publication discloses that when increasing or decreasing the weight coefficient in the evaluation function, it is performed while watching the CRT screen, that is, using the CRT screen as a tool is disclosed. It was not shown how to determine the value of.

In the conventional evaluation function, the basic idea is to substitute the target value into the control amount of equation (1) in order to make the control amount expressed by equation (1) coincide with the target value, The solution was to solve the equation for the manipulated variable and determine the manipulated variable M to be determined.

[Problems to be solved by the invention]

However, a strong correlation exists between the operating end M _i and M _j, the independence so not seen such a controlled object, the value of the manipulated variable M to match the control amount to the target value Becomes a large value. In general, since the manipulated variable M has a control limit, the answer simply solved by the simultaneous equation of the equation (1) is an unrealizable value. That is, in a controlled object having n independent operation amounts, it is possible to operate the n control amounts within the limit of the operation amount, but if there is a strong correlation between the operation amounts, , N is difficult to control independently.

When control is performed in such a system as to make the control amount equal to the target value, the operation amount always reaches the upper and lower limit values, and the operation of the plant becomes extremely unstable.

Such a correlation between the manipulated variables usually largely depends on operating conditions. In actual operation, under certain conditions, n control amounts can be controlled stably in operation with n operation amounts, so the operator operates as many control amounts as possible to improve quality. With certain conditions
If an attempt is made to operate the individual control variables, the operation will become unstable, leading to an accident.Therefore, the control variables that allow a certain amount of error must be free to some extent, and the operation must be performed by paying attention to the minimum required control variable. .

An object of the present invention relates to a control method using an evaluation function that enables a system to exhibit the best performance in a system in which a plurality of control amounts are controlled by a plurality of operation amounts with a correlation.

[Means for solving the problem]

In order to achieve the above object, a control method using an evaluation function of the present invention squares a deviation amount of each of a plurality of control amounts with respect to each target value, multiplies the value by a weighting factor, and calculates all the multiplication values. Are summed to obtain an evaluation function, and a plurality of operation amounts correlated with the plurality of control amounts are operated so as to minimize the value of the evaluation function, thereby performing control to bring the plurality of control amounts closer to a target value. In the control method using the evaluation function, when the number of independently controlled control variables decreases and the correlation between the control variables is strong, the weight coefficient of the weighting coefficient is increased in terms other than the specific term among the terms including the control variable. It is characterized in that the size is reduced.

[Action]

According to the above configuration, when the number of independently controlled control variables is reduced due to the operating conditions and the correlation between the control variables is strong, among the evaluation function terms related to the control variables having a strong correlation, a term other than a specific term is used. Then, the magnitude of the weight coefficient is set small. As a result, it is possible to prevent the operation amount having a strong correlation from reaching the operation limit while sacrificing a defect in the control amount within an allowable range, thereby stabilizing the operation. Conversely, in operating conditions where each manipulated variable is independent, equalizing the weighting factor of each controlled variable ensures operational stability and at the same time, each controlled variable matches the target value. Can be done.

〔Example〕

Hereinafter, as one embodiment of the present invention, shape control of a rolled material in a rolling plant will be described.

As shown in FIG. 2, the rolling mill 10 includes a pair of work rolls 11, an intermediate roll 12, and a backup roll 13, each of which is provided with a rolling force. Rolled material clamped
14 is to be rolled. The shape of the rolled material 14 is detected by a shape detector 15 installed on the exit side of the rolling mill 1.

By the way, as shown in FIG. 3, the shape of a rolled material is generally represented by the distribution of the elongation in the longitudinal direction of the rolled material due to rolling in the width direction of the plate. This is quantitatively represented by the elongation difference ratio ε, which is obtained by the following equation.

Here, l _0: reference line length in the longitudinal direction of the rolled material l: rolled material wave at l ₀ section arc length x: an arbitrary position in the plate width direction of the rolled material.

The shape control according to the present embodiment is to control the distribution of the elongation difference ratio ε to a target value.

The distribution of the difference in elongation ε is determined by the roll deflection due to the rolling force,
It is determined by the roll shape, the thickness distribution of the rolled material, and the like. Generally, the means for operating the shape of the rolled material include a work roll 11
Work roll bender (not shown) that gives deflection to
There is an intermediate roll bender (not shown) that provides bending to the intermediate roll 12. These two vendors are provided on the drive side and the operation side of the rolling mill.
Since there are cases where the operation is performed symmetrically and cases where the operation is performed asymmetrically, this embodiment has four types of operation amounts.

On the other hand, in order to control the distribution of the elongation difference ε, it is necessary to recognize the elongation difference ε again as a control variable. Various methods have been proposed, and one of them is a method of expressing a difference in elongation percentage in the sheet width direction by a coefficient of a fourth order power series shown in the following equation.

ε = a ₁ x + a ₂ x ² + a ₃ x ³ + a ₄ x ⁴ (3) where x: coordinates a _i (i = 1 to 4) in the width direction of the rolled material: width series coefficient.

Then, the width series a _i (i =
The relationship with (1) to (4) is expressed by the following equation.

Where F ₁ : work roll bender (symmetric component) F ₂ : 〃 (asymmetric component) F ₃ : intermediate roll bender (symmetric component) F ₄ : 〃 (asymmetric component) G _ij : transmission of ΔF _j and Δa _i Function Δ: a symbol representing a change.

In addition, the symmetric component of each vendor has little effect on Δa ₁ , Δa ₃ , and the asymmetric component has Δa ₂ ,
By not affecting Δa ₄ , equation (4) can be further transformed into the following equation.

Here, since equations (5) and (6) can be handled independently,
Hereinafter, the control target represented by the expression (5) will be described.

G changes depending on rolling conditions, and particularly greatly affects the width of the rolled material. Since the intermediate roll and the work roll usually have different roll diameters, the shape of the bending distribution of the roll by the bender differs. However, as the sheet width of the rolled material becomes narrower, the deflection distribution shapes of the rolls in contact with the rolled material become substantially the same, which means that there is a strong correlation between ΔF ₁ and ΔF ₃ .

Therefore, when trying to control the shape of a rolled material having a narrow sheet width for both Δa ₂ and Δa ₄ , the values of ΔF ₁ and ΔF ₃ reach the upper and lower limits, not only rolling becomes unstable, but also the shape becomes As a result, the defect itself is not fixed.

Therefore, in the present embodiment, a control system as shown in FIG. 1 is applied to the above phenomenon.

First, the shape detection device 1 outputs the elongation difference rate distribution ε (x) to the shape recognition device 2. The shape recognition device 2 uses ε
The fourth-order function coefficient a _i (i = 1 to 4) of (x) is output to the optimal control device 3. The optimal control device 3 calculates the shape target value a
_{Using the ir} (i = 1 to 4) and the actual product a _i (i = 1 to 4), the bender force ΔF _i (i = 1 to 4) is set so as to minimize the value of the evaluation function J defined by the following equation. 4) is determined and the binder of the rolling mill is operated.

J = w ₁ (Δa _1r −Δa ₁ ) ² + w ₂ (Δa _2r −Δa ₂ ) ² + w ₃ (Δa _3r −Δa ₃ ) ² + w ₄ (Δa _4r −Δa ₄ ) ² ...
(7) Here, w _i (i = 1 to 4) is a weight coefficient. In addition,
The w _{i (i} = 1~4) is a function of plate width of the rolled material, .DELTA.a ₂ when the plate width becomes narrow, since .DELTA.a ₄ is the correlation is stronger, w ₄ is small compared to the wide plate width following It is determined to be a value.
The determined value of w is output from the weighting factor setting device 4 to the optimal control device 3, and the work roll bender and the intermediate roll bender are controlled.

Therefore, when operating with narrow rolled material,
Higher order components (Δa ₃ , Δa ₄ ) of the shape defect are somewhat sacrificed, and large shape defect components (Δa ₁ , Δa ₂ ) are concentrated and controlled.

As a result, it is possible to secure a stable operation without reaching the limit value of the binder, and it is also possible to correct a low-level rough empty defect with respect to a defective shape.

[Effects of the Invention] As described above, according to the present invention, it is possible to select a weighting coefficient of an evaluation function to an optimal value in accordance with the control capability of a plant that changes depending on operating conditions, and to improve product quality. Improvements and operational stability can be ensured.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a control system according to the present invention,
FIG. 2 is a schematic diagram of a rolling plant to which the present invention is applied, and FIG. 3 is a diagram illustrating the shape of a rolled material. DESCRIPTION OF SYMBOLS 1 ... Shape detection device, 2 ... Shape recognition device, 3 ... Optimal control device, 4 ... Weight coefficient setting device, 10 ... Rolling machine, 11 ... Work roll, 12 ... Intermediate roll, 13 ... Backup roll. 14 ... rolled material, 15 ... shape detector.

Claims (1)

(57) [Claims] 1. An evaluation function is obtained by squaring a deviation amount of each of a plurality of control amounts with respect to each target value, multiplying the squared value by a weighting coefficient, and summing all the multiplied values to obtain an evaluation function. In a control method using an evaluation function for controlling a plurality of manipulated variables correlated with the plurality of controlled variables so as to be a minimum to bring the plurality of controlled variables closer to a target value, wherein the control is independently controlled. When the number of variables is reduced and the mutual correlation between the controlled variables is strong, an evaluation function characterized by reducing the magnitude of the weighting coefficient in terms other than the specific term among the terms including the controlled variable is used. Control method.