KR19980035770A - Calculation of Optimum Gain for Feed Forward Automatic Width Control in Plate Milling Process - Google Patents

Abstract

The present invention relates to a feedforward automatic width control optimum gain calculation method in a thick plate process, and more particularly, to a feedforward automatic width control method using a rolling model and a feedforward control model The present invention relates to a feedforward automatic width control optimization gain calculation method in a thick plate process in which a transfer function of an output side plate width variation with respect to a side plate width variation is derived formally and an optimal control gain is thereby calculated.

As a trial and error method by the conventional simulation, the optimal gain value according to the plasticity coefficient, the milling constant and the width recovery rate should be tabulated and selected in advance. If the range of plasticity coefficient is wide, In the case where parameters such as the constant of the millimeter and the recovery rate of the width are changed, it is troublesome to re-calculate the gain value again by simulation or classical method, The gain value obtained by the method of the present invention is set as a function of the mill constant, the plasticity coefficient, and the width recovery rate, so that the program can be simplified and it is possible to eliminate the hassle of correcting the program or correcting the gain again will be.

Description

Calculation of Optimum Gain for Feed Forward Automatic Width Control in Plate Milling Process

The present invention relates to a feedforward automatic width control optimum gain calculation method in a thick plate process, and more particularly to a feedforward automatic width control optimum gain control method using a rolling model and a feedforward control model The present invention relates to a feedforward automatic width control optimum gain calculation method in a thick plate process in which a transfer function of an output side plate width variation with respect to a side plate width variation is derived formally and an optimal control gain is thereby calculated.

Generally, there is a process of controlling the plate width through an Ezer rolling roll (horizontal rolling roll) and then controlling the plate thickness through a vertical rolling roll in an iron plate process in a thick plate process. The plate width performed by the Ezer rolling roll The feedforward method is used in a controlled manner.

The principle of the feedforward automatic widthwise control is to measure the width deviation from the width measuring device located at the front end of the EZR rolling roll and to measure the width position of the steel plate on which the width deviation is measured from the time depending on the distance between the EZR rolling roll and the width measuring period and the rolling speed Is calculated on the basis of the measured width deviation at the time of entry into the Ezer rolling roll, and is input to the position control system, thereby controlling the width of the sheet.

In the conventional method using the feedforward plate width control method as described above, in the method of setting the control gains that affect the accuracy of the feedforward automatic plate width control, it is necessary to use a rough value obtained from existing experience or a trial and error method The accurate width control can not be performed and thus the defect occurrence rate is greatly increased to cause a disruption in the production process and accordingly the width shear loss is increased in the correction line of the thick plate process, There is a problem.

The present invention has been made to solve the above problems and to achieve improvements.

SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to provide a feedforward automatic width control method and apparatus capable of optimally controlling the output width variation by using a rolling model and a feedforward control model, And the feedforward automatic width control optimization gain calculation method in the thick plate process in which the optimum control gain is calculated as a function of the specific constant, the plasticity coefficient, and the width recovery rate.

As a technical means for achieving the object of the present invention, in the method of calculating the feed forward automatic width control optimum gain in the thick plate process of the present invention, the width W is measured and the width deviation (Wi) 40), and the automatic width control (AWC) computer 40 calculates the optimal control gain (Gf) by using the rolling model and the control algorithm using the width deviation? Wi corresponding to the input width deviation (We = F / M + S) as a function of the linearized eccentricity, the plasticity coefficient, the Edger inlet side width Wi and the gap between two vertical rolls, And the load fluctuation amount is expressed as a function of the eccentric number, the plasticity coefficient, the fluctuation amount on the inlet side side, and the variation amount of the low gap, and the output fluctuation amount after the horizontal rolling from the width variation model is expressed as , A step of expressing the variation of the force as a function of the first step; (M), the plasticity coefficient (Q), and the thickness of the iron plate at the time when the position of the iron plate on which the width deviation is measured is inserted into the Ezer rolling roll from the time of the Ezer rolling roll and the width measuring period and the time corresponding to the rolling speed, A second step of calculating a pushdown amount command value? S * from the control gain Gf; A third step of expressing the dynamic characteristics of the hydraulic control by a Laplace transfer function and calculating a gap constant amount command value DELTA S * and a roll gap variation amount DELTA S which is a low duty ratio from the low dynamic characteristic transfer function to the hydraulic pressure; A fourth step of calculating an output width variation amount? Wo by assigning the load power amount determination? F and the screw down determination amount command value? S * to the roll gap variation amount? S; A fifth step of calculating the width control transfer function? Wo /? Wi by substituting the roll gap variation into the output width variation? Wo; A sixth step of calculating an optimum gain (Gf) for minimizing? Wo against? Wi from the width control transfer function? Wo /? Wi; . ≪ / RTI >

FIG. 1 is a configuration diagram showing a feedforward automatic width control apparatus according to the present invention,

FIG. 2 is a mill characteristic diagram for deriving a rolling model according to the present invention,

FIG. 3 is a reference diagram for deriving a simplified width variation model according to the present invention,

FIG. 4 is a flow chart showing a feed forward automatic width control optimum gain calculating method in the thick plate process according to the present invention,

FIG. 5 is a block diagram showing a rolling modification model, a simple width change model, a feedforward control algorithm, and a feedforward automatic width control optimized gain calculation system modeled from the dynamic characteristics of a hydraulic system under a hydraulic pressure according to the present invention.

Description of the Related Art [0002]

10: width measuring instrument 20: edger rolling roll

30: horizontal rolling roll 40: automatic width control (AWC) computer

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a configuration of an apparatus for performing a feedforward automatic width control optimization gain calculation method in a thick plate process according to the present invention will be described with reference to the accompanying drawings.

FIG. 1 is a configuration diagram of a feedforward automatic width control apparatus according to the present invention. Referring to FIG. 1, the apparatus for performing a feedforward automatic width control control optimum gain calculating method in a thick plate process according to the present invention comprises: After measuring the plate width with respect to the steel plate conveyed by the roller, the deviation? Wi from the target width value set in advance is calculated, and the point at which the plate is inserted into the low roller is tracked, and the plate width deviation from the rolling model and control gains An automatic sheet width control (AWC) computer 40 having a function of calculating an opening correction amount DELTA S * according to the sheet size, an Eger rolling roll 20 for controlling the sheet width by correcting the opening degree by an instruction value from the computer, And a horizontal rolling roll for controlling the thickness of the plate.

FIG. 2 is a view showing a mill characteristic diagram for deriving a rolling modification model according to the present invention, FIG. 3 is a reference diagram for deriving a simplified width variation model according to the present invention, FIG. 5 is a flow chart showing an automatic gain control method for automatic width control; FIG. 5 is a flow chart showing a method for calculating optimum gain from a rolling modification model, a simple width change model, a feedforward control algorithm, and a feedforward automatic width control modeled from low- Is a block diagram for deriving the equation.

The process of calculating the optimum value of the control gain Gf used for calculating the opening correction amount DELTA S * of the automatic width control thus configured will be described in detail below with reference to the accompanying drawings.

Referring to FIG. 4, in a first step 41, a linearized eccentricity, a plasticity coefficient, an Edger inlet side width (Wi, We) and a gap (s) The model is expressed as a function of the amount of fluctuation of the load force, the plasticity coefficient, the fluctuation amount of the Ezer inlet / outlet side, and the amount of the variation in the amount of the gap, by merging with the metric model (We = F / M + S) (Wo) of the material according to the whet characteristics in the automatic width control (AWC) computer 40, and the low gap (W0) S), and then calculates the load power quantity (ΔF), which is a minute variation, from the load force.

More specifically, the equation for calculating the load force F from the mill characteristic diagram shown in FIG. 1 is expressed by the following equation (1).

... ... ... ... (One)

Where F is the load force, M (= ∂F / ∂S) is the mill constant [ton / mm], Q is the plasticity factor (Material Stiffness = -∂F / ∂Wi) [ton / (M) and plasticity factor (Q) are calculated by the host computer, and the automatic width control (W) is calculated by the host computer. It is transmitted to the computer through communication.

From the above equation (1), the output width Wo is expressed by the following equation (2).

... ... ... ... (2)

Therefore, when the equation (2) is substituted into the equation (1), the calculation formula for calculating the load force F is expressed by the following equation (3) .

... ... ... ... (3)

... ... ... ... (4)

From the simplified width variation model shown in Fig. 2, the output width Wo is expressed by the following equations (5) and (6), and the following equation (6)

... ... ... ... (5)

... ... ... ... (6)

... ... ... ... (7)

Here, We is a plate width after edging, and? Is a width recovery ratio after horizontal rolling, and is generally known to have a value of about 0.5 to 0.7.

Next, in the second step (42), the width deviation at the time when the position of the iron plate on which the width deviation is measured from the time of the width measuring period and the time taken by the rolling speed, (? S *) is calculated from the melt index (M), the plasticity coefficient (Q) and the control gain (Gf).

Specifically, as described above, the principle of feedforward automatic width control is to measure the width deviation from the width measuring device located at the upstream side of the edge rolling roll, to measure the distance between the edge rolling roll and the width measuring period and the time , The amount of pressure reduction corresponding to the measured width deviation is calculated at the time when the position of the iron plate on which the width deviation is measured is entered into the Ezer rolling roll and is input to the position control system so as to control the plate width. The automatic width control (AWC) computer 40 that controls the automatic width control (AWC) computer 40 calculates the push-pull correction amount DELTA S * as shown in the following equation (8).

... ... ... ... (8)

Here, Gf is a feedforward control gain. From the above results, the feedforward automatic width control optimum gain calculation system is modeled as shown in FIG. 5. In FIG. 5, reference numeral 58 denotes a low dynamic characteristic of the hydraulic pressure, which can be expressed by the equations (9) and (10) in consideration of the dynamic characteristics of the controller, the sub valve and the cylinder (not shown).

... ... ... ... (9)

... ... ... ... (10)

K = K1 / K2 (1 + Ts) (T: Time constant) is the dynamic characteristic of the servo valve, K3 / s is the dynamic characteristic of the cylinder, K1 / K2 is the proportional controller gain, K3.

Next, in the third step 43, the dynamic characteristics of the lower part are expressed by the Laplace transfer function, and the roll gap variation amount (DELTA S), which is the amount of the gap between the gap constant amount command value (DELTA S *) and the low- .

Specifically, the roll gap variation amount ΔS from the fifth road is the same as the following equation (11), and the equation (8) is substituted into the following equation (11).

... ... ... ... (11)

... ... ... ... (12)

On the other hand, in the fourth step 44, the output-side fluctuation amount? Wo is calculated by putting the load-power determination amount? F and the down-pressure amount determination command value? S * in the roll gap variation amount? Specifically, the output width variation? Wo is expressed by the following equation (13) by substituting the above equation (4) into the above equation (12).

... ... ... ... (13)

In the fifth step 45, the roll width variation amount? S is substituted into the output width variation? Wo to calculate the width transfer function? Wo /? Wi, (13), the width transfer function? Wo /? Wi is expressed by the following equation (14).

... (14)

Finally, in the sixth step 46, the optimum gain Gf for minimizing? Wo from? Wo /? Wi to? Wi is calculated. The equation (14) In the method of selecting the gain (Gf) for minimizing? Wo with respect to Wi, the width transfer function? Wo /? Wi at the steady state, that is, when s = .

... ... ... ... (15)

In the formula (15), if the molecular term is minimum, the width term transfer function? Wo /? Wi is minimized so that the molecular term is set to zero so that the molecular term is minimized.

... ... ... ... (16)

If the control gain Gf satisfying the above equation (16) is obtained, the following equation (17) is obtained.

... ... ... ... (17)

According to the present invention, it is verified through the following procedure whether the value obtained by the equation (17) agrees well with the optimum gain value obtained by the trial and error method. In the feed forward configuration diagram shown in FIG. 5, the width deviation? Wi measured from the width measuring instrument is assumed to be expressed by the following equation (18).

... ... ... ... (18)

Here, ω1 = 2πf1 = 2π × 5 [rad / sec], ω2 = 2πf2 = 2π × 1 [rad / sec]

K1 = 0.5, T = 0.0014, K2 = 0.0345 and K3 = 70, and K = K1 K2 K3 = 0.5 x 0.0345 70 = 1.2075.

The mill constant (M) was set to M = 100 [ton / mm] using the value of the two plate mill constants and the plasticity factor (Q) = 2,3,10 [ton / Respectively. The width recovery rate (β) is set to 0.6 when the plasticity factor is 2 [ton / mm], and to 0.5 when the plasticity factor is 10 [ton / mm].

The standard deviation (?) Of the outgoing width fluctuation? Wo in the fifth degree according to the plasticity coefficient and the width recovery ratio? Through the selected parameters is obtained by the following equation (19) Table 1 shows the feed forward gain (Gf) according to the outgoing width deviation () and the plasticity coefficient (Q).

... ... ... ... (19)

Here, the number of samples N = 5000, .

[Table 1]

As shown in Table 1, it can be seen that the optimum feedforward gain for Case 1 (CASE 1) is about 70 to 80, that for Case 2 is about 50 to 60, and that for Case 3 is about 10 to 15 connect.

The optimum gain (Gf) is obtained for each case by using the above equation (17), as shown in Table 2 below.

[Table 2]

It can be seen that the optimum gain (Gf) obtained by the trial and error method in the above Tables 1 and 2 and the optimum gain (Gf) calculated by the method of the present invention coincide very well.

As a trial and error method by the conventional simulation, the optimal gain value according to the plasticity coefficient, the milling constant and the width recovery rate should be tabulated and selected in advance. If the range of plasticity coefficient is wide, In the case where parameters such as the constant of the millimeter and the recovery rate of the width are changed, it is troublesome to re-calculate the gain value again by simulation or classical method, The gain value obtained by the method of the present invention is set as a function of the mill constant, the plasticity coefficient, and the width recovery rate, so that the program can be simplified and it is possible to eliminate the hassle of correcting the program or correcting the gain again There is a special effect.

The above description is only an explanation of one embodiment of the present invention, and the present invention can be variously modified and modified within the scope of its constitution. It will be readily understood by those skilled in the art that the feed forward automatic width control optimum gain calculation method in the thick plate process is not limited to the above described embodiments.

Claims (1)

(AWi) computer 40. The automatic width control (AWC) computer 40 calculates the width deviation? Wi corresponding to the input width deviation from the width width? (Gf) using a rolling model and a control algorithm, (We = F / M + S) as a function of the linearized eccentricity, plasticity factor, Edger inlet side width (Wi, We) and gap between two vertical rolls The load fluctuation amount is expressed as a function of the coercive force, the plasticity coefficient, the fluctuation amount on the Ezer side and the fluctuation amount on the Ezer side, and the output width variation after the horizontal rolling from the width variation model is represented by the following equation: A step of expressing the function as a function of the variation; (M), the plasticity coefficient (Q), and the thickness of the iron plate at the time when the position of the iron plate on which the width deviation is measured is inserted into the Ezer rolling roll from the time of the Ezer rolling roll and the width measuring period and the time corresponding to the rolling speed, A second step of calculating a pushdown amount command value? S * from the control gain Gf; A third step of expressing the dynamic characteristics of the hydraulic control by a Laplace transfer function and calculating a gap constant amount command value DELTA S * and a roll gap variation amount DELTA S which is a low duty ratio from the low dynamic characteristic transfer function to the hydraulic pressure; A fourth step of calculating an output width variation amount? Wo by assigning the load power amount determination? F and the screw down determination amount command value? S * to the roll gap variation amount? S; A fifth step of calculating the width control transfer function? Wo /? Wi by substituting the roll gap variation into the output width variation? Wo; A sixth step of calculating an optimum gain (Gf) for minimizing? Wo against? Wi from the width control transfer function? Wo /? Wi; And calculating a feed forward automatic width control optimum gain in the thick plate process.