JP2011143447A - Method of determining control gain in rolling mill and rolling mill - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To determine the optimum control gain to a rolling mill after taking the dispersion of property of a rolled material into consideration. <P>SOLUTION: In this method of determining the control gain in the rolling mill, when performing gauge control to the rolling mill 1 for rolling the rolled material W by using British Iron and Steel Research Association AGC and monitor AGC, the variation of the plastic coefficient Q of the rolled material W is given in the form of probability density function f(Q) and the control gain K<SB>B</SB>of the British Iron and Steel Research Association AGC and the control gain K<SB>M</SB>of the monitor AGC are determined by using the optimum design method. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a technique for determining an optimum control gain in a rolling mill in consideration of variations in characteristics of rolled material.

Conventionally, when manufacturing thick steel sheets by hot rolling, a target thickness value has been established on the exit side of the rolling mill, and the deviation from this target thickness value has exceeded the allowable tolerance. Regarding the part (off gauge), it was not possible to make it into a product, and measures such as discarding were performed.
For this reason, it is necessary to reduce the length of the off-gauge of the rolled material as much as possible from the viewpoint of reducing the manufacturing cost, and a technique for controlling the plate thickness with high accuracy is employed in the rolling mill.

As a sheet thickness control technique in a rolling mill, an automatic control technique called AGC (Automatic Gauge Control) is widely used. For example, there are those disclosed in Patent Documents 1 to 3.
In Patent Document 1, the material to be rolled after the previous process is obtained from a model simulating the latter process, which is given with a control gain as a parameter, during a period in which the rolled material moves from a predetermined previous process to a predetermined subsequent process. Disclosed is a rolling control method for controlling the post-process by determining a control gain that achieves an optimum result by simulation.

Patent Document 2 discloses a method for controlling a sheet thickness when rolling a steel strip using a reversible rolling mill having an AGC function, and a rolling position and rolling load in the longitudinal direction of the steel strip in the previous pass, and an entry / exit plate Disclosed is a sheet thickness control method in a reversible rolling mill, wherein a reduction position in this pass is controlled using a measured value of thickness.
Patent Document 3, finishing materials longitudinal temperature in rolling mill to predict the temperature of the Ar ₃ transformation point of the rolled material and prediction calculation, low and high portions than Ar ₃ transformation point to the boundary of Ar ₃ transformation point Disclosed is a sheet thickness control method in hot rolling, characterized in that the sheet thickness control gain is changed in a portion.

Japanese Patent Laid-Open No. 7-75811 JP-A-9-19707 Japanese Patent Laid-Open No. 9-38708

However, even in the widely used AGC control technology, the “rolling material characteristics” such as the plate temperature and plasticity coefficient change depending on the operating conditions, so the optimum design of the control gain for the rolling mill (the most appropriate control gain) It has been pointed out that it is difficult to determine.
For example, in the technique of Patent Document 1, the plate thickness after the previous process is measured, the result is input to the control unit, and an optimal control gain is calculated and applied to the actual machine. However, this control gain design method does not take into account factors such as plate temperature and crystal grain size that are difficult to measure and variations in plastic coefficient associated therewith.

In particular, when the technique of Patent Document 1 is adopted in the final rolling stand of a continuous rolling mill, it is often difficult to actually measure the plate temperature at the final rolling stand, and it is difficult to obtain an estimated value of the plate temperature. In fact, it is extremely difficult to obtain an accurate plasticity coefficient under such circumstances.
The technique of Patent Document 2 is similar to the technique of Patent Document 1, and calculates the distribution of the plastic coefficient in the longitudinal direction from the previous pass and uses it for control of the next pass.

  In this technology, the plasticity coefficient is assumed to be invariant between the previous pass and the next pass, but in reality, if the plate thickness of the rolled material in the previous pass and the thickness of the rolled material in the next pass are different, the plasticity coefficient is also changed. Different. In particular, in the hot rolling process where the rolling reduction is large, since the plate thickness of the rough rolling (previous process) and the finishing process (next process) are greatly different, the plastic coefficient is also greatly different, and the plate temperature is also changed. The plasticity coefficient cannot be obtained, and as a result, there is a difficulty that optimal control cannot be performed. Therefore, the actual situation is that the technique of Patent Document 2 cannot be adopted for hot rolling.

  In the technique of Patent Document 3, a plate temperature is estimated, a plasticity coefficient is calculated based on the obtained estimated temperature, and a control gain is changed based on the calculated plastic coefficient. However, when this technique is adopted, it is often difficult to actually measure and estimate the plate temperature at the actual site, and therefore, the calculation of the plastic coefficient is often out of place. In addition, since the plastic coefficient greatly varies depending on the plate temperature and the crystal grain size, there is a problem that optimal control cannot be performed without considering them.

  In summary, considering that a certain rolled material is rolled, it is difficult to know in real time the characteristic values (such as plasticity coefficient) of the rolled material that is about to be rolled. This is because it is not easy to actually measure the plate temperature, crystal grain size and the like necessary for obtaining the characteristic value of the target rolled material. In addition, even for rolled materials of the same steel type, the characteristic values are likely to vary from one rolled material to another due to differences in sheet temperature and the like.

As described above, it is very difficult to optimally design the control gain for the rolling mill under the situation that the characteristic value of the rolled material varies (not a single value but exhibits a certain distribution). Patent Documents 1 to 3 described above do not disclose a technique that can avoid such a situation.
Therefore, in view of the above problems, the present invention is a technique for determining an optimum control gain for a rolling mill after reflecting the phenomenon that the characteristic value of the rolled material varies (presents a distribution with the characteristic value of the rolled material). The purpose is to propose.

In order to achieve the above-described object, the present invention takes the following technical means.
That is, the method for determining the control gain in the rolling mill according to the present invention uses the screw AGC and the monitor AGC to control the thickness of the rolling mill for rolling the rolled material. It is given in the form of a density function f (Q), and the control gain K _{B of the} screw AGC and the control gain K _M of the monitor AGC are determined using an optimum design method.

Preferably, the probability density function f (Q) is different depending on the steel type or plate temperature of the rolled material.
In addition, the evaluation function may include the off-gauge length of the rolled material and the probability density function f (Q) of the plasticity coefficient Q as variables.
Furthermore, in determining the said control gain K _B control gain K _M, it is highly preferred to use a PSO (Particle Swarm Optimization) method.

On the other hand, the rolling mill according to the present invention is a rolling mill provided with a control unit that uses a screw AGC and a monitor AGC to perform sheet thickness control on a rolling mill that rolls a rolled material, and the control unit includes the control described above. by performing the gain determination method, characterized in that it is configured to determine a control gain K _M of the control gain K _B and the monitor AGC control of Vistula AGC control.

  According to the control gain determination method of the present invention, it is possible to determine the optimum control gain for the rolling mill while reflecting the phenomenon that the characteristic value of the rolled material varies.

It is the figure which showed typically the rolling mill with which this invention is applied. It is a control block diagram of the rolling mill which concerns on this invention. It is the figure which showed the length of the off gauge (conventional example). It is the figure which showed distribution of the plasticity coefficient of a rolling material. It is the figure which showed the relationship between the control gain in Bisla AGC and the control gain in monitor AGC. It is the figure which showed the off gauge length at the time of controlling plate | board thickness with the control method of this invention (solution A). It is the figure which showed the off gauge length at the time of controlling plate | board thickness with the control method of this invention (solution B).

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
Drawing 1 is a mimetic diagram showing rolling mill 1 of this embodiment.
The rolling mill 1 includes a pair of upper and lower work rolls 2 and 2 that roll the rolled material W, and a backup roll 3 that supports the work roll 2 from behind. Further, the rolling mill 1 is provided with a reduction device 4 that makes the gap between the pair of work rolls 2 and 2 variable. The reduction device 4 moves the upper backup roll 3 up and down to manipulate the gap (roll gap) between the work rolls 2 and 2, thereby changing the sheet thickness on the outlet side of the rolling mill 1. Further, the rolling mill 1 is provided with a load meter 5 for measuring the rolling load, and a thickness gauge 6 for measuring the thickness of the rolled material W is provided on the exit side of the rolling mill 1.

The rolled material W transferred from the upstream side is sandwiched between the pair of work rolls 2 and 2 and is pressed down to become a rolled material W having a predetermined plate thickness and discharged downstream. If the predetermined thickness is not achieved by one rolling, a plurality of reverse rollings are performed according to a predetermined pass schedule.
The rolling mill 1 of the present embodiment is provided with a control unit 7 that controls the roll gap in order to control the thickness of the rolled material W with high accuracy. The control unit 7 has a function of executing screw machine AGC that issues a command to the reduction device 4 based on the actual value of the rolling load measured by the load meter 5. In addition, it has a function of executing a monitor AGC that issues a command to the reduction device 4 based on the actual thickness value of the rolled material W measured by the thickness gauge 6. Both the output value of the screw AGC and the output value of the monitor AGC are input to the reduction device 4.

In FIG. 2, a control system including a model of the rolling mill 1 to be controlled, a screw AGC, and a monitor AGC is shown as control blocks.
In FIG. 2, T is a time constant of pressure unit 4, Q is plastic coefficient representing the deformed difficulty of the rolled material W, L is the dead time of a plate thickness measurement by the thickness gauge 6, K _M is the control of the monitor AGC gain, K _B is the nominal value of the control gain, M _N is mill modulus of Vistula AGC.

  The screwdriver AGC is a control controller that suppresses fluctuations in the plate thickness corresponding to the load change based on the result measured by the load meter 5 based on the following gauge meter type.

The gauge meter equation is a general model equation representing a rolling phenomenon, where h is a sheet thickness, S is a roll gap, P is a load, and M is a mill constant indicating the rigidity of the rolling mill 1.
On the other hand, the monitor AGC is a control controller that issues a command to the reduction device 4 based on the actual thickness value of the rolled material W measured by the thickness gauge 6. Due to equipment limitations, the thickness gauge 6 can be installed only at a location away from the roll, and therefore there is always a dead time L in the thickness gauge 6 measurement. For this reason, the monitor AGC cannot respond instantaneously to variations in plate thickness due to load disturbance.

The screw thickness AGC alone cannot control the plate thickness to the target value, but since the load meter 5 is installed immediately below the roll, the plate thickness variation due to disturbance can be suppressed instantaneously.
FIG. 3 shows a simulation result (an example of a plate thickness change at the tip of the rolled material W) when the thickness of the rolled material W is controlled using the control system of the rolling mill 1 described above.
As apparent from FIG. 3, the plate thickness at the foremost portion of the rolled material W is out of the tolerance, and enters the tolerance after a while. The part until the plate thickness falls within the tolerance is called an off gauge, and shortening this part is one of the control issues. In addition, a second problem is to suppress fluctuations in the plate thickness due to load disturbances in a steady portion where the plate thickness is stable within a tolerance. Furthermore, since the plate thickness behavior varies depending on the value of the plastic coefficient Q for each rolled material W, the third problem is to design the control gain in consideration of this variation.

In order to solve these problems, the present inventors consider that it is important to make two AGCs (monitor AGC, screw AGC) function in a well-balanced manner, and an optimum gain determination method (control gain K of the monitor AGC) for that purpose. _M, thought determination method) of the control gain K _B of Vistula AGC.
Hereinafter, a method for determining the control gain in the rolling mill 1 will be described.

First, the present inventors decided to determine the optimum control gain by adopting the optimization problem technique, and adopted PSO (Particle Swarm Optimization) as a technique for solving the optimization problem. PSO is a technique for obtaining an optimal solution by searching using a large number of particles. The applicants of the present application associate each particle with a control gain pair (a pair of the control gain K _M of the monitor AGC and the control gain K _B of the screw AGC), and express the coordinates of the particles as a control gain value. did.

  The position and velocity of the i-th particle in the search space are defined as shown in equations (2) and (3).

Further, x _i is sequentially updated by the following expression.

In the present embodiment, the plastic coefficient Q is expressed by a probability density function f (Q) in order to reflect that the sheet thickness behavior varies due to the value of the plastic coefficient Q being different for each rolled material W. That is, the plasticity coefficient Q is expressed in the form of a probability density function f (Q) based on the distribution of past rolling record values.
Specifically, assuming that the plastic coefficient Q is a normal distribution, the average μ of the plastic coefficient obtained from the past actual values and the standard deviation σ are used to determine the equation (6).

In order to obtain the evaluation function value A _i of the i-th particle, calculation is first executed with Q = Q ₁ , K _B = K _Bi , and K _M = K _Mi to obtain the off gauge length u ₁ . Similarly, repeated work seeking off-gage length u ₂ when the plastic factor Q is changed with Q = Q _2, to obtain u _1, u _2, · · ·, a u _m.
In the present embodiment, in order to shorten the off-gauge length in consideration of variations, the evaluation function value A _i is a variable of the off-gauge length of the rolled material W and the probability density function f (Q) as shown in Equation (7). As a form to prepare as.

Determined both by solving an optimization problem using the PSO, the control gain K _M of the monitor AGC, the optimum value of the control gain K _B of Vistula AGC setting plastic factor Q and the evaluation function A _i as described above can do.
The specific solution procedure for the optimization problem using PSO is as follows.
(Procedure 1): Select m values of Q and set them as Q ₁ , Q ₂ ,..., Q _m .
(Procedure 2): _Assuming that the initial values of K _Bi , K _Mi (i = 1, 2,..., N) are random values of −1 ≦ K _Bi ≦ 2 and −1 ≦ K _Mi ≦ 3, n Initialize the coordinates of individual particles. Further, k = 1.
(Procedure 3): An evaluation function value A _i is obtained for each particle, and x ^{best, k} _i , x ^{best, k} _swarm are determined.
(Procedure 4): If k = k _max , the point at which the evaluation function value is the smallest in the entire particles up to step k is set as the solution x ^{* and the process} is terminated. If k <k _max , return to step 3 with k = k + 1. Note that k _max is the number of repetitions, and a value is set in advance.

As a result of executing the calculation (simulation) with the plasticity coefficient Q = Q _j , u _j = ∞ if the plate thickness diverges or the simulation result (plate thickness deviation) does not fall within the tolerance within a predetermined time. Further, after the specified time, the steady portion is set, and u _j = ∞ is also set when the thickness variation in the steady portion exceeds the specified range.
By setting and minimizing the evaluation function A _i as described above, the off-gauge length u _i in the plastic coefficient Q having a high probability of occurrence can be preferentially shortened, and the plate thickness due to variations in the value of the plastic coefficient Q It is possible to obtain the control gains K _B and K _M that can suppress the variation of the behavior itself and can suppress the fluctuation in the thickness of the steady portion within the specified range.

An example (result of simulation of the rolling mill 1) in which the rolling mill 1 is controlled using the control gain determination method in the rolling mill described above will be described below.
The simulation conditions were that the initial value of the plate thickness deviation was 1, the target plate thickness deviation value was 0, the simulation start time was 0 [sec], and the end time was 20 [sec]. The unsteady part was a part of 0 to 5 [sec], and the tolerance of the thickness deviation of the unsteady part was ± 0.05. The steady part was a portion of 15 to 20 [sec], and the allowable range of fluctuations in plate thickness at the steady part was ± 0.01. As a load disturbance d, a sine wave having an amplitude of 10 and an angular frequency of 10 [rad / sec] was applied. Regarding the variation of the plastic coefficient Q, the average μ = 400, the standard deviation σ = 50, and the number of Qs m = 13.

FIG. 4 shows 13 plastic coefficient Q values and respective probability density function values f (Q). Regarding the parameters of PSO, the number of particles n = 30, the number of repetitions k _max = 30, and the weight parameters were w = 0.9, c ₁ = 0.8, and c ₂ = 0.8, respectively.
In the present embodiment, since the solution obtained by the PSO optimization is not always optimal, verification of optimality is performed using a plurality of solutions.

Specifically, one set was obtained until one solution x ^* was obtained, and verification was performed using 100 solutions x ^* obtained by 100 sets of experiments.
FIG. 5 shows a plot of 100 solutions. In FIG. 5, A is the solution with the smallest evaluation value (value of the evaluation function), B, C, and D are the evaluation values in order 1, respectively. It is the second and third largest solution.

Except for the solutions B, C, and D, which have large evaluation values and are far from other solutions, the solution is 0.68 ≦ K _B ≦ 0.92 and 0.90 ≦ K _M ≦ 1.05. It can be confirmed that the distribution is almost in a straight line.
FIG. 6 shows the plate thickness change using the screw AGC control gain K _B of the solution A, the monitor AGC control gain K _M, and the values of the 13 plastic coefficients Q.

FIG. 7 shows a plate thickness change using the screw B AGC control gain K _B of the solution B, the monitor AGC control gain K _M , and 13 Q values. Since FIGS. 6 and 7 are results for 13 Q values, 13 waveforms are drawn.
From FIG. 6 and FIG. 7, it was confirmed that both the solutions A and B can suppress the fluctuation of the plate thickness in the steady portion within an allowable range of ± 0.01. Comparing FIG. 6 and FIG. 7, it can be seen that the off-gauge is shorter and the variation is smaller when the solution A is used. Therefore, the optimality verification method using 100 solutions is effective, and it can be said that the solution A is close to the optimal solution.

From the above, it was confirmed that the optimal control gain that can shorten off-gauge, suppress plate thickness variation, and reduce variation in plate thickness variation can be designed.
To summarize the above, by using the method of this application that designs the optimal control gain after expressing the variation in the plasticity coefficient Q with a probability density function, it is possible to reduce off-gauge, suppress plate thickness variation, and reduce variation in plate thickness variation. And efficient rolling can be performed.

By the way, it should be thought that embodiment disclosed this time is an illustration and restrictive at no points. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.
For example, in the description of the embodiment, the description has been given by exemplifying a single rolling mill that rolls a rolled material in a hot rolling process, but the present invention is not limited to this. The technology of the present invention can be employed in cold rolling, and can also be employed in a continuous rolling device composed of a plurality of rolling mills.

DESCRIPTION OF SYMBOLS 1 Rolling machine 2 Work roll 3 Backup roll 4 Reduction device 5 Load meter 6 Sheet thickness meter 7 Control part W Rolled material

Claims (5)

When performing thickness control for a rolling mill for rolling a rolled material using a screw AGC and a monitor AGC,
The given in the form of a rolled material of the plastic factor Q of the variation of the probability density function f (Q), determining a control gain K _M of the control gain K _B and the monitor AGC of the Vistula AGC using the optimum design method A method for determining a control gain in a rolling mill.   The method for determining a control gain in a rolling mill according to claim 1, wherein the probability density function f (Q) is different depending on a steel type or a plate temperature of the rolled material.   3. The control gain determination in the rolling mill according to claim 1, wherein the evaluation function has an off-gauge length of the rolled material and a probability density function f (Q) of the plastic coefficient Q as variables. Method. The control gain K _B and controlled in its gain K to determine _M, PSO (Particle Swarm Optimization) method for determining the control gains in the rolling mill according to claim 1, characterized by using a technique. A rolling mill provided with a control unit that uses a screw AGC and a monitor AGC to control the thickness of a rolling mill for rolling a rolled material,
Wherein, by performing been determined how control gain according to any one of claims 1 to 4, and a control gain K _M of the control gain K _B and the monitor AGC control of Vistula AGC control A rolling mill characterized in that it is configured to determine.