CN112859595A - Method for determining optimal control quantity of edge thinning of cold-rolled strip steel based on variable regulation and control efficacy - Google Patents

Method for determining optimal control quantity of edge thinning of cold-rolled strip steel based on variable regulation and control efficacy Download PDF

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CN112859595A
CN112859595A CN202011642544.XA CN202011642544A CN112859595A CN 112859595 A CN112859595 A CN 112859595A CN 202011642544 A CN202011642544 A CN 202011642544A CN 112859595 A CN112859595 A CN 112859595A
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李旭
王鹏飞
段树威
张欣
刘印忠
张殿华
张洪波
李文田
孙超
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Northeastern University China
Yanshan University
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Abstract

The invention provides a method for determining optimal control quantity of edge thinning of cold-rolled strip steel based on variable regulation efficiency, which comprises the steps of establishing a variable regulation efficiency coefficient matrix of each regulating mechanism to be controlled on a cold continuous rolling production line by a finite element simulation method, establishing a variable regulation function expression of each regulating mechanism to be controlled according to the variable regulation efficiency coefficient matrix of each regulating mechanism to be controlled, and establishing an initial control quantity X of each regulating mechanism to be controlled according to the initial control quantity X of each regulating mechanism to be controlledsThe method comprises the steps of translating a variable regulation function, establishing penalty functions of all mechanisms to be controlled according to boundary conditions to obtain a final optimized objective function, and solving an optimal control quantity by utilizing a powell and interior point penalty function method solution.

Description

Method for determining optimal control quantity of edge thinning of cold-rolled strip steel based on variable regulation and control efficacy
Technical Field
The invention relates to the technical field of metallurgical rolling, in particular to a method for determining optimal control quantity of edge thinning of cold-rolled strip steel based on variable regulation and control effects.
Background
In the production of edge thinning of cold-rolled silicon steel, the edge thinning is mainly controlled by the transverse movement (roll shifting) of working rolls of the first three racks. The main control idea of edge thinning control is based on a plate shape closed-loop control method, but the regulation efficacy coefficient of each plate shape adjusting mechanism in the plate shape closed-loop control is invariable and is a fixed value. In the edge thinning control, the influence of the transverse displacement of the working roll of the adjusting mechanism on the edge thinning is changed, namely, the adjusting and controlling efficiency coefficient is a variable value, the adjusting and controlling capability of the adjusting and controlling efficiency coefficient changes along with the change of the transverse displacement, and how to establish a target function under the condition of the change of the adjusting and controlling capability is difficult to perform multipoint control.
The scholars at home and abroad adopt a single-point and three-point control mode aiming at the characteristic, and can not realize sufficient control on the thinning of the edge part. On the basis of analyzing the regulation and control characteristics of the edge thinning roll shifting, the process of regulating and controlling the change of the efficiency coefficient is researched, and the aim of fully controlling the edge thinning can be fulfilled by constructing a target function and realizing the multipoint control of the edge thinning under the condition of considering the variable and controllable efficiency coefficient.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for determining the optimal control quantity of the edge thinning of cold-rolled strip steel based on the variable regulation efficacy, which comprises the following steps:
step 1: establishing a variable regulation and control efficiency coefficient matrix of each regulating mechanism to be controlled on a cold continuous rolling production line by a finite element simulation method, wherein the variable regulation and control efficiency coefficient matrix comprises the following steps:
step 1.1: establishing a simulation model of each adjusting mechanism to be controlled by using finite element software, and obtaining influence quantity of each adjusting mechanism to be controlled on edge thinning at different positions under different control quantities through simulation analysis;
step 1.2: constructing a variable regulation and control efficiency coefficient matrix according to all influence quantities corresponding to each regulating mechanism to be controlled, wherein the variable regulation and control efficiency coefficient matrix is expressed as follows:
Figure BDA0002880189420000011
in the formula (I), the compound is shown in the specification,
Figure BDA0002880189420000012
indicates that the s-th regulating mechanism to be controlled is in the control quantity xiLower pair distance strip steel edge NjThe influence of the edge thinning at the position, J representing the total number of positions to be detected, xIThe method comprises the steps of representing the maximum control quantity of an adjusting mechanism to be controlled, representing the adjusting times of the adjusting mechanism to be controlled from the minimum control quantity to the maximum control quantity, and representing the total number of the adjusting mechanisms to be controlled by S;
step 2: establishing a variable modulation function expression of each adjusting mechanism to be controlled according to the variable modulation efficiency coefficient matrix of each adjusting mechanism to be controlled;
and step 3: according to the initial control quantity X of each regulating mechanism to be controlledsTranslating the I variable modulation and control functions constructed in the step 2 through coordinate translation, and translating the translated function expression Fi,s(xs) As follows below, the following description will be given,
Fi,s(xs)＝2bi,s+B1i,s×xs+B2i,s×(xs-Xs)2+B2i,s×(Xs)2
and 4, step 4: according to the control target quantity delta given by the control systemjEstablishing target functions of all to-be-controlled adjusting mechanismsThe number of the cores Min is counted,
Figure BDA0002880189420000021
in the formula, N is the minimum value of I, J;
and 5: according to the boundary conditions, the penalty functions of all the mechanisms to be controlled are established, wherein the penalty function g of the s-th mechanism to be controlleds,m(xs) As indicated by the general representation of the,
gs,1(xs)＝(xs-Xs)
gs,2(xs)＝(xs-(limit_xs-Xs))
in the formula, limit _ xsThe regulation limiting quantity of the regulation mechanism to be controlled is represented by the s, m represents the order of magnitude of a penalty function, and m is 1 and 2;
step 6: establishing a final optimized objective function phi (x) according to the penalty functions and the objective functions of all the adjustment mechanisms to be controlleds,r(k)) As indicated by the general representation of the,
Figure BDA0002880189420000022
r(k-1)·c＝r(k)
where k is the number of iterations, r(k)A penalty factor of the kth time, and c is a reduction factor;
and 7: solving phi (x) by using a solution method of powell and an interior point penalty function methods,r(k)) Taking x corresponding to the minimum valuesAs the optimum control quantity of the adjusting mechanism to be controlled.
The step 2 comprises the following steps:
step 2.1: according to the influence quantity of the ith row in the variable control efficiency coefficient matrix of the s-th to-be-controlled adjusting mechanism
Figure BDA0002880189420000023
And corresponding control quantity xiEstablishing the s th tone to be controlledIth variable control function expression f of regulating mechanismi,s(xs)，
fi,s(xs)＝bi,s+B1i,s×(xs)1+B2i,s×(xs)2
In the formula, bi,sRepresenting the intercept of a quadratic function, B1i,s、B2i,sCoefficient of first order term, second order term, x representing a quadratic functionsRepresenting the control quantity to be solved of the s-th regulating mechanism to be controlled;
step 2.2: let I equal to 1,2, … I, repeat step 2.1 to establish I modified control function expressions for the s-th actuator to be controlled.
The invention has the beneficial effects that:
the invention provides a method for determining optimal control quantity of edge thinning of cold-rolled strip steel based on variable control efficiency, which comprises the steps of establishing a variable control efficiency function expression of each adjusting mechanism to be controlled, establishing a target function Min of the adjusting mechanism, establishing penalty functions of all adjusting mechanisms to be controlled by considering boundary conditions in the actual control process to obtain a final optimal target function, and finally obtaining the optimal control quantity of the adjusting mechanism by solving through Powell and inner point penalty function methods.
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FIG. 1 is a flow chart of a method for determining an optimal control quantity of edge thinning of cold-rolled strip steel based on variable control efficiency.
FIG. 2 is a graph showing the effect of different work roll control amounts on edge thinning in the first frame of the present invention.
FIG. 3 is a graph showing the effect of different work roll control amounts on edge thinning in the second frame of the present invention.
FIG. 4 is a graph showing the effect of different work roll control amounts on edge thinning in the third frame of the present invention.
FIG. 5 is a flow chart of solving the optimal control quantity by a Powell and interior point penalty function method solver according to the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific examples. The first three stands in the five-stand cold continuous rolling have different influence rules due to different rolling reduction, so the first three stands need to be regarded as three different regulating mechanisms to be controlled, the table of parameters and production process parameters of the five-stand cold continuous rolling mill adopted in the embodiment is shown in table 1,
TABLE 1 table of parameters of tandem rolling and production process
Figure BDA0002880189420000031
Figure BDA0002880189420000041
As shown in fig. 1, a method for determining an optimal control amount of edge drop of a cold-rolled strip steel based on a variable control efficiency includes:
step 1: establishing a simulation model by a finite element simulation method, taking the influence effect of different control quantities of each adjusting mechanism on the thinning of the strip steel edge, establishing a variable control efficiency coefficient matrix of each adjusting mechanism to be controlled on a cold continuous rolling production line, wherein each adjusting mechanism obtains a two-dimensional variable control efficiency coefficient matrix, and the method comprises the following steps:
step 1.1: establishing a simulation model of each adjusting mechanism to be controlled by using finite element software ABAQUS, and obtaining influence quantity of each adjusting mechanism to be controlled on edge thinning at different positions under different control quantities through simulation analysis;
step 1.2: constructing a variable regulation and control efficiency coefficient matrix according to all influence quantities corresponding to each regulating mechanism to be controlled, wherein the variable regulation and control efficiency coefficient matrix is expressed as follows:
Figure BDA0002880189420000042
in the formula (I), the compound is shown in the specification,
Figure BDA0002880189420000043
indicates that the s-th regulating mechanism to be controlled is in the control quantity xiLower pair distance strip steel edge NjThe influence of the edge thinning at the position, J representing the total number of positions to be detected, xIThe method comprises the steps of representing the maximum control quantity of an adjusting mechanism to be controlled, representing the adjusting times of the adjusting mechanism to be controlled from the minimum control quantity to the maximum control quantity, and representing the total number of the adjusting mechanisms to be controlled by S;
for the first three stands in a five-stand cold continuous rolling, the quantity x is controlledi10mm,20mm,30mm, … mm and 120mm, respectively, the variable control efficiency coefficient matrix established by each adjusting mechanism is as follows,
Figure BDA0002880189420000044
step 2: establishing a variable modulation function expression of each adjusting mechanism to be controlled according to the variable modulation efficiency coefficient matrix of each adjusting mechanism to be controlled, wherein the variable modulation function expression comprises the following steps:
step 2.1: according to the influence quantity of the ith row in the variable control efficiency coefficient matrix of the s-th to-be-controlled adjusting mechanism
Figure BDA0002880189420000051
And corresponding control quantity xiEstablishing the ith variable control function expression f of the s-th to-be-controlled adjusting mechanismi,s(xs)，
fi,s(xs)＝bi,s+B1i,s×(xs)1+B2i,s×(xs)2
In the formula, bi,sRepresenting the intercept of a quadratic function, B1i,s、B2i,sCoefficient of first order term, second order term, x representing a quadratic functionsRepresenting the control quantity to be solved of the s-th regulating mechanism to be controlled;
step 2.2: let I equal to 1,2, … I, repeat step 2.1 to establish I modified control function expressions of the S-th mechanism to be controlled, and for S mechanisms to be controlled, S × I modified control function expressions need to be established.
The graph of the influence of different working roll control quantities of different racks on the side thinning obtained through finite element simulation is shown in fig. 2-4, wherein different curves in the graph represent different variable modulation function curves obtained through fitting. Table 1 is a parameter table of a modulation and control function expression of the first rack, table 2 is a parameter table of a modulation and control function expression of the second rack, and table 3 is a parameter table of a modulation and control function expression of the third rack.
TABLE 1 parameter table of modified modulation function expressions for a first chassis
Figure BDA0002880189420000052
TABLE 2 Parametric Table of modified modulation function expressions for the second rack
Figure BDA0002880189420000053
Figure BDA0002880189420000061
TABLE 3 Parametric Table of modified tuning function expressions for the third bay
Figure BDA0002880189420000062
And step 3:
in the actual control process, when the optimal solution is solved, the optimal solution is in a certain state, namely the current position of the adjusting mechanism, which is referred to as the state that a "solving starting point x" generally exists0", according to the control amount X of the present control apparatus10，X20，X30And the control quantity of the working roll shifting of the first frame, the second frame and the third frame in the current period is represented in sequence. Considering the effect of variable regulation and control, the different solving starting points have different influences on the edge thinning, so thatAnd (3) carrying out coordinate translation on the established edge control function, wherein if the original curve is y ═ f (x), the changed curve is
y-f(x0)＝f(x-x0)
According to the initial control quantity X of each regulating mechanism to be controlledsTranslating the I variable modulation and control functions constructed in the step 2 through coordinate translation, and translating the translated function expression Fi,s(xs) As follows below, the following description will be given,
Fi,s(xs)＝2bi,s+B1i,s×xs+B2i,s×(xs-Xs)2+B2i,s×(Xs)2
and 4, step 4: according to the control target quantity delta given by the control systemjEstablishing the objective function Min of all the regulating mechanisms to be controlled,
Figure BDA0002880189420000063
in the formula, N is the minimum value of I, J;
wherein the objective function of the first gantry is represented as:
MinS1＝[△1-(f1,1(x1-X10)+f1,1(X10))]2+[△2-(f2,1(x1-X10)+f2,1(X10))]2
+…+[△N-(fN,1(x1-X10)+fN,1(X10))]2
＝[△1-F1,1(x1)]2+[△2-F2,1(x1)]2+…+[△N-FN,1(x1)]2
the objective function of the second gantry is expressed as:
MinS2＝[△1-(f1,2(x2-X10)+f1,2(X10))]2+[△2-(f2,2(x2-X10)+f2,2(X10))]2
+…+[△N-(fN,2(x2-X10)+fN,2(X10))]2
＝[△1-F1,2(x2)]2+[△2-F2,2(x2)]2+…+[△N-FN,2(x2)]2
the objective function of the third gantry is expressed as:
MinS3＝[△1-(f1,3(x3-X10)+f1,3(X10))]2+[△2-(f2,3(x3-X10)+f2,3(X10))]2
+…+[△N-(fN,3(x3-X10)+fN,3(X10))]2
＝[△1-F1,3(x3)]2+[△2-F2,3(x3)]2+…+[△N-FN,3(x3)]2
the objective function of the first three racks is denoted MinS＝MinS1+MinS2+MinS3；
And 5: according to the boundary conditions, the penalty functions of all the mechanisms to be controlled are established, wherein the penalty function g of the s-th mechanism to be controlleds,m(xs) As indicated by the general representation of the,
gs,1(xs)＝(xs-Xs)
gs,2(xs)＝(xs-(limit_xs-Xs))
in the formula, limit _ xsThe regulation limiting quantity of the regulation mechanism to be controlled is represented by the s, m represents the order of magnitude of a penalty function, and m is 1 and 2;
boundary conditions, maximum and minimum actuator due to the actual control problem being solvedThe amount of the traversing, therefore, when the control is required according to the actual production demand, the control amount is limited, namely, the boundary conditions are increased, the boundary conditions are appeared in the objective function by means of a penalty function, and the maximum traversing amount is set to be 120, namely, limit _ x1＝limit_x2＝limit_x3＝120mm；
The initial boundary is
0≤x1≤limit_x1
0≤x2≤limit_x2
0≤x3≤limit_x3
Initial boundary modification for reasons of initial control points
0-X10≤x1≤limit_x1-X10
0-X20≤x2≤limit_x2-X20
0-X30≤x3≤limit_x3-X30
The boundary condition is expressed in the objective function by means of a penalty function, and the above boundary condition needs to be converted into the penalty function:
g1,1(x1)＝0-X10-x1≤0
g1,2(x1)＝x1-(limit_x1-X10)≤0
g2,1(x2)＝0-X20-x2≤0
g2,2(x2)＝x2-(limit_x2-X20)≤0
g3,1(x3)＝0-X30-x3≤0
g3,2(x3)＝x3-(limit_x3-X30)≤0
step 6: establishing a final optimized objective function phi (x) according to the penalty functions and the objective functions of all the adjustment mechanisms to be controlleds,r(k)) As indicated by the general representation of the,
Figure BDA0002880189420000081
r(k-1)·c＝r(k)
where k is the number of iterations, r(k)A penalty factor of the kth time, and c is a reduction factor;
and 7: solving phi (x) by using a solution method of powell and an interior point penalty function methods,r(k)) Taking x corresponding to the minimum valuesAs the optimum control quantity of the adjusting mechanism to be controlled.
The final optimization objective function of the first three racks is determined by the calculation as follows:
Figure BDA0002880189420000082
r(k-1)·c＝r(k)
in the formula, r(k)A penalty factor of k, a reduction factor c, of 0.7 r(0)And 3 is taken, and x represents the optimal control quantity of a certain rack. When the optimization objective function takes the minimum value, obtaining an optimal solution, wherein a solution is solved by adopting a powell and interior point penalty function method, a solving flow chart is shown in FIG. 5, the solution is realized by adopting matlab programming, and S1, determining an initial point of a feasible region; s2, solving the objective function, wherein the objective function meets the requirement, the solving is finished, the requirement cannot be met, and the extreme point of the time is the initial point of the next solving; s3, constructing a new objective function, updating the penalty factor and solving; the steps S2 and S3 are circulated until the optimal solution is solved, and the optimal control quantity x is solved1,x2,x3And the control signals are respectively output to the first stand, the second stand and the third stand, so that the optimal control of the edge thinning of the five-stand cold continuous rolling is realized.

Claims (2)

1. A method for determining the optimal control quantity of the edge thinning of cold-rolled strip steel based on the variable regulation efficacy is characterized by comprising the following steps:
step 1: establishing a variable regulation and control efficiency coefficient matrix of each regulating mechanism to be controlled on a cold continuous rolling production line by a finite element simulation method, wherein the variable regulation and control efficiency coefficient matrix comprises the following steps:
step 1.1: establishing a simulation model of each adjusting mechanism to be controlled by using finite element software, and obtaining influence quantity of each adjusting mechanism to be controlled on edge thinning at different positions under different control quantities through simulation analysis;
step 1.2: constructing a variable regulation and control efficiency coefficient matrix according to all influence quantities corresponding to each regulating mechanism to be controlled, wherein the variable regulation and control efficiency coefficient matrix is expressed as follows:
Figure FDA0002880189410000011
j＝1,2,…,J,i＝1,2,…I，s＝1,2,…,S
in the formula (I), the compound is shown in the specification,
Figure FDA0002880189410000012
indicates that the s-th regulating mechanism to be controlled is in the control quantity xiLower pair distance strip steel edge NjThe influence of the edge thinning at the position, J representing the total number of positions to be detected, xIThe method comprises the steps of representing the maximum control quantity of an adjusting mechanism to be controlled, representing the adjusting times of the adjusting mechanism to be controlled from the minimum control quantity to the maximum control quantity, and representing the total number of the adjusting mechanisms to be controlled by S;
step 2: establishing a variable modulation function expression of each adjusting mechanism to be controlled according to the variable modulation efficiency coefficient matrix of each adjusting mechanism to be controlled;
and step 3: according to the initial control quantity X of each regulating mechanism to be controlledsTranslating the I variable modulation and control functions constructed in the step 2 through coordinate translation, and translating the translated function expression Fi,s(xs) As follows below, the following description will be given,
Fi,s(xs)＝2bi,s+B1i,s×xs+B2i,s×(xs-Xs)2+B2i,s×(Xs)2
in the formula, bi,sRepresenting the intercept of a quadratic function, B1i,s、B2i,sCoefficient of first order term, second order term, x representing a quadratic functionsIndicating the s th conditioner to be controlledConstructing a control quantity to be solved;
and 4, step 4: according to the control target quantity delta given by the control systemjEstablishing the objective function Min of all the regulating mechanisms to be controlled,
Figure FDA0002880189410000013
N＝min{I,J}
in the formula, N is the minimum value of I, J;
and 5: according to the boundary conditions, the penalty functions of all the mechanisms to be controlled are established, wherein the penalty function g of the s-th mechanism to be controlleds,m(xs) As indicated by the general representation of the,
gs,1(xs)＝(xs-Xs)
gs,2(xs)＝(xs-(limit_xs-Xs))
in the formula, limit _ xsThe regulation limiting quantity of the regulation mechanism to be controlled is represented by the s, m represents the order of magnitude of a penalty function, and m is 1 and 2;
step 6: establishing a final optimized objective function phi (x) according to the penalty functions and the objective functions of all the adjustment mechanisms to be controlleds,r(k)) As indicated by the general representation of the,
Figure FDA0002880189410000021
r(k-1)·c＝r(k)
where k is the number of iterations, r(k)A penalty factor of the kth time, and c is a reduction factor;
and 7: solving phi (x) by using a solution method of powell and an interior point penalty function methods,r(k)) Taking x corresponding to the minimum valuesAs the optimum control quantity of the adjusting mechanism to be controlled.
2. The method for determining the optimal control quantity of the edge thinning of the cold-rolled steel strip based on the variable regulation efficiency as claimed in claim 1, wherein the step 2 comprises the following steps:
step 2.1: according to the influence quantity of the ith row in the variable control efficiency coefficient matrix of the s-th to-be-controlled adjusting mechanism
Figure FDA0002880189410000022
And corresponding control quantity xiEstablishing the ith variable control function expression f of the s-th to-be-controlled adjusting mechanismi,s(xs)，
fi,s(xs)＝bi,s+B1i,s×(xs)1+B2i,s×(xs)2
Step 2.2: let I equal to 1,2, … I, repeat step 2.1 to establish I modified control function expressions for the s-th actuator to be controlled.
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