CN112859595B - 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 PDFInfo
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Abstract
The invention provides a method for determining the optimal control quantity of edge thinning of cold-rolled strip steel based on variable regulation and control efficacy, which establishes each part on a cold continuous rolling production line by a finite element simulation methodThe variable control function coefficient matrix of the adjustment mechanism to be controlled is established according to the variable control function coefficient matrix of each adjustment mechanism to be controlled, and the variable control function expression of each adjustment mechanism to be controlled is established according to the initial control quantity X of each adjustment 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
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:
in the formula (I), the compound is shown in the specification,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 the objective function Min of all the regulating mechanisms to be controlled,
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: according to the penalty function and the objective function of all the regulating mechanisms to be controlled, the final establishment is carried outIs optimized by the objective function phi (x)s,r(k)) As indicated by the general representation of the,
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 mechanismAnd 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 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.
Drawings
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
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:
in the formula (I), the compound is shown in the specification,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,
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 mechanismAnd 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
TABLE 2 Parametric Table of modified modulation function expressions for the second rack
TABLE 3 Parametric Table of modified tuning function expressions for the third bay
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 control, different solving starting points have different influences on the edge thinning, so that the coordinate translation is performed on the established edge control function, and 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,
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;
the boundary conditions, because of the actual control problem solved, the maximum and minimum traverse amount exists in the execution mechanism, so when the control is needed according to the actual production requirement, the control amount needs to be limited, namely, the boundary conditions are added, the boundary conditions appear in the objective function in a penalty function mode, the maximum traverse amount is set as 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,
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:
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 (1)
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:
in the formula (I), the compound is shown in the specification,indicates that the s-th regulating mechanism to be controlled is in the control quantity xiLower pair distance strip steel edge NjInfluence of edge thinning at positionJ denotes 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 functionsRepresenting the control quantity to be solved of the s-th regulating mechanism to be controlled;
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,
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 _ xsDenotes the s th waitingControlling the adjustment limiting quantity of the adjusting mechanism, wherein m represents the order of the 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,
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 optimal control quantity of the regulating 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 mechanismAnd 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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