CN105710137B - A kind of cold-rolling mill multivariable board-shape control method based on constrained optimization method - Google Patents
A kind of cold-rolling mill multivariable board-shape control method based on constrained optimization method Download PDFInfo
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- B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
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Abstract
A kind of cold-rolling mill multivariable board-shape control method based on constrained optimization method, methods described step are：Designed for solving the Multi-variables optimum design model of profile regulation mechanism optimal adjustment amount；By the canonical form that Multi-variables optimum design model conversion is optimization problem；Design solves the initial search point of canonical form Multi-variables optimum design problem；Search mechanisms of the design along each change in coordinate axis direction；Scanned for along each change in coordinate axis direction, calculate the candidate value of optimum point；Design search stop criterion；Establish cold-rolling mill multivariable plat control system model.Control method of the present invention can be converted to multivariable plate shape Optimized model a series of single argument optimization problem, have the advantages that computational efficiency is high, save controller memory space, can parallel computation, be very suitable for the cold rolled sheet shape control system's development with multiple profile regulation mechanisms.
Description
Technical Field
The invention relates to the technical field of metallurgical rolling, in particular to a multi-variable strip shape control method of a cold rolling mill based on a constraint optimization algorithm.
Background
It is known that in the production of a cold rolled strip, when the strip is deformed in a non-uniform manner in the width direction, a plate-shape defect such as buckling, wave-shape or the like is generated. With the deterioration of global environment and the increasing aggravation of energy crisis, steel for industrial industries such as automobiles, household appliances, packaging and the like is continuously developed towards high strength and light weight so as to realize energy conservation and emission reduction. The requirements of the industries on cold-rolled steel strips are continuously increased, and simultaneously, higher and higher requirements on the plate shape quality of the cold-rolled steel strips are provided. From the production practice, the thinner and stronger the rolled strip, the more prominent the problem of plate shape defects will be, which restricts the further development of the related industries.
The quality of the strip shape is of great importance for cold-rolled steel strip products. In order to improve the quality of the cold-rolled strip steel, a six-roller mill with strong control capability on the strip shape is mostly adopted to produce the cold-rolled thin strip steel at present. For example, a common six-roller UCM cold rolling mill is usually provided with a mechanical plate shape adjusting mechanism such as a working roller bending roller, a middle roller bending roller, a roller inclination mechanism, a middle roller transverse moving mechanism and the like, and compared with a common four-roller mill, the plate shape control capability is greatly enhanced. The increase of the strip shape adjusting mechanisms improves the strip shape adjusting capability of the rolling mill, but also causes the modeling of a strip shape control system of the rolling mill to be more complicated. The process of the shape control is that the shape control is matched and comprehensively applied according to the size and the characteristics of the adjusting capacity of each shape adjusting mechanism, and then the shape deviation is controlled and eliminated. Therefore, an accurate control mathematical model is formulated, the optimal distribution of the adjustment quantity of each strip shape adjusting mechanism is realized, and the precondition for realizing the high-precision strip shape control process is provided.
Disclosure of Invention
The invention aims to provide a multi-variable strip shape control method of a cold rolling mill based on a constraint optimization algorithm, which has the advantages of high calculation efficiency, saving storage space of a controller, capability of parallel calculation, high control precision and strong system operation stability.
In order to realize the purpose, the following technical scheme is adopted: the control method comprises the steps of formulating an optimization model for solving the optimal regulating quantity of each plate shape regulating mechanism through mathematical modeling, and designing a multivariable optimization algorithm with global convergence around the optimization model; the multivariable optimization algorithm converts a multivariable plate-shaped optimization problem with constraint into a series of univariate optimization problems which can be searched along the coordinate direction; a step length acceleration method is designed, and through an iterative process, the target function can be quickly reduced, so that the optimal adjustment quantity of each plate shape adjusting mechanism is obtained;
the method comprises the following specific steps:
step 1, designing a multivariable optimization model for solving the optimal regulating quantity of a plate shape regulating mechanism for bending a working roll, bending a middle roll, inclining a roll and transversely moving the middle roll; adopting the weighted square sum of the residual plate shape deviation as an objective function of an optimization model; the mechanical design limit of each plate shape adjusting mechanism is used as a constraint condition;
step 2, converting a multivariable optimization model for solving the optimal adjustment quantity of the plate-shaped adjusting mechanism into a standard form of an optimization problem;
step 3, designing an initial search point for solving a standard form multivariable optimization problem;
step 4, designing a search mechanism along each coordinate axis direction;
step 5, searching along each coordinate axis direction, and calculating a candidate value of an optimal point;
step 6, designing a search termination criterion;
and 7, establishing a multi-variable strip shape control model of the cold rolling mill based on a constraint optimization algorithm.
Further, in step 1, the mechanical design limit of each plate shape adjusting mechanism is used as a constraint condition, and the optimization model is as follows:
wherein J (Δ u) is an objective function of the optimization model; delta u is the adjustment vector of each plate shape adjusting mechanism to be solved, and delta u belongs to R n (ii) a m is the number of strip shape measuring sections in the width direction of the strip; n is the number of the plate-shaped adjusting mechanisms; i and j are respectively the serial number of the measuring section and the serial number of the adjusting mechanism; g i Weighting factors for the plate shape deviation of the ith measurement section; Δ y i Is the plate shape deviation of the ith measurement section; Δ u j Is the adjustment quantity of the jth plate-shaped adjusting mechanism to be solved; eff ij The shape regulation efficiency coefficient of the jth plate shape regulating mechanism to the ith measuring section; BL j And BU j Respectively designing a lower limit and an upper limit of the mechanical design of the jth plate-shaped adjusting mechanism; u. of j Is the set value of the current control period of the jth plate shape adjusting mechanism.
Further, in step 2, the multivariate optimization model after being converted into the standard form is:
wherein f (x) is an objective function of the optimization model; x is the optimal regulating quantity vector of each plate-shaped regulating mechanism to be solved; Ω is an allowable set of constraints; l and u are respectively the lower limit and the upper limit of the optimal adjustment quantity of each plate shape adjusting mechanism.
Further, the specific method of step 3 is as follows: selecting an initial point x 0 E.g. omega, initial step length t 0 E (0, infinity), the initial search direction is any coordinate axis direction e i And i ∈ {1,..., n }; let the loop count variable initially be 1, i.e.: k =1,k ∈ { 1., K }, K = (1., ∞), K is a threshold for the total number of cycles, and three search termination thresholds ∈ are set 1 ，ε 2 And ε 3 ∈(0,1)。
Further, the specific method of step 4 is as follows: first along the coordinate axis e 1 Maximum step size t of direction search max And x is k +t max ·e 1 E is omega; from x k-1 At a step size of t = min { t } 0 ,t max Along a coordinate axis e 1 Starts to search in the positive direction to obtain a new point x after the first search k (11) ＝x k-1 +t·e 1 (ii) a If there is t>, 0 and f (x) k (11) )<f(x k-1 ) Let t = min { t } 0 /δ,t max Accelerating the search in the direction until the constraint boundary point or the objective function value is found to be decreased; if t = t max Or f (x) k (11) )>f(x k-1 ) Returning to the previous searching point and taking the point as an end point along the searching direction; if along the coordinate axis e 1 If the forward search of (2) does not decrease the objective function value, the coordinate axis e is set 1 The negative direction of (2) as the search direction; in this case the maximum search step in that direction needs to be recalculated, i.e.: t is t max And x k -t max ·e 1 E Ω, the search step then becomes t = min { t } 0 ,t max }; according to the formula e 1 The same search mode is searched in the positive direction to obtain the search end point x in the direction k (1) (ii) a If along the coordinate axis e 1 If the value of the objective function is not reduced by the positive and negative direction searches, the initial search point x is obtained k-1 Will be the end point x searched along the coordinate axis k (1) (ii) a Similarly, the search for other coordinate axis directions is performed according to this mechanism.
Further, the specific method of step 5 is as follows: first along the coordinate axis e 2 Maximum step size t of direction search max And x is k +t max ·e 2 E is omega; from x k (1) At a step size of t = min { t } 0 ,t max Along a coordinate axis e 2 Starts to search in the positive or negative direction to obtain the coordinate axis e 2 End point x of k (1) (ii) a By parity of reasoning, the third coordinate axis direction e is completed 3 To the nth coordinate axis direction e n The candidate optimal point x after the k searches are completed can be obtained k (n) (ii) a At this time, let x k ＝x k (n) (ii) a If not | | x k -x k-1 ||<ε 1 And if the iteration number K does not exceed the iteration number threshold K, making K = K +1, and according to the mechanism designed in the step four, selecting the coordinate direction e 1 Starting to the nth coordinate axis direction e n Restarting a new round of search; if the iteration number K is equal to the set iteration number threshold value K, x k Will be the optimal solution x to the optimization problem in step 2 * 。
Further, the specific method of step 6 is as follows: judging the termination of the searching process, wherein the judgment criterion comprises the checking of the searching step length and the variation of the objective function value; if the search step t 0 Is already small enough, i.e. satisfies t 0 <ε 2 (ii) a Or the variation of the objective function value is small enough, namely, | | f (x) is satisfied k )-f(x k-1 )||<ε 3 Then x at this time k Will be the optimal solution x to the optimization problem in step 2 * (ii) a Otherwise, shrink the search step length, let t 0 ＝θ·t 0 Then according to the searching mechanism designed in step 4, the coordinate direction e is used 1 Starting in the direction of coordinate axes e n A new round of search is restarted.
Further, the specific method in step 7 is as follows: establishing a multivariable strip shape closed-loop control model according to the constrained multivariable global optimization method established in the steps 3-6; and calculating the optimal regulating quantity of each plate shape regulating mechanism in each control period on line by a formulated global optimization method to be used as an input value of each plate shape regulating mechanism controller.
Compared with the prior art, the invention has the following advantages:
1. the global optimization method adopting a non-derivation mode can avoid solving complex objective function gradient information, does not need to construct a complex model based on the gradient information, and is beneficial to actual engineering development.
2. The method converts the multivariable strip shape optimization model into a series of univariate optimization problems, has the characteristics of high calculation efficiency, saving of storage space of a controller and capability of parallel calculation, and is very suitable for development of a cold-rolled strip shape control system with a plurality of strip shape adjusting mechanisms.
3. The control method has the advantages of high calculation precision, good universality, high plate shape control precision, strong system operation stability and the like after the detection of field practical application.
Drawings
FIG. 1 is a graph of the efficacy coefficient of each profile control of the method of the present invention.
FIG. 2 is a diagram of an algorithm for searching along a coordinate direction according to the method of the present invention.
FIG. 3 is a block diagram of a multivariable strip closed-loop control system of the method of the present invention.
FIG. 4 is a diagram of a multivariable strip shape control algorithm structure of a cold rolling mill based on a constraint optimization algorithm.
FIG. 5 is a plot of the drop trajectory of the objective function value for the method of the present invention.
FIG. 6 is a schematic diagram of a multivariable strip shape closed-loop control system of a 1450mm five-stand cold continuous rolling mill according to the method of the present invention. FIG. 7 is a profile of a flatness target value versus a flatness measurement value for the method of the present invention.
FIG. 8 is a CPU load graph of the method of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples:
example 1: this example 1 discloses the process of multivariable strip shape optimization algorithm in the final frame plate shape closed-loop control system of a 1450mm five-stand cold continuous rolling mill. The plate shape adjusting mechanism comprises a roll inclination, a working roll positive/negative bending roll, a middle roll positive bending roll and a middle roll transverse moving, and main control parameters and rolling parameters are shown in a table 1.
TABLE 1 Main parameters of the Rolling Mill
The control method comprises the steps of formulating an optimization model for solving the optimal regulating quantity of each plate shape regulating mechanism through mathematical modeling, and designing a multivariable optimization algorithm with global convergence around the optimization model; the multivariable optimization algorithm converts the multivariable plate shape optimization problem with constraints into a series of univariate optimization problems which can be searched along the coordinate direction; a step length acceleration method is designed, and the target function can be quickly lowered through an iterative process, so that the optimal adjustment quantity of each plate shape adjusting mechanism is obtained;
as shown in fig. 4, the specific steps are as follows:
step 1, designing a multivariable optimization model for solving the optimal regulating quantity of the plate shape regulating mechanism of the working roll bending roll, the middle roll bending roll, the roll inclination and the middle roll transverse moving. The establishment of the optimization model comprises three basic elements which are respectively used for determining a complete decision variable, a clear objective function expression and a constraint condition. For multivariable strip shape control, the adjustment quantity of the strip shape adjusting mechanism to be solved and the corresponding value interval thereof can be used as decision variables and constraint conditions of an optimization model. And the target of the strip shape control is to eliminate the residual strip shape deviation to the maximum extent, so that the strip shape deviation remained after the action of each strip shape adjusting mechanism is taken as the target function of the optimization model. The smaller the residual plate shape deviation is, the better the adjustment quantity of the plate shape adjusting mechanism is. It is considered that whether the objective function is a univariate function or a multivariate function, it must be a convex function or only have a peak to guarantee a globally optimal solution. The weighted sum of squares of the residual plate shape deviation is therefore used as the objective function of the optimization model. The optimization model for calculating the optimum adjustment for each strip shape adjustment mechanism can be expressed as:
wherein J (Δ u) is an objective function of the optimization model; delta u is the adjustment vector of each plate shape adjusting mechanism to be solved, and delta u belongs to R n (ii) a m is the number of strip shape measuring sections in the width direction of the strip; n is the number of the plate-shaped adjusting mechanisms; i and j are respectively a measuring section serial number and an adjusting mechanism serial number; g i Weighting factors for the plate shape deviation of the ith measurement section; Δ y i Is the plate shape deviation of the ith measurement section; Δ u j Is the adjustment quantity of the jth plate-shaped adjusting mechanism to be solved; eff ij The adjustment efficiency coefficient of the jth plate shape adjusting mechanism to the plate shape of the ith measuring section is obtained; BL j And BU j Respectively designing a lower limit and an upper limit of the mechanical design of the jth plate-shaped adjusting mechanism; u. of j Is the set value of the current control period of the jth plate shape adjusting mechanism. The shape multivariable optimization model is established based on the shape regulation efficacy, so that the shape regulation efficacy coefficient of each shape regulation mechanism needs to be calculated and determined. The strip shape regulation efficiency coefficient represents the variation of a strip shape value caused by a strip shape regulating mechanism under the condition of generating unit regulating quantity, and the calculation method is as follows:
wherein Eff is a matrix of the plate shape regulation efficacy coefficient, and Eff is in the same size as R m×n (ii) a U is the adjustment vector of each plate shape adjusting mechanism, and delta U belongs to R n (ii) a Δ Y is the amount of change in shape of the induced plate, and Δ Y ∈ R m 。
FIG. 1 shows the calculated profile shape control efficiency coefficient curves of the profile shape adjusting mechanisms such as the work roll bending, the middle roll transverse moving and the roll inclination.
Since the final stand of the 1450mm five stand cold continuous mill was the UCM mill, there were four plate shape adjustment mechanisms in total, so the number of adjustment mechanisms in this example model was 4, i.e., n =4. In order to simplify the data processing process of the control system, the actual number of measurement sections and the target plate shape and the plate shape deviation at each measurement section are equivalent to the plate shape target value and the plate shape deviation value at 20 measurement sections, that is, m in the model is 20. The remaining parameters of the model in this example are shown in table 2.
TABLE 2 principal parameters of the multivariate strip shape optimization model
Mechanical design positive limit BU of the individual plate shape adjusting mechanisms in this example j Negative limit BL j Set to 100% and-100%, respectively. 100% represents that the actuator has reached a positive adjustment limit, and 100% represents that a negative adjustment limit has been reached. The adjustment, the set value and the actual value of each profile adjustment means are defined as percentages of the mechanical limit. The strip shape value and the strip shape deviation value represent 10 of the elongation 5 The power factor is dimensionless like the power factor of the shape control.
Step 2, converting a multivariable optimization model for solving the optimal adjustment quantity of the plate-shaped adjusting mechanism into a standard form of an optimization problem;
to introduce the multivariate optimization algorithm more clearly, the multivariate strip optimization model is transformed into a standard form of the multivariate optimization problem. The multivariate optimization model after conversion to the standard form is:
wherein f (x) is an objective function of the optimization model; x is the optimal regulating quantity vector of each plate-shaped regulating mechanism to be solved; Ω is an allowable set of constraints; l and u are respectively the lower limit and the upper limit of the optimal adjustment quantity of each plate shape adjusting mechanism. These parameters can all be derived from the data given in step 1. For this optimization problem, if the allowed point x is not a stagnation point of the function f (x), then there must be one allowed y to satisfyk belongs to {1,. Eta., n }. If t = (y-x) k >, 0, and considering Ω is the box constraint, then there are:
in the formula:is the gradient of the objective function f (x) at coordinate x; e.g. of the type k is an orthogonal set of coordinate directions, and k ∈ {1,..., n }.
Due to the fact thatWith continuity, and the allowed set Ω is a convex set, there must be a positive value λ satisfying:
f(x+t·e k )<f(x),x+t·e k ∈Ω,t∈(0,λ)
when t = (y-x) k &When lt is 0, it is represented by-e k Instead of e k . Thus, for any allowed point x, even if it is notIs the function stagnation point, but a coordinate direction exists necessarily to enable the objective function to have strict decline. This direction may be a positive direction of the coordinate axis or a negative direction of the coordinate axis.
Step 3, designing and solving an initial search point of a standard form multivariable optimization problem; selecting an initial point x 0 E.g. omega, initial step length t 0 E (0, infinity), the initial search direction being any coordinate axis direction e i And i ∈ {1,..., n }; let the loop count variable initially be 1, i.e.: k =1,k ∈ { 1., K }, K = (1., ∞), K is a threshold for the total number of cycles, and three search termination thresholds ∈ are set 1 ，ε 2 And ε 3 ∈(0,1)。
In this embodiment 1, the initial point is selected as x 0 = (0.5,0.5,0.5,0.5,0.5) and f (x) 0 ) =57.32483, initial step t 0 =1, initial search direction e 1 =1,0,0,0, the step-size reduction factor and the step-size acceleration factor are δ = θ =0.5, respectively, the threshold K =4000 for the total number of cycles, and three search termination thresholds are set to be ∈ respectively 1 ＝10 -6 ，ε 2 ＝10 -6 And ε 3 ＝10 -7 。
Step 4, designing a search mechanism along each coordinate axis direction; first along the coordinate axis e 1 Maximum step size t of direction search max =0.5, then from x 0 = (0.5,0.5,0.5,0.5,0.5) at step t = min {1,0.5} along coordinate axis e 1 Starts to search in the positive direction, and obtains a new point x after the first search 1 (11) ＝x 0 +t·e 1 . If there is t>, 0 and f (x) 1 (11) )<f(x 0 ) Let t = min { t } 0 /0.5,t max I.e. speeding up the search in that direction until the constraint boundary point is searched for or the value of the objective function falls again. If t = t max Or f (x) 1 (11) )>f(x 0 ) Then return to the previous search point and take that point as the end point along the search direction. If along the coordinate axis e 1 If the positive direction search can not make the objective function value decrease, the coordinate axis e is set 1 In the negative direction ofFor the search direction, and recalculate the search step size according to 1 The same search mode is searched in the positive direction of the direction to obtain the search end point x of the direction k (1) . Similarly, the search for other coordinate axis directions is performed according to this mechanism.
Step 5, searching along each coordinate axis direction according to the searching mechanism designed in the step 4, calculating a candidate value of an optimal point, and determining the optimal point of the objective function according to a search termination criterion;
first along the coordinate axis e 2 Maximum step size t of direction search max And x is k +t max ·e 2 E is omega; from x k (1) At step size t = min { t } 0 ,t max Along a coordinate axis e 2 Starts to search in the positive or negative direction to obtain the coordinate axis e 2 End point x of k (1) (ii) a By parity of reasoning, the third coordinate axis direction e is completed 3 To the nth coordinate axis direction e n The candidate optimal point x after the k searches are completed can be obtained k (n) (ii) a At this time, let x k ＝x k (n) (ii) a If not | | x k -x k-1 ||<ε 1 And if the iteration number K does not exceed the iteration number threshold K, making K = K +1, and according to the mechanism designed in the step four, selecting the coordinate direction e 1 Starting to the nth coordinate axis direction e n Restarting a new round of search; if the iteration number K is equal to the set iteration number threshold value K, x k Will be the optimal solution x to the optimization problem in step 2 * . The trajectory of the drop of the objective function value during the optimization is shown in fig. 5, and the number of iterations and the main results are shown in table 3.
TABLE 3 model optimization results
After the steps 4 and 5 are completed, search iteration in each coordinate axis direction can be completed, and the specific algorithm structures of the steps 4 and 5 are shown in fig. 2.
Step 6, designing a search termination criterion; judging the termination of the searching process, wherein the judgment criterion comprises the check of the searching step length and the variable quantity of the objective function value; if the search step t 0 Is already small enough, i.e. satisfies t 0 <ε 2 (ii) a Or the variation of the objective function value is small enough, namely, | | f (x) is satisfied k )-f(x k-1 )||<ε 3 Then x at this time k Will be the optimal solution x of the optimization problem in step 2 * (ii) a Otherwise, shrink the search step length, let t 0 ＝θ·t 0 Then according to the searching mechanism designed in step 4, the coordinate direction e is used 1 Starting in the direction of coordinate axes e n A new round of search is restarted. If the algorithm generates a sequence of iterations { x } k Converge to a limit point, each limit point will be the stagnation point of the multivariate optimization problem, or an approximation of the stagnation point.
And 7, establishing a multi-variable strip shape control model of the cold rolling mill based on a constraint optimization algorithm. Establishing a multivariable strip shape closed-loop control model according to the constrained multivariable global optimization method established in the steps 3-6; the optimal adjustment quantity of each strip shape adjusting mechanism in each control period is calculated on line through a formulated global optimization method and is used as an input value of each strip shape adjusting mechanism controller, as shown in fig. 3. In fig. 3, Δ Y represents a deviation vector between the target strip shape and the measured strip shape; eff represents a plate shape regulation efficiency coefficient matrix of the plate shape regulating mechanism; Δ U = { Δ U tr ,Δu wrb ,Δu irb ,Δu irs Expressing the optimal adjustment amount of each strip shape adjustment mechanism calculated by a multivariate optimization model; Δ u tr ,Δu wrb ,Δu irb ,Δu irs Respectively representing the optimal adjustment amounts of roll inclination, work roll bending, intermediate roll bending and intermediate roll transverse movement; u = { U = tr ,u wrb ,u irb ,Δu irs Representing the actual value vector of each plate shape adjusting mechanism in the current control period; p represents the vector of the set value of each strip shape adjusting mechanism in the next control cycle.
According to the strip shape deviation and the determined strip shape regulation and control efficiency coefficient, the optimal regulating quantity of each strip shape regulating mechanism in each control period is calculated on line through a formulated global optimization method and is used as an input value of each strip shape regulating mechanism controller, and therefore the strip shape of the rolling mill is continuously, dynamically and in real time controlled, and a multivariable strip shape closed-loop control system of a 1450mm five-stand cold continuous rolling mill formulated in the embodiment is shown in fig. 6.
FIG. 7 is a set of profile target values and profile measurement values of the strip along the width direction of the strip after the optimization model is put into operation. As can be seen from the data analysis, the measured value of the strip shape is basically consistent with the target value, the deviation of the strip shape at each measuring section is very small, and the deviation is basically within +/-2I-Unit, so that the strip shape control precision is higher.
FIG. 8 shows the CPU load profile during rolling (model SIMATIC TDC CPU551, available from Siemens). As can be seen from the figure, the designed multivariable plate shape optimization algorithm does not occupy excessive system resources, and the CPU is in a lower stable operation interval.
The above-mentioned embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solution of the present invention by those skilled in the art should fall within the protection scope defined by the claims of the present invention without departing from the spirit of the present invention.
Claims (4)
1. A multi-variable strip shape control method of a cold rolling mill based on a constraint optimization algorithm is characterized in that the control method is to formulate an optimization model for solving the optimal regulating variable of each strip shape regulating mechanism through mathematical modeling, and design a multi-variable optimization algorithm with global convergence around the optimization model; the multivariable optimization algorithm converts a multivariable plate-shaped optimization problem with constraint into a series of univariate optimization problems which can be searched along the coordinate direction; a step length acceleration method is designed, and through an iterative process, the target function can be quickly reduced, so that the optimal adjustment quantity of each plate shape adjusting mechanism is obtained;
the method comprises the following specific steps:
step 1, designing a multivariable optimization model for solving the optimal regulating quantity of a plate shape regulating mechanism for bending a working roll, bending a middle roll, inclining a roll and transversely moving the middle roll; adopting the weighted square sum of the residual plate shape deviation as a target function of an optimization model; the mechanical design limit of each plate shape adjusting mechanism is used as a constraint condition;
the mechanical design limit of each plate shape adjusting mechanism is used as a constraint condition, and the optimization model is as follows:
wherein J (Δ u) is an objective function of the optimization model; delta u is the adjustment vector of each plate shape adjusting mechanism to be solved, and delta u belongs to R n (ii) a m is the number of strip shape measuring sections in the width direction of the strip; n is the number of the plate-shaped adjusting mechanisms; i and j are respectively a measuring section serial number and an adjusting mechanism serial number; g i Weighting factors for the plate shape deviation of the ith measurement section; Δ y i Is the plate shape deviation of the ith measurement section; Δ u j Is the adjustment quantity of the jth plate-shaped adjusting mechanism to be solved; eff ij The shape regulation efficiency coefficient of the jth plate shape regulating mechanism to the ith measuring section; BL j And BU j Respectively designing a lower limit and an upper limit for the machinery of the jth plate-shaped adjusting mechanism; u. of j Is the set value of the current control period of the jth plate shape adjusting mechanism;
step 2, converting a multivariable optimization model for solving the optimal adjustment quantity of the plate-shaped adjusting mechanism into a standard form of an optimization problem;
the multivariate optimization model after conversion to the standard form is:
wherein f (x) is an objective function of the optimization model; x is the optimal regulating quantity vector of each plate-shaped regulating mechanism to be solved; Ω is an allowable set of constraints; l and u are respectively the lower limit and the upper limit of the optimal regulating quantity of each plate-shaped regulating mechanism;
step 3, designing an initial search point for solving a standard form multivariable optimization problem;
selecting an initial point x 0 E.g. omega, initial step length t 0 E (0, infinity), the initial search direction being any coordinate axis direction e i And i ∈ {1,..., n }; let the loop count variable initially be 1, i.e.: k =1,k ∈ { 1., K }, K = (1., ∞), K is a threshold for the total number of cycles, and three search termination thresholds ∈ are set 1 ，ε 2 And ε 3 ∈(0,1)；
Step 4, designing a search mechanism along each coordinate axis direction;
first along the coordinate axis e 1 Maximum step size t of direction search max And x is k +t max ·e 1 E is omega; from x k-1 At a step size of t = min { t } 0 ,t max Along a coordinate axis e 1 Starts to search in the positive direction to obtain a new point x after the first search k (11) ＝x k-1 +t·e 1 (ii) a If there is t>, 0 and f (x) k (11) )<f(x k-1 ) Let t = min { t } 0 /δ,t max Accelerating the search in the direction until the constraint boundary point or the objective function value is found to be decreased; if t = t max Or f (x) k (11) )>f(x k-1 ) Returning to the previous searching point and taking the point as an end point along the searching direction; if along the coordinate axis e 1 If the positive direction search can not make the objective function value decrease, the coordinate axis e is set 1 The negative direction of (2) as the search direction; in this case the maximum search step in that direction needs to be recalculated, i.e.: t is t max And x k -t max ·e 1 E Ω, the search step then becomes t = min { t } 0 ,t max }; according to the formula e 1 The same search mode is searched in the positive direction to obtain the search end point x in the direction k (1) (ii) a If along the coordinate axis e 1 If the value of the objective function is not reduced by the positive and negative direction searches, the initial search point x is obtained k-1 Will be the end point x searched along the coordinate axis k (1) (ii) a Similarly, the search for other coordinate axis directions is also carried out according to the mechanism;
step 5, searching along each coordinate axis direction, and calculating a candidate value of an optimal point;
step 6, designing a search termination criterion;
and 7, establishing a multi-variable strip shape control model of the cold rolling mill based on a constraint optimization algorithm.
2. The multi-variable strip shape control method of the cold rolling mill based on the constraint optimization algorithm, according to claim 1, is characterized in that the specific method in the step 5 is as follows: first along the coordinate axis e 2 Maximum step size t of direction search max And x is k +t max ·e 2 E is omega; from x k (1) At step size t = min { t } 0 ,t max Along a coordinate axis e 2 Starts to search in the positive or negative direction to obtain the coordinate axis e 2 End point x of k (1) (ii) a By parity of reasoning, the third coordinate axis direction e is completed 3 To the nth coordinate axis direction e n The candidate optimal point x after the k searches are completed can be obtained k (n) (ii) a At this time, let x k ＝x k (n) (ii) a If not | | x k -x k-1 ||<ε 1 And if the iteration number K does not exceed the iteration number threshold K, making K = K +1, and according to the mechanism designed in the step four, selecting the coordinate direction e 1 Starting to the nth coordinate axis direction e n Restarting a new round of search; if the iteration number K is equal to the set iteration number threshold value K, x k Will be the optimal solution x to the optimization problem in step 2 * 。
3. The multi-variable strip shape control method of the cold rolling mill based on the constraint optimization algorithm, according to claim 1, is characterized in that the specific method in the step 6 is as follows: judging the termination of the searching process, wherein the judgment criterion comprises the checking of the searching step length and the variation of the objective function value;if the search step t 0 Is already small enough, i.e. satisfies t 0 <ε 2 (ii) a Or the variation of the objective function value is small enough, namely, | | f (x) is satisfied k )-f(x k-1 )||<ε 3 Then x at this time k Will be the optimal solution x to the optimization problem in step 2 * (ii) a Otherwise, shrink the search step length, let t 0 ＝θ·t 0 Then according to the searching mechanism designed in step 4, the coordinate direction e is used 1 Starting in the direction of coordinate axes e n A new round of search is restarted.
4. The multi-variable strip shape control method of the cold rolling mill based on the constraint optimization algorithm, according to claim 1, is characterized in that the specific method in the step 7 is as follows: establishing a multivariable strip shape closed-loop control model according to the constrained multivariable global optimization method established in the steps 3-6; and calculating the optimal regulating quantity of each plate shape regulating mechanism in each control period on line by a formulated global optimization method to be used as an input value of each plate shape regulating mechanism controller.
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| CN109433830B (en) * | 2018-11-06 | 2020-01-07 | 燕山大学 | Cold-rolled plate shape closed-loop control method and system |
| CN109513751A (en) * | 2018-11-13 | 2019-03-26 | 燕山大学 | A kind of removing method and system of exit plate shape deviation |
| CN112207136B (en) * | 2020-09-08 | 2021-07-16 | 燕山大学 | Strip constant tension loop control method based on rolling mill torsional vibration test analysis |
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| AT345237B (en) * | 1976-12-28 | 1978-09-11 | Voest Ag | DEVICE FOR ROLLING STRIP OR TABLE-SHAPED ROLLED MATERIAL |
| JPS55144314A (en) * | 1979-04-28 | 1980-11-11 | Nippon Steel Corp | Bending-preventing rolling method of rolling material in reversing type rolling mill |
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