CN111856932A - Cold strip mill plate shape closed-loop control method based on influence matrix recursive identification - Google Patents

Cold strip mill plate shape closed-loop control method based on influence matrix recursive identification Download PDF

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CN111856932A
CN111856932A CN202010633658.1A CN202010633658A CN111856932A CN 111856932 A CN111856932 A CN 111856932A CN 202010633658 A CN202010633658 A CN 202010633658A CN 111856932 A CN111856932 A CN 111856932A
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shape
matrix
control
plate shape
strip
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CN111856932B (en
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刘乐
亓鲁刚
亢克松
方一鸣
李晓刚
向永光
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Yanshan University
Tangshan Iron and Steel Group Co Ltd
HBIS Co Ltd Tangshan Branch
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Yanshan University
Tangshan Iron and Steel Group Co Ltd
HBIS Co Ltd Tangshan Branch
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/28—Control of flatness or profile during rolling of strip, sheets or plates

Abstract

The invention relates to a cold strip mill strip shape closed-loop control method based on influence matrix recursive identification, and belongs to the technical field of steel rolling strip shape control methods. The technical scheme is as follows: firstly, based on a progressive least square method of fading memory, carrying out online identification on an influence matrix of the change of characteristic coefficients of a strip shape mode from the control increment of a strip shape adjusting mechanism to the change of the characteristic coefficients of the strip shape mode corresponding to the actual strip shape, further carrying out self-correction on parameters of the strip shape controller, and calculating the control quantity of the strip shape adjusting mechanism according to the characteristic coefficient deviation of the target strip shape and the actual strip shape. The invention has the beneficial effects that: the method has the advantages of improving the influence of the shape pattern recognition on the matrix precision and the shape control precision, being simple to realize, having high operation speed, being capable of well meeting the requirement of high real-time property of shape control, having high shape control precision, being suitable for on-line application, being convenient to implement and the like.

Description

Cold strip mill plate shape closed-loop control method based on influence matrix recursive identification
Technical Field
The invention relates to a cold strip mill strip shape closed-loop control method based on influence matrix recursive identification, and belongs to the technical field of steel rolling strip shape control methods.
Background
The current mainstream rolling mill is provided with plate shape regulating and controlling mechanisms such as a roll tilting mechanism, a work roll bending mechanism, a middle roll bending mechanism and a middle roll transverse moving mechanism, and the plate shape deviation can be better eliminated and the plate shape quality can be improved only by adopting a reasonable plate shape closed-loop control method and mutually matching various regulating and controlling means. According to different evaluation modes of the strip shape deviation, the strip shape closed-loop control method mainly comprises a strip shape closed-loop control method based on a measurement section and a strip shape closed-loop control method based on a strip shape mode. Although the former plate shape measurement information can be directly used for calculating feedback control quantity, the actual plate shape adjusting mechanism cannot be specifically applied to a certain measurement section along the plate width direction, that is, no enough actuating mechanism can achieve the purpose of eliminating the plate shape deviation on the certain measurement section. The latter judges which defect mode the plate shape belongs to or the combination of several defect modes by processing the plate shape measurement information, wherein the elimination of several common plate shape mode defects approximately corresponds to the functions of several common adjusting means, the characteristic coefficient of the plate shape mode obtained by identification is fed back to a plate shape control system, the adjusting quantity of a plate shape actuating mechanism can be calculated, and the calculating process is simpler and more effective than the former, so the latter is often adopted in the plate shape control method.
In the prior art, document 1 is an influence matrix method (zhangxiulingling. cold strip mill intelligent identification and intelligent control research of plate shape [ doctor academic thesis of Yanshan university ].2002:60-80) proposed by zhangxilingling, which is an important development direction in a plate shape closed-loop control method based on plate shape mode identification, and the method considers that the adjustment action of any one plate shape adjusting mechanism has influence on various plate shape defects, and does not consider that the traditional control strategy considers that the roll inclination adjustment can only eliminate a primary mode component in the plate shape deviation, and the roll bending force change only eliminates a secondary mode component in the plate shape deviation, and the like; the method tests according to the plate shape neural network simulation model to obtain the static relation data between various plate shape regulating mechanism increments and various plate shape mode component changes, and the online control of the plate shape is realized by establishing an influence matrix to exert the regulating and controlling capability of each plate shape control means. However, the static influence matrix method cannot meet the requirement of people on higher control of the plate shape aiming at the change of the actual rolling working condition.
In document 2, for the defects of the traditional effect function method and the plate shape static influence matrix, an intelligent model is proposed to reflect the real-time change characteristic of the influence matrix, and the influence matrix is solved by establishing a fuzzy neural network plate shape dynamic influence matrix model based on clustering (which billows, research and application of an intelligent model for online control of a wide strip cold rolling mill plate shape [ doctor academic thesis at Yanshan university ].2008: 41-75). However, the inherent weak popularization performance of the intelligent method makes it difficult to realize stable work in the actual rolling process, and the specific implementation difficulty of the intelligent method is high, so that the strip shape control method based on the influence matrix is difficult to be put into practical application due to the factors.
Document 3 is a patent with application number CN201010617064.8, and proposes a cold-rolled strip steel strip shape closed-loop control method based on influence matrix self-learning, which is simple and fast in calculation, and easy to implement, in order to overcome the disadvantage of solving the influence matrix by using an intelligent method in the prior art. The modeling method for establishing the influence matrix prior value table of the typical working condition points based on a small amount of sample information has high calculation speed but limited model precision.
In summary, the literature according to the prior art shows that there are some deficiencies affecting the matrix model accuracy under the condition of rolling condition changes.
Disclosure of Invention
The invention aims to provide a closed-loop control method for the strip shape of a cold strip rolling mill based on recursive identification of an influence matrix, which adopts a fading memory recursive least square identification algorithm, identifies the strip shape influence matrix on line according to real-time data information, performs strip shape adaptive control to improve the strip shape mode identification influence matrix precision and the strip shape control precision, is simple to realize, has high operation speed, can well meet the requirement of high strip shape control real-time property, has the advantages of high strip shape control precision, suitability for on-line application, convenience in implementation and the like, and effectively solves the problems in the background technology.
The technical scheme of the invention is as follows: a closed-loop control method for the shape of a cold strip mill based on recursive identification of an influence matrix comprises the following steps: (1) considering the time lag of the strip shape detection, establishing an influence matrix model expression of the change of the characteristic coefficient from the control increment of the strip shape adjusting mechanism to the actual strip shape mode, wherein the model is also suitable for systems with different numbers of adjusting mechanisms; (2) considering the material quality of the strip steel, selecting N groups of adjusting mechanisms to adjust the corresponding data of the increment and the characteristic coefficient variable quantity of the shape mode from the previous steel coil production data of the same steel type (if the new steel type is the previous steel coil production data of the similar steel type), and obtaining the initial value of the influence matrix by adopting a one-time completion least square method; (3) and finally, automatically calculating the control quantity of the plate shape adjusting mechanism according to the deviation between the target plate shape mode and the actual plate shape mode and the control matrix, and further automatically correcting the plate shape to enable the actual plate shape to be consistent with the target plate shape.
In the step (1), the expression of the plate shape influence matrix model is shown as the following formula:
Δat(k)＝GΔu(k-τ)+e(k)
In the formula (I), the compound is shown in the specification,
Figure BDA0002566900000000041
called an influence matrix, has a slow time-varying characteristic and represents the increment delta u of the plate shape adjusting mechanismj(k-τ)(j＝1,2,L,Ia，IaFor the number of adjustment mechanisms) for each strip shape standard pattern characteristic coefficient Δ ati(k) (i ═ 1,2, L,4) in a model relationship, where gijFor the influence coefficient of the jth slat shape adjusting mechanism on the ith slat shape mode,
Figure BDA0002566900000000042
the increment is adjusted for the plate-shaped adjusting structure,
Figure BDA0002566900000000043
representing the variation of the actual characteristic coefficient of the plate shape at the front moment and the rear moment,
Figure BDA0002566900000000044
is an error term; τ is the number of slab detection lag steps.
In the step (2), the influence matrix G can pass through each row vector Gi(i ═ 1,2, L,4) by discriminative estimation, giThe identification and estimation method comprises the following steps: the ith relation of equation (1):
Figure BDA0002566900000000045
and (3) taking K as tau +1, tau +2, K and tau + N from the field sampling data to obtain a relation equation of N groups of actuator adjustment increments to the plate-shaped standard mode characteristic coefficients:
ΔatiN＝ΦNgi T+eN
in the formula (I), the compound is shown in the specification,
Figure BDA0002566900000000046
Figure BDA0002566900000000051
initial value P obtained by one-time completion of least square method calculationNAnd
Figure BDA0002566900000000052
as follows:
Figure BDA0002566900000000053
and then obtaining an estimated value of the influence matrix G:
Figure BDA0002566900000000054
the step (3) specifically comprises the following steps:
(a) an influence matrix is identified in an online recursion manner by adopting a fading memory least square method with forgetting factors; with the increasing production data, new observed data Δ a is obtained when k ═ τ + N +1 ti(τ+N+1)，Δuj(N +1), then
Figure BDA0002566900000000055
The new impact matrix is calculated using a recursive formula as follows:
Figure BDA0002566900000000056
wherein, mu is more than 0 and less than 1, which is a forgetting factor; considering that the performance change of the adjusting mechanism of the rolling mill is a slow time-varying process, the value of mu is 0.95, so that the estimated value of a new influence matrix is obtained:
Figure BDA0002566900000000061
(b) calculating a control matrix; when I isaWhen the number is equal to 4, the number is 4,
Figure BDA0002566900000000062
for the matrix, from equation (1) and taking into account the time shift, the strip-form actuator adjustment incremental expression can be obtained:
Figure BDA0002566900000000063
in the formula (I), the compound is shown in the specification,
Figure BDA0002566900000000064
is a control matrix;
note: if it is
Figure BDA0002566900000000065
Instead of being square, the shape control matrix C (k) may be formed by a generalized inverse of the influencing matrix
Figure BDA0002566900000000066
Instead of this; when I isaWhen the ratio is less than 4, the reaction solution is,
Figure BDA0002566900000000067
for a column full rank, the control matrix calculation formula is as follows:
Figure BDA0002566900000000068
when I isaWhen the pressure is higher than 4, the pressure is higher,
Figure BDA0002566900000000069
for a full row rank, the control matrix calculation formula is shown as follows:
Figure BDA00025669000000000610
(c) calculating a controller output; in order to obtain the control amount u (k +1) ═ u (k) + Δ u (k +1) at the next time, the control increment Δ u (k +1) is calculated first, and k in equation (7) is replaced with k +1, and further:
Δu(k+1)＝C(k)Δat(k+τ+1)＝C(k)(at(k+τ+1)-at(k+τ))
the design hopes that the actual shape of the next moment (namely k +1 moment) can reach the target shape, namely at(k+τ+1)＝arAnd then:
Δu(k+1)＝C(k)(ar-at(k+τ))
in the formula atCalculation expression of (k + τ)Can be derived as:
Figure BDA00025669000000000611
the control increment expression (7) can then be written as:
Figure BDA0002566900000000071
The controller final output is expressed as:
u(k+1)＝u(k)+Δu(k+1)
(d) updating the recursive computation matrix PN+1、
Figure BDA0002566900000000072
And a control quantity, i.e.
Figure BDA0002566900000000073
Figure BDA0002566900000000074
And
Figure BDA0002566900000000075
returning to the step (a).
The invention has the beneficial effects that: the method adopts a fading memory recursive least square identification algorithm, identifies the strip shape influence matrix on line according to real-time data information, performs strip shape adaptive control to improve the strip shape pattern recognition influence matrix precision and the strip shape control precision, is simple to realize, has high operation speed, can well meet the requirement of high strip shape control real-time property, and has the advantages of high strip shape control precision, suitability for on-line application, convenience in implementation and the like.
Drawings
FIG. 1 is a block diagram of a cold strip mill strip shape closed loop adaptive control principle based on impact matrix recursive identification;
FIG. 2 is a block diagram of a cold strip mill strip shape closed loop adaptive control process based on impact matrix recursive identification;
FIG. 3 is a graph of initial time flatness before adaptive control of flatness profiles according to an embodiment of the present invention;
FIG. 4 is a graph of the strip shape after the strip shape is adaptively controlled in 16 steps according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions of the embodiments of the present invention with reference to the drawings of the embodiments, and it is obvious that the described embodiments are a small part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person of ordinary skill in the art without creative work based on the embodiments of the present invention belong to the protection scope of the present invention.
A closed-loop control method for the shape of a cold strip mill based on recursive identification of an influence matrix comprises the following steps: (1) considering the time lag of the strip shape detection, establishing an influence matrix model expression of the change of the characteristic coefficient from the control increment of the strip shape adjusting mechanism to the actual strip shape mode, wherein the model is also suitable for systems with different numbers of adjusting mechanisms; (2) considering the material quality of the strip steel, selecting N groups of adjusting mechanisms to adjust the corresponding data of the increment and the characteristic coefficient variable quantity of the shape mode from the previous steel coil production data of the same steel type (if the new steel type is the previous steel coil production data of the similar steel type), and obtaining the initial value of the influence matrix by adopting a one-time completion least square method; (3) and finally, automatically calculating the control quantity of the plate shape adjusting mechanism according to the deviation between the target plate shape mode and the actual plate shape mode and the control matrix, and further automatically correcting the plate shape to enable the actual plate shape to be consistent with the target plate shape.
In the step (1), the expression of the plate shape influence matrix model is shown as the following formula:
Δat(k)＝GΔu(k-τ)+e(k)
in the formula (I), the compound is shown in the specification,
Figure BDA0002566900000000081
called moment of influence Matrix with slow time varying characteristic and representing incremental value Delauu of plate shape regulating mechanismj(k-τ)(j＝1,2,L,Ia，IaFor the number of adjustment mechanisms) for each strip shape standard pattern characteristic coefficient Δ ati(k) (i ═ 1,2, L,4) in a model relationship, where gijFor the influence coefficient of the jth slat shape adjusting mechanism on the ith slat shape mode,
Figure BDA0002566900000000091
the increment is adjusted for the plate-shaped adjusting structure,
Figure BDA0002566900000000092
representing the variation of the actual characteristic coefficient of the plate shape at the front moment and the rear moment,
Figure BDA0002566900000000093
is an error term; τ is the number of slab detection lag steps.
In the step (2), the influence matrix G can pass through each row vector Gi(i ═ 1,2, L,4) by discriminative estimation, giThe identification and estimation method comprises the following steps: the ith relation of equation (1):
Figure BDA0002566900000000094
and (3) taking K as tau +1, tau +2, K and tau + N from the field sampling data to obtain a relation equation of N groups of actuator adjustment increments to the plate-shaped standard mode characteristic coefficients:
ΔatiN＝ΦNgi T+eN
in the formula (I), the compound is shown in the specification,
Figure BDA0002566900000000095
Figure BDA0002566900000000096
initial value P obtained by one-time completion of least square method calculationNAnd
Figure BDA0002566900000000097
as follows:
Figure BDA0002566900000000098
and then obtaining an estimated value of the influence matrix G:
Figure BDA0002566900000000101
the step (3) specifically comprises the following steps:
(a) an influence matrix is identified in an online recursion manner by adopting a fading memory least square method with forgetting factors; with the increasing production data, new observed data Δ a is obtained when k ═ τ + N +1ti(τ+N+1)，Δuj(N +1), then
Figure BDA0002566900000000102
The new impact matrix is calculated using a recursive formula as follows:
Figure BDA0002566900000000103
wherein, mu is more than 0 and less than 1, which is a forgetting factor; considering that the performance change of the adjusting mechanism of the rolling mill is a slow time-varying process, the value of mu is 0.95, so that the estimated value of a new influence matrix is obtained:
Figure BDA0002566900000000104
(b) calculating a control matrix; when I isaWhen the number is equal to 4, the number is 4,
Figure BDA0002566900000000105
for the matrix, from equation (1) and taking into account the time shift, the strip-form actuator adjustment incremental expression can be obtained:
Figure BDA0002566900000000106
in the formula (I), the compound is shown in the specification,
Figure BDA0002566900000000107
is a control matrix;
note: if it is
Figure BDA0002566900000000108
Instead of being square, the shape control matrix C (k) may be formed by a generalized inverse of the influencing matrix
Figure BDA0002566900000000109
Instead of this; when I isaWhen the ratio is less than 4, the reaction solution is,
Figure BDA00025669000000001010
for a column full rank, the control matrix calculation formula is as follows:
Figure BDA0002566900000000111
when I isaWhen the pressure is higher than 4, the pressure is higher,
Figure BDA0002566900000000112
for a full row rank, the control matrix calculation formula is shown as follows:
Figure BDA0002566900000000113
(c) calculating a controller output; in order to obtain the control amount u (k +1) ═ u (k) + Δ u (k +1) at the next time, the control increment Δ u (k +1) is calculated first, and k in equation (7) is replaced with k +1, and further:
Δu(k+1)＝C(k)Δat(k+τ+1)＝C(k)(at(k+τ+1)-at(k+τ))
the design hopes that the actual shape of the next moment (namely k +1 moment) can reach the target shape, namely at(k+τ+1)＝arAnd then:
Δu(k+1)＝C(k)(ar-at(k+τ))
in the formula atThe computational expression of (k + τ) can be derived as:
Figure BDA0002566900000000114
the control increment expression (7) can then be written as:
Figure BDA0002566900000000115
the controller final output is expressed as:
u(k+1)＝u(k)+Δu(k+1)
(d) Updating the recursive computation matrix PN+1、
Figure BDA0002566900000000116
And a control quantity, i.e.
Figure BDA0002566900000000117
Figure BDA0002566900000000118
And
Figure BDA0002566900000000119
returning to the step (a).
Example (b):
taking a high-strength steel 1620mm cold strip rolling mill as an example, a simulation model of the rolling mill is established. The rolling mill is provided with four plate shape regulating means of roll inclination, work roll bending, intermediate roll bending and intermediate roll transverse movement. And (3) importing the actual strip steel data into a simulation platform for control verification, wherein the rolling basic parameters for testing are shown in table 1. The strip shape closed-loop self-adaptive control method of the cold strip rolling mill based on influence matrix recursive identification is used for controlling, the control principle is shown in figure 1, and the specific implementation steps are as follows:
TABLE 1 Rolling basic parameter Table for test
Figure BDA0002566900000000121
Figure BDA0002566900000000131
1. And (3) considering the slab shape detection time lag, establishing an influence matrix model expression from the control increment of four slab shape adjusting mechanisms to the change of the characteristic coefficient of the actual slab shape mode, wherein the distance between a slab shape instrument and the central line of the rolling mill is 2.88m, the rolling speed is 5.76m/s, the system lag is 0.5 second, the slab shape control period is selected to be 0.5 second, and tau is 1. The expression of the plate shape influence matrix model is shown as follows:
Δat(k)＝GΔu(k-τ)+e(k)
in the formula (I), the compound is shown in the specification,
Figure BDA0002566900000000132
2. selecting corresponding data of adjusting increment and plate shape mode characteristic coefficient variable quantity of N-100 groups of adjusting mechanisms from previous steel coil production data of the same steel type, and obtaining an initial value P of an influence matrix by adopting a one-time completion least square method N，
Figure BDA0002566900000000133
Comprises the following steps:
Figure BDA0002566900000000134
Figure BDA0002566900000000135
3. in each control period of the plate-shaped closed-loop control, firstly, on-line recursive identification is carried out by adopting an evanescent memory least square method with forgetting factors
Figure BDA0002566900000000136
Deriving an influence matrix
Figure BDA0002566900000000141
Then calculating an inverse matrix of the influence matrix to obtain a plate shape control matrix C (k), and finally automatically calculating to obtain a control quantity u (k +1) of the plate shape adjusting mechanism according to the deviation between the target plate shape mode and the actual plate shape mode and the control matrix, thereby realizing the purpose of realizingAnd automatically correcting the plate shape to make the actual plate shape consistent with the target plate shape. The adaptive control process flow is shown in fig. 2.
The experimental results of the strip shape control are shown in fig. 3 and 4. The graph shows the shape comparison curves before the shape adaptive control and after the 16-step control, wherein the orange solid line is the target shape, and the bar graph is the actual value of the shape. FIG. 3 shows that the actual plate shape of each measurement channel at the initial moment almost deviates from the target plate shape curve, and the root mean square error RMSE of each channel of the plate shape is 1.8349I; the plate shape curve after 16-step control simulation is shown in fig. 4, and it can be seen that the actual value of the plate shape is consistent with the target plate shape in most of the channels except for a few channels at the edge of the operation side strip steel and the target plate shape, and the root mean square error RMSE of each channel is 0.8262I, thereby verifying the effectiveness of the method provided by the invention in plate shape regulation.

Claims (4)

1. A closed-loop control method for the shape of a cold strip mill based on recursive identification of an influence matrix is characterized by comprising the following steps: (1) considering the time lag of the strip shape detection, establishing an influence matrix model expression of the change of the characteristic coefficient from the control increment of the strip shape adjusting mechanism to the actual strip shape mode, wherein the model is also suitable for systems with different numbers of adjusting mechanisms; (2) considering the material quality of the strip steel, selecting N groups of regulating mechanisms to regulate corresponding data of increment and plate shape mode characteristic coefficient variation from previous steel coil production data of the same steel type, and obtaining an initial value of an influence matrix by adopting a one-time completion least square method; (3) and finally, automatically calculating the control quantity of the plate shape adjusting mechanism according to the deviation between the target plate shape mode and the actual plate shape mode and the control matrix, and further automatically correcting the plate shape to enable the actual plate shape to be consistent with the target plate shape.
2. The closed-loop control method for the cold strip mill strip shape based on the influence matrix recursive identification is characterized in that: in the step (1), the expression of the plate shape influence matrix model is shown as the following formula:
Δat(k)＝GΔu(k-τ)+e(k)
In the formula (I), the compound is shown in the specification,
Figure RE-FDA0002653484270000011
called an influence matrix, has a slow time-varying characteristic and represents the increment delta u of the plate shape adjusting mechanismj(k-τ)(j＝1,2,L,Ia，IaFor the number of adjustment mechanisms) for each strip shape standard pattern characteristic coefficient Δ ati(k) (i ═ 1,2, L,4) in a model relationship, where gijFor the influence coefficient of the jth slat shape adjusting mechanism on the ith slat shape mode,
Figure RE-FDA0002653484270000021
the increment is adjusted for the plate-shaped adjusting structure,
Figure RE-FDA0002653484270000022
representing the variation of the actual characteristic coefficient of the plate shape at the front moment and the rear moment,
Figure RE-FDA0002653484270000023
is an error term; τ is the number of slab detection lag steps.
3. The closed-loop control method for the cold strip mill strip shape based on the influence matrix recursive identification is characterized in that: in the step (2), the influence matrix G can pass through each row vector Gi(i ═ 1,2, L,4) by discriminative estimation, giThe identification and estimation method comprises the following steps: the ith relation of equation (1):
Figure FDA0002566899990000024
and (3) taking K as tau +1, tau +2, K and tau + N from the field sampling data to obtain a relation equation of N groups of actuator adjustment increments to the plate-shaped standard mode characteristic coefficients:
ΔatiN＝ΦNgi T+eN
in the formula (I), the compound is shown in the specification,
Figure FDA0002566899990000025
Figure FDA0002566899990000026
initial value P obtained by one-time completion of least square method calculationNAnd
Figure FDA0002566899990000027
as follows:
Figure FDA0002566899990000028
and then obtaining an estimated value of the influence matrix G:
Figure FDA0002566899990000031
4. the closed-loop control method for the cold strip mill strip shape based on the influence matrix recursive identification is characterized in that: the step (3) specifically comprises the following steps:
(a) An influence matrix is identified in an online recursion manner by adopting a fading memory least square method with forgetting factors; with the increasing production data, new observed data Δ a is obtained when k ═ τ + N +1ti(τ+N+1)，Δuj(N +1), then
Figure FDA0002566899990000032
The new impact matrix is calculated using a recursive formula as follows:
Figure FDA0002566899990000033
wherein, mu is more than 0 and less than 1, which is a forgetting factor; considering that the performance change of the adjusting mechanism of the rolling mill is a slow time-varying process, the value of mu is 0.95, so that the estimated value of a new influence matrix is obtained:
Figure FDA0002566899990000034
(b) calculating a control matrix; when I isaWhen the number is equal to 4, the number is 4,
Figure FDA0002566899990000035
for the matrix, from equation (1) and taking into account the time shift, the strip-form actuator adjustment incremental expression can be obtained:
Figure FDA0002566899990000036
in the formula (I), the compound is shown in the specification,
Figure FDA0002566899990000041
is a control matrix;
note: if it is
Figure FDA0002566899990000042
Instead of being square, the shape control matrix C (k) may be formed by a generalized inverse of the influencing matrix
Figure FDA0002566899990000043
Instead of this; when I isaWhen the ratio is less than 4, the reaction solution is,
Figure FDA0002566899990000044
for a column full rank, the control matrix calculation formula is as follows:
Figure FDA0002566899990000045
when I isaWhen the pressure is higher than 4, the pressure is higher,
Figure FDA0002566899990000046
for a full row rank, the control matrix calculation formula is shown as follows:
Figure FDA0002566899990000047
(c) calculating a controller output; in order to obtain the control amount u (k +1) ═ u (k) + Δ u (k +1) at the next time, the control increment Δ u (k +1) is calculated first, and k in equation (7) is replaced with k +1, and further:
Δu(k+1)＝C(k)Δat(k+τ+1)＝C(k)(at(k+τ+1)-at(k+τ))
the design hopes that the actual shape of the next moment (namely k +1 moment) can reach the target shape, namely a t(k+τ+1)＝arAnd then:
Δu(k+1)＝C(k)(ar-at(k+τ))
in the formula atThe computational expression of (k + τ) can be derived as:
Figure FDA0002566899990000048
the control increment expression (7) can then be written as:
Figure FDA0002566899990000049
the controller final output is expressed as:
u(k+1)＝u(k)+Δu(k+1)
(d) updating the recursive computation matrix PN+1、
Figure FDA0002566899990000051
And a control quantity, i.e.
Figure FDA0002566899990000052
And
Figure FDA0002566899990000053
returning to the step (a).
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