CN109865749A - A kind of hot continuous rolling thickness-loop integrated system is against linear quadric form control method - Google Patents
A kind of hot continuous rolling thickness-loop integrated system is against linear quadric form control method Download PDFInfo
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Abstract
The present invention relates to a kind of hot continuous rolling thickness-loop integrated systems against linear quadric form control method, according to the kinetic model of looper control system and thickness control system, using State-space Method, hot continuous rolling thickness-loop integrated system continuous state space model is established；Continuous state space model based on foundation, selects the sampling period appropriate, using zero-order holder method, carries out discretization to continuous model obtained, obtains thickness-loop integrated system separate manufacturing firms model；On this basis, the inverse liner quadratic regulator device (ILQ) of design synthesis system.It solves in existing hot continuous rolling control system, it, can not Multivariable Coupling problem between processing system by thickness control system (AGC) and looper control system as two independent control systems.The coordination optimization control to thickness, tension and angle in hot continuous rolling control system may be implemented in the technical solution provided according to embodiments of the present invention.
Description
Technical field
The present invention relates to the coordination optimizations of plate belt hot rolling technical field more particularly to Hot Strip Rolling multivariable control system
Control.
Background technique
Hot continuous rolling due to strip connection and become an entirety, between machine frame inside and rack due to tension and there is
It influences each other, in the case where system performance requirements are not high, can roughly think that the tension between rack is small and constant.Cause
And the control between the second flow of the AGC system strip plate thickness controlled and tower-loop control, tension and between each rack can
It is independent to be approximately considered.But the tension in conventional hot continuous rolling machine control cannot be guaranteed it is constant, tension be it is extremely active because
Element, influencing each other between AGC system and loop system can not ignore, and become the key for further increasing product quality.
At present in actual production, thickness, angle and tension control system are respectively independently controlled, and are unable between each system of Coordination Treatment
Coupling, therefore study thickness-loop system comprehensively control it is imperative.
The present invention is based on the hot continuous rolling multi-variable system separate manufacturing firms model of foundation, with improve thickness control accuracy with
Strip tension stability is performance indicator, considers the uncertain factors such as scene interference, modeling error and Parameter Perturbation, proposes one
Kind is suitable for the inverse linear quadric form control method of hot continuous rolling thickness-loop integrated system.The more traditional PID control of the control method
Method processed has stronger robustness, is more suitable for processing environment hot continuous rolling production scene complicated and changeable, and the present invention is mentioned
Control method out is based on discrete state-space model, and control algolithm can be converted into STL language, imports and controls into PLC
Device processed, to realize the coordination optimization control of thickness, angle and tension in hot continuous rolling system.
Summary of the invention
The purpose of the present invention is to provide a kind of hot continuous rolling thickness-loop integrated systems against linear quadric form control method,
To solve in the control of existing Hot Strip Rolling, using thickness control system and looper control system as two independent subsystems into
Row processing, the problem of can not being coordinated and optimized to thickness, angle and tension.
In order to solve the above technical problems, it is inverse linear that the present invention provides a kind of hot continuous rolling thickness-loop integrated systems
Quadric form control method establishes hot continuous rolling thickness according to the kinetic model of hot continuous rolling looper control system and thickness control system
Degree-loop integrated system continuous state space model, selects the sampling period appropriate, using zero-order holder method, to continuous
State-space model carries out discretization.Thickness based on discretization-loop integrated system state-space model utilizes inverse linear two
Secondary type principle, design thickness-loop integrated system controller.
Detailed process includes:
Step 1: according to the kinetic model of hot continuous rolling looper control system and thickness control system, utilizing state space point
Analysis method establishes thickness-loop integrated system continuous state space model of the i-th rack Yu i+1 rack:
Wherein, state variable xi=[Δ θi ΔωL,i Δσout,i Δωi ΔMi ΔSi+1]T；Control variable is ui
=[Δ ωr,i ΔMr,i ΔSr,i+1]T；Disturbance variable is di=[Δ hin,i ΔTin,i]T；Output variable is yi=[Δ θi Δ
σout,i Δhout,i+1]T；Ai, Bi, Ci, DiFor state space equation coefficient matrix.
In formula, Δ σout,iFor the i-th rack outlet tension increment；ΔθiFor the i-th loop angle step；ΔωL,iIt is living for i-th
Cover roller angular speed increment；ΔωiFor the i-th breast roller angular speed increment；Δωi+1For i+1 breast roller angular speed increment；
ΔMiFor the i-th loop motor output torque increment；ΔSi+1For i+1 rack roll gap increment；Δωr,iFor the i-th rack main transmission
Motor control amount；Δωr,i+1For i+1 rack main driving motor control amount；ΔMr,iFor the i-th loop driving motor control amount；Δ
hin,iFor the i-th rack inlet thickness variable quantity；Δσin,iFor the i-th rack entrance tension variation amount；ΔSr,i+1For i+1 breast roll
Stitch regulated quantity；ΔTin,iFor the i-th rack entrance tension variation amount；Δhout,i+1For i+1 rack outlet amounts of thickness variation；
Step 2: the sampling period T of setting hot continuous rolling control system, it is using matlab software that hot continuous rolling thickness-loop is comprehensive
Conjunction control system continuous state space model conversation is discrete space state model:
Wherein,Value can be used MATALB state-space model handling implement case calculating:
Step 3: linear transformation being carried out to the hot continuous rolling separate manufacturing firms model acquired, ILQ controller is made it have and sets
State-space model needed for meter:
AA=Γ-1AclΓ (3)
BA=Γ-1Bcl (4)
In formula
Step 4: to systematic observation matrix (Acl, Bcl) carry out POLE PLACEMENT USING, the characteristic value { s of computing systemiDominant pole
Corresponding feature vector { fi}:
Wherein { siAnd { fiValue can be used MATALB eigen vector extracting tool case calculating:
[fi,si]=eig (Acl, Bcl)
Step 5: { the f that step 4 is calculatediLinear coordinate transformation (formula 5) is carried out, obtain systematic observation matrix
(AA, BA) feature vector { fiA, and extract feature vector { fiAIn [ti] and [gi] matrix, calculate [F1] matrix (formula
6):
fiA=Γ-1fi (5)
F1=-GT1 -1 (6)
In formula, feature vector fiA=[ti gi]T；T1=[t1,t2,…tn]；G=[g1,g2,…gn]
Step 6: selection nonsingular matrix V=I selects weighted factorIt calculates
Matrix
Step 7: the matrix being calculated according to step 6Calculating matrix { σi, and solve weighting matrix Σ:
Σ=σ Γ (9)
In formula, Γ=diag (γ1,γ2,…,γm),γi> 0；
Step 8: to system (AA,BA) using ILQ theory progress expected pole assignment, the matrix [F solved based on step 51]
The weighting matrix Σ solved with step 7 calculates state feedback matrix KA, the control of ILQ controller is then obtained by linear transformation
Rate K processedFAnd KI:
KA=V-1ΣV[F1, I] and=Σ [F1,I] (10)
[KF,KI]=[F1,I]Γ-1 (11)
Step 9: to gained controller Matlab codes are transferred to the STL language codes of PLC, import looper controller with
Gage controller；Controller uses event driven manner, and when sampled data reaches controller, controller is calculated at once,
And actuator is controlled signal is transmitted to, and actuator reads control signal according to the fixed sampling period, control input is generated, thus
Realize that the coordination optimization of looper control system and thickness control system controls.
Compared to the prior art, technical solution of the present invention have it is following the utility model has the advantages that
It is put forward for the first time using the inverse line style quadratic form technology based on separate manufacturing firms model, studies hot continuous rolling control system
Coordination optimization control problem between middle loop system and thickness system, solves in current actual production, thickness, angle and tension
Control system is respectively independently controlled, the coupling being unable between each system of Coordination Treatment, to reach while improve strip thickness
Spend the purpose of precision and tension stability.
Different to control (LQ) with traditional quadratic form, inverse liner quadratic regulator proposed by the invention solves most first
Excellent and stable feedback rate control KFAnd KI, the solution of corresponding weighting matrices Q, R and Riccati equation is then determined, to avoid
Solution to weighting matrix, simplifies control algolithm.
Due to introducing state feedback matrix K in inverse property type quadratic form algorithm proposed by the inventionA, there is controller
Stronger robustness is applicable to processing environment hot continuous rolling production scene complicated and changeable.
Since the present invention is to carry out hot continuous rolling thickness-loop integrated system control method based on separate manufacturing firms model
Design, therefore the inverse line style quadric form control method invented can directly be transferred to the STL language codes of SIEMENS PLC, lead
Enter in looper controller and gage controller.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, below will be to needed in the embodiment attached
Figure is briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, for this field
For those of ordinary skill, without any creative labor, example implementation can also be carried out according to these attached drawings.
Fig. 1 is a kind of hot continuous rolling thickness-loop based on separate manufacturing firms model provided by embodiment of the present invention
Flow diagram of the integrated system against Linear-Quadratic Problem；
Fig. 2 is the structure chart of research object thickness loop integrated system in the embodiment of the present invention；
Fig. 3 is inverse line style quadratic form algorithm design flow diagram in the embodiment of the present invention:
Fig. 4 is thickness-loop integrated system ILQ control algolithm structure chart designed in the embodiment of the present invention；
Fig. 5 be in present example system supplied materials thickness disturbance under thickness, angle and tension response curve graph；
Fig. 6 be in present example system roll eccentricities disturbance under thickness, angle and tension response curve graph.
Specific embodiment
With reference to Fig. 1-Fig. 4, a kind of hot continuous rolling thickness-loop integrated system is against linear quadric form control method, even according to heat
The kinetic model for rolling looper control system and thickness control system establishes hot continuous rolling thickness-loop integrated system continuous state
Spatial model selects the sampling period appropriate, using zero-order holder method, carries out discretization to continuous state space model.
Thickness based on discretization-loop integrated system state-space model, utilizes inverse Linear-Quadratic Problem principle, design thickness-loop
The controller of integrated system.
Detailed process includes:
Step 1: according to the kinetic model of hot continuous rolling looper control system and thickness control system, utilizing state space point
Analysis method establishes thickness-loop integrated system continuous state space model of the i-th rack Yu i+1 rack:
Wherein, state variable xi=[Δ θi ΔωL,i Δσout,i Δωi ΔMi ΔSi+1]T；Control variable is ui
=[Δ ωr,i ΔMr,i ΔSr,i+1]T；Disturbance variable is di=[Δ hin,i ΔTin,i]T；Output variable is yi=[Δ θi Δ
σout,i Δhout,i+1]T；
Wherein, Δ σout,iFor the i-th rack outlet tension increment；ΔθiFor the i-th loop angle step；ΔωL,iIt is living for i-th
Cover roller angular speed increment；ΔωiFor the i-th breast roller angular speed increment；Δωi+1For i+1 breast roller angular speed increment；
ΔMiFor the i-th loop motor output torque increment；ΔSi+1For i+1 rack roll gap increment；Δωr,iFor the i-th rack main transmission
Motor control amount；Δωr,i+1For i+1 rack main driving motor control amount；ΔMr,iFor the i-th loop driving motor control amount；Δ
hin,iFor the i-th rack inlet thickness variable quantity；Δσin,iFor the i-th rack entrance tension variation amount；
Step 2: the sampling period T of setting hot continuous rolling control system, it is using matlab software that hot continuous rolling thickness-loop is comprehensive
Conjunction control system continuous state space model conversation is discrete space state model:
Wherein,Value can be used MATALB state-space model handling implement case calculating:
Step 3: linear transformation being carried out to the hot continuous rolling separate manufacturing firms model acquired, ILQ controller is made it have and sets
State-space model needed for meter:
AA=Γ-1AclΓ (3)
BA=Γ-1Bcl (4)
In formula
Step 4: to systematic observation matrix (Acl, Bcl) carry out POLE PLACEMENT USING, the characteristic value { s of computing systemiDominant pole
Corresponding feature vector { fi}:
Wherein { siAnd { fiValue can be used MATALB eigen vector extracting tool case calculating:
[fi,si]=eig (Acl, Bcl)
Step 5: { the f that step 4 is calculatediLinear coordinate transformation (formula 5) is carried out, obtain systematic observation matrix
(AA, BA) feature vector { fiA, and extract feature vector { fiAIn [ti] and [gi] matrix, calculate [F1] matrix (formula
6):
fiA=Γ-1fi (5)
F1=-GT1 -1 (6)
In formula, feature vector fiA=[ti gi]T；T1=[t1,t2,…tn]；G=[g1,g2,…gn]
Step 6: selection nonsingular matrix V=I selects weighted factorIt calculates
Matrix
Step 7: the matrix being calculated according to step 6Calculating matrix { σi, and solve weighting matrix Σ:
Σ=σ Γ (9)
In formula, Γ=diag (γ1,γ2,…,γm),γi> 0；
Step 8: to system (AA,BA) using ILQ theory progress expected pole assignment, the matrix [F solved based on step 51]
The weighting matrix Σ solved with step 7 calculates state feedback matrix KA, the control of ILQ controller is then obtained by linear transformation
Rate K processedFAnd KI:
KA=V-1ΣV[F1, I] and=Σ [F1,I] (10)
[KF,KI]=[F1,I]Γ-1 (11)
Step 9: to gained controller Matlab codes are transferred to the STL language codes of PLC, import looper controller with
Gage controller；Controller uses event driven manner, and when sampled data reaches controller, controller is calculated at once,
And actuator is controlled signal is transmitted to, and actuator reads control signal according to the fixed sampling period, control input is generated, thus
Realize that the coordination optimization of looper control system and thickness control system controls.
Dynamic is carried out with thickness-loop integrated system of the 5th rack of certain factory 1700mm hot continuous rolling production line and the 6th rack to grind
Study carefully, it is continuous can to obtain thickness-loop integrated system for the related data of each parameter reference table 1 and the 5th rack and the 6th rack in table 2
State-space model are as follows:
In formula:
1 production line rolling equipment parameter of table
2 rolling procedure of table and device parameter
Select sampling period Ts=0.025s, using zero-order holder method, by thickness-loop integrated system continuous state
Spatial model is converted into separate manufacturing firms model:
In formula:
Establish thickness-loop integrated system augmented state space matrix are as follows:
Wherein, AA=Γ-1AclΓ, BA=Γ-1BclΓ
According to thickness-each output valve of loop integrated system expected response, the desired dominant pole of system is selected are as follows:
sa=[- 2.69+2.41i-2.69-2.41i-20-25-30-35]
Non-dominant pole are as follows:
sb=[- 40-45-50]
Structural matrix S is as follows:
S=[- 2.69+2.41i-2.69-2.41i-20-25-30-35-40-45-50]
To (Acl Bcl) POLE PLACEMENT USING is carried out, calculate dominant pole saCorresponding feature vector fi, it is as follows:
To feature vector fiCarry out linear coordinate transformation fiA=Γ-1fi, it can obtain:
According to formula fiA=[ti gi]T, extract and obtain [ti] and [gi]:
T1=[t1,t2,…tn], G=[g1,g2,…gn]
According to formulaIt can obtain:
V=I is taken, when not introducing weighting matrix, obtains the lower limit value of Σ diagonal element are as follows:
σi> 19862；
Weighting matrix Π is selected, as follows:
Calculating matrixObtain the lower limit value of Σ diagonal element are as follows:
σi> 40.9608
According to formula [KF KI]=[F1 I]Γ-1, calculate KF0And KI0, it is as follows:
The inverse line style quadric form control method that will be invented, the STL of SIEMENS PLC is directly transferred to using MATLAB software
Language codes import in looper controller and gage controller, carry out actual production verifying.
When supplied materials thickness fluctuation and roll eccentricities disturb, controlled using traditional PI independent control and ILQ comprehensive coordination,
The response curve of each output quantity as shown in figs. 5 and 6,.When supplied materials thickness fluctuation, the thickness fluctuation amount of ILQ control is PI control
The 33.2% of system, when roll eccentricities, the thickness fluctuation amount of ILQ control is the 23.9% of PI control, since ILQ control can be to thickness
Degree, tension and angle carry out coordination optimization control, so that the anti-interference ability of system is improved.
In conclusion the present invention has comprehensively considered the coupling of thickness system and loop system, simultaneous thickness system and loop
The state equation of system establishes thickness-loop integrated system state-space model.And on its basis, a kind of ILQ is devised
Theoretical algorithm, and this algorithm is applied in the design of thickness-loop integrated system controller.By selecting the integrated system phase
The adjusting of the leading closed-loop pole and weighting matrix hoped realizes the coordination optimization control to thickness, tension and angle
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Within mind and principle, any modification, equivalent substitution, improvement and etc. done be should be included within the scope of the present invention.This
The content being not described in detail in description of the invention belongs to the well-known technique of those skilled in the art.
Claims (1)
1. a kind of hot continuous rolling thickness-loop integrated system is against linear quadric form control method, which is characterized in that this method include with
Lower step:
Step 1: according to the kinetic model of hot continuous rolling looper control system and thickness control system, utilizing state space analysis
Method establishes thickness-loop integrated system continuous state space model of the i-th rack Yu i+1 rack:
Wherein, state variable xi=[Δ θi ΔωL,i Δσout,i Δωi ΔMi ΔSi+1]T；Control variable is ui=[Δ
ωr,i ΔMr,i ΔSr,i+1]T；Disturbance variable is di=[Δ hin,i ΔTin,i]T；Output variable is yi=[Δ θi Δσout,i
Δhout,i+1]T；Ai, Bi, Ci, DiFor state space equation coefficient matrix.
In formula, Δ σout,iFor the i-th rack outlet tension increment；ΔθiFor the i-th loop angle step；ΔωL,iFor the i-th loop back roll
Angular speed increment；ΔωiFor the i-th breast roller angular speed increment；Δωi+1For i+1 breast roller angular speed increment；ΔMiFor
I-th loop motor output torque increment；ΔSi+1For i+1 rack roll gap increment；Δωr,iFor the i-th rack main driving motor control
Amount processed；Δωr,i+1For i+1 rack main driving motor control amount；ΔMr,iFor the i-th loop driving motor control amount；Δhin,iFor
I-th rack inlet thickness variable quantity；Δσin,iFor the i-th rack entrance tension variation amount；ΔSr,i+1For i+1 rack roll gap adjustment
Amount；ΔTin,iFor the i-th rack entrance tension variation amount；Δhout,i+1For i+1 rack outlet amounts of thickness variation；
Step 2: the sampling period T of setting hot continuous rolling control system is controlled hot continuous rolling thickness-loop synthesis using matlab software
System continuous state space model conversation processed is discrete space state model:
Wherein,For separate manufacturing firms model coefficient,Value that MATALB state can be used is empty
Between model treatment tool box sys calculate:
Sys=ss (Ai,Bi,Ci,Di),
Step 3: linear transformation being carried out to the hot continuous rolling separate manufacturing firms model acquired, makes it have ILQ controller design institute
The state-space model needed:
AA=Γ-1AclΓ (3)
BA=Γ-1Bcl (4)
In formula
In formula, I is unit matrix
Step 4: to systematic observation matrix (Acl, Bcl) carry out POLE PLACEMENT USING, the characteristic value { s of computing systemiDominant pole institute it is right
Feature vector { the f answeredi}:
Wherein { siAnd { fiValue can be used MATALB eigen vector extracting tool case calculating:
[fi,si]=eig (Acl, Bcl)
Step 5: { the f that step 4 is calculatediLinear coordinate transformation (formula 5) is carried out, obtain systematic observation matrix (AA, BA)
Feature vector { fiA, and extract feature vector { fiAIn [ti] and [gi] matrix, calculate [F1] matrix (formula 6):
fiA=Γ-1fi (5)
F1=-GT1 -1 (6)
In formula, feature vector fiA=[ti gi]T；T1=[t1,t2,…tn]；G=[g1,g2,…gn]
Step 6: selection nonsingular matrix V=I, calculating matrix
In formula, Π is the weight variable factor；
Step 7: the matrix being calculated according to step 6Calculating matrix { σi, and solve weighting matrix Σ:
Σ=σ Γ (9)
In formula, Γ is the regulated variable factor；
Step 8: to system (AA,BA) using ILQ theory progress expected pole assignment, the matrix [F solved based on step 51] and step
The rapid 7 weighting matrix Σ solved, calculate state feedback matrix KA, the control rate K of ILQ controller is then obtained by linear transformationF
And KI:
KA=V-1ΣV[F1, I] and=Σ [F1,I] (10)
[KF,KI]=[F1,I]Γ-1 (11)
Step 9: to gained controller Matlab codes are transferred to the STL language codes of PLC, importing looper controller and thickness
Controller；Controller uses event driven manner, and when sampled data reaches controller, controller is calculated at once, and will
Control signal is transmitted to actuator, and actuator reads control signal according to the fixed sampling period, control input is generated, to realize
The control of the coordination optimization of looper control system and thickness control system.
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| CN111185486A (en) * | 2020-01-17 | 2020-05-22 | 北京科技大学 | Online evaluation method based on loop stability of strip steel finishing mill group |
| CN111378915A (en) * | 2020-03-09 | 2020-07-07 | 包头钢铁（集团）有限责任公司 | Method for improving tension control precision of vertical loop of galvanizing unit |
| CN114918264A (en) * | 2022-07-22 | 2022-08-19 | 太原科技大学 | Strip steel tension-width control method with gain compensator |
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| CN111185486A (en) * | 2020-01-17 | 2020-05-22 | 北京科技大学 | Online evaluation method based on loop stability of strip steel finishing mill group |
| CN111378915A (en) * | 2020-03-09 | 2020-07-07 | 包头钢铁（集团）有限责任公司 | Method for improving tension control precision of vertical loop of galvanizing unit |
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