CN105573355B - The liquid tank level control method of fractional order state space Predictive function control - Google Patents
The liquid tank level control method of fractional order state space Predictive function control Download PDFInfo
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Abstract
The invention discloses a kind of liquid tank level control methods of fractional order state space Predictive function control.This method of the present invention is defined using Gr ü nwald Letnikov fractional calculus fractional order state-space model being converted into discrete form first, it is then based on fractional order state-space model and obtains prediction output model, and fractional order integration is introduced into object function, the object function for being finally based on fractional order state-space model and choosing devises fractional order state space prediction function controller.The present invention can apply to the real process object of fractional model description well, improve the shortcoming of the PFC methods control new fractional-order system based on integer rank state-space model, the degree of freedom of adjusting control device parameter is increased simultaneously, good control performance is obtained, and the needs of destilling tower actual production process can be met well.
Description
Technical field
The invention belongs to technical field of automation, are related to a kind of distillation based on fractional order state space Predictive function control
Liquid tank level control method in the process.
Background technology
Distillation process is the important process process of many Chemical Manufactures, requires to exist due to energy consumption and to production
Diversity and complexity, destilling tower process model building and operation optimization and control seems of crucial importance.And with Product Precision and
The requirements such as safety operation increasingly improve, and the modeling process of controlled device increasingly complicates during destilling tower, this is multiple for destilling tower
Miscellaneous production process can not be described accurately with integer model, can more accurately description object feature with fractional model
With assessment properties of product.
In the actual production process, PID control is widely used Industrial Process Control Methods, but traditional PI D
Control method and integer model PREDICTIVE CONTROL (MPC) method are not very well, no to the control effect of new fractional-order system model
Control accuracy and product demand higher and higher in destilling tower actual production process can be met, this just needs research to have good control
The controller of performance processed controls the practical controlled device described with fractional model.Traditional state-space model PREDICTIVE CONTROL
Integer model is all based on, and for fractional order state-space model, if by integer scalariform state space Model Predictive Control
Method is expanded in fractional order state-space model forecast Control Algorithm, that will effectively make up integer model PREDICTIVE CONTROL side
Deficiency of the method in new fractional-order system is controlled, and better control effect can be obtained, while can also promote MPC in new fractional-order system
In utilization.Predictive function control (PFC) is a kind of control method relatively simple in model predictive control method, has and calculates
The advantages that amount is less, control effect is good, if it is possible to pfc controller is designed based on more accurate fractional model, it will be apparent
Improve the performance of control system.
Invention content
The purpose of the present invention is being directed to liquid tank level object in the distillation process of fractional order state-space model description, carry
For liquid tank level control method in a kind of distillation process based on fractional order state space Predictive function control, to maintain score
The balance of the liquid tank level of rank state-space model description, ensures good control performance.This method uses Gr ü first
Fractional order state-space model is converted into discrete form by the definition of nwald-Letnikov fractional calculus, is then based on score
Rank state-space model obtains prediction output model, and fractional order integration is introduced object function, is finally based on fractional order state
Spatial model and the object function chosen devise fractional order state space prediction function controller.
This method can apply to the real process object of fractional model description well, improve based on integer scalariform
The shortcoming of the PFC methods control new fractional-order system of state space model, while the degree of freedom of adjusting control device parameter is increased,
Good control performance is obtained, and the needs of destilling tower actual production process can be met well.
The technical scheme is that being acquired by data, model foundation, predicting the means such as mechanism, optimization, one is established
Liquid tank level control method in distillation process of the kind based on fractional order state space Predictive function control, this method can be carried effectively
The control performance of high system.
The step of the method for the present invention, includes：
Step 1, the fractional order state-space model for establishing controlled device in real process, specifically：
The real-time inputoutput data of 1.1 acquisition real process objects establishes the fractional order state space of the controlled device
Model, form are as follows：
Y (t)=Cx (t)
Wherein, x, y, u are respectively state vector, output and the input of controlled device, and α is vectorial for fractional order order, and α=
[α1,α2,…,αn]T, A, B, C is respectively sytem matrix,For order αlFractional order differential symbol.
1.2 for function f (t), has been defined by Gr ü nwald-Letnikov fractional calculus,
Wherein, h is sampling step length, and [t/h] is the integer part of t/h.
1.3 can be by fractional order of the model conversion in step 1.1 for following discrete form using the definition in step 1.2
State-space model：
Y (k+1)=Cx (k+1)
Step 2, the fractional order prediction function controller based on fractional order state-space model design controlled device, specifically such as
Under：
2.1, according to the state-space model in step 1.3, obtain the model prediction output valve at following k+i moment, form is such as
Under：
Wherein, P is prediction time domain, and y (k+i) is the model prediction output valve of k+i moment controlled devices, i=1,2 ..., P.
2.2 in algorithm of predictive functional control, selects a basic function i.e. jump function, by the model prediction in step 2.1
Output is converted to the prediction output model of matrix form, and form is as follows：
Y=Gx (k)+Su (k)-Ψ
Wherein,
The prediction output model of 2.3 amendment current time controlled devices, the prediction model after being corrected, form are as follows：
E=[e (k+1), e (k+2) ..., e (k+P)]T
E (k+i)=yp(k)-y(k)
Wherein, yp(k) be k moment controlled devices real output value, y (k) is the model prediction output valve at k moment, e (k
+ i) it is the real output value of k+i moment controlled devices and the difference of model prediction output.
2.4 choose the reference locus y of predictive functional control algorithmr(k+i) and object function JF, form is as follows：
yr(k+i)=λiyp(k)+(1-λi)c(k)
Wherein, yr(k+i) it is the reference locus at k+i moment, λ is the softening coefficient of reference locus, and c (k) is setting for k moment
Definite value,Representative function f (t) is in [ht1,ht2] on γ times integration.
According to the definition of Gr ü nwald-Letnikov fractional calculus, to above-mentioned object function sampling time h carry out from
Dispersion, and the reference locus value after discretization and the error amount of prediction output are weighted, it obtains after being weighted to error term
Object function, form are as follows：
Wherein,
Yr=[yr(k+1),yr(k+2),…,yr(k+P)]T
Q=hγdiag(q1mP-1,q2mP-2,…,qP-1m1,qPm0)
2.5 solve controlled quentity controlled variable according to the object function in step 2.4, and form is as follows：
U (k)=(STQS)-1STQ(Yr-Gx(k)+Ψ-E)
2.6 at the k+ η moment, recycles the control for solving fractional order prediction function controller successively according to the step in 2.1 to 2.5
Amount u (k+ η) (η=1,2,3 ...) processed, and acted on controlled device.
The present invention proposes liquid tank level in a kind of distillation process based on fractional order state space Predictive function control
Control method, this method obtains prediction output model based on fractional order state-space model, and fractional order integration is introduced target
Function improves the deficiency of the PFC methods control new fractional-order system based on integer rank state-space model, increases adjusting control
The degree of freedom of device parameter obtains good control performance, and can meet the needs of actual production process well, promotes pre-
Survey utilization of the function control method in new fractional-order system.
Specific embodiment
By taking liquid tank level control in destilling tower actual production process as an example：
Fractional model is obtained by the real-time level data of fluid reservoir, the regulating measure of liquid tank level control system is control
The valve opening of the cooling water flow of distillation process processed.
Step 1, the fractional order state-space model for establishing liquid tank level in destilling tower actual production process, specifically：
The real-time inputoutput data of 1.1 acquisition distillation process liquid tank levels establishes the score scalariform of liquid tank level
State space model：
Y (t)=Cx (t)
Wherein, x, y, u are respectively the state vector of liquid tank level object, liquid level and the valve of cooling water flow are controlled to open
Degree, α is vectorial for fractional order order, α=[α1,α2,…,αn]T, A, B, C is respectively sytem matrix,For
Order αlFractional order differential symbol.
1.2 for function f (t), has been defined by Gr ü nwald-Letnikov fractional calculus,
Wherein, h is sampling step length, and [t/h] is the integer part of t/h.
1.3 can be by fractional order of the model conversion in step 1.1 for following discrete form using the definition in step 1.2
State-space model：
Y (k+1)=Cx (k+1)
Step 2, the fractional order anticipation function that liquid tank level in distillation process is designed based on fractional order state-space model
Controller, it is specific as follows：
2.1, according to the state-space model in step 1.3, obtain the model prediction output at following k+i moment, form is such as
Under：
Wherein, P is prediction time domain, and y (k+i) is the model prediction output valve of k+i moment controlled devices, i=1,2 ..., P.
2.2 in algorithm of predictive functional control, selects a basic function i.e. jump function, by the model prediction in step 2.1
Output is converted to the prediction output model of matrix form, and form is as follows：
Y=Gx (k)+Su (k)-Ψ
Wherein,
2.3 correct the prediction output model of liquid tank level in current time distillation process, the prediction mould after being corrected
Type, form are as follows：
E=[e (k+1), e (k+2) ..., e (k+P)]T
E (k+i)=yp(k)-y(k)
Wherein, yp(k) it is the liquid level of distilling fluid reservoir in production process at the k moment, y (k) is the model prediction output at k moment
Value, e (k+i) are to distill the liquid level of fluid reservoir and the difference of model prediction output in production process the k+i moment.
2.4 choose the reference locus y of predictive functional control algorithmr(k+i) and object function JF, form is as follows：
yr(k+i)=λiyp(k)+(1-λi)c(k)
Wherein, yr(k+i) it is the reference locus at k+i moment, λ is the softening coefficient of reference locus, and c (k) is setting for k moment
Definite value,Representative function f (t) is in [ht1,ht2] on γ times integration.
According to the definition of Gr ü nwald-Letnikov fractional calculus, to above-mentioned object function sampling time h carry out from
Dispersion, and the reference locus value after discretization and the error amount of prediction output are weighted, it obtains after being weighted to error term
Object function, form are as follows：
Wherein,
Yr=[yr(k+1),yr(k+2),…,yr(k+P)]T
Q=hγdiag(q1mP-1,q2mP-2,…,qP-1m1,qPm0)
2.5 solve controlled quentity controlled variable according to the object function in step 2.4, and form is as follows：
U (k)=(STQS)-1STQ(Yr-Gx(k)+Ψ-E)
2.6 at the k+ η moment, recycles the control for solving fractional order prediction function controller successively according to the step in 2.1 to 2.5
Amount u (k+ η) (η=1,2,3 ...) processed, and acted on the valve of control fluid reservoir cooling water flow.
Claims (1)
1. the liquid tank level control method of fractional order state space Predictive function control, it is characterised in that the specific step of this method
Suddenly it is：
Step 1, the fractional order state-space model for establishing controlled device in real process, specifically：
The real-time inputoutput data of 1.1 acquisition real process objects establishes the fractional order state space mould of the controlled device
Type, form are as follows：
Y (t)=Cx (t)
Wherein, x, y, u are respectively state vector, output and the input of controlled device, and α is vectorial for fractional order order, α=[α1,
α2,…,αn]T, A, B, C is respectively sytem matrix,For order αlFractional order differential symbol, l=1,2 ..., n；
1.2 for function f (t), has been defined by Gr ü nwald-Letnikov fractional calculus,
Wherein, h is sampling step length, and [t/h] is the integer part of t/h；
1.3 can be by score scalariform of the model conversion in step 1.1 for following discrete form using the definition in step 1.2
State space model：
Y (k+1)=Cx (k+1)
Wherein,
Step 2, the fractional order prediction function controller based on fractional order state-space model design controlled device, it is specific as follows：
2.1, according to the state-space model in step 1.3, obtain the model prediction output valve at following k+i moment, form is as follows：
Wherein, P is prediction time domain, and y (k+i) is the model prediction output valve of k+i moment controlled devices, i=1,2 ..., P；
2.2 in algorithm of predictive functional control, selects a basic function i.e. jump function, and the model prediction in step 2.1 is exported
The prediction output model of matrix form is converted to, form is as follows：
Y=Gx (k)+Su (k)-Ψ
Wherein,
The prediction output model of 2.3 amendment current time controlled devices, the prediction model after being corrected, form are as follows：
E=[e (k+1), e (k+2) ..., e (k+P)]T
E (k+i)=yp(k)-y(k)
Wherein, yp(k) be k moment controlled devices real output value, y (k) is the model prediction output valve at k moment, and e (k+i) is
The real output value of k+i moment controlled devices and the difference of model prediction output；
2.4 choose the reference locus y of predictive functional control algorithmr(k+i) and object function JF, form is as follows：
yr(k+i)=λiyp(k)+(1-λi)c(k)
Wherein, yr(k+i) it is the reference locus at k+i moment, λ is the softening coefficient of reference locus, and c (k) is the setting value at k moment,Representative function f (t) is in [ht1,ht2] on γ times integration；
It is discrete in sampling time h progress to above-mentioned object function according to the definition of Gr ü nwald-Letnikov fractional calculus
Change, and the reference locus value after discretization and the error amount of prediction output are weighted, obtain the mesh after being weighted to error term
Scalar functions, form are as follows：
Wherein,
Yr=[yr(k+1),yr(k+2),…,yr(k+P)]T
Q=hγdiag(q1mP-1,q2mP-2,…,qP-1m1,qPm0)
When,To q<0,qiFor reference locus with
Predict the error term weighting coefficient of output；
2.5 solve controlled quentity controlled variable according to the object function in step 2.4, and form is as follows：
U (k)=(STQS)-1STQ(Yr-Gx(k)+Ψ-E)
2.6 at the k+ η moment, recycles the control for solving fractional order prediction function controller successively according to the step in 2.1 to 2.5
U (k+ η), η=1,2,3 ... are measured, and is acted on controlled device.
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| CN105182755A (en) * | 2015-10-08 | 2015-12-23 | 杭州电子科技大学 | Fractional order PFC method of industrial heating furnace system |
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| CN104794101A (en) * | 2015-04-08 | 2015-07-22 | 河海大学 | Fractional order nonlinear system state estimating method |
| CN105182755A (en) * | 2015-10-08 | 2015-12-23 | 杭州电子科技大学 | Fractional order PFC method of industrial heating furnace system |
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