CN107092188A - A kind of GPC algorithm of CSTR system - Google Patents
A kind of GPC algorithm of CSTR system Download PDFInfo
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Abstract
The present invention relates to a kind of GPC algorithm of CSTR system, nonlinear model is set up to CSTR system, and be converted into the output forecast model based on U models；Reference locus is set, generalized predictive control is carried out to the output forecast model, the pseudo- input of system is obtained；Then calculating is iterated using Secant Method and obtains actually entering for system；The present invention is combined with U models using Secant Method so that solution about actually enter nonlinear equation when, it is to avoid the derivation problem run into during using Newton iterative, and reduce the calculating time, while having faster convergence rate；Simplify Control of Nonlinear Systems design problem.
Description
Technical field
The present invention relates to a kind of GPC algorithm of CSTR system, belong to nonlinear system
Control technology field.
Background technology
In petrochemical industry, CSTR (CSTR) plays an important role in chemical reaction, it
With the advantage such as low cost, heat-exchange capacity be strong.Meanwhile, it has higher researching value in model and control aspect.
During CSTR, the conversion ratio too high or too low for temperature that can all influence the depth of reaction and react, so as to influence the quality of product.
In a word, the control of reactor temperature and reactant concentration is always the study hotspot of chemical process control field.For non-linear
For system, typically using linearization technique, but linearization technique has some limitations, and most linear control
Method processed is not directly applicable Nonlinear System Design, so one general mathematical model of construction, for research Nonlinear Dynamic
The modelling control method of state system is most important, and this general mathematical modeling is exactly U models.By nonlinear dynamic system
The representation of multinomial model U models, so as to conveniently with linear control system design method to nonlinear Control
System is controlled.
Generalized predictive control (abbreviation GPC) is keeping the on-line identification of minimal variance self-tuning control, output prediction, minimum
On the basis of output variance control, the rolling optimization plan in dynamic matrix control (DMC) and model cootrol algorithm (MAC) has been drawn
Slightly, while having the performance of Self Adaptive Control and PREDICTIVE CONTROL.GPC is based on parameter model, introduces unequal prediction length
With control length, system design is flexible, with features such as forecast model, rolling optimization and online feedback corrections, with good
Good control performance and robustness.
Newton iteration method needs to calculate function and the numerical value of first derivative in the calculating of every step, and this is equivalent to two letters of calculating
Numerical value, the used time is relatively more.And Secant Method is that on the basis of Newton method, the derivative in Newton method is replaced using difference coefficient, so
The calculating time can be reduced, the difficulty calculated is reduced.Compared with Newton method, the convergence rate of Secant Method is also than faster, meter
Evaluation time comparison of comparing is short, and with super-linear convergence.
The content of the invention
The technical problems to be solved by the invention are to provide a kind of Generalized Prediction control of CSTR system
Algorithm processed, by linear system control design case approach application into Control of Nonlinear Systems design, can effectively simplify nonlinear system
System control design case.
In order to solve the above-mentioned technical problem the present invention uses following technical scheme：The present invention devises a kind of continuous stirred tank
The GPC algorithm of formula reactor assembly, comprises the following steps：
Step 1. builds the nonlinear model structure corresponding to CSTR system, and by nonlinear model
The U model expressions that structure is converted to, obtain the U model expressions corresponding to CSTR system, Ran Houjin
Enter step 2；
Step 2. builds according to the regulatory factor of CSTR system feedback and meets the continuous of preset requirement
Stirred-tank reactor system exporting change track；Subsequently into step 3；
Step 3. is according to the intermediate parameters of generalized predictive controller in CSTR system, with reference to diophantus
Equation, for the U model expressions corresponding to CSTR system, obtains CSTR system
The corresponding output forecast model based on U models, subsequently into step 4；
Step 4. solves the initial solution and recurrence formula for obtaining Diophantine equation, subsequently into step 5；
Step 5. is according to the intermediate parameters of generalized predictive controller in CSTR system, with reference to diophantus
The initial solution and recurrence formula of equation, mould is predicted for the output based on U models corresponding to CSTR system
Type is solved, and multi-step prediction output valve is obtained, subsequently into step 6；
Step 6. output forecast model based on U models, Yi Jiduo according to corresponding to CSTR system
Step prediction output valve, with reference to the constructed CSTR system exporting change track for meeting preset requirement, is obtained
The optimal control law of generalized predictive controller, then according to generalized predictive controller optimal control law, acquisition continuously stirs autoclave
The pseudo- input quantity of reactor assembly, and enter step 7；
Step 7. uses Secant Method, and the pseudo- input quantity for CSTR system is solved, and is connected
The amount of actually entering of continuous stirred-tank reactor system.
It is used as a preferred technical solution of the present invention：In the step 1, using the rank method of deploying of Taylor three and algebraically
Conversion, is changed for the nonlinear model structure corresponding to CSTR system, obtains continuous stirred tank
U model expressions corresponding to formula reactor assembly.
It is used as a preferred technical solution of the present invention：The step 2, according to CSTR system feedback
Regulatory factor, build meet preset requirement CSTR system exporting change track it is as follows：
Wherein, yr(k+j) expectation concentration of (k+j) moment CSTR system output-response thing, j are represented
∈ { 1 ..., P }, P is maximum predicted step number, Yr(k+1)=[yr(k+1),yr(k+2),…,yr(k+P)] it is to connect at (k+1) moment
The expected matrix of continuous stirred-tank reactor system output-response thing concentration, ω (k) is k moment CSTRs system
The setting value of system reactant concentration, β=[βr,βr 2,…,βr P],Gr=[1- βr,1-βr 2,…,1-βr P],βrFor regulatory factor, one
As take [0,1).
It is used as a preferred technical solution of the present invention：In the step 3, according in CSTR system
The intermediate parameters of generalized predictive controller, with reference to Diophantine equation, for the U moulds corresponding to CSTR system
Type expression formula, history and following input and output as corresponding to generalized predictive controller using CSTR system
Information, obtains the output forecast model based on U models corresponding to CSTR system as follows：
Y (k+j)=Ej(z-1)ΔU(k+j-1)+Fj(z-1)y(k)+Ej(z-1)ξ(k+j)
Wherein, the concentration of y (k+j) expressions CSTR system (k+j) moment institute output-response thing, Δ=
1-z-1, z moves the factor, E after beingj(z-1) and Fj(z-1) be generalized predictive controller intermediate parameters,
Fj(z-1)=fj,0, ξ (k+j) is the white noise acoustic jamming at (k+j) moment, and y (k) represents the CSTR system k moment
The concentration of institute's output-response thing, Δ U (k+j-1) represents the optimal control law at (k+j+1) moment.
It is used as a preferred technical solution of the present invention：In the step 4, by recursion interative computation, solution is lost
The initial solution of kind figure equation, wherein, as j=1, take E1(z-1)=1 can be obtained：F1(z-1)=1；And its recurrence formula：
It is used as a preferred technical solution of the present invention：The step 5, according to wide in CSTR system
The intermediate parameters of adopted predictive controller, with reference to the recurrence formula in Diophantine equation initial solution, for continuously stirring autoclave reaction
Output forecast model based on U models corresponding to device system is solved, and obtains multi-step prediction output valve Yp(k+1) it is as follows：
Yp(k+1)=G Δs Up+F(z-1)y(k)
Wherein, Yp(k+1)=[yp(k+1|k),yp(k+2|k),…,yp(k+P|k)]T, yp(k+1 | k) represent k moment institutes
The y of predictionp(k+1) value；ΔUp=[Δ U (k), Δ U (k+1) ..., Δ U (k+M-1)]T, Δ U (k) is generalized predictive control
The optimal control law of device, M is maximum control step number；Yp(k+1) reaction at CSTR system k+1 moment is represented
Thing predicts output valve；
G represents generalized predictive controller parameter, is asked by Diophantine equation
Solution gained；F(z-1)=[F1(z-1),F2(z-1),…,FP(z-1)]T, E (z-1)=[E1(z-1),E2(z-1),…,EP(z-1)]T。
It is used as a preferred technical solution of the present invention：The step 6, according to CSTR system, institute is right
Should the output forecast model based on U models, and multi-step prediction output valve obtains the future of CSTR system
Output vector Y (k+1) is as follows：
Y (k+1)=Yp(k+1)+E(z-1) ξ (k+1)=G Δs Up+F(z-1)y(k)+E(z-1)ξ(k+1)
And further combined with the constructed CSTR system exporting change track Y for meeting preset requirementr
(k+1), the following output vector Y (k+1) of CSTR system is substituted into the performance of classical generalized predictive control
Target function, the performance index function for obtaining the generalized predictive controller based on U models is as follows：
JP=E [G Δs Up+F(z-1)y(k)+E(z-1)ξ(k+1)-Yr(k+1)]T
Q[GΔUp+F(z-1)y(k)+E(z-1)ξ(k+1)-Yr(k+1)]+ΔUP T(k)λΔUP(k)
Wherein：Q=diag (q1,q2,…,qP) be predicated error weight matrix, λ=diag (λ1,λ2,…,λM) it is control
The weight matrix of increment processed；
By solving equation：The optimal control law for obtaining generalized predictive controller is as follows：
ΔUP(k)=(GTQG+λ)-1GTQ[Yr(k+1)-F(z-1)y(k)]
Δ U (k)=d1 T[Yr(k+1)-F(z-1)y(k)]
Wherein, d1 TRepresenting matrix (GTQG+λ)-1GTQ the 1st row, finally, according to equation below：
U (k)=Δ U (k)+U (k-1)
Obtain the pseudo- input quantity U (k) of CSTR system.
It is used as a preferred technical solution of the present invention：The step 7, using Secant Method, as follows：
Solved for the pseudo- input quantity U (k) of CSTR system, acquisition continuously stirs autoclave reaction
The amount of the actually entering u (k) of device system, wherein, subscript l is iterations, and N is execution Taylor three rank expansion side in the step 1
The maximum times corresponding to the CSTR system amount of actually entering, a are obtained after methodz(k) continuous stirred tank is represented
Formula reactor assembly performs the coefficient after the rank method of deploying of Taylor three.
A kind of GPC algorithm of CSTR system of the present invention uses above technical side
Case compared with prior art, with following technique effect：A kind of CSTR system that the present invention is designed it is wide
Adopted predictive control algorithm, nonlinear model is set up to CSTR system, and be converted into based on U models
Export forecast model；Reference locus is set, generalized predictive control is carried out to the output forecast model, the pseudo- input of system is obtained；
Then calculating is iterated using Secant Method and obtains actually entering for system；The present invention is combined using Secant Method with U models, is made
When solving the nonlinear equation about actually entering, it is to avoid the derivation problem run into during using Newton iterative,
And the calculating time is reduced, while having faster convergence rate；Simplify Control of Nonlinear Systems design problem.
Brief description of the drawings
Fig. 1 is the block diagram of the Secant Method in present invention design；
Fig. 2 is that a kind of framework of the GPC algorithm of CSTR system shows designed by the present invention
It is intended to.
Embodiment
The embodiment of the present invention is described in further detail with reference to Figure of description.
As depicted in figs. 1 and 2, the present invention devises a kind of Generalized Prediction of CSTR system (CSTR)
In control algolithm, practical application, following steps are specifically included：
The nonlinear model structure that step 1. is built corresponding to CSTR system (CSTR) is as follows：
Wherein：Y represents the concentration of some reactant in CSTR system (CSTR), as continuously stirring
The output of tank reactor system (CSTR)；U represents that reactant enters the flow velocity of CSTR system (CSTR),
As CSTR system (CSTR) input, controller output is represented in Control System Design.
Then changed using the rank method of deploying of Taylor three and algebraically, for CSTR system (CSTR)
Corresponding nonlinear model structure is changed, and obtains the U models corresponding to CSTR system (CSTR)
Expression formula, and enter step 2.
, can after being deployed by the rank of Taylor series three in above-mentioned control, it is assumed that be zero-order holder between controller and object
To obtain following expression formula：
Consider the interference or influence of noise of actuator, be into the expression-form of U models by above-mentioned model conversation：
Y (k+1)=U (k)+ξ (k+1)/Δ
U (k)=a0(k)+a1(k)u(k)+a2(k)u2(k)+a3(k)u3(k)
Wherein：ξ (k) is the white noise acoustic jamming at k moment, and U (k) represents the output of generalized predictive controller, a0(k)、a1(k)、
a2And a (k)3(k) CSTR system (CSTR) performs the coefficient after the rank method of deploying of Taylor three, TsIt is sampling
Cycle；
The expression formula that general random U models are given below is as follows：
Y (k)=U (k-1)+ξ (k)/Δ (1)
Wherein：Δ=1-z-1, z moves the factor after being, above-mentioned expression formula is defined as to the controlled device of generalized predictive controller
Model.
The regulatory factor that step 2. is fed back according to CSTR system (CSTR), structure meets preset requirement
CSTR system (CSTR) exporting change track it is as follows；Subsequently into step 3.
yr(k+j)=βr jyr(k)+(1-βr j)ω(k)
Wherein, yr(k+j) expectation of (k+j) moment CSTR system (CSTR) output-response thing is represented
Concentration, j ∈ { 1 ..., P }, P is maximum predicted step number, Yr(k+1)=[yr(k+1),yr(k+2),…,yr(k+P)] it is (k+1)
The expected matrix of moment CSTR system (CSTR) output-response thing concentration, ω (k) is to continuously stir at the k moment
The setting value of tank reactor system (CSTR) reactant concentration, β=[βr,βr 2,…,βr P],Gr=[1- βr,1-βr 2,…,1-
βr P],βrFor regulatory factor, typically take [0,1).
Step 3. according to the intermediate parameters of generalized predictive controller in CSTR system (CSTR), with reference to
Diophantine equation, for the U model expressions corresponding to CSTR system (CSTR), by generalized predictive control
Device is continuously stirred using history corresponding to CSTR system (CSTR) and following input/output information
Output forecast model based on U models corresponding to tank reactor system (CSTR) is as follows, subsequently into step 4.
Y (k+j)=Ej(z-1)ΔU(k+j-1)+Fj(z-1)y(k)+Ej(z-1)ξ(k+j)
Wherein, y (k+j) represents the dense of CSTR system (CSTR) (k+j) moment institute output-response thing
Degree, Δ=1-z-1, z moves the factor, E after beingj(z-1) and Fj(z-1) be generalized predictive controller intermediate parameters,Fj(z-1)=fj,0, ξ (k+j) is the white noise acoustic jamming at (k+j) moment, and y (k) represents to continuously stir
The concentration of tank reactor system (CSTR) k moment institutes output-response thing, Δ U (k+j-1) represents the optimal control at (k+j+1) moment
System rule.
Specifically, in moment k, generalized predictive controller utilizes past and following CSTR system
(CSTR) input/output information, carrys out the concentration y (k+j) of following output-response thing of forecasting system；In order to obtain (k+j) moment
Prediction output, now introduce one group of Diophantine equation it is as follows：
1=(1-z-1)Ej(z-1)+z-jFj(z-1) (2)
Wherein：Ej(z-1) and Fj(z-1) be generalized predictive controller intermediate parameters,
Fj(z-1)=fj,0,degFj(z-1)=0
Formula (1) both sides are multiplied by after Δ multiplied by with E simultaneouslyj(z-1)：
(1-z-1)Ej(z-1) y (k)=Ej(z-1)ΔU(k-1)+Ej(z-1)ξ(k)
Diophantine equation is substituted into above formula, z is multiplied byjAnd arrange：
Y (k+j)=Ej(z-1)ΔU(k+j-1)+Fj(z-1)y(k)+Ej(z-1)ξ(k+j)
(3)
The formula is the output forecast model based on U models；
Next following definition is provided：
yp(k+j | k)=Ej(z-1)ΔU(k+j-1)+Fj(z-1)y(k)
(4)
Following expression can then be obtained：Y (k+j)=yp(k+j|k)+Ej(z-1)ξ(k+j)
Wherein, Section 1 exports for optimum prediction, and Section 2 is predicated error.
Step 4. solves the initial solution for obtaining Diophantine equation by recursion interative computation, wherein, as j=1, take E1
(z-1)=1 can be obtained：F1(z-1)=1；And its recurrence formula：Subsequently into step 5.
The specific process for solving Diophantine equation is as follows：
1=(1-z-1)Ej(z-1)+z-jFj(z-1)
1=(1-z-1)Ej+1(z-1)+z-(j+1)Fj+1(z-1)
Above-mentioned two formula is subtracted each other into arrangement to obtain：
Because all low power term coefficients of the right untill (j-1) is secondary of above formula are all 0.Therefore Ej+1With EjBefore (j-1)
The coefficient of item must be equal, therefore has：
Above formula substitution Diophantine equations are obtained：Fj+1(z-1)=z [Fj(z-1)-ej+1,j(1-z-1)]；
Above formula expansion can be obtained：Then recurrence formula can be obtained：
As j=1, E is taken1(z-1)=1 can be obtained：F1(z-1)=1, this is the initial solution of Diophantine equations.
Step 5. according to the intermediate parameters of generalized predictive controller in CSTR system (CSTR), with reference to
Recurrence formula in Diophantine equation initial solution, U models are based on for CSTR system (CSTR) is corresponding
Output forecast model solved, obtain multi-step prediction output valve Yp(k+1) it is as follows；Subsequently into step 6.
Yp(k+1)=G Δs Up+F(z-1)y(k)
Wherein, Yp(k+1)=[yp(k+1|k),yp(k+2|k),…,yp(k+P|k)]T, yp(k+1 | k) represent k moment institutes
The y of predictionp(k+1) value；ΔUp=[Δ U (k), Δ U (k+1) ..., Δ U (k+M-1)]T, Δ U (k) is generalized predictive control
The optimal control law of device, M is maximum control step number；Yp(k+1) CSTR system (CSTR) the k+1 moment is represented
Reactant prediction output valve.
G represents generalized predictive controller parameter, is asked by Diophantine equation
Solution gained；F(z-1)=[F1(z-1),F2(z-1),…,FP(z-1)]T, E (z-1)=[E1(z-1),E2(z-1),…,EP(z-1)]T。
Step 6. output forecast model based on U models according to corresponding to CSTR system (CSTR),
And multi-step prediction output valve, export and become with reference to the constructed CSTR system (CSTR) for meeting preset requirement
Change track, obtain the optimal control law of generalized predictive controller, then according to generalized predictive controller optimal control law, connected
The pseudo- input quantity of continuous stirred-tank reactor system (CSTR), and enter step 7.
Above-mentioned steps 6, specific implementation procedure is as follows：
The output forecast model based on U models, Yi Jiduo according to corresponding to CSTR system (CSTR)
Step prediction output valve, the following output vector Y (k+1) for obtaining CSTR system (CSTR) is as follows：
Y (k+1)=Yp(k+1)+E(z-1) ξ (k+1)=G Δs Up+F(z-1)y(k)+E(z-1)ξ(k+1)
And further combined with constructed CSTR system (CSTR) exporting change for meeting preset requirement
Track Yr(k+1) it is, that the classical broad sense of following output vector Y (k+1) substitution of CSTR system (CSTR) is pre-
The performance index function of observing and controlling, the performance index function for obtaining the generalized predictive controller based on U models is as follows：
JP=E [G Δs Up+F(z-1)y(k)+E(z-1)ξ(k+1)-Yr(k+1)]T
Q[GΔUp+F(z-1)y(k)+E(z-1)ξ(k+1)-Yr(k+1)]+ΔUP T(k)λΔUP(k)
Wherein：Q=diag (q1,q2,…,qP) be predicated error weight matrix, λ=diag (λ1,λ2,…,λM) it is control
The weight matrix of increment processed；
By solving equation：The optimal control law for obtaining generalized predictive controller is as follows：
ΔUP(k)=(GTQG+λ)-1GTQ[Yr(k+1)-F(z-1)y(k)]
Δ U (k)=d1 T[Yr(k+1)-F(z-1)y(k)]
Wherein, d1 TRepresenting matrix (GTQG+λ)-1GTQ the 1st row, finally, according to equation below：
U (k)=Δ U (k)+U (k-1)
Obtain the pseudo- input quantity U (k) of CSTR system (CSTR).
Step 7. uses Secant Method, as follows：
Solved for the pseudo- input quantity U (k) of CSTR system (CSTR), obtain continuous stirred tank
The amount of the actually entering u (k) of formula reactor assembly (CSTR), wherein, subscript l is iterations, and N is to perform Thailand in the step 1
Strangle and maximum times corresponding to CSTR system (CSTR) amount of actually entering are obtained after three rank method of deploying, az
(k) represent that CSTR system (CSTR) performs the coefficient after the rank method of deploying of Taylor three.
The GPC algorithm of CSTR system designed by above-mentioned technical proposal, to continuously stirring
Mix tank reactor system and set up nonlinear model, and be converted into the output forecast model based on U models；Setting refers to rail
Mark, generalized predictive control is carried out to the output forecast model, obtains the pseudo- input of system；Then meter is iterated using Secant Method
Calculation obtains actually entering for system；The present invention is combined using Secant Method with U models so that non-about what is actually entered solving
During linear equation, it is to avoid the derivation problem run into during using Newton iterative, and reduce the calculating time, have simultaneously
Faster convergence rate；Simplify Control of Nonlinear Systems design problem.
Embodiments of the present invention are explained in detail above in conjunction with accompanying drawing, but the present invention is not limited to above-mentioned implementation
Mode, can also be on the premise of present inventive concept not be departed from the knowledge that those of ordinary skill in the art possess
Make a variety of changes.
Claims (8)
1. a kind of GPC algorithm of CSTR system, it is characterised in that comprise the following steps：
Step 1. builds the nonlinear model structure corresponding to CSTR system, and by nonlinear model structure
The U model expressions be converted to, obtain the U model expressions corresponding to CSTR system, subsequently into step
Rapid 2；
Step 2. builds according to the regulatory factor of CSTR system feedback and meets continuously stirring for preset requirement
Tank reactor system exporting change track；Subsequently into step 3；
Step 3. is according to the intermediate parameters of generalized predictive controller in CSTR system, with reference to diophantus side
Journey, for the U model expressions corresponding to CSTR system, obtains CSTR system institute
Output forecast model of the correspondence based on U models, subsequently into step 4；
Step 4. solves the initial solution and recurrence formula for obtaining Diophantine equation, subsequently into step 5；
Step 5. is according to the intermediate parameters of generalized predictive controller in CSTR system, with reference to Diophantine equation
Initial solution and recurrence formula, enter for the output forecast model based on U models corresponding to CSTR system
Row is solved, and multi-step prediction output valve is obtained, subsequently into step 6；
Step 6. output forecast model based on U models according to corresponding to CSTR system, and multistep are pre-
Output valve is surveyed, with reference to the constructed CSTR system exporting change track for meeting preset requirement, broad sense is obtained
The optimal control law of predictive controller, then according to generalized predictive controller optimal control law, acquisition continuously stirs autoclave reaction
The pseudo- input quantity of device system, and enter step 7；
Step 7. uses Secant Method, and the pseudo- input quantity for CSTR system is solved, and acquisition is continuously stirred
Mix the amount of actually entering of tank reactor system.
2. a kind of GPC algorithm of CSTR system according to claim 1, its feature exists
In：In the step 1, changed using the rank method of deploying of Taylor three and algebraically, for CSTR system institute
Corresponding nonlinear model structure is changed, and obtains the U model expressions corresponding to CSTR system.
3. a kind of GPC algorithm of CSTR system according to claim 2, its feature exists
In：The step 2, according to the regulatory factor of CSTR system feedback, structure meets the continuous of preset requirement
Stirred-tank reactor system exporting change track is as follows：
yr(k+j)=βr jyr(k)+(1-βr j)ω(k)
Wherein, yr(k+j) expectation concentration of (k+j) moment CSTR system output-response thing, j ∈ are represented
{ 1 ..., P }, P is maximum predicted step number, Yr(k+1)=[yr(k+1),yr(k+2),…,yr(k+P)] it is that (k+1) moment is continuous
The expected matrix of stirred-tank reactor system output-response thing concentration, ω (k) is k moment CSTR systems
The setting value of reactant concentration, β=[βr,βr 2,…,βr P],Gr=[1- βr,1-βr 2,…,1-βr P],βrFor regulatory factor, typically
Take [0,1).
4. a kind of GPC algorithm of CSTR system according to claim 3, its feature exists
In：In the step 3, according to the intermediate parameters of generalized predictive controller in CSTR system, with reference to losing kind
Figure equation, for the U model expressions corresponding to CSTR system, by generalized predictive controller using continuously
History corresponding to stirred-tank reactor system and following input/output information, obtain CSTR system institute
Output forecast model of the correspondence based on U models is as follows：
Y (k+j)=Ej(z-1)ΔU(k+j-1)+Fj(z-1)y(k)+Ej(z-1)ξ(k+j)
Wherein, y (k+j) represents the concentration of CSTR system (k+j) moment institute output-response thing, Δ=1-z-1, z moves the factor, E after beingj(z-1) and Fj(z-1) be generalized predictive controller intermediate parameters,Fj
(z-1)=fj,0, ξ (k+j) is the white noise acoustic jamming at (k+j) moment, and y (k) represents CSTR system k moment institutes
The concentration of output-response thing, Δ U (k+j-1) represents the optimal control law at (k+j+1) moment.
5. a kind of GPC algorithm of CSTR system according to claim 4, its feature exists
In：In the step 4, by recursion interative computation, the initial solution for obtaining Diophantine equation is solved, wherein, as j=1, take E1
(z-1)=1 can be obtained：F1(z-1)=1；And its recurrence formula：
6. a kind of GPC algorithm of CSTR system according to claim 5, its feature exists
In：The step 5, according to the intermediate parameters of generalized predictive controller in CSTR system, with reference to diophantus
Recurrence formula in equation initial solution, mould is predicted for the output based on U models corresponding to CSTR system
Type is solved, and obtains multi-step prediction output valve Yp(k+1) it is as follows：
Yp(k+1)=G Δs Up+F(z-1)y(k)
Wherein, Yp(k+1)=[yp(k+1|k),yp(k+2|k),…,yp(k+P|k)]T, yp(k+1 | k) represent that the k moment is predicted
Yp(k+1) value；ΔUp=[Δ U (k), Δ U (k+1) ..., Δ U (k+M-1)]T, Δ U (k) is generalized predictive controller
Optimal control law, M is maximum control step number；Yp(k+1) represent that the reactant at CSTR system k+1 moment is pre-
Survey output valve；
G represents generalized predictive controller parameter, by Diophantine Equation Solution institute
；F(z-1)=[F1(z-1),F2(z-1),…,FP(z-1)]T, E (z-1)=[E1(z-1),E2(z-1),…,EP(z-1)]T。
7. a kind of GPC algorithm of CSTR system according to claim 6, its feature exists
In：The step 6, the output forecast model based on U models according to corresponding to CSTR system, and multistep
Output valve is predicted, the following output vector Y (k+1) for obtaining CSTR system is as follows：
Y (k+1)=Yp(k+1)+E(z-1) ξ (k+1)=G Δs Up+F(z-1)y(k)+E(z-1)ξ(k+1)
And further combined with the constructed CSTR system exporting change track Y for meeting preset requirementr(k+1),
The following output vector Y (k+1) of CSTR system is substituted into the performance indications letter of classical generalized predictive control
Number, the performance index function for obtaining the generalized predictive controller based on U models is as follows：
JP=E [G Δs Up+F(z-1)y(k)+E(z-1)ξ(k+1)-Yr(k+1)]T
Q[GΔUp+F(z-1)y(k)+E(z-1)ξ(k+1)-Yr(k+1)]+ΔUP T(k)λΔUP(k)
Wherein：Q=diag (q1,q2,…,qP) be predicated error weight matrix, λ=diag (λ1,λ2,…,λM) it is that control increases
The weight matrix of amount；
By solving equation：The optimal control law for obtaining generalized predictive controller is as follows：
ΔUP(k)=(GTQG+λ)-1GTQ[Yr(k+1)-F(z-1)y(k)]
Δ U (k)=d1 T[Yr(k+1)-F(z-1)y(k)]
Wherein, d1 TRepresenting matrix (GTQG+λ)-1GTQ the 1st row, finally, according to equation below：
U (k)=Δ U (k)+U (k-1)
Obtain the pseudo- input quantity U (k) of CSTR system.
8. a kind of GPC algorithm of CSTR system according to claim 7, its feature exists
In：The step 7, using Secant Method, as follows：
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Device system is answered to perform the coefficient after the rank method of deploying of Taylor three.
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