CN110069015A - A kind of method of Distributed Predictive function control under non-minimumization state-space model - Google Patents
A kind of method of Distributed Predictive function control under non-minimumization state-space model Download PDFInfo
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Abstract
The invention discloses the Distributed Predictive function control methods under a kind of non-minimumization state-space model, include the following steps: step 1, establish Distributed Predictive function control non-minimumization state-space model;Distributed Predictive function controls controller under step 2, design non-minimumization state-space model.The present invention passes through the means such as data acquisition, model foundation, prediction mechanism, optimization, establish the Distributed Predictive function control method under one kind non-minimumization state-space model, using this method under the premise of guaranteeing compared with high control precision and stability, deficiency of traditional anger Distributed Predictive function control method in the multivariable process control containing Nonself-regulating plant can be effectively made up, and meets the needs of actual industrial process.
Description
Technical field
The invention belongs to field of automation technology, the Distributed Predictive letter being related under one kind non-minimumization state-space model
The design method of number control.
Background technique
Distributed Predictive function controls (DPFC) although control effect is preferable, the rapidity of system should not enough,
Especially in the case where introducing interference, restores stable overlong time again, may not reached requirement in some industrial process,
Interfere simultaneously introducing, and in the lesser situation of setting value, output cannot perfect tracking fixed valure, there are small
Deviation, although deviation very little, is implicitly present in.During actual industrial production, with the control precision and peace to product
The requirement of full operation is higher and higher, and also it is necessary to eliminate for some small deviations.Therefore, for Distributed Predictive function control into
The certain improvement of row is necessary.
Summary of the invention
The advantages of providing state-space method based on non-minimum state space (NMSS) Model Predictive Control, such as analysis are held
Easily, structure designs simple etc..For the fact that, the invention proposes a kind of new non-minimum state-space models of extension
(EMSMS), the influence it considers output error, measurement output and input to Model Predictive Control controller design, extension
Non-minimum state-space model PREDICTIVE CONTROL maintain the good advantage of state-space model, and prevent tracking error into one
Step increases, and can control error well.Here in conjunction with extension non-minimum state spatial model and Distributed Predictive function
Control had both maintained Distributed Predictive function and has controlled preferable control effect, while having improved the fast of system to a certain extent
Speed.
The technical scheme is that establishing one by means such as data acquisition, model foundation, prediction mechanism, optimizations
Distributed Predictive function control method under kind non-minimumization state-space model is being guaranteed using this method compared with high control precision
Under the premise of stability, traditional anger Distributed Predictive function control method can be effectively made up containing the changeable of Nonself-regulating plant
The deficiency in process control is measured, and meets the needs of actual industrial process.
The step of the method for the present invention includes:
Step 1, Distributed Predictive function control the foundation of non-minimumization state-space model, comprise the concrete steps that:
1.1, the multivariable N input N output large scale system in industrial process is regarded as and purely retarded is added by N number of one order inertia
(FOPDT) the N input N output multivariable one order inertia of the subsystem composition of model, available following form adds purely retarded
(FOPDT) model system:
Wherein, K11,…,Kij,…,KnnFor the steady-state gain that j-th of multivariable process object input exports i-th, i
=1 ..., n;J=1 ..., n, T11,…,Tij,…,TnnThe time that i-th is exported for j-th of multivariable process object input
Constant, τ11,…,τij,…,τnnThe lag time that i-th is exported for j-th of multivariable process object input.
1.2, transmission function of the input of j-th of object to the output of i-th of object are as follows:
1.3, in sampling time TsUnder the conditions of, discretization is carried out to step 1.2, available:
Wherein, k indicates moment, d=τij/TsInteger part, αij=e-Ts/Tij, yi(k),yiIt (k-1) is respectively i-th
The output at k moment and k-1 moment of a subsystem, uiIt (k-d-1) is input of i-th of subsystem at the k-d-1 moment, uj
It (k-d-1) is input of j-th of subsystem at the k-d-1 moment,Reflect other subsystems
Input the influence exported to i-th of subsystem.
1.4, it to the first-order difference after the model orientation of discretization, obtains:
Wherein, Δ yi(k),Δyi(k-1) be respectively i-th of subsystem the output increment at k moment and k-1 moment,
ΔuiIt (k-d-1) is input increment of i-th of subsystem at the k-d-1 moment, Δ ujIt (k-d-1) is j-th of subsystem in k-d-1
The input increment at moment,The input of other subsystems is reflected to export i-th of subsystem
Influence increment.
1.5, by step 1.3 and step 1.4;It can obtain:
Δxi,j(k+1)=Ai,j,mΔxi,j(k)+Bi,j,mΔui(k)+Di,j,mΔuj(k)
Δyi(k+1)=Ci,j,mΔxi,j(k+1)
Wherein, Δ xi,j(k)=[Δ yi(k),Δui(k-1),…,Δui(k-d), Δ uj(k-1),…,Δuj(k-d)]T,
Δui(k-1),,Δui(k-d), Δ uj(k-1),…,Δuj(k-d) k-1 is respectively indicated ..., k-d, the input increment at moment,
Output increment;Δxi,j(k+1)=[Δ yi(k+1),Δui(k) ..., Δ ui(k-d+1), Δ uj(k),…,Δuj(k-d+1)
]T, Δ yi(k+1),Δui(k-d+1), Δ uj(k-d+1) respectively indicate i-th of subsystem the k+1 moment output increment,
Input increment, j-th subsystem input increment at k-d+1 moment of i-th of subsystem at the k-d+1 moment, T representing matrix
Transposition symbol.
Bi,j,m=[0 1000 ... 0]T;
Ci,j,m=[1 00 ... 000 0];
Di,j,m=[0 ... 0010 ... 0]T;
1.6, according to step 1.5, non-minimum state-space model can be obtained:
zi(k+1)=Azi(k)+BΔui(k)+DΔuj(k)+CΔri(k+1)
Wherein:ei(k)=yi(k)-ri(k)
ei(k+1)=ei(k)+Ci,j,mAi,j,mΔxi,j(k)+Ci,j,mBi,j,mΔui(k)+Di,j,mBi,j,mΔuj(k)-Δri
(k+1)
riIt (k) is the reference rail at k moment
Mark, Δ riIt (k+1) is the reference locus increment at k+1 moment, ei(k), eiIt (k+1) is respectively k, etching system output and reference when k+1
The error of track.
The design of Distributed Predictive function control controller, specific steps under step 2, non-minimumization state-space model
It is:
2.1, it according to step 1.6, can obtain:
Zi=Gzi(k)+SΔUi,j+ΨΔRi
Wherein, P indicates optimization time domain, and M indicates control time domain
ΔUi,j=[Δ ui(k) Δui(k+1) … Δui(k+M-1),Δuj(k) Δuj(k+1) … Δuj(k+M-
1)]T
ΔRi=[Δ ri(k+1) Δri(k+2) … Δri(k+P)]T
ri(k+ii)=λiiyi(k)+(1-λii)ci(k), ii=1,2 ..., P
λ indicates the softening factor, ci(k) setting value at i-th of subsystem k moment, Δ r are indicatedi(k+1), Δ ri(k+
2) ..., Δ ri(k+P) k+1 is respectively indicated ..., k+P moment reference locus increment.
2.2, i-th of subsystem objectives function is taken:
Ji=Zi TQi,mZi+ΔUi,j TRi,j,mΔUi,j
Wherein, Qi,m=block diag (Qi,1,Qi,2,…,Qi,P-1,Qi,P)
ri,1,…,ri,M,rj,1,…,rj,MI-th, j subsystem is respectively indicated from the reference locus at 1 ..., k moment
Value.
2.3, it can be obtained by step 2.2:
ΔUi,j=-(STQi,mS+Ri,j,m)-1STQi,m(Gzi(k)+ΨΔRi)
ui(k)=[1 0 ... 0] Δ Ui,j+ui(k-1)
Wherein, ui(k), ui(k-1) control amount at i-th of subsystem k, k-1 moment is respectively indicated.
2.4, the controlling increment Δ U of i-th of subsystem is utilizedi,j, obtain the practical control amount u of i-th of subsystemi(k)=
[1 0 … 0]ΔUi,j+ui(k-1) i-th of subsystem is acted on;Then the 1st ..., n son can be similarly found out respectively
The control amount of system.
Specific embodiment
The invention will be further described below.
By taking general predictive control as an example:
Drum Water Level Control System for Boiler is a typical multivariable complex object, and regulating measure is using control water-supply valve
Valve opening.
The foundation of step 1, Drum Water Level Control System for Boiler model, comprises the concrete steps that:
1.1, the multivariable N input N output large scale system in Drum Water Level Control System for Boiler is regarded as by N number of single order
Inertia adds the subsystem of purely retarded (FOPDT) model to form, and the N input N output multivariable single order of available following form is used
Property adds purely retarded (FOPDT) model system:
Wherein, K11,…,Kij,…,KnnThe stable state that i-th is exported for j-th of Drum Water Level Control System for Boiler input
Gain, i=1 ..., n;J=1 ..., n, T11,…,Tij,…,TnnIt is j-th of Drum Water Level Control System for Boiler input to i-th
The time constant of a output, τ11,…,τij,…,τnnI-th is exported for j-th of Drum Water Level Control System for Boiler input
Lag time.
1.2, in Drum Water Level Control System for Boiler the input of j-th of object to the transmission function of the output of i-th of object
Are as follows:
1.3, in sampling time TsUnder the conditions of, discretization is carried out to step 1.2, available:
Wherein, k indicates moment, d=τij/TsInteger part, αij=e-Ts/Tij, yi(k),yiIt (k-1) is respectively i-th
The steam water-level at k moment and k-1 moment of a subsystem, uiIt (k-d-1) is valve of i-th of subsystem at the k-d-1 moment
Door aperture, ujIt (k-d-1) is valve opening of j-th of subsystem at the k-d-1 moment,Reflection
Other subsystems input the influence to i-th of subsystem steam water-level.
1.4, it to the first-order difference after the model orientation of discretization, obtains:
Wherein, Δ yi(k),Δyi(k-1) be respectively i-th of subsystem the steam water-level at k moment and k-1 moment
Increment, Δ uiIt (k-d-1) is valve opening increment of i-th of subsystem at the k-d-1 moment, Δ ujIt (k-d-1) is j-th of subsystem
The valve opening increment united at the k-d-1 moment,The input of other subsystems is reflected to i-th
The influence increment of a subsystem steam water-level.
1.5, by step 1.3 and step 1.4;It can obtain:
Δxi,j(k+1)=Ai,j,mΔxi,j(k)+Bi,j,mΔui(k)+Di,j,mΔuj(k)
Δyi(k+1)=Ci,j,mΔxi,j(k+1)
Wherein, Δ xi,j(k)=[Δ yi(k),Δui(k-1),…,Δui(k-d), Δ uj(k-1),…,Δuj(k-d)]T,
Δui(k-1),…,Δui(k-d), Δ uj(k-1),…,Δuj(k-d) k-1 is respectively indicated ..., k-d, the moment
Valve opening increment, steam water-level increment;Δxi,j(k+1)=[Δ yi(k+1),Δui(k),…,Δui(k-d+1), Δ uj
(k),…,Δuj(k-d+1)]T, Δ yi(k+1),Δui(k-d+1), Δ uj(k-d+1) respectively indicate i-th of subsystem in k+
The steam water-level increment at 1 moment, i-th of subsystem are in the valve opening increment at k-d+1 moment, j-th of subsystem in k-d+1
The valve opening increment at quarter, the transposition symbol of T representing matrix.
Bi,j,m=[0 1000 ... 0]T;
Ci,j,m=[1 00 ... 000 0];
Di,j,m=[0 ... 0010 ... 0]T;
1.6, according to step 1.5, non-minimum state-space model can be obtained:
zi(k+1)=Azi(k)+BΔui(k)+DΔuj(k)+CΔri(k+1)
Wherein:ei(k)=yi(k)-ri(k)
ei(k+1)=ei(k)+Ci,j,mAi,j,mΔxi,j(k)+Ci,j,mBi,j,mΔui(k)+Di,j,mBi,j,mΔuj(k)-Δri
(k+1)
riIt (k) is the reference rail at k moment
Mark, Δ riIt (k+1) is the reference locus increment at k+1 moment, ei(k), ei(k+1) be respectively k, when k+1 etching system steam water-level with
The error of reference locus.
The design of step 2, Drum Water Level Control System for Boiler controller, comprises the concrete steps that:
2.1, it according to step 1.6, can obtain:
Zi=Gzi(k)+SΔUi,j+ΨΔRi
Wherein, P indicates optimization time domain, and M indicates control time domain
ΔUi,j=[Δ ui(k) Δui(k+1) … ui(k+M-1),Δuj(k) Δuj(k+1) … Δuj(k+M-
1)]T
ΔRi=[Δ ri(k+1) Δri(k+2) … Δri(k+P)]T
ri(k+ii)=λiiyi(k)+(1-λii)ci(k), ii=1,2 ..., P
λ indicates the softening factor, ci(k) setting value at i-th of subsystem k moment, Δ r are indicatedi(k+1), Δ ri(k+
2) ..., Δ ri(k+P) k+1 is respectively indicated ..., k+P moment reference locus increment.
2.2, i-th of subsystem objectives function is taken:
Ji=Zi TQi,mZi+ΔUi,j TRi,j,mΔUi,j
Wherein, Qi,m=block diag (Qi,1,Qi,2,…,Qi,P-1,Qi,P)
ri,1,…,ri,M,rj,1,…,rj,MI-th, j subsystem is respectively indicated from the reference locus at 1 ..., k moment
Value.
2.3, it can be obtained by step 2.2:
ΔUi,j=-(STQi,mS+Ri,j,m)-1STQi,m(Gzi(k)+ΨΔRi)
ui(k)=[1 0 ... 0] Δ Ui,j+ui(k-1)
Wherein, ui(k), ui(k-1) valve opening at i-th of subsystem k, k-1 moment is respectively indicated.
2.4, the valve opening increment Delta U of i-th of subsystem is utilizedi,j, obtain the practical valve opening of i-th of subsystem
ui(k)=[1 0 ... 0] Δ Ui,j+ui(k-1) i-th of subsystem is acted on;Then can similarly find out respectively the 1st ...,
The valve opening of n subsystem.
Claims (3)
1. the Distributed Predictive function control method under a kind of non-minimumization state-space model, includes the following steps:
Step 1 establishes Distributed Predictive function control non-minimumization state-space model;
Distributed Predictive function controls controller under step 2, design non-minimumization state-space model.
2. the Distributed Predictive function control method under non-minimumization state-space model as described in claim 1, feature
It is:
Step 1 is specific as follows:
1.1, the multivariable N input N output large scale system in industrial process is regarded as and purely retarded is added by N number of one order inertia
(FOPDT) the N input N output multivariable one order inertia of the subsystem composition of model, available following form adds purely retarded
(FOPDT) model system:
Wherein, K11,…,Kij,…,KnnFor the steady-state gain that j-th of multivariable process object input exports i-th, i=
1,…,n;J=1 ..., n, T11,…,Tij,…,TnnThe time exported for j-th of multivariable process object input to i-th is normal
Number, τ11,…,τij,…,τnnThe lag time that i-th is exported for j-th of multivariable process object input;
1.2, transmission function of the input of j-th of object to the output of i-th of object are as follows:
1.3, in sampling time TsUnder the conditions of, discretization is carried out to step 1.2, available:
Wherein, k indicates moment, d=τij/TsInteger part,yi(k),yiIt (k-1) is respectively i-th of subsystem
The output at k moment and k-1 moment, uiIt (k-d-1) is input of i-th of subsystem at the k-d-1 moment, uj(k-d-1) it is
Input of j-th of subsystem at the k-d-1 moment,The input of other subsystems is reflected to i-th
The influence of a subsystem output;
1.4, it to the first-order difference after the model orientation of discretization, obtains:
Wherein, Δ yi(k),Δyi(k-1) be respectively i-th of subsystem the output increment at k moment and k-1 moment, Δ ui
It (k-d-1) is input increment of i-th of subsystem at the k-d-1 moment, Δ ujIt (k-d-1) is j-th of subsystem at the k-d-1 moment
Input increment,It reflects other subsystems and inputs the shadow exported to i-th of subsystem
Ring increment;
1.5, by step 1.3 and step 1.4;It can obtain:
Δxi,j(k+1)=Ai,j,mΔxi,j(k)+Bi,j,mΔui(k)+Di,j,mΔuj(k)
Δyi(k+1)=Ci,j,mΔxi,j(k+1)
Wherein, Δ xi,j(k)=[Δ yi(k),Δui(k-1),…,Δui(k-d), Δ uj(k-1),…,Δuj(k-d)]T, Δ ui
(k-1),…,Δui(k-d), Δ uj(k-1),…,Δuj(k-d) k-1 is respectively indicated ..., k-d is the input increment at moment, defeated
Increment out;Δxi,j(k+1)=[Δ yi(k+1),Δui(k),…,Δui(k-d+1), Δ uj(k),…,Δuj(k-d+1)]T,
Δyi(k+1),Δui(k-d+1), Δ uj(k-d+1) respectively indicate i-th of subsystem the k+1 moment output increment, i-th
Input increment, j-th subsystem input increment at k-d+1 moment of a subsystem at the k-d+1 moment, T representing matrix turn
Set symbol;
Bi,j,m=[0 1000 ... 0]T;
Ci,j,m=[1 00 ... 000 0];
Di,j,m=[0 ... 0010 ... 0]T;
1.6, according to step 1.5, non-minimum state-space model can be obtained:
zi(k+1)=Azi(k)+BΔui(k)+DΔuj(k)+CΔri(k+1)
Wherein:ei(k)=yi(k)-ri(k)ei(k+1)=ei(k)+Ci,j, mAi,j,mΔxi,j(k)+Ci,j,mBi,j,mΔui(k)+Di,j,mBi,j,mΔuj(k)-Δri(k+1)riIt (k) is the reference locus at k moment, Δ ri
It (k+1) is the reference locus increment at k+1 moment, ei(k), eiIt (k+1) is respectively k, etching system output and reference locus when k+1
Error.
3. the Distributed Predictive function control method under non-minimumization state-space model as claimed in claim 2, feature
Be: step 2 is specific as follows:
2.1, it according to step 1.6, can obtain:
Zi=Gzi(k)+SΔUi,j+ΨΔRi
Wherein, P indicates optimization time domain, and M indicates control time domain
ΔUi,j=[Δ ui(k) Δui(k+1) … Δui(k+M-1),Δuj(k) Δuj(k+1) … Δuj(k+M-1)]T
ΔRi=[Δ ri(k+1) Δri(k+2) … Δri(k+P)]T
ri(k+ii)=λiiyi(k)+(1-λii)ci(k), ii=1,2 ..., P
λ indicates the softening factor, ci(k) setting value at i-th of subsystem k moment, Δ r are indicatedi(k+1), Δ ri(k+2) ..., Δ ri
(k+P) k+1 is respectively indicated ..., k+P moment reference locus increment;
2.2, i-th of subsystem objectives function is taken:
Ji=Zi TQi,mZi+ΔUi,j TRi,j,mΔUi,j
Wherein, Qi,m=block diag (Qi,1,Qi,2,…,Qi,P-1,Qi,P)
ri,1,…,ri,M,rj,1,…,rj,MRespectively indicate value of i-th, the j subsystem from the reference locus at 1 ..., k moment;
2.3, it can be obtained by step 2.2:
ΔUi,j=-(STQi,mS+Ri,j,m)-1STQi,m(Gzi(k)+ΨΔRi)
ui(k)=[1 0 ... 0] Δ Ui,j+ui(k-1)
Wherein, ui(k), ui(k-1) control amount at i-th of subsystem k, k-1 moment is respectively indicated;
2.4, the controlling increment Δ U of i-th of subsystem is utilizedi,j, obtain the practical control amount u of i-th of subsystemi(k)=[1 0
… 0]ΔUi,j+ui(k-1) i-th of subsystem is acted on;Then the control of the 1st ..., n subsystem is similarly found out respectively
Amount.
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