CN110069015B - Distributed prediction function control method under non-minimized state space model - Google Patents

Distributed prediction function control method under non-minimized state space model Download PDF

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CN110069015B
CN110069015B CN201910431800.1A CN201910431800A CN110069015B CN 110069015 B CN110069015 B CN 110069015B CN 201910431800 A CN201910431800 A CN 201910431800A CN 110069015 B CN110069015 B CN 110069015B
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张日东
吴胜
欧丹林
蒋超
高福荣
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Zhejiang Bonyear Technology Co ltd
Hangzhou Dianzi University
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Hangzhou Dianzi University
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Abstract

The invention discloses a distributed prediction function control method under a non-minimized state space model, which comprises the following steps: step 1, establishing a distributed prediction function numerical control non-minimized state space model; and 2, designing a distributed prediction function control controller under a non-minimized state space model. The invention establishes a distributed prediction function control method under a non-minimized state space model through means of data acquisition, model establishment, prediction mechanism, optimization and the like, can effectively make up the defects of the traditional anger distributed prediction function control method in multivariable process control containing non-self-balancing objects on the premise of ensuring higher control precision and stability by utilizing the method, and meets the requirements of the actual industrial process.

Description

Distributed prediction function control method under non-minimized state space model
Technical Field
The invention belongs to the technical field of automation, and relates to a design method of distributed prediction function control under a non-minimized state space model.
Background
Although the Distributed Predictive Function Control (DPFC) has a good control effect, the rapidity of the system is not good enough, particularly, in the case of introducing disturbance, the time for recovering the stability is too long again, some industrial processes may not meet the requirements, and in the case of introducing disturbance and having a small set value, the output cannot perfectly track the set value, so that a slight deviation exists, but the deviation is very small. In the actual industrial production process, as the requirements on the control precision and safe operation of products are higher and higher, some small deviations need to be eliminated. Therefore, there is a need for certain improvements in distributed prediction function control.
Disclosure of Invention
Predictive control based on non-minimum state space (NMSS) models provides the advantages of state space methods, such as ease of analysis, simplicity of structural design, and the like. In view of this fact, the present invention proposes a new extended non-minimum state space model (EMSMS) in which the influence of output errors, measurement outputs and inputs on the design of the model predictive control controller is taken into account, and the extended non-minimum state space model predictive control maintains the good advantages of the state space model and prevents further increase of tracking errors, making it possible to control errors well. The minimum state space model of the extended state is combined with the distributed prediction function control, so that the better control effect of the distributed prediction function control is kept, and the rapidity of the system is improved to a certain extent.
The technical scheme of the invention is that a distributed prediction function control method under a non-minimized state space model is established through means of data acquisition, model establishment, prediction mechanism, optimization and the like, and the method can effectively make up the defects of the traditional anger distributed prediction function control method in multivariable process control containing non-self-balancing objects on the premise of ensuring higher control precision and stability, and meet the requirements of actual industrial processes.
The method comprises the following steps:
step 1, establishing a non-minimized state space model by a distributed prediction function control, which comprises the following specific steps:
1.1, considering a multivariable N input N output large-scale system in an industrial process as a subsystem consisting of N first-order inertia plus pure hysteresis (FOPDT) models, an N input N output multivariable first-order inertia plus pure hysteresis (FOPDT) model system in the following form can be obtained:
Figure BDA0002068778070000021
wherein, K11,…,Kij,…,KnnA steady state gain for the jth input to the ith output of the multivariable process object, i ═ 1, …, n; j is 1, …, n, T11,…,Tij,…,TnnTime constant, τ, for the jth input to ith output of a multivariable process object11,…,τij,…,τnnThe lag time for the jth input to the ith output for a multivariable process object.
1.2, the transfer function of the input of the jth object to the output of the ith object is:
Figure BDA0002068778070000022
1.3 at sampling time TsDiscretizing the step 1.2 under the condition to obtain:
Figure BDA0002068778070000023
where k denotes a time, and d ═ τij/TsInteger part of (a)ij＝e-Ts/Tij，yi(k),yi(k-1) the output at time k and time k-1, u, of the ith subsystem, respectivelyi(k-d-1) is the input of the ith subsystem at time k-d-1, uj(k-d-1) isThe input of the jth subsystem at time k-d-1,
Figure BDA0002068778070000024
reflecting the effect of other subsystem inputs on the ith subsystem output.
1.4, obtaining the first difference after the discretization model orientation:
Figure BDA0002068778070000025
wherein, Δ yi(k),Δyi(k-1) the output increments at time k and k-1, Δ u, for the ith subsystem, respectivelyi(k-d-1) is the input increment of the ith subsystem at time k-d-1, Δ uj(k-d-1) is the input increment of the jth subsystem at time k-d-1,
Figure BDA0002068778070000031
reflecting the incremental effect of other subsystem inputs on the ith subsystem output.
1.5, 1.3 and 1.4; the following can be obtained:
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)＝[Δyi(k),Δui(k-1),…,Δui(k-d)，Δuj(k-1),…,Δuj(k-d)]T，Δui(k-1),,Δui(k-d)，Δuj(k-1),…,Δuj(k-d) represents k-1, …, k-d, input increment at time, output increment, respectively; Δ xi,j(k+1)＝[Δyi(k+1),Δui(k),…，Δui(k-d+1)，Δuj(k),…,Δuj(k-d+1)]T，Δyi(k+1),Δui(k-d+1)，Δuj(k-d +1) represents the output increment of the ith subsystem at the time point of k +1, and the ith subsystem at the time point of k-d +1The input increment of the moment, the input increment of the jth subsystem at the moment k-d +1, and T represents the transposed symbol of the matrix.
Figure BDA0002068778070000032
Bi,j,m＝[0 1 0 0 0 … 0]T；
Ci,j,m＝[1 0 0 … 0 0 0 0]；
Di,j,m＝[0 … 0 0 1 0 … 0]T；
1.6, according to step 1.5, a non-minimum state space model can be obtained:
zi(k+1)＝Azi(k)+BΔui(k)+DΔuj(k)+CΔri(k+1)
wherein:
Figure BDA0002068778070000033
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)
Figure BDA0002068778070000041
ri(k) reference trajectory for time k, Δ ri(k +1) is the reference track increment at time k +1, ei(k)，eiAnd (k +1) is the error between the system output and the reference track at the moment k and k +1 respectively.
Step 2, designing a distributed prediction function control controller under a non-minimized state space model, which comprises the following specific steps:
2.1, according to step 1.6, one can obtain:
Zi＝Gzi(k)+SΔUi,j+ΨΔRi
wherein P represents an optimized time domain, and M represents a control time domain
Figure BDA0002068778070000042
Figure BDA0002068778070000043
ΔUi,j＝[Δui(k) Δui(k+1) … Δui(k+M-1),Δuj(k) Δuj(k+1) … Δuj(k+M-1)]T
ΔRi＝[Δri(k+1) Δri(k+2) … Δri(k+P)]T
ri(k+ii)＝λiiyi(k)+(1-λii)ci(k),ii＝1,2,…,P
λ denotes the softening factor, ci(k) Denotes the setting value, Δ r, at the time of the ith subsystem ki(k+1)，Δri(k+2)，…，Δri(k + P) denotes the reference trajectory increment at the time of k + 1.
2.2, taking an ith subsystem objective function:
Ji＝Zi TQi,mZi+ΔUi,j TRi,j,mΔUi,j
wherein Q isi,m＝block diag(Qi,1,Qi,2,…,Qi,P-1,Qi,P)
Figure BDA0002068778070000051
ri,1,…,ri,M,rj,1,…,rj,MWhich respectively represent the values of the reference trajectory at the i, j subsystems from 1.
2.3, from step 2.2:
ΔUi,j＝-(STQi,mS+Ri,j,m)-1STQi,m(Gzi(k)+ΨΔRi)
ui(k)＝[1 0 … 0]ΔUi,j+ui(k-1)
wherein u isi(k)，uiAnd (k-1) respectively represents the control quantity of the ith subsystem k, k-1 time.
2.4 control increment Δ U with ith subsystemi,jObtaining the actual control quantity u of the ith subsystemi(k)＝[1 0 … 0]ΔUi,j+ui(k-1) operating on the ith subsystem; then, the control variables of the 1 st, the.
Detailed Description
The present invention is further described below.
Taking boiler drum water level control as an example:
the boiler drum water level control system is a typical multivariable complex object, and the regulating means adopts the control of the opening degree of a water supply valve.
Step 1, establishing a boiler drum water level control system model, which comprises the following specific steps:
1.1, considering a multivariable N input N output large-scale system in a boiler drum water level control system as a subsystem consisting of N first-order inertia plus pure hysteresis (FOPDT) models, an N input N output multivariable first-order inertia plus pure hysteresis (FOPDT) model system in the following form can be obtained:
Figure BDA0002068778070000061
wherein, K11,…,Kij,…,KnnThe steady state gain of the jth input to the ith output of the boiler drum water level control system is 1, …, n; j is 1, …, n, T11,…,Tij,…,TnnTime constant, tau, for jth input to ith output of boiler drum level control system11,…,τij,…,τnnThe lag time of the jth input to the ith output of the boiler drum level control system is determined.
1.2, the transfer function of the input of the jth object to the output of the ith object in the boiler steam drum water level control system is as follows:
Figure BDA0002068778070000062
1.3 at sampling time TsDiscretizing the step 1.2 under the condition to obtain:
Figure BDA0002068778070000063
where k denotes a time, and d ═ τij/TsInteger part of (a)ij＝e-Ts/Tij，yi(k),yi(k-1) drum levels at time k and time k-1, u, of the ith subsystem, respectivelyi(k-d-1) is the valve opening of the ith subsystem at time k-d-1, uj(k-d-1) is the valve opening of the jth subsystem at time k-d-1,
Figure BDA0002068778070000064
reflecting the influence of other subsystem inputs on the steam drum level of the ith subsystem.
1.4, obtaining the first difference after the discretization model orientation:
Figure BDA0002068778070000065
wherein, Δ yi(k),Δyi(k-1) drum level increments at time k and at time k-1, Δ u, for the ith subsystem, respectivelyi(k-d-1) is the valve opening increment of the ith subsystem at the moment k-d-1, delta uj(k-d-1) is the valve opening increment of the jth subsystem at the moment k-d-1,
Figure BDA0002068778070000071
reflects the influence of other subsystem inputs on the steam drum level of the ith subsystemAnd (4) increasing.
1.5, 1.3 and 1.4; the following can be obtained:
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)＝[Δyi(k),Δui(k-1),…,Δui(k-d)，Δuj(k-1),…,Δuj(k-d)]T，
Δui(k-1),…,Δui(k-d)，Δuj(k-1),…,Δuj(k-d) respectively represents k-1, …, k-d, the increment of valve opening and the increment of steam drum water level at the moment; Δ xi,j(k+1)＝[Δyi(k+1),Δui(k),…,Δui(k-d+1)，Δuj(k),…,Δuj(k-d+1)]T，Δyi(k+1),Δui(k-d+1)，ΔujAnd (k-d +1) respectively represents the drum water level increment of the ith subsystem at the moment of k +1, the valve opening increment of the ith subsystem at the moment of k-d +1 and the valve opening increment of the jth subsystem at the moment of k-d +1, and T represents a transposed symbol of the matrix.
Figure BDA0002068778070000072
Bi,j,m＝[0 1 0 0 0 … 0]T；
Ci,j,m＝[1 0 0 … 0 0 0 0]；
Di,j,m＝[0 … 0 0 1 0 … 0]T；
1.6, according to step 1.5, a non-minimum state space model can be obtained:
zi(k+1)＝Azi(k)+BΔui(k)+DΔuj(k)+CΔri(k+1)
wherein:
Figure BDA0002068778070000073
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)
Figure BDA0002068778070000081
ri(k) reference trajectory for time k, Δ ri(k +1) is the reference track increment at time k +1, ei(k)，eiAnd (k +1) is the error between the system steam drum water level and the reference track at the moment k and k +1 respectively.
Step 2, designing a boiler drum water level control system controller, which comprises the following specific steps:
2.1, according to step 1.6, one can obtain:
Zi＝Gzi(k)+SΔUi,j+ΨΔRi
wherein P represents an optimized time domain, and M represents a control time domain
Figure BDA0002068778070000082
Figure BDA0002068778070000083
ΔUi,j＝[Δui(k) Δui(k+1) … ui(k+M-1),Δuj(k) Δuj(k+1) … Δuj(k+M-1)]T
ΔRi＝[Δri(k+1) Δri(k+2) … Δri(k+P)]T
ri(k+ii)＝λiiyi(k)+(1-λii)ci(k),ii＝1,2,…,P
λ denotes the softening factor, ci(k) Denotes the setting value, Δ r, at the time of the ith subsystem ki(k+1)，Δri(k+2)，…，Δri(k + P) denotes the reference trajectory increment at the time of k + 1.
2.2, taking an ith subsystem objective function:
Ji＝Zi TQi,mZi+ΔUi,j TRi,j,mΔUi,j
wherein Q isi,m＝block diag(Qi,1,Qi,2,…,Qi,P-1,Qi,P)
Figure BDA0002068778070000091
ri,1,…,ri,M,rj,1,…,rj,MWhich respectively represent the values of the reference trajectory at the i, j subsystems from 1.
2.3, from step 2.2:
ΔUi,j＝-(STQi,mS+Ri,j,m)-1STQi,m(Gzi(k)+ΨΔRi)
ui(k)＝[1 0 … 0]ΔUi,j+ui(k-1)
wherein u isi(k)，uiAnd (k-1) respectively represents the valve opening degree at the moment of the ith subsystem k, k-1.
2.4 valve opening increment delta U by using ith subsystemi,jObtaining the actual valve opening u of the ith subsystemi(k)＝[1 0 … 0]ΔUi,j+ui(k-1) operating on the ith subsystem; then, in the same way, the valve opening of the 1 st, the n th subsystems can be determined respectively.

Claims (1)

1. A distributed prediction function control method under a non-minimized state space model comprises the following steps:
step 1, establishing a distributed prediction function numerical control non-minimized state space model;
the step 1 is as follows:
1.1, considering a multivariable N input N output large-scale system in an industrial process as a subsystem consisting of N first-order inertia plus pure hysteresis (FOPDT) models, an N input N output multivariable first-order inertia plus pure hysteresis (FOPDT) model system in the following form can be obtained:
Figure FDA0003247918870000011
wherein, K11,…,Kij,…,KnnA steady state gain for the jth input to the ith output of the multivariable process object, i ═ 1, …, n; j is 1, …, n, T11,…,Tij,…,TnnTime constant, τ, for the jth input to ith output of a multivariable process object11,…,τij,…,τnnA lag time for a jth input to an ith output of the multivariable process object;
1.2, the transfer function of the input of the jth object to the output of the ith object is:
Figure FDA0003247918870000012
1.3 at sampling time TsDiscretizing the step 1.2 under the condition to obtain:
Figure FDA0003247918870000013
where k denotes a time, and d ═ τij/TsThe integer part of (a) is,
Figure FDA0003247918870000015
yi(k),yi(k-1) the output at time k and time k-1, u, of the ith subsystem, respectivelyi(k-d-1) is the input of the ith subsystem at time k-d-1, uj(k-d-1) is the input of the jth subsystem at time k-d-1,
Figure FDA0003247918870000014
reflecting the influence of other subsystem inputs on the ith subsystem output;
1.4, obtaining the first difference after the discretization model orientation:
Figure FDA0003247918870000021
wherein, Δ yi(k),Δyi(k-1) the output increments at time k and k-1, Δ u, for the ith subsystem, respectivelyi(k-d-1) is the input increment of the ith subsystem at time k-d-1, Δ uj(k-d-1) is the input increment of the jth subsystem at time k-d-1,
Figure FDA0003247918870000022
reflecting the influence increment of other subsystem inputs on the ith subsystem output;
1.5, 1.3 and 1.4; the following can be obtained:
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)＝[Δyi(k),Δui(k-1),…,Δui(k-d)，Δuj(k-1),…,Δuj(k-d)]T，Δui(k-1),…,Δui(k-d)，Δuj(k-1),…,Δuj(k-d) represents k-1, …, k-d, input increment at time, output increment, respectively; Δ xi,j(k+1)＝[Δyi(k+1),Δui(k),…,Δui(k-d+1)，Δuj(k),…,Δuj(k-d+1)]T，Δyi(k+1),Δui(k-d+1)，Δuj(k-d +1) represents the output increment of the ith subsystem at the moment of k +1 and the output of the ith subsystem at the moment of k-d +1The input increment and the input increment of the jth subsystem at the moment of k-d +1, wherein T represents a transposed symbol of the matrix;
Figure FDA0003247918870000023
Bi,j,m＝[0 1 0 0 0 … 0]Τ；
Ci,j,m＝[1 0 0 … 0 0 0 0]；
Di,j,m＝[0 … 0 0 1 0 0]Τ；
1.6, according to step 1.5, a non-minimum state space model can be obtained:
zi(k+1)＝Azi(k)+BΔui(k)+DΔuj(k)+CΔri(k+1)
wherein:
Figure FDA0003247918870000031
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)
Figure FDA0003247918870000032
ri(k) reference trajectory for time k, Δ ri(k +1) is the reference track increment at time k +1, ei(k)，ei(k +1) are errors between the system output and the reference track at the moment k and k +1 respectively;
step 2, designing a distributed prediction function control controller under a non-minimized state space model;
the step 2 is as follows:
2.1, according to step 1.6, one can obtain:
Zi＝Gzi(k)+SΔUi,j+ΨΔRi
wherein P represents an optimized time domain, and M represents a control time domain
Figure FDA0003247918870000033
Figure FDA0003247918870000034
ΔUi,j＝[Δui(k) Δui(k+1) … Δui(k+M-1),Δuj(k) Δuj(k+1) … Δuj(k+M-1)]Τ
ΔRi＝[Δri(k+1) Δri(k+2) … Δri(k+P)]Τ
ri(k+ii)＝λiiyi(k)+(1-λii)ci(k),ii＝1,2,…,P
λ denotes the softening factor, ci(k) Denotes the setting value, Δ r, at the time of the ith subsystem ki(k+1)，Δri(k+2)，…，Δri(k + P) represents k +1,.., k + P time reference track increment, respectively;
2.2, taking an ith subsystem objective function:
Ji＝Zi TQi,mZi+ΔUi,j TRi,j,mΔUi,j
wherein Q isi,m＝block diag(Qi,1,Qi,2,…,Qi,P-1,Qi,P)
Figure FDA0003247918870000041
ri,1,…,ri,M,rj,1,…,rj,MRespectively representing the values of the reference track of the ith subsystem and the jth subsystem at the time of 1,.. multidot.k;
2.3, from step 2.2:
ΔUi,j＝-(STQi,mS+Ri,j,m)-1STQi,m(Gzi(k)+ΨΔRi)
ui(k)＝[1 0 … 0]ΔUi,j+ui(k-1)
wherein u isi(k)，ui(k-1) respectively representing the control quantity of the ith subsystem k at the moment k, k-1;
2.4 control increment Δ U with ith subsystemi,jObtaining the actual control quantity u of the ith subsystemi(k)＝[1 0 … 0]ΔUi,j+ui(k-1) operating on the ith subsystem; then, the control quantities of the 1 st, the.
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