CN102023574B - Optimal method for controlling mixed model of first-order reaction continuous stirred tank reactor (CSTR) - Google Patents
Optimal method for controlling mixed model of first-order reaction continuous stirred tank reactor (CSTR) Download PDFInfo
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- CN102023574B CN102023574B CN2010106169566A CN201010616956A CN102023574B CN 102023574 B CN102023574 B CN 102023574B CN 2010106169566 A CN2010106169566 A CN 2010106169566A CN 201010616956 A CN201010616956 A CN 201010616956A CN 102023574 B CN102023574 B CN 102023574B
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Abstract
The invention discloses an optimal method for controlling a mixed model of a first-order reaction continuous stirred tank reactor (CSTR). The method can ensure that the first-order reaction CSTR can rapidly, accurately, stably operate under the following two conditions: a transient process that a system is started and then operates into a certain stable operating point, and a transient process that the system converts into the other stable working point from a certain stable operating point. Compared with the existing first-order reaction CSTR control method, the method provided by the invention has obvious advantages.
Description
Technical field
The present invention relates to a kind of hybrid system model framework optimal control method, relate in particular to a kind of hybrid system model framework optimal control method that is used for first kernel response CSTR (CSTR).
Background technology
Actual first kernel response CSTR demonstrates very strong nonlinear characteristic.Though the nonlinear Control technology had obtained bigger development in the last few years, do not form unified theory and method so far as yet, in industry practice, also fail to obtain good application.Its main cause is following: at first, existing gamma controller method for designing often needs an accurate nonlinear model, is not an easy thing yet obtain accurate nonlinear model; Secondly, even accurate nonlinear model is arranged, also very complicated based on the design of Controller of nonlinear model; In addition, gamma controller also has certain scope of application, in case exceed this scope, control performance will reduce even lose efficacy.Solving one of nonlinear Control problem effective way is multi-model process; Its basic thought is that the whole operation space with system is divided into the plurality of sub zone; Set up a simple local linear model/controller at each subregion then, constitute world model/controller by local linear model/controller at last.
Yet; Scheduling in the multi-model process between a plurality of model/controllers; Be not to be the scheduling of under Unified frame, carrying out; If thereby make and coordinate badly between each partial model/controller that then the control performance of total system just can't guarantee, also possibly cause the shake of output even the instability of total system.Describe if can concentrate on all dynamic perfromances of these subsystems under the united frame; And then the controller of the design overall situation, this will help eliminating the shake that causes when model switches, and alleviate vibration; The robustness of enhanced system, thus control accuracy improved.The theoretical technical support of hybrid system that development in recent years is got up for realizing that such purpose provides, the MPC control method that for example has the scholar to propose based on the MLD model.
The overall MPC controller that on MLD model basis, designs can carry out optimal control in dynamic to system at the multidate information of the whole subsystems of each sampling instant utilization, moves under unified, whole performance index with the assurance system.Yet; The MLD model method is the hybrid system modeling method that is based upon on the logical relation basis, thereby only is applicable to the one type of hybrid system that switches according to state, in addition; Choose the different logical variable and also can cause the not unique of MLD model, and then bring difficulty for modelling verification.
Summary of the invention
The objective of the invention is to the deficiency to prior art, what a kind of first kernel response CSTR was provided mixes the model optimization control method, and the present invention is applicable to the first kernel response process of in CSTR, using coolant temperature control material concentration.
In order to realize above-mentioned purpose, the present invention takes following technical scheme: a kind of hybrid system model framework optimal control method that is used for first kernel response CSTR (CSTR) may further comprise the steps:
(1) first kernel response CSTR device is carried out state space modeling, and confirm the working range and the interior steady operation point of each working range of its operate as normal.
(2) according to the state-space model of first kernel response CSTR, confirm its hybrid system Optimization Model, specifically comprise following two sub-steps:
Near (I) steady operation point in each scope with the state-space model linearization of first kernel response CSTR.
(II) set up its hybrid system Optimization Model according to the inearized model of first kernel response CSTR.
(3) according to the hybrid system Optimization Model, use ILOG CPLEX software to find the solution the control signal parameter, specifically comprise following two sub-steps:
(I) is converted into the accessible form of ILOG CPLEX software with first kernel response CSTR.
(II) found the solution its hybrid system Optimization Model, confirms the control signal parameter.
(4) according to the synthetic control signal of control signal parameter, implement control.
The invention has the beneficial effects as follows, method of the present invention can guarantee first kernel response CSTR under two kinds of situation fast, accurately, stably the operation: from system start-up to stable operation in the transient process of a certain stable operating point; Be transformed into the transient process of another one stable operating point from a certain stable operating point.This method is compared with existing first kernel response CSTR control method, and advantage is especially remarkable.
Description of drawings
Fig. 1 is an application scenarios first kernel response CSTR synoptic diagram of the present invention, wherein,
C AfFor the substance A input concentration,
T 0For feeding temperature,
qFeed rate,
C AConcentration when carrying out chemical reaction for substance A,
TFor temperature of reactor,
q cFor coolant rate,
T CfBe coolant rate.
Fig. 2 is the discretization method synoptic diagram that uses among the present invention.
Fig. 3 is the analogous diagram (transition between the steady operation point) that multi-model soft handover control method and the method for the invention are controlled first kernel response CSTR respectively, among the figure, and [Y
*, U
*] be patent describing method gained curve of the present invention, [Y
Sf, U
Sf] be multi-model soft handover control method gained curve.
Fig. 4 is the analogous diagram (transient process that CSTR starts) that multi-model soft handover control method and the method for the invention are controlled first kernel response CSTR respectively, among the figure, and [Y
*, U
*] be patent describing method gained curve of the present invention, [Y
Sf, U
Sf] be multi-model soft handover control method gained curve.
Embodiment
For overcoming the shortcoming of traditional multi-model control and the control of MLD model, the present invention proposes a kind of based on the NLS optimal control method that mixes model framework in addition.One aspect of the present invention has kept employing and has mixed the advantage that model framework synthesizes the some linear subsystems of NLS; Make all dynamic perfromances of subsystem concentrate under the united frame and describe that the assurance system moves under unified, whole performance index.On the other hand, the present invention adopts total space discretization method, not only can be applicable to the hybrid system that switches according to state; And can be applicable to the hybrid system that switches according to the time; In addition, confirm that the model of setting up like this that mixes is unique because the binary variable choosing method is unique.At first, utilization mixes model framework NLS is synthesized at the resulting some linear subsystems of different operating point linearization, sets up the optimal control proposition under the Unified frame; Then, introduce binary variable, the resulting model that mixes is carried out discretize, be converted into MINLP to resulting optimal control proposition and find the solution in the total space.When total space discretize, this paper adopts finite element orthogonal configuration method to reduce the dimension of gained MINLP, reduces with this and finds the solution complicacy.At last, introduce auxiliary variable and replace continuous variable and the product of binary variable in the MINLP constraint condition, MINLP is converted into MIQP finds the solution.In addition, the present invention adopts the rolling optimization strategy to remedy the model mismatch that discretize is brought.
Patent of the present invention is applied to the transient process of conversion between startup transient process and the steady operation point of first kernel response CSTR, uses based on the optimal control method that mixes model framework.The principle that mixes the model framework optimal control is: the state-space model of CSTR in its each steady operation point linearization, as the mode of hybrid system, and then is set up the hybrid system model of CSTR; Confirm the performance index of CSTR operate as normal, assign a topic in conjunction with the model framework optimal control that mixes of its hybrid system modelling CSTR; Use is converted into the planning of MIXED INTEGER quadratic form based on the discretization method of finite element configuration with the optimal control proposition; Use the rolling optimization strategy that CSTR is controlled after obtaining control signal, make CSTR according to predetermined scheme operation.
Patent of the present invention is applied to the transient process of conversion between startup transient process and the steady operation point of first kernel response CSTR.First kernel response CSTR carries out first kernel response in CSTR, promptly in CSTR, add certain material A, and behind the entering CSTR, chemical reaction product matter B takes place A, and reaches the process of chemical equilibrium.Styrene bulk thermal polymerization process for example, preceding two steps of propylene polymerization (in totally three steps, preceding two steps carry out in CSTR, and are first kernel responses) or the like.For this type reaction, behind the selected CSTR device, the form of state-space model is fixed, and the Model parameter value is provided by chemical machinery slip-stick artist and chemical process slip-stick artist with the span of the variable of waiting to make a strategic decision.
The present invention is used for the hybrid system model framework optimal control method of first kernel response CSTR, may further comprise the steps:
1, the device of first kernel response CSTR shown in the accompanying drawing 1 is carried out state space modeling, and confirm the working range and the interior steady operation point of each working range of its operate as normal.
So-called first kernel response promptly adds certain material A in CSTR, behind the entering CSTR, chemical reaction product matter B takes place A, and reaches the process of chemical equilibrium.Styrene bulk thermal polymerization process for example, preceding two steps of propylene polymerization (in totally three steps, preceding two steps carry out in CSTR, and are first kernel responses) or the like.Shown in accompanying drawing 1.The state-space model of setting up first kernel response CSTR is as follows:
Wherein,
Be the concentration of substance A
C A, also be output variable simultaneously;
It is the CSTR temperature
T yIt is output variable; U is a coolant temperature
T Cf, be control variable; All variablees all are dimensionless groups, and value does
Rest parameter all is the chemical reaction preset parameter; General value is:
;
;
, and
.
Specific reaction, working range and steady operation point are provided by the chemical process slip-stick artist.This first kernel response CSTR has 3 working range Ω
1=[0,0.35), Ω
2=[0.35,0.78), Ω
3There is a steady operation point=[0.78,1] in each working range, when
x 1During ∈ [0.78,1], its steady operation point does
Xs 1=[
x 1 , x 2]
T =[0.856,0.886]
T , when
x 1During ∈ [0.35,0.78], its steady operation point does
Xs 2=[
x 1 , x 2]
T =[0.5528,0.7517]
T , when
x 1During ∈ [0,0.35], its steady operation point does
Xs 3=[
x 1 , x 2]
T =[0.2353,0.705]
T
2,, confirm its hybrid system Optimization Model according to the state-space model of first kernel response CSTR.
Near (I) steady operation point in each scope with the state-space model linearization of first kernel response CSTR.
3 the working point linearizations of state-space model in 3 working ranges with first kernel response CSTR obtain 3 linearization state-space model groups, and are as follows:
Formula (2) has 3 continuous lines sexual state system of equations, when
y∈ Ω
1The time, the 1st continuous lines sexual state equation is in running order, and corresponding opereating specification is Ω
1=[0,0.35).3 continuous lines sexual state equations can be regarded 3 mode of hybrid system as; When 0≤
Y<0.35 the time, the 1st state equation is in running order, and other state equation is in off working state, then
Y<0.35 can be called the discrete event of hybrid system, and the switching of system works mode is the result of this discrete event effect;
yValue determined that which continuous lines sexual state equation is in running order, show as the influence of discrete event to continuous system, the evolution of each continuous lines sexual state equation does again
yEvolution created condition, show as the influence of continuous system to discrete event.Therefore, it is approximate that (2) formula can be described as first kernel response CSTR shown in the formula (1) under the hybrid system model framework, and each continuous lines sexual state equation can be described as a mode of this hybrid system model.
(II) set up its hybrid system Optimization Model according to the inearized model of first kernel response CSTR.
Set up first kernel response CSTR hybrid system Optimization Model.The controlled target of first kernel response CSTR is to make CSTR fast, accurately and stably carry out the transition to dbjective state from original state, therefore, uses following objective function:
Wherein,
Q 1=1,
Q 2=0.95,
Q 3=0.85.Then first kernel response CSTR hybrid system Optimization Model is:
(3), use ILOG CPLEX software to find the solution the control signal parameter according to the hybrid system Optimization Model.
(I) is converted into the accessible form of ILOG CPLEX software with first kernel response CSTR.
Hybrid system Optimization Model (4) is converted into the accessible form of ILOG CPLEX.Take the discretization method shown in the accompanying drawing 2, the hybrid system optimal control of former NLS is assigned a topic is converted into the MIQP problem, and concrete grammar is following:
The time domain [0,10] of first kernel response CSTR operation is divided into 10 sections, and each section is called a finite element, and each finite element length is 1.Introduce 3 binary variables in each finite element
y 1,
y 2,
y 33 mode of difference corresponding (2).In each finite element, there is and have only a mode to be in state of activation.For improving solving precision; Be unlikely to introduce a large amount of decision variable constraints again; Insert three collocation points in each finite element, with Radau collocation method processing target function and state equation, with state variable and the control variable on approximate each finite element of second order Lagrange interpolation polynomial.In the middle of process industrial, therefore state variable must, must add to guarantee successional linear equality constraints between the finite element boundary state variable constantly continuously.Through after the finite element orthogonal configuration shown in Figure 2, formula (4) can be converted into the expressed MIXED INTEGER quadratic form planning (MIQP) of formula (5): formula (5) as follows:
J?≈?∑
ne i=1
∑
3 j=1
Coe j [
Q 1 （x i,j -x e ）
2+
?Q 2 u i,j 2]
s.t.?∑
3 k=1
l k （
τ j ）
x i,k -?
h∑
M m=1
（
A m z 1 i,m +B m z 2 i,m ?+d j ?y i,m ）?=0
∑
M m=1
y i,m =1
l 1（1）
x i,0
+
l 2（1）
x i,1
+
l 3（1）
x i,2
-
x i+1
,0
=0
x i,j -
θ 2 y i,1
-
θ 3 y i,2
-…-
θ M+1
y i,M ≤0
-x i,j +
θ 1 y i,1
+
θ 2 y i,2
+…+
θ M y i,M ≤0
-
θ M+1
y i,m +
z 1 i,m ≤0
θ 1 y i,m -
z 1 i,m ≤0
-
x i,j -
θ 1 y i,m +
z 1 i,m ≤-
θ 1
x i,j ?+
θ M+1
y i,m -
z 1 i,m ≤
θ M+1
-
?cy i,m +
z 2 i,m ≤0
b?y i,m -
z 2 i,m ≤0
-
u i,j -
?b?y i,m +
z 2 i,m ≤-
?b
u i,j +
?c?y i,m -
z 2 i,m ≤
c
θ 1≤
x i,j ≤
θ M+1
,?
b≤
u i,j ≤
c
The implication and the numerical value of each unknown quantity are as follows in the formula (5):
z 1 i,m =?x i,j ?y i,m ，
z 2 i,m =u i,j ?y i,m ?Q 1=1.0，
Q 2=0.95，
Q 3=0.85，
Coe 1=?1.024972，
Coe 2=?0.752806，
Coe 3=?0.222222，
n e =10，
M=3，
τ 1=?0.155051
，
τ 2=?0.844949，
τ 3=1，
，
θ 1=0，
θ 2=0.35，
θ 3=0.78，
θ 4=1，
b=-2，
c=2，
B 1=[0,0.3]
T，
B 2=[0,0.3]
T，
B 3=[0,0.3]
T，
A 1=
，
A 2=
，
A 3=
。
Transform the numerical solution of separating the formula of being (4) of the represented MIQP of back formula (5).
(II) found the solution its hybrid system Optimization Model, confirms the control signal parameter.
According to ILOG CPLEX software operation instructions, find the solution formula (5) with the cplexmiqp in the software, what obtain formula (5) waits that the variable of making a strategic decision is as follows:
The state variable parameter:
x 1
,1
,
x 1
,2
,
x 1
,3
,
x 2
,1
,
x 10
,1
,
x 10
,2
,
x 10
,3
The control signal parameter:
u 1
,1
,
u 1
,2
,
u 1
,3
,
u 2
,1
,
u 10
,1
,
u 10
,2
,
u 10
,3
Binary variable:
y 1
,1
,
y 1
,2
,
y 1
,3
,
y 2
,1
,
y 10
,1
,
y 10
,2
,
y 10
,3
State variable parameter, binary variable and auxiliary variable do not have practical significance to implementing control method, and auxiliary variable is no longer listed at this.
4, according to the synthetic control signal of control signal parameter, implement control.
Use the synthetic control signal of gained control signal parameter, method is following:
Give up
u 2
,1
,
u 2
,2
,
u 2
,3
,
u 3
,1
,
u 10
,1
,
u 10
,2
,
u 10
,3
, use
u 1
,1
,
u 1
,2
,
u 1
,3
Synthesize control signal according to following mode:
Wherein,
t 1=0.155051,
t 2=0.844949,
t 3=1.On time domain [0,1], control signal does
u(
t).
With the control signal on the time domain [0,1]
u(
t) use D/A converter output by computing machine, and be converted into industry standard signal (4 ~ 20mA), be applied on the hot water valve in the accompanying drawing 1, change coolant temperature through regulating hot water flow, reach the purpose of control substance A concentration.
Work as the time
t=1 o'clock, control signal
u(
t) ineffective.With
t=1 o'clock substance A concentration and temperature of reactor
TBe original state, (II) in the repeating step (3) and step (4) can obtain the control signal on the time domain [0,1]
u ' (
t), but at this moment
t=1, therefore, control signal
u ' (
t) effect time domain be [1,2].Work as the time
t=2 o'clock, control signal
u ' (
t) ineffective, repeat above step.(II) and step (4) in the continuous like this repeating step (3) just can make first kernel response CSTR move according to schedule.The method that applies control like this is called the rolling optimization method.Rolling optimization is the optimization of a kind of limited period, and the relative form of at every turn optimizing performance index is identical, but its absolute form is different, and the time domain that is promptly comprised is passed forward.Through on-line optimization repeatedly, can reach the purpose that remedies model mismatch, this is that traditional multi-model control method can't be accomplished.
Like accompanying drawing 3 and shown in Figure 4, [Y
*, U
*] be patent gained curve of the present invention, [Y
Sf, U
Sf] be traditional multi-model control method gained curve, [Y
*, U
*] control signal with respect to [Y
Sf, U
Sf] change comparatively slowly, more help actuator tracking control signal exactly, on the contrary,, then be unfavorable for the tracking of actuator if the control signal vibration is too violent.
Rolling optimization is the optimization of a kind of limited period, and the relative form of at every turn optimizing performance index is identical, but its absolute form is different, and the time domain that is promptly comprised is passed forward.Through on-line optimization repeatedly, can reach the purpose that remedies model mismatch, this is that traditional multi-model control method can not be accomplished.
Claims (3)
1. a hybrid system model framework optimal control method that is used for first kernel response CSTR (CSTR) is characterized in that, may further comprise the steps:
(1) first kernel response CSTR device is carried out state space modeling, and confirm the working range and the interior steady operation point of each working range of its operate as normal;
(2), confirm its hybrid system Optimization Model according to the state-space model of first kernel response CSTR;
(3), find the solution the control signal parameter according to the hybrid system Optimization Model;
(4) according to the synthetic control signal of control signal parameter, implement control;
Wherein, in the said step (1), the state-space model of the first kernel response CSTR of foundation is shown below:
Wherein,
Be the concentration of substance A
C A, also be output variable simultaneously;
It is the CSTR temperature
T yIt is output variable; U is a coolant temperature
T Cf, be control variable; All variablees all are dimensionless groups, and value does
Rest parameter all is the chemical reaction preset parameter, and general value is:
,
,
, and
This first kernel response CSTR has 3 working range Ω
1=[0,0.35), Ω
2=[0.35,0.78), Ω
3There is a steady operation point=[0.78,1] in each working range, when
x 1During ∈ [0.78,1], its steady operation point does
Xs 1=[
x 1 , x 2]
T =[0.856,0.886]
T , when
x 1During ∈ [0.35,0.78], its steady operation point does
Xs 2=[
x 1 , x 2]
T =[0.5528,0.7517]
T , when
x 1During ∈ [0,0.35], its steady operation point does
Xs 3=[
x 1 , x 2]
T =[0.2353,0.705]
T
According to the said first kernel response CSTR of claim 1 mix the model optimization control method, it is characterized in that said step (2) specifically comprises following two sub-steps:
(A) near the steady operation point in each scope with the state-space model linearization of first kernel response CSTR;
(B), set up its hybrid system Optimization Model according to the inearized model of first kernel response CSTR.
According to the said first kernel response CSTR of claim 1 mix the model optimization control method, it is characterized in that said step (3) specifically comprises following two sub-steps:
(a) first kernel response CSTR is converted into the accessible form of ILOG CPLEX software;
(b) find the solution its hybrid system Optimization Model, confirm the control signal parameter.
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| CN103324086B (en) * | 2013-06-08 | 2016-01-20 | 浙江大学 | A kind of batch reactor control system based on accurately punishment optimization |
| CN103309234B (en) * | 2013-06-08 | 2015-12-09 | 浙江大学 | A kind of batch reactor control system optimized based on orthogonal configuration |
| CN103995469A (en) * | 2014-05-30 | 2014-08-20 | 河海大学 | Method for designing controller of non-minimum-phase constant-temperature continuous stirred tank reactor |
| CN104035336B (en) * | 2014-05-30 | 2017-01-11 | 河海大学 | Method for designing non-linear controller of MIMO non-minimum phase CSTR |
| CN104950670B (en) * | 2015-06-10 | 2017-06-23 | 浙江大学 | A kind of integrated Multiple Model Control Method of CSTR |
| CN105893654B (en) * | 2016-03-11 | 2018-10-26 | 中南大学 | A kind of Robust Predictive Control method of single order continuous stirred tank reactor |
| CN106126784A (en) * | 2016-06-16 | 2016-11-16 | 上海电机学院 | A kind of Optimized model of continuous stirred tank reactor |
| CN109870908A (en) * | 2019-02-27 | 2019-06-11 | 南京理工大学 | A kind of sampling control method for continuous stirred tank reactor system |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101626825A (en) * | 2007-03-08 | 2010-01-13 | 伊士曼化工公司 | Polyester production system employing an unagitated esterification reactor |
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-
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- 2010-12-31 CN CN2010106169566A patent/CN102023574B/en not_active Expired - Fee Related
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101626825A (en) * | 2007-03-08 | 2010-01-13 | 伊士曼化工公司 | Polyester production system employing an unagitated esterification reactor |
Non-Patent Citations (3)
| Title |
|---|
| 李晓理等.《连续搅拌釜的模糊多模型自适应控制》.《系统仿真学报》.2009,第21卷(第7期),全文. * |
| 杜静静等.基于MLD模型的CSTR建模和控制(英文).《Chinese Journal of Chemical Engineering》.2007,(第04期),说明书第2部分-第6部分. * |
| 陈申等.CSTR的非线性自适应控制.《信息与控制》.1992,第21卷(第2期),全文. * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102999704A (en) * | 2012-12-03 | 2013-03-27 | 复旦大学 | Method for predicting free radical polymerization in continuous stirring kettle type reactor through Monte Carlo simulation |
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