CN105893654A - Robust predictive control method for first-order continuous stirred tank reactor (CSTR) - Google Patents
Robust predictive control method for first-order continuous stirred tank reactor (CSTR) Download PDFInfo
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Abstract
The invention discloses a robust predictive control method for a first-order continuous stirred tank reactor (CSTR). The method comprises the following steps: building a dynamic mathematical model of a non-linear CSTR system off line through a modeling method of a nonlinear state-dependent ARX model; secondly, constructing a non-linear dynamic variable linear polyhedral model capable of packing the CSTR system by using the structural features of the non-linear ARX model and change information of future non-linear dynamic features of the system contained in the model; and lastly, designing a CSTR system robust predictive control algorithm which is based on the non-linear ARX model, considers the robust stability of a CSTR system restraint, has good control performance and can realize optimal output tracking by resolving a convex optimization problem according to a min-max optimization principle based on an invariant set design method under the situation that steady-state balance point information of the CSTR system is unknown.
Description
Technical field
The invention belongs to automatic control technology field, relate to a kind of Robust Prediction control based on the modelling of Nonlinear A RX
Method processed, particularly relates to a kind of Robust Predictive Control method for single order CSTR (CSTR).
Background technology
CSTR (Continuous Stirred Tank Reactor, referred to as CSTR) is a kind of
Common nonlinear chemical reaction device, owing to its heat-exchange capacity is strong, the advantage such as constant product quality and low cost, raw at chemical industry
The nucleus equipment produced occupies critical role, is widely used in the commercial production such as dyestuff, pharmaceutical reagent, food and synthetic material
In.The control variable of CSTR system mainly includes the temperature of reactant, concentration etc., to the control effect of these variablees by direct shadow
Ring the quality of production to chemical products.
In the past few decades, it is quite ripe that Prediction and Control Technology based on linear model has developed, but the work of reality
Industry process object is not necessarily all suitable as linear system and designs to be controlled device, and such as CSTR system, rectifying tower system etc. are multiple
Miscellaneous process object, working range is big, and set point change is big, presents the strongest nonlinear characteristic.For this kind of strong nonlinearity
Work process, unless the parameter tuning of linear regulator obtains the most conservative, otherwise Control platform will significantly deteriorate.Given this, for
Most non-linear chemical process, it is necessary to use nonlinear prediction method.For first kernel response CSTR system, present is strong
Nonlinear characteristic, current Nonlinear Predictive Control there has also been many achievements.In nonlinear prediction method, typically use
Nonlinear model predicts the output that first kernel response CSTR process is following, in each sampling instant, non-linear by line solver
Input quantity, quantity of state and the output of CSTR process are retrained by planning problem.But, should at actual industrial CSTR
In with, this kind of control algolithm yet suffers from some distinct disadvantage.On the one hand, actual industrial CSTR object be typically multivariate,
Close coupling, time-varying, the complex nonlinear processes of constraint, the accurate mathematical model of these complication systems is difficult to obtain；On the other hand,
This kind of algorithm the most not yet solves the problems such as such as control system convergence, robustness and closed-loop system stability.Although
Nonlinear Predictive Control achieves bigger development in recent years, but the most not yet forms a kind of unification, effective
Theory and method, industry CSTR system actual application in also fail to obtain good effect.Therefore, for complicated non-thread
Property the modeling of industry CSTR process accurate mathematical complexity, and the stability of systematic control algorithm, robust in actual applications
Property etc. problem, a kind of nonlinear system modeling systematic, attainable and control method become problem demanding prompt solution.
Through the literature search of prior art is found, the modeling for non-linear CSTR system currently mainly and controlling party
Method has: " assembly Predictive Control System based on Model Predictive Control and control method thereof " (application number: 200910197512.0),
" the hybrid model optimal control method of first kernel response CSTR " (application number: 201010616956.6),
" there is the moving horizon estimation method of multi-speed sample CSTR " (application number: 201310311184.9),
" the integrated Multiple Model Control Method of a kind of CSTR " (application number: 201510315584.6).Above-mentioned master
The technical characterstic wanting patent of invention is: the system dynamics shape set up on the basis of being all based on the mechanism model of non-linear CSTR system
State space model, particularly noteworthy: foregoing invention technology is all the state in known or given non-linear CSTR system
The modeling carried out on the premise of homeostasis dot information and controller design.Up to the present, great majority are for CSTR system
Non-linear predication control method is the nonlinear system shape of design under the hypothesis of the homeostasis dot information of known CSTR system
State is followed the tracks of or output tracking algorithm.But, because inevitably there is immeasurable disturbance in the non-linear CSTR system of actual industrial
Or modeling error etc., the homeostasis dot information of its system is unknown or immesurable.Therefore, for this kind of system balancing point
The output tracking Robust Predictive Control algorithm of the non-linear CSTR system under information the unknown premise is only in actual control and needs to be solved
Subject matter certainly.
Summary of the invention
It is an object of the invention to, for the deficiency in above-mentioned background technology, it is proposed that a kind of single order continuous stirring autoclave is anti-
Answering the Robust Predictive Control method based on the modelling of Nonlinear A RX of device (CSTR), the method utilizes Nonlinear A RX model
The Parameters variation information that construction features and model contain, constructs that can to wrap up single order continuous CSTR mission nonlinear dynamic
Variable linear polyhedral model, in the case of unknown single order continuous CSTR systematic steady state equilibrium point information, designs non-based on this
The robust stability of linear ARX model, realize the Robust Predictive Control algorithm of Optimal Output Tracking.
For solving above-mentioned technical problem, the technical solution adopted in the present invention is: a kind of single order continuous stirring autoclave reaction
The Robust Predictive Control method of device, it is characterised in that comprise the following steps:
1) first kernel response CSTR system off-line is set up the nonlinear state interdependent ARX model knot of descriptive system dynamic characteristic
Structure is as follows:
Wherein:For depending on state
The Gauss Nonlinear A RX coefficient of amount w (t)；ξ (t+1) is white Gaussian noise；State vector w (t)=[Tr(t)T Tr(t-1)T]T,
Tr(t)TOutput for t system；{zj,λj| j=TrOr TcIt is center vector and the zoom factor of RBF neural； Transposition for constant coefficient；X be x be 2 norms； It it is the corresponding weight coefficient of Gauss neural networks；
Nonlinear parameter { zj,λj| j=TrOr TcAnd linear dimensionsAll by SNPOM optimization method offline optimization meter
Obtain；
2) the Parameters variation information structure that construction features based on the interdependent ARX model of above-mentioned nonlinear state and model contain
Produce a kind of variable linear polyhedral model that can wrap up Nonlinear Dynamic；Particularly as follows:
The Nonlinear A RX model conversion describing first kernel response CSTR system is become following polynomial construction:
The desired output of definition first kernel response CSTR system isIt is defined as follows deviation variables simultaneously:
Wherein: Tc(t+j) it is the control input quantity in t+j moment；Tc(t+j-1) it is the control input quantity in t+j-1 moment；Tr
(t+i) it is the control output in t+i moment；Control for the t+j moment inputs increment；Control for the t+i moment
Output bias processed；Desired output for t system；The output bias of a step forward prediction is obtained by above formula
As follows:
Wherein:Meansigma methods for the modeling error ξ (t+1 | t) of Nonlinear A RX model；ξ(t+1|t)；
Two state-space models of descriptive system current behavior X (t+1 | t) obtained and behavior X in future (t+g+1 | t)
Structure is as follows:
Wherein, coefficient matrices At,Bt, Ξ (t) and X (t | t) it is the detectable parameter of t and state respectively；Following unknown
State matrix [At+g|t,Bt+g|t] by State-Dependent coefficient constant a1,t+g|tAnd b1,t+g|tConstitute, at t coefficient constant a1,t+g|t
And b1,t+g|tOccurrence unknown, but coefficient constant a can be obtained according to the above-mentioned derivation of equation1,t+g|tAnd b1,t+g|tBy Gaussian bases
Network is constituted, it may thus be appreciated that the bound of its constant, obtains unknown state matrix [A furthert+g|t,Bt+g|t] can be by following two
Individual convex linear polyhedron dynamically wraps up:
Wherein:For polyhedron time-varying linear coefficient, and Polyhedron summit is Al(A1,A2) and Bk(B1,B2), wherein: matrix Al=A1Or A2:
The A as l=1l=A1, the A as l=2l=A2, in like manner matrix Bk=B1Or B2: the B as k=1k=B1, the B as k=2k=B2。
Al, BkIn each element bound information of State-Dependent function type coefficient from mission nonlinear ARX model calculate:
Wherein:For the corresponding weight coefficient of Gauss neural networks, by SNPOM side
Method optimization obtains；For the function about variable w (t)Higher limit,For about variable w (t)
FunctionLower limit；For about variable w
The function of (t)Higher limit,For about change
The function of amount w (t)Lower limit.
3) based on above-mentioned structure, CSTR mission nonlinear dynamic variable linear polyhedral model can be wrapped up, utilize
The min-max principle of optimality, based on invariant set method for designing, in the case of unknown CSTR systematic steady state equilibrium point information, design
Based on this Nonlinear A RX model can by solve convex optimization problem realize Optimal Output Tracking Robust Predictive Control method:
Wherein: symbol * represents the symmetrical structure of matrix；W=1, R=0.2； Z is a symmetrical matrix；F (t)=YG-1For feedback gain matrix；Qlk, Qαβ, wherein l, k, α, β=1 or
2, for solving the intermediary matrix variable of convex optimization problem；In above-mentioned LMI, coefficient matrices At,BtWhen being t with Ξ (t)
Carve the parameter matrix recorded；X (t | t) is the state vector that t has recorded；Y,G,Qlk, Z andIt is and minimizes
Intermediate variable in variable γ solution procedure, is solving minimization problemTime, majorized function can according to above-mentioned about
Bundle condition Automatic-searching meets the intermediate variable Y minimum for γ made, G, Qlk, Z andWhether exist, in finding suitably
Between variable Y, G, Qlk, Z andTime, then t minimizes Optimization Solution process and terminates.In t, by solving above-mentioned line
Property MATRIX INEQUALITIES convex optimization problem obtain optimal control increment inputThe controlled quentity controlled variable of the corresponding system that acts on is defeated
Enter forThus, by regulation coolant temperature T in real timecT (), reaches system output-response device
Reaction temperature TrT () follows the tracks of given target trajectory.
Compared with prior art, the present invention is had the beneficial effect that
Up to the present, great majority are steady in known CSTR system for the non-linear predication control methods of CSTR system
The lower design of hypothesis of state equilibrium point information.Additionally, this type of is based on predictive control algorithm known to homeostasis dot information not
It is applicable to the steady state equilibrium point continually varying situation of system.But, the non-linear CSTR system of actual industrial, because of inevitable
Existence immeasurable disturbance or modeling error etc., the homeostasis dot information of its system is unknown or immesurable or becomes continuously
Change.Therefore, for the output tracking Robust Prediction of the non-linear CSTR system under this kind of system balancing dot information the unknown premise
Control algolithm is only in actual control subject matter to be solved.The structure of patent utilization Nonlinear A RX model of the present invention is special
The change information of the system non-linear dynamic characteristic in future that point and model contain, is configured to wrap up CSTR mission nonlinear
Dynamic variable linear polyhedral model, utilizes the min-max principle of optimality, based on invariant set method for designing, in unknown CSTR system
In the case of system homeostasis dot information, design robust based on this Nonlinear A RX model, that consider CSTR system restriction steady
Determine, control performance is good, can realize the Robust Predictive Control algorithm of Optimal Output Tracking by solving convex optimization problem.
Accompanying drawing explanation
Fig. 1 is the first kernel response CSTR systematic difference scene schematic diagram that patent of the present invention relates to.
Detailed description of the invention
First kernel response CSTR systematic difference scene schematic diagram of the present invention is as shown in Figure 1.In first kernel response CSTR system
Heat release, irreversible reaction occur in system, and reactant is A, product is B, and reaction raw materials A enters reaction with stable flow velocity
Device, the reaction mass of reactor is with same stable flow velocity outflow reactor.Phase in first kernel response CSTR system as shown in Figure l
Related parameter and value be: in reactor, the concentration of component A is CA, reactor reaction temperature is Tr, coolant temperature is Tc, reaction
Thing A input concentration is CAf=1mol/L, feed rate is Qf=100L/min, feeding temperature is Tf=350K, reactor volume
For V=100L, specific heat is Cp=0.239J/g K, heat-transmission coefficient is UA with the product of reactor surface areah=5 × 104J/
(min·k).In first kernel response CSTR system of the present invention, the control input of system is coolant temperature Tc, control to be output as
Reactor reaction temperature Tr, by regulation coolant temperature T in real timec, reach system output-response device reaction temperature TrFollow the tracks of given
Target trajectory.
The Shandong based on the modelling of Nonlinear A RX of a kind of single order CSTR (CSTR) of the present invention
Rod forecast Control Algorithm: first, utilizes the identification technology of data-driven, uses a kind of interdependent ARX model of nonlinear state
Modeling method, off-line sets up the dynamic mathematical models of non-linear CSTR system.Secondly, nonlinear state interdependent ARX mould is utilized
The Parameters variation information structuring that the construction features of type and model contain goes out a kind of variable linear that can wrap up Nonlinear Dynamic
Polyhedral model.Finally, in the case of unknown system homeostasis dot information, design robust based on Nonlinear A RX model
Stablize, control performance is good, can realize the Robust Predictive Control algorithm of Optimal Output Tracking by solving convex optimization problem.
Robust Predictive Control its feature of method based on the modelling of Nonlinear A RX of a kind of first kernel response CSTR system exists
In, the method comprises the following steps:
1) the dynamic modeling data of first kernel response CSTR system are gathered
Control input coolant temperature T according to first kernel response CSTR systemcWith control output-response device reaction temperature TrIt
Between relation, it is thus achieved that the Identification Data of response system dynamic characteristic.Control output in t first kernel response CSTR system is
Reactor reaction temperature TrT (), the input quantity of corresponding t is coolant temperature Tc(t).Gather first kernel response CSTR system
Inputoutput data 2500 point, the sampling time is 25min, and the sampling period is 0.01min.It is applicable to identification system non-linear
The dynamic modeling data of ARX mathematical model should be the various mode fully exciting first kernel response CSTR system in its effective range
Data with dynamic characteristic.
2) using the modeling method of the interdependent ARX model of a kind of nonlinear state, off-line sets up the dynamic of non-linear CSTR system
State mathematical model
In step 1) obtain on the basis of system identification data, use a kind of Nonlinear A RX modeling method, off-line builds one
The dynamic mathematical models of rank reaction CSTR system.A kind of Nonlinear A RX number describing first kernel response CSTR system of the present invention
Model structure is as follows:
First kernel response CSTR system off-line is set up the nonlinear state interdependent ARX model structure of descriptive system dynamic characteristic
As follows:
Wherein:For depending on state
The Gauss Nonlinear A RX coefficient of amount w (t)；ξ (t+1) is white Gaussian noise；State vector w (t)=[Tr(t)T Tr(t-1)T]T,
Tr(t)TOutput for t system；{zj,λj| j=TrOr TcIt is center vector and the zoom factor of RBF neural；Transposition for constant coefficient；X is 2 norms；It it is the corresponding weight coefficient of Gauss neural networks；Non-
Linear dimensions { zj,λj| j=TrOr TcAnd linear dimensions All it is calculated by SNPOM optimization method offline optimization and (refers to: Peng H, Ozaki
T, Haggan-Ozaki V, Toyoda Y.2003, A parameter optimization method for the radial
Basis function type models), such as: linear dimensions Non-thread
Property parameter
3) foundation can wrap up the variable linear polyhedral model of first kernel response CSTR mission nonlinear dynamic characteristic
In order to set up the variable linear polyhedral model that can wrap up first kernel response CSTR mission nonlinear dynamic characteristic, first
First the Nonlinear A RX model conversion of formula (1) structure describing first kernel response CSTR system is become following polynomial construction:
The desired output of definition first kernel response CSTR system isIt is defined as follows deviation variables simultaneously:
Wherein: Tc(t+j) it is the control input quantity in t+j moment；Tc(t+j-1) it is the control input quantity in t+j-1 moment；Tr
(t+i) it is the control output in t+i moment；Control for the t+j moment inputs increment；Moment
Control output bias；Desired output for t system.
Output bias by the available step forward prediction of formula (2) and formula (3)As follows:
Wherein:For the modeling error meansigma methods of Nonlinear A RX model (2), can pass through to control in real time in system
During historical sample mean value calculation is obtained.The ψ defined such as formula (5)tThe absolute value of variable | ψt|, it is regarded as controlling
Whether system enters the index of stable equilibrium point, because working as | ψt| during equal to zero, now system input quantity { Tc(t) } it is controlled quentity controlled variable
Input optimum, output { Tr(t) } it is also stabilized in desired outputOn.By above-mentioned ψtDefinition and formula (4) can root
The following nonlinear characteristic of lower linear time-varying model (6) approximation first kernel response CSTR system according to this, simultaneously by designing one group
Good system controlling increment inputMake to meet | ψt+j|t| equal to zero, come specification system
The optimum following dynamic characteristic track of system output increment is as follows:
Wherein:
By formula (2) it can be seen that because the quantity of state following in t cannot obtain, and then the coefficient matrix in formula (6)
ak,t+jAnd bk,t+jAlso cannot accurately obtain.But according to the available following coefficient square of feature knowable to model parameter up-and-down boundary
Battle array ak,t+jAnd bk,t+jExcursion, thus construct the variable linear polyhedron mould that can wrap up object Nonlinear Dynamic
Type.
First following system mode is defined vectorial:
Can get two state skies that matrix polynomial model (4) is the most corresponding with (6) by defining above-mentioned state vector
Between model structure as follows:
With
System mode vector X in above-mentioned formula (9) (t | t), Ξ (t) and state matrix [At,Bt] all can obtain in off-line identification
Formula (5) is passed through on the basis of the mission nonlinear ARX model (2) arrived, and (8) and (9) are derived from.Meanwhile, according to non-thread
Property ARX model (2) and model (10), it can be deduced that to-be matrix [At+j|t,Bt+j|t] scope of (j >=1), can be by such as
Lower two convex linear polyhedrons dynamically wrap up:
Wherein:For polyhedron time-varying linear coefficient, and Polyhedron summit is Al(A1,A2) and Bk(B1,B2), wherein: matrix Al=A1Or A2:
The A as l=1l=A1, the A as l=2l=A2, in like manner matrix Bk=B1Or B2: the B as k=1k=B1, the B as k=2k=B2。
Al, BkIn each element bound information of State-Dependent function type coefficient from mission nonlinear ARX model calculate:
In sum, it is thus achieved that local linear state-space model (9) be used for representing the current behavior of nonlinear system, be
System non-linear behavior in the future is then dynamically wrapped up by the convex polyhedron model (10) of a linear dimensions time-varying, wherein dynamic matrix
At+j|tBelong to convex polyhedron Ω shown in formula (11)A, dynamic matrix Bt+j|tBelong to convex polyhedron Ω shown in formula (12)B.During based on this
Time-varying Linear Systems polyhedral model, can design and obtain optimum control by the linear programming problem solving the constraint of band LMI
The Robust Predictive Control device of amount processed.
4) output tracking under a kind of feasible system equilibrium point information unknown situation based on the modelling of Nonlinear A RX
Robust Predictive Control algorithm.
Based on step 3) in structure two baggage systems non-linear dynamic characteristics linear polyhedral model (9) and
(10) the min-max principle of optimality, is utilized, based on invariant set method for designing, in the feelings of unknown CSTR systematic steady state equilibrium point information
Under condition, a kind of output tracking Robust Predictive Control algorithm of design is as follows:
First, definition X (t+j | t) is the t+j system state amount of t model prediction,For t prediction
The input controlling increment of t+j, selects the optimization object function of following belt restraining:
Wherein: W >=0 and R ＞ 0 are for controlling weight coefficient.For control
System input increment restriction.According to the basic thought of pseudo-min-max Robust Predictive Control algorithm, above-mentioned Infinite horizon object function quilt
It is divided into following two parts:
Above formula controls input incrementFor the controlled quentity controlled variable of object function calculating to be optimized, following control input increases
Amount is then obtained by following STATE FEEDBACK CONTROL rate:
A kind of Infinite horizon predictive control algorithm comprehensive based on LMI as provided below.First, definition is such as
Lower Quadratic Function Optimization:
V (j, t)=X (t+j | t)TP(j,t)X(t+j|t),j≥1. (20)
Wherein:In t, forAssume V
(j, t) meets such as lower inequality:
As j=1 to ∞, by cumulative for formula (21) summation, availableWorst case under the upper limit constraint as follows:
Therefore, pseudo-min-max Robust Predictive Control problem (17) can convert following optimization problem:
If there is Liapunov matrix Plk(l, k=1,2), then can build what a time dependent parameter relied on
Liapunov matrix is as follows:
Then the solving to be converted into and solve following convex optimization problem at each sampling instant t of optimization problem (23):
Wherein: symbol * represents the symmetrical structure of matrix；W=1, R=0.2； Z is a symmetrical matrix；F (t)=YG-1For feedback gain matrix.In above-mentioned LMI, At,
Bt, Ξ (t) and X (t | t) are the parameter that recorded of t and state respectively.Qlk、QαβFor solving the intermediary matrix of convex optimization problem
Variable, wherein l, k, α, β value is 1 or 2；Y,G,Qlk, Z andIt is the middle change minimizing in variable γ solution procedure
Amount, is solving minimization problemTime, majorized function can meet, according to above-mentioned constraints Automatic-searching, the γ made
Minimum intermediate variable Y, G, Qlk, Z andWhether exist, when finding suitable intermediate variable Y, G, Qlk, Z and
Time, then t minimizes Optimization Solution process and terminates.In t, ask by solving the convex optimization of above-mentioned LMI
Topic (25) can obtain the input of optimal control incrementThe controlled quentity controlled variable input of the corresponding system that acts on isThus, by regulation coolant temperature T in real timecT (), reaches the reaction of system output-response device
Temperature TrT () follows the tracks of given target trajectory.
Claims (2)
1. the Robust Predictive Control method of a single order CSTR, it is characterised in that comprise the following steps:
1) first kernel response CSTR system off-line is set up the nonlinear state interdependent ARX model structure of descriptive system dynamic characteristic such as
Under:
Wherein:For depending on quantity of state w
The Gauss Nonlinear A RX coefficient of (t)；ξ (t+1) is white Gaussian noise；State vector w (t)=[Tr(t)T Tr(t-1)T]T,Tr
(t)TOutput for t system；{zj,λj| j=TrOr TcIt is center vector and the zoom factor of RBF neural； Or TcIt it is the transposition of constant coefficient；It is 2 norms； It it is the corresponding weight coefficient of Gauss neural networks；Nonlinear parameter { zj,λj| j=TrOr
TcAnd linear dimensionsAll optimized by SNPOM
Method offline optimization is calculated；
2) the Parameters variation information structuring that construction features based on the interdependent ARX model of above-mentioned nonlinear state and model contain goes out
A kind of variable linear polyhedral model that can wrap up Nonlinear Dynamic；Particularly as follows:
The Nonlinear A RX model conversion describing first kernel response CSTR system is become following polynomial construction:
It is defined as follows deviation variables:
Wherein: Tc(t+j) it is the control input quantity in t+j moment；Tc(t+j-1) it is the control input quantity in t+j-1 moment；Tr(t+i)
Control output for the t+i moment；Control for the t+j moment inputs increment；Control for the t+i moment is defeated
Deviate；Desired output for t system；The output bias of a step forward prediction is obtained by above formulaAs follows:
Wherein:Meansigma methods for the modeling error ξ (t+1 | t) of Nonlinear A RX model；
Two state-space model structures of descriptive system current behavior X (t+1 | t) obtained and behavior X in future (t+g+1 | t)
As follows:
Wherein, coefficient matrices At,Bt, Ξ (t) and X (t | t) are the parameter matrix that records of t and state vector respectively；Future is not
Know state matrix [At+g|t,Bt+g|t] by State-Dependent coefficient constant a1,t+g|tAnd b1,t+g|tConstitute, unknown state matrix [At+g|t,
Bt+g|t] dynamically wrapped up by following two convex linear polyhedrons:
Wherein:For polyhedron time-varying linear coefficient, and
Wherein: matrix Al=A1Or A2: the A as l=1l=A1, the A as l=2l=A2,
In like manner matrix Bk=B1Or B2: the B as k=1k=B1, the B as k=2k=B2；Al, BkIn each element from mission nonlinear ARX
In model, the bound information of State-Dependent function type coefficient calculates:
Wherein,For the corresponding weight coefficient of Gauss neural networks, excellent by SNPOM method
Change obtains；For the function about variable w (t)Higher limit,For about variable w (t)
FunctionLower limit；For about variable w
The function of (t)Higher limit,For about change
The function of amount w (t)Lower limit；Represent for arbitrary w (t)；
3) based on above-mentioned structure, CSTR mission nonlinear dynamic variable linear polyhedral model can be wrapped up, utilize min-
The max principle of optimality, based on invariant set method for designing, in the case of unknown CSTR systematic steady state equilibrium point information, design based on
This Nonlinear A RX model can by solve convex optimization problem realize Optimal Output Tracking Robust Predictive Control method:
L, k, α, β=1 or 2
Wherein: symbol * represents the symmetrical structure of matrix；W=1, R=0.2；Z is a symmetrical matrix；F (t)=YG-1For feedback gain matrix；
Qlk、Qαβ, for solving the intermediary matrix variable of convex optimization problem, wherein l, k, α, β value is 1 or 2, for solving convex optimization problem
Intermediary matrix variable；In above-mentioned LMI, coefficient matrices At,BtIt is the parameter square that t has recorded with Ξ (t)
Battle array；X (t | t) is the state vector that t has recorded；Y,G,Qlk, Z andIt is and minimizes in variable γ solution procedure
Intermediate variable, is solving minimization problemTime, majorized function can be full according to above-mentioned constraints Automatic-searching
The intermediate variable Y that the γ that foot makes is minimum, G, Qlk, Z andWhether exist, when finding suitable intermediate variable Y, G, Qlk, Z andTime, then t minimizes Optimization Solution process and terminates；In t, by solving the convex of above-mentioned LMI
Optimization problem obtains the input of optimal control incrementThe controlled quentity controlled variable input of the corresponding system that acts on isBy regulation coolant temperature T in real timecT (), reaches system output-response device reaction temperature Tr
T () follows the tracks of given target trajectory.
The Robust Predictive Control method of single order CSTR the most according to claim 1, it is characterised in thatThe constant coefficient being between 0 to 1.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610139588.8A CN105893654B (en) | 2016-03-11 | 2016-03-11 | A kind of Robust Predictive Control method of single order continuous stirred tank reactor |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610139588.8A CN105893654B (en) | 2016-03-11 | 2016-03-11 | A kind of Robust Predictive Control method of single order continuous stirred tank reactor |
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| CN106933107A (en) * | 2017-05-15 | 2017-07-07 | 中南大学 | A kind of output tracking Robust Predictive Control method based on the design of multifreedom controlling amount |
| CN107092188A (en) * | 2017-05-27 | 2017-08-25 | 南京邮电大学 | A kind of GPC algorithm of CSTR system |
| CN108446480A (en) * | 2018-03-15 | 2018-08-24 | 厦门大学 | One kind being suitable for one-dimensional piston flow reactor dynamical model solution method |
| CN109507882A (en) * | 2018-11-20 | 2019-03-22 | 中南大学 | A kind of fast robust forecast Control Algorithm based on RBF-ARX model |
| CN109581870A (en) * | 2018-11-27 | 2019-04-05 | 中国工程物理研究院化工材料研究所 | The temperature in the kettle dynamic matrix control method of energetic material reaction kettle |
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| CN110045611A (en) * | 2019-04-24 | 2019-07-23 | 华北电力大学 | A kind of Robust Iterative Learning model predictive control method applied to batch stirred tank reactor |
| CN110262231A (en) * | 2019-05-29 | 2019-09-20 | 江苏大学 | Disturbance observation method based on the smooth continuous stirred tank reactor system of differential |
| CN110489891A (en) * | 2019-08-23 | 2019-11-22 | 江南大学 | A kind of industrial process time-varying uncertainty method based on more born of the same parents' space filterings |
| CN111324852A (en) * | 2020-03-06 | 2020-06-23 | 常熟理工学院 | Method of CSTR reactor time delay system based on state filtering and parameter estimation |
| CN111694277A (en) * | 2020-06-12 | 2020-09-22 | 华北电力大学 | Nonlinear stochastic model prediction control method based on multi-step state feedback |
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| CN108446480B (en) * | 2018-03-15 | 2020-07-31 | 厦门大学 | Dynamic model solving method suitable for one-dimensional plug flow reactor |
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| CN110489891B (en) * | 2019-08-23 | 2020-11-17 | 江南大学 | Industrial process time-varying parameter estimation method based on multi-cell spatial filtering |
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