CN104375475B - The optimal control method of Batch reaction processes in batch reactor - Google Patents
The optimal control method of Batch reaction processes in batch reactor Download PDFInfo
- Publication number
- CN104375475B CN104375475B CN201410409098.6A CN201410409098A CN104375475B CN 104375475 B CN104375475 B CN 104375475B CN 201410409098 A CN201410409098 A CN 201410409098A CN 104375475 B CN104375475 B CN 104375475B
- Authority
- CN
- China
- Prior art keywords
- control
- formula
- output
- polynomial
- predictive controller
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
Abstract
The present invention provides a kind of optimal control method of Batch reaction processes in batch reactor, include the following steps：S100：Using TLBO algorithms, according to the economic optimization index received, reference locus of the optimal value track of control object as key-course is calculated；S200：In Batch reaction processes, ensure the input/output signal bounded of closed-loop system using a linear Generalized predictive controller, using the nonlinear terms of a nonlinear neural network generalized predictive controller compensation system, linear generalized predictive controller or nonlinear neural network generalized predictive controller are selected according to default performance of handoffs index in each sampling instant, the optimal value track for obtaining controlled device tracking S100；S300：Influence of the disturbance in system to output is entered by a bottom controller suppression, elimination, and then the value of control object is exported.
Description
Technical Field
The invention relates to the field of control optimization of a batch reaction process in a batch reactor, in particular to an optimal control method of the batch reaction process.
Background
However, because the intermittent reaction process has the characteristics of strong nonlinearity, lack of steady-state operation conditions, uncertainty of the reaction process and the like, the process optimization and control have certain difficulty, and therefore, a more effective optimization and control strategy is provided as a crucial link in the intermittent reaction process
The optimization of the batch reaction process faces generally nonlinear, obvious dynamic characteristic and large-scale complex optimization problems, and certain difficulties exist when the traditional mathematical optimization algorithm is adopted to process the problems. In recent years, research on the problem is active, biegler and other people focus on solving a large-scale optimization problem by a simultaneous algorithm, and apply the problem to aspects such as nonlinear model prediction control, parameter estimation, data adjustment and process synthesis, and Engel adopts feedback control methods such as self-optimization control and real-time optimization to realize optimal process operation. While the intelligent optimization algorithm can well solve the dynamic optimization problem of batch biochemical reaction process according to iterative computing capability of a computer, certain defects exist in the aspects of searching and optimizing performance when the dynamic optimization problem is solved by adopting the intelligent optimization algorithm, for example, because the solution of the PSO algorithm is a process of gradually losing diversity, the algorithm has poor local optimizing capability and is easy to generate premature convergence phenomenon.
The advanced control of the intermittent reaction process is represented by the problem of how to accurately track the optimally set trajectory without violating operating conditions and constraints after the optimal trajectory is determined by upper-layer optimization. Because the operating conditions of the batch process have high nonlinearity, the control strategies such as linear Model Predictive Control (MPC) lack the capability of compensating nonlinearity, and the control requirements of the batch reaction process cannot be met. Therefore, how to establish an optimal control strategy which can not only consider economic benefits but also ensure good overall control effect of the system is a problem which needs to be solved at present.
Disclosure of Invention
The invention aims to solve the technical problem of how to combine the economic benefit optimization of the system and the tracking effect of the optimal reference track in the industrial control of the intermittent reaction process, and finally achieve the effect of improving the economic benefit of the whole system.
In order to solve the technical problem, the method for optimally controlling the batch reaction process comprises the following steps:
s100: calculating an optimal value track of a control object as a reference track of a control layer by adopting a TLBO algorithm according to the received economic optimization index;
s200: in the intermittent reaction process, a linear generalized prediction controller is adopted to ensure that input and output signals of a closed-loop system are bounded, a nonlinear neural network generalized prediction controller is adopted to compensate a nonlinear item of the system, and the linear generalized prediction controller or the nonlinear neural network generalized prediction controller is selected at each sampling moment according to a preset switching performance index, so that a controlled object tracks an optimal value track obtained by S100;
s300: and the influence of the disturbance entering the system on the output is inhibited and eliminated through a bottom controller, and the value of the control object is output.
In the step S100, the following steps are included:
s101: dividing a time interval into n identical sections, wherein variables of control objects in each section are all invariant, and obtaining n control parameters to be optimized, so that an infinite-dimensional time variable is dispersed into a finite-dimensional time variable;
s102: selecting one of the n control parameters to be optimized as a teacher in the TLBO algorithm, and the rest as students in the TLBO algorithm;
s103: and carrying out TLBO optimization to obtain an optimal value track of a control object as a reference track of a control layer.
The linear estimation model M adopted by the linear generalized predictive controller 1 Is shown as
In the formula: where k represents the sampling instant; y (k) and u (k) are respectively the output and the input of the system; a (z) -1 )、B(z -1 ) To about the backward shift operator z -1 A, b are coefficients of the polynomial
M 1 Model parameters ofThe dead zone identification algorithm can be obtained as follows:
in the formula (I), the compound is shown in the specification,delta > 0 is a known normal number
In the linear generalized predictive controller, the optimization performance index adopted at the time k is expressed as:
in the formula, w r (k+j)＝aw r (k+j-1)+(1-a)y ref (k + j) is the desired value of the output of the control object, where a is the softening factor, 0<a<1，y ref To output a reference trajectory. N is an optimized time domain; n is a radical of hydrogen u To control the time domain; lambda [ alpha ] j 、r j Is a weighting coefficient sequence;
the control increment of the linear generalized predictive controller is as follows:
in the formula
F＝[F 1 (z -1 )，…，F N (z -1 )] T
H＝[H 1 (z -1 )，…，H N (z -1 )] T
M＝[M 1 (z -1 )，…，M N (z -1 )] T
In the formula, each variable parameter is obtained according to the equations (6) and (7) of the loss-of-energy map introduced in the process of solving the control increment, e, f, g and h are respectively polynomial coefficients, and beta is a step factor.
Estimation model M adopted by the nonlinear neural network generalized predictive controller 2 Can be expressed as
In the formula: wherein k represents a sampling instant; y (k) and u (k) are respectively the output and the input of the system; a (z) -1 )、B(z -1 ) To about a backward shift operator z -1 A, b are coefficients thereof
M 2 Model parameters of (2)The identification algorithm of (2) is as follows
In the formula (I), the compound is shown in the specification,delta > 0 is a known normal number
For the estimation of non-linear terms of neural networks, i.e.
Wherein z (k) = [ y (k),. -, y (k-n) a +1),...,Δu(k),...,Δu(k-n b )] T Psi (z (k)) is the basis function of the neural network,is a weight matrix of the neural network.
The optimization performance index adopted by the nonlinear neural network generalized predictive controller at the moment k is expressed as follows:
S j is a weighted polynomial and selects a weighted polynomial s j (z -1 ) So that
(S j (z -1 )+E j (z -1 ))v(k+j-1)＝M j (z -1 )v(k-1),j＝1,2,...,N (12)
Wherein
M is a nonlinear polynomial coefficient, and M is a polynomial coefficient.
The control increment of the nonlinear neural network generalized predictive controller is as follows:
the handover performance index is expressed as:
wherein T is a positive integer, and c.gtoreq.0 is a constant. i =1 for a linear model, i =2 for a non-linear model, e i (l) The output error of the ith model at time k.
In the invention, the whole control structure mainly comprises three layers. The upper layer structure is used for solving the dynamic optimization problem of the process by considering a process dynamic model and adopting a TLBO algorithm aiming at the optimization problem in the intermittent reaction process so as to obtain the maximum economic benefit, and is called an optimization layer, and the optimization layer calculates the optimal value track of a control object (such as reaction temperature) as the reference track of a control layer; the lower layer structure aims at the control problem in the intermittent reaction process, takes the nonlinearity in the intermittent reaction process into consideration, the controller adopts a stepped generalized predictive controller based on multi-model switching, the controller is composed of a linear generalized predictive controller, a nonlinear neural network generalized predictive controller and a switching mechanism and is called an MPC layer, the MPC layer adopts a rolling optimization predictive algorithm to adjust the process variables under the condition of meeting the dynamic behavior of the model, the expected variables track the optimization set value, the bottom layer is a PID controller which is mainly used for restraining and eliminating the influence of disturbance entering the process on the output and is called a basic control layer. The three-layer structure works together to achieve the desired goal of the system.
Drawings
FIG. 1 is a schematic diagram of a hierarchical optimization control architecture in an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating the optimization effect of the TLBO algorithm in an embodiment of the present invention;
FIG. 3 is a diagram illustrating TLBO algorithm and single model based GPC simulation results in accordance with an embodiment of the present invention;
FIG. 4 is a diagram illustrating simulation results in an embodiment of the invention.
Detailed Description
The method for optimizing and controlling the process of a batch reaction in a batch reactor according to the present invention will be described in detail with reference to fig. 1 to 4, which are alternative embodiments of the present invention, and it is considered that those skilled in the art can modify and decorate the present invention without departing from the spirit and scope of the present invention.
The conception of the method is as follows:
the whole control structure mainly comprises three layers.
The upper layer structure is used for solving the dynamic optimization problem of the process by considering a process dynamic model aiming at the optimization problem in the intermittent reaction process and adopting a TLBO algorithm so as to obtain the maximum economic benefit, and the upper layer structure is called an optimization layer, and the optimization layer calculates the optimal value track of a control object (such as reaction temperature) as the reference track of a control layer; the lower layer structure aims at the control problem in the intermittent reaction process, takes the nonlinearity in the intermittent reaction process into consideration, the controller adopts a stepped generalized predictive controller based on multi-model switching, the controller is composed of a linear generalized predictive controller, a nonlinear neural network generalized predictive controller and a switching mechanism and is called an MPC layer, the MPC layer adopts a rolling optimization predictive algorithm to adjust the process variables under the condition of meeting the dynamic behavior of the model, the expected variables track the optimization set value, the bottom layer is a PID controller which is mainly used for restraining and eliminating the influence of disturbance entering the process on the output and is called a basic control layer. The three-layer structure works together to achieve the desired goal of the system.
The technical scheme adopted by the method for solving the technical problem is as follows:
an optimal control strategy design of a batch reaction process comprises the following steps:
s1: as shown in FIG. 1, a decision maker determines economic optimization indexes of an intermittent process, and embodies the implementation mode of maximizing economic benefit and minimizing consumption cost and the implementation constraint in an economic objective function phi and a constraint condition d in an optimization layer, and the optimization layer obtains an optimal set value track of object output (such as reaction temperature) by optimizing the economic objective function.
That is, step S100: calculating an optimal value track of a control object as a reference track of a control layer by adopting a TLBO algorithm according to the received economic optimization index;
s2: tracking upper layer optimization to obtain an optimal set value. The multi-model control system consists of a linear generalized prediction controller, a nonlinear neural network generalized prediction controller and a switching mechanism, wherein the linear generalized prediction controller ensures that input and output signals of a closed-loop system are bounded, the nonlinear neural network generalized prediction controller compensates nonlinear items of the system, the performance of the system is improved, and an optimal controller is selected at each sampling moment according to a switching performance index, so that a controlled object can well track an optimal set value track;
that is, step S200: in the intermittent reaction process, a linear generalized predictive controller is adopted to ensure that input and output signals of a closed-loop system are bounded, a nonlinear neural network generalized predictive controller is adopted to compensate nonlinear terms of the system, the linear generalized predictive controller or the nonlinear neural network generalized predictive controller is selected at each sampling moment according to a preset switching performance index, and a controlled object is enabled to track an optimal value track obtained by S100;
s3: the optimized track is sent to a bottom layer controller for regulation (such as a PID controller and the like). The influence of the disturbance entering the process on the output is inhibited and eliminated through the action of the bottom layer controller. Sending final variable values to execution structures
Namely, S300: and the influence of the disturbance entering the system on the output is inhibited and eliminated through a bottom controller, and the value of the control object is output.
In the step S1, the step of obtaining the optimal value track of the control object by adopting the TLBO algorithm comprises the following steps:
step1. Time interval [ t 0 ,t f ]Are divided into the same N d All the variables in each section are invariable to obtain N d And (4) discretizing the infinite-dimension time variable into a finite-dimension time variable by using the control parameter to be optimized, namely determining the dimension of the problem.
And step2, defining an optimization problem and initializing optimization problem parameters, initializing group membership, iterative algebra and limiting conditions of the optimization problem.
And step3, generating an initial population randomly according to the population membership and the problem dimension.
Step4, teacher stage, teacher teaches students knowledge, and teacher stage process is carried out.
And step5, in the student stage, students can mutually communicate to improve the achievement.
Step6. Repeat Step4, step5 until the termination condition is met
Viewed from another point, in the step S100 (i.e., step S1), the following steps may be included:
s101: dividing a time interval into n identical sections, wherein variables of control objects in each section are all invariant, and obtaining n control parameters to be optimized, so that an infinite-dimensional time variable is dispersed into a finite-dimensional time variable;
s102: selecting one of n control parameters to be optimized as a teacher in the TLBO algorithm, and the rest as students in the TLBO algorithm;
s103: TLBO optimization is carried out, and the optimal value track of the control object is obtained and used as the reference track of the control layer.
It should be noted that TLBO (Teaching-Learning-Based Optimization: TLBO) algorithm refers to a Teaching-Learning Optimization algorithm.
The multi-model generalized predictive controller in step S2 is designed as follows
Assume that the batch process nonlinear system is represented as
A(z -1 )Δy(k)＝B(z -1 )Δu(k-1)+v(k-1) (1)
In the formula, y (k) and u (k) are respectively the output and the input of the system; Δ =1-z -1 Is a difference operator; v (k-1) is a non-linear term; a (z) -1 )、B(z -1 ) To about the backward shift operator z -1 Multiple item ofFormula (II) is shown.
v(k-1)＝o(y(k-1),...,y(k-n a ),Δu(k-1),...,Δu(k-n b -1))·Δ
Δu(k-1)＝u(k-1)-u(k-2)
A multi-model control system is designed according to a nonlinear system (1), and the control system is composed of a linear generalized predictive controller, a nonlinear neural network generalized predictive controller and a switching mechanism. The process of solving the controlled variable by linear GPC and nonlinear neural network GPC in the multimode controller and the controller switching index are explained below.
1. Linear generalized predictive control
Linear estimation model M of system 1 Can be expressed as
In the formula: wherein k represents a sampling instant; y (k) and u (k) are respectively the output and the input of the system; a (z) -1 )、B(z -1 ) To about the backward shift operator z -1 A and b are coefficients of the polynomial;
M 1 model parameters of (2)The dead zone identification algorithm can be used as follows:
in the formula (I), the compound is shown in the specification,δ>, 0 is a known normal number
Using optimized performance index at time k
In the formula, w r (k+j)＝aw r (k+j-1)+(1-a)y ref (k + j) is the desired value of the control object output, where a is the softening factor, 0<a<1，y ref To output a reference trajectory. N is an optimized time domain; n is a radical of u To control the time domain; lambda [ alpha ] j 、r j Identifying the obtained parameters as the weighting coefficient sequenceIs substituted into the parameter polynomial A 1 (z -1 ),B 1 (z -1 ) And introduces two drop-map equations as follows:
B(z -1 )E j (z -1 )＝G j (z -1 )+z -j H j (z -1 ) (6)
in the formula
E j (z -1 )＝1+e j,1 z -1 +…+e j,j-1 z -(j-1)
G j (z -1 )…＝g j,0 +g j,1 z -1 +…+g j,j-1 z -(j-1)
Minimizing the performance index function (4), the control increment of the linear controller is:
in the formula
F＝[F 1 (z -1 )，…，F N (z -1 )] T
H＝[H 1 (z -1 )，…，H N (z -1 )] T
M＝[M 1 (z -1 )，…，M N (z -1 )] T
Wherein e, f, g, h are each polynomial coefficient, beta is step factor
2 nonlinear neural network generalized predictive controller
Neural network nonlinear estimation model M of system 2 Can be expressed as
In the formula:
wherein k represents a sampling instant; y (k) and u (k) are respectively the output and the input of the system; a (z) -1 )、B(z -1 ) To about a backward shift operator z -1 A and b are coefficients of the polynomial;
M 2 model parameters of (2)The identification algorithm is as follows
In the formula (I), the compound is shown in the specification,delta > 0 is a known normal number
For estimating the non-linear term for neural networks, i.e.
Wherein z (k) = [ y (k) ], y (k-n) a +1),...,Δu(k),...,Δu(k-n b )] T Ψ (z (k)) is the basis function of the neural network for the input vector of the system,is a weight matrix of the neural network.
Using the optimized performance index at time k
S j Is a weighted polynomial s and selects a weighted polynomial j (z -1 ) So that
(S j (z -1 )+E j (z -1 ))v(k+j-1)＝M j (z -1 )v(k-1),j＝1,2,...,N (12)
Wherein
M is a nonlinear polynomial coefficient, and M is a polynomial coefficient.
Identifying the obtained parametersIs substituted into the parameter polynomial A 2 (z -1 ),B 2 (z -1 ) Identifying the obtained nonlinear termSubstituting into the parameter model (8), introducing the loss-of-energy graph formulas (5) and (6), minimizing the performance index function (11), and obtaining the control increment of the neural network controller as follows:
3. controller switch indicator
On the premise of ensuring the stability of a closed-loop switching system, the following switching performance index [16] can be selected
Wherein T is a positive integer, and c ≧ 0 is a constant. i =1 for a linear model, i =2 for a non-linear model, e i (l) The output error of the ith model at time k. Mu.s i (l) And inputting the control quantity of the ith model at the moment k. The former part of the switching performance index formula processes the part with larger model estimation error, and the part is accumulated from the initial moment, so that the stability of a closed-loop switching system can be ensured; the second half is a part with smaller processing model error, and is accumulated at a limited time, so that the dynamic performance of the system is improved.
And at the moment k, switching to a corresponding controller according to the minimum value of the performance index, and taking the output of the controller as the input of the system.
Compared with the prior art, the invention has the following beneficial effects:
1. reduce the system cost consumption and improve the system economic benefit
2. Improving the global control capability of the system
3. By adopting TLBO algorithm, better optimization effect can be obtained
The invention is further described with reference to the following figures and specific examples:
as will be seen from the following examples, the process is at least one method for optimizing the control of the reaction temperature in a batch reactor. Therefore, the control object referred to in this embodiment is the reaction temperature of the batch reactor.
Referring to the block diagram of FIG. 1, a batch reactor was selected as the study case to perform the steps in sequence. In order to verify the optimization control strategy of the invention, simulation research is carried out on the optimization control case of a batch reactor, and the reaction process of the batch reactor is as follows:
wherein: a is a reactant, B is a target product, and C is a byproduct. In order to maximize the economic efficiency of the entire reaction process, the conversion of B at the end of the reaction must be maximized as much as possible. The reaction temperature is controlled between 298K and 398K in the whole reaction process, the reaction is an exothermic reaction, the temperature of the reactor is controlled by a jacket cooling method, so that the product quality of the reaction process is improved, and the operation safety is ensured.
k 1 ＝4000exp(-2500/T) (17)
k 2 ＝620000exp(-5000/T) (18)
Q r ＝ΔH 1 (k 1 x 1 V)+ΔH 2 (k 2 x 2 V) (20)
In the formula, x 1 、x 2 Represents the mole fractions of the reactant A and the target product B of 30; k is a radical of 1 、k 2 Represents a reaction rate constant; t is the reaction temperature; f cw 、C pcw 、ΔT cw The flow rate of cooling water, the temperature difference of a hot melting inlet and a cooling water outlet are measured; q r 、ρ、C pr Respectively representing reaction heat, reactant density and reactant hot melt; Δ H 1 、ΔH 2 Is the reaction enthalpy; v is the reactor capacity. The system model is divided into an optimization model part and a control model part for implementation, wherein the model of the optimization part is formed by an economic objective function maxJ = x 2 (t f ) And formulae (15) to (18), whichMedian parameter value range x 1 ,x 2 ∈[0,1]，T∈[298,398]. The control section model is composed of equations (19) to (20). The values of the parameters of the system model are shown in Table 1
TABLE 1 batch reactor Process parameters
Optimizing the optimized part of the batch reactor by adopting a dynamic optimization algorithm based on TLBO, wherein the problem dimension N in the optimization algorithm d =10, the number of classes is set to 30, and the number of iterations is 100. And optimizing to obtain an optimal track of the reaction temperature of the batch reactor, taking the solution as a set value for controlling the reaction temperature, and designing a single-model linear generalized predictive controller and a nonlinear multi-model generalized predictive controller respectively in the control part. The control target is the optimal reference track T obtained by optimizing the reaction temperature tracking of the reactor r . Selecting the prediction time domain length and the control time domain length as N =4 and N, respectively u =2, initial parameter of adaptive model a i ,b i All take 0.01, each coefficient of the weighting matrix is 1, and the step factor beta is constantly 1. For a multimode controller, the learning rate r =0.01, the number of hidden nodes l =20, and the parameter c =20, t =5 in the switching criterion. The results of the dynamic optimization of the reaction temperature are shown in FIG. 2:
from the analysis of the reaction mechanism model, the higher the temperature is, the reaction rate constant k 1 ,k 2 The larger the concentration of the reactant A is, the lower the concentration of the target product B is in the initial stage of the reaction, the higher the reaction temperature is favorable for the production of the product B, and the amount of the by-product C produced is also smaller because the concentration of the target product B is lower at this time. As the reaction proceeds, the reaction temperature should be gradually lowered, decreasing the reaction rate constant k 1 ,k 2 Thus, the target product B can be accumulated, and the concentration of the target product B can be increased. The optimization results in this context are shown in FIG. 2, where the reaction temperature gradually decreases as the reaction proceeds, and corresponds to the results analyzed by the mechanism model, thus indicating the effectiveness of the dynamic optimization algorithmAnd (4) the feasibility and feasibility.
And taking the dynamically optimized solution as a reference track of a set value of a lower-layer controller, and respectively adopting a linear single-model GPC controller and a nonlinear multi-model GPC controller to control, wherein the control results are shown in figures 3 and 4. In the figure, the red dotted line represents the temperature optimum value trajectory obtained by dynamic optimization, and the blue solid line represents the control output of the control. When the control is performed by using the linear single-model GPC (as shown in fig. 3), the magnitude of the set value is largely changed at the initial stage of the reaction, the deviation between the control output value and the set value is large, and the tracking effect is poor. When the nonlinear multi-model GPC is used for control (as shown in fig. 4), the deviation between the control output value and the set value is small, that is, the output is closer to the optimal reference trajectory, so that the control effect of the nonlinear multi-model GPC controller is better than that of the linear single-model GPC controller.
The final yield of target product B was 0.610625, which is very close to the optimum of 0.610775. In conclusion, by adopting a double-layer optimization control strategy based on a TLBO dynamic optimization algorithm and a nonlinear multi-model GPC controller, the batch reaction process can be effectively controlled, and the yield of the target product can be improved.
Claims (7)
1. An optimal control method for a batch reaction process in a batch reactor is characterized by comprising the following steps: the method comprises the following steps:
s100: calculating an optimal value track of a control object as a reference track of a control layer by adopting a TLBO algorithm according to the received economic optimization index;
s200: in the intermittent reaction process, a linear generalized predictive controller is adopted to ensure that input and output signals of a closed-loop system are bounded, a nonlinear neural network generalized predictive controller is adopted to compensate nonlinear terms of the system, the linear generalized predictive controller or the nonlinear neural network generalized predictive controller is selected at each sampling moment according to a preset switching performance index, and a controlled object is enabled to track an optimal value track obtained by S100;
s300: the influence of disturbance entering a system on output is inhibited and eliminated through a bottom controller, and then the value of a control object is output;
the linear estimation model M adopted by the linear generalized predictive controller 1 Is shown as
In the formula:
is A (z) -1 ) The coefficient of (a);is B (z) -1 ) The coefficient of (a); Δ u (k) = u (k) -u (k-1) representing the amount of change in the control action u (k), where k represents the sampling instant; y (k) and u (k) are respectively the output and the input of the system; a (z) -1 )、B(z -1 ) To about a backward shift operator z -1 A and b are coefficients thereof, n a Is a polynomial A (z) -1 ) Order of (1), n b Is a polynomial B (z) -1 ) The order of (2);
M 1 model parameters of (2)The dead zone identification algorithm can be obtained as follows:
in the formula (I), the compound is shown in the specification,delta > 0 is a known normal number
Estimation model M adopted by nonlinear neural network generalized predictive controller 2 Can be expressed as
In the formula: ；
wherein k represents a sampling instant; y (k) and u (k) are respectively the output and the input of the system; a (z) -1 )、B(z -1 ) To about a backward shift operator z -1 A and b are coefficients thereof, n a Is a polynomial A (z) -1 ) Order of (1), n b Is a polynomial B (z) -1 ) The order of (a);
M 2 model parameters of (2)The identification algorithm of (2) is as follows
In the formula (I), the compound is shown in the specification,delta > 0 is a known normal number
For estimating the non-linear term for neural networks, i.e.
Wherein, the first and the second end of the pipe are connected with each other,as model M 2 An output of (d);the estimated values of the nonlinear terms at different moments are obtained; z (k) = [ y (k) ], y (k-n) a +1),...,Δu(k),...,Δu(k-n b )] T Ψ (z (k)) is the basis function of the neural network for the input vector of the system,is a weight matrix of the neural network.
2. A method for the optimal control of a batch reaction process in a batch reactor according to claim 1, wherein: in the step S100, the following steps are included:
s101: dividing a time interval into n identical sections, wherein variables of control objects in each section are all invariant, and obtaining n control parameters to be optimized, so that an infinite-dimensional time variable is dispersed into a finite-dimensional time variable;
s102: selecting one of the n control parameters to be optimized as a teacher in the TLBO algorithm, and the rest as students in the TLBO algorithm;
s103: TLBO optimization is carried out, and the optimal value track of the control object is obtained and used as the reference track of the control layer.
3. A method for the optimized control of a batch reaction process in a batch reactor as claimed in claim 1, characterized in that: in the linear generalized predictive controller, the switching performance index adopted at the time k is represented as:
in the formula, w r (k+j)＝aw r (k+j-1)+(1-a)y ref (k + j) is the desired value of the control object output, where a is the softening factor, 0 < a < 1, y ref To output a reference trajectory; y (k + j) is the j step prediction for the output y (k) at time k; Δ u (k + j-1) = u (k + j-1) -u (k + j-2) is the j-1 step prediction for the input increment Δ u (k) at time k; n is an optimized time domain; n is a radical of u To control the time domain; lambda j 、r j Is a sequence of weighting coefficients.
4. A method for the optimized control of a batch reaction process in a batch reactor as claimed in claim 1, characterized in that: the control increment of the linear generalized predictive controller is as follows:
in the formula
F＝[F 1 (z -1 )，…，F N (z -1 )] T
H＝[H 1 (z -1 )，…，H N (z -1 )] T
M＝[M 1 (z -1 )，…，M N (z -1 )] T
The variable parameters in the formula are obtained according to a lost-to-noise graph equation introduced in the process of solving the control increment, and the lost-to-noise graph formula is
B(z -1 )E j (z -1 )＝G j (z -1 )+z -j H j (z -1 ) (7)
In the formula
e, f, g and h are respectively polynomial coefficients; Δ u 1 (k) Is a control increment; w is a r (k + j) is a reference trajectory; n is an optimized time domain; n is a radical of u Is a control time domain; lambda i Is a weighting coefficient; beta is the step factor.
5. A method for the optimized control of a batch reaction process in a batch reactor as claimed in claim 1, characterized in that: the switching performance index adopted by the nonlinear neural network generalized predictive controller at the moment k is expressed as follows:
wherein N is an optimized time domain; n is a radical of hydrogen u Is a control time domain; y (k + j) is the j step prediction of the output y; Δ u (k + j-1) is the control prediction increment; r is a radical of hydrogen j 、λ j Is a weight coefficient; w (k + j) is an optimal reference track; z is a radical of -1 Is a backward shift operator;the noise estimation value is the time k + j-1; v (k + j-1) is noise at the moment k + j-1;
S j (z -1 ) Is a weighted polynomial and selects a weighted polynomial E j (z -1 ) So that
(S j (z -1 )+E j (z -1 ))v(k+j-1)＝M j (z -1 )v(k-1),j＝1,2,...,N (12)
Wherein
M j (z -1 ) Is a nonlinear term polynomial coefficient, m i Is a polynomial coefficient of term, n m Is a polynomial M j (z -1 ) The order of (a).
6. A method for the optimal control of a batch reaction process in a batch reactor according to claim 1, wherein: the control increment of the nonlinear neural network generalized predictive controller is as follows:
in the formula (I), the compound is shown in the specification,
F＝[F 1 (z -1 )，…，F N (z -1 )] T
H＝[H 1 (z -1 )，…，H N (z -1 )] T
M＝[M 1 (z -1 )，…，M N (z -1 )] T
the variable parameters in the formula are obtained according to a lost-to-noise graph equation introduced in the process of solving the control increment, and the lost-to-noise graph formula is
B(z -1 )E j (z -1 )＝G j (z -1 )+z -j H j (z -1 )
In the formula
R is a weight coefficient R j A constructed weighting matrix; w is the future expected output vector; λ is a weight coefficient; beta is a step factor; e.g. of the type j,j-1 、Are all coefficients of a weighted polynomial;B(z -1 ) Is the structural polynomial of the system.
7. A method for the optimized control of a batch reaction process in a batch reactor as claimed in claim 1, characterized in that: the handover performance index is expressed as:
wherein T is a positive integer, c ≧ 0 is a constant, i =1 denotes a linear model, i =2 denotes a nonlinear model, e i (l) For the output error of the ith model at time k, μ i (l) For the control quantity input of the ith model at the time k,is a regression vector.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410409098.6A CN104375475B (en) | 2014-08-19 | 2014-08-19 | The optimal control method of Batch reaction processes in batch reactor |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201410409098.6A CN104375475B (en) | 2014-08-19 | 2014-08-19 | The optimal control method of Batch reaction processes in batch reactor |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104375475A CN104375475A (en) | 2015-02-25 |
| CN104375475B true CN104375475B (en) | 2018-05-04 |
Family
ID=52554470
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201410409098.6A Expired - Fee Related CN104375475B (en) | 2014-08-19 | 2014-08-19 | The optimal control method of Batch reaction processes in batch reactor |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104375475B (en) |
Families Citing this family (17)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105676632A (en) * | 2016-01-26 | 2016-06-15 | 沈阳化工大学 | Model-free adaptive optimized control method for PVC polymerization process |
| CN107045287A (en) * | 2017-05-11 | 2017-08-15 | 东南大学 | Coordinated Control Systems and control method based on Prediction and Control Technology |
| CN107180279B (en) * | 2017-06-14 | 2020-08-25 | 重庆科技学院 | QPSO-DMPC-based reaction regeneration system optimization control method |
| CN107894754A (en) * | 2017-11-13 | 2018-04-10 | 浙江大学 | A kind of batch reactor optimal control system based on Self Adaptive Control node |
| CN107957680B (en) * | 2017-11-20 | 2020-07-07 | 太原理工大学 | Controller for batch reactor reaction process based on survival information potential |
| CN107976942B (en) * | 2017-11-22 | 2020-11-24 | 海南师范大学 | 2D constraint fault-tolerant control method for intermittent process of infinite time domain optimization |
| CN109254531B (en) * | 2017-11-29 | 2021-10-22 | 辽宁石油化工大学 | Method for optimal cost control of a multi-stage batch process with time lag and disturbances |
| CN108803314B (en) * | 2017-12-13 | 2021-07-23 | 杭州电子科技大学 | Novel compound tracking control method for chemical intermittent process |
| CN108803315B (en) * | 2017-12-13 | 2021-06-18 | 杭州电子科技大学 | Intelligent tracking control method for chemical intermittent process |
| US11048281B2 (en) * | 2018-06-12 | 2021-06-29 | Robert Bosch Gmbh | Real-time capable control strategy for hydraulic systems while systematically taking into consideration control (rate) and state variable constraints |
| CN110426956B (en) * | 2019-07-30 | 2021-07-23 | 中国矿业大学 | Intermittent process optimal compensation control strategy based on process migration model |
| CN110687937B (en) * | 2019-10-14 | 2021-09-28 | 东北大学 | Water tank liquid level control method based on multivariable generalized minimum variance decoupling control |
| CN110579970B (en) * | 2019-10-24 | 2023-02-03 | 海南师范大学 | Intermittent process terminal constraint prediction control method under 2D rolling optimization |
| CN111812979B (en) * | 2020-06-17 | 2022-12-30 | 东南大学 | Multivariable generalized predictive control method applied to double-effect lithium bromide absorption refrigeration system |
| CN113687632B (en) * | 2021-01-25 | 2024-01-26 | 南京工业大学 | Variable period collaborative optimization control method for intermittent reaction process |
| CN114114909B (en) * | 2021-11-11 | 2024-03-22 | 海南师范大学 | Intermittent process 2D output feedback prediction control method based on particle swarm optimization |
| CN116571190B (en) * | 2023-07-14 | 2023-09-12 | 昆明理工大学 | Reaction kettle control system and method for lignin modified phenolic resin |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5740033A (en) * | 1992-10-13 | 1998-04-14 | The Dow Chemical Company | Model predictive controller |
| JP2002268722A (en) * | 2001-03-09 | 2002-09-20 | Takenaka Komuten Co Ltd | Production management system |
| CN103425048A (en) * | 2013-05-22 | 2013-12-04 | 上海交通大学 | Multi-model generalized predictive control system based on dynamic optimization and control method thereof |
| CN103472723A (en) * | 2013-08-19 | 2013-12-25 | 上海交通大学 | Predictive control method and system based on multi-model generalized predictive controller |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9046882B2 (en) * | 2010-06-30 | 2015-06-02 | Rockwell Automation Technologies, Inc. | Nonlinear model predictive control of a batch reaction system |
-
2014
- 2014-08-19 CN CN201410409098.6A patent/CN104375475B/en not_active Expired - Fee Related
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5740033A (en) * | 1992-10-13 | 1998-04-14 | The Dow Chemical Company | Model predictive controller |
| JP2002268722A (en) * | 2001-03-09 | 2002-09-20 | Takenaka Komuten Co Ltd | Production management system |
| CN103425048A (en) * | 2013-05-22 | 2013-12-04 | 上海交通大学 | Multi-model generalized predictive control system based on dynamic optimization and control method thereof |
| CN103472723A (en) * | 2013-08-19 | 2013-12-25 | 上海交通大学 | Predictive control method and system based on multi-model generalized predictive controller |
Non-Patent Citations (3)
| Title |
|---|
| 基于广义预测控制的迭代学习算法在间歇过程中的应用;樊雷;《中国优秀硕士学位论文全文数据库》;20060915(第9期);第1-74页 * |
| 间歇反应过程的预测控制与实时仿真平台验证;崔远;《中国优秀硕士学位论文全文数据库》;20080815(第8期);第1-53页 * |
| 间歇过程优化与先进控制综述;陈治纲 等;《化工自动化及仪表》;20031221;第30卷(第3期);第1-6页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104375475A (en) | 2015-02-25 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN104375475B (en) | The optimal control method of Batch reaction processes in batch reactor | |
| Li et al. | Offset-free fuzzy model predictive control of a boiler–turbine system based on genetic algorithm | |
| CN111443681B (en) | Multi-model predictive control design method for supercritical thermal power generating unit coordinated control system | |
| Ellis et al. | Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems | |
| Mujtaba et al. | Neural network based modelling and control in batch reactor | |
| Musmade et al. | Design of sliding mode control scheme for nonlinear processes for improved performance | |
| Alamo et al. | A gradient-based strategy for the one-layer RTO+ MPC controller | |
| CN104950681A (en) | Fuzzy predictive control system for combustion process of lime kiln as well as control method of system | |
| Alhamad et al. | On-line multi-variable predictive control of molar mass and particle size distributions in free-radical emulsion copolymerization | |
| Wang et al. | Adaptive decoupling switching control of the forced-circulation evaporation system using neural networks | |
| Ławryńczuk | Explicit nonlinear predictive control algorithms with neural approximation | |
| Sun et al. | Process knowledge-based random forest regression for model predictive control on a nonlinear production process with multiple working conditions | |
| CN110373510B (en) | Molten steel quality narrow window control method and system based on bimodal switching | |
| Mallaiah et al. | A simulated annealing optimization algorithm based nonlinear model predictive control strategy with application | |
| Lakshminarayanan et al. | Empirical modelling and control of processes with recycle: some insights via case studies | |
| Vasičkaninová et al. | Neural network predictive control of a chemical reactor | |
| CN104111605B (en) | The controller and control method of single-input single-output integrator plant production process | |
| Lee et al. | Value function-based approach to the scheduling of multiple controllers | |
| Zhou et al. | Data modeling for quality prediction using improved orthogonal incremental random vector functional-link networks | |
| Shi et al. | Two-layer predictive control of a continuous biodiesel transesterification reactor | |
| Zanoli et al. | Model Predictive Control with horizons online adaptation: A steel industry case study | |
| Yang et al. | Adaptive decentralized PID controllers design using JITL modeling methodology | |
| Nevado et al. | A new control strategy for IKN-type coolers | |
| CN111221252B (en) | Predictive controller parameter analysis setting method for industrial system with fractional hysteresis | |
| Munusamy et al. | Approximate dynamic programming based control of hyperbolic PDE systems using reduced-order models from method of characteristics |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20180504 Termination date: 20200819 |