CN107908110B - Tubular reactor dynamic optimization system based on control grid refinement - Google Patents

Tubular reactor dynamic optimization system based on control grid refinement Download PDF

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CN107908110B
CN107908110B CN201711116200.3A CN201711116200A CN107908110B CN 107908110 B CN107908110 B CN 107908110B CN 201711116200 A CN201711116200 A CN 201711116200A CN 107908110 B CN107908110 B CN 107908110B
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flow rate
tubular reactor
module
rate control
concentration
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CN107908110A (en
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刘兴高
李国栋
王雅琳
卢建刚
阳春华
孙优贤
桂卫华
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Zhejiang University ZJU
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Abstract

The invention discloses a tubular reactor dynamic optimization system based on control grid refinement, which consists of a tubular reactor, a flow rate sensor, an analog-to-digital converter, a field bus network, a DCS, a main control room flow rate and product concentration display, a digital-to-analog converter at the flow rate control valve end and a flow rate control valve. A control room engineer specifies the concentration of each reaction material in the feeding of the tubular reactor, the DCS obtains a flow rate control strategy for maximizing the concentration of a target product at the tail end of the tubular reactor through a control grid refinement optimization method, the flow rate control strategy is converted into an opening instruction of a flow rate control valve and is sent to a digital-to-analog converter at the end of the flow rate control valve through a field bus network, the flow rate control valve executes corresponding actions, a flow rate sensor collects the flow rate of the tubular reactor in real time and sends the flow rate to the DCS, and the control room engineer can master the production process at any time. The invention can maximize the concentration of the target product at the tail end of the tubular reactor and realize the potential excavation and efficiency improvement.

Description

Tubular reactor dynamic optimization system based on control grid refinement
Technical Field
The invention relates to the field of reactor control, in particular to a tubular reactor dynamic optimization system based on control grid refinement. The flow rate of the tubular reactor can be automatically controlled to maximize the concentration of the target product, thereby improving the production efficiency of the reactor.
Background
The tubular reactor belongs to a plug flow reactor, and is widely applied to petrochemical industry, fine chemical industry and other industrial production, such as propylene polymerization production.
For a tubular reactor with a fixed tube length, when material parameters such as a raw material quota ratio, concentration and the like are determined, a key factor influencing the product yield is the flow velocity of reactants, namely the flow rate. Because the production process requirements of different products are different, the automatic flow rate control of the tubular reactor according to the production process requirements has important significance.
At present, the control method of the domestic tubular reactor rarely adopts a dynamic optimization theory and a corresponding method, parameters in the controller are often set according to the existing experience, and the production efficiency needs to be further improved. The product concentration of the tubular reactor after the dynamic optimization method is adopted can be further improved, and the potential excavation and efficiency improvement are realized.
Disclosure of Invention
In order to improve the concentration of the target product of the tubular reactor, the invention provides a tubular reactor dynamic optimization system based on control grid refinement.
The purpose of the invention is realized by the following technical scheme: the tubular reactor dynamic optimization system based on control grid refinement can automatically control the flow rate of the tubular reactor to maximize the concentration of a target product at the tail end of the tubular reactor. The method is characterized in that: the system consists of a tubular reactor 11, a flow rate sensor 12, an analog-to-digital converter 13, a field bus network 14, DCS15, a main control room flow rate and product concentration display 16, a digital-to-analog converter 17 at the end of a flow rate control valve and a flow rate control valve 18. A control room engineer specifies the concentration of each reaction material in the feeding of the tubular reactor, the DCS obtains a flow rate control strategy for maximizing the concentration of a target product at the tail end of the tubular reactor through a control grid refinement optimization method, the flow rate control strategy is converted into an opening instruction of a flow rate control valve and is sent to a digital-to-analog converter at the end of the flow rate control valve through a field bus network, the flow rate control valve executes corresponding actions, a flow rate sensor collects the flow rate of the tubular reactor in real time and sends the flow rate to the DCS, and the control room engineer can master the production process at any time. The operation process of the system comprises the following steps:
step A1: a control room engineer specifies the concentration of each reactant in the feed to the tubular reactor, the target product for which the concentration needs to be maximized, and the flow rate control requirements;
step A2: the DCS executes an internal control grid refinement optimization method to obtain a flow rate control strategy for maximizing the concentration of the target product at the tail end of the tubular reactor;
step A3: the DCS converts the flow rate control strategy obtained through calculation into an opening instruction of the flow rate control valve, and sends the opening instruction to a digital-to-analog converter at the end of the flow rate control valve through a field bus network, so that the flow rate control valve executes corresponding action according to the received control instruction;
step A4: the flow rate sensor of the tubular reactor collects the flow rate in real time, the flow rate is returned to the DCS through the analog-to-digital converter by using a field bus network and is displayed in the main control room, so that an engineer in the control room can master the production process at any time.
The DCS comprises an information acquisition module, an initialization module, a control grid refinement module, an ODE solving module, a gradient calculation module, a Non-linear Programming (NLP) problem solving module, a refinement convergence judgment module and a control instruction output module. The information acquisition module comprises three submodules of feeding concentration state acquisition, target product acquisition and flow rate control requirement acquisition, and the NLP problem solving module comprises three submodules of optimizing direction calculation, optimizing step length calculation and NLP convergence judgment.
The production process of a tubular reactor can be described as:
Figure BDA0001466436520000021
wherein t represents a change in the tube length direction; u (t) represents the flow rate; x (t) represents the concentration of material in the tubular reactor varying along the length of the tube; f (-) is a system of differential equations established based on material balance, energy balance, etc. From this description, it can be seen that the process of producing the target product in the tubular reactor can be represented mathematically by a set of differential equations.
To maximize the concentration of the target product in the tubular reactor, x1(t) represents the concentration of the target product as it varies along the length of the tube, the final expression for this problem is:
Figure BDA0001466436520000022
wherein, t0Denotes the feed inlet of the tubular reactor, tfRepresenting the end of the tubular reactor and J represents the objective function to be maximized. The problem is essentially a dynamic optimization problem. However, conventional methods for solving such problems haveLow efficiency and poor precision, and is difficult to meet the requirement of high efficiency in actual production.
The technical scheme adopted by the invention for solving the technical problems is as follows: a control grid refinement optimization method is integrated in the DCS, and a set of dynamic optimization control system is constructed on the basis of the control grid refinement optimization method. The complete structure of the system comprises a tubular reactor 21, a flow rate sensor 22, an analog-to-digital converter 23, a field bus network 24, a DCS25, a main control room flow rate and product concentration display 26, a digital-to-analog converter 27 at the flow rate control valve end, and a flow rate control valve 28.
The operation process of the system comprises the following steps:
step A1: a control room engineer specifies the concentration of each reactant in the feed to the tubular reactor, the target product for which the concentration needs to be maximized, and the flow rate control requirements;
step A2: the DCS executes an internal control grid refinement optimization method to obtain a flow rate control strategy for maximizing the concentration of the target product at the tail end of the tubular reactor;
step A3: the DCS converts the flow rate control strategy obtained through calculation into an opening instruction of the flow rate control valve, and sends the opening instruction to a digital-to-analog converter at the end of the flow rate control valve through a field bus network, so that the flow rate control valve executes corresponding action according to the received control instruction;
step A4: the flow rate sensor of the tubular reactor collects the flow rate in real time, the flow rate is returned to the DCS through the analog-to-digital converter by using a field bus network and is displayed in the main control room, so that an engineer in the control room can master the production process at any time.
The DCS comprises an information acquisition module, an initialization module, a control grid refinement module, an ODE solving module, a gradient calculation module, a Non-linear Programming (NLP) problem solving module, a refinement convergence judgment module and a control instruction output module. The information acquisition module comprises three submodules of feeding concentration state acquisition, target product acquisition and flow rate control requirement acquisition, and the NLP problem solving module comprises three submodules of optimizing direction calculation, optimizing step length calculation and NLP convergence judgment.
In order to obtain a flow rate control strategy for maximizing the concentration of a target product at the tail end of the tubular reactor, the control grid fine optimization method executed by the DCS comprises the following operation steps:
step B1: the information acquisition module 31 acquires the initial concentration of the reaction materials, the target product of which the concentration needs to be maximized and the flow rate control requirement specified by an engineer;
step B2: the initialization module 32 starts to run, parameterizes with a piecewise constant, sets the number of segments N of the pipe length and the corresponding control grid toInitial guess of parameterized vector of flow rate control strategy
Figure BDA0001466436520000032
Setting the computational accuracy tol of NLP problem1Convergence accuracy tol of sum mesh refinement2The number of iterations k1And number of refinements k2Setting zero;
step B3: when k is2When 0, execute step B4; otherwise, the control mesh is refined by the control mesh refinement module 33
Figure BDA0001466436520000033
Refining to obtain new control gridAnd corresponding parameterized vector
Figure BDA0001466436520000035
Step B4: obtaining the material concentration of the iteration through the ODE solving module 34
Figure BDA0001466436520000036
And an objective function value
Step B5: the book is acquired by the gradient calculation module 35Sub-iterative gradient information
Figure BDA0001466436520000038
When k is1When 0, directly executing the step B7 by skipping the step B6;
step B6: the NLP problem solving module 36 operates to judge convergence through the NLP convergence judging module, if so
Figure BDA0001466436520000039
Objective function value from last iterationThe absolute value of the difference is less than the accuracy tol1If yes, determining that the convergence is satisfied, and executing step B9; if convergence is not satisfied, continuing to step B7;
step B7: by using
Figure BDA0001466436520000041
Value of (1) is covered
Figure BDA0001466436520000042
And will iterate the number of times k1Increasing by 1;
step B8: the NLP problem solving module 36 obtains a ratio by calculating the optimizing direction and the optimizing step size using the objective function values and gradient information obtained in steps B4 and B5
Figure BDA0001466436520000043
More optimal new flow rate control strategy
Figure BDA0001466436520000044
After the step is executed, jumping to the step B4 again;
step B9: the refinement convergence determination module 37 operates to recordWhen k is2When the value is 0, the step B10 is executed, otherwise, the judgment is made
Figure BDA0001466436520000046
And the last refined objective function value
Figure BDA0001466436520000047
Whether the absolute value of the difference is less than the accuracy tol2If yes, the convergence is judged to be satisfied, the flow rate control strategy of the iteration is converted into an opening instruction of the flow rate control valve to be output, otherwise, the convergence is not satisfied, and the refinement times k are set2:＝k2+1, continue to execute step B3 until the refinement convergence determination module is satisfied.
The control grid refinement module is realized by adopting the following steps:
step C1: calculating the left slope at a grid node by the following equationAnd right slope
Figure BDA0001466436520000049
(k＝1,…,N-1)：
Figure BDA00014664365200000410
Figure BDA00014664365200000411
Wherein u iskThe k-th component, t, of a parameterized vector u representing a flow rate control strategykRepresents ukAnd uk+1A mesh node in between.
Step C2: if the mesh node tkIf the left and right slopes meet the following requirements, the node is removed from the grid:
wherein epsiloneIs a small positive real number. Grid node tkAfter removal of ukAnd uk+1The corresponding grids are merged into a new grid, and the parameters on the new grid are updated to (u)k+uk+1)/2。
Step C3: if the mesh node tkThe left slope at (b) satisfies:
Figure BDA00014664365200000413
wherein epsiloniIs one greater than epsilonePositive real number of (1), then at [ tk-1,tk]Inserting grid nodes upwards; if the mesh node tkThe right slope at (b) satisfies:
then at [ tk-1,tk]And inserting grid nodes. In practical application, the number of the added nodes can be freely set according to the absolute value of the left slope and the right slope.
Step C4: and generating a new control grid and a corresponding parameterization vector according to the nodes removed and inserted in the steps C2 and C3.
The ODE solving module adopts a four-step Runge-Kutta method, and the calculation formula is as follows:
Figure BDA0001466436520000051
wherein t represents a change in the longitudinal direction of the tube, and tiDenotes the integration time, t, selected by the Runge-Kutta methodi+1Indicating that it is at time tiThe integration step h is the difference between any two adjacent integration moments, x (t)i) Denotes the distance t from the inlet of the tubular reactoriThe material concentration, F (-) is a function describing a state differential equation, and K1, K2, K3 and K4 respectively represent function values of 4 nodes in the Runge-Kutta method integration process.
The gradient calculation module adopts an accompanying method:
step D1: let λ (t) be the co-modal vector, whose value is determined by the adjoint equation:
Figure BDA0001466436520000052
wherein, tfDenotes the end of a tubular reactor, H denotes the Hamiltonian, and H ═ L + λ (t)TF, L is the integral term of the objective function, Φ x (t)f)]Is the steady state term of the objective function.
Step D2: for the adjoint equation, a four-step Runge-Kutta method is adopted to obtain the value of the co-modal vector lambda (t) at each integration moment, and the calculation formula is as follows:
Figure BDA0001466436520000061
wherein t represents a change in the longitudinal direction of the tube, and tiSolving the selected integration time, t, in the module for ODEi+1Indicating that it is at time tiThe latter integration time, and ti+1＝ti+ h, h is the integration step, and Q1, Q2, Q3 and Q4 respectively represent the function values of 4 nodes in the integration process of the Runge-Kutta method.
Step D3: based on the obtained value of the co-modal vector λ (t), gradient information is obtained by the following formula
Figure BDA0001466436520000062
Figure BDA0001466436520000063
Wherein the content of the first and second substances,
Figure BDA0001466436520000064
andto representThe first and second components, and so on.
The NLP problem solving module is realized by adopting the following steps:
step E1: if it is not
Figure BDA0001466436520000067
Objective function value from last iteration
Figure BDA0001466436520000068
Is less than the accuracy tol1If yes, judging that the convergence is satisfied, and returning to the flow rate control strategy obtained by the iteration; if convergence is not satisfied, continuing to step E2;
step E2: by usingValue of (1) is covered
Figure BDA00014664365200000610
And will iterate the number of times k1Increasing by 1;
step E3: control strategy for flow rate
Figure BDA00014664365200000611
As a point in vector space, denoted as P1，P1The corresponding objective function value is
Figure BDA00014664365200000612
Step E4: from point P1Starting from the selected NLP algorithm and point P1Information of the gradient of
Figure BDA00014664365200000613
Constructing a direction of optimization in vector space
Figure BDA00014664365200000614
And step size
Figure BDA00014664365200000615
Step E5, by formula
Figure BDA00014664365200000616
Constructing correspondences in vector space
Figure BDA00014664365200000617
Another point P of2So that P is2Corresponding objective function valueRatio of
Figure BDA00014664365200000619
Preferably, wherein I is
Figure BDA00014664365200000620
A vector of the same dimension.
The invention has the following beneficial effects: the tubular reactor dynamic optimization system based on control grid refinement can calculate the optimal flow rate control strategy of the tubular reactor, can adapt to the optimal control curve of the problem, particularly find the discontinuous point of the problem, and can obtain higher precision; after the adaptive strategy is adopted, the initial estimation value of the next optimal control curve is the optimal curve of the current iteration, so that the faster convergence speed can be obtained, and the calculation time required for obtaining the optimal control strategy is reduced. The invention can maximize the concentration of the target product in the tubular reactor and realize excavation and synergy.
Drawings
FIG. 1 is a functional schematic of the present invention;
FIG. 2 is a schematic structural view of the present invention;
FIG. 3 is a block diagram of the DCS internal module of the present invention;
Detailed Description
As shown in fig. 1, the production process of a tubular reactor can be described as:
Figure BDA0001466436520000071
wherein t represents a change in the tube length direction; u (t) represents the flow rate; x (t) represents the concentration of material in the tubular reactor varying along the length of the tube; f (-) is a system of differential equations established based on material balance, energy balance, etc. From this description, it can be seen that the process of producing the target product in the tubular reactor can be represented mathematically by a set of differential equations.
To maximize the concentration of the target product in the tubular reactor, x1(t) represents the concentration of the target product as it varies along the length of the tube, the final expression for this problem is:
Figure BDA0001466436520000072
wherein, t0Denotes the feed inlet of the tubular reactor, tfRepresenting the end of the tubular reactor and J represents the objective function to be maximized. The problem is essentially a dynamic optimization problem. However, the conventional method has the defects of low efficiency and poor precision in solving the problems, and is difficult to meet the requirement of high efficiency in actual production.
The technical scheme adopted by the invention for solving the technical problems is as follows: a control grid refinement optimization method is integrated in the DCS, and a set of dynamic optimization control system is constructed on the basis of the control grid refinement optimization method. The complete structure of the system is shown in fig. 2, and comprises a tubular reactor 21, a flow rate sensor 22, an analog-to-digital converter 23, a fieldbus network 24, a DCS25, a main control room flow rate and product concentration display 26, a digital-to-analog converter 27 at the flow rate control valve end, and a flow rate control valve 28.
The operation process of the system comprises the following steps:
step A1: a control room engineer specifies the concentration of each reactant in the feed to the tubular reactor, the target product for which the concentration needs to be maximized, and the flow rate control requirements;
step A2: the DCS executes an internal control grid refinement optimization method to obtain a flow rate control strategy for maximizing the concentration of the target product at the tail end of the tubular reactor;
step A3: the DCS converts the flow rate control strategy obtained through calculation into an opening instruction of the flow rate control valve, and sends the opening instruction to a digital-to-analog converter at the end of the flow rate control valve through a field bus network, so that the flow rate control valve executes corresponding action according to the received control instruction;
step A4: the flow rate sensor of the tubular reactor collects the flow rate in real time, the flow rate is returned to the DCS through the analog-to-digital converter by using a field bus network and is displayed in the main control room, so that an engineer in the control room can master the production process at any time.
The DCS comprises an information acquisition module, an initialization module, a control grid refinement module, an ODE solving module, a gradient calculation module, a Non-linear Programming (NLP) problem solving module, a refinement convergence judgment module and a control instruction output module. The information acquisition module comprises three submodules of feeding concentration state acquisition, target product acquisition and flow rate control requirement acquisition, and the NLP problem solving module comprises three submodules of optimizing direction calculation, optimizing step length calculation and NLP convergence judgment.
In order to obtain a flow rate control strategy for maximizing the concentration of a target product at the tail end of the tubular reactor, the control grid fine optimization method executed by the DCS comprises the following operation steps:
step B1: the information acquisition module 31 acquires the initial concentration of the reaction materials, the target product of which the concentration needs to be maximized and the flow rate control requirement specified by an engineer;
step B2: the initialization module 32 starts to run, parameterizes with a piecewise constant, sets the number of segments N of the pipe length and the corresponding control grid to
Figure BDA0001466436520000081
Initial guess of parameterized vector of flow rate control strategy
Figure BDA0001466436520000082
Setting the computational accuracy tol of NLP problem1Convergence accuracy tol of sum mesh refinement2The number of iterations k1And number of refinements k2Setting zero;
step B3: when k is2When 0, execute step B4; otherwise, by controllingGrid refinement module 33 pairs control grids
Figure BDA0001466436520000083
Refining to obtain new control gridAnd corresponding parameterized vector
Figure BDA0001466436520000085
Step B4: obtaining the material concentration of the iteration through the ODE solving module 34
Figure BDA0001466436520000086
And an objective function value
Figure BDA0001466436520000087
Step B5: obtaining the gradient information of the iteration through the gradient calculation module 35
Figure BDA0001466436520000088
When k is1When 0, directly executing the step B7 by skipping the step B6;
step B6: the NLP problem solving module 36 operates to judge convergence through the NLP convergence judging module, if so
Figure BDA0001466436520000089
Objective function value from last iteration
Figure BDA00014664365200000810
The absolute value of the difference is less than the accuracy tol1If yes, determining that the convergence is satisfied, and executing step B9; if convergence is not satisfied, continuing to step B7;
step B7: by using
Figure BDA00014664365200000811
Value of (1) is covered
Figure BDA00014664365200000812
And will iterate the number of times k1Increasing by 1;
step B8: the NLP problem solving module 36 obtains a ratio by calculating the optimizing direction and the optimizing step size using the objective function values and gradient information obtained in steps B4 and B5
Figure BDA00014664365200000813
More optimal new flow rate control strategy
Figure BDA00014664365200000814
After the step is executed, jumping to the step B4 again;
step B9: the refinement convergence determination module 37 operates to record
Figure BDA0001466436520000091
When k is2When the value is 0, the step B10 is executed, otherwise, the judgment is made
Figure BDA0001466436520000092
And the last refined objective function value
Figure BDA0001466436520000093
Whether the absolute value of the difference is less than the accuracy tol2If yes, the convergence is judged to be satisfied, the flow rate control strategy of the iteration is converted into an opening instruction of the flow rate control valve to be output, otherwise, the convergence is not satisfied, and the refinement times k are set2:＝k2+1, continue to execute step B3 until the refinement convergence determination module is satisfied.
The control grid refinement module is realized by adopting the following steps:
step C1: calculating the left slope at a grid node by the following equation
Figure BDA0001466436520000094
And right slope
Figure BDA0001466436520000095
(k＝1,…,N-1)：
Figure BDA0001466436520000097
Wherein u iskThe k-th component, t, of a parameterized vector u representing a flow rate control strategykRepresents ukAnd uk+1A mesh node in between.
Step C2: if the mesh node tkIf the left and right slopes meet the following requirements, the node is removed from the grid:
wherein epsiloneIs a small positive real number. Grid node tkAfter removal of ukAnd uk+1The corresponding grids are merged into a new grid, and the parameters on the new grid are updated to (u)k+uk+1)/2。
Step C3: if the mesh node tkThe left slope at (b) satisfies:
Figure BDA0001466436520000099
wherein epsiloniIs one greater than epsilonePositive real number of (1), then at [ tk-1,tk]Inserting grid nodes upwards; if the mesh node tkThe right slope at (b) satisfies:
Figure BDA00014664365200000910
then at [ tk-1,tk]And inserting grid nodes. In practical application, the number of the added nodes can be freely set according to the absolute value of the left slope and the right slope.
Step C4: and generating a new control grid and a corresponding parameterization vector according to the nodes removed and inserted in the steps C2 and C3.
The ODE solving module adopts a four-step Runge-Kutta method, and the calculation formula is as follows:
Figure BDA0001466436520000101
wherein t represents a change in the longitudinal direction of the tube, and tiDenotes the integration time, t, selected by the Runge-Kutta methodi+1Indicating that it is at time tiThe integration step h is the difference between any two adjacent integration moments, x (t)i) Denotes the distance t from the inlet of the tubular reactoriThe material concentration, F (-) is a function describing a state differential equation, and K1, K2, K3 and K4 respectively represent function values of 4 nodes in the Runge-Kutta method integration process.
The gradient calculation module adopts an accompanying method:
step D1: let λ (t) be the co-modal vector, whose value is determined by the adjoint equation:
Figure BDA0001466436520000102
wherein, tfDenotes the end of a tubular reactor, H denotes the Hamiltonian, and H ═ L + λ (t)TF, L is the integral term of the objective function, Φ x (t)f)]Is the steady state term of the objective function.
Step D2: for the adjoint equation, a four-step Runge-Kutta method is adopted to obtain the value of the co-modal vector lambda (t) at each integration moment, and the calculation formula is as follows:
Figure BDA0001466436520000103
wherein t represents a change in the longitudinal direction of the tube, and tiSolving the selected integration time, t, in the module for ODEi+1Indicating that it is at time tiThe latter integration time, and ti+1＝ti+ h, h is the integration step, Q1, Q2, Q3 and Q4 respectively represent the integration process of Runge-Kutta methodFunction values of 4 nodes.
Step D3: based on the obtained value of the co-modal vector λ (t), gradient information is obtained by the following formula
Figure BDA0001466436520000112
Wherein the content of the first and second substances,
Figure BDA0001466436520000113
and
Figure BDA0001466436520000114
to represent
Figure BDA0001466436520000115
The first and second components, and so on.
The NLP problem solving module is realized by adopting the following steps:
step E1: if it is not
Figure BDA0001466436520000116
Objective function value from last iteration
Figure BDA0001466436520000117
Is less than the accuracy tol1If yes, judging that the convergence is satisfied, and returning to the flow rate control strategy obtained by the iteration; if convergence is not satisfied, continuing to step E2;
step E2: by usingValue of (1) is covered
Figure BDA0001466436520000119
And will iterate the number of times k1Increasing by 1;
step E3: control strategy for flow rate
Figure BDA00014664365200001110
As a point in vector space, denoted as P1，P1The corresponding objective function value is
Figure BDA00014664365200001111
Step E4: from point P1Starting from the selected NLP algorithm and point P1Information of the gradient ofConstructing a direction of optimization in vector space
Figure BDA00014664365200001113
And step size
Figure BDA00014664365200001114
Step E5, by formula
Figure BDA00014664365200001115
Constructing correspondences in vector space
Figure BDA00014664365200001116
Another point P of2So that P is2Corresponding objective function value
Figure BDA00014664365200001117
Ratio of
Figure BDA00014664365200001118
Preferably, wherein I isA vector of the same dimension.
Example 1
Parallel reactions occur in a tubular reactor: a → B and A → C, reaction rate constants are k1And k2B is the target product, C is a by-product, and the aim is to control the choked flow rate so that product B is in the reactorThe concentration at the end was maximal. By xA(t) and xB(t) represents the concentration of materials A and B along the length of the tube, respectively, and u (t) k1L/v (t) is a physical quantity directly related to the choked flow rate, where L is the reactor length and v (t) is the choked flow rate. Finally, the optimal control problem can be simplified as:
Figure BDA0001466436520000121
wherein J represents the concentration of the material B to be maximized, tfRepresenting the end of the tubular reactor, t represents the change in length along the length of the tube, x (0) the initial concentration of materials a and B at the inlet of the tubular reactor. In order to obtain a flow rate control strategy for maximizing the concentration of a target product B at the tail end of the tubular reactor, a DCS operation control grid fine optimization method is adopted, the operation process is shown in FIG. 3, and the execution steps are as follows:
step F1: the information acquisition module 31 obtains the initial concentration x (0) ═ 10 of the reaction material specified by the engineer]TThe target product B with the concentration needing to be maximized and the flow rate control requirement of 0 to u (t) to 5;
step F2: the initialization module 32 starts to run, parameterizes with a piecewise constant, sets the number of segments of the pipe length to 8, and sets the corresponding control grid
Figure BDA0001466436520000122
Initial guess u of parameterized vector for uniform partitioning, flow rate control strategy(k)To 0.5, the calculation accuracy tol of the NLP problem is set1Convergence accuracy tol of sum mesh refinement2Are respectively 10-7And 10-6The number of iterations k1And number of refinements k2Setting zero;
step F3: when k is2When 0, step F4 is executed; otherwise, the control mesh is refined by the control mesh refinement module 33
Figure BDA0001466436520000123
Refining to obtain new control gridAnd corresponding parameterized vector
Figure BDA0001466436520000125
Step F4: obtaining the material concentration of the iteration through the ODE solving module 34
Figure BDA0001466436520000126
And an objective function value
Figure BDA0001466436520000127
Step F5: obtaining the gradient information of the iteration through the gradient calculation module 35When k is1Step F7 is directly performed skipping step F6 when 0;
step F6: the NLP problem solving module 36 operates to judge convergence through the NLP convergence judging module, if so
Figure BDA0001466436520000129
Objective function value from last iteration
Figure BDA00014664365200001210
The absolute value of the difference is less than the accuracy tol1If yes, determining that the convergence is satisfied, and executing step F9; if the convergence is not satisfied, continuing to perform step F7;
step F7: by using
Figure BDA00014664365200001211
Value of (1) is coveredAnd will iterate the number of times k1Increasing by 1;
step F8: the NLP problem solving module 36 uses the objective function values and gradient information obtained in steps F4 and F5 by calculating an optimizing methodStep size of direction and optimization, ratio of gain
Figure BDA00014664365200001213
More optimal new flow rate control strategy
Figure BDA00014664365200001214
After the step is completed, the step goes to step F4 again;
step F9: the refinement convergence determination module 37 operates to record
Figure BDA0001466436520000131
When k is2When 0, the process proceeds to step F10, otherwise, it is judged
Figure BDA0001466436520000132
And the last refined objective function valueWhether the absolute value of the difference is less than the accuracy tol2If yes, the convergence is judged to be satisfied, the flow rate control of the iteration is converted into the opening instruction of the mixed flow rate valve and output, otherwise, the convergence is not satisfied, and the refining times k are set2:＝k2+1, continue to execute step F3 until the refinement convergence determination module is satisfied.
And finally, the DCS converts the flow rate control strategy obtained by the control grid refinement optimization method into an opening instruction of the flow rate control valve, and sends the opening instruction to a digital-to-analog converter at the end of the flow rate control valve through the field bus network, so that the flow rate control valve executes corresponding actions according to the received control instruction, meanwhile, the flow rate sensor is used for collecting the flow rate distributed along the length of the pipe of the tubular reactor in real time, and the flow rate is returned to the DCS through the field bus network after passing through the analog-to-digital converter and is displayed in the main control chamber.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and is not intended to limit the practice of the invention to these embodiments. For those skilled in the art to which the invention pertains, several simple deductions or substitutions may be made without departing from the inventive concept, which should be construed as falling within the scope of the present invention.

Claims (1)

1. The tubular reactor dynamic optimization system based on control grid refinement can automatically control the flow rate of the tubular reactor so as to maximize the concentration of a target product at the tail end of the tubular reactor; the method is characterized in that: the system is composed of a tubular reactor (11), a flow rate sensor (12), an analog-to-digital converter (13), a field bus network (14), a distributed control system (15), a main control room flow rate and product concentration display (16), a digital-to-analog converter (17) at the end of a flow rate control valve, and a flow rate control valve (18); a control room engineer specifies the concentration of each reaction material in the feeding of the tubular reactor, the distributed control system obtains a flow rate control strategy which enables the concentration of a target product to be maximum at the tail end of the tubular reactor through a control grid refinement optimization method, converts the flow rate control strategy into an opening instruction of a flow rate control valve, sends the opening instruction to a digital-to-analog converter at the end of the flow rate control valve through a field bus network, enables the flow rate control valve to execute corresponding actions, and enables a flow rate sensor to acquire the flow rate of the tubular reactor in real time and send the flow rate back to the distributed control system, so that the control room engineer can master the; the operation process of the system comprises the following steps:
step A1: a control room engineer specifies the concentration of each reactant in the feed to the tubular reactor, the target product for which the concentration needs to be maximized, and the flow rate control requirements;
step A2: executing an internal control grid refinement optimization method by the distributed control system to obtain a flow rate control strategy for maximizing the concentration of a target product at the tail end of the tubular reactor;
step A3: the distributed control system converts the flow rate control strategy obtained by calculation into an opening instruction of the flow rate control valve, and sends the opening instruction to a digital-to-analog converter at the end of the flow rate control valve through a field bus network, so that the flow rate control valve executes corresponding action according to the received control instruction;
step A4: the flow rate sensor of the tubular reactor collects the flow rate in real time, the flow rate passes through the analog-to-digital converter and is returned to the distributed control system by a field bus network, and the flow rate is displayed in the main control room, so that an engineer in the control room can master the production process at any time;
the distributed control system comprises an information acquisition module, an initialization module, a control grid refinement module, an ODE solving module, a gradient calculation module, a Non-linear Programming (NLP) problem solving module, a refinement convergence judgment module and a control instruction output module; the information acquisition module comprises three submodules of feeding concentration state acquisition, target product acquisition and flow rate control requirement acquisition, and the NLP problem solving module comprises three submodules of optimizing direction calculation, optimizing step length calculation and NLP convergence judgment;
in order to obtain a flow rate control strategy for maximizing the concentration of the target product at the tail end of the tubular reactor, the control grid fine optimization method executed by the distributed control system comprises the following operation steps:
step B1: the information acquisition module (31) acquires the initial concentration of the reaction materials, target products needing to maximize the concentration and flow rate control requirements specified by a control room engineer;
step B2: the initialization module (32) starts to operate, parameterizes by adopting a piecewise constant, and sets the number N of segments of the pipe length and the corresponding control grid as
Figure FDA0002242056190000011
Initial guess of parameterized vector of flow rate control strategy
Figure FDA0002242056190000012
Setting the computational accuracy tol of NLP problem1Convergence accuracy tol of sum mesh refinement2The number of iterations k1And number of refinements k2Setting zero;
step B3: when k is2When 0, execute step B4; otherwise, the control grid is refined by a control grid refinement module (33)
Figure FDA0002242056190000021
Refining to obtain new control grid
Figure FDA0002242056190000022
And corresponding parameterized vector
Figure FDA0002242056190000023
Step B4: obtaining the material concentration of the iteration through an ODE solving module (34)
Figure FDA0002242056190000024
And an objective function value
Figure FDA0002242056190000025
Step B5: obtaining gradient information of the iteration through a gradient calculation module (35)When k is1When 0, directly executing the step B7 by skipping the step B6;
step B6: the NLP problem solving module (36) operates, the convergence judgment is carried out through the NLP convergence judgment module, and if the convergence judgment module is used, the convergence judgment is carried out
Figure FDA0002242056190000027
Objective function value from last iteration
Figure FDA0002242056190000028
The absolute value of the difference is less than the accuracy tol1If yes, determining that the convergence is satisfied, and executing step B9; if convergence is not satisfied, continuing to step B7;
step B7: by using
Figure FDA0002242056190000029
Value of (1) is coveredAnd will iterate the number of times k1Increasing by 1;
step B8: NLP problem solving modelA block (36) obtains a ratio by calculating a seek direction and a seek step length using the objective function values and gradient information obtained in steps B4 and B5
Figure FDA00022420561900000211
More optimal new flow rate control strategy
Figure FDA00022420561900000212
After the step is executed, jumping to the step B4 again;
step B9: the refined convergence judgment module (37) runs and records
Figure FDA00022420561900000213
When k is2When the value is 0, the step B10 is executed, otherwise, the judgment is made
Figure FDA00022420561900000214
And the last refined objective function value
Figure FDA00022420561900000215
Whether the absolute value of the difference is less than the accuracy tol2If yes, the convergence is judged to be satisfied, the flow rate control strategy of the iteration is converted into an opening instruction of the flow rate control valve to be output, otherwise, the convergence is not satisfied, and the refinement times k are set2:＝k2+1, continuing to execute the step B3 until the refinement convergence judgment module is satisfied;
the control grid refinement module is realized by adopting the following steps:
step C1: calculating the left slope at a grid node by the following equationAnd right slope
Figure FDA00022420561900000217
Figure FDA00022420561900000218
Figure FDA00022420561900000219
Wherein u iskParameterized vector representing flow rate control strategy
Figure FDA00022420561900000220
The k component of (a), tkRepresents ukAnd uk+1A mesh node in between;
step C2: if the mesh node tkIf the left and right slopes meet the following requirements, the node is removed from the grid:
Figure FDA0002242056190000031
wherein epsiloneIs a small positive real number; grid node tkAfter removal of ukAnd uk+1The corresponding grids are merged into a new grid, and the parameters on the new grid are updated to (u)k+uk+1)/2；
Step C3: if the mesh node tkThe left slope at (b) satisfies:
Figure FDA0002242056190000032
wherein epsiloniIs one greater than epsilonePositive real number of (1), then at [ tk-1,tk]Inserting grid nodes upwards; if the mesh node tkThe right slope at (b) satisfies:
Figure FDA0002242056190000033
then at [ tk-1,tk]Inserting grid nodes upwards; in actual application, the number of the added nodes can be freely set according to the absolute value of the left slope and the right slope;
step C4: generating a new control grid and corresponding parameterized vectors according to the nodes removed and inserted in the steps C2 and C3;
the ODE solving module adopts a four-step Runge-Kutta method, and the calculation formula is as follows:
Figure FDA0002242056190000034
wherein t represents a change in the longitudinal direction of the tube, and tiDenotes the integration time, t, selected by the Runge-Kutta methodi+1Indicating that it is at time tiThe integration step h is the difference between any two adjacent integration moments, x (t)i) Denotes the distance t from the inlet of the tubular reactoriThe material concentration, F (-) is a function describing a state differential equation, and K1, K2, K3 and K4 respectively represent function values of 4 nodes in the Runge-Kutta method integration process;
the gradient calculation module adopts an accompanying method:
step D1: let λ (t) be the co-modal vector, whose value is determined by the adjoint equation:
Figure FDA0002242056190000041
wherein, tfDenotes the end of a tubular reactor, H denotes the Hamiltonian, and H ═ L + λ (t)TF, L is the integral term of the objective function, Φ x (t)f)]A steady state term that is an objective function;
step D2: for the adjoint equation, a four-step Runge-Kutta method is adopted to obtain the value of the co-modal vector lambda (t) at each integration moment, and the calculation formula is as follows:
wherein t represents a change in the longitudinal direction of the tube, and tiSolving the selected integration time, t, in the module for ODEi+1Indicating that it is at time tiThe latter integration time, and ti+1＝ti+ h, h is the integration step length, and Q1, Q2, Q3 and Q4 respectively represent function values of 4 nodes in the Runge-Kutta method integration process;
step D3: based on the obtained value of the co-modal vector λ (t), gradient information is obtained by the following formula
Wherein the content of the first and second substances,
Figure FDA0002242056190000045
and
Figure FDA0002242056190000046
to represent
Figure FDA0002242056190000047
The first and second components of (a), and so on;
the NLP problem solving module is realized by adopting the following steps:
step E1: performing steps B6-B7;
step E2: control strategy for flow rate
Figure FDA0002242056190000048
As a point in vector space, denoted as P1，P1The corresponding objective function value is
Figure FDA0002242056190000049
Step E3: from point P1Starting from the selected NLP algorithm and point P1Information of the gradient of
Figure FDA00022420561900000410
Constructing a direction of optimization in vector space
Figure FDA00022420561900000411
And step size
Figure FDA00022420561900000412
Step E4, by formula
Figure FDA0002242056190000051
I construct the corresponding u in vector space(k1)Another point P of2So that P is2Corresponding objective function value
Figure FDA0002242056190000052
Ratio of
Figure FDA0002242056190000053
Preferably, wherein I is
Figure FDA0002242056190000054
A vector of the same dimension.
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