CN107831663A - A kind of batch reactor optimal control system based on adaptive congestion control algorithm node - Google Patents
A kind of batch reactor optimal control system based on adaptive congestion control algorithm node Download PDFInfo
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract
The invention discloses a kind of batch reactor optimal control system based on adaptive congestion control algorithm node, the system is by batch reactor body, the liquid phase flowmeter at batch reactor end, analog-digital converter, fieldbus networks, DCS, master control room feed rate is shown, the digital analog converter at flow control valve end, flow control valve are formed.After control room engineer specifies production process duration and feed rate control requirement, DCS obtains the feed rate control strategy for making target product maximum production and is converted to the opening degree instruction of flow control valve, the digital analog converter at flow control valve end is sent to by fieldbus networks, make flow control valve according to the control instruction corresponding actions received, liquid phase flowmeter gathers reactor feed speed and is passed back to DCS in real time, control room engineer is grasped production process at any time.The present invention can maximize the yield of target product in batch reactor, realize enhancing efficiency by relying on tapping internal latent power.
Description
Technical Field
The invention relates to the field of reactor control, in particular to an optimal control system of a batch reactor based on a self-adaptive optimization control node. The system enables automatic optimal control of the batch reactor feed rate to improve the yield of the target product.
Background
The intermittent reactor is widely applied to the fields of petrochemical industry, biological medicine, life health and the like. In actual production, when the initial concentration of material, production time and other factors are determined, the most critical factor affecting product yield is the substrate feed rate. Because the production process requirements of different products are different, the method has important significance for automatically carrying out optimal control on the feeding rate of the batch reactor according to the production process requirements. At present, the control method of the domestic batch reactor rarely adopts an optimal control theory and a corresponding method, and parameters in the controller are often set according to the prior experience. After the optimal control method is adopted, the yield of the target product in the batch reactor can be further improved, and the potential excavation and efficiency improvement are realized.
Disclosure of Invention
In order to improve the yield of target products in a batch reactor, the invention provides an optimal control system of the batch reactor based on an adaptive optimization control node, which takes DCS as an implementation carrier of an optimal control method.
The purpose of the invention is realized by the following technical scheme: an optimal control system of a batch reactor based on a self-adaptive optimization control node can automatically and optimally control the feeding rate of the batch reactor so as to improve the yield of a target product. The system consists of an intermittent reactor body, a liquid phase flowmeter at the end of the intermittent reactor, an analog-digital converter, a field bus network, a DCS, a main control room feeding rate display, a digital-analog converter at the end of a flow control valve and the flow control valve. The operation process of the system comprises the following steps:
step A1: a control room engineer sets the duration of the production process and the feed rate control requirements;
step A2: the DCS executes an internal adaptive optimization control node optimal control method and calculates a feeding rate control strategy for maximizing the yield of a target product;
step A3: the DCS converts the obtained feeding rate control strategy into an opening instruction of the flow control valve, and sends the opening instruction to a digital-to-analog converter of the flow control valve through a field bus network, so that the flow control valve makes corresponding action according to the received control instruction;
step A4: the liquid phase flowmeter at the end of the batch reactor collects the feeding rate of the batch reactor in real time, the feeding 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 constraint condition processing module, a control vector parameterization module, a Nonlinear Programming (NLP) problem solving module, a termination condition judgment module, a self-adaptive control node distribution module, a time scale conversion module and a control instruction output module.
The production process of the target product in a batch reactor can be described as:
wherein t represents time, t 0 Denotes the start time of the production process, t f Represents the end time of the production process; x (t) = [ x = 1 (t),x 2 (t),...,Referred to as state variables, representing the concentration of material or a relevant parameter in the batch reactor, x 0 Is the initial value of the same, and,is its first derivative; u (t) denotes the feed rate of the batch reactor, u l 、u u Respectively as its lower limit and upper limit;is a differential equation set established according to conservation of materials and energy;is a constraint condition established on material concentration or related parameters and feeding rate in the production process.
Suppose to use phi x (t) f )]Representing the final yield of the target product, such that the product is producedThe maximized mathematical model can be expressed as:
wherein J [ u (t) ] represents the control target, determined by the feed rate u (t). This problem is essentially an optimal control problem.
The technical scheme adopted by the invention for solving the problem is as follows: an optimal control method of a self-adaptive optimization control node is integrated in the DCS, and a set of optimal control system is constructed on the basis of the optimal control method. The structure of the control system comprises an intermittent reactor body, a liquid phase flowmeter at the end of the intermittent reactor, an analog-to-digital converter, a field bus network, a DCS, a main control room feeding rate display, a digital-to-analog converter at the end of a flow control valve and the flow control valve.
The operation process of the system is as follows:
step C1: a control room engineer sets the duration of the production process and the feed rate control requirements;
and step C2: the DCS executes an internal adaptive optimization control node optimal control method and calculates a feeding rate control strategy for maximizing the yield of a target product;
and C3: the DCS converts the obtained feeding rate control strategy into an opening instruction of the flow control valve, and sends the opening instruction to a digital-to-analog converter of the flow control valve through a field bus network, so that the flow control valve makes corresponding action according to the received control instruction;
and C4: the liquid phase flowmeter at the end of the batch reactor collects the feeding rate of the batch reactor in real time, the feeding 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 integrating the optimal control method of the self-adaptive optimization control node is the core of the invention, and comprises an information acquisition module, an initialization module, a constraint condition processing module, a control vector parameterization module, a Nonlinear Programming (NLP) problem solving module, a termination condition judgment module, a self-adaptive control node distribution module, a time scale conversion module and a control instruction output module.
The information acquisition module comprises two submodules of production process duration acquisition and feeding rate control requirement acquisition.
The constraint condition processing module is used for processing constraint conditions in the mathematical model (2)The mathematical model (2) can be converted into:
wherein G is i (i＝1,2,...,n g ) Is composed ofThe ith component of (1), rho is not less than 0 as a penalty factor, delta>, 0 is a smoothing factor, and
introducing new state variablesMake it satisfy
The mathematical model (3) can then be converted into:
wherein, the first and the second end of the pipe are connected with each other,in order to be able to make an extensive state variable,as a result of which the initial value, is an augmented system of differential equations.
The control vector parameterization module adopts a piecewise constant strategy to realize the feeding rate control, and the control vector parameterization module specifically comprises the following steps:
suppose the entire control time domain t 0 ,t f ]Is divided into p (p)>, 0) control subintervals [ t k-1 ,t k ) (k =1,2,. Gtoreq., p), and
t 0 <t 1 <…<t p-1 <t p ＝t f (7)
thus, u (t) can be expressed as:
wherein the content of the first and second substances,is constant and represents u (t) in the control subinterval [ t ] k-1 ,t k ) Value of internal parameter, χ k (t) is a unit switching function, which is defined as follows:
thus, the feed rate control parameter may be derived from a vectorAnd (4) showing.
The NLP problem solving module comprises two submodules of Sequence Quadratic Programming (SQP) solving and simultaneous differential equation system solving. The system of simultaneous differential equations comprises a system of equations
And system of equations
Wherein the content of the first and second substances,
solving simultaneous differential equations (10) and (11) by using a fourth-order Runge-Kutta algorithm, so as to obtain an objective function value of the mathematical model (6) and first-order gradient information of the objective function to the control parameter vector:
the adaptive control node allocation module provides a strategy for adaptively allocating control nodes, which specifically comprises the following steps:
the optimal value of the objective function obtained by the first iteration is assumed to be J *l The optimum control parameter is The corresponding control grid isBy dividing Delta l Each control subinterval in the control grid is halved to obtain a control gridAnd initial control parameters
For theWherein the current value isRespective parameters ofTo evaluate its effect on the amount of decrease of the objective function J, a definition is madeThe sensitivity to J is:
wherein, the first and the second end of the pipe are connected with each other,represents the largest integer not exceeding (j + 1)/2.
Assumed to be in the control intervalIn the interior of said container body,respectively obtaining the optimal control parameter values of the (l-1) th time and the (l) th time. If the following conditions are satisfied:
wherein epsilon uv >, 0 is given threshold value, then order
s 2k-1 =0 and s 2k ＝0 (17)
For a l' Control node inIf it is retained in the next iteration, it is satisfied that:
wherein r is su >, 0 is a given coefficient,for average sensitivity, it is defined as follows:
if equation (18) is not satisfied, the control node is eliminated.
When the control nodeAndare all eliminated, if the following conditions are satisfied
Wherein a given coefficient r sl ∈(0,r su ]、ε uh >, 0, then the node is controlledShould also be eliminated.
Through the steps of controlling the grid to halve, eliminating the control node and the like, the control grid delta l' Control grid delta that can be used as the next iteration l+1 。
The time scale conversion module is used for converting the current mathematical model (6) to a new time scale so as to optimize the control grid obtained by the self-adaptive control node distribution module, and specifically comprises the following steps:
for a newly inserted control nodeIf it satisfies
Wherein a given coefficient r ss ≥r su Then the control node is considered to be an important control node. Thus, the subintervals are controlledAndconsidered as an important control subinterval, the length of which can be optimized as a variable to find a control nodeThe optimal position of (a).
Suppose that P control subintervals [ t ] exist in the whole control time domain after being adjusted by the self-adaptive control node allocation module k-1 ,t k ) (k =1,2, \8230;, P), the length of each control sub-interval being in θ k Is expressed and has an initial value of
For the non-important control subintervals, the lengths of the control subintervals are constant and do not need to be optimized. For the important control subintervals, it is assumed that the control subintervals are divided into R (R ≧ 1) moieties, and the R-th (1 ≦ R ≦ R) moieties containing n r (n r Not less than 2) continuous control subintervals, and the lengths of all the control subintervals meet the following requirements:
the time scale transfer function is introduced as follows:
wherein tau is a new time variable,denotes the largest integer not exceeding τ. In this way, the mathematical model (6) can be converted on a new time scale into:
wherein, the first and the second end of the pipe are connected with each other,
the DCS generates the flow control valve opening command in the following process:
step D1: the information acquisition module acquires the duration of the production process and the feeding rate control requirement specified by an engineer;
step D2: the initialization module runs to set the initial control grid number p and the initial feeding rate control strategyInitial guess of valueThe constant value rho is more than or equal to 0 and delta>0、ε uv >0、ε uh >0、r su >0、r sl ∈(0,r su ]、r ss ≥r su Setting the maximum number of iterations l max 1 or more and a termination error tol J >, 0, and let iteration count l =0;
and D3: the constraint condition processing module converts the mathematical model (2) into a mathematical model (6);
step D4: the control vector parameterization module adopts a piecewise constant strategy to represent a feeding rate control curve, if l =0, a control time domain is equally divided into p segments to obtain a current control grid, and all control parameter values are made to beOtherwise, adopt Delta l As the current control grid, the parameter value in each control subinterval is in the corresponding control time domainA value of (d);
step D5: an SQP solving module in the NLP problem solving module operates, and obtains an objective function value and first-order gradient information of the objective function to the control parameter vector through a simultaneous differential equation solving module to finally obtain an objective function optimal value J under the current control grid *l And corresponding optimal control parameters
Step D6: the termination condition judging module operates for l>, 0, if l = l max Or
Executing step D10, otherwise, executing step D7;
step D7: self-adaptive control node distribution module operates to obtain new control grid delta l+1 ；
And D8: let iteration count l = l +1, if l = l max If yes, executing the step D9, otherwise, turning to the step D4;
step D9: d4, converting the mathematical model (6) into a mathematical model (25) on a new time scale by the time scale conversion module, and turning to the step D4;
step D10: and the control instruction output module outputs the obtained optimal feeding rate control strategy.
The invention has the following beneficial effects: the optimal control system of the batch reactor based on the sensitivity adaptive optimization control node analysis can calculate the optimal feeding rate control strategy of the batch 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 for obtaining the optimal feeding rate control strategy is reduced. The invention can maximize the concentration of the target product in the batch reactor and realize excavation and synergism.
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;
FIG. 4 is a graph of the feed rate control strategy obtained for the example 1 implementation;
fig. 5 is a graph of the variation of the state variables for the feed rate control strategy of fig. 4.
Detailed Description
As shown in fig. 1, the process of producing a target product in a batch reactor can be described as:
where t represents time, t 0 Denotes the start time of the production process, t f Represents the end time of the production process; x (t) = [ x = 1 (t),x 2 (t),...,Referred to as state variables, representing the concentration of material or a relevant parameter in the batch reactor, x 0 Is the initial value of the same, and,is its first derivative; u (t) denotes the feed rate of the batch reactor, u l 、u u Respectively as its lower limit and upper limit;a differential equation set is established according to material conservation and energy conservation;is a constraint condition established on material concentration or related parameters and feeding rate in the production process.
Suppose with Φ x (t) f )]Representing the final yield of the target product, the mathematical model that maximizes the product yield can be expressed as:
wherein J [ u (t) ] represents the control target and is determined by the feed rate u (t). This problem is essentially an optimal control problem.
The technical scheme adopted by the invention for solving the problem is as follows: an optimal control method of a self-adaptive optimization control node is integrated in the DCS, and a set of optimal control system is constructed on the basis of the optimal control method. The structure of the control system is shown in fig. 2, and the control system comprises a batch reactor body, a liquid phase flowmeter at the batch reactor end, an analog-to-digital converter, a field bus network, a DCS, a main control room feeding rate display, a digital-to-analog converter at the flow control valve end, and a flow control valve.
The operation process of the system is as follows:
and C5: a control room engineer sets the duration of the production process and the feed rate control requirements;
and C6: the DCS executes an internal self-adaptive optimization control node optimal control method and calculates a feeding rate control strategy for maximizing the yield of a target product;
step C7: the DCS converts the obtained feeding rate control strategy into an opening instruction of the flow control valve, and sends the opening instruction to a digital-to-analog converter of the flow control valve through a field bus network, so that the flow control valve makes corresponding action according to the received control instruction;
step C8: a liquid phase flowmeter at the end of the batch reactor collects the feeding rate of the batch reactor in real time, the feeding rate is fed back 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 integrating the optimal control method for the adaptive optimization control node is the core of the present invention, and as shown in fig. 3, the DCS includes an information acquisition module, an initialization module, a constraint condition processing module, a control vector parameterization module, a Nonlinear Programming (NLP) problem solving module, a termination condition judgment module, an adaptive control node allocation module, a time scale conversion module, and a control instruction output module.
The information acquisition module comprises two submodules of production process duration acquisition and feeding rate control requirement acquisition.
The constraint condition processing module is used for processing constraint conditions in the mathematical model (2)The mathematical model (2) can be converted into:
wherein G is i (i＝1,2,...,n g ) Is composed ofThe ith component of (1), rho is not less than 0 as a penalty factor, delta>, 0 is a smoothing factor, and
introducing new state variablesMake it satisfy
The mathematical model (3) can then be converted into:
wherein, the first and the second end of the pipe are connected with each other,in order for the state variable to be augmented,as an initial value thereof, the value of, is an augmented system of differential equations.
The control vector parameterization module adopts a piecewise constant strategy to realize the feeding rate control, and the control vector parameterization module specifically comprises the following steps:
suppose the entire control time domain t 0 ,t f ]Is divided into p (p)>, 0) control subintervals [ t k-1 ,t k ) (k =1,2,. Ang., p), and
t 0 <t 1 <…<t p-1 <t p ＝t f (34)
thus, u (t) can be expressed as:
wherein, the first and the second end of the pipe are connected with each other,is constant, indicates that u (t) is in the control subinterval [ t ] k-1 ,t k ) Value of internal parameter, χ k (t) is a unit switching function, which is defined as follows:
thus, the feed rate control parameter may be derived from a vectorAnd (4) showing.
The NLP problem solving module comprises two submodules of Sequence Quadratic Programming (SQP) solving and simultaneous differential equation set solving. The system of simultaneous differential equations comprises a system of equations
And system of equations
Wherein, the first and the second end of the pipe are connected with each other,
solving simultaneous differential equations (10) and (11) by using a fourth-order Runge-Kutta algorithm to obtain an objective function value of the mathematical model (6) and first-order gradient information of the objective function to the control parameter vector:
the adaptive control node allocation module provides a strategy for adaptively allocating control nodes, which specifically comprises the following steps:
the optimal value of the objective function obtained by the first iteration is assumed to be J *l The optimum control parameter is The corresponding control grid isBy dividing Delta l Is halved to obtain a control gridAnd initial control parameters
For theWherein the current value isRespective parameters ofTo evaluate its effect on the amount of decrease of the objective function J, a definition is madeThe sensitivity to J was:
wherein the content of the first and second substances,represents the largest integer not exceeding (j + 1)/2.
Assumed to be in the control intervalIn the interior of said container body,respectively the optimal control parameter values obtained at the (l-1) th time and the (l) th time. If the following conditions are satisfied:
wherein epsilon uv >, 0 is given threshold value, then order
s 2k-1 =0 and s 2k ＝0 (44)
For a l' Control node inIf it is retained in the next iteration, it is satisfied that:
wherein r is su >, 0 is a given coefficient,for average sensitivity, it is defined as follows:
if equation (18) is not satisfied, the control node is eliminated.
When the control nodeAndare all eliminated, if the following conditions are satisfied
Wherein a given coefficient r sl ∈(0,r su ]、ε uh >, 0, then the node is controlledShould also be eliminated.
Through the steps of halving the control grid, eliminating the control nodes and the like, the control grid delta l' Control grid delta that can be used as the next iteration l+1 。
The time scale conversion module is used for converting the current mathematical model (6) to a new time scale so as to optimize the control grid obtained by the self-adaptive control node distribution module, and specifically comprises the following steps:
for a newly inserted control nodeIf it is satisfied with
Wherein a given coefficient r ss ≥r su Then the control node is considered to be an important control node. Thus, the subintervals are controlledAndconsidered as an important control subinterval, the length of which can be optimized as a variable to find a control nodeThe optimal position of (a).
Suppose that P control subintervals [ t ] exist in the whole control time domain after being adjusted by the self-adaptive control node allocation module k-1 ,t k ) (k =1,2, \ 8230;, P), the length of each control subinterval being in θ k Is expressed and has an initial value of
For the non-important control subintervals, the length of the control subintervals is constant and does not need to be optimized. For the important control subintervals, it is assumed that the control subintervals are divided into R (R ≧ 1) moieties, and the R-th (1 ≦ R ≦ R) moieties containing n r (n r Not less than 2) continuous control subintervals, and the lengths of all the control subintervals meet the following conditions:
the time scale transfer function is introduced as follows:
wherein tau is a new time variable,denotes the largest integer not exceeding τ. In this way, the mathematical model (6) can be converted on a new time scale into:
wherein the content of the first and second substances,
the DCS generates the flow control valve opening command according to the following process:
step D1: the information acquisition module acquires the duration of the production process and the feeding rate control requirement specified by an engineer;
step D2: the initialization module operates to set the initial control grid number p and the initial guess value of the feeding rate control strategySetting constant value rho ≧ 0, delta>0、ε uv >0、ε uh >0、r su >0、r sl ∈(0,r su ]、r ss ≥r su Setting the maximum number of iterations l max 1 or more and a termination error tol J >, 0, and let iteration count l =0;
and D3: the constraint condition processing module converts the mathematical model (2) into a mathematical model (6);
and D4: the control vector parameterization module adopts a piecewise constant strategy to represent a feeding rate control curve, if l =0, a control time domain is equally divided into p segments to obtain a current control grid, and all control parameter values are made to beOtherwise, adopt Delta l As the current control grid, the parameter value in each control subinterval is in the corresponding control time domainA value of (d);
step D5: an SQP solving module in the NLP problem solving module operates, and obtains an objective function value and first-order gradient information of the objective function to the control parameter vector through a simultaneous differential equation solving module to finally obtain an objective function optimal value J under the current control grid *l And corresponding optimal control parameters
Step D6: the termination condition judging module operates for l>, 0, if l = l max Or
Executing step D10, otherwise, executing step D7;
step D7: self-adaptive control node distribution module operates to obtain new control grid delta l+1 ；
Step D8: let iteration count l = l +1, if l = l max If yes, executing the step D9, otherwise, turning to the step D4;
step D9: the time scale conversion module converts the mathematical model (6) into a mathematical model (25) on a new time scale, and then the step D4 is carried out;
step D10: and the control instruction output module outputs the obtained optimal feeding rate control strategy.
Examples 1
The mathematical model for secreted protein production in a batch reactor is as follows:
wherein x is 1 (t)、x 2 (t)、x 3 (t)、x 4 (t) the concentrations (g/L) of the secretory protein, total serum protein, microorganism and substrate, respectively, x 5 (t) represents the batch reactor volume (L) and u (t) represents the substrate feed rate (L/h).
The control room engineer will set the duration t of this production process f And (c) inputting the required information of the feeding rate of 0 to u (t) to 2 which is not less than 15h into an information acquisition module of the DCS. The DCS immediately starts to operate the optimal control method of the adaptive optimization control node, and the operation process thereof is shown in fig. 3, and includes:
step E1: the initialization module 2 operates to set the initial control grid number p =10, the initial guess value of the feed rate control strategyConstant values ρ =0, δ =10 are set -10 、ε uv ＝10 -6 、ε uh ＝10 -3 、r su ＝0.25、r sl ＝0.2、r ss =1.45, set maximum number of iterations l max =4 and termination error tol J ＝10 -4 And let iteration count l =0;
step E2: the constraint condition processing module 3 operates to convert the mathematical model (55) into the form of the mathematical model (6);
step E3: the control vector parameterization module 4 adopts a piecewise constant strategy to represent a feed rate control curve, if l =0, the control time domain is equally divided into p segments to obtain a current control grid, and all control parameter values are made to beOtherwise, adopt Δ l As the current control grid, the parameter value in each control subinterval is in the corresponding control time domainA value of (d);
step E4: the SQP solving module in the NLP problem solving module 5 operates, and obtains an objective function value and first-order gradient information of the objective function to the control parameter vector through the simultaneous differential equation solving module, and finally obtains an objective function optimal value J under the current control grid *l And corresponding optimal control parameters
And E5: the termination condition judgment module 6 operates for l>, 0, if l = l max Or
Executing step E9, otherwise, executing step E6;
step E6: the adaptive control node distribution module 7 operates to obtain a new control grid delta l+1 ；
Step E7: let iteration count l = l +1, if l = l max If not, go to step E3;
and E8: the time scale conversion module 8 converts the mathematical model (6) into a mathematical model (25) on a new time scale, and the step E3 is carried out;
and E9: the control instruction output module 9 outputs the obtained optimal feed rate control strategy.
The optimal feeding rate control curve obtained by the optimal control method of the adaptive optimization control node is shown in fig. 4, and completely meets the set feeding rate control requirement. FIG. 5 shows the variation curves of the various state variables in the batch reactor, and it can be seen that the yield x of secreted protein in the production process 1 (t)x 5 (t) is increasing, and reaches a maximum at the end of the production process.
And finally, outputting a flow control valve opening instruction output by the DCS to a digital-to-analog converter at the flow control valve end through the field bus network, enabling the flow control valve to correspondingly act according to the received control instruction, simultaneously acquiring the feeding rate of the intermittent reactor in real time by using a liquid phase flowmeter, returning the feeding rate to the DCS through the analog-to-digital converter and the field bus network, and displaying the feeding rate in a main control chamber.
The above-described embodiments are intended to illustrate rather than to limit the invention, and any modifications and variations of the present invention are within the spirit of the invention and the scope of the appended claims.
Claims (1)
1. An optimal control system of a batch reactor based on a self-adaptive optimization control node can automatically and optimally control the feeding rate of the batch reactor so as to improve the yield of a target product. The method is characterized in that: the system consists of an intermittent reactor body, a liquid phase flowmeter at the end of the intermittent reactor, an analog-digital converter, a field bus network, a DCS, a main control room feeding rate display, a digital-analog converter at the end of a flow control valve and the flow control valve. The operation process of the system comprises the following steps:
step A1: a control room engineer sets the duration of the production process and the feed rate control requirements;
step A2: the DCS executes an internal adaptive optimization control node optimal control method and calculates a feeding rate control strategy for maximizing the yield of a target product;
step A3: the DCS converts the obtained feeding rate control strategy into an opening instruction of the flow control valve, and sends the opening instruction to a digital-to-analog converter of the flow control valve through a field bus network, so that the flow control valve makes corresponding action according to the received control instruction;
step A4: the liquid phase flowmeter at the end of the batch reactor collects the feeding rate of the batch reactor in real time, the feeding 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 constraint condition processing module, a control vector parameterization module, a Nonlinear Programming (NLP) problem solving module, a termination condition judgment module, a self-adaptive control node distribution module, a time scale conversion module and a control instruction output module.
The production process of the target product in a batch reactor can be described as:
where t represents time, t 0 Denotes the start time of the production process, t f Represents the end time of the production process; referred to as state variables, representing the concentration of material or a relevant parameter in the batch reactor, x 0 Is the initial value of the same, and,is its first derivative; u (t) represents the feed rate of a batch reactor, u l 、u u Respectively as its lower limit and upper limit;is a differential equation set established according to conservation of materials and energy;is a constraint condition established on material concentration or related parameters and feeding rate in the production process.
Suppose with Φ x (t) f )]Indicating the final yield of the target product, such that the product is producedThe maximized mathematical model can be expressed as:
wherein J [ u (t) ] represents the control target and is determined by the feed rate u (t).
The information acquisition module comprises two submodules of production process duration acquisition and feeding rate control requirement acquisition.
The constraint condition processing module is used for processing constraint conditions in the mathematical model (2)The mathematical model can be converted into:
wherein G is i (i＝1,2,...,n g ) Is composed ofThe ith component of (1), rho is not less than 0 as a penalty factor, delta>, 0 is a smoothing factor, and
introducing new state variablesMake it satisfy
The mathematical model (3) can be further converted into:
wherein, the first and the second end of the pipe are connected with each other,in order for the state variable to be augmented,as an initial value thereof, the value of, is an augmented system of differential equations.
The control vector parameterization module adopts a piecewise constant strategy to realize the feeding rate control, and the control vector parameterization module specifically comprises the following steps:
suppose the entire control time domain t 0 ,t f ]Is divided into p (p)>, 0) control subintervals [ t k-1 ,t k ) (k =1,2,. Gtoreq., p), and
t 0 <t 1 <…<t p-1 <t p ＝t f (7)
thus, u (t) can be expressed as:
wherein the content of the first and second substances,is constant and represents u (t) in the control subinterval [ t ] k-1 ,t k ) Value of internal parameter, χ k (t) is a unit switching function, which is defined as follows:
thus, the feed rate control parameter may be derived from a vectorAnd (4) showing.
The NLP problem solving module comprises two submodules of Sequence Quadratic Programming (SQP) solving and simultaneous differential equation system solving. The system of simultaneous differential equations comprises a system of equations
And system of equations
Wherein the content of the first and second substances,
solving simultaneous differential equations (10) and (11) by using a fourth-order Runge-Kutta algorithm, so as to obtain an objective function value of the mathematical model (6) and first-order gradient information of the objective function to the control parameter vector:
the adaptive control node allocation module provides a strategy for adaptively allocating control nodes, which specifically comprises the following steps:
the optimal value of the objective function obtained by the first iteration is assumed to be J *l The optimum control parameter is The corresponding control grid isBy dividing Δ l Is halved to obtain a control gridAnd initial control parameters
For theWherein the current value isRespective parameters ofTo evaluate its effect on the amount of decrease of the objective function J, a definition is madeThe sensitivity to J was:
wherein, the first and the second end of the pipe are connected with each other,represents the largest integer not exceeding (j + 1)/2.
Suppose inControl intervalIn the interior of said container body,respectively the optimal control parameter values obtained at the (l-1) th time and the (l) th time. If the following conditions are satisfied:
wherein epsilon uv >, 0 is given threshold value, then order
s 2k-1 =0 and s 2k ＝0 (17)
For delta l' Control node in (1)If it is retained in the next iteration, it is satisfied that:
or
Wherein r is su >, 0 is a given coefficient,for average sensitivity, it is defined as follows:
if equation (18) is not satisfied, the control node is eliminated.
When the control nodeAndare all eliminated, if the following conditions are satisfied
And is
Wherein a given coefficient r sl ∈(0,r su ]、ε uh >, 0, then the control nodeShould also be eliminated.
Through the steps of halving the control grid, eliminating the control nodes and the like, the control grid delta l' Control grid delta that can be used as next iteration l+1 。
The time scale conversion module is used for converting the current mathematical model (6) to a new time scale so as to optimize the control grid obtained by the adaptive control node distribution module, and the specific steps are as follows:
for a newly inserted control nodeIf it satisfies
Or
Wherein a given coefficient r ss ≥r su Then the control node is considered to be an important control node. Thus, controlling the subintervalAndconsidered as an important control subinterval, the length of which can be optimized as a variable to find a control nodeThe optimal position of (a).
Suppose that P control subintervals [ t ] exist in the whole control time domain after being adjusted by the self-adaptive control node allocation module k-1 ,t k ) (k =1,2, \8230;, P), the length of each control sub-interval being in θ k Is expressed and has an initial value of
For the non-important control subintervals, the length of the control subintervals is constant and does not need to be optimized. For the important control subintervals, they are assumed to be divided into R (R ≧ 1) parts, and the R-th (1 ≦ R ≦ R) part containing n r (n r Not less than 2) continuous control subintervals, and the lengths of all the control subintervals meet the following conditions:
the time scale transfer function is introduced as follows:
wherein tau is a new time variable,representing no more than τThe largest integer. In this way, the mathematical model (6) can be converted on a new time scale into:
wherein the content of the first and second substances,
the DCS generates the flow control valve opening command according to the following process:
step B1: the information acquisition module acquires the duration of the production process and the feeding rate control requirement specified by an engineer;
and step B2: the initialization module operates to set the initial control grid number p and the initial guess value of the feeding rate control strategyThe constant value rho is more than or equal to 0 and delta>0、ε uv >0、ε uh >0、r su >0、r sl ∈(0,r su ]、r ss ≥r su Setting the maximum number of iterations l max 1 or more and a termination error tol J >, 0, and let iteration count l =0;
and step B3: the constraint condition processing module converts a mathematical model of a production process of a target product in the batch reactor;
and step B4: the control vector parameterization module adopts a piecewise constant strategy to represent a feeding rate control curve, if l =0, a control time domain is equally divided into p segments to obtain a current control grid, and all control parameter values are made to beOtherwise, adopt Delta l As the current control grid, the parameter value in each control subinterval is in the corresponding control time domainA value of (d);
and step B5: an SQP solving module in the NLP problem solving module operates, and obtains an objective function value and first-order gradient information of the objective function to the control parameter vector through a simultaneous differential equation solving module to finally obtain an objective function optimal value J under the current control grid *l And corresponding optimal control parameters
Step B6: the termination condition judgment module operates for l>, 0, if l = l max Or
Executing the step B10, otherwise, executing the step B7;
and step B7: the adaptive control node distribution module operates to obtain a new control grid delta l+1 ；
And step B8: let iteration count l = l +1, if l = l max If yes, executing the step B9, otherwise, turning to the step B4;
step B9: the time scale conversion module converts the mathematical model to a new time scale and then transfers the time scale to the step B4;
and step B10: and the control instruction output module outputs the obtained optimal feeding rate control strategy.
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