CN114019802A - Sampling control method and system for two-stage chemical reactor system - Google Patents

Sampling control method and system for two-stage chemical reactor system Download PDF

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CN114019802A
CN114019802A CN202111316300.7A CN202111316300A CN114019802A CN 114019802 A CN114019802 A CN 114019802A CN 202111316300 A CN202111316300 A CN 202111316300A CN 114019802 A CN114019802 A CN 114019802A
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chemical reactor
reactor system
stage chemical
sampling
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段朝霞
韩雨辰
戴君
吴泽成
封雨纯
封虎
曾寅寅
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Hohai University HHU
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • 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
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention discloses a sampling control method and a sampling control system for a two-stage chemical reactor system, wherein a Lyapunov function and a control signal thereof are respectively designed aiming at the condition that whether the system is switched in a sampling period or not by establishing a state space model of the two-stage chemical reactor system, and the sampling period and the average residence time are designed, so that the stability of a closed-loop system is finally proved, and the complete sampling control method for the two-stage chemical reactor system is obtained. By designing the gain and the sampling period of the controller, the design process is flexible, a more appropriate controller can be designed according to different conditions, the control effect is obvious, the control cost can be obviously reduced, and the method has higher engineering practical value.

Description

Sampling control method and system for two-stage chemical reactor system
Technical Field
The invention relates to the technical field of control science and control engineering, in particular to a sampling control method and a sampling control system of a two-stage chemical reactor system.
Background
The two-stage chemical reactor is a common nonlinear system, and has the advantages of strong heat exchange capacity, stable product quality, low cost and the like, so that the two-stage chemical reactor plays an important role in core equipment of chemical production and is widely applied to industrial production of dyes, medical reagents, food, synthetic materials and the like. The control variables of the system mainly comprise the temperature, the concentration and the like of reactants, and the control effect on the variables directly influences the production quality of chemical products. Therefore, the two-stage chemical reactor system has higher research value in the aspects of model and control.
With the integration and development of control theory and computer technology, sampling control schemes become research hotspots, and unlike continuous time control systems, sampling control systems are composed of continuous time controlled objects and sampling controllers. In a sampling control system, a controller is constructed using only information of measurable system states at sampling times. The time interval between two sampling instants is called the sampling period. Subsequently, the discrete control signal is converted into a continuous time control signal by the zero-order keeper, i.e. the control quantity is held in the sampling interval, so that the continuous signal is used as the input of the controlled object to control the system in the whole sampling period. Currently, there is still a need for more intensive control strategy research for two-stage chemical reactor systems.
Disclosure of Invention
The technical purpose is as follows: in view of the above technical problems, the present invention provides a sampling control method for a two-stage chemical reactor system, which improves the control strategy of the two-stage chemical reactor system, so that the system has better performance under different operating conditions.
The technical scheme is as follows: in order to achieve the technical purpose, the invention adopts the following technical scheme:
a sampling control method for a two-stage chemical reactor system, characterized by sequentially performing:
establishing a mathematical model of the two-stage chemical reactor system according to the structure of the two-stage chemical reactor system, and further establishing a state space model of the two-stage chemical reactor system according to the mathematical model;
secondly, introducing coordinate transformation on the basis of the state space model of the two-stage chemical reactor system established in the first step, and constructing a corresponding Lyapunov function and a corresponding control law according to the condition that whether the two-stage chemical reactor system is switched in a sampling period;
step three, designing a sampling period;
and step four, designing the average residence time, and constructing the Lyapunov function again to prove the stability of the closed-loop system.
Preferably, in step one, the mathematical model of the two-stage chemical reactor system is represented by formula (1):
Figure BDA0003343794530000021
wherein q isσV is the volume of the reactor for the feed flow rate,
Figure BDA0003343794530000022
inlet concentration of reactant, CAIs the concentration of reactant A, a0Is the reaction rate constant, E is the activation energy, R is the gas constant, TCSTRIs the reactor temperature;
Figure BDA0003343794530000023
reactant inlet temperature,. DELTA.H reaction enthalpy,. rho fluid density, CPHeat capacity of a fluid, UA is heat transfer constant, VPIs the volume of fluid, TcThe coolant temperature.
Preferably, in step one, according to equation (1), a state space model of the two-stage chemical reactor system is established as shown in equation (2):
Figure BDA0003343794530000024
wherein x is1，x2The status of the system is indicated,
Figure BDA0003343794530000025
σ (t) is the switching signal, u represents the controller input, f1,σ(t),f2,σ(t)Respectively represent corresponding states x1And state x2Continuous non-linear function of h1,σ(t),h2,σ(t)Representing the control gain, the controller input u is represented as:
Figure BDA0003343794530000026
tkthe kth sampling instant.
Preferably, in the second step, if the two-stage chemical reactor system is switched within one sampling period, the following steps (2.1) and (2.2) are performed, and if the two-stage chemical reactor system is not switched within one sampling period, the following steps (3) and (4) are performed:
(2.1) switching signals to satisfy σ (t) within one sampling periodk)＝σ(tk+1) Introducing a coordinate transformation:
z1＝x1,
z2,l＝x2-α1,l, (4)
x1，x2indicating the system state, α1,lIs a virtual controller;
the control signals are designed as:
Figure BDA0003343794530000031
wherein the content of the first and second substances,
Figure BDA0003343794530000032
Figure BDA0003343794530000033
h 1,lare respectively h1,lMaximum and minimum values of (a), λ1,l、c1,l、c2,lIs a normal number;
(2.2) constructing the Lyapunov function as
Figure BDA0003343794530000034
The derivation is:
Figure BDA0003343794530000035
d, alpha is a normal number, such that
Figure BDA0003343794530000036
To obtain
Figure BDA0003343794530000037
Further obtaining:
Vn,l(tk+1)≤δVn,l(tk) (8)
wherein the content of the first and second substances,
Figure BDA0003343794530000047
t is a sampling period;
(2.3) switching signals to satisfy σ (t) within one sampling periodk)＝l,σ(tk+1) Introducing a coordinate transformation:
z1＝x1,
z2,m＝x2-α1,m,
the control signals are:
Figure BDA0003343794530000042
wherein γ > 0;
(2.4) constructing the Lyapunov function
Figure BDA0003343794530000043
And (5) obtaining a derivative:
Figure BDA0003343794530000044
order to
Figure BDA0003343794530000045
Obtaining:
Figure BDA0003343794530000046
let PmIs a positive definite matrix, V2,m＝ZTPmZ，Z＝[x1,x2]TObtaining:
V2,m(tk+1)＜υV2,l(tk) (12)
wherein the content of the first and second substances,
Figure BDA0003343794530000051
maxm∈2λ(Pm)，minm∈2λ(Pm) Are respectively a matrix PmMaximum and minimum eigenvalues of.
Preferably, in step three, the sampling period is:
Figure BDA0003343794530000052
wherein d and alpha are normal numbers.
Preferably, in step four, the average residence time is designed to be:
Figure BDA0003343794530000053
reconstructing the Lyapunov function
Figure BDA0003343794530000054
Obtaining:
Figure BDA0003343794530000055
wherein, t0Indicating an initial time, N0 is a positive integer,
Figure BDA0003343794530000056
a sampling control system for a two-stage chemical reactor system is characterized by comprising the two-stage chemical reactor system with more than two switching states and a control module, wherein the control module is connected with the two-stage chemical reactor system;
wherein the control module comprises a processor, a memory communicatively coupled to the processor; the memory stores instructions executable by the at least one processor to cause the processor to perform the sampling control method for a two-stage chemical reactor system.
Preferably, the two-stage chemical reactor system comprises more than two raw material tanks serving as a first stage of the system and reaction tanks CSTR serving as a second stage of the system, wherein each raw material tank is filled with chemical raw materials A with different concentrations, and each reaction tank CSTR is provided with a reactant feeding hole, a reaction product discharging hole, a coolant inlet and a coolant outlet;
a reversing valve is arranged at a reactant feed inlet of the reaction tank CSTR and used for switching a raw material tank for inputting reactant raw materials into the reaction tank.
Has the advantages that: due to the adoption of the technical scheme, the invention has the following technical effects:
(1) the method is used for controlling the two-stage chemical reactor system, the design process is flexible by designing the gain and the sampling period of the controller, and a more appropriate controller can be designed according to different conditions;
(2) the method of the invention takes the sampling control as a novel control strategy, has obvious control effect, can obviously reduce the control cost, is more convenient to realize by a microprocessor and has higher engineering practical value.
(3) The method is suitable for a chemical reactor system with two or more switching states, and the sampling control has the advantages of high flexibility, strong reliability, stable system operation and the like.
Drawings
FIG. 1 is a flow chart of a sampling control method of a two-stage chemical reactor system model in the present invention;
FIG. 2 is a schematic diagram of the structure of a two-stage chemical reactor system according to the present invention.
Detailed Description
The present invention will be described in detail below with reference to specific embodiments shown in the drawings.
The invention provides a sampling control method for a two-stage chemical reactor system model, and fig. 1 shows a method flow chart, wherein 1 is to establish a state space model of the two-stage chemical reactor system, 2 is to design a control signal, 3 is to design a proper sampling period, and 4 is to design a proper average residence time. Taking the two-stage chemical reactor system model shown in fig. 2, taking two material tanks as an example, i.e. 2 switching states, the sampling control method of the two-stage chemical reactor system provided by the present invention can also be applied to 3 or more than 3 switching states. The system shown in fig. 2 comprises a first material Tank1 and a second material Tank2 as a first stage of the system, and a reaction Tank CSTR (Continuous Stirred-Tank Reactor) as a second stage of the system, and further comprises a monitor Supervisor and a Selector Valve arranged at a Reactant inlet of the reaction Tank, wherein the reaction Tank CSTR is provided with a Reactant Feed port Reactant Feed, a reaction Product discharge port Product, a coolant inlet and a coolant outlet, the first material Tank and the second material Tank are filled with chemical materials a with different concentrations, material output ports of the first material Tank and the second material Tank are connected to the Reactant Feed port of the reaction Tank through a reversing Valve, and a switching state of the reversing Valve is monitored by the monitor, and Reactant materials with different concentrations are input into the reaction Tank through the switching reversing Valve.
The method comprises the following specific steps:
step one, establishing a state model of a two-stage chemical reactor system:
Figure BDA0003343794530000071
wherein q isσV is the volume of the reactor for the feed flow rate,
Figure BDA0003343794530000072
inlet concentration of reactants, labeled in FIG. 2
Figure BDA0003343794530000073
The position of (1) is the reactant inlet; cAThe concentration of the reactant A after stirring in the reactor, a0Is the reaction rate constant, E is the activation energy, R is the gas constant, TCSTRIs the reactor temperature;
Figure BDA0003343794530000074
reactant inlet temperature,. DELTA.H reaction enthalpy,. rho fluid density, CPHeat capacity of a fluid, UA is heat transfer constant, VρIs the volume of fluid, TcThe coolant temperature.
According to equation (1), a state space model of the following two-stage chemical reactor system can be established:
Figure BDA0003343794530000075
wherein x is1＝CA，x2＝TCSTRWhich is representative of the state of the system,
Figure BDA0003343794530000076
σ (t) is the switching signal, u represents the controller input, f1,σ(t),f2,σ(t)Represents an unknown continuous non-linear function, h1,σ(t),h2,σ(t)Representing the control gain. The controller inputs are represented as:
Figure BDA0003343794530000077
wherein, tkIs the kth sampling instant, k is 0,1,2, …
Step two, designing a control signal:
when the switching signal satisfies sigma (t) within one sampling periodk)＝σ(tk+1) Introducing a coordinate transformation:
z1＝x1,
z2,l＝x2-α1,l, (4)
z1,z2,lis a system state, α1,lIs a virtual controller. The control signals are designed as:
Figure BDA0003343794530000081
wherein the content of the first and second substances,
Figure BDA0003343794530000082
Figure BDA0003343794530000083
h 1,lare respectively h1,lMaximum and minimum values of (a), λ1,l,c1,l，c2,lIs a normal number.
Constructing a Lyapunov function of
Figure BDA0003343794530000084
The derivation is:
Figure BDA0003343794530000085
d, alpha are normal numbers. Order to
Figure BDA0003343794530000086
To obtain
Figure BDA0003343794530000087
Further obtaining:
Vn,l(tk+1)≤δVn,l(tk) (8)
Figure BDA0003343794530000088
δ＝(e-T+d2(1-e-T))2。
when the switching signal satisfies sigma (t) within one sampling periodk)＝l,σ(tk+1) Constructing the Lyapunov function as m
Figure BDA0003343794530000089
The control signals are:
Figure BDA0003343794530000091
wherein γ > 0. Let T be the sampling period, further obtain
Figure BDA0003343794530000092
Order to
Figure BDA0003343794530000093
To obtain
Figure BDA0003343794530000094
Let PmIs a positive definite matrix, V2,m＝ZTPmZ，Z＝[x1,x2]TThe following can be obtained:
V2,m(tk+1)＜υV2,l(tk), (12)
wherein the content of the first and second substances,
Figure BDA0003343794530000095
maxm∈2λ(Pm)，minm∈2λ(Pm) Are respectively a matrix PmMaximum and minimum eigenvalues of.
Step three, designing a sampling period T:
as shown in formula (13):
Figure BDA0003343794530000096
the length of the sampling period and the length of the residence time both relate to the stability of the system, the larger the sampling period is, the lower the communication cost is, but the too large sampling period may cause the system to be unstable, so the sampling period is usually designed to be less than a certain value, for example, the relationship satisfying the equation (13) can be designed.
Step four, designing proper average residence time:
within a certain sampling period, switching behavior may or may not occur, and the average residence time is expressed as the average residence time in both states. The stability of the closed loop system is demonstrated by designing the appropriate average residence time.
The average residence time is designed as:
Figure BDA0003343794530000097
constructing the Lyapunov function
Figure BDA0003343794530000101
Then, the following results were obtained:
Figure BDA0003343794530000102
where k denotes the kth sample, t0Denotes the initial time, N0Is a positive integer and is a non-zero integer,
Figure BDA0003343794530000103
the whole closed loop system can be gradually stabilized.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (8)

1. A sampling control method for a two-stage chemical reactor system, characterized by sequentially performing:
establishing a mathematical model of the two-stage chemical reactor system according to the structure of the two-stage chemical reactor system, and further establishing a state space model of the two-stage chemical reactor system according to the mathematical model;
secondly, introducing coordinate transformation on the basis of the state space model of the two-stage chemical reactor system established in the first step, and constructing a corresponding Lyapunov function and a corresponding control law according to the condition that whether the two-stage chemical reactor system is switched in a sampling period;
step three, designing a sampling period;
and step four, designing the average residence time, and constructing the Lyapunov function again to prove the stability of the closed-loop system.
2. The sampling control method for a two-stage chemical reactor system according to claim 1, wherein in the first step, the mathematical model of the two-stage chemical reactor system is represented by formula (1):
Figure FDA0003343794520000011
wherein q isσV is the volume of the reactor for the feed flow rate,
Figure FDA0003343794520000012
inlet concentration of reactant, CAIs the concentration of reactant feedstock A after stirring in the reactor, a0Is the reaction rate constant, E is the activation energy, R is the gas constant, TCSTRIs the reactor temperature;
Figure FDA0003343794520000013
reactant inlet temperature,. DELTA.H reaction enthalpy,. rho fluid density, CPHeat capacity of a fluid, UA is heat transfer constant, VPIs the volume of fluid, TcThe coolant temperature.
3. The sampling control method for a two-stage chemical reactor system according to claim 2, wherein in the first step, according to equation (1), the state space model of the two-stage chemical reactor system is established as shown in equation (2):
Figure FDA0003343794520000014
wherein x is1＝CA，x2＝TCSTRThe status of the system, is indicated,
Figure FDA0003343794520000015
σ (t) is the switching signal, u represents the controller input, f1,σ(t),f2,σ(t)Respectively represent corresponding states x1And state x2Continuous non-linear function of h1,σ(t),h2,σ(t)Representing the control gain, the controller input u is represented as:
Figure FDA0003343794520000021
tkthe kth sampling instant.
4. The sampling control method for a two-stage chemical reactor system according to claim 1, wherein in the second step, if the two-stage chemical reactor system is switched in one sampling period, the following steps (2.1) and (2.2) are performed, and if the two-stage chemical reactor system is not switched in one sampling period, the following steps (2.3) and (2.4) are performed:
(2.1) switching signals to satisfy σ (t) within one sampling periodk)＝σ(tk+1) Introducing a coordinate transformation:
z1＝x1,
z2,l＝x2-α1,l, (4)
x1，x2indicating the system state, α1,lIs a virtual controller;
the control signals are designed as:
Figure FDA0003343794520000022
wherein the content of the first and second substances,
Figure FDA0003343794520000023
Figure FDA0003343794520000024
Figure FDA0003343794520000025
are respectively h1,lMaximum and minimum values of (a), λ1,l、c1,l、c2,lIs a normal number;
(2.2) constructing the Lyapunov function as
Figure FDA0003343794520000026
The derivation is:
Figure FDA0003343794520000027
d, alpha is a normal number, such that
Figure FDA0003343794520000031
To obtain
Figure FDA0003343794520000032
Further obtaining:
Vn,l(tk+1)≤δVn,l(tk) (8)
wherein the content of the first and second substances,
Figure FDA0003343794520000033
δ＝(e-T+d2(1-e-T))2t is a sampling period;
(2.3) switching signals to satisfy σ (t) within one sampling periodk)＝l,σ(tk+1) Introducing a coordinate transformation:
z1＝x1,
z2,m＝x2-α1,m,
the control signals are:
Figure FDA0003343794520000034
wherein γ > 0;
(2.4) constructing the Lyapunov function
Figure FDA0003343794520000035
And (5) obtaining a derivative:
Figure FDA0003343794520000036
order to
Figure FDA0003343794520000037
Obtaining:
Figure FDA0003343794520000041
let PmIs a positive definite matrix, V2,m＝ZTPmZ，Z＝[x1,x2]TObtaining:
V2,m(tk+1)＜υV2,l(tk) (12)
wherein the content of the first and second substances,
Figure FDA0003343794520000042
maxm∈2λ(Pm)，，inm∈2λ(Pm) Are respectively a matrix PmMaximum and minimum eigenvalues of.
5. The sampling control method for a two-stage chemical reactor system according to claim 4, wherein in step three, the sampling period is:
Figure FDA0003343794520000043
wherein d and alpha are normal numbers.
6. A sampling control method for a two-stage chemical reactor system according to any of claims 4 and 5, wherein in the fourth step, the average residence time is designed to be:
Figure FDA0003343794520000044
reconstructing the Lyapunov function
Figure FDA0003343794520000045
Obtaining:
Figure FDA0003343794520000046
wherein, t0Denotes the initial time, N0Is a positive integer and is a non-zero integer,
Figure FDA0003343794520000047
7. a sampling control system for a two-stage chemical reactor system is characterized by comprising the two-stage chemical reactor system with more than two switching states and a control module, wherein the control module is connected with the two-stage chemical reactor system;
wherein the control module comprises a processor, a memory communicatively coupled to the processor; the memory stores instructions executable by the at least one processor to cause the processor to perform the sampling control method for a two-stage chemical reactor system of any of claims 1 to 6.
8. A sampling control system for a two-stage chemical reactor system according to claim 7, wherein: the two-stage chemical reactor system comprises more than two raw material tanks serving as a first stage of the system and reaction tanks CSTR serving as a second stage of the system, wherein chemical raw materials A with different concentrations are filled in each raw material tank, and each reaction tank CSTR is provided with a reactant feeding hole, a reaction product discharging hole, a coolant inlet and a coolant outlet;
a reversing valve is arranged at a reactant feed inlet of the reaction tank CSTR and used for switching a raw material tank for inputting reactant raw materials into the reaction tank.
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Cited By (1)

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Publication number Priority date Publication date Assignee Title
CN116520712A (en) * 2023-07-03 2023-08-01 贵阳职业技术学院 Self-adaptive regulation and control method, system, terminal and medium for feeding amount of reaction container

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109870908A (en) * 2019-02-27 2019-06-11 南京理工大学 A kind of sampling control method for continuous stirred tank reactor system

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109870908A (en) * 2019-02-27 2019-06-11 南京理工大学 A kind of sampling control method for continuous stirred tank reactor system

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116520712A (en) * 2023-07-03 2023-08-01 贵阳职业技术学院 Self-adaptive regulation and control method, system, terminal and medium for feeding amount of reaction container
CN116520712B (en) * 2023-07-03 2023-08-22 贵阳职业技术学院 Self-adaptive regulation and control method, system, terminal and medium for feeding amount of reaction container

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