Intelligent constrained output feedback control method for chemical continuous stirred tank reactor

Abstract

The application provides an intelligent constraint output feedback control method for a chemical continuous stirred tank reactor, and the method comprises the following steps: constructing a kinetic model for estimating the concentration and temperature inside the continuous stirred tank reactor (CSTR); constructing a state observer through a fuzzy logic system, estimating the unknown state inside the CSTR system by using the state observer, and feeding back the estimated value to the fuzzy logic system; designing a concentration virtual controller of the CSTR system, constructing an obstacle Lyapunov function, converting the concentration tracking problem into a constraint problem, realizing the coupling control link from the concentration to the temperature; based on the output of the concentration virtual controller, designing a controller to make the concentration reach the desired effect and control the temperature in the safe range, realizing the intelligent constraint output feedback control of the continuous stirred tank reactor; and the application realizes that the continuous stirred tank reactor (CSTR) can reach the desired operating state.

Description

Technical Field

[0001] This invention relates to the field of chemical reaction control technology, and in particular to an intelligent constraint output feedback control method for a continuous stirred chemical reactor. Background Technology

[0002] With the continuous development of the chemical industry, the continuous stirred tank reactor (CSTR), as a core piece of equipment in chemical processing, directly affects product quality, production efficiency, and safety through its control precision and stability. Traditional CSTR control systems rely on precise mathematical models and a large amount of sensor data to maintain operating conditions. This method is costly and inflexible, making it difficult to respond to unknown disturbances or nonlinear changes in real time.

[0003] Fuzzy logic systems have emerged as a solution due to their ability to handle uncertainties and nonlinear problems. By introducing fuzzy state observers, the reliance on dense measurement data can be reduced, while key parameters such as temperature and concentration within a continuous stirred tank reactor (CSTR) can be accurately estimated, enabling more efficient process control.

[0004] In practical industrial applications, continuous stirred tank reactor (CSTR) systems often face sudden changes in operating conditions or external disturbances, which places higher demands on the control system. Traditional fixed-parameter controllers may not be able to guarantee stability and response speed under such circumstances. Therefore, it is necessary to develop a control strategy that can adaptively adjust and maintain high precision, ensuring rapid recovery to the ideal operating state when encountering unknown disturbances. To enhance anti-interference capability and adaptability, an adaptive mechanism also needs to be introduced to dynamically compensate for unforeseen changes. Summary of the Invention

[0005] The technical problem to be solved by this invention is the complexity of information processing and the sensitivity to unknown interference in existing continuous stirred tank reactor (CSTR) systems.

[0006] This invention proposes an intelligent constraint output feedback control method for a continuous stirred chemical reactor, the method comprising the following steps:

[0007] A kinetic model is constructed to estimate the concentration and temperature inside a continuous stirred tank reactor (CSTR). A state observer is constructed using a fuzzy logic system. The state observer is used to estimate the unknown state inside the CSTR system, and the estimated value is fed back to the fuzzy logic system.

[0008] Design a concentration virtual controller for the CSTR system, construct a barrier Lyapunov function, transform the concentration tracking problem into a constraint problem, and realize a coupled control link from concentration to temperature;

[0009] Based on the output of the concentration virtual controller, a controller was designed to achieve the desired concentration and keep the temperature within a safe range, thus realizing intelligent constraint output feedback control of the continuous stirred reactor.

[0010] Furthermore, the dynamic model is as follows:

[0011]

[0012] Where x1 is the chemical reaction concentration, x2 is the chemical reaction temperature, u is the initial reaction input concentration, and D... a It is the Damokhler number, Φ is the activation energy, and B is the activation energy. h y is the heat of reaction, β is the heat transfer coefficient, exp is an exponential function with the real number e as the base, and y represents the output of the CSTR system. This represents the rate of change of chemical reaction concentration over time. It represents the rate of change of temperature in a chemical reaction over time.

[0013] Furthermore, a method for estimating unknown states within the CSTR system by constructing a state observer through a fuzzy logic system and using the state observer is as follows:

[0014] A fuzzy logic system is defined, which can be represented as:

[0015]

[0016] in, This represents the output of the fuzzy logic system. This represents the output value of the h-th fuzzy rule. Let represent the estimated value of the adaptive parameter vector for the h-th fuzzy rule. The fuzzy basis function representing the state estimate of the h-th fuzzy rule;

[0017] When using a state observer to estimate the unknown states within a CSTR system, the state observer is set as follows:

[0018]

[0019] Where n = 2, Let Π be the gain matrix of the state observer, where Π = [k1, k2, ..., k n ] T Let B be the gain matrix for the output error, where B = [0...0...1]. T To control the gain matrix of the input, τ i =[0...1...0] T To select a vector, C i=[0...1...0] is the output matrix, This represents the state estimation vector of the state observer. Let represent the estimated value of the i-th state, and y represent the output of the CSTR system. q is the output estimate of the state observer, and q is the control input of the CSTR system; as well as Let i = {1, 2} represent the unknown function, and let i = {1, 2} represent the concentration and temperature of the chemical reaction, respectively. A fuzzy logic system is used to approximate the unknown function. h = {1, 2} represents a fuzzy rule.

[0020] Furthermore, the concentration virtual controller of the CSTR system is designed, and a barrier Lyapunov function is constructed to transform the concentration tracking problem into a constraint problem.

[0021] Step 3.1: Define the time-varying barrier Lyapunov function:

[0022]

[0023]

[0024] Where V1 and V2 represent the BLF functions of chemical reaction concentration and chemical reaction temperature, respectively; z i Let be the error at step i. For observation error, Let x be the i-th chemical reaction state. i The estimated value, and These are the time-varying state constraint functions for chemical reaction concentration and temperature, respectively. Similarly... Let p be the time-varying state constraint function for the i-th step, and γ be a positive matrix. i The positive constant set in step i, For the error of the adaptive parameter vector, θ i This is the optimal adaptive parameter vector. For θ i The estimated value, and That is, the estimated value of the optimal adaptive parameter vector for the i-th chemical reaction, i = {1, 2}, which means that when i = 1, the concentration of the chemical reaction is studied, and when i = 2, the temperature of the chemical reaction is studied.

[0025] Step 3.2: Taking the derivatives with respect to V1 and V2 respectively, we get:

[0026]

[0027] in, For observation error, Let x be the i-th chemical reaction state.i The estimated value, Let z be the time-varying state constraint function at step i. i For the error at step i, similarly... z1 and z2 are the time-varying state constraint function and tracking error of the chemical reaction concentration, respectively; z2 is the error of the chemical reaction temperature; λ is a positive design parameter; p and Q are both positive matrices; σ and k′ are set positive constants; c i and γ i The positive constant set in step i, For the error of the adaptive parameter vector, θ i This is the optimal adaptive parameter vector. For θ i The estimated values ​​are i = {1, 2}; δ = {δ1′, δ2′}. T For a known constant, similarly, δ i ′ is a known constant designed in the i-th step, where i = {1, 2};

[0028] Step 3.3: The method for designing the concentration virtual controller of the CSTR system is as follows:

[0029]

[0030] The controller for the continuous stirred tank reactor (CSTR) is designed as follows:

[0031]

[0032] in, The control gain function is positive for the chemical reaction concentration. The control gain function is positive for the chemical reaction temperature, and ψ1 and ψ2 are set positive constants. Where z1 is the tracking error of the chemical reaction concentration, and z2 is the error of the chemical reaction temperature. and Let be the time-varying state constraint functions for chemical reaction concentration and temperature, respectively. for The first derivative, for The first derivative; α1 is the concentration virtual controller, y d To track the signal, y is the system's control output. This is an estimate of the concentration of the chemical reaction. Concentration state estimate The fuzzy basis functions, c1, c2, κ and k are positive constants in the design. This is an estimate of the optimal adaptive parameter vector for the chemical reaction concentration;

[0033]

[0034] in, For observer error, This is an estimate of the concentration of the chemical reaction. The given value is an estimate of the chemical reaction temperature, and the range of values ​​for x1 is... State estimate fuzzy basis functions, State estimate fuzzy basis functions, Where z1 is the tracking error of the chemical reaction concentration, and z2 is the error of the chemical reaction temperature. and Let be the time-varying state constraint functions for chemical reaction concentration and temperature, respectively, where α1 is the concentration virtual controller, and y is the temperature. d To track the signal, y is the system's control output. and These are the estimated values ​​of the optimal adaptive parameter vectors for chemical reaction concentration and temperature, respectively. It is the adaptive law of chemical reaction concentration.

[0035] Furthermore, the adaptive law of chemical reaction concentration and temperature and The definition is as follows:

[0036]

[0037] Where γ1, γ2, and σ are defined positive constants. and These are the state estimates. and fuzzy basis functions; and and Let z1 and z2 be the time-varying state constraint functions for chemical reaction concentration and temperature, respectively, where z1 is the tracking error for chemical reaction concentration and z2 is the error for chemical reaction temperature. and These are the optimal adaptive parameter vector estimates for chemical reaction concentration and temperature, respectively.

[0038] For the dynamic model, a state observer, controller u2, virtual controller α1, and adaptive rate are designed. and To ensure that the error variable converges to near the origin and the closed-loop system achieves semi-global stability, we can substitute the above variables into V1 and V2 respectively and obtain the following results using Young's inequality: and And ultimately, an equation is obtained that satisfies... The form of, by We can obtain that ρ=min{2[(λ min (Q)-i) / λ min (P)],2c i ,2σ}, Where i = {1, 2}.

[0039] The advantages and positive effects of this invention are:

[0040] 1. This invention, by introducing a fuzzy state observer, enables accurate estimation of internal states such as temperature and concentration in a continuous stirred tank reactor (CSTR) system when the system state is unknown, thereby reducing the cost of the control system and improving efficiency; the designed adaptive control strategy can achieve system state stability.

[0041] 2. This invention is specifically applied to the control of a continuous stirred tank reactor system. By introducing a fuzzy state observer, the estimation of the unknown system state is realized. It mainly enables the continuous stirred tank reactor (CSTR) to reach the desired operating state and effectively handles the influence of abnormalities or external disturbances. Attached Figure Description

[0042] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. However, it should be understood that these drawings are designed for illustrative purposes only and are not intended to limit the scope of the present invention. Furthermore, unless specifically indicated, these drawings are intended only to conceptually illustrate the structural construction described herein and are not necessarily drawn to scale.

[0043] Figure 1 A flowchart of an intelligent constraint output feedback control method for a continuous stirred chemical reactor provided in this embodiment of the invention;

[0044] Figure 2 This is a state tracking diagram of a continuous stirred tank reactor (CSTR) system provided in an embodiment of the present invention.

[0045] Figure 3 An observation error diagram of the CSTR system for continuous stirred tank reactor provided in an embodiment of the present invention;

[0046] Figure 4 Trajectory diagram of adaptive parameter vector estimation values ​​for a continuous stirred tank reactor (CSTR) system provided in an embodiment of the present invention;

[0047] Figure 5 A controller trajectory diagram of a continuous stirred tank reactor (CSTR) system provided in an embodiment of the present invention;

[0048] in, Figure 2 middle, and k c These represent the upper and lower bounds of the concentration state x1 in the chemical reaction, respectively. Figure 3 In this context, e1 represents the observation error χ. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of this invention. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0050] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0051] like Figure 1 As shown in the figure, this embodiment provides an intelligent constraint output feedback control method for a continuous stirred chemical reactor, the method including the following steps:

[0052] A kinetic model is constructed to estimate the temperature and concentration inside a continuous stirred tank reactor (CSTR). A state observer is built using a fuzzy logic system. The state observer is used to estimate the unknown state inside the CSTR system, and the estimated value is fed back to the fuzzy logic system.

[0053] Design a concentration virtual controller for the CSTR system, construct a barrier Lyapunov function, transform the concentration tracking problem into a constraint problem, and realize a coupled control link from concentration to temperature;

[0054] Based on the output of the concentration virtual controller, a controller was designed to achieve the desired concentration and keep the temperature within a safe range, thus realizing intelligent constraint output feedback control of the continuous stirred reactor.

[0055] Specifically, the dynamic model is as follows:

[0056]

[0057] Where x1 is the chemical reaction concentration, x2 is the chemical reaction temperature, u is the initial reaction input concentration, and D... a It is the Damokhler number, Φ is the activation energy, and B is the activation energy. h y is the heat of reaction, β is the heat transfer coefficient, exp is an exponential function with the real number e as the base, and y represents the output of the CSTR system. This represents the rate of change of chemical reaction concentration over time. It represents the rate of change of temperature in a chemical reaction over time.

[0058] The method for estimating unknown states within a CSTR system by constructing a state observer using a fuzzy logic system is as follows:

[0059] A fuzzy logic system is defined, which can be represented as:

[0060]

[0061] in, This represents the output of a fuzzy logic system. The fuzzy basis function represents the state estimate of the h-th fuzzy rule. This represents the output value of the h-th fuzzy rule. This represents the estimated value of the adaptive parameter vector for the h-th fuzzy rule;

[0062]

[0063] in, This represents the output of the fuzzy logic system. This represents the i-th input variable in the h-th rule. The membership function, where N represents the total number of fuzzy rules, and i = {1, 2}; This represents the output value of the h-th fuzzy rule. This represents an estimated value indicating the concentration of a chemical reaction. An estimated value representing the temperature of a chemical reaction;

[0064] Fuzzy basis functions It can be represented as:

[0065]

[0066] Using vectors To represent the fuzzy logic system, the fuzzy logic system equation (13) can be written as:

[0067]

[0068] When using a state observer to estimate the unknown states within a CSTR system, the state observer is set as follows:

[0069]

[0070] Where n = 2, Let Π be the gain matrix of the state observer, where Π = [k1, k2, ..., k n ] T Let B be the gain matrix for the output error, where B = [0...0...1]. T To control the gain matrix of the input, τ i =[0...1...0] T To select a vector, C i =[0...1...0] is the output matrix, This represents the state estimation vector of the state observer. Let represent the estimated value of the i-th state, and y represent the output of the CSTR system. q is the output estimate of the state observer, and q is the control input of the CSTR system; as well as Let i = {1, 2} represent the unknown function, corresponding to the study of chemical reaction concentration and temperature, respectively. A fuzzy logic system is used to approximate the unknown function. h = {1, 2} represents a fuzzy rule;

[0071] The method for designing a concentration virtual controller for a CSTR system, constructing a barrier Lyapunov function, and transforming the concentration tracking problem into a constraint problem is as follows:

[0072] Step 3.1: Define the time-varying barrier Lyapunov function:

[0073]

[0074] Where V1 and V2 represent the BLF functions of chemical reaction concentration and chemical reaction temperature, respectively; z i Let be the error at step i. For observation error, Let x be the i-th chemical reaction state. i The estimated value, and These are the time-varying state constraint functions for chemical reaction concentration and temperature, respectively. Similarly... Let p be the time-varying state constraint function for the i-th step, and γ be a positive matrix. i The positive constant set in step i, For the error of the adaptive parameter vector, θ i This is the optimal adaptive parameter vector. For θ i The estimated value, and That is, the estimated value of the optimal adaptive parameter vector for the i-th chemical reaction, i = {1, 2}, which means that when i = 1, the concentration of the chemical reaction is studied, and when i = 2, the temperature of the chemical reaction is studied.

[0075] Step 3.2: Taking the derivatives with respect to V1 and V2 respectively, we get:

[0076]

[0077] in, For observation error, Let x be the i-th chemical reaction state. i The estimated value, Let z be the time-varying state constraint function at step i. i For the error at step i, similarly... z1 and z2 are the time-varying state constraint function and tracking error of the chemical reaction concentration, respectively; z2 is the error of the chemical reaction temperature; λ is a positive design parameter; p and Q are both positive matrices; σ and k′ are set positive constants; c i and γ i The positive constant set in step i, For the error of the adaptive parameter vector, θ i This is the optimal adaptive parameter vector. For θ i The estimated values ​​are i = {1, 2}; δ = {δ1′, δ2′}. T For a known constant, similarly, δ i ′ is a known constant designed in the i-th step, where i = {1, 2}.

[0078] Step 3.3: The method for designing the virtual controller for the chemical reaction concentration of the CSTR system is as follows:

[0079]

[0080] Furthermore, the controller for the continuous stirred tank reactor (CSTR) is designed as follows:

[0081]

[0082] in, The control gain function is positive for chemical reaction concentration. The control gain function is positive for the chemical reaction temperature, and ψ1 and ψ2 are set positive constants. Where z1 is the tracking error of chemical reaction concentration, and z2 is the error of chemical reaction temperature. and Let be the time-varying state constraint functions for chemical reaction concentration and temperature, respectively. for The first derivative, for The first derivative; α1 is the concentration virtual controller, y d To track the signal, y is the system's control output. This is an estimate of the concentration of the chemical reaction. Concentration state estimate The fuzzy basis functions, c1, c2, κ and k are positive constants in the design. This is an estimate of the optimal adaptive parameter vector for the chemical reaction concentration;

[0083]

[0084] in, For observer error, This is an estimate of the concentration of the chemical reaction. The given value is an estimate of the chemical reaction temperature, and the range of values ​​for x1 is... State estimate fuzzy basis functions, State estimate fuzzy basis functions, Where z1 is the tracking error of chemical reaction concentration, and z2 is the error of chemical reaction temperature. and Let be the time-varying state constraint functions for chemical reaction concentration and temperature, respectively, where α1 is the concentration virtual controller, and y is the temperature. d To track the signal, y is the system's control output. and These are the estimated values ​​of the optimal adaptive parameter vectors for chemical reaction concentration and temperature, respectively. It is the adaptive law of chemical reaction concentration.

[0085] Adaptive law of chemical reaction concentration and temperature and The definition is as follows:

[0086]

[0087] Where γ1, γ2, and σ are defined positive constants. and These are the state estimates. and fuzzy basis functions; and and Let z1 and z2 be the time-varying state constraint functions for chemical reaction concentration and temperature, respectively, where z1 is the tracking error for chemical reaction concentration and z2 is the error for chemical reaction temperature. and These are the optimal adaptive parameter vector estimates for chemical reaction concentration and temperature, respectively.

[0088] For the dynamic model, a state observer, controller u2, virtual controller α1, and adaptive rate are designed. and To ensure that the error variable converges to near the origin and the closed-loop system achieves semi-global stability, we can substitute the above variables into V1 and V2 respectively and obtain the following results using Young's inequality: and And ultimately, an equation is obtained that satisfies... The form of, by We can obtain that ρ=min{2[(λ min (Q)-i) / λ min (P)],2c i ,2σ}, Where i = {1, 2}.

[0089] In this embodiment, a state observer is first constructed using a fuzzy logic system to estimate in real time the unmeasurable states caused by model nonlinearity (such as the reaction rate term) and parameter uncertainty, thus providing the controller with accurate... and Eliminating the influence of model uncertainties is the foundation for subsequent control design. Then, a virtual controller α1 for the concentration loop is designed to transform the concentration tracking problem into a constraint problem. The concentration error z1 drives the temperature controller through α1, establishing a coupled control link of "concentration → temperature". Finally, based on the virtual control output α1, the actual control input u2 is designed to achieve the desired concentration and control the temperature within a safe range, realizing intelligent constraint output feedback control of the continuous stirred reactor. Fuzzy logic and adaptive laws jointly overcome model nonlinearity, while the BLF function ensures process safety (such as preventing reaction runaway).

[0090] As an example, in this embodiment, such as Figure 2 The image shown is a state tracking diagram of a continuous stirred tank reactor (CSTR) system; from Figure 2 It can be seen from the observed system state It achieved good tracking results for the actual system state x1; such as Figure 3 The figure shown is an observation error diagram of the CSTR (Continuous Stirred Tank Reactor) system. Figure 3 It can be seen from the observed system state Compared to the actual system state x1, the error is smaller; such as Figure 4The figure shows the trajectory of the adaptive parameter vector estimates for the CSTR (Continuous Stirred Tank Reactor) system. and Boundedness directly supports the stability of a closed-loop system. Its convergence and boundedness are key to ensuring the convergence of tracking errors and that the system state satisfies constraints, indicating that the control strategy can effectively handle uncertainties and constraints in practical applications; for example... Figure 5 The figure shows the controller trajectory diagram of the CSTR system for continuous stirred tank reactors. It visually verifies that the system's tracking performance and convergence can be guaranteed through dynamic adjustment, while also ensuring the boundedness of the control input and system state, thus meeting the safety and constraint requirements in practical engineering.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A smart constraint output feedback control method for a continuous stirred chemical reactor, characterized in that, The method includes the following steps: A kinetic model is constructed to estimate the concentration and temperature inside a continuous stirred tank reactor (CSTR). A state observer is constructed using a fuzzy logic system. The state observer is used to estimate the unknown state inside the CSTR system, and the estimated value is fed back to the fuzzy logic system. Design a concentration virtual controller for the CSTR system, construct a barrier Lyapunov function, transform the concentration tracking problem into a constraint problem, and realize a coupled control link from concentration to temperature; Based on the output of the concentration virtual controller, the controller of CSTR is designed to achieve the desired concentration and control the temperature within a safe range, realizing intelligent constraint output feedback control of the continuous stirred reactor. The method for designing the concentration virtual controller of the CSTR system is as follows: ； The controller for the continuous stirred tank reactor (CSTR) is designed as follows: ； in, The control gain function is positive for chemical reaction concentration. The control gain function is positive for the chemical reaction temperature. and For the set positive numbers, , ,in To account for the tracking error of chemical reaction concentration, To account for the error in chemical reaction temperature, and Let be the time-varying state constraint functions for chemical reaction concentration and temperature, respectively. for The first derivative, for The first derivative; For concentration virtual controller, For the controller of CSTR, To track signals, To track signals The second derivative, For the system's control output, This is an estimate of the concentration of the chemical reaction. Concentration state estimate fuzzy basis functions, , , , , and For the design of positive constants, This is an estimate of the optimal adaptive parameter vector for the chemical reaction concentration; ； in, This is the observation error of the concentration in the first step of the chemical reaction. , , This is an estimate of the concentration of the chemical reaction. Given an estimated value for the temperature of a chemical reaction. The range of values ​​is , State estimate fuzzy basis functions, State estimate fuzzy basis functions, , ,in To account for the tracking error of chemical reaction concentration, To account for the error in chemical reaction temperature, and Let be the time-varying state constraint functions for chemical reaction concentration and temperature, respectively. For concentration virtual controller, To track signals, For the system's control output, and These are the estimated values ​​of the optimal adaptive parameter vectors for chemical reaction concentration and temperature, respectively. It is the adaptive law of chemical reaction concentration.

2. The intelligent constraint output feedback control method for a continuous stirred chemical reactor according to claim 1, characterized in that, The dynamic model is as follows: ； in, It refers to the concentration of a chemical reaction. It is the temperature of a chemical reaction. It is the temperature of the unreacted coolant. It is a Damokhler number. It is activation energy. It is the heat of reaction. It is the heat transfer coefficient. It is a real number An exponential function with base 0. This indicates the output of the CSTR system; This represents the rate of change of chemical reaction concentration over time. It represents the rate of change of temperature in a chemical reaction over time.

3. The intelligent constraint output feedback control method for a continuous stirred chemical reactor according to claim 1, characterized in that, The method for estimating unknown states within a CSTR system by constructing a state observer using a fuzzy logic system is as follows: A fuzzy logic system is defined, which can be represented as: ； in, This represents the output of the fuzzy logic system. Indicates the first The output value of the fuzzy rule, , Indicates the first The estimated value of the adaptive parameter vector of the fuzzy rule. , Indicates the first The fuzzy basis function of the state estimate of the fuzzy rule. Representing fuzzy rules, Indicates the total number of fuzzy rules; When using a state observer to estimate the unknown states within a CSTR system, the state observer is set as follows: ； in, , Here is the gain matrix of the state observer. The gain matrix is ​​the output error. To control the input gain matrix, To select a vector, For the output matrix, This represents the state estimation vector of the state observer. Indicates the first The estimated value of each state, This represents the output of the CSTR system. It is the output estimate of the state observer. It is the control input of the CSTR system; , as well as Represents an unknown function. These represent studies on chemical reaction concentration and temperature, respectively, using a fuzzy logic system to approximate the unknown function. .

4. The intelligent constraint output feedback control method for a continuous stirred chemical reactor according to claim 3, characterized in that, The method for designing a concentration virtual controller for a CSTR system, constructing a barrier Lyapunov function, and transforming the concentration tracking problem into a constraint problem is as follows: Step 3.1: Define the time-varying barrier Lyapunov function: ； ； in, and The BLF functions represent the chemical reaction concentration and the chemical reaction temperature, respectively. For the first Step error, This is the observation error of the concentration in the first step of the chemical reaction. concentration of chemical reaction The estimated value, and These are the time-varying state constraint functions for chemical reaction concentration and temperature, respectively. Similarly... For the first The time-varying state constraint function of the step. It is a positive matrix. For the first The set positive numbers, For the error of the adaptive parameter vector, This is the optimal adaptive parameter vector. for The estimated value, and That is, the first The estimated value of the optimal adaptive parameter vector for a chemical reaction. That is to say The concentration of chemical reactions was studied at that time. The temperature of chemical reactions was studied. Step 3.2: For each and Taking the derivative, and using Young's inequality to shrink the formula during the differentiation process, we get: ； ； in, This is the observation error of the concentration in the first step of the chemical reaction. concentration of chemical reaction The estimated value, , For the first The time-varying state constraint function of the step. For the first Similarly, the error of the step. , and These are the time-varying state constraint function for the chemical reaction concentration and the tracking error, respectively. It's an error in the chemical reaction temperature. Positive design parameters and All are positive matrices. and For the set positive numbers, and For the first The set positive numbers, For the error of the adaptive parameter vector, This is the optimal adaptive parameter vector. for The estimated value, ; The known constants designed in step 1, The known constants are designed for step 2.

5. The intelligent constraint output feedback control method for a continuous stirred chemical reactor according to claim 4, characterized in that, Adaptive law of chemical reaction concentration and temperature and The definition is as follows: ； ； in, and For the set positive numbers, and These are the state estimates. and fuzzy basis functions; and , and Let be the time-varying state constraint functions for chemical reaction concentration and temperature, respectively. To account for the tracking error of chemical reaction concentration, To account for the error in chemical reaction temperature, and These are the optimal adaptive parameter vector estimates for chemical reaction concentration and temperature, respectively. For dynamic models, state observers and controllers are designed. Virtual controller and adaptive rate and To ensure that the error variable converges to near the origin and the closed-loop system achieves semi-global stability, substitute the above variables into... and And by using Young's inequality, we can obtain and And finally, an equation is obtained that satisfies... The form of, by We can obtain, , ,in .

Images