A method and system for asymmetric pre-set performance control of a cascade continuous stirred reactor independent of initial conditions.

Abstract

This invention relates to the field of automatic control technology, and in particular to a method and system for asymmetric preset performance control of a cascade continuous stirred reactor without initial conditions. The method includes establishing a mechanistic model of the cascade continuous stirred reactor, transforming it into an error equation for the cascade continuous stirred reactor, pre-specifying that the change in reactant concentration error at the output of the cascade continuous stirred reactor satisfies a banded constraint space, converting the banded constraint space into a symmetric constraint space, constructing a radical-type algebraic saturation function to map the symmetric constraint space into a bounded symmetric constraint space, superimposing an exponential finite-time decay function on the bounded symmetric constraint space to construct a bounded symmetric constraint space without initial conditions, constructing a barrier Lyapunov function based on the bounded symmetric constraint space without initial conditions, and designing an asymmetric preset performance controller without initial conditions using the backstepping method. This invention enables the stable, safe, and rapid operation of the cascade continuous stirred reactor.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and in particular to a method and system for asymmetric preset performance control of a cascade continuous stirred reactor independent of initial conditions. Background Technology

[0002] Reactors are equipment used in chemical production to carry out various physical changes and chemical reactions, and are widely used in industries such as plastics, chemical fibers, synthetic rubber, pharmaceuticals, paints, fuels, and pesticides. Cascade continuous stirred reactors, by connecting two or more reactors in series, overcome the shortcomings of single reactors, such as short reaction times and the need for intermittent operation, thus meeting the modern industrial pursuit of efficiency, safety, and product quality. The control precision and response speed of cascade continuous stirred reactors directly affect the quality of the final product and the economic benefits of the enterprise; therefore, the automatic control technology of cascade continuous stirred reactors has received widespread attention from engineers in the control field. Initially, engineers used methods such as PID, fuzzy PID, and feedback linearization to design controllers for cascade continuous stirred reactors. However, these controllers could not guarantee global system stability and were susceptible to external interference, making it difficult to meet the requirements for precise control of cascade continuous stirred reactors. To address this, engineers have applied nonlinear control and preset performance control techniques to the control of cascade continuous stirred reactors. This has improved the transient and steady-state characteristics of the controller, enhancing control accuracy and response rate to some extent. However, traditional preset performance control also suffers from the following problems: its constraint space is large, failing to effectively constrain tracking errors, resulting in significant tracking error fluctuations and overshoot; it requires prior knowledge of the initial tracking error value, making it difficult to design the preset performance function; furthermore, it cannot guarantee tracking error convergence within a finite time, exhibiting poor anti-interference capabilities, which also hinders its application in cascade continuous stirred reactor control. In conclusion, designing a high-performance controller that is independent of the initial state of the tracking error and has stricter constraints is beneficial for improving the production efficiency and product quality of cascade continuous stirred reactors, thereby creating greater economic benefits for enterprises. Summary of the Invention

[0003] This invention provides a method and system for asymmetric preset performance control of a cascade continuous stirred reactor without initial conditions. It effectively solves the problems of traditional preset performance control methods, which rely on tracking error initial values, have large transient process fluctuations, large overshoot, slow convergence speed, and control effects that depend on accurate mathematical models. This enables the cascade continuous stirred reactor to operate stably, safely, and rapidly, thereby improving production efficiency and product quality.

[0004] To achieve the above objectives, the present invention employs the following technical solution: A method for asymmetric pre-set performance control of a cascade continuous stirred reactor independent of initial conditions includes the following steps: Step 1: Based on the working mechanism of the cascade continuous stirred reactor, establish a mechanistic model of the cascade continuous stirred reactor; Step 2: Transform the mechanistic model of the cascade continuous stirred reactor into the error equation of the cascade continuous stirred reactor; Step 3: According to the process requirements, pre-specify the constraint space for the change in reactant concentration at the output of the cascade continuous stirred reactor as a band constraint space; Step 4: Using variable transformation, convert the strip constraint space in Step 3 into a symmetric constraint space; Step 5: Construct a radical algebraic saturation function. Utilize the boundedness of the radical algebraic saturation function to map the symmetric constraint space in Step 4 into a bounded symmetric constraint space where the initial value of the output reactant concentration error is bounded. Step 6: Construct an independent initial condition bounded symmetric constraint space containing the initial value of the output reactant concentration error by superimposing an exponential finite-time decay function on the bounded symmetric constraint space of Step 5. Step 7: Construct a barrier Lyapunov function using the bounded symmetric constraint space of the independent initial conditions from Step 6, and design an asymmetric preset performance controller with independent initial conditions using the backstepping method.

[0005] Furthermore, the cascade continuous stirred reactor in step 1 is composed of reactor A and reactor B connected in series. The input end of reactor A receives the reaction mixture, the output end of reactor A is connected to the input end of reactor B, reactor B outputs the final product, and at the same time feeds back some of the unreacted mixture to the input end of reactor A.

[0006] Furthermore, the steps for establishing the mechanistic model of the cascade continuous stirred reactor are as follows: Suppose that the two reactors in a cascade continuous stirred reactor are reactor A and reactor B, and the reactant concentrations in the two reactors are respectively... and The volumes are respectively and The residence time of the reactants in reactors A and B is and The reaction rate constant is and The circulation velocity is and The feed rate is The system uncertainty and external disturbance function are: and The mechanistic model of a cascade continuous stirred reactor is as follows: ; ; in, The concentration of reactants in reactor A The derivative, The concentration of reactants in reactor B The derivative, For reactor operating time, For reactor A, the time-varying time-delay, For the time-varying time delay of reactor B, For the reactants in reactor A Concentration at time, For the reactants in reactor B Concentration at time, To control the input.

[0007] Furthermore, step 2 specifically includes the following steps: When the cascade continuously stirred reactors reach equilibrium, the reactant concentrations in reactors A and B reach their equilibrium points. At these equilibrium points, the desired reactant concentrations in both reactors are... and satisfy: ; ; in, Let A be the desired concentration of reactants in reactor A. This represents the expected concentration of reactants in reactor B. Take the error variable as Then the systematic error equation is: ; ; in, , , , , , , and It is an unknown function; The tracking error for reactant concentration in reactor A. The tracking error for reactant concentration in reactor B, for The derivative, for The derivative, For the control direction of reactor A, For the control direction of reactor B, This is a disturbance to reactor A. This is a disturbance in reactor B.

[0008] Furthermore, step 3 specifically includes the following process: According to process requirements, the specified banded constraint space that the reactant concentration error output from the cascade continuous stirred reactor should meet is: ; in, , ; ; and These are the upper and lower bounds of the banded constraint space, respectively. , , , , These are all design parameters for a strip-shaped constrained space, selected according to process requirements; and These are the initial values ​​for the upper and lower bounds of the band constraint space, respectively. These are the initial design parameters for the upper bound of the banded constraint space. These are the initial design parameters for the lower bound of the banded constraint space. and These are the steady-state values ​​of the upper and lower bounds of the banded constraint space, respectively; , It is the convergence rate; , It is a pre-specified time parameter, representing the time required for the system to reach steady state.

[0009] Furthermore, step 4 specifically includes the following steps: For the error in step 3 Perform the following transformation: ; Transform the strip-shaped constrained space into a symmetric constrained space, i.e. ; in, , Upper bound of symmetric constrained space and the lower world The difference.

[0010] Furthermore, step 5 specifically includes the following steps: The constructed radical-type algebraic saturation function is: ; because Therefore, regardless What is the initial value? , yes exist The value at time; Thus, the symmetric constraint space in step 4 is mapped to the initial value of the output reactant concentration error. The bounded symmetric constrained space, i.e.: ; in, .

[0011] Furthermore, step 6 specifically includes the following steps: The exponential finite-time decay function is constructed as follows: ; And define the bounded symmetric constraint space with independent initial conditions as: ; in, ; The time constant of the exponential finite-time decay function represents the maximum time it takes for the reactant concentration error from the cascade continuous stirred reactor to enter the banded constraint space in step 3, and is specified according to actual needs; since , For function initial value, Therefore, the initial value of the reactant concentration error output by the transformed cascade continuous stirred reactor It must fall within a bounded symmetric constraint space that is independent of initial conditions.

[0012] Furthermore, step 7 specifically includes the following steps: Step 7.1: Estimate the function using linear function 1 The upper bound, that is ; in, This represents the true value of the slope of the linear function 1. , It is the estimation error of linear function 1. The control quantity introduced to enhance the controller's anti-interference capability. ; Step 7.2: Construct a first-order low-pass filter ,in, It is the input of the filter. It is the output of the filter. Filter output The derivative; , Design parameters for a first-order filter; and let the filtering error be... ; Step 7.3: Construct the barrier Lyapunov function 1. : ; in, , The true value of the slope of the linear function 1 Compared with the estimated value The error between; Step 7.4: Design virtual control quantities using the backstepping method. and the estimated slope of the linear function 1 The derivative is ; ; in, The slope estimate of the linear function 1 The derivative; , The design parameters are estimated for linear function 1; Upper bound of the banded constraint space The derivative, Lower bound of the banded constraint space The derivative, For function The derivative; , The interference coefficient; , For error Feedback gain; Step 7.5: Estimate the function using linear function 2 The upper bound, that is ; in, This represents the true value of the slope of the linear function 2. , It is the estimation error of the linear function 2; Step 7.6: Construct the Lyapunov function 2 as : ; in, , This refers to the tracking error in the second step of the backstepping method; , The true value of the slope of the linear function 2 Compared with the estimated value The error between and; Step 7.7: Design the control input using the backstepping method. and the estimated value of the slope of the linear function 2 The derivative is ; ; in, The slope estimate of the linear function 2 The derivative, For error Feedback gain, The design parameters are estimated for the linear function 2.

[0013] A cascade continuous stirred reactor independent of initial conditions asymmetric preset performance control system, comprising: The material concentration detection module consists of two independent material concentration detection sensors, A and B, which are used to measure the concentration of the final product output from reactors A and B, respectively. After being converted into digital signals, the signals are sent to the material concentration control module. The material temperature detection module consists of a thermocouple temperature measurement circuit, including temperature sensor A and temperature sensor B, which are used to measure the temperature of the material in reactor A and reactor B. The controller module consists of a microcontroller system and a human-machine interface device, and includes two parts: a material temperature control module and a material concentration control module. The material temperature control module consists of two independent PID control loops, including PID controller A and PID controller B, which are used to control the temperature of reactors A and B in a cascade continuous stirred reactor. The material concentration control module runs an asymmetric preset performance control method for the cascade continuous stirred reactor independent of initial conditions within the microcontroller. The microcontroller output is connected to the material flow rate regulating valve. By changing the flow rate of the reactants flowing into the cascade continuous stirred reactor, the module ensures that the cascade continuous stirred reactor can quickly track the desired signal. The temperature control module, composed of a linear temperature-controlled chiller, changes the temperature of the coolant flowing into the jacket of the cascade continuous stirred reactor under the control of the material temperature control module, thereby ensuring that the temperature of the reactants in reactors A and B remains constant at the optimal working state. The material flow rate regulating valve receives the output signal from the material concentration control module and controls the material flow rate flowing into the cascade continuous stirred reactor. The human-machine interface device is used to interact with the temperature regulation module and the material concentration control module and to display control information.

[0014] Compared with the prior art, the beneficial effects of the present invention are: 1) A new band-shaped constraint space is proposed, and a preset performance control technology is used to make the concentration error of the final product output by the cascade continuous stirred reactor vary within the band-shaped constraint space, which significantly reduces the fluctuation and overshoot of the final product output by the cascade continuous stirred reactor and improves the control speed of the system. 2) By introducing novel radical algebraic saturation functions and exponential finite-time decay functions, this invention effectively solves the limitation of traditional preset performance control methods that rely on the initial value of tracking error, broadens the applicability of preset performance control, and improves the stability of the system. 3) The radical algebraic saturation function used in this invention can not only map any initial tracking error to a bounded range, but also effectively solves the drawbacks of changing the sign of the tracking error in the traditional square algebraic saturation function and the complex operation of the hyperbolic tangent algebraic saturation function. 4) This invention uses linear functions to estimate unknown functions in the control design process and adopts adaptive laws to identify the parameters of linear functions. It does not require an accurate cascade continuous reactor mechanism model and maintains system stability under parameter perturbations and time-varying disturbances. 5) This invention effectively solves the problems of existing cascade continuous stirred reactor preset performance control methods relying on tracking error initial values, large transient process fluctuations, large overshoot, slow convergence speed, and control effects relying on precise mathematical models. It enables cascade continuous stirred reactors to operate stably, safely, and rapidly, improves production efficiency and product quality, reduces raw material loss, and enhances economic benefits. Attached Figure Description

[0015] Figure 1 This is a flowchart of the method described in this invention.

[0016] Figure 2 This is a schematic diagram comparing the strip-shaped constraint space described in this invention with the traditional preset performance control constraint space.

[0017] Figure 3 This is a schematic diagram of the principle of unrelated initial conditions in this invention.

[0018] Figure 4 This is a schematic diagram of the system described in this invention.

[0019] Figure 5 This is a flowchart illustrating the implementation process of the asymmetric preset performance algorithm described in this invention.

[0020] Figure 6 This is a schematic diagram comparing the effect of the present invention on the control of reactant concentration output from reactor B.

[0021] Figure 7 This is a schematic diagram comparing the effect of the present invention on the control of reactant concentration at the output of reactor B. Figure 8 This is a schematic diagram comparing the output signals of the material concentration controller of the present invention.

[0022] Figure 9 This is a schematic diagram comparing the effect of the present invention on the control of reactant concentration at the output of reactor A.

[0023] Figure 10 This is a schematic diagram of the linear function slope estimation process in this invention. Detailed Implementation

[0024] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings: See Figure 1 This is a flowchart of the method of the present invention. The present invention provides a method for asymmetric pre-set performance control of a cascade continuous stirred reactor independent of initial conditions, comprising the following steps: Step 1: Based on the working mechanism of the cascade continuous stirred reactor, establish a mechanistic model of the cascade continuous stirred reactor; The cascade continuous stirred reactor consists of reactor A and reactor B connected in series. The input end of reactor A receives the reaction mixture, and the output end of reactor A is connected to the input end of reactor B. Reactor B outputs the final product and at the same time feeds back some of the unreacted mixture to the input end of reactor A. The mechanistic model of the cascade continuous stirred reactor is established, and the steps are as follows: Suppose that the two reactors in a cascade continuous stirred reactor are reactor A and reactor B, and the reactant concentrations in the two reactors are respectively... and The volumes are respectively and The residence time of the reactants in reactors A and B is and The reaction rate constant is and The circulation velocity is and The feed rate is The system uncertainty and external disturbance function are: and The mechanistic model of a cascade continuous stirred reactor is as follows: (1) (2) in, The concentration of reactants in reactor A The derivative, The concentration of reactants in reactor B The derivative, For reactor operating time, For reactor A, the time-varying time-delay, For the time-varying time delay of reactor B, For the reactants in reactor A Concentration at time, For the reactants in reactor B Concentration at time, This is the control input for the system.

[0025] Step 2: Transform the mechanistic model of the cascade continuous stirred reactor into the error equation of the cascade continuous stirred reactor; When the cascade continuously stirred reactors reach equilibrium, the reactant concentrations in reactors A and B reach their equilibrium points. At these equilibrium points, the desired reactant concentrations in both reactors are... and satisfy: (3) (4) in, Let A be the desired concentration of reactants in reactor A. This represents the expected concentration of reactants in reactor B. Take the error variable as Then the systematic error equation is: (5) (6) in, , , , , , , and It is an unknown function; The tracking error for reactant concentration in reactor A. The tracking error for reactant concentration in reactor B, for The derivative, for The derivative, For the control direction of reactor A, For the control direction of reactor B, This is a disturbance to reactor A. This is a disturbance in reactor B.

[0026] Step 3: According to the process requirements, pre-specify the constraint space for the change in reactant concentration at the output of the cascade continuous stirred reactor as a band constraint space; To reduce the fluctuations and overshoot of the reactant concentration output from the cascade continuous stirred reactor during transient processes, the banded constraint space that the error variation of the reactant concentration output from the cascade continuous stirred reactor should satisfy, according to process requirements, is specified as follows: (7) in, , (8) (9) and These are the upper and lower bounds of the banded constraint space, respectively. , , , The design parameters for the strip-shaped constrained space need to be selected according to the process requirements; and These are the initial values ​​for the upper and lower bounds of the band constraint space, respectively. These are the initial design parameters for the upper bound of the banded constraint space. These are the initial design parameters for the lower bound of the banded constraint space. and These are the steady-state values ​​of the upper and lower bounds of the banded constraint space, respectively. It is the convergence rate. It is a pre-specified time parameter, representing the time required for the system to reach steady state; See Figure 2 This is a schematic diagram comparing the strip-shaped constraint space described in this invention with the traditional preset performance control constraint space; the figure shows... This is the upper bound of the strip-shaped constraint space described in this invention and the traditional preset performance control constraint space. This is the lower bound of the banded constraint space described in this invention. This serves as the lower bound of the traditional preset performance control constraint space; by Figure 2 It can be seen that the constraint space of traditional preset performance control is trumpet-shaped, while the constraint space used in this invention is strip-shaped. The strip-shaped constraint space used in this invention has stricter constraints in the early stage of control, which can greatly reduce the fluctuation and overshoot of the system.

[0027] Step 4: Using variable transformation, convert the strip constraint space in Step 3 into a symmetric constraint space; For the error in step 3 Perform the following transformation (10) Transform the strip-shaped constrained space into a symmetric constrained space, i.e. (11) in, , Upper bound of symmetric constrained space and the lower world The difference.

[0028] Step 5: Construct a radical algebraic saturation function. Utilize the boundedness of the radical algebraic saturation function to map the symmetric constraint space in Step 4 into a bounded symmetric constraint space where the initial value of the output reactant concentration error is bounded. The constructed radical-type algebraic saturation function is: (12) because Therefore, regardless What is the initial value? ( yes exist (Value at time); Thus, the symmetric constraint space in step 4 is mapped to the initial value of the output reactant concentration error. A bounded symmetric constrained space, i.e. (13) in, .

[0029] Step 6: Construct an independent initial condition bounded symmetric constraint space containing the initial value of the output reactant concentration error by superimposing an exponential finite-time decay function on the bounded symmetric constraint space of Step 5. This specifically includes the following steps: The exponential finite-time decay function is constructed as follows: 14) And define the bounded symmetric constraint space with independent initial conditions as (15) in, (16) The time constant of the exponential finite-time decay function represents the maximum time that the reactant concentration error output from the cascade continuous stirred reactor enters the banded constraint space in step 3, and can be specified according to actual needs; See Figure 3 This is a schematic diagram illustrating the principle of unrelated initial conditions in this invention; in the diagram, It is the upper bound of a bounded symmetric constraint space independent of initial conditions. It is a lower bound of a bounded symmetric constraint space independent of initial conditions. It is the tracking error after transformation. yes initial value, yes The initial value; by Figure 3 It can be known that: ,and Therefore, the initial value of the reactant concentration error output by the transformed cascade continuous stirred reactor It must fall within a bounded symmetric constraint space independent of initial conditions, thus solving the limitation that traditional preset performance control requires prior knowledge of the initial value of the tracking error.

[0030] Step 7: Construct a barrier Lyapunov function using the bounded symmetric constraint space with independent initial conditions from Step 6, and design an asymmetric pre-defined performance controller with independent initial conditions using the backstepping method. This includes the following steps: Step 7.1: Estimate the function using linear function 1 The upper bound, that is (17) in, The true value of the slope of the linear function 1. It is the estimation error of linear function 1. The control quantity introduced to enhance the controller's anti-interference capability. , ; Step 7.2: Construct a first-order low-pass filter ,in, It is the input of the filter. It is the output of the filter. Filter output The derivative, Design parameters for a first-order filter; and let the filtering error be... ; Step 7.3: Construct the barrier Lyapunov function 1. : (18) in, The true value of the slope of the linear function 1 Compared with the estimated value The error between; Step 7.4: Design virtual control quantities using the backstepping method. and the estimated slope of the linear function 1 The process is as follows: calculate derivative achievable (19) in, From equation (17) and It can be known that: (20) in, This is an estimate of the slope of the linear function 1.

[0031] Substituting equation (20) into equation (19) yields (twenty one) According to Young's inequality transformation, we can obtain: (twenty two) (twenty three) (twenty four) (25) in, It is the interference coefficient; Design virtual control law and the estimated slope of the linear function 1 The derivative (adaptive law) is (26) (27) in, For error Feedback gain, The design parameters are estimated for linear function 1; Substituting equations (22)-(27) into equation (21), we get (28) According to the first-order filter, we can obtain: (29) in, It is the filtering error. The derivative of . Assume , in, It is a continuous function. For simplicity, let's... remember ; Substituting equation (29) into equation (28), we get: (30) According to Young's inequality, we can conclude that: (31) Substituting equation (31) into equation (30), we get: (32) in, ; because , It can be transformed into: (33) in , The gain of the barrier Lyapunov function 1; Step 7.5: Estimate the function using linear function 2 The upper bound, namely: (34) in, The true value of the slope of the linear function 2. It is the estimation error of the linear function 2; Step 7.6: Construct the Lyapunov function 2 as : (35) in, This refers to the tracking error in the second step of the backstepping method. The true value of the slope of the linear function 2 Compared with the estimated value The error between and; Step 7.7: Design the actual control law using the backstepping method. and the estimated value of the slope of the linear function 2 The process of obtaining the derivative is as follows: Calculate tracking error derivative have to (36) Based on the first-order filter defined in step 7.2, we can obtain: (37) beg derivative have to: (38) Substituting equations (36)-(37) into equation (38), we get: (39) From equation (34) and It can be known that: (40) in, This is an estimate of the slope of the linear function 2; Substituting equation (40) into equation (39), we get: (41) According to Young's inequality, we can obtain: (42) (43) Substituting equations (42) and (43) into equation (41), we get: (44) Design the actual control law and the estimated value of the slope of the linear function 2 The derivative (adaptive law) is: (45) (46) in, For error Feedback gain, The estimated value of the slope of the linear function 2. The derivative, The design parameters are estimated for the linear function 2; Substituting equations (45) and (46) into equation (44), we get: (47) According to Young's inequality, we can conclude that: (48) Substituting equation (48) into equation (47), we get: (49) in, The gain of the Lyapunov function 2; The overall Lyapunov function is: (50) Then, the total Li function derivative for: (51) in, For the total Lyapunov function Gain, It is a positive number; According to the Lyapunov stability criterion, the controller designed in this invention is stable.

[0032] See Figure 4 This is a schematic diagram of the system described in this invention. Figure 4 It is known that: a method and system for asymmetric preset performance control of a cascade continuous stirred reactor independent of initial conditions includes: The material concentration detection module consists of two independent material concentration detection sensors, A and B, which are used to measure the concentration of the final product output from reactors A and B, respectively. After being converted into digital signals, the signals are sent to the material concentration control module. The material temperature detection module consists of a thermocouple temperature measurement circuit, including temperature sensor A and temperature sensor B, which are used to measure the temperature of the material in reactor A and reactor B. The controller module consists of a microcontroller system and a human-machine interface device, and includes two parts: a material temperature control module and a material concentration control module. The material temperature control module consists of two independent PID control loops, including PID controller A and PID controller B, which are used to control the temperature of reactors A and B in a cascade continuous stirred reactor. The material concentration control module runs an asymmetric preset performance control method for the cascade continuous stirred reactor independent of initial conditions within the microcontroller. The microcontroller output is connected to the material flow rate regulating valve. By changing the flow rate of the reactants flowing into the cascade continuous stirred reactor, the module ensures that the cascade continuous stirred reactor can quickly track the desired signal. The temperature control module, composed of a linear temperature-controlled chiller, changes the temperature of the coolant flowing into the jacket of the cascade continuous stirred reactor under the control of the material temperature control module, thereby ensuring that the temperature of the reactants in reactors A and B remains constant at the optimal working state. The material flow rate regulating valve receives the output signal from the material concentration control module and controls the material flow rate flowing into the cascade continuous stirred reactor. The human-machine interface device is used to interact with the temperature regulation module and the material concentration control module and to display control information.

[0033] The following embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments. Unless otherwise specified, the methods used in the following embodiments are conventional methods.

[0034]

Example

[0035] The cascade continuous stirred tank reactor model is as follows: ; ; in, , , , , , .

[0036] To demonstrate the effectiveness of the proposed algorithm, a cascade continuous stirred reactor model was selected, with the following parameters: Initial state of cascade continuous stirred reactor Low-pass filter initial parameters: initial value of adaptive law Other design parameters are as follows: For comparison, we also simulated a traditional preset performance controller. The simulation parameters of the traditional preset performance controller are as follows: The simulation parameters for the controller without a preset performance control method are as follows: Simulations were conducted to verify the advantages of the proposed asymmetric preset performance control method with independent initial conditions compared to traditional control methods. Figure 5 This is a flowchart illustrating the implementation process of the asymmetric preset performance algorithm described in this invention. Figure 6 This is a comparative schematic diagram of the effect of this invention on the control of reactant concentration at the output of reactor B (regardless of initial conditions). In the diagram, the present invention shows the error curve of reactant concentration at the output of reactor B when controlled by this invention; comparison method 1 shows the error curve of reactant concentration at the output of reactor B when controlled by traditional preset performance; and comparison method 2 shows the error curve of reactant concentration at the output of reactor B when controlled by traditional backstepping method. Figure 6 It can be seen that, because the initial value of the reactant concentration error output by reactor B does not fall within the preset performance function range, traditional preset performance control cannot converge and therefore cannot complete the control; although traditional backstepping control can converge, its transient and steady-state performance is poor, and the tracking error can only converge to... The control method of this invention not only guarantees system convergence but also possesses the best transient and steady-state performance, with the tracking error eventually converging to... .

[0037] Figure 7 This is a schematic diagram (with a banded constraint space) comparing the control effect of the present invention on the output reactant concentration of reactor B. In the diagram, the present invention shows the error curve of the output reactant concentration of reactor B when controlled by the present invention; Comparison Method 1 shows the error curve of the output reactant concentration of reactor B when using the independent initial condition control method proposed in this invention on the basis of traditional preset performance control; Comparison Method 2 shows the error curve of the output reactant concentration of reactor B when using traditional backstepping control. Figure 6 and Figure 7It can be seen that when the initial value of the reactant concentration error output by reactor B falls outside the range of the preset performance function, the introduction of the irrelevant initial condition control method proposed in this invention can not only bring the previously non-convergent traditional preset performance control to convergence, but also bring it to convergence. This demonstrates the effectiveness of the independent initial condition control method proposed in this invention; furthermore, by Figure 7 Furthermore, the following conclusions can be drawn: Compared with traditional preset performance control that incorporates the proposed independent initial condition control method, the control method of this invention has better transient characteristics and smaller transient fluctuations. The overshoot of this invention is zero, while the overshoot of traditional preset performance control that incorporates the proposed independent initial condition control method is [missing information]. This also fully demonstrates that the strip-shaped constraint space proposed in this invention is more conducive to improving the transient characteristics of the system.

[0038] Figure 8 This is a comparative schematic diagram of the output signals of the material concentration controller of the present invention. In the diagram, the output result of the material concentration controller is shown when the present invention is used for control; comparison method 1 shows the output result of the material concentration controller when using the independent initial condition control method proposed in this invention on the basis of traditional preset performance control; comparison method 2 shows the output result of the material concentration controller when using traditional backstepping control. Figure 8 It is known that the output signals of the above three controllers are all bounded and physically achievable; however, the output signal range of the material concentration controller based on the present invention is smaller, the signal is smoother, and it is easier to implement.

[0039] Figure 9 This is a schematic diagram comparing the control effect of the present invention on the output reactant concentration of reactor A; in the diagram, the present invention shows the error curve of the output reactant concentration of reactor A when controlled by the present invention. Comparison method 1 is the error of the output reactant concentration of reactor A when using the independent initial condition control method proposed in this invention on the basis of traditional preset performance control. Comparison method 2 is the error of the output reactant concentration of reactor A when using traditional backstepping control. Figure 9 It can be seen that, compared with the other two control methods, the control method of this invention has the smallest transient fluctuation and overshoot; the overshoot of the method in this paper is... The overshoot values ​​of the other two methods are respectively and .

[0040] Figure 10 This is a schematic diagram of the linear function slope estimation process in this invention; from Figure 10 It can be seen that the slope estimation of linear function 1 Slope estimation of linear function 2 All converge.

[0041] In this embodiment, both states in the cascade continuous stirred reactor represent concentration errors. In other specific embodiments, temperature, flow rate, etc., can also be included, which can be adjusted according to specific actual needs to achieve essentially the same technical effect.

[0042] In this embodiment, there are two stirring motors. In actual application, the number can be adjusted according to specific needs to achieve the same technical effect.

[0043] In this embodiment, two material concentration detection sensors are used. In other specific embodiments, other substances can also be used to measure their concentrations according to actual needs.

[0044] In this embodiment, a square root algebraic saturation function is used to transform the tracking error. Under other application conditions, other saturation functions can also be used to achieve the same technical effect.

[0045] In this embodiment, two temperature sensors are used to measure the internal temperature of the reactor. In other application examples, multiple temperature measurements can be performed according to actual needs to achieve the same technical effect.

[0046] In this example, a strip constraint is used. In other application examples, asymmetric constraints of other shapes can be used according to actual needs to achieve the same technical effect.

[0047] The above-disclosed embodiments are merely specific examples of the present invention and are not intended to limit the scope of the present invention. The present invention is not limited to the above-described embodiments. Any person skilled in the art can independently and creatively modify and improve the technical solutions and ideas of the present invention through practical application and theoretical derivation based on the inventive concept of the present invention, and all such modifications and improvements should fall within the scope of protection of the present invention.

Claims

1. A method for asymmetric pre-setting performance control of a cascade continuous stirred reactor independent of initial conditions, characterized in that, Includes the following steps: Step 1: Based on the working mechanism of the cascade continuous stirred reactor, establish a mechanistic model of the cascade continuous stirred reactor; Step 2: Transform the mechanistic model of the cascade continuous stirred reactor into the error equation of the cascade continuous stirred reactor; Step 3: According to the process requirements, pre-specify the constraint space for the change in reactant concentration at the output of the cascade continuous stirred reactor as a band constraint space; Step 4: Using variable transformation, convert the strip constraint space in Step 3 into a symmetric constraint space; Step 5: Construct a radical algebraic saturation function. Utilize the boundedness of the radical algebraic saturation function to map the symmetric constraint space in Step 4 into a bounded symmetric constraint space where the initial value of the output reactant concentration error is bounded. Step 6: Construct an independent initial condition bounded symmetric constraint space containing the initial value of the output reactant concentration error by superimposing an exponential finite-time decay function on the bounded symmetric constraint space of Step 5. Step 7: Construct a barrier Lyapunov function using the bounded symmetric constraint space of the independent initial conditions from Step 6, and design an asymmetric preset performance controller with independent initial conditions using the backstepping method.

2. The method for asymmetric pre-setting performance control of a cascade continuous stirred reactor independent of initial conditions according to claim 1, characterized in that, The cascade continuous stirred reactor in step 1 consists of reactor A and reactor B connected in series. The input of reactor A receives the reaction mixture, and the output of reactor A is connected to the input of reactor B. Reactor B outputs the final product and simultaneously feeds back some of the incompletely reacted mixture to the input of reactor A.

3. The method for asymmetric pre-setting performance control of a cascade continuous stirred reactor independent of initial conditions according to claim 2, characterized in that, The steps for establishing the mechanistic model of the cascade continuous stirred reactor are as follows: Suppose that the two reactors in a cascade continuous stirred reactor are reactor A and reactor B, and the reactant concentrations in the two reactors are respectively... and The volumes are respectively and The residence time of the reactants in reactors A and B is and The reaction rate constant is and The circulation velocity is and The feed rate is The system uncertainty and external disturbance function are: and The mechanistic model of a cascade continuous stirred reactor is as follows: ； ； in, The concentration of reactants in reactor A The derivative, The concentration of reactants in reactor B The derivative, For reactor operating time, For reactor A, the time-varying time-delay, For the time-varying time delay of reactor B, For the reactants in reactor A Concentration at time, For the reactants in reactor B Concentration at time, For controlling input.

4. The method for asymmetric pre-set performance control of a cascade continuous stirred reactor independent of initial conditions according to claim 3, characterized in that, Step 2 specifically includes the following steps: When the cascade continuously stirred reactors reach equilibrium, the reactant concentrations in reactors A and B reach their equilibrium points. At these equilibrium points, the desired reactant concentrations in both reactors are... and satisfy: ； ； in, Let A be the desired concentration of reactants in reactor A. This represents the expected concentration of reactants in reactor B. Take the error variable as Then the systematic error equation is: ； ； in, , , , , , , and It is an unknown function; The tracking error for reactant concentration in reactor A. The tracking error for reactant concentration in reactor B, for The derivative, for The derivative, For the control direction of reactor A, For the control direction of reactor B, This is a disturbance to reactor A. This is a disturbance in reactor B.

5. The method for asymmetric pre-set performance control of a cascade continuous stirred reactor independent of initial conditions according to claim 4, characterized in that, Step 3 specifically includes the following process: According to process requirements, the specified banded constraint space that the reactant concentration error output from the cascade continuous stirred reactor should meet is: ； in, , ； ； and These are the upper and lower bounds of the banded constraint space, respectively; , , , , These are all design parameters for a strip-shaped constrained space, selected according to process requirements; and These are the initial values ​​for the upper and lower bounds of the band constraint space, respectively. These are the initial design parameters for the upper bound of the banded constraint space. These are the initial design parameters for the lower bound of the banded constraint space. and These are the steady-state values ​​of the upper and lower bounds of the banded constraint space, respectively; , It is the convergence rate; , It is a pre-specified time parameter, representing the time required for the system to reach steady state.

6. The method for asymmetric pre-setting performance control of a cascade continuous stirred reactor independent of initial conditions according to claim 5, characterized in that, Step 4 specifically includes the following steps: For the error in step 3 Perform the following transformation: ; Transform the strip-shaped constrained space into a symmetric constrained space, i.e. ; in, , Upper bound of symmetric constrained space and the lower world The difference.

7. The method for asymmetric pre-set performance control of a cascade continuous stirred reactor independent of initial conditions according to claim 6, characterized in that, Step 5 specifically includes the following steps: The constructed radical-type algebraic saturation function is: ; because Therefore, regardless What is the initial value? , yes exist The value at time; Thus, the symmetric constraint space in step 4 is mapped to the initial value of the output reactant concentration error. A bounded symmetric constrained space, namely: ； in, .

8. The method for asymmetric pre-set performance control of a cascade continuous stirred reactor independent of initial conditions according to claim 6, characterized in that, Step 6 specifically includes the following steps: The exponential finite-time decay function is constructed as follows: ； And define the bounded symmetric constraint space with independent initial conditions as: ； in, ; The time constant of the exponential finite-time decay function represents the maximum time it takes for the reactant concentration error from the cascade continuous stirred reactor to enter the banded constraint space in step 3, and is specified according to actual needs; since , For function initial value, Therefore, the initial value of the reactant concentration error output by the transformed cascade continuous stirred reactor It must fall within a bounded symmetric constraint space that is independent of initial conditions.

9. The method for asymmetric pre-set performance control of a cascade continuous stirred reactor independent of initial conditions according to claim 8, characterized in that, Step 7 specifically includes the following steps: Step 7.1: Estimate the function using linear function 1 The upper bound, that is ； in, This represents the true value of the slope of the linear function 1. , It is the estimation error of linear function 1. The control quantity introduced to enhance the controller's anti-interference capability. ; Step 7.2: Construct a first-order low-pass filter ,in, It is the input of the filter. It is the output of the filter. Filter output The derivative; , Design parameters for a first-order filter; and let the filtering error be... ; Step 7.3: Construct the barrier Lyapunov function 1. : ； in, , The true value of the slope of the linear function 1 Compared with the estimated value The error between; Step 7.4: Design virtual control quantities using the backstepping method. The estimated value of the slope of the linear function 1 The derivative is ； ； in, The slope estimate of the linear function 1 The derivative; , The design parameters are estimated for linear function 1; Upper bound of the banded constraint space The derivative, Lower bound of the banded constraint space The derivative, For function The derivative; , The interference coefficient; , For error Feedback gain; Step 7.5: Estimate the function using linear function 2 The upper bound, that is ； in, This represents the true value of the slope of the linear function 2. , It is the estimation error of the linear function 2; Step 7.6: Construct the Lyapunov function 2 as : ； in, , This refers to the tracking error in the second step of the backstepping method; , The true value of the slope of the linear function 2 Compared with the estimated value The error between and; Step 7.7: Design the control input using the backstepping method. and the estimated value of the slope of the linear function 2 The derivative is ； ； in, The slope estimate of the linear function 2 The derivative, For error Feedback gain, The design parameters are estimated for the linear function 2.

10. A system for implementing the asymmetric preset performance control method for a cascade continuous stirred reactor independent of initial conditions as described in any one of claims 1-9, characterized in that, include: The material concentration detection module consists of two independent material concentration detection sensors, A and B, which are used to measure the concentration of the final product output from reactors A and B, respectively. After being converted into digital signals, the signals are sent to the material concentration control module. The material temperature detection module consists of a thermocouple temperature measurement circuit, including temperature sensor A and temperature sensor B, which are used to measure the temperature of the material in reactor A and reactor B. The controller module consists of a microcontroller system and a human-machine interface device, and includes two parts: a material temperature control module and a material concentration control module. The material temperature control module consists of two independent PID control loops, including PID controller A and PID controller B, which are used to control the temperature of reactors A and B in a cascade continuous stirred reactor. The material concentration control module runs an asymmetric preset performance control method for the cascade continuous stirred reactor independent of initial conditions within the microcontroller. The microcontroller output is connected to the material flow rate regulating valve. By changing the flow rate of the reactants flowing into the cascade continuous stirred reactor, the module ensures that the cascade continuous stirred reactor can quickly track the desired signal. The temperature control module, composed of a linear temperature-controlled chiller, changes the temperature of the coolant flowing into the jacket of the cascade continuous stirred reactor under the control of the material temperature control module, thereby ensuring that the temperature of the reactants in reactors A and B remains constant at the optimal working state. The material flow rate regulating valve receives the output signal from the material concentration control module and controls the material flow rate flowing into the cascade continuous stirred reactor. The human-machine interface device is used to interact with the temperature regulation module and the material concentration control module and to display control information.

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