Anti-interference control method for main reactant concentration in continuous stirring reaction kettle process

Abstract

The invention provides an anti-interference control method for the concentration of a main reactant in a continuous stirring reaction kettle process, belongs to the technical field of chemical process control, and solves the problem that in the chemical process of producing cyclopentanol by catalyzing electrophilic water with cyclopentadienoic acid, the concentration of the main reactant is not influenced. The technical problem that the concentration of a main reactant is difficult to track a set value without steady-state errors under the conditions of fluctuation of feeding concentration, uncertainty and external disturbance of the continuous stirring reaction kettle is solved. According to the technical scheme, the method comprises the steps of constructing a model pre-estimation compensator and an anti-interference control structure, designing a four-dimensional decision model, carrying out parameter collaborative optimization by adopting a multi-target genetic optimization algorithm, and carrying out optimal solution selection based on a TOPSIS method. Under the condition of feed concentration fluctuation, the dynamic response speed and the anti-interference capability of the system can be remarkably improved, and faster adjustment time, smaller overshoot and stronger robustness can be realized in linear and nonlinear models.

Description

Technical Field

[0001] This invention relates to the field of chemical process control technology, specifically to a method for controlling the concentration of main reactants in a continuous stirred reactor. Background Technology

[0002] Continuously stirred tank reactors (CSTRs) are core equipment in chemical production processes, and their control performance directly affects product quality, operational safety, and overall economic benefits. However, CSTR systems typically exhibit strong nonlinear and time-varying dynamic characteristics and model uncertainties, and are susceptible to various external disturbances such as feed concentration and temperature, making it difficult for traditional control methods to achieve high-precision closed-loop regulation. This problem is particularly pronounced in complex reaction processes such as emulsion polymerization.

[0003] Saldívar-Guerra et al. (2020) established a detailed mathematical model for elastomer emulsion polymerization in their paper "Continuous Stirred-Tank Reactor Modeling for the Production of Elastomers by Emulsion Polymerization." Their research showed that the reaction process is kinetically complex and extremely sensitive to operating conditions, especially reaction temperature. Even small temperature deviations can significantly affect the polymerization rate and product molecular weight distribution, and may lead to runaway reactions, severely impacting product consistency and even equipment safety. Similarly, Houtzer and Hill (1977), in their study on food sterilization processes, "Effect of Temperature Deviation on Process Sterilization Value with Continuous Agitating Reports," pointed out that temperature fluctuations in CSTRs directly affect the sterilization value (i.e., the cumulative effect of the objective function), thus posing a risk to the hygiene and safety of the final product. These studies collectively demonstrate that achieving high-precision and robust control of key parameters such as temperature and main reactant concentration in CSTRs is of significant industrial importance.

[0004] To address the aforementioned challenges, this invention proposes "a method for controlling the concentration of main reactants in a continuous stirred reactor based on the synergistic optimization of model prediction compensation and disturbance rejection control." The core innovation of this invention lies in constructing a synergistic optimization framework that transcends the simple superposition of control strategies. By establishing a four-dimensional decision model and introducing a multi-objective genetic algorithm (such as NSGA-II) to systematically and synergistically tune the control parameters of the model prediction compensator and the extended state observer, this method effectively solves the inherent trade-off between dynamic response speed and disturbance rejection capability. When feed concentration fluctuates, the proposed strategy not only achieves rapid setpoint tracking but also provides real-time estimation and compensation for unmodeled dynamics and external disturbances, thus achieving robust control with zero steady-state error, fast response, and low overshoot under both linear and nonlinear conditions. This invention compensates for the shortcomings of existing control strategies in synergistic design at the system optimization level, providing a practical and innovative solution for high-precision control of CSTRs. Summary of the Invention

[0005] The purpose of this invention is to provide a disturbance rejection control method for the concentration of the main reactant in a continuous stirred reactor process. This method is based on the synergistic optimization of model prediction compensation and disturbance rejection control, and is applicable to the continuous stirred reactor for the production of cyclopentanol from cyclopentadiene via acid-catalyzed electrophilic hydration. By combining the advantages of model prediction compensation with the dynamic disturbance suppression characteristics of the extended state observer (ESO), this method effectively enables the output of the continuous stirred reactor to track the set value without steady-state error when the feed concentration parameter is within a certain perturbation range, thus solving the control problem under uncertainty and external disturbances in this chemical process.

[0006] The inventive concept of this invention is as follows: This invention introduces a model predictor compensator and disturbance rejection control strategy into the dynamic model control of a continuous stirred reactor, constructs a corresponding control structure, designs a four-dimensional decision model, and transforms the controller parameter tuning problem into a frequency domain multi-objective optimization problem. An improved multi-objective genetic algorithm is used to collaboratively optimize key parameters, the Pareto optimal solution is screened based on the TOPSIS method, and closed-loop verification is completed through quantitative feedback theory. This method demonstrates faster settling time, smaller overshoot, and stronger robustness in both linear and nonlinear models under fluctuating feed concentration conditions.

[0007] To achieve the above-mentioned objectives, the present invention employs the following technical solution: a disturbance rejection control method for a continuous stirred reactor, comprising the following steps:

[0008] Step S1: Establish a dynamic model for the continuous stirred reactor system. The core of its adaptive disturbance rejection control process lies in the three deeply coupled loops (reactant A concentration c). A Concentration c of main reactant B BThe feed concentration (c) is controlled in tandem with the reactor temperature (T). A0 External disturbances such as temperature T0 and internal coupled disturbances such as reaction heat are dynamically adjusted to maintain stable concentration and temperature under strongly nonlinear and strongly coupled conditions, ultimately ensuring high-quality production of the main reactant B. Specifically:

[0009]

[0010]

[0011]

[0012] in,

[0013]

[0014] c A and c B K represents the concentrations of reactant A and main reactant B, respectively. i Here, F is the rate coefficient, F is the dilution rate, and T is the temperature.

[0015] Step S2: Based on the dynamic mathematical model established in step S1, obtain the linearized model under different working conditions. and nominal model A disturbance rejection control structure is constructed, the control structure comprising:

[0016] Model predictor compensator It is used to predict and compensate the original system output. The compensated system output satisfies the minimum phase characteristic and has no time delay.

[0017] Extended State Observer (ESO) is used to estimate and compensate for the total disturbance of the system;

[0018] Pre-filter This is used to improve system tracking performance;

[0019] Feedback controller Feedback control ensures the stability and disturbance rejection performance of the system.

[0020] Step S2.1: Construct the model prediction compensator The model predictor compensator is represented as follows:

[0021]

[0022] in, For the Lagrange operator, The linearized model as described in claim 1 The estimate, The ideal nominal model is one that meets the requirements of minimum phase and does not contain time delay. According to the formula Decomposition yielded, satisfy ;

[0023] Step S2.2: Construct an extended state observer, which is represented as follows:

[0024]

[0025] Among them, feed flow rate The manipulated variable in the main reactant B concentration control loop. for Laplace transform, The actual measured value of the concentration of the main reactant B. Concentration of main reactant B The estimated compensation value, This is the inverse Laplace transform operator. , and The nominal model as described in claim 1 State-space model parameters, These are the observed states and total perturbations of the state-space model. The observer bandwidth gain of ESO. The parameters to be optimized are... The nominal model as described in claim 1 The system order, through optimization This ensures the accuracy of ESO observations.

[0026] Step S2.3: Construct the pre-filter The pre-filter is represented as follows:

[0027]

[0028] in, for column vectors, These are adjustable parameters for the pre-filter. for The number of poles included. This can be adjusted... This optimizes the system's dynamic response characteristics and ensures the achievement of tracking performance indicators.

[0029] Step S2.4: Construct a feedback controller, which is represented as follows:

[0030]

[0031] in, For the bandwidth parameters of the feedback controller, , By adjusting This optimizes the system's stability and anti-interference performance.

[0032] Manipulated variable in the main reactant B concentration control loop The calculation is as follows:

[0033]

[0034] in, .

[0035] Step S3: Calculate the constraint boundary corresponding to the disturbance rejection control structure described in step S2 based on the robust stability and anti-interference performance requirements in the selected frequency domain;

[0036] Step S3.1: The disturbance rejection control structure according to claim 1 is equivalent to a two-degree-of-freedom control structure, the structure including an equivalent pre-filter. Equivalent controller Equivalent controlled object and post-filter ;

[0037] The equivalent pre-filter It is a pre-filter The first element and a forward channel equivalent part It is connected in series, wherein the equivalent structure of the forward channel is as follows:

[0038]

[0039] The equivalent controller The structure is as follows:

[0040]

[0041] The equivalent controlled object Its structure is as follows:

[0042]

[0043] The post-filter Its structure is as follows:

[0044]

[0045] Step S3.2: Based on the control requirements, establish robust stability index and disturbance rejection performance index. The robust stability index is determined by the resonant peak value of the closed-loop system, and the disturbance rejection performance index includes input disturbance suppression index and output disturbance suppression index.

[0046] Step S3.3: Apply the equivalent pre-filter described in step S3.1 Equivalent controller Equivalent controlled object Substituting the robust stability index and disturbance rejection performance index from step S3.2, the equivalent controller is characterized in polar coordinates. and equivalent controlled object Frequency characteristics:

[0047]

[0048] in, The imaginary unit, For frequency, and They are respectively and amplitude, and They are respectively and The phase angle.

[0049] Step S3.4: At the selected frequency Below, amplitude As unknown variables, the robust stability index and disturbance rejection performance index in step S3.3 are converted into information about... The system of quadratic inequalities in one variable is calculated, and the constraint boundary formed by the system of quadratic inequalities in one variable is calculated in the Nichols diagram.

[0050] Step S4: Establish a four-dimensional multi-objective optimization model: Select the square of the open-loop gain of the controller. Deviation from the preset target boundary in the low-frequency region High-frequency stability performance and tracking performance As the objective function, a constrained minimization problem is constructed, and a multi-objective algorithm is used to solve the Pareto optimal solution set;

[0051] Step S4.1: Construct the objective function, selecting the square of the open-loop gain of the controller. Deviation from the preset target boundary in the low-frequency region High-frequency stability performance and tracking performance The objective function is specifically represented as follows:

[0052]

[0053]

[0054]

[0055]

[0056] in, The equivalent controller as described in claim 3 Open-loop gain, The number of selected frequency points, For the first A selected frequency point, It is the boundary curve of the low-frequency band. It is the system's open-loop frequency response. and They represent the frequencies respectively. The deviation in gain and phase, Indicates frequency The distance between the open-loop frequency response of the system and the stability boundary. It refers to the number of frequency points in the high-frequency band. Let i be the closed-loop system amplitude frequency at the i-th selected frequency. For the first The amplitude frequency of an ideal closed-loop system at a selected frequency. N is the maximum number of frequencies considered in tracking performance.

[0057] Step S4.2: Introduce the corresponding constraints. Specifically:

[0058]

[0059] low frequency band

[0060] High frequency band

[0061] other

[0062] in, This represents the amplitude of the system's open-loop frequency response at that frequency point. Indicates frequency The input disturbance, output disturbance, and tracking performance metrics of the subsystem. It represents the boundary between tracking performance and disturbance rejection performance. Indicates frequency The robust stability index of the system is as follows. It is the robust stability boundary.

[0063] Step S4.3: Transform the controller parameter tuning problem into a frequency domain multi-objective optimization problem. Specifically, it is described as follows:

[0064] ,

[0065] Step S4.4: Population Initialization and Encoding. Real-number encoding is used, with the dimension of each chromosome corresponding to the bandwidth parameter K of the feedback controller to be optimized and the observer bandwidth gain L. Based on the physical meaning of the controller parameters and engineering experience, the value range of each parameter is set, and an initial population of 30-50 is randomly generated, with each chromosome representing a set of parameter combinations. .

[0066] Step S4.5: Fitness Calculation and Constraint Handling. For each chromosome in the population, substitute it into the system model to calculate the objective function. and check the constraints. .

[0067] If the chromosome satisfies all constraints, the fitness is calculated using the Pareto ranking plus crowding distance (Pareto ranking reflects the dominance of solutions, and crowding distance reflects the diversity of solutions).

[0068] If a chromosome does not meet the constraints, a penalty function is introduced to reduce its fitness, making it more likely to be eliminated in subsequent selections.

[0069] Step S4.6: Perform three genetic operations on the chromosomes:

[0070] 1. Selection: A tournament mechanism is used to select outstanding individuals to ensure that high fitness traits are preserved.

[0071] 2. Crossover: By arithmetic crossover, the genes of the two parents are fused to generate new offspring that possess the characteristics of both.

[0072] 3. Mutation: Introduce Gaussian random perturbation to enhance population diversity, avoid premature convergence, and improve global search capabilities.

[0073] Step S4.7: Iteration Termination and Result Output. The iteration terminates when the number of iterations reaches a preset maximum (e.g., 200 generations) or the population fitness tends to converge. The optimal solution for the Pareto front is selected from the final population, and the corresponding combination of controller parameters is output. This is the result of the search for the best outcome.

[0074] Further, step S5 includes the following steps:

[0075] Step S5.1: Eliminate the difference in magnitude of the objective functions, and for each candidate solution in the Pareto front solution set, minimize four objective functions. The reverse range standardization formula is used. Map each indicator value to the [0,1] interval. Let be the original value of the i-th candidate solution for the j-th objective.

[0076] Step S5.2: Match system performance priorities and assign weights to the four objectives based on system characteristics, matching the key performance priorities of multi-objective optimization: Stability (weight) =0.4), tracking performance (weight) =0.3+ =0.15), dynamic response speed (weight) =0.15).

[0077] Step S5.3: Standardized value of each candidate solution Multiply by the weight of the corresponding target. We obtain the weighted standardized value:

[0078]

[0079] This step combines the "quality of the target performance" with the "priority weight of the target," making subsequent decisions more aligned with the control requirements of non-minimum phase systems.

[0080] Step S5.4: Determine the positive ideal solution (PIS), the maximum value of the weighted standardized value of each indicator, i.e. The minimum value of the weighted standardized values ​​of each index, along with the Negative Ideal Solution (NIS), is...

[0081] Step S5.5: Calculate the distance from each candidate solution to the positive and negative ideal solutions using Euclidean distance, as shown in the formula:

[0082]

[0083] Step S5.6: Define the comprehensive proximity of the i-th candidate solution as: . The larger the value, the better the overall performance of the solution.

[0084] Step S5.7: Closeness of all candidate solutions Sort in descending order and select. The largest candidate solution, and the corresponding parameter combination, is taken as the final optimal objective.

[0085] Step S6: Assign the obtained optimal parameter combination to the controller, and perform time-domain simulation verification using the QFT closed-loop verification framework to verify the effectiveness of the designed controller and pre-filter under model parameter uncertainty.

[0086] Meanwhile, the present invention proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed, it implements the steps of the method described in the present invention.

[0087] Furthermore, the present invention proposes a computer-readable storage medium having a computer program stored thereon, the computer program being configured to implement the steps of the method described in the present invention when invoked by a processor.

[0088] Finally, the present invention provides a computer program product comprising a computer program / instructions that, when executed by a processor, implement the steps of the method described in the present invention.

[0089] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0090] (1) This invention targets the reaction process in a continuous stirred reactor, combining the compensation advantages of model prediction compensation with the characteristics of disturbance rejection control synergistic optimization, and successfully integrates the forward-looking compensation advantage of the prediction compensator with the dynamic disturbance suppression capability of the extended state observer. This synergistic design effectively overcomes the shortcomings of traditional industrial processes in adapting to time-varying and time-delayed conditions, and can effectively solve the control problems in industrial processes.

[0091] (2) Regarding the optimization of controller parameters, this invention employs an improved multi-objective genetic algorithm to achieve online self-tuning of controller parameters. Compared to traditional methods, this scheme can generate the Pareto optimal solution set in a short time and quickly select the optimal parameter combination that balances response speed and robustness through the TOPSIS decision framework. This intelligent optimization algorithm is fast, has good adaptability, and improves the efficiency and stability of system operation.

[0092] (3) Based on the collaborative optimization of model predictor compensator and disturbance rejection control, this invention combines a multi-objective adaptive genetic algorithm with the TOPSIS decision framework. This not only solves the long-standing problem of balancing time delay compensation and disturbance rejection control in chemical processes, but also provides reliable technical support for the intelligent upgrading of process industries. While ensuring system stability, this method exhibits faster dynamic response speed, shorter settling time, smaller overshoot, and better anti-interference capability, and has broad prospects for widespread application. Attached Figure Description

[0093] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0094] Figure 1 This is a structural diagram of a continuous stirred reactor for controlling the concentration of the main reactant, as provided in Example 1 of the present invention.

[0095] Figure 2 This is a diagram of an equivalent control model for the concentration of the main reactant in a continuous stirred reactor, as provided in Example 1 of this invention.

[0096] Figure 3 This is a flowchart of a method for controlling the concentration of the main reactant in a continuous stirred reactor, as provided in Example 1 of the present invention.

[0097] Figure 4 This is a flowchart of a multi-objective optimization algorithm provided in Example 1 of the present invention.

[0098] Figure 5 This is a graph showing the evaluation results of the TOPSIS method provided in Example 1 of this invention.

[0099] Figure 6 This is a graph showing the comparison results of the linear model tracking performance provided in Example 1 of this invention.

[0100] Figure 7 This is a schematic diagram comparing the dynamic performance of the linear model input perturbation in Example 1 of the present invention.

[0101] Figure 8 This is a comparison chart of component concentration changes provided in Example 2 of the present invention.

[0102] Figure 9 This is a comparison diagram of the temperature loop adjustment process provided in Example 3 of the present invention. Detailed Implementation

[0103] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0104] Example 1

[0105] See Figures 1 to 3 The technical solution provided in this embodiment is a method for controlling the concentration of the main reactant in a continuous stirred reactor. In the concentration control of the continuous stirred reactor for producing cyclopentanol from cyclopentadiene by adding water, a model predictor compensator and an extended state observer (ESO) are introduced. The controller parameters are optimized collaboratively through a multi-objective optimization algorithm to achieve robust control of the reactor under feed concentration fluctuations.

[0106] Figure 1 , Figure 2This is a schematic diagram of the model structure of the method proposed in this embodiment. For a continuous stirred reactor with feed concentration parameter perturbation, a concentration control model and disturbance estimate are designed. A collaborative structure of model predictor compensator and disturbance rejection control is proposed. By generating a compensation signal and observing the total system disturbance, the influence of uncertainty and external disturbances on the main reactant concentration is suppressed, improving the system's dynamic response and steady-state accuracy. A four-dimensional decision model is constructed with settling time, overshoot, and disturbance rejection capability as indicators. A multi-objective genetic optimization algorithm is used to collaboratively optimize the controller parameters. Based on the TOPSIS method, the optimal parameter configuration is selected from the Pareto solution set to ensure that the reactor output can track the setpoint without steady-state error. See [link to relevant documentation]. Figure 6 The SP-ADRC mentioned in this patent is the method described in this patent. ADRC is a common disturbance rejection control method. It can be concluded that the method described in this patent further improves the control performance and robustness of the system.

[0107] Figure 3 The flowchart of the method proposed in this embodiment is as follows: A method for controlling the concentration of the main reactant in a continuous stirred reactor includes the following steps:

[0108] Step S1: Establish a dynamic mathematical model of the continuous stirred reactor process. The model shall include at least the molar balance equation of reactant A, the molar balance equation of the main reactant B, and the reactor energy balance equation.

[0109] Step S2: Based on the dynamic mathematical model established in step S1, obtain the linearized model under different working conditions. and nominal model A disturbance rejection control structure is constructed, the control structure comprising:

[0110] Model predictor compensator It is used to predict and compensate the original system output. The compensated system output satisfies the minimum phase characteristic and has no time delay.

[0111] Extended State Observer (ESO) is used to estimate and compensate for the total disturbance of the system;

[0112] Pre-filter This is used to improve system tracking performance;

[0113] Feedback controller Feedback control ensures the stability and disturbance rejection performance of the system.

[0114] Step S3: Calculate the constraint boundary corresponding to the disturbance rejection control structure described in step S2 based on the robust stability and anti-interference performance requirements in the selected frequency domain;

[0115] Step S4: Establish a four-dimensional multi-objective optimization model: Select the square of the open-loop gain of the controller. Deviation from the preset target boundary in the low-frequency region High-frequency stability performance and tracking performance As the objective function, a constrained minimization problem is constructed, and a multi-objective algorithm is used to solve the Pareto optimal solution set;

[0116] Step S5: Using the TOPSIS multi-attribute decision method, select the controller parameter combination with the best overall performance from the Pareto optimal solution set described in Step S4;

[0117] Step S6: Apply the controller parameter combination obtained in step S5 to the disturbance rejection control structure described in step S2 to control the concentration of the main reactant in the continuous stirred reactor in real time.

[0118] Specifically, step S2 includes the following steps:

[0119] Step S2.1: Construct the model prediction compensator The model predictor compensator is represented as follows:

[0120]

[0121] in, For the Lagrange operator, The linearized model as described in claim 1 The estimate, The ideal nominal model is one that meets the requirements of minimum phase and does not contain time delay. According to the formula Decomposition yielded, satisfy ;

[0122] Step S2.2: Construct an extended state observer, which is represented as follows:

[0123]

[0124] Among them, feed flow rate The manipulated variable in the main reactant B concentration control loop. for Laplace transform, The actual measured value of the concentration of the main reactant B. Concentration of main reactant B The estimated compensation value, This is the inverse Laplace transform operator. , and The nominal model as described in claim 1 State-space model parameters, These are the observed states and total perturbations of the state-space model. The observer bandwidth gain of ESO. The parameters to be optimized are... The nominal model as described in claim 1 The system order, through optimization This ensures the accuracy of ESO observations.

[0125] Step S2.3: Construct the pre-filter The pre-filter is represented as follows:

[0126]

[0127] in, for column vectors, These are adjustable parameters for the pre-filter. for The number of poles included. This can be adjusted... This optimizes the system's dynamic response characteristics and ensures the achievement of tracking performance indicators.

[0128] Step S2.4: Construct a feedback controller, which is represented as follows:

[0129]

[0130] in, For the bandwidth parameters of the feedback controller, , By adjusting This optimizes the system's stability and anti-interference performance.

[0131] Manipulated variable in the main reactant B concentration control loop The calculation is as follows:

[0132]

[0133] in, .

[0134] Specifically, step S3 includes the following steps:

[0135] Step S3.1: The disturbance rejection control structure according to claim 1 is equivalent to a two-degree-of-freedom control structure, the structure including an equivalent pre-filter. Equivalent controller Equivalent controlled object and post-filter ;

[0136] The equivalent pre-filter It is a pre-filter The first element and a forward channel equivalent part It is connected in series, wherein the equivalent structure of the forward channel is as follows:

[0137]

[0138] The equivalent controller The structure is as follows:

[0139]

[0140] The equivalent controlled object Its structure is as follows:

[0141]

[0142] The post-filter Its structure is as follows:

[0143]

[0144] Step S3.2: Based on the control requirements, establish robust stability index and disturbance rejection performance index. The robust stability index is determined by the resonant peak value of the closed-loop system, and the disturbance rejection performance index includes input disturbance suppression index and output disturbance suppression index.

[0145] Step S3.3: Apply the equivalent pre-filter described in step S3.1 Equivalent controller Equivalent controlled object Substituting the robust stability index and disturbance rejection performance index from step S3.2, the equivalent controller is characterized in polar coordinates. and equivalent controlled object Frequency characteristics:

[0146]

[0147] in, The imaginary unit, For frequency, and They are respectively and amplitude, and They are respectively and The phase angle.

[0148] Step S3.4: At the selected frequency Below, amplitude As unknown variables, the robust stability index and disturbance rejection performance index in step S3.3 are converted into information about... The system of quadratic inequalities in one variable is calculated, and the constraint boundary formed by the system of quadratic inequalities in one variable is calculated in the Nichols diagram.

[0149] Specifically, step S4 includes the following steps:

[0150] Step S4.1: Construct the objective function, selecting the square of the open-loop gain of the controller. Deviation from the preset target boundary in the low-frequency region High-frequency stability performance and tracking performance The objective function is specifically represented as follows:

[0151]

[0152]

[0153]

[0154]

[0155] in, The equivalent controller as described in claim 3 Open-loop gain, The number of selected frequency points, For the first A selected frequency point, It is the boundary curve of the low-frequency band. It is the system's open-loop frequency response. and They represent the frequencies respectively. The deviation in gain and phase, Indicates frequency The distance between the open-loop frequency response of the system and the stability boundary. It refers to the number of frequency points in the high-frequency band. Let i be the closed-loop system amplitude frequency at the i-th selected frequency. For the first The amplitude frequency of an ideal closed-loop system at a selected frequency. N is the maximum number of frequencies considered in tracking performance.

[0156] Step S4.2: Introduce the corresponding constraints. The optimization problem requires that the sum of all constraints be 0. ),

[0157] Wherein: ϕ1 is the frequency response amplitude monotonicity constraint, ϕ2 is the low-frequency band performance boundary constraint (such as tracking and disturbance rejection indicators), ϕ3 is the high-frequency band robust stability constraint (the response must be within the boundary), and ϕ4 is the closed-loop amplitude range constraint (avoid exceeding the allowable range).

[0158] Step S4.3: Transform the controller parameter tuning problem into a frequency domain multi-objective optimization problem, which manifests as minimizing the target direction. .

[0159] Step S4.4: Using real-number encoding, the dimension of each chromosome corresponds to the bandwidth parameter K of the feedback controller to be optimized and the observer bandwidth gain L. An initial population of 30-50 is randomly generated, with each chromosome representing a set of parameter combinations. .

[0160] Step S4.5: Fitness Calculation and Constraint Handling. For each chromosome in the population, substitute it into the system model to calculate the objective function J1-J4, and check the constraints. If all constraints are satisfied... Fitness is calculated using Pareto rank plus crowding distance; if the constraints are not met, a penalty function is introduced to reduce the fitness.

[0161] Step S4.6: Perform three genetic operations on the chromosomes:

[0162] 1. Selection: A tournament mechanism is used to select outstanding individuals to ensure that high fitness traits are preserved.

[0163] 2. Crossover: By arithmetic crossover, the genes of the two parents are fused to generate new offspring that possess the characteristics of both.

[0164] 3. Mutation: Introduce Gaussian random perturbation to enhance population diversity, avoid premature convergence, and improve global search capabilities.

[0165] Step S4.7: Iteration Termination and Result Output. The iteration terminates when the number of iterations reaches a preset maximum (e.g., 200 generations) or the population fitness tends to converge. The optimal solution for the Pareto front is selected from the final population, and the corresponding combination of controller parameters is output. This is the result of the search for the best outcome.

[0166] Specifically, step S4 includes the following steps:

[0167] Step S5.1: Eliminate the difference in magnitude of the objective functions, and for each candidate solution in the Pareto front solution set, minimize four objective functions. The reverse range standardization formula is used. Map each indicator value to the [0,1] interval. Let be the original value of the i-th candidate solution for the j-th objective.

[0168] Step S5.2: Match system performance priorities and assign weights to the four objectives based on system characteristics to match the key performance priorities of multi-objective optimization: stability (weight θ3=0.4), tracking performance (weight θ2=0.3+θ4=0.15), and dynamic response speed (weight θ1=0.15).

[0169] Step S5.3: Standardized value of each candidate solution Multiply by the weight of the corresponding target. We obtain the weighted standardized value:

[0170]

[0171] This step combines the "quality of the target performance" with the "priority weight of the target," making subsequent decisions more aligned with the control requirements of non-minimum phase systems.

[0172] Step S5.4: Determine the positive ideal solution (PIS), the maximum value of the weighted standardized value of each indicator, i.e. The minimum value of the weighted standardized values ​​of each index, along with the Negative Ideal Solution (NIS), is...

[0173] Step S5.5: Calculate the distance from each candidate solution to the positive and negative ideal solutions using Euclidean distance, as shown in the formula:

[0174]

[0175] Step S5.6: Define the comprehensive similarity of the i-th candidate solution as: . The larger the value, the better the overall performance of the solution.

[0176] Step S5.7: Closeness of all candidate solutions Sort in descending order and select. The largest candidate solution, and the corresponding parameter combination, is taken as the final optimal objective.

[0177] Example 2

[0178] See Figure 6 and Figure 7 Linear model simulation was performed on the CSTR. First, the system model was linearized to obtain the transfer function. Then, the linearized model is controlled using the control structure and parameter selection method proposed in this example. The comparison of the tracking and disturbance rejection capabilities of the linear model IAE between SP-ADRC and ADRC is observed to verify the effectiveness and superiority of the control strategy.

[0179] Figure 6The results show a comparison of linear model tracking performance. Under experimental conditions with completely identical control parameters, the SP-ADRC method described in this claim exhibits superior response characteristics compared to the traditional active disturbance rejection method (ADRC). It achieves stable tracking of the reference value within 7 hours, while the traditional ADRC system takes more than 10 hours to stabilize, thus reducing the settling time by 32.4%. This significant difference indicates that the introduction of a predictive compensation mechanism effectively improves the dynamic response speed of the system. Figure 7 The anti-interference capabilities of the two control strategies were further compared through input disturbance experiments. When a step disturbance of magnitude 1 was applied at t=1h, the SP-ADRC system recovered steady-state control within 5.2 hours, while the ADRC system took as long as 8.9 hours. The disturbance suppression time of the SP-ADRC system was reduced by 41.6% compared to the ADRC system. This comparison verifies the advantage of the model predictor compensator in improving system robustness.

[0180] Table 1

[0181]

[0182] As shown in Table 1, the tracking IAE of SP-ADRC slightly increased from 8.8661 of ADRC to 9.2162 (an increase of about 3.95%), while its disturbance rejection IAE significantly decreased from 0.0104 to 0.0061 (a decrease of about 41.35%). This fully demonstrates that the disturbance feedforward compensation of the model predictor compensator can effectively improve the disturbance rejection performance of the system. Moreover, although the tracking IAE is slightly increased compared to ADRC, the overall settling time is shorter, which can achieve better overall results in many application scenarios.

[0183] Example 3

[0184] See Figure 9 A nonlinear dynamic model was constructed for the continuous stirred reactor model to perform control simulation, specifically described as follows:

[0185]

[0186]

[0187]

[0188] in

[0189]

[0190] and These represent the concentrations of reactant A and main reactant B, respectively. For rate coefficient, For dilution rate, The value is temperature. In this embodiment, the same SP-ADRC controller structure and parameters as in Embodiment 1 are used to control the nonlinear model, verifying the superiority and robustness of the control structure.

[0191] Figure 9 The dynamic response to changes in component concentration is demonstrated, with a focus on analyzing the concentration of component B ( The control performance was assessed when the operating point jumped from 0.9 mol / L to 0.8 mol / L. Experiments comparing the response curves of SP-ADRC and traditional ADRC showed that SP-ADRC achieved faster adjustment speed while minimizing overshoot, significantly improving control efficiency. Furthermore, the IAE values ​​(integral absolute error) in Table 2 further validated the superiority of the SP-ADRC strategy: In control tasks, the IAE value of SP-ADRC is 8.2455, slightly better than ADRC's 8.3475; for In the task of resisting disturbances caused by concentration changes, SP-ADRC (11.0665) also performs better than ADRC. This indicates that SP-ADRC can suppress concentration fluctuations more effectively, especially under nonlinear conditions, and can eliminate deviations more quickly, enabling the CSTR system to output stably.

[0192] Table 2

[0193]

[0194] Table 2 reflects the dynamic process of the manipulated variable, including the variation curves of temperature T and heat transfer rate. The dynamic response of the manipulated variable in the figure shows that the scheme can coordinate the control input and output relationship, avoid drastic fluctuations, and thus achieve stable regulation under complex operating conditions.

[0195] comprehensive Figure 9 Based on the experimental results and data analysis in Table 2, the SP-ADRC control strategy described in this claim demonstrates advantages in nonlinear simulation systems. SP-ADRC optimizes performance through smaller overshoot and faster response. The system exhibits excellent step tracking performance. Building upon this, the combination of model predictive compensator and disturbance rejection control demonstrates superior robustness and stability under conditions influenced by temperature and other factors. This SP-ADRC strategy balances dynamic response speed and steady-state accuracy, making it suitable for addressing scenarios with variable coupling and strong nonlinearity in CSTR processes. It can provide a reliable solution for disturbance rejection control in CSTR processes.

[0196] Example 4: This example proposes an electronic system, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method steps of the present invention.

[0197] Example 5: This example proposes a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the method of the present invention, which will not be described in detail here.

[0198] Example 6: This example proposes a computer program product, including a computer program / instructions. When the computer program / instructions are executed by a processor, the steps of implementing the method of the present invention will not be repeated here.

[0199] It should be noted that the processing flow of Examples 1-3 corresponds to the specific steps of the method provided in Example 1 of this invention, and has the corresponding functional modules and beneficial effects of the method. Technical details not described in detail in this embodiment can be found in the method provided in Example 1 of this invention.

[0200] The program code used to implement the methods of this application may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0201] The specific implementation schemes described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific implementation schemes of the present invention and are not intended to limit the scope of the present invention. Any equivalent changes and modifications made by those skilled in the art without departing from the concept and principles of the present invention should fall within the scope of protection of the present invention.

Claims

1. A method for disturbance rejection control of main reactant concentration in a continuous stirred reactor process, characterized in that, Includes the following steps: Step S1: Establish a dynamic mathematical model of the continuous stirred reactor process. The dynamic mathematical model includes at least the molar balance equation of reactant A, the molar balance equation of the main reactant B, and the reactor energy balance equation. Step S2: Based on the dynamic mathematical model established in step S1, obtain the linearized model under different working conditions. and nominal model Construct an anti-disturbance control structure; Step S3: Calculate the constraint boundary corresponding to the disturbance rejection control structure described in step S2 based on the robust stability and anti-interference performance requirements in the selected frequency domain; Step S4: Establish a four-dimensional multi-objective optimization model: Select the square of the open-loop gain of the controller. Deviation from the preset target boundary in the low-frequency region High-frequency stability performance and tracking performance As the objective function, a constrained minimization problem is constructed, and a multi-objective algorithm is used to solve the Pareto optimal solution set; Step S5: Using the TOPSIS multi-attribute decision method, select the controller parameter combination with the best overall performance from the Pareto optimal solution set described in Step S4; Step S6: Apply the controller parameter combination obtained in step S5 to the disturbance rejection control structure described in step S2 to control the concentration of the main reactant in the continuous stirred reactor in real time.

2. The method for disturbance rejection control of main reactant concentration in a continuous stirred reactor process according to claim 1, characterized in that, Step S2 includes the following steps: Step S2.1: Construct the model prediction compensator The model predictor compensator is represented as follows: ； in, For the Lagrange operator, For the linearized model The estimate, The ideal nominal model is one that meets the requirements of minimum phase and does not contain time delay. According to the formula Decomposition yielded, satisfy ; Step S2.2: Construct an extended state observer, which is represented as follows: ； Among them, feed flow rate The manipulated variable in the main reactant B concentration control loop. for Laplace transform, The actual measured value of the concentration of the main reactant B. Concentration of main reactant B The estimated compensation value, For the inverse Laplace transform operator, , and For nominal model State-space model parameters, For the observed states and total perturbations of the state-space model, the observer bandwidth gain of the ESO is... The parameters to be optimized are... For nominal model The system order, through optimization This ensures the accuracy of ESO observations; Step S2.3: Construct the pre-filter The pre-filter is represented as follows: ； in, for column vectors, These are adjustable parameters for the pre-filter. for The number of poles included can be adjusted by... This optimizes the system's dynamic response characteristics and ensures the achievement of tracking performance indicators; Step S2.4: Construct a feedback controller, which is represented as follows: ； in, For the bandwidth parameters of the feedback controller, , By adjusting This optimizes the system's stability and anti-interference performance; Manipulated variable in the main reactant B concentration control loop The calculation is as follows: ； in, .

3. The method for disturbance rejection control of main reactant concentration in a continuous stirred reactor process according to claim 1, characterized in that, In step S2, constructing the disturbance rejection control structure includes: Model predictor compensator It is used to predict and compensate the original system output. The compensated system output satisfies the minimum phase characteristic and has no time delay. Extended State Observer (ESO) is used to estimate and compensate for the total disturbance of the system; Pre-filter This is used to improve system tracking performance; Feedback controller Feedback control ensures the system's stability and disturbance rejection performance.

4. The method for disturbance rejection control of main reactant concentration in a continuous stirred reactor process according to claim 3, characterized in that, Step S3 includes the following steps: Step S3.1: Based on the disturbance rejection control structure constructed in step S2, it is equivalent to a two-degree-of-freedom control structure, which includes an equivalent pre-filter. Equivalent controller Equivalent controlled object and post-filter ; The equivalent pre-filter It is a pre-filter The first element and a forward channel equivalent part It is connected in series, wherein the equivalent structure of the forward channel is as follows: ； The equivalent controller The structure is as follows: ； The equivalent controlled object Its structure is as follows: ； The post-filter Its structure is as follows: ； Step S3.2: Based on the control requirements, establish robust stability index and disturbance rejection performance index. The robust stability index is determined by the resonant peak value of the closed-loop system, and the disturbance rejection performance index includes input disturbance suppression index and output disturbance suppression index. Step S3.3: Apply the equivalent pre-filter described in step S3.1 Equivalent controller Equivalent controlled object Substituting the robust stability index and disturbance rejection performance index from step S3.2, the equivalent controller is characterized in polar coordinates. and equivalent controlled object Frequency characteristics: ； in, The imaginary unit, For frequency, and They are respectively and amplitude, and They are respectively and The phase angle; Step S3.4: At the selected frequency Below, amplitude As unknown variables, the robust stability index and disturbance rejection performance index in step S3.3 are converted into information about... The system of quadratic inequalities in one variable is calculated, and the constraint boundary formed by the system of quadratic inequalities is calculated in the Nichols diagram.

5. The method for disturbance rejection control of main reactant concentration in a continuous stirred reactor process according to claim 1, characterized in that, Step S4 includes the following steps: Step S4.1: Construct the objective function, selecting the square of the open-loop gain of the controller. Deviation from the preset target boundary in the low-frequency region High-frequency stability performance and tracking performance As the objective function, it is expressed as follows: ； ； ； ； in, For equivalent controller Open-loop gain, The number of selected frequency points, For the first A selected frequency point, It is the boundary curve of the low-frequency band. It is the system's open-loop frequency response. and They represent the frequencies respectively. The deviation in gain and phase, Indicates frequency The distance between the open-loop frequency response of the system and the stability boundary. It refers to the number of frequency points in the high-frequency band. Let i be the closed-loop system amplitude frequency at the i-th selected frequency. For the first The amplitude frequency of an ideal closed-loop system at a selected frequency. N is the maximum number of frequencies considered in the tracking performance; Step S4.2: Introduce the corresponding constraints. The optimization problem requires that the sum of all constraints be 0. ), Where: ϕ1 is the frequency response amplitude monotonicity constraint, ϕ2 is the low-frequency performance boundary constraint, ϕ3 is the high-frequency robust stability constraint, and ϕ4 is the closed-loop amplitude range constraint; Step S4.3: Transform the controller parameter tuning problem into a frequency domain multi-objective optimization problem, which is expressed as minimizing the objective function. ; Step S4.4: Using real-number encoding, the dimension of each chromosome corresponds to the bandwidth parameter K of the feedback controller to be optimized and the observer bandwidth gain L. An initial population of 30-50 is randomly generated, with each chromosome representing a set of parameter combinations. ; Step S4.5: Fitness calculation and constraint handling. For each chromosome in the population, substitute it into the system model to calculate the objective function. And check the constraints; if all constraints are satisfied... Fitness is calculated using Pareto ranking and crowding distance; if constraints are not met, a penalty function is introduced to reduce fitness. Step S4.6: Perform three genetic operations on the chromosomes; Step S4.7: Iteration Termination and Result Output. When the number of iterations reaches the preset maximum or the population fitness tends to converge, the iteration is terminated. The optimal solution of the Pareto front is selected from the final population, and the corresponding combination of controller parameters is output. This is the result of the search for the best outcome.

6. The method for disturbance rejection control of main reactant concentration in a continuous stirred reactor process according to claim 1, characterized in that, Step S4.6: Perform the following genetic operations on the chromosomes: 1) Selection: A tournament mechanism is used to select outstanding individuals to ensure that high fitness traits are preserved; 2) Crossover: By arithmetic crossover, the genes of the two parents are fused to generate new offspring that possess characteristics of both parents; 3) Mutation: Introduce Gaussian random perturbation to enhance population diversity, avoid premature convergence, and improve global search capabilities.

7. The method for disturbance rejection control of main reactant concentration in a continuous stirred reactor process according to claim 1, characterized in that, Step S5 includes the following steps: Step S5.1: Eliminate the difference in magnitude of the objective functions, and for each candidate solution in the Pareto front solution set, minimize four objective functions. The reverse range standardization formula is used. Map each indicator value to the [0,1] interval. This represents the original value of the i-th candidate solution for the j-th objective. Step S5.2: Match system performance priorities and assign weights to the four objectives based on system characteristics, matching the key performance priorities of multi-objective optimization: stability, tracking performance, and dynamic response speed; Step S5.3: Standardized value of each candidate solution Multiply by the weight of the corresponding target. We obtain the weighted standardized value: ； By combining the "quality of the target performance" with the "priority weight of the target", subsequent decisions are made in line with the control requirements of non-minimum phase systems. Step S5.4: Determine the positive ideal solution PIS, the maximum value of the weighted standardized value of each indicator, i.e. The minimum value of the weighted standardized values ​​of each index, compared with the negative ideal solution NIS, is... ; Step S5.5: Calculate the distance from each candidate solution to the positive and negative ideal solutions using Euclidean distance, as shown in the formula: ； Step S5.6: Define the comprehensive similarity of the i-th candidate solution as: , The larger the value, the better the overall performance of the solution; Step S5.7: Closeness of all candidate solutions Sort in descending order and select. The largest candidate solution, and the corresponding parameter combination, is taken as the final optimal objective.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed, it implements the steps of the method as described in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program is configured to implement the steps of the method according to any one of claims 1 to 7 when invoked by a processor.

10. A computer program product, comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 7.

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