Intelligent control method for pickling process

Abstract

The invention belongs to the technical field of intelligent control of a pickling process, and particularly relates to an intelligent control method for the pickling process. In order to solve the problems that traditional control depends on manpower, multi-parameter coupling processing is poor, data reliability is low, and quality evaluation lags behind, the method comprises the steps that the pickling process, the environment, steel wire processing parameters and steel wire surface image data are collected, preprocessing (denoising and missing value filling) is carried out, and a quality score is generated to construct a database; constructing a knowledge graph based on a database to identify a causal relationship, and obtaining a parameter importance degree; inputting a neural network mapping model (including an attention layer and dual-channel feature extraction) to predict a quality score, and generating an optimization control parameter in combination with multi-objective optimization; and parameters are dynamically adjusted through an adaptive PID algorithm. According to the method, the data reliability, the prediction precision and the process adaptability are improved, and the pickling quality and efficiency are optimized.

Description

Technical Field

[0001] This invention belongs to the field of intelligent control technology for pickling processes, and particularly relates to an intelligent control method for pickling processes. Background Technology

[0002] In the pickling process of steel production, acid is used to remove oxide scale from the surface of steel wire, and the process effect directly affects the quality of the steel wire. Traditional pickling control relies heavily on manual experience or simple closed-loop control, making it difficult to comprehensively handle the coupled effects of multiple parameters such as acid concentration, acid temperature, steel wire running speed, and ambient temperature and humidity. Parameter acquisition suffers from discreteness, noise, and missing values, resulting in low data reliability. The assessment of steel wire surface quality is mostly based on offline detection, which has a lag and cannot reflect the process status in real time. There is a lack of quantitative analysis of the importance of each parameter, and adjustments are prone to neglecting the balance between energy consumption and quality, resulting in resource waste or quality fluctuations. Furthermore, when parameters exceed reasonable ranges, dynamic adaptive adjustment is difficult to achieve, leading to poor pickling quality stability and low efficiency. Therefore, there is an urgent need for a control method that can integrate multiple parameters and achieve intelligent prediction and dynamic optimization. Summary of the Invention

[0003] In view of the technical problems existing in the background art described above, the present invention proposes an intelligent control method for pickling processes.

[0004] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0005] S1. Collect pickling process parameters, environmental parameters, steel wire treatment parameters and steel wire surface image data, preprocess the collected data, generate quality scores through image processing algorithms, and construct a process database.

[0006] S2. Construct a knowledge graph based on the process database, identify the causal relationship between parameters, wherein the causal relationship is the correlation between image quality score and influencing parameters, and obtain the importance parameter of each influencing parameter;

[0007] S3. Combine the influencing parameters and importance parameters to create a neural network mapping model between the input process parameters and the quality score;

[0008] S4. Based on the constructed neural network mapping model, the quality score is predicted, and the optimal control parameters are generated by combining the multi-objective optimization algorithm.

[0009] S5. The obtained optimized control parameters are used to control the pickling process, and the adaptive PID algorithm is used to dynamically adjust the parameters by comparing the real-time quality score with the predicted value.

[0010] Preferably, the pickling process parameters, environmental parameters, steel wire treatment parameters, and steel wire surface image data are as follows: the pickling process parameters include acid concentration, acid temperature, acid flow rate, and acid level; the environmental parameters include the ambient temperature and humidity of the pickling workshop; the steel wire treatment parameters include the steel wire running speed, steel wire thickness, and pickling time; and the steel wire surface image data are images of the surface of the steel wire collected after pickling.

[0011] As a preferred approach, the collected pickling process parameters, environmental parameters, and steel wire processing parameters are preprocessed. Data curves are obtained using the least squares method, and the data curves are denoised. Missing values ​​are filled into the denoised data to obtain the preprocessed data. The collected steel wire surface image data are then scored using the YOLO algorithm to achieve quality evaluation.

[0012] Preferably, the preprocessing operation for the collected pickling process parameters, environmental parameters, and steel wire treatment parameters specifically includes:

[0013] For any parameter i, the discretely acquired data is first fitted to a time-dependent continuous curve using the least squares method, and the fitting function is: ,in These are the fitting coefficients. Given the order of the polynomial, the coefficients are solved by minimizing the squared residuals, thus transforming discrete data into continuous curve data.

[0014] Reasonable fluctuation range of calculation parameters in the process Construct the filter correction function ,in Let be the mean of the i-th parameter. To ensure a reasonable fluctuation range width, when When the value exceeds a reasonable range, it is corrected by an exponential function decay.

[0015] The parameter curves corrected by the above filtering correction function are then subjected to a second correction using a sliding window mean filter. ,in, For the window radius, The sampling interval;

[0016] For the denoised data curves, the missing value types are identified by the missing time, including short-term and long-term missing values. For short-term missing values, a weighted moving average method is used, with weights dynamically allocated based on parameter importance. ,in For short-term missing values, The importance of the parameter at time m. For time t, with an interval of m sampling gaps The historical data, M is the number of historical moments participating in the weighted average;

[0017] For long-term missing data, Pearson correlation coefficient analysis was used to identify three strongly correlated parameters in the currently filled data curve, and the data was then filled using a multiple linear regression model. ,in, For long-term missing values, The contemporaneous values ​​of the associated parameters, These are the regression coefficients;

[0018] Finally, the preprocessed parameter data is output, and the parameter data is normalized to obtain a time-continuous and missing standardized parameter sequence.

[0019] Preferably, step S2 constructs a knowledge graph based on the process database to identify causal relationships between parameters. These causal relationships are the correlation between image quality scores and influencing parameters. The specific implementation of obtaining the importance parameters for each influencing parameter includes:

[0020] First, a knowledge graph is constructed to identify causal relationships and calculate the impact of each influencing parameter on the quality score. ,in, For causal strength, For the fine-tuning amount of the i-th parameter, The corresponding rating changes;

[0021] Introducing a cost sensitivity coefficient to correct for causal strength. ,in, The corrected causal strength. For the unit adjustment of the i-th parameter, the energy consumption cost is... To average out energy consumption costs;

[0022] The importance of influencing parameters is calculated by combining causal strength and sensitivity to quality fluctuations. The calculation method is as follows: ,in, For parameters The standard deviation of the quality score during fluctuations This represents the total standard deviation of the quality score under the influence of all parameters.

[0023] Preferably, a neural network mapping model is used to combine influence parameters and importance parameters, and input process parameters with quality scores. The construction of the neural network mapping model includes an input layer, an attention layer, a hidden layer, a fusion layer, and an output layer.

[0024] Input layer: Includes inputs of influencing parameters and the degree of importance of those parameters;

[0025] Attention layer: Assigns input weights based on importance parameters to enhance the influence of key parameters on the model;

[0026] Hidden layer: Employs a dual-channel feature extraction structure. Main channel: 3-layer fully connected network with ReLU activation function, used to learn the nonlinear mapping between parameters and quality score; Auxiliary channel: 1-layer LSTM network, inputting the time sequence of parameters to capture the lag effect of dynamic parameter changes on the current quality score.

[0027] Fusion layer: The static features of the main channel are concatenated with the temporal features of the auxiliary channel, and the features are fused through a fully connected network;

[0028] Output layer: 1 neuron, outputting the predicted image quality score. The activation function is a linear function.

[0029] Preferably, the implementation of generating the optimized control influence parameters in step S4 using a multi-objective optimization algorithm specifically includes:

[0030] The objective function of the multi-objective optimization algorithm is: Where N represents the number of parameters, and the constraint condition of the objective function is that the parameters are adjusted within a set reasonable fluctuation range. Furthermore, the parameter adjustment amount each time must be less than or equal to the set safety adjustment threshold.

[0031] Based on the defined multi-objective function, the Pareto solution set is iteratively generated using a multi-objective particle swarm optimization algorithm to obtain the optimal control influence parameters. .

[0032] Preferably, step S5 uses the obtained optimized control influence parameters to control the pickling process, and dynamically adjusts the influence parameters using an adaptive PID algorithm by comparing the real-time collected quality scores with the predicted values. The specific implementation of this method is as follows:

[0033] First, calculate the quality deviation. ,in Let be the predicted value of the quality score at time t. The actual quality score collected in real time at time t, and the rate of change of deviation. Mass deviation strength ;

[0034] Update PID parameters. ; , ,in For the proportional, integral, and derivative coefficients of the PID controller, These are the proportional, integral, and derivative coefficients of the updated PID.

[0035] For the i-th influencing parameter, the PID controller output adjustment quantity The updated parameters satisfy ,in This is the updated value after adaptive PID adjustment.

[0036] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0037] 1. By integrating multidimensional static and dynamic process parameters and constructing a knowledge graph to quantify the causal strength of each parameter on the quality score, the model achieves accurate identification and weighted processing of influencing factors, significantly improving the reliability and representativeness of the model input.

[0038] 2. A dual-channel feature extraction structure is adopted. The three-layer fully connected network of the main channel describes the static nonlinear mapping, and the LSTM network of the auxiliary channel captures the temporal lag effect. The fusion of the two significantly enhances the model's prediction accuracy for complex working conditions.

[0039] 3. By combining the optimized control parameters with real-time quality score feedback, the adaptive PID algorithm dynamically adjusts the process parameters, which can continuously correct deviations while ensuring stable system operation, thus improving the adaptability and robustness of the pickling process. Attached Figure Description

[0040] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a schematic diagram of the structural flow of an intelligent control method for pickling processes; Detailed Implementation

[0042] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0043] Numerous specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways than those described herein, and therefore the invention is not limited to the specific embodiments disclosed in the following specification.

[0044] In this embodiment, to address the shortcomings of traditional pickling control, which relies heavily on manual experience or simple closed-loop control, making it difficult to comprehensively handle the coupled effects of multiple parameters such as acid concentration, acid solution temperature, steel wire running speed, and ambient temperature and humidity; the problems of parameter acquisition including discreteness, noise, and missing values ​​leading to low data reliability; the offline detection-based assessment of steel wire surface quality resulting in lag and inability to reflect the process status in real time; and the lack of quantitative analysis of the importance of each parameter, which can easily lead to neglect of the balance between energy consumption and quality during adjustment, resulting in resource waste or quality fluctuations, an intelligent control method for the pickling process is proposed. The specific implementation is as follows: Figure 1 As shown.

[0045] First, pickling process parameters, environmental parameters, steel wire treatment parameters, and steel wire surface image data are collected. The collected data are preprocessed, and a quality score is generated through image processing algorithms to construct a process database.

[0046] The pickling process parameters, environmental parameters, steel wire processing parameters, and steel wire surface image data are as follows: the pickling process parameters include acid concentration, acid temperature, acid flow rate, and acid level; the environmental parameters include the ambient temperature and humidity of the pickling workshop; the steel wire processing parameters include the steel wire running speed, steel wire thickness, and pickling time; and the steel wire surface image data are images of the surface of the steel wire collected after pickling.

[0047] To address the issues of high discreteness, significant noise interference, and frequent missing values ​​leading to low data reliability in traditional pickling parameter acquisition, preprocessing is performed on the acquired pickling process parameters, environmental parameters, and steel wire processing parameters. Data curves are obtained using the least squares method, and these curves are then denoised. Missing values ​​are imputed in the denoised data to obtain preprocessed data. Finally, the YOLO algorithm is used to score the quality of the acquired steel wire surface image data. Specifically, for any parameter i, the discretely acquired data is first fitted to a time-dependent continuous curve using the least squares method, with the fitting function being... ,in These are the fitting coefficients. To determine the order of the polynomial, the coefficients are solved by minimizing the squared residuals, thus transforming discrete data into continuous curve data; the reasonable fluctuation range of the process parameters is calculated. Construct the filter correction function ,in Let be the mean of the i-th parameter. To ensure a reasonable fluctuation range width, when When the value exceeds a reasonable range, an exponential function is used for attenuation correction; the parameter curve after the above filtering correction function is then subjected to a second correction using a sliding window mean filter. ,in, For the window radius, The sampling interval is defined as follows: For the denoised data curve, the missing value type is identified by the missing time, including short-term and long-term missing values. For short-term missing values, a weighted moving average method is used, with weights dynamically allocated based on parameter importance. ,in For short-term missing values, The importance of the parameter at time m is calculated using the Pearson coefficient. For time t, with an interval of m sampling gaps Historical data, where M is the number of historical moments participating in the weighted average; for long-term missing data, Pearson correlation coefficient analysis is used to identify three strongly correlated parameters in the currently filled data curve, which are then filled using a multiple linear regression model: ,in, For long-term missing values, The contemporaneous values ​​of the associated parameters, The regression coefficients are used; finally, the preprocessed parameter data is output, and the parameter data is normalized to obtain a time-continuous and missing standardized parameter sequence.

[0048] A knowledge graph is constructed based on a process database to identify causal relationships between parameters. These causal relationships are the association between image quality scores and influencing parameters, thus determining the importance of each influencing parameter. Specifically, the knowledge graph is first constructed, causal relationships are identified, and the impact of each influencing parameter on the quality score is calculated. ,in, For causal strength, For the fine-tuning amount of the i-th parameter, To reflect the corresponding changes in ratings, a cost sensitivity coefficient is introduced to correct for the causal strength. ,in, The corrected causal strength. For the unit adjustment of the i-th parameter, the energy consumption cost is... To average the energy consumption cost of regulation; the importance of influencing parameters is calculated, combining causal strength and sensitivity to quality fluctuations, using the following calculation method: ,in, For parameters The standard deviation of the quality score during fluctuations This represents the total standard deviation of the quality score under the influence of all parameters.

[0049] A neural network mapping model is constructed by combining influencing parameters and importance parameters to map input process parameters to quality scores. The network mapping model consists of an input layer, an attention layer, a hidden layer, a fusion layer, and an output layer. The input layer includes the influencing parameters and their importance parameters. The attention layer assigns input weights based on the importance parameters to amplify the influence of key parameters on the model. The hidden layer employs a dual-channel feature extraction structure: the main channel is a 3-layer fully connected network with ReLU activation to learn the nonlinear mapping between parameters and quality scores; the auxiliary channel is a 1-layer LSTM network that takes the time sequence of input parameters to capture the lagged impact of dynamic parameter changes on the current quality score. The fusion layer concatenates the static features of the main channel with the time sequence features of the auxiliary channel, performing feature fusion through a fully connected network. The output layer consists of one neuron that outputs the predicted image quality score. The activation function is a linear function. Specifically, in this model, firstly, in the input layer, all parameters affecting image quality and their importance values ​​are normalized and combined into a unified input vector to ensure that each parameter is within a similar numerical range. Next, in the attention layer, normalized weights are calculated based on the importance values ​​of each parameter and applied to the corresponding parameters to highlight the influence of key factors on subsequent learning. Then, the hidden layer is entered, employing a dual-channel feature extraction structure: the main channel consists of three fully connected layers, each using the ReLU activation function to capture the complex nonlinear relationship between the input static features and the quality score; the auxiliary channel feeds the time series of parameters into a single-layer LSTM network to capture the lagged effect of historical changes on the current score. Then, in the fusion layer, the feature vector output from the static channel is concatenated with the feature vector output from the time series channel, and then refined through a fully connected layer to form a fused feature representation. Finally, in the output layer, a linear neuron maps the fused features to the final image quality score prediction value, ensuring that the output is consistent with the true score. This structure achieves accurate prediction of the quality score under the combined influence of static and dynamic parameters.

[0050] Based on the constructed neural network mapping model, quality scores are predicted, and optimal control parameters are generated using a multi-objective optimization algorithm. The objective function of the multi-objective optimization algorithm is: Where N represents the number of parameters, and the constraint condition of the objective function is that the parameters are adjusted within a set reasonable fluctuation range. Furthermore, the parameter adjustment amount each time must be less than or equal to the set safe adjustment threshold; based on the set multi-objective function, the Pareto solution set is iteratively generated using a multi-objective particle swarm optimization algorithm to obtain the optimized control influence parameters. Specifically, in the implementation process, firstly, an objective function is constructed based on process requirements, and reasonable fluctuation ranges and safe adjustment thresholds for the parameters are defined as constraints. Next, the vector of parameters to be optimized is encoded as a particle swarm population, with each particle representing a set of parameter configurations, and its position and velocity are randomly initialized. In each iteration, the objective function value for each particle is calculated, and solutions that satisfy the constraints are stored in an external archive. Simultaneously, the optimal Pareto solution set in the archive is selected based on non-dominated sorting and crowding distance. Then, according to the update rules of the particle swarm optimization algorithm, the velocity and position of each particle are dynamically adjusted by combining inertia weights, self-awareness terms, and group cooperation terms to ensure that the parameters change smoothly within the safe threshold. After the update, the objective function is evaluated and constraints are checked again at the new position; unacceptable solutions are corrected or discarded. This process is repeated until the predetermined number of iterations or convergence conditions are reached, and finally, the Pareto front solution set is extracted from the archive as the optimized control parameters.

[0051] Finally, the optimized control parameters are used to control the pickling process, and the parameters are dynamically adjusted using an adaptive PID algorithm by comparing the real-time quality scores with the predicted values. Specifically, the quality deviation is first calculated. ,in Let be the predicted value of the quality score at time t. The actual quality score collected in real time at time t, and the rate of change of deviation. Mass deviation strength Update PID parameters. ; , ,in For the proportional, integral, and derivative coefficients of the PID controller, Here are the proportional, integral, and derivative coefficients of the updated PID controller; for the i-th influencing parameter, the PID controller output adjustment is... ,in For the integral variable, the updated parameter satisfies ,in This is the updated value after adaptive PID adjustment. The updated value is used to control the pickling process, continuously monitoring the quality score at the next moment. This cycle repeats, ensuring stable operation while continuously optimizing parameters, ultimately achieving refined adaptive control of pickling quality.

[0052] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments for application in other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. An intelligent control method for pickling processes, characterized in that, Includes the following steps: S1. Collect pickling process parameters, environmental parameters, steel wire treatment parameters and steel wire surface image data, preprocess the collected data, generate quality scores through image processing algorithms, and construct a process database. S2. Construct a knowledge graph based on the process database, identify the causal relationship between parameters, wherein the causal relationship is the correlation between image quality score and influencing parameters, and obtain the importance parameter of each influencing parameter; S3. Combine the influencing parameters and importance parameters to create a neural network mapping model between the input process parameters and the quality score; S4. Based on the constructed neural network mapping model, the quality score is predicted, and the optimal control parameters are generated by combining the multi-objective optimization algorithm. S5. The obtained optimized control parameters are used to control the pickling process, and the adaptive PID algorithm is used to dynamically adjust the parameters by comparing the real-time quality score with the predicted value.

2. The intelligent control method for pickling process according to claim 1, characterized in that, The pickling process parameters, environmental parameters, steel wire processing parameters, and steel wire surface image data are as follows: the pickling process parameters include acid concentration, acid temperature, acid flow rate, and acid level; the environmental parameters include the ambient temperature and humidity of the pickling workshop; the steel wire processing parameters include the steel wire running speed, steel wire thickness, and pickling time; and the steel wire surface image data are images of the surface of the steel wire collected after pickling.

3. The intelligent control method for pickling process according to claim 2, characterized in that, The collected pickling process parameters, environmental parameters, and steel wire treatment parameters were preprocessed. Data curves were obtained using the least squares method. The data curves were then denoised. Missing values ​​were filled into the denoised data to obtain the preprocessed data. The quality score of the collected steel wire surface image data is achieved using the YOLO algorithm.

4. The intelligent control method for pickling process according to claim 3, characterized in that, The specific steps for preprocessing the collected pickling process parameters, environmental parameters, and steel wire treatment parameters are as follows: For any parameter i, the discretely acquired data is first fitted to a time-dependent continuous curve using the least squares method, and the fitting function is: ,in These are the fitting coefficients. Given the order of the polynomial, the coefficients are solved by minimizing the squared residuals, thus transforming discrete data into continuous curve data. Reasonable fluctuation range of calculation parameters in the process Construct the filter correction function ,in Let be the mean of the i-th parameter. To ensure a reasonable fluctuation range width, when When the value exceeds a reasonable range, it is corrected by an exponential function decay. The parameter curves corrected by the above filtering correction function are then subjected to a second correction using a sliding window mean filter. ,in, For the window radius, The sampling interval; For the denoised data curves, the missing value types are identified by the missing time, including short-term and long-term missing values. For short-term missing values, a weighted moving average method is used, with weights dynamically allocated based on parameter importance. ,in For short-term missing values, The importance of the parameter at time m. For time t, with an interval of m sampling gaps The historical data, M is the number of historical moments participating in the weighted average; For long-term missing data, Pearson correlation coefficient analysis was used to identify three strongly correlated parameters in the currently filled data curve, and the data was then filled using a multiple linear regression model. ,in, For long-term missing values, The contemporaneous values ​​of the associated parameters, These are the regression coefficients; Finally, the preprocessed parameter data is output, and the parameter data is normalized to obtain a time-continuous and missing standardized parameter sequence.

5. The intelligent control method for pickling process according to claim 1, characterized in that, Step S2 constructs a knowledge graph based on the process database to identify causal relationships between parameters. These causal relationships are the correlation between image quality scores and influencing parameters. The specific implementation of obtaining the importance parameters of each influencing parameter includes: First, a knowledge graph is constructed to identify causal relationships and calculate the impact of each influencing parameter on the quality score. ,in, For causal strength, For the fine-tuning amount of the i-th parameter, The corresponding rating changes; Introducing a cost sensitivity coefficient to correct for causal strength. ,in, The corrected causal strength. For the unit adjustment of the i-th parameter, the energy consumption cost is... To average out energy consumption costs; The importance of influencing parameters is calculated by combining causal strength and sensitivity to quality fluctuations. The calculation method is as follows: ,in, For parameters The standard deviation of the quality score during fluctuations This represents the total standard deviation of the quality score under the influence of all parameters.

6. The intelligent control method for pickling process according to claim 1, characterized in that, A neural network mapping model that combines influencing parameters and importance parameters to input process parameters and quality scores is constructed, including an input layer, an attention layer, a hidden layer, a fusion layer, and an output layer. Input layer: Includes inputs of influencing parameters and the degree of importance of those parameters; Attention layer: Assigns input weights based on importance parameters to enhance the influence of key parameters on the model; Hidden layer: Employs a dual-channel feature extraction structure. Main channel: 3-layer fully connected network with ReLU activation function, used to learn the nonlinear mapping between parameters and quality score; Auxiliary channel: 1-layer LSTM network, inputting the time sequence of parameters to capture the lag effect of dynamic parameter changes on the current quality score. Fusion layer: The static features of the main channel are concatenated with the temporal features of the auxiliary channel, and the features are fused through a fully connected network; Output layer: 1 neuron, outputting the predicted image quality score. The activation function is a linear function.

7. The intelligent control method for pickling process according to claim 1, characterized in that, The specific implementation of generating the optimal control influence parameters in step S4 by combining the multi-objective optimization algorithm includes: The objective function of the multi-objective optimization algorithm is: Where N represents the number of parameters, and the constraint condition of the objective function is that the parameters are adjusted within a set reasonable fluctuation range. Furthermore, the parameter adjustment amount each time must be less than or equal to the set safety adjustment threshold. Based on the defined multi-objective function, the Pareto solution set is iteratively generated using a multi-objective particle swarm optimization algorithm to obtain the optimal control influence parameters. .

8. The intelligent control method for pickling process according to claim 1, characterized in that, Step S5 uses the obtained optimized control influence parameters to control the pickling process, and dynamically adjusts the influence parameters using an adaptive PID algorithm by comparing the real-time collected quality scores with the predicted values. The specific implementation of this step is as follows: First, calculate the quality deviation. ,in Let be the predicted value of the quality score at time t. The actual quality score collected in real time at time t, and the rate of change of deviation. Mass deviation strength ; Update PID parameters. ; , ,in For the proportional, integral, and derivative coefficients of the PID controller, These are the proportional, integral, and derivative coefficients of the updated PID. For the i-th influencing parameter, the PID controller output adjustment quantity The updated parameters satisfy ,in This is the updated value after adaptive PID adjustment.

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