Stamped engine active disturbance rejection control design method based on seagull optimization algorithm

Abstract

A design of active disturbance rejection control for a ramjet engine based on the seagull optimization algorithm. First, the random forest algorithm is used to extract the pressure output quantity that is most sensitive to the control quantity, and a tracking differentiator is added to soften the starting link, and the given pressure signal is smoothed and denoised to obtain the pressure signal and the differential signal of the pressure. Then, the state is observed through an improved extended state observer, and the internal disturbance and external disturbance of the ramjet engine system are regarded as an overall disturbance and observed, and then fed back to the control algorithm. Furthermore, the overall error of the ESO is compensated into the control system through nonlinear state error feedback for compensation. The control parameters are tuned by an improved adaptive seagull optimization algorithm. The present invention can achieve that the ramjet engine operates according to the specified control pressure command step. While meeting the command, it can greatly reduce the disturbance and error generated during the pressure step jump, simplify the complexity of parameter tuning, and improve the convergence speed and optimization accuracy of the optimization process.

Description

Technical Field

[0001] The present invention relates to the design of active disturbance rejection control for a ramjet engine based on the seagull optimization algorithm, belonging to the field of aeroengine control. Background Art

[0002] The model used in the present invention is a certain type of ramjet engine. The ramjet engine is a new type of advanced aviation science and technology for high-speed flight. Among them, the pressure regulation control in the combustion chamber of the ramjet engine is one of the key factors related to the high-performance operation of the ramjet engine. The pressure regulation system of the ramjet engine belongs to a complex multi-input multi-output system with strong coupling. There is more than one controlled pressure and control quantity. Each controlled pressure is affected by multiple control quantities, and each control quantity affects multiple controlled pressures at the same time. Especially in the control scenario of few controls for many, such as 3 control quantities of the ramjet engine controlling 10 groups of controlled pressures. Therefore, variable selection is very important in a complex multi-input multi-output system. Appropriate selection of characteristic variables can help construct a better controller, and can help further understand the control correlation of these variables and help analyze the working performance of the engine.

[0003] For the along-the-way pressure in the combustion chamber of the ramjet engine, it is usually affected by various disturbance factors. For example, during the actual working process, it is affected by environmental factors such as temperature and pressure, and the along-the-way pressure in the engine combustion chamber will change to varying degrees. This increases the control difficulty, and it is very necessary to design a controller with good anti-interference ability. Active Disturbance Rejection Control (ADRC) is a control method proposed by Professor Han Jingqing. Adopting ADRC can turn the complex control object of the ramjet engine into a simple integral series type control object, and at the same time solve the contradiction between the response speed and overshoot, and solve the influence of the unknown part of the model and external disturbances on the ramjet engine. However, ADRC requires a large number of parameters to be tuned, and the tuning is rather cumbersome. It is necessary to use a new type of optimization algorithm to realize the self-tuning of control parameters.

[0004] In view of the above, in order to overcome the deficiencies in the current design of the ramjet engine pressure regulation system, the present invention proposes a design of active disturbance rejection control for a ramjet engine based on the seagull optimization algorithm. The random forest variable selection algorithm is adopted to screen the characteristic pressures that can best represent the control quantities, eliminate variables with low correlation and redundant characteristic pressures, and perform dimensionality reduction on high-dimensional data; and the nonlinear function of the extended state observer in the active disturbance rejection controller is improved to enhance the robust control effect; at the same time, the improved seagull optimization algorithm is used to realize the self-tuning of control parameters, improve the control accuracy and control speed, and reduce the difficulty of parameter tuning, which has important engineering significance in the application of ramjet engines. Summary of the Invention

[0005] In view of the deficiencies of the prior art, the present invention proposes a self-disturbance rejection control design for a ramjet engine based on the seagull optimization algorithm.

[0006] The technical solution of the present invention:

[0007] A self-disturbance rejection control design method for a ramjet engine based on the seagull optimization algorithm, the steps are as follows:

[0008] S1: Based on the control objective of more controlled variables than control variables, realize m control variables to control n groups of controlled variables, where m < n. Select m groups of along-path pressures from n groups of controlled pressures as the most effective pressure controlled variables, and determine the controlled variables by combining the method of random forest variable selection;

[0009] S1.1 According to the control requirements of the ramjet engine, run the engine model to obtain the output pressure data. The controlled variables are P = [p1,... p i ,... p n T That is, class variables, and the control variables are U = [u1,... u i ,... u n T , u i and p i are variables in the same loop; Take the pressure data output by the engine model as the original training set D. Each data contains M features, K is the number of samples, and j is the number of classification trees;

[0010] S1.2 Extract the training subset, randomly select K samples from the original training set D with replacement, and repeat K times as the training subset; The part of the original training set D except the sampled training subset is used as the out-of-bag data set, denoted by OOB;

[0011] S1.3 Build classification trees. First, randomly select l features from M features to form a feature subset. Select the splitting point according to the sample features, divide the splitting point into child nodes, and at the same time divide the training subset into the corresponding nodes. Repeat the hierarchical division until all nodes are obtained; Execute the above process in a loop until j classification trees are established to form a random forest t, where t ∈ {t i , i = 1, 2,..., j};

[0012] S1.4 Statistically calculate the importance w of variables at non-zero child nodes, calculate the importance of all variables in a loop, take the mean value as the final judgment basis, arrange the importance of variables, and select the most important 3 groups of variables;

[0013] S1.5 Evaluate the results obtained by the classification tree, calculate the correlation coefficient R 2 , and verify the effectiveness;

[0014] ​​S2: According to the basic principle of auto-disturbance rejection, build three parts of the ADRC controller, namely the tracking differentiator TD, the extended state observer ESO, and the nonlinear state error feedback NLSEF. Improve the nonlinear function fal among them to construct a new extended state observer ESO and nonlinear state error feedback NLSEF;

[0015] S2.1 Design the tracking differentiator TD

[0016] Given that the efficiency of the nonlinear TD is higher than that of the linear TD, and this control system is a discrete system, the fastest discrete function is introduced:

[0017]

[0018] In the formula: fhan is a function symbol; fh is the output value of the fhan function; k is the k-th step of the discrete simulation; v1(k) is the discrete signal to be tracked; v2(k) is the derivative of the discrete signal to be tracked; h is the simulation step size; u is the control target; h0 is the filtering factor;

[0019] The calculation of fhan(v1(k)-u(t), v2(k), r, h0) is as follows:

[0020]

[0021] In the formula: r is the parameter to be adjusted, fsg(v, d)=(sign(v + d)-sign(v - d)) / 2, sign() is the sign function; d, a, a0, a1, a2, y are intermediate process variables in the function calculation and do not have actual physical meanings;

[0022] S2.2 Design the extended state observer ESO

[0023] Establish a second-order extended state observer in the following form for each of the three-direction channels:

[0024]

[0025] In the formula: e is the error term. By selecting appropriate parameters β 01 , β 02 , β 03 , such that the ESO constructed by the above formula can estimate the state of the object and the extended state in real time. Here, the bandwidth tuning method is used to determine the parameter configuration, that is, β 01 = 3ω, β 02 = 3ω 2 , β 03 = ω 3 , where ω is the bandwidth of the extended state observer, which needs to be set according to requirements and is also a parameter to be adjusted; g i (e), i = 1, 2 satisfies e·gi (e) A suitable non - linear function fal(e, α i , δ), where

[0026]

[0027] In the formula: α is a constant between 0 and 1, and δ is the length of the linear segment interval;

[0028] S2.3 Improve the fal function in the extended state observer

[0029] The extended state observer is the core part of the whole active disturbance rejection controller, and the fal function is the core of the extended state observer. It can be seen from the expression of the traditional fal function that this non - linear function is linear when the absolute value of the error is relatively small, and rises exponentially and does not converge when the error is relatively large. To solve this problem, the present invention designs a new non - linear function newfal as follows to replace the traditional non - linear function fal. For the sake of distinction, x in the formula is the error, which is equivalent to e in fal.

[0030]

[0031] When the absolute value of the error is large, the output value of the newfal function converges to a fixed constant, which is significantly smaller than the output value of the fal function, avoiding the problem that the non - linear function does not converge due to the continuous increase of the error. At the same time, the newfal function is smoother and has better convergence near the origin, effectively overcoming the problem that the traditional fal function has a large slope due to the existence of an inflection point near the origin. It can be seen from the above two formulas that when the input error value approaches 0, the output gain of the fal function tends to infinity, which is likely to cause system oscillation; when the input error is small, the output gain of the newfal function is higher than that of the fal function; when the input error is large, the output gain of the newfal function is significantly lower than that of the fal function. Therefore, the newfal function designed by the present invention better embodies the engineering idea of "small error, large gain; large error, small gain" than the fal function.

[0032] The improved second - order extended state observer is as follows, where b is the compensation factor;

[0033]

[0034] S2.4 Non - linear state error feedback design;

[0035] Take the difference between the output of the tracking differentiator and the output of the extended state observer and perform non - linear combination, and compensate the total disturbance estimated by the extended state observer in real - time to obtain the control quantity of the system, which is specifically expressed as follows:

[0036] u0 = K pnewfal(x1,α1)+K d newfal(x2,α2)

[0037] where: u0 is the output of the nonlinear state feedback module, K p and K d are the control quantity gains respectively. According to the basic principle of active disturbance rejection control, the system control rate after compensating for internal and external disturbances is obtained as shown in the following formula, where u is the control quantity;

[0038]

[0039] S3: Design an improved seagull optimization algorithm to autonomously tune the main parameters of the active disturbance rejection controller. Specifically, a heuristic population evolution strategy based on the concepts of attraction and repulsion is proposed; the improved seagull optimization algorithm is as follows:

[0040] S3.1 Initialize the seagull population P s , with the maximum number of iterations being M_max, and initialize the additional variables A and B;

[0041] S3.2 Calculate the fitness values of the initial population, mark the optimal individual, and the fitness function fitness is calculated as follows:

[0042]

[0043] where: t p is time, and e(t p ) is the above control error, that is, the fitness function is the integral of the product of time and the absolute value of the error;

[0044] S3.3 Update the seagull positions according to the migration and attack operations. To avoid collisions with other seagulls, the positions are updated, and the position update formula is:

[0045] C s (t) = A × P s (x),

[0046] where: C s (t) represents the new position without position conflicts with other seagulls, and P s (x) represents the current position of the seagull;

[0047] S3.4 Calculate the fitness values of the new population and update the optimal individual; after avoiding overlapping positions with other seagulls, the seagulls will move in the direction of the best position; the best position direction update formula is:

[0048] M s (t) = B × (P best (x) - P s (x))

[0049] Where: M s (t) represents the convergence direction of the individual to the best seagull, and P best (x) represents the optimal position; when the seagull approaches the best position: after the seagull moves to a position where it does not collide with other seagulls, it moves in the direction of the best position and reaches a new position; the position update formula is:

[0050] H s (t) = |C s (t) + M s (t)|

[0051] Where: H s (t) is the new position of the seagull;

[0052] S3.5 As can be seen from the above, the population update is too dependent on the optimal individual. If the global optimal individual falls into a local optimum, it may cause the update of the entire population to stagnate, and the algorithm is prone to premature convergence. Therefore, the present invention improves the search method of the seagull optimization algorithm. By improving the search method of the above seagull optimization algorithm, a heuristic population evolution strategy based on the concepts of attraction and repulsion is proposed. The improved position update formula is as follows:

[0053]

[0054] Where: represents the updated position, represents the position component of the j H th individual in the i H th dimension, H b,iH represents the global optimal individual, represents the global worst individual, and r1 and r2 are both random numbers uniformly distributed in the range of [0, 1]; in the above formula represents the attracting effect of the optimal individual, represents the repulsive effect of the worst individual;

[0055] S3.6 Attack stage: During the migration process, seagulls continuously change the attack speed and angle with their wings. When attacking prey, they perform a spiral motion in the air; the motion behavior of seagulls in a three-dimensional plane is described as follows:

[0056] x H = r H × cos(k H )

[0057] y H = r H × sin(k H )

[0058] z H = rH ×k H

[0059]

[0060] where: r H is the radius of each spiral motion of the seagull, k H is a random angle value within 0 to 2π, u H and v H are the relevant constants of the spiral shape, used to control the spiral radius, usually taken as 1, and e is the base of the natural logarithm;

[0061] S3.7 Update the attack position of the seagull. Combining the new position of the seagull, the overall seagull position update formula is obtained as:

[0062] P s (t) = (H s ×x H ×y H ×z H ) + P best (t)

[0063] where: P s (t) is the attack position of the seagull;

[0064] S3.8 Judge whether the termination condition is satisfied. If so, stop the iteration and output the optimal parameter value. Otherwise, jump to S3.3 to continue the iteration;

[0065] S3.9 According to the optimal parameter value obtained in S3.8, pass it to the active disturbance rejection controller;

[0066] S4: Verify the superiority of the improved active disturbance rejection controller, and build a Simulink model in Matlab for simulation experiments.

[0067] The beneficial effects of the present invention are as follows: For a ramjet engine, the along - path pressure fluctuation caused by temperature, pressure, and noise is a disturbance to the engine. Especially in the transformation of the along - path pressure command, it poses a high requirement for the real - time disturbance rejection control of the engine. In the design of the active disturbance rejection control of a ramjet engine optimized by seagulls according to the present invention, the active disturbance rejection controller is applied to the pressure regulation system. The random forest algorithm is used to extract the pressure output quantity that is most sensitive to the control quantity. An improved adaptive seagull optimization algorithm is proposed to tune the control parameters, which simplifies the complexity of parameter tuning and improves the convergence speed and optimization accuracy of the optimization process. Brief Description of the Drawings

[0068] Figure 1 is the design flow chart of the active disturbance rejection control of a ramjet engine based on the seagull optimization algorithm;

[0069] Figure 2 It is the framework diagram of the active disturbance rejection control structure;

[0070] Figure 3 It is the flow chart of random forest variable selection;

[0071] Figure 4 It is the flow chart of the improved seagull optimization algorithm;

[0072] Figure 5 It is the control effect diagram of a certain type of ramjet engine after being disturbed under a certain working condition;

[0073] Figure 6 It is the control effect diagram of a certain type of ramjet engine after the continuous step change of the pressure along the way under a certain working condition. Specific implementation manners

[0074] The following further elaborates on the present invention in combination with the accompanying drawings in the embodiments of the invention. Obviously, the described embodiments are only a part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0075] As Figure 1 shown, a design of active disturbance rejection control for a ramjet engine based on the seagull optimization algorithm mainly includes the following steps:

[0076] S1: Based on the variable control objective, select 3 groups of pressures along the way from 10 groups of controlled pressures as the most effective pressure controlled variables, and determine the controlled variables in combination with the method of random forest variable selection.

[0077] S2: According to the basic principle of active disturbance rejection, build three parts of the tracking differentiator TD, extended state observer ESO, and nonlinear state error feedback NLSEF of the ADRC controller, and improve the nonlinear function fal.

[0078] S3: Design an improved seagull optimization algorithm to autonomously optimize the main parameters of the active disturbance rejection controller. Specifically, propose a heuristic population evolution strategy based on the concepts of attraction and repulsion.

[0079] S4: Verify the superiority of the improved active disturbance rejection controller, and build a Simulink model in Matlab for simulation experiments.

[0080] As Figure 2 , the steps to determine the controlled quantity are as follows:

[0081] S1: Based on the control objective of having more controlled variables than controlling variables, achieve the control of n groups of controlled variables with m control variables, where m < n. Select m groups of along - path pressures from the n groups of controlled pressures as the most effective controlled pressure variables, and determine the controlled variables by combining the method of random forest variable selection;

[0082] S1.1 According to the control requirements of the ramjet engine, run the engine model to obtain the output pressure data. The controlled variables are P = [p1, … p i , … p n T That is, the class variables, and the control variables are U = [u1, … u i , … u n T , u i and p i are variables in the same loop; Take the pressure data output by the engine model as the original training set D. Each data contains M features, K is the number of samples, and j is the number of classification trees;

[0083] S1.2 Extract the training subset. Randomly select K samples from the original training set D with replacement and repeat K times as the training subset; The part of the original training set D except the sampled training subset is used as the out - of - bag data set, denoted as OOB;

[0084] S1.3 Build classification trees. First, randomly select l features from the M features to form a feature subset. Select the splitting point according to the sample features, divide the splitting point into child nodes, and at the same time divide the training subset into the corresponding nodes. Repeat the hierarchical division until all nodes are obtained; Loop through the above process until j classification trees are established to form a random forest t, where t ∈ {t i , i = 1, 2, …, j};

[0085] S1.4 Statistically calculate the importance w of variables at non - zero child nodes. Loop through the calculation to obtain the importance of all variables, take the mean as the final judgment basis, arrange the importance of variables, and select the most important 3 groups of variables;

[0086] S1.5 Evaluate the results obtained by the classification trees, calculate the correlation coefficient R 2 , and verify the effectiveness;

[0087] Take ntree = 100, leaf = 5, where ntree is the number of trees and leaf is the number of leaves. After a large number of experimental trainings and analyses, it is concluded that the 5th, 6th, and 7th groups of pressures among the 10 groups of pressures have the highest correlation with the three groups of control variables, and the calculated R 2 = 0.89 > 0.5, indicating that the variable selection is effective.

[0088] S2: As Figure 3 ​​As shown in the figure, the tracking differentiator TD, the extended state observer ESO, and the nonlinear state error feedback NLSEF of the ADRC controller are built.

[0089] S2.1 Design the tracking differentiator TD

[0090] Since the efficiency of the nonlinear TD is higher than that of the linear TD, and the control system in this case is a discrete system, the fastest discrete function is introduced:

[0091]

[0092] In the formula: fhan is the function symbol; fh is the output value of the fhan function; k is the k-th step of the discrete simulation; v1(k) is the discrete signal to be tracked; v2(k) is the derivative of the discrete signal to be tracked; h is the simulation step size; u is the control target; h0 is the filtering factor;

[0093] The calculation of fhan(v1(k)-u(t), v2(k), r, h0) is as follows:

[0094]

[0095] In the formula: r is the parameter to be adjusted, fsg(v, d) = (sign(v + d) - sign(v - d)) / 2, sign() is the sign function; d, a, a0, a1, a2, y are intermediate process variables in the function calculation and do not have actual physical meanings;

[0096] S2.2 Design the extended state observer ESO

[0097] For each of the three-direction channels, a second-order extended state observer in the following form is established:

[0098]

[0099] In the formula: e is the error term. By selecting appropriate parameters β 01 , β 02 , β 03 , such that the ESO constructed by the above formula can estimate the state of the object and the extended state in real time. Here, the bandwidth tuning method is used to determine the parameter configuration, that is, β 01 = 3ω, β 02 = 3ω 2 , β 03 = ω 3 , where ω is the bandwidth of the extended state observer, which needs to be set according to requirements and is also a parameter to be adjusted; g i (e), i = 1, 2 is an appropriate nonlinear function fal(e, α i (e) ≥ 0, and take i , δ), take

[0100]

[0101] where: α is a constant between 0 and 1, and δ is the length of the linear segment interval;

[0102] S2.3 Improve the fal function in the extended state observer

[0103] The extended state observer is the core part of the entire active disturbance rejection controller, and the fal function is the core of the extended state observer. It can be seen from the expression of the traditional fal function that this non-linear function is linear when the absolute value of the error is relatively small, and exponentially increasing and non-convergent when the error is relatively large. To address this problem, the present invention designs a new non-linear function newfal as follows to replace the traditional non-linear function fal. For the sake of distinction, in the formula, x is the error, which is equivalent to e in fal.

[0104]

[0105] When the absolute value of the error is large, the output value of the newfal function converges to a fixed constant, which is significantly smaller than the output value of the fal function, avoiding the problem of non-convergence of the non-linear function due to the continuously increasing error. At the same time, the newfal function is smoother and has better convergence near the origin, effectively overcoming the problem of a large slope caused by the inflection point of the traditional fal function near the origin. It can be seen from the above two formulas that when the input error value approaches 0, the output gain of the fal function tends to infinity, which is likely to cause system oscillation; when the input error is small, the output gain of the newfal function is higher than that of the fal function; when the input error is large, the output gain of the newfal function is significantly lower than that of the fal function. Therefore, the newfal function designed in the present invention better embodies the engineering idea of "small error, large gain; large error, small gain" than the fal function.

[0106] The improved second-order extended state observer is as follows, where b is the compensation factor;

[0107]

[0108] S2.4 Nonlinear state error feedback design;

[0109] The output of the tracking differentiator is subtracted from the output of the extended state observer and non-linearly combined, and the total disturbance estimated by the extended state observer is compensated in real time to obtain the control quantity of the system, which is specifically expressed as follows:

[0110] u0 = K p newfal(x1, α1) + K d newfal(x2, α2)

[0111] where: u0 is the output of the nonlinear state feedback module, K p , K d are the control quantity gains respectively. According to the basic principle of active disturbance rejection control, the system control law after compensating for internal and external disturbances is shown as follows, where u is the control quantity;

[0112]

[0113] S3: Figure 4 is the flow chart of the improved seagull optimization algorithm. Through the improved seagull optimization algorithm, the main parameters of the active disturbance rejection controller are autonomously tuned. The parameters to be tuned are the set of parameters to be tuned obtained from the above-mentioned tracking differentiator, extended state observer, and nonlinear state error feedback law, that is, the time constant r of the tracking differentiator, ω of the linear extended state observer, compensation factor b, and K of the nonlinear state error feedback NLSEF p and K d . The set vector of the above-mentioned parameters to be tuned is the seagull population, each parameter represents a seagull in the population, and the ideal optimal solution of the parameter to be tuned is the best position of the seagull.

[0114] S4: Verify the superiority of the improved active disturbance rejection controller, and build a Simulink model in Matlab for simulation experiments.

[0115] As Figure 5 shown, when the simulation step is 10, the engine pressure is disturbed and the pressure along the way decreases. When the simulation step is 20, the controller starts to resist the disturbance. When the controller resists the disturbance, it is affected by noise. After self-tuning of the controller parameters, a better parameter combination 1 is obtained: r = 500, ω0 = 10.5, ω1 = 7.5, ω2 = 7.5, K p1 = 90, K d1 = 0, K p2 = 80, K d2 = 0, K p3 = 88, K d3 = 0, b0 = 89, b1 = -4, b2 = 0.5. After 15.65 time steps, the disturbance is compensated and the controlled pressure value reaches the value before the disturbance.

[0116] As Figure 6 shown, the pressure along the ramjet engine has a total of 5 step jumps. Starting from the simulation step of 20, a pressure step occurs every 50 simulation steps. In order to track 5 consecutive pressure command changes, active disturbance rejection control is performed, and a better parameter combination 2 is obtained: r = 500, ω0 = 11.5, ω1 = 8, ω2 = 10, K p1 = 150, K d1 = 0, Kp2 = 300, K d2 = 0, K p3 = 220, K d3 = 0, b0 = 89, b1 = -10, b2 = 0.5. The controller starts to act when the simulation step size is 20, and within no more than 15 simulation step times, the controlled pressure value reaches the target pressure value 5 times.

[0117] In summary, the active disturbance rejection control design of the ramjet engine based on the seagull optimization algorithm can effectively compensate for the disturbances generated by internal and external factors of the system, and at the same time can effectively eliminate the disturbance influence brought by changing the pressure command, realizing real-time control during the pressure step change.

Claims

1. A self-disturbance rejection control design method for a ramjet engine based on the seagull optimization algorithm, characterized in that, The steps are as follows: S1: Based on the control objective of having more controlled variables than controlling variables, implement m control variables to control n groups of controlled variables, where m < n. Select m groups of along - path pressures from the n groups of controlled pressures as the most effective pressure - controlled variables, and determine the controlled variables by combining the method of random forest variable selection; S1.1 According to the control requirements of the ramjet engine, run the engine model to obtain the output pressure data. The controlled variable is P = [p1, … p i , … p n T That is, the class variable, and the control variable is U = [u1, … u i , … u n T , u i and p i are variables in the same loop; Take the pressure data output by the engine model as the original training set D. Each data contains M features, K is the number of samples, and j is the number of classification trees;​​ S1.2 Extract the training subset. Randomly select K samples from the original training set D with replacement and repeat K times as the training subset; the part of the original training set D except for the sampled training subset is used as the out - of - bag data set, denoted by OOB; S1.3 Build a classification tree. First, randomly select l features from M features to form a feature subset. Select a split point according to the sample features, divide the split point into child nodes, and at the same time divide the training subset into the corresponding nodes. Repeat the hierarchical division layer by layer until all nodes are obtained. Loop through the above process until j classification trees are established to form a random forest t, where t ∈ {t i , i = 1, 2, …, j}; S1.4 Statistically calculate the importance w of variables at non - zero child nodes, loop to calculate the importance of all variables, take its mean as the final judgment basis, arrange the importance of variables, and select the most important 3 groups of variables; S1.5 Evaluate the results obtained from the classification tree and calculate the correlation coefficient R 2 to verify the effectiveness; S2: According to the basic principle of active disturbance rejection, build three parts of the ADRC controller: the tracking differentiator TD, the extended state observer ESO, and the non - linear state error feedback NLSEF. And improve the non - linear function fal, construct a new extended state observer ESO and non - linear state error feedback NLSEF; S2.1 Design the tracking differentiator TD Given that the non - linear TD is more efficient than the linear TD and this control system is a discrete system, so introduce the fastest discrete function: In the formula: fhan is the function symbol; fh is the output value of the fhan function; k is the k - th step of the discrete simulation; v1(k) is the discrete signal to be tracked; v2(k) is the derivative of the discrete signal to be tracked; h is the simulation step size; u is the control target; h0 is the filtering factor; The calculation of fhan(v1(k)-u(t),v2(k),r,h0) is as follows: In the formula: r is the parameter to be adjusted, fsg(v,d)=(sign(v + d)-sign(v - d)) / 2, sign() is the sign function; d, a, a0, a1, a2, y are intermediate process variables in the function calculation and have no actual physical meaning; S2.2 Design the extended state observer ESO Establish a second - order extended state observer in the following form for each of the three - direction channels: where: e is the error term, and by selecting appropriate parameters β 01 , β 02 , β 03 , such that the ESO constructed by the above equation can estimate the state of the object and the expanded state in real time. Here, the bandwidth tuning method is used to determine the parameter configuration, that is, β 01 = 3ω, β 02 = 3ω 2 , β 03 = ω 3 , where ω is the bandwidth of the extended state observer, which needs to be set according to requirements and is also a parameter that needs to be adjusted; g i (e), i = 1, 2 are appropriate nonlinear functions that satisfy e·g i (e) ≥ 0, fal(e, α i , δ), take In the formula: α is a constant between 0 and 1, δ is the length of the linear segment interval; S2.3 Improve the fal function in the extended state observer Design a new non - linear function newfal to replace the above - mentioned traditional non - linear function fal. For the sake of distinction, in the following formula, x is the error and e is the natural base; The improved second - order extended state observer is as follows, b is the compensation factor; S2.4 Non - linear state error feedback design; Take the difference between the output of the tracking differentiator and the output of the extended state observer and perform non - linear combination, and compensate the total disturbance estimated by the extended state observer in real - time to obtain the control quantity of the system, which is specifically expressed as follows: u0 = K p newfal(x1, α1) + K d newfal(x2, α2) where: u0 is the output of the nonlinear state feedback module, K p , K d are the control quantity gains respectively. According to the basic principle of active disturbance rejection control, the system control rate after compensating for internal and external disturbances is obtained as shown in the following formula, where u is the control quantity; S3: Design an improved seagull optimization algorithm to autonomously optimize the main parameters of the active disturbance rejection controller. Specifically, propose a heuristic population evolution strategy based on the concepts of attraction and repulsion; the improved seagull optimization algorithm is as follows: S3.1 Seagull population P s Initialize, with the maximum number of iterations being M_max, and initialize the additional variables A and B; S3.2 Calculate the fitness value of the initial population and mark the optimal individual. The fitness function fitness is calculated as follows: where: t p is time, and e(t p ) is the above control error, that is, the fitness function is the integral of the product of time and the absolute value of the error; S3.3 Update the seagull positions according to the migration and attack operations. To avoid collisions with other seagulls, update the positions. The position update formula is as follows: C s C(t) = A × P s C(x), Where: C s (t) represents a new position that does not conflict with the positions of other seagulls, and P s (x) represents the current position of the seagull; S3.4 Calculate the fitness values of the new population and update the optimal individual. After avoiding overlapping positions with other seagulls, the seagulls will move in the direction of the best position. The best position direction update formula is as follows: M s (t) = B×(P best (x) - P s (x)) Where: M s (t) represents the convergence direction of an individual to the best seagull, and P best (x) represents the optimal position; When the seagull approaches the best position: After the seagull moves to a position where it does not collide with other seagulls, it moves in the direction of the best position and reaches a new position; The position update formula is: H s (t) = |C s (t) + M s (t)| where: H s (t) is the new position of the seagull; S3.5 Improve the search method of the above seagull optimization algorithm, and propose a heuristic population evolution strategy based on the concepts of attraction and repulsion. The improved position update formula is as follows: Wherein: represents the updated position, represents the jth H individual's position component in the ith H dimension, H b,iH represents the globally optimal individual, represents the globally worst individual, and both r1 and r2 are random numbers uniformly distributed within the range of [0, 1]; in the above formula represents the attracting effect of the optimal individual, represents the repulsive effect of the worst individual; S3.6 Attack phase: During migration, seagulls continuously change the attack speed and angle with their wings. When attacking prey, they perform spiral-shaped movements in the air. The movement behavior of seagulls in a three-dimensional plane is described as follows: x H = r H × cos(k H ) y H = r H × sin(k H ) z H = r H × k H where: r H is the radius of each spiral motion of the seagull, k H is a random angle value within 0 to 2π, u H and v H are related constants of the spiral shape used to control the spiral radius, usually taken as 1, and e is the base of the natural logarithm; S3.7 Update the attack positions of the seagulls. Combining the new positions of the seagulls, the overall seagull position update formula is obtained as follows: P s (t) = (H s × x H × y H × z H ) + P best (t) Where: P s (t) is the attacking position of the seagull; S3.8 Determine whether the termination condition is satisfied. If so, stop the iteration and output the optimal parameter values; otherwise, jump to S3.3 to continue the iteration; S3.9 According to the optimal parameter values obtained in S3.8, pass them to the active disturbance rejection controller; S4: Verify the superiority of the improved active disturbance rejection controller. Build a Simulink model in Matlab for simulation experiments.

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