A Fuzzy Neural Network-Based PID Liquid Level Control Method Based on an Improved Dung Beetle Algorithm

Abstract

This invention discloses a fuzzy neural network PID liquid level control method based on an improved dung beetle algorithm, belonging to the field of automatic control technology. It solves the technical problem of insufficient ergodicity in common chaotic mappings. The technical solution includes the following steps: S1, establishing a mathematical model of the ozone dissolving tank liquid level control system; S2, designing the improved dung beetle algorithm; S3, designing a fuzzy neural network PID controller; S4, simulation experiments and performance verification of the ozone dissolving tank liquid level control system. The beneficial effects of this invention are: In the dung beetle algorithm, this invention adopts a population initialization strategy combining ICMIC chaotic mapping and back-learning, significantly improving the uniformity of the initial solution and the global ergodicity capability; ICMIC mapping has infinitely folded chaotic characteristics, which can solve the problem of insufficient ergodicity in common chaotic mappings, while the back-learning strategy further expands the search space, making the population distribution more diversified.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and in particular to a fuzzy neural network PID liquid level control method based on an improved dung beetle algorithm. Background Technology

[0002] Ozone dissolution tank level control is a crucial technical aspect in semiconductor cleaning, as the stability of the liquid level directly affects ozone dissolution efficiency and cleaning effectiveness. However, liquid level control systems generally suffer from nonlinearity, dynamic lag, and insufficient disturbance rejection capabilities, making traditional PID control inadequate for practical applications.

[0003] In existing methods, fuzzy PID and fuzzy neural network PID have been used for nonlinear system control. However, fuzzy PID relies on manually set rules, making it difficult to adapt to complex operating conditions. While fuzzy neural networks can achieve online adjustment, they lack effective parameter optimization algorithms, resulting in insufficient control accuracy. To address these issues, intelligent optimization algorithms have been gradually introduced in recent years. However, traditional optimization algorithms such as particle swarm optimization (PSO) are prone to getting trapped in local optima in high-dimensional searches, limiting their application in liquid level control.

[0004] To address this, a fuzzy neural network PID level control method based on an improved dung beetle algorithm was developed, aiming to improve dynamic response speed, control accuracy, and anti-disturbance capability, and to provide a stable and efficient level regulation solution for complex working conditions such as ozone dissolution tanks. Summary of the Invention

[0005] To address the issues of strong nonlinearity, dynamic lag, and insufficient disturbance rejection capability in the liquid level control system of ozone dissolving tanks, this invention proposes a fuzzy neural network PID liquid level control method based on an improved dung beetle algorithm. By improving the optimization algorithm and adjusting online parameters, the dynamic response speed and steady-state accuracy of the liquid level control are enhanced, meeting the requirements for liquid level stability under complex operating conditions.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] The fuzzy neural network PID liquid level control method based on the improved dung beetle algorithm includes the following steps:

[0008] S1. Establishment of System Mathematical Model

[0009] The operation of an ozone dissolving tank involves a complex physicochemical reaction process. Its liquid level control is influenced by environmental conditions and the dynamic characteristics of the equipment, exhibiting nonlinearity and dynamic hysteresis, which poses a significant challenge to the modeling of the control system. To achieve precise control of the ozone dissolving tank liquid level, this paper models the liquid level control system based on the principle of mass conservation and simplifies it into a first-order inertial hysteresis model based on the actual operating characteristics of the system.

[0010] According to the law of conservation of mass, the dynamic rate of change of the liquid level in the tank can be expressed as the difference between the inflow rate and the outflow rate, that is:

[0011]

[0012] In the formula, A is the cross-sectional area of ​​the tank, h is the height of the liquid level at any time, and Fi and Fo are the inflow and outflow rates, respectively.

[0013] Drawing an analogy between a liquid level system and an electrical system, the cross-sectional area A of the tank can be replaced by a capacitor C, thus:

[0014]

[0015] The resistance R can be written as:

[0016]

[0017] The inflow rate Fi is directly proportional to the rotational speed N of the magnetic levitation pump, which can be expressed as:

[0018] F i =kN

[0019] Meanwhile, it is assumed that the rotational speed N of the magnetic levitation pump is controlled by the control signal U, that is:

[0020] N=K m U

[0021] Therefore, we can conclude that:

[0022]

[0023] After performing a Laplace transform and rearranging, we get:

[0024]

[0025] Finally, the control signal U is obtained. (s) With liquid level height H (s) Transfer function between:

[0026]

[0027] In the process of level control in an ozone dissolution tank, there is a certain response delay due to changes in level caused by liquid flow. Changes in the inflow rate require a delay time τ to have a significant impact on the liquid level in the tank. Its transfer function is expressed as:

[0028]

[0029] Where k is the system gain, K mLet be the motor gain, τ be the lag time constant, R be the flow resistance, and C be the equivalent capacitance. Based on experimental measurements, k = 6.35 × 10⁻⁶. -5 ,K m =600, R=60, C=2.59, τ=-7, substituting the parameters, we get:

[0030]

[0031] S2. Improved Dung Beetle Algorithm (IDBO) Design

[0032] To improve the optimization accuracy and global search capability of the Dung Beetle Algorithm (DBO) in parameter optimization of complex liquid level control systems, this paper proposes an improved DBO algorithm (IDBO) based on ICMIC chaotic initialization, a back-learning strategy, and a nonlinear dynamic adjustment mechanism. The specific improved design is as follows:

[0033] (1) Introduce ICMIC chaotic initialization and reverse learning strategy

[0034] In the population initialization process of the Dung Beetle Algorithm (DBO), traditional methods typically generate initial population solutions randomly. However, randomly generated initial solutions may lead to uneven population distribution, limiting the algorithm's global search capability and affecting subsequent optimization accuracy and convergence speed. To address this issue, this paper proposes an improved method based on ICMIC chaotic mapping and a reverse learning strategy to enhance the diversity and coverage of the population initialization phase.

[0035] First, the ICMIC chaotic map is used to generate the initial population solution. As an infinitely folding chaotic map, the ICMIC map has higher global ergodicity and stronger chaotic properties. Compared to the common Tent and Logistic maps, it can more evenly cover the search space, avoiding the problem of the initial population being too concentrated or unevenly distributed. The mathematical expression of the ICMIC chaotic map is:

[0036]

[0037] In the formula, Z n It is the chaotic variable of the current population, α is the chaotic control parameter, and its value range is (0, 1).

[0038] Secondly, based on the population solutions generated by ICMIC, a reverse learning strategy is introduced to further expand the search space. The reverse learning strategy increases population diversity by generating a reverse solution for each initial solution, thereby improving global search capability. The mathematical expression of the reverse learning strategy is:

[0039] OZ i =K×(Z) max +Zmin )-Z i

[0040] In the formula, OZ i It corresponds to each initial solution Z i The inverse solution of Z. max and Z min These represent the maximum and minimum values ​​in the initial solution, respectively; K is a random value within the range (0,1).

[0041] (2) Introduce ICMIC chaotic initialization and reverse learning strategy

[0042] In the Dung Beetle Algorithm (DBO), the parameter R is a crucial dynamic adjustment factor determining the search range of the population, directly impacting the balance between global search and local exploitation. Traditional DBO algorithms typically employ a linear decreasing strategy to update the parameter R, calculated using the following formula:

[0043]

[0044] Where t represents the current iteration number and T is the maximum iteration number.

[0045] While the linear decreasing strategy can maintain a large search range in the early stages and promote global search, the rapid decrease of R in the later stages may lead to an excessively rapid contraction of the search range, limiting the optimization accuracy and convergence performance of the algorithm, thus causing the population to get trapped in local optima. To further improve the optimization capability of the algorithm, this paper draws on the idea of ​​dynamic weight adjustment mechanism and makes a nonlinear improvement to the calculation of parameter R, so that it can adapt to the search requirements of different optimization stages.

[0046] The improved nonlinear dynamic adjustment mechanism calculates the parameter R using the following formula:

[0047]

[0048] In this formula, the nonlinear dynamic adjustment mechanism introduces a logarithmic function and a nonlinear variation term to keep the parameter R at a large value in the early stage to enhance the global search capability, while gradually decreasing R in the later stage of iteration to improve the accuracy of local development, thereby achieving a dynamic balance between global search and local development.

[0049] Compared to the traditional linear decreasing strategy, the nonlinear dynamic adjustment mechanism further reduces the risk of local optima and makes the search range more adaptable to the optimization needs at different stages by dynamically adjusting the weight factor R. Experimental results show that this mechanism can significantly improve the global search capability and optimization efficiency of the DBO algorithm, and effectively improve the convergence performance and robustness of the algorithm in high-dimensional complex problems.

[0050] S3. Fuzzy Neural Network PID Controller Design To address the problems of nonlinearity, dynamic lag, and insufficient disturbance rejection in the ozone dissolution tank level control system, this paper designs a fuzzy neural network PID controller based on the improved dung beetle algorithm (IDBO). The controller mainly consists of three parts: an IDBO algorithm module, a fuzzy neural network module, and a PID controller module.

[0051] (1) Controller Design

[0052] First, the proportional factor CK of the PID controller is adjusted using the IDBO algorithm. p CK i CK d Global optimization was performed, and the initial parameter K was determined by combining the ZN tuning method and actual debugging results. p0 K i0 K d0 The optimal initial parameters are obtained. Then, the fuzzy neural network dynamically adjusts the PID parameter increment ΔK based on the liquid level error e and its rate of change ec. p ΔK i ΔK d Finally, the PID controller generates a control signal u(t) based on the real-time adjusted parameters, which drives the magnetic levitation pump to regulate the water supply flow rate, thereby achieving stable control of the liquid level.

[0053] (2) Fuzzy control reasoning

[0054] This paper designs fuzzy control rules based on the liquid level error e and the error change rate ec, totaling 49 rules, for dynamically adjusting the PID control parameter ΔK. p ΔK i ΔK d The input and output variables are represented by seven fuzzy subsets: {NB, NM, NS, ZO, PS, PM, PB}.

[0055] (3) Fuzzy Neural Network

[0056] The topology of a fuzzy neural network includes an input layer, a fuzzification layer, a fuzzy inference layer, a normalization layer, and an output layer. In a fuzzy neural network PID controller, the input signals e and ec are processed sequentially through each layer, and finally, the three adjustable parameters ΔK of the PID controller are generated at the output layer. p ΔK i ΔK d .

[0057] The first layer is the input layer, with two nodes: error and error rate of change. Its function is to process the input vector x. i = [x1, x2] T Each component is transmitted to the next layer. The input and output are:

[0058]

[0059] In the formula, For the input values ​​of the first-level nodes, This is the output value of the first-level node.

[0060] The second layer is the fuzzification layer, containing two inputs, each corresponding to one of the seven linguistic variable values. Its function is to calculate the membership function of each component of the input vector to the fuzzy set of each linguistic variable value and map it to the fuzzy subset. The input and output are:

[0061]

[0062] In the formula, This is the input value for the second-level node. c is the output value of the second-level node. ij σ is the center value of the membership function; ij b is the width of the function curve. ij For shape parameters.

[0063] The third layer is the fuzzy inference layer. Each node in this layer represents a fuzzy rule from the fuzzy rule base. Its function is to calculate the fitness of each fuzzy rule. The input and output are:

[0064]

[0065] In the formula, l = 1, 2, ..., 49; i1 = i2 = 1, 2, ..., 7; This is the input value for the 3rd layer node; This is the output value of the third-layer node. The fourth layer is the normalization layer, with the same number of nodes as the third layer. Its function is to perform normalization operations on the output of the fuzzy inference layer. The input and output are:

[0066]

[0067] In the formula, This is the input value for the 4th layer node; This is the output value of the 4th layer node.

[0068] The fifth layer is the output layer, which performs a weighted summation of the deblurred output. Each node in this layer represents an output variable, and there are three nodes in total, ΔK. P ΔK I ΔK D The input and output are:

[0069]

[0070]

[0071] In the formula, k = 1, 2, 3; ω ij These are the weights for the output layer network; This is the input value for the 5th layer node; This is the output value of the 5th layer node.

[0072] (4) Parameter adaptive adjustment

[0073] The fuzzy neural network PID controller completes the calculation through forward propagation, and outputs ΔK. p ΔK i ΔK d These parameter changes are applied to the actuator via a PID controller, further adjusting the system output. By comparing the error with the target value y(t), if the error does not meet the target requirements, an adaptive parameter adjustment process is initiated. This process adjusts the central parameter C of the membership function in the fuzzy neural network using the error signal. ij Width parameter σ ij And the membership shape parameter w ij To reduce the error signal, the objective function for error correction is defined as:

[0074]

[0075] In the formula, r(t) represents the desired liquid level of the system, and y(t) represents the actual liquid level of the system.

[0076] To minimize the objective function E, the parameters of the fuzzing layer, including the center, width, and shape parameters of the membership function, are dynamically adjusted based on error feedback. The iterative update formulas for each parameter are as follows:

[0077]

[0078] In the formula, n is the iteration step size of the network; λ is the inertia coefficient, used to balance historical information and current updates; η is the learning rate, controlling the update speed of the parameters; Δc ij (n), Δσ ij (n), Δω ij (n) represents the change in each parameter, calculated based on the current error feedback.

[0079] S4. Simulation Experiment and Performance Verification of Liquid Level Control System

[0080] To verify the performance of the fuzzy neural network PID control method based on the improved dung beetle algorithm (IDBO-FNN-PID) in the ozone dissolving tank level control system, simulation experiments based on the MATLAB / Simulink platform were designed and carried out. The main components included: performance evaluation of the improved dung beetle algorithm (IDBO) using standard single-peak and multi-peak functions, focusing on testing its global optimization capability and convergence speed to verify its effectiveness as a controller parameter optimization tool; comparative analysis of the proposed algorithm with other control algorithms to evaluate the dynamic response performance of each method in the level control task, including response time, overshoot, and steady-state error; simulation of external disturbances such as water supply and drainage flow fluctuations and motor speed disturbances to test the recovery time and level stability of different control algorithms under disturbances, verifying the anti-disturbance capability of the proposed control method; and sinusoidal signal following experiments to test the response speed and following accuracy of each control algorithm in the dynamic input signal tracking task, evaluating its adaptability in complex dynamic conditions.

[0081] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0082] (1) In the traditional Dung Beetle Algorithm (DBO), this invention adopts a population initialization strategy that combines ICMIC chaotic mapping and back learning, which significantly improves the uniformity of the initial solution and the global traversal capability. ICMIC mapping has infinitely folded chaotic characteristics, which can solve the problem of insufficient traversal of common chaotic mappings. At the same time, the back learning strategy further expands the search space, making the population distribution more diversified, and laying a good foundation for subsequent optimization.

[0083] (2) This invention solves the problem that traditional linear decreasing strategies are prone to getting trapped in local optima in the later stages by performing nonlinear optimization on the key parameter R in the DBO algorithm. The improved dynamic adjustment mechanism maintains a large search range in the early stage to enhance the global search capability, while gradually reducing R in the later stage to improve the accuracy and efficiency of local development, thus achieving a dynamic balance between global search and local development.

[0084] (3) By combining a fuzzy neural network with a PID controller, this invention can dynamically adjust the controller parameters based on the liquid level error and the rate of change of the error. Especially under complex dynamic conditions, the improved PID controller effectively reduces steady-state error and overshoot, shortens response time, and its dynamic performance is far superior to traditional methods. Attached Figure Description

[0085] 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.

[0086] Figure 1 This is a structural diagram of the ozone dissolving tank system in this invention.

[0087] Figure 2 This is a structural diagram of the IDBO optimized fuzzy neural network PID controller in this invention.

[0088] Figure 3 This is a diagram of the topology of the fuzzy neural network in this invention.

[0089] Figure 4 This is a graph showing the convergence curve of the function iteration in this invention.

[0090] Figure 5 This is a comparative experimental diagram of the present invention. Detailed Implementation

[0091] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0092] Example 1

[0093] This invention provides a fuzzy neural network PID liquid level control method based on an improved dung beetle algorithm, comprising the following steps:

[0094] S1. Establishment of System Mathematical Model

[0095] The ozone dissolving tank level control system is a typical dynamic nonlinear system, whose level is influenced by the combined effects of influent flow rate, effluent flow rate, and the system's own dynamic characteristics. To achieve precise level control, this paper establishes a mathematical model of the system based on the principle of mass conservation and experimentally fits the system parameters to meet actual operating conditions. Considering the dynamic hysteresis characteristics of the tank level, a first-order inertial hysteresis model is used to model the system, resulting in the system's transfer function:

[0096]

[0097] S2. Improved Dung Beetle Algorithm (IDBO) Design

[0098] To improve the global optimization capability and convergence accuracy of the traditional Dung Beetle Algorithm (DBO) in liquid level control parameter optimization, this invention proposes an improved Dung Beetle Algorithm (IDBO) based on ICMIC chaotic mapping, a back learning strategy, and a nonlinear dynamic adjustment mechanism. The specific steps include:

[0099] (1) Population initialization based on ICMIC chaotic mapping and reverse learning

[0100] In the population initialization phase of the dung beetle algorithm, traditional methods typically generate the population solution randomly. However, this can lead to uneven initial population distribution, affecting the algorithm's global search capability. This invention proposes a population initialization method based on a combination of ICMIC chaotic mapping and reverse learning.

[0101] The ICMIC chaotic map is an infinitely folding chaotic map with good global traversal. Compared to traditional Logistic and Tent maps, it can cover the search space more uniformly. Its mathematical expression is as follows:

[0102]

[0103] In the formula, Z n is the chaotic variable of the current population, and α is the chaotic control parameter of the ICMIC mapping, with a value range of (0, 1). To further expand the population coverage, a reverse learning strategy is introduced to generate a reverse solution for each solution, which is used to supplement the diversity of the population. The formula for reverse learning is:

[0104] OZ i =K×(Z) max +Z min )-Z i

[0105] In the formula, OZ i It corresponds to each initial solution Z i The inverse solution of Z. max and Z min These represent the maximum and minimum values ​​in the initial solution, respectively; K is a random value within the range (0,1).

[0106] (2) Nonlinear dynamic adjustment of parameters

[0107] In the traditional DBO algorithm, the control parameter R is usually updated using a linear decreasing strategy, and its update formula is:

[0108]

[0109] In the formula, t represents the current iteration number, and T is the maximum iteration number.

[0110] To address the aforementioned issues, this paper draws upon the dynamic weight adjustment concept of the flood algorithm and performs nonlinear optimization on the calculation of parameter R. The weight parameter R is dynamically adjusted to adapt to the search requirements at different iteration stages, and its formula is as follows:

[0111]

[0112] Where T is the maximum number of iterations and t is the current number of iterations.

[0113] This method can maintain a large global search capability in the early stage and gradually enhance the local development accuracy in the later stage, thereby achieving a dynamic balance of the search range and avoiding the population from getting trapped in local optima.

[0114] S3, Fuzzy Neural Network PID Controller Design

[0115] To address the issues of nonlinearity, dynamic lag, and insufficient disturbance rejection in the level control system of ozone dissolution tanks, this paper designs a fuzzy neural network PID controller based on the improved dung beetle algorithm (IDBO). The controller mainly consists of three parts: an IDBO algorithm module, a fuzzy neural network module, and a PID controller module, as detailed below:

[0116] (1) Device architecture design

[0117] The overall architecture of the IDBO-optimized fuzzy neural network PID controller includes the following steps: First, the initial parameters of the PID controller are obtained through the ZN tuning method to meet the basic performance requirements of liquid level control; second, the initial parameters of the PID controller are globally optimized using the IDBO algorithm to obtain the optimal initial parameters; then, the fuzzy neural network dynamically adjusts the increment of the PID parameters according to the liquid level error and the error change rate, enabling the controller to adapt to complex dynamic operating conditions; finally, the PID controller generates a control signal U(t) based on the optimized and dynamically adjusted parameters, which is used to drive the magnetic levitation pump to regulate the water supply flow rate, thereby achieving precise control of the liquid level.

[0118] (2) Fuzzy control rule design

[0119] The fuzzy control section is designed based on the level error *e* and the error change rate *ec*. The fuzzy subsets of both input and output variables are defined as {NB, NM, NS, ZO, PS, PM, PB}, representing large negative, medium negative, small negative, zero, small positive, medium positive, and large positive, respectively. The level error represents the difference between the target level and the actual level, and the error change rate represents the trend of the level error. The output is the dynamic adjustment (i.e., increment) of the PID parameters, corresponding to ΔK. p ΔK i ΔK d The fuzzy rule base includes 49 control rules in the form of "IF-THEN" statements, such as "if e and ec then ΔK". p ΔK i andΔK d The rule base, derived from engineering experience and experimental debugging, describes the relationship between liquid level error and parameter adjustment.

[0120] (3) Fuzzy Neural Network Structure Design

[0121] Fuzzy neural networks are used in PID controllers to achieve online adjustment, and their topology includes the following five layers:

[0122] The first layer is the input layer, with two nodes: error and error rate of change. Its function is to process the input vector x. i = [x1, x2] T Each component is transmitted to the next layer. The input and output are:

[0123]

[0124]

[0125] In the formula, For the input values ​​of the first-level nodes, This is the output value of the first-level node.

[0126] The second layer is the fuzzification layer, containing two inputs, each corresponding to one of the seven linguistic variable values. Its function is to calculate the membership function of each component of the input vector to the fuzzy set of each linguistic variable value and map it to the fuzzy subset. The input and output are:

[0127]

[0128] In the formula, This is the input value for the second-level node. c is the output value of the second-level node. ij σ is the center value of the membership function; ij b is the width of the function curve. ij For shape parameters.

[0129] The third layer is the fuzzy inference layer. Each node in this layer represents a fuzzy rule from the fuzzy rule base. Its function is to calculate the fitness of each fuzzy rule. The input and output are:

[0130]

[0131] In the formula, l = 1, 2, ..., 49; i1 = i2 = 1, 2, ..., 7; This is the input value for the 3rd layer node; This is the output value of the third-layer node. The fourth layer is the normalization layer, with the same number of nodes as the third layer. Its function is to perform normalization operations on the output of the fuzzy inference layer. The input and output are:

[0132]

[0133] In the formula, This is the input value for the 4th layer node; This is the output value of the 4th layer node.

[0134] The fifth layer is the output layer, which performs a weighted summation of the deblurred output. Each node in this layer represents an output variable, and there are three nodes in total, ΔK. P ΔK I ΔK D The input and output are:

[0135]

[0136] In the formula, k = 1, 2, 3; ω ij These are the weights for the output layer network; This is the input value for the 5th layer node; This is the output value of the 5th layer node.

[0137] (4) Parameter adaptive adjustment

[0138] To further improve the controller's adaptability under complex dynamic conditions, this paper designs a parameter adaptive adjustment mechanism based on error feedback. The specific method is as follows:

[0139] The membership function parameters of the fuzzy neural network are adjusted through error feedback to minimize the liquid level error. The objective function is defined as follows:

[0140]

[0141] In the formula, r(t) represents the desired liquid level of the system, and y(t) represents the actual liquid level of the system.

[0142] The parameters of the fuzzy neural network, including the center parameter C of the membership function, are updated using gradient descent. ij Width parameter σ ij and shape parameter w ij :

[0143]

[0144] In the formula, n is the iteration step size of the network; λ is the inertia coefficient, used to balance historical information and current updates; η is the learning rate, controlling the update speed of the parameters; Δc ij (n), Δσ ij (n), Δω ij (n) represents the change in each parameter, calculated based on the current error feedback.

[0145] S4. Simulation Experiment and Performance Verification of Liquid Level Control System

[0146] To verify the performance of the proposed fuzzy neural network PID control method (IDBO-FNN-PID) based on an improved dung beetle algorithm in the ozone dissolution tank level control system, a series of simulation experiments based on the MATLAB / Simulink platform were designed and conducted. The experiments included algorithm performance testing, dynamic response testing, disturbance rejection capability testing, and dynamic tracking capability testing.

[0147] (1) Performance testing of the improved Dung Beetle Algorithm (IDBO)

[0148] The improved IDBO algorithm was evaluated using standard test functions, with unimodal and multimodal functions selected as benchmarks. Each algorithm was run independently 50 times, with a population size of 30 and a maximum number of iterations of 500. Experimental results show that IDBO exhibits stronger global search capability and optimization accuracy in the unimodal test function, and higher local optimization capability and consistency in the multimodal test function. Furthermore, the IDBO algorithm converges significantly faster than other algorithms, quickly approaching the theoretical optimum in the initial stage while maintaining the smoothness of the convergence curve, demonstrating the ability to escape local optima and higher optimization stability.

[0149] (2) Step response experiment

[0150] This experiment simulates the liquid level control process using a step response and compares the dynamic response performance of four control algorithms. A step signal is used as input to test the overshoot, settling time, and system response speed of each algorithm. The algorithm of this invention (IDBO-FNN-PID) demonstrates superior dynamic performance, with an overshoot of only 2% and a system response time of 35 seconds. In comparison, the overshoots of traditional PID, fuzzy PID, and fuzzy neural network PID are 17.6%, 12.6%, and 7.7%, respectively, and the settling times are 79 seconds, 70 seconds, and 58 seconds, respectively. Compared with other methods, IDBO-FNN-PID reduces the overshoot by 15.6%, 10.6%, and 5.7%, respectively, and shortens the settling time by 55.7%, 50.0%, and 39.7%, respectively. Experimental results show that the algorithm of this invention exhibits significant advantages in response speed and overshoot suppression, and can improve the efficiency and stability of the liquid level control process in the ozone dissolution tank system.

[0151] (3) Anti-interference capability test

[0152] To verify the system's stability under external disturbances, a disturbance signal with an amplitude of 0.2 was applied after 100 seconds of system operation, lasting for 7 seconds, simulating the impact of flow fluctuations on liquid level control under actual operating conditions. The experiment compared the dynamic response performance of four control algorithms under the disturbance signal.

[0153] The results show that all four control algorithms exhibited varying degrees of overshoot under disturbance signals, but the proposed method (IDBO-FNN-PID) demonstrated the best disturbance rejection capability. The overshoot after disturbance was only 0.6%, which was 83.3%, 81.8%, and 62.5% lower than that of traditional PID, fuzzy PID, and fuzzy neural network PID, respectively. The settling time was 31 seconds, which was 18.4%, 13.9%, and 8.8% shorter than the 38, 36, and 34 seconds of other control methods, respectively. The IDBO-FNN-PID control method can restore the system to a stable state in a shorter time with minimal level fluctuations, further demonstrating its excellent stability and rapid response capability.

[0154] (4) Dynamic signal tracking experiment

[0155] To verify the signal dynamic tracking performance of this method, a sinusoidal signal tracking experiment was designed. The experiment compared the dynamic response performance of four control algorithms in the sinusoidal signal tracking task. Traditional PID showed significant lag and large fluctuations in the output during sinusoidal signal changes, resulting in weak tracking ability. Fuzzy PID improved tracking performance through fuzzy rules, but lag still existed during rapid signal changes. Fuzzy neural network PID further improved the system's response capability and reduced phase lag, but slight tracking errors remained at high frequencies. Our proposed method (IDBO-FNN-PID) exhibited the best tracking performance, significantly reducing phase lag and tracking error, and the output trajectory closely matched the target sinusoidal signal. Experimental results show that IDBO-FNN-PID can quickly and accurately track dynamic input signals, with a smooth and stable output waveform, demonstrating excellent real-time response capability and tracking accuracy, providing a reliable solution for complex dynamic signal control tasks.

[0156] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A fuzzy neural network PID liquid level control method based on an improved dung beetle algorithm, characterized in that, Includes the following steps: S1. Mathematical Model Establishment of Ozone Dissolution Tank Level Control System To achieve control of the liquid level in the ozone dissolving tank, the liquid level control system of the ozone dissolving tank is modeled based on the principle of mass conservation, and simplified into a first-order inertial lag model in combination with the actual operating characteristics of the liquid level control system of the ozone dissolving tank. S2. Improved Dung Beetle Algorithm Design To improve the optimization accuracy and global search capability of the traditional dung beetle algorithm in the parameter optimization of complex liquid level control systems, an improved dung beetle algorithm based on ICMIC chaotic initialization, reverse learning strategy and nonlinear dynamic adjustment mechanism was designed. In step S2, the specific design improvements are as follows: (1) Introduce ICMIC chaotic initialization and reverse learning strategy An improved method based on ICMIC chaotic mapping and reverse learning strategy is proposed to enhance the diversity and coverage of the population initialization stage. First, the initial population solution is generated using the ICMIC chaotic mapping; the mathematical expression for the ICMIC chaotic mapping is: In the formula, Z n Z is the chaotic variable of the current population. n+1 It is the chaotic variable obtained from the next iteration calculation, α is the chaotic control parameter, and its value range is (0, 1); Secondly, based on the population solutions generated by ICMIC, a reverse learning strategy is introduced to further expand the search space. The reverse learning strategy increases population diversity by generating a reverse solution for each initial solution, thereby improving the global search capability. The mathematical expression of the reverse learning strategy is: OZ i =K×(Z max +Z min )-Z i In the formula, OZ i It corresponds to each initial solution Z i The inverse solution of Z; max and Z min These represent the maximum and minimum values ​​in the initial solution, respectively; K is a random value within the range (0,1). (2) Introduce ICMIC chaotic initialization and reverse learning strategy The improved nonlinear dynamic adjustment mechanism calculates the parameter R using the following formula: Among them, the nonlinear dynamic adjustment mechanism introduces a logarithmic function and a nonlinear change term to keep the parameter R at a large value in the early stage to enhance the global search capability, while gradually reducing R in the later stage of iteration to improve the accuracy of local development, thereby achieving a dynamic balance between global search and local development. S3, Fuzzy Neural Network PID Controller Design To address the issues of nonlinearity, dynamic lag, and insufficient anti-disturbance capability in the ozone dissolution tank level control system, a fuzzy neural network PID controller based on the improved dung beetle algorithm was designed. S4. Simulation Experiment and Performance Verification of Ozone Dissolution Tank Level Control System To verify the performance of the improved dung beetle algorithm in the ozone dissolution tank level control system, a simulation experiment based on the MATLAB / Simulink platform was designed and carried out.

2. The fuzzy neural network PID liquid level control method based on the improved dung beetle algorithm according to claim 1, characterized in that: In step S1, according to the law of conservation of mass, the dynamic rate of change of the liquid level in the tank can be expressed as the difference between the inflow rate and the outflow rate, that is: In the formula, A is the cross-sectional area of ​​the tank, h is the height of the liquid level at any time, Fi and Fo are the inflow and outflow rates, respectively, and d is the differential symbol; Drawing an analogy between a liquid level system and an electrical system, we can replace the cross-sectional area A of the tank with a capacitor C, and thus: The resistance R can be written as: The inflow rate Fi is directly proportional to the rotational speed N of the magnetic levitation pump, expressed as: F i =kN Meanwhile, it is assumed that the rotational speed N of the magnetic levitation pump is controlled by the control signal U, that is: N=K m U Therefore, we can conclude that: After performing a Laplace transform and rearranging, we get: Finally, the control signal U is obtained. (s) With liquid level height H (s) Transfer function between: In the process of level control in an ozone dissolution tank, there is a response delay due to changes in level caused by liquid flow. Changes in the inflow rate require a delay time τ to have a significant impact on the liquid level in the tank. Its transfer function is expressed as: Where k is the system gain, K m Let be the motor gain, τ be the lag time constant, R be the flow resistance, and C be the equivalent capacitance. Based on experimental measurements, k = 6.35 × 10⁻⁶. -5 ,K m =600, R=60, C=2.59, τ=-7, substituting the parameters, we get:

3. The fuzzy neural network PID liquid level control method based on the improved dung beetle algorithm according to claim 1, characterized in that: In step S3, the fuzzy neural network PID controller based on the improved dung beetle algorithm comprises three parts: an IDBO algorithm module, a fuzzy neural network module, and a PID controller module. (1) Controller Design First, the improved dung beetle algorithm is used to adjust the proportional factor CK of the PID controller. p CK i CK d Global optimization was performed, and the initial parameter K was determined by combining the ZN tuning method and actual debugging results. p0 K i0 K d0 To obtain the optimal initial parameters; Then, the fuzzy neural network dynamically adjusts the PID parameter increment ΔK based on the liquid level error e and its rate of change ec. p ΔK i ΔK d ; Finally, the PID controller generates a control signal u(t) based on the real-time adjusted parameters, which drives the magnetic levitation pump to adjust the water supply flow rate, thereby achieving stable control of the liquid level. (2) Fuzzy control reasoning A fuzzy control rule based on the liquid level error e and the error change rate ec was designed, consisting of 49 rules, to dynamically adjust the PID control parameter ΔK. p ΔK i ΔK d The input and output variables adopt 7 fuzzy subsets {NB, NM, NS, ZO, PS, PM, PB}. (3) Fuzzy Neural Network The topology of a fuzzy neural network includes an input layer, a fuzzification layer, a fuzzy inference layer, a normalization layer, and an output layer. In a fuzzy neural network PID controller, the input signals e and ec are processed sequentially through each layer, and finally, the three adjustable parameters ΔK of the PID controller are generated at the output layer. p ΔK i ΔK d ; The first layer is the input layer, with two nodes: error and error rate of change. Its function is to process the input vector x. i = [x1, x2] T Each component is transmitted to the next layer; the input and output are: In the formula, For the input values ​​of the first-level nodes, This is the output value of the first-level node; The second layer is the fuzzification layer, containing two inputs, each corresponding to seven linguistic variable values. Its function is to calculate the membership function of each component of the input vector belonging to the fuzzy set of each linguistic variable value, and map it to a fuzzy subset. The input and output are: In the formula, This is the input value for the second-level node. c is the output value of the second-level node. ij σ is the center value of the membership function; ij b is the width of the function curve. ij For shape parameters; The third layer is the fuzzy inference layer. Each node in the fuzzy inference layer represents a fuzzy rule in the fuzzy rule base; its function is to calculate the fitness of each fuzzy rule; the input and output are: In the formula, l = 1, 2, ..., 49; i1 = i2 = 1, 2, ..., 7; This is the input value for the 3rd layer node; This is the output value of the 3rd layer node; The fourth layer is the normalization layer. It has the same number of nodes as the third layer and its function is to perform normalization operations on the output of the fuzzy inference layer. The input and output are: In the formula, This is the input value for the 4th layer node; This is the output value of the 4th layer node; The fifth layer is the output layer, which performs a weighted summation of the deblurred output. Each node in the output layer represents an output variable, and there are three nodes in total, namely ΔK. P ΔK I ΔK D Input and output are: In the formula, k = 1, 2, 3; ω ij These are the weights for the output layer network. This is the input value for the 5th layer node; This is the output value of the 5th layer node; (4) Parameter adaptive adjustment The fuzzy neural network PID controller completes the calculation through forward propagation, and outputs ΔK. p ΔK i ΔK d The parameter changes are applied to the actuator through the PID controller, further adjusting the system output. By comparing the error with the target value y(t), if the error does not meet the target requirements, the system enters a parameter adaptive adjustment process. This process adjusts the central parameter C of the membership function in the fuzzy neural network using the error signal. ij Width parameter σ ij And the membership shape parameter w ij To reduce the error signal, the objective function for error correction is defined as: In the formula, r(t) represents the desired liquid level of the system, and y(t) represents the actual liquid level of the system. To minimize the objective function E, the parameters of the fuzzing layer are dynamically adjusted based on error feedback, including the center, width, and shape parameters of the membership function; the iterative update formulas for each parameter are as follows: In the formula, n is the iteration step size of the network; λ is the inertia coefficient, used to balance historical information and current updates; η is the learning rate, controlling the update speed of the parameters; Δc ij (n), Δσ ij (n), Δω ij (n) represents the change in each parameter, calculated based on the current error feedback.

4. The fuzzy neural network PID liquid level control method based on the improved dung beetle algorithm according to claim 1, characterized in that: Step S4, the simulation experiment based on the MATLAB / Simulink platform, includes the following parts: The performance of the improved dung beetle algorithm was evaluated using standard unimodal and multimodal functions to test its global optimization capability and convergence speed, and to verify its effectiveness as a controller parameter optimization tool. The improved dung beetle algorithm was compared and analyzed with other control algorithms to evaluate the dynamic response performance of each method in liquid level control tasks, including response time, overshoot and steady-state error. Simulate external disturbances such as fluctuations in water supply and drainage flow and motor speed disturbances, test the recovery time and level stability of different control algorithms under disturbances, and verify the anti-disturbance capability of the fuzzy neural network PID ozone dissolution tank level control method based on the improved dung beetle algorithm. Through sinusoidal signal tracking experiments, the response speed and tracking accuracy of each control algorithm in dynamic input signal tracking tasks are tested, and their adaptability in complex dynamic working conditions is evaluated.

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