Fuzzy neural network PID (Proportion Integration Differentiation) pressure control method based on improved black-wing algorithm

Abstract

The invention provides a fuzzy neural network PID (Proportion Integration Differentiation) pressure control method based on an improved black wing plinary algorithm, and belongs to the technical field of engineering. The technical problems of strong nonlinearity, dynamic lag and insufficient anti-interference capability in an ozone dissolving tank pipeline pressure control system are solved. According to the technical scheme, the method comprises the following steps that S1, pressure modeling is conducted on a water outlet pipeline of an ozone water tank; s2, improving the design of a black-wing optimization algorithm IBKA; s3, designing a fuzzy neural network PID controller; and S4, performing simulation experiment and performance verification on the pressure control system. The method has the beneficial effects that the dynamic response speed and the steady-state precision of pressure control are improved by improving an optimization algorithm and adjusting online parameters, and the requirement for pressure stability under the complex working condition is met.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial process control, and particularly relates to a fuzzy neural network PID pressure control method based on an improved black-winged kite algorithm. Background Art

[0002] The pressure control of the ozone dissolution tank pipeline is a key link in the semiconductor cleaning process, and the stability of its pressure directly affects the supply continuity of ozone water and the cleaning effect. However, in actual production, due to the concurrent use of multiple water outlets, the pipeline pressure fluctuates. At the same time, the system generally has complex characteristics such as nonlinearity, time-variation, and coupling, making it difficult for traditional PID to balance the requirements of fast response and high precision in pressure control, and it is prone to problems such as large overshoot, long adjustment time, or large steady-state error.

[0003] In existing methods, fuzzy PID and fuzzy neural network PID have been used for nonlinear system control, but there are still limitations. Fuzzy PID relies on manual rule setting and is difficult to adapt to complex working conditions; although fuzzy neural network PID can be adjusted online, it lacks effective parameter optimization support, resulting in limited control accuracy. To solve these problems, intelligent optimization algorithms have been gradually introduced. However, traditional optimization algorithms are prone to falling into local optima during high-dimensional search, and there are technical problems of premature convergence and insufficient convergence speed, which limit their application effects in pressure control. Summary of the Invention

[0004] Aiming at the technical problems of strong nonlinearity, dynamic lag, and insufficient anti-interference ability in the ozone dissolution tank pipeline pressure control system, the present invention proposes a fuzzy neural network PID pressure control method based on an improved black-winged kite algorithm. By improving the optimization algorithm and online parameter adjustment, the dynamic response speed and steady-state accuracy of pressure control are improved to meet the requirements of pressure stability under complex working conditions; by using an intelligent optimization algorithm to perform online adaptive parameter tuning on the fuzzy neural network PID controller, it can be applied to scenarios such as ozone water generation and pipeline transportation systems in semiconductor manufacturing that have high-precision and high-stability requirements for water supply pressure, aiming to improve the dynamic response speed, control accuracy, and anti-interference ability, and provide a stable and efficient pressure regulation scheme for the complex working conditions of the ozone dissolution tank pipeline.

[0005] To achieve the above invention purpose, the technical solution adopted by the present invention is specifically as follows: A fuzzy neural network PID pressure control method based on an improved black-winged kite algorithm, comprising the following steps:

[0006] S1. Modeling the pressure of the water outlet pipeline of the ozone water tank

[0007] Concurrent use of multiple water outlets will cause severe fluctuations in pipeline pressure, thus affecting the stability and continuity of the ozone water cleaning process; to achieve precise regulation of pipeline pressure, it is necessary to first study the dynamic characteristics of the water supply system and establish a reasonable mathematical model. The present invention mainly divides the system into the following three parts: the magnetic levitation pump speed control link, the pipeline pressure control link, and other control and detection links; finally, the transfer functions of each part are integrated through series-parallel relationships to obtain the overall system model.

[0008] The operating characteristics of the magnetic levitation pump can be expressed as a first-order inertia link, and its transfer function is:

[0009]

[0010] In the formula, G1(s) is the transfer function of the magnetic levitation pump speed control part; K1 is the gain of the magnetic levitation pump, indicating the influence of the input signal (regulation signal) on the output speed; T1 is the time constant, reflecting the dynamic response speed of the magnetic levitation pump.

[0011] The pressure control part of the pipeline is determined by the dynamic relationship between flow and pressure, and can be approximated as a first-order system with a lag characteristic, and its transfer function is:

[0012]

[0013] In the formula, G2(s) is the transfer function of the pipeline pressure control part; K2 is the pressure gain, indicating the influence of flow change on the pipeline pressure; T2 is the time constant of the pressure control system, reflecting the inertia of the system; τ is the time delay, indicating the delay characteristic of the pipeline pressure response to the change in pump flow.

[0014] In the control system, the conversion, gain adjustment, and signal preprocessing of signals can be approximated as a proportional link, and its transfer function is:

[0015] G3(s) = K3

[0016] In the formula, G3(s) is the transfer function of the signal detection and method link; K3 is the gain of the system detection and control link.

[0017] Combining the magnetic levitation pump speed control part, the pipeline pressure control part, and other detection links, the transfer function of the total system is:

[0018] G(s) = G1(s)·G2(s)·G3(s)

[0019] Substituting the transfer functions of each part, we get:

[0020]

[0021] After arrangement, we get:

[0022]

[0023] Where K = K1·K2·K3. According to the experimental measurements, T1 = 0.58, T2 = 10, τ = 6, and K = 24. Substituting the parameters, we get:

[0024]

[0025] S2. Design of Improved Black-winged Kite Optimization Algorithm (IBKA)

[0026] Aiming at the problems that the basic Black-winged Kite Algorithm (BKA) is prone to falling into local optimum and having a slow convergence speed in high-dimensional non-linear optimization, and considering that the ozone dissolution tank pipeline pressure control system faced by the present invention has characteristics such as strong non-linearity, coupling and time-variation, traditional optimization methods often have defects such as insufficient search, low optimization efficiency, and being unable to jump out of local extreme points when performing parameter optimization. Therefore, the present invention makes the following three improvements to BKA in key links such as population initialization, individual interaction and migration stages, forming the Improved Black-winged Kite Algorithm (IBKA). These improvements aim to enhance the algorithm's adaptive ability to non-linear complex environments, accelerate the global convergence speed and avoid premature convergence, so as to provide robust and efficient parameter optimization support for the subsequent fuzzy neural network PID.

[0027] (1) Reverse learning based on lens imaging

[0028] In high-dimensional parameter search, if the quality and diversity of the initial population are insufficient, it often causes the controller to "locate" in some remote areas from the very beginning during tuning, making it difficult to jump to a better area for search, resulting in the subsequent controller being unable to well suppress pressure overshoot or large-amplitude oscillation.

[0029] When initializing BKA, for the current individual, construct a "reverse solution" within its feasible domain; if the fitness of the reverse solution is better after being mapped by the lens, replace the original solution, otherwise retain the original solution, so as to improve the quality and diversity of the initial solution. The mathematical form of lens imaging can be expressed as:

[0030]

[0031] In the formula, x i is the current individual in the initial population, is the reverse solution space of x i , n is the adjustment factor, BK lb represents the lower bound of the solution, BK ub represents the upper bound of the solution, and f(·) is the fitness function.

[0032]

[0033] Wherein, t is the current iteration number, and T is the maximum iteration number.

[0034] This improvement can prevent the initial solutions from aggregating in a very small number of regions, and greatly improve the global optimization ability of the algorithm in the later stage. For the pipeline pressure, the more dispersed and high-quality the initial tuning parameters are, the more opportunities there are to quickly find a controller setting with a shorter response time and smaller overshoot, ultimately improving the pressure regulation effect.

[0035] (2) Horizontal and vertical crossover strategy

[0036] In the attack stage of the Black-winged Kite Algorithm (BKA), the black-winged kite will choose two modes, high-altitude dive or short-distance precise attack, according to factors such as wind speed, so as to achieve the balance between global exploration and local exploitation. However, if there is a lack of information exchange among individuals in the population, the algorithm may have insufficient search in the later iteration. This will lead to the controller parameters being trapped in local sub-optimality, manifested as insufficient regulation accuracy or anti-interference ability of the pressure. Therefore, the present invention adds a horizontal and vertical crossover strategy after the attack stage, and retains the superior individuals through the "parent-offspring" competition:

[0037] The formula for the horizontal crossover operation is as follows:

[0038] MS hc MS(i,n) = r1 × x(i,n) + (1 - r1) × x(j,n) + c1 × (x(i,n) - x(j,n))

[0039] MS hc MS(j,n) = r2 × x(j,n) + (1 - r2) × x(i,n) + c2 × (x(j,n) - x(i,n))

[0040] Wherein, MS hc MS(i,n) and MS hc MS(j,n) respectively represent the positions of the new individuals generated by the previous-generation black-winged kites i and j. x(i,n) and x(j,n) are the positions of the previous-generation black-winged kites in the nth dimension respectively; r1 and r2 are random numbers within [0,1], and c1 and c2 are random numbers within [-1,1].

[0041] The formula for the vertical crossover operation is as follows:

[0042] MS vc MS(i,n1) = r × x(i,n1) + (1 - r) × x(i,n2)

[0043] Wherein, MS vc MS(i,n1) represents the offspring individual obtained by vertically crossing the n1th and n2th dimensions of x(i), and r is a random number within [0,1].

[0044] When the pipeline pressure model has large - range fluctuations or complex non - linearities, later information interaction enables the algorithm to continuously discover new solutions and avoid being "trapped" by certain local parameter combinations. This is crucial for quickly suppressing pressure shocks and ensuring steady - state accuracy, and can continuously optimize the adjustment time and overshoot in the later stage, thereby obtaining better dynamic and steady - state performance.

[0045] (3) Levy flight

[0046] During the migration stage, although the black - winged kite algorithm introduces a dynamic leader - selection mechanism that enables the population to dynamically change leaders according to fitness and guides the population towards the optimal solution, there is a problem that all individuals blindly follow the optimal individual during the migration stage, which leads to a decrease in population diversity. Therefore, the present invention combines the Levy flight strategy, which helps the black - winged kite algorithm explore long - distance regions in space during the migration stage. This can enhance the global search ability of the black - winged kite optimization algorithm. When θ is close to 0, the tangent slope becomes smaller, that is, the step - size change becomes smaller, and the final solution approaches the current solution, which is suitable for local search. When θ is close to , the tangent slope becomes larger, that is, the step - size change becomes larger, and the final solution is far from the current solution, which is suitable for global search. The position update formula is:

[0047]

[0048]

[0049] In the formula, Levy(λ) is the Levy flight function, is the leading scorer (current optimal solution) of the j - th dimension of the black - winged kite at the t - th iteration of the current position, is the position of the i - th individual in the j - th dimension at the t - th iteration; The Levy flight probability density function and the formula for generating a random step - size are as follows:

[0050] Levy~u = t λ , 1≤λ≤3

[0051]

[0052] In the formula, that is, when updating, Levy(λ) is represented by S; when calculating, the parameter β takes the value of 1.5, The value of σ is:

[0053]

[0054] This improvement can prevent the initial solutions from gathering in a very small number of regions and greatly enhance the global nature of the algorithm's later - stage optimization. For pipeline pressure, the more dispersed and high - quality the initial tuning parameters are, the more opportunities there are to quickly find a controller setting with a shorter response time and smaller overshoot, ultimately improving the pressure regulation effect.

[0055] S3. Design of Fuzzy Neural Network PID Controller

[0056] To solve the problems of nonlinearity, dynamic lag, and insufficient anti-interference ability in the pipeline pressure control system of the ozone dissolution tank, the present invention designs a fuzzy neural network PID controller based on the improved black-winged kite algorithm (IBKA), which mainly includes three parts: the IBKA algorithm module, the fuzzy neural network module, and the PID controller module:

[0057] (1) Controller Design

[0058] First, the proportionality factors CK p 、CK i 、CK d of the PID controller are globally optimized by the IBKA algorithm, and the initial parameters K p0 、K i0 、K d0 determined by combining the Z-N tuning method and the actual debugging effect are used to obtain the optimal initial parameters. Then, the fuzzy neural network dynamically adjusts the PID parameter increments ΔK p 、ΔK i 、ΔK d according to the pressure error e and its change rate ec. Finally, the PID controller generates a control signal u(t) according to the real-time adjusted parameters to drive the magnetic levitation pump to adjust the water supply flow rate, thereby realizing the stable control of the pressure.

[0059] (2) Fuzzy Control Inference

[0060] The present invention designs fuzzy control rules based on the pressure error e and the error change rate ec, a total of 49 rules, which are used to dynamically adjust the PID control parameters ΔK p 、ΔK i 、ΔK d . The input variables and output variables adopt 7 fuzzy subsets {NB, NM, NS, ZO, PS, PM, PB}.

[0061] (3) Fuzzy Neural Network

[0062] The topological structure of the fuzzy neural network includes an input layer, a fuzzification layer, a fuzzy inference layer, a normalization layer, and an output layer. In the fuzzy neural network PID controller, the input signals e and ec are processed layer by layer in sequence, and finally three adjustable parameters ΔK p 、ΔK i 、ΔK d of the PID controller are generated at the output layer.

[0063] The first layer is the input layer, which has 2 nodes, namely the error and the error change rate. Its function is to input the vector x i =[x1, x2] TEach component is transmitted to the next layer. The input and output are as follows:

[0064]

[0065] In the formula, is the input value of the nodes in the first layer, is the output value of the nodes in the first layer.

[0066] The second layer is the fuzzification layer, which contains 2 inputs, and each input corresponds to 7 linguistic variable values respectively. Its function is to calculate the membership functions of each component of the input vector belonging to the fuzzy sets of each linguistic variable value and map them to the fuzzy subsets. The input and output are as follows:

[0067]

[0068] In the formula, is the input value of the nodes in the second layer, is the output value of the nodes in the second layer, c ij is the central value of the membership function; σ ij is the width of the function curve, b ij is the shape parameter.

[0069] The third layer is the fuzzy inference layer, and each node in this 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 as follows:

[0070]

[0071] In the formula, l = 1, 2,..., 49; i1 = i2 = 1, 2,..., 7; is the input value of the nodes in the third layer; is the output value of the nodes in the third layer.

[0072] The fourth layer is the normalization layer, and the number of nodes in this layer is the same as that in the third layer. Its function is to perform normalization operations on the output of the fuzzy inference layer. The input and output are as follows:

[0073]

[0074] In the formula, is the input value of the nodes in the fourth layer; is the output value of the nodes in the fourth layer.

[0075] The fifth layer is the output layer, and its function is to perform weighted summation on the defuzzified output. Each node in this layer represents an output variable, and there are 3 nodes in total, which are ΔK P 、ΔK I 、ΔK D . The input and output are as follows:

[0076]

[0077] where \(k = 1, 2, 3\); \(\omega\) ij is the network weight of the output layer; is the input value of the node in the 5th layer; is the output value of the node in the 5th layer.

[0078] (4) Parameter Adaptive Adjustment

[0079] The fuzzy neural network PID controller is completed through forward propagation calculation, and the outputs \(\Delta K\) p , \(\Delta K\) i , \(\Delta K\) d . These parameter variations act on the actuator through the PID controller to further adjust the system output. By comparing with the target value \(y(t)\), if the error does not meet the target requirements, it enters the parameter adaptive adjustment process. This process adjusts the central parameter \(C\) ij , width parameter \(\sigma\) ij , and membership shape parameter \(w\) ij of the membership function in the fuzzy neural network through the error signal to reduce the error signal. The objective function for defining the corrected error is:

[0080]

[0081] where \(r(t)\) is the expected pressure of the given system, and \(y(t)\) is the actual pressure of the system.

[0082] To minimize the objective function \(E\), based on error feedback, the parameters of the fuzzification layer are dynamically adjusted, including the center, width, and shape parameters of the membership function. The iterative update formulas for each parameter are as follows:

[0083]

[0084] where \(n\) is the iterative step of the network; \(\lambda\) is the inertia coefficient used to balance historical information and current updates; \(\eta\) is the learning rate that controls the parameter update speed; \(\Delta c\) ij (n), \(\Delta\sigma\) ij (n), \(\Delta\omega\) ij (n) respectively represent the variations of each parameter, which are calculated based on the current error feedback.

[0085] S4. Simulation Experiment and Performance Verification of the Pressure Control System

[0086] To verify the performance of the algorithm of the present invention (IBKA-FNN-PID) in the pipeline pressure control system of the ozone dissolution tank, a simulation experiment environment is specifically built on the MATLAB / Simulink platform, and research and comparison are carried out around the following aspects: First, several typical unimodal functions and multimodal functions are selected to evaluate the performance of the improved black-winged kite optimization algorithm (IBKA), and its global optimization ability and convergence speed in the high-dimensional complex search space are mainly observed; in the pipeline pressure control simulation model, traditional PID, fuzzy PID, fuzzy neural network PID and IBKA-FNN-PID proposed by the present invention are respectively used for control, and their response time, overshoot and steady-state error and other indicators in the pressure regulation process are compared.

[0087] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0088] 1. The present invention uses lens imaging reverse learning in the black-winged kite optimization algorithm BKA, making the initial population distribution more uniform and the coverage range wider; and through the horizontal and vertical crossover operation, the information exchange efficiency between individuals is improved, enhancing the global search ability and local fine development ability of the algorithm in the later stage.

[0089] 2. The present invention introduces Levy flight in the migration stage of the black-winged kite algorithm, enabling individuals to perform long-distance random jumps and avoiding premature convergence to local optima; the dynamic optimal leading mechanism ensures efficient deep optimization can still be carried out in the later stage of iteration, significantly improving the convergence accuracy and stability of the entire algorithm.

[0090] 3. The present invention online corrects the PID parameters through a fuzzy neural network, comprehensively utilizes the non-linear mapping ability of fuzzy inference and the self-learning characteristics of the neural network, realizes precise control of the pipeline pressure of the ozone dissolution tank, significantly reduces the steady-state error and overshoot, and at the same time speeds up the response speed, which is superior to the traditional method. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] The drawings are used to provide further understanding of the present invention, and constitute a part of the specification, and are used to explain the present invention together with the embodiments of the present invention, and do not constitute a limitation to the present invention.

[0092] Figure 1 It is the structure diagram of the pipeline system of the ozone dissolution tank in the present invention.

[0093] Figure 2 It is the structure diagram of the IBKA-optimized fuzzy neural network PID controller in the present invention.

[0094] Figure 3 It is the topological structure diagram of the fuzzy neural network in the present invention.

[0095] Figure 4 It is the function iteration convergence curve diagram in the present invention.

[0096] Figure 5 This is the step response experimental comparison graph of the present invention.

[0097] Figure 6 This is the anti-interference experimental comparison graph of the present invention. Detailed implementation manners

[0098] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0099] Embodiment 1

[0100] Refer to Figure 1 and Figure 6 This embodiment provides its technical solution as a fuzzy neural network PID pressure control method based on an improved black-winged kite algorithm, including the following steps:

[0101] S1. Pressure modeling of the water outlet pipeline of the ozone water tank

[0102] The pipeline pressure control system of the ozone dissolution tank is a complex non-linear dynamic system, and its pressure change is jointly affected by pump flow, pipeline resistance and system lag characteristics. In order to achieve precise regulation of the pressure, the present invention constructs a mathematical model of the system and identifies key parameters in combination with experimental data to ensure that the model can accurately reflect the actual working conditions. A second-order inertial lag system is used to describe the dynamic lag characteristics of the pipeline pressure, and finally the transfer function of the system is obtained as follows:

[0103]

[0104] S2. Design of the improved black-winged kite optimization algorithm (IBKA)

[0105] The present invention needs to achieve high-precision and fast dynamic control of the pressure in the ozone dissolution tank pipeline with non-linear time-varying and frequent interference. Aiming at the problems that the traditional black-winged kite optimization algorithm (BKA) is prone to fall into local optimum and has a slow convergence speed during the high-dimensional search process, an improved optimization strategy is proposed to enhance the global search ability of the algorithm, improve the optimization efficiency, and enhance the adaptability of the control system. So that the controller can achieve fast response and steady-state accuracy, thereby ensuring the stable supply of pipeline pressure. The main improvement measures include the following key links:

[0106] (1) Lens imaging reverse learning strategy

[0107] In high-dimensional parameter search, if the quality and diversity of the initial population are insufficient, it often causes the controller to "locate" in some remote areas from the very beginning during tuning, making it difficult to jump to a better area for search, resulting in the subsequent controller being unable to effectively suppress pressure overshoot or large oscillations.

[0108] In the algorithm initialization stage, to enhance the diversity of the population and improve the quality of the initial solution, the present invention introduces a lens imaging reverse learning strategy. This method constructs a "reverse solution" for the current individual and screens the advantages and disadvantages based on the fitness function, thereby improving the uniform distribution of the solutions and avoiding the population falling into local optima in the initial stage.

[0109]

[0110] where x i is the current individual in the initial population, is the reverse solution space of x i , n is a regulation factor, BK lb represents the lower bound of the solution, BK ub represents the upper bound of the solution, and f(·) is the fitness function.

[0111]

[0112] This improvement can prevent the initial solutions from aggregating in a very small number of areas, greatly enhancing the global nature of the algorithm's later optimization. For pipeline pressure, the more dispersed and high-quality the initial tuning parameters are, the more opportunities there are to quickly find a controller setting with a shorter response time and smaller overshoot, ultimately improving the pressure regulation effect.

[0113] (2) Vertical and horizontal cross information exchange mechanism

[0114] After the attack stage, there is a lack of effective information exchange among individuals in the traditional BKA algorithm, which easily leads to the search being confined to local areas and reduces the global optimization ability. This causes the controller parameters to be trapped in local sub-optima, manifested as insufficient regulation accuracy or anti-interference ability of the pressure. Therefore, the present invention introduces a vertical and horizontal cross information exchange mechanism to enable individuals to perform information recombination in different dimensions, so as to enhance the coverage of the search space and improve the optimization accuracy:

[0115] The formula for the horizontal cross operation is as follows:

[0116] MS hc (i,n) = r1 × x(i,n) + (1 - r1) × x(j,n) + c1 × (x(i,n) - x(j,n))

[0117] MS hc (j,n) = r2 × x(j,n) + (1 - r2) × x(i,n) + c2 × (x(j,n) - x(i,n))

[0118] Wherein, MS hc (i, n) and MS hc (j, n) respectively represent the positions of the new individuals generated by the previous-generation black-winged kites i and j. x(i, n) and x(j, n) are the positions of the previous-generation black-winged kites in the nth dimension respectively; r1 and r2 are random numbers within [0, 1], and c1 and c2 are random numbers within [-1, 1].

[0119] The formula for the longitudinal crossover operation is as follows:

[0120] MS vc (i, n1) = r × x(i, n1) + (1 - r) × x(i, n2)

[0121] Wherein, MS vc (i, n1) represents the offspring individual obtained by the longitudinal crossover of the n1th and n2th dimensions of x(i), and r is a random number within [0, 1].

[0122] When the pipeline pressure model has large-range fluctuations or complex nonlinearities, the later information interaction can enable the algorithm to continuously discover new solutions and avoid being "trapped" by certain local parameter combinations. This is crucial for quickly suppressing pressure shocks and ensuring steady-state accuracy, and can continuously optimize the adjustment time and overshoot in the later stage, thereby obtaining better dynamic and steady-state performances.

[0123] (3) Levy flight

[0124] During the migration stage, black-winged kite individuals usually update their positions based on the current optimal solution. However, this method may lead to a decline in the overall search ability of the population, especially in complex multi-modal optimization problems, it is easy to fall into local optima. Therefore, the present invention introduces a Levy flight strategy during the migration stage, and utilizes its long-distance jumping characteristics to increase the search range and enhance the global search ability. The position update formula is:

[0125]

[0126] Wherein, Levy(λ) is the Levy flight function, is the previous optimal solution of the leading scorer of the jth dimension of the black-winged kite at the tth iteration of the current position; the Levy flight probability density function and the formula for generating a random step size are as follows:

[0127] Levy ~ u = t -λ , 1 ≤ λ ≤ 3

[0128]

[0129] Wherein, that is, when updating, Levy(λ) is represented by S; when calculating, the parameter β takes the value of 1.5, The value of σ is:

[0130]

[0131] S3. Design of Fuzzy Neural Network PID Controller

[0132] In order to solve the problems of nonlinearity, dynamic lag, and insufficient anti-interference ability in the pipeline pressure control system of the ozone dissolution tank, the present invention designs a fuzzy neural network PID controller based on the improved black-winged kite algorithm (IBKA), which mainly includes three parts: the IBKA algorithm module, the fuzzy neural network module, and the PID controller module:

[0133] (1) Controller Design

[0134] The overall architecture of the fuzzy neural network PID controller optimized based on IBKA includes the following steps: First, obtain the initial parameters of the PID controller through the Z-N tuning method to meet the basic performance requirements of pressure control; Second, use the IBKA algorithm to globally optimize the initial parameters of the PID controller to obtain the optimal initial parameters; Then, the fuzzy neural network dynamically adjusts the PID parameter increment according to the pressure error and the error change rate, enabling the controller to adapt to complex dynamic working conditions; Finally, the PID controller generates a control signal U(t) according to the optimized and dynamically adjusted parameters to drive the magnetic levitation pump to adjust the water supply flow rate, thereby achieving precise control of the pipeline pressure.

[0135] (2) Design of Fuzzy Control Rules

[0136] The fuzzy control part is designed based on the pressure error e and the error change rate ec. The fuzzy subsets of the input and output variables are both defined as {NB, NM, NS, ZO, PS, PM, PB}, which represent large negative, medium negative, small negative, zero, small positive, medium positive, and large positive respectively. The pressure error represents the difference between the target pressure and the actual pressure, and the error change rate represents the change trend of the pressure error; the output is the dynamic adjustment amount (i.e., increment) of the PID parameters, corresponding to ΔK p 、ΔK i 、ΔK d respectively. 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 and ΔK d ". The rule base is obtained based on engineering experience and experimental debugging and is used to describe the relationship between the pressure error and the parameter adjustment.

[0137] (3) Design of Fuzzy Neural Network Structure

[0138] The fuzzy neural network is used in the PID controller for online adjustment, and its topological structure includes the following five layers:

[0139] The first layer is the input layer, which has 2 nodes, namely the error and the error change rate. Its function is to transmit each component of the input vector x i =[x1, x2] T to the next layer. The input and output are as follows:

[0140]

[0141] In the formula, is the input value of the nodes in the first layer, is the output value of the nodes in the first layer.

[0142] The second layer is the fuzzification layer, which contains 2 inputs, and each input corresponds to 7 linguistic variable values respectively. Its function is to calculate the membership degrees of each component of the input vector belonging to the fuzzy sets of each linguistic variable value, and map them to the fuzzy subsets. The input and output are as follows:

[0143]

[0144] In the formula, is the input value of the nodes in the second layer, is the output value of the nodes in the second layer, c ij is the central value of the membership function; σ ij is the width of the function curve, b ii is the shape parameter.

[0145] The third layer is the fuzzy inference layer, and each node in this 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 as follows:

[0146]

[0147] In the formula, l = 1, 2,..., 49; i1 = i2 = 1, 2,..., 7; is the input value of the nodes in the third layer; is the output value of the nodes in the third layer.

[0148] The fourth layer is the normalization layer, and the number of nodes in this layer is the same as that in the third layer. Its function is to perform a normalization operation on the output of the fuzzy inference layer. The input and output are as follows:

[0149]

[0150] In the formula, is the input value of the nodes in the fourth layer; is the output value of the nodes in the fourth layer.

[0151] The fifth layer is the output layer, whose function is to perform weighted summation on the deblurred output. Each node in this layer represents an output variable, and there are a total of 3 nodes, namely ΔK P , ΔK I , ΔK D . The input and output are as follows:

[0152]

[0153] In the formula, k = 1, 2, 3; ω ij is the network weight of the output layer; is the input value of the node in the fifth layer; is the output value of the node in the fifth layer.

[0154] (4) Parameter Adaptive Adjustment

[0155] In order to further improve the adaptability of the controller under complex dynamic working conditions, the present invention designs a parameter adaptive adjustment mechanism based on error feedback. The specific method is as follows:

[0156] Adjust the membership function parameters of the fuzzy neural network through error feedback to minimize the pressure error. The objective function is defined as:

[0157]

[0158] In the formula, r(t) is the expected pressure of the given system, and y(t) is the actual pressure of the system.

[0159] Use the gradient descent method to update the parameters of the fuzzy neural network, including the center parameter C ij of the membership function, the width parameter σ ij , and the shape parameter w ij :

[0160]

[0161] In the formula, n is the iteration step of the network; λ is the inertia coefficient, which is used to balance historical information and current updates; η is the learning rate, which controls the parameter update speed; Δc ij (n), Δσ ij (n), Δω ij (n) respectively represent the change amounts of each parameter, which are calculated based on the current error feedback.

[0162] S4. Pressure Control System Simulation Experiment and Performance Verification

[0163] In order to verify the performance of the fuzzy neural network PID (IBKA-FNN-PID) control method based on the improved black kite algorithm optimization in the ozone dissolving tank pipeline pressure control system, the present invention designed and carried out a simulation experiment based on the MATLAB / Simulink platform. The experiment mainly includes the following aspects:

[0164] (1) Improved Black Kite Algorithm IBKA Performance Test

[0165] The performance of the improved IBKA algorithm was evaluated using standard test functions, and unimodal functions and multimodal functions were selected as test benchmarks. Each algorithm was run independently 50 times, with a population size of 30 and a maximum number of iterations of 500. The experimental results show that, in terms of convergence speed, IBKA can reduce the objective function value to a very small value level faster in all test functions, exceeding BKA, and significantly outperforming algorithms such as GWO, RIME, WOA, and PSO, showing stronger global search and local fine optimization capabilities; in terms of final convergence accuracy, IBKA can usually obtain a better final solution than BKA on different test functions, even if BKA has converged in the middle and late stages, IBKA can still further explore smaller objective function values. Overall, IBKA is superior in search stability and in-depth development capabilities. Most of the other algorithms (such as GWO, RIME, WOA, and PSO) stay at higher objective function values ​​or converge slowly in these tests, tend to converge prematurely or locally, and lack sufficient late-stage development capabilities.

[0166] (2) Pressure control experiment

[0167] This experiment simulated the pressure control process through step response and compared the performance of four control algorithms in terms of dynamic response performance. The experiment used a step signal as input to test the performance indicators of each control algorithm, such as overshoot, adjustment time and system response speed. The algorithm of the present invention (IBKA-FNN-PID) performed well in dynamic performance, with almost no overshoot and a system adjustment time of 45s. In contrast, the overshoot of traditional PID and fuzzy PID was 10% and 5% respectively, and the adjustment time was 76s and 65s respectively. Fuzzy neural network PID also had almost no overshoot, but the adjustment time was 55s. In comparison, the adjustment time of the algorithm of the present invention was shortened by 40.8%, 30.8% and 18.1% respectively. The experimental results show that the algorithm of the present invention has significant advantages in response speed and overshoot suppression, and can improve the efficiency and stability of the pressure control process of the ozone dissolving tank system.

[0168] Table 1 Comparison of step response dynamic performance of four control algorithms

[0169]

[0170] Example 2

[0171] To verify the anti-interference performance of the method proposed in the present invention, a disturbance signal with an amplitude of 0.2 was applied when the system ran for 100 seconds, and the duration was 7 seconds. The dynamic response performances of 4 control algorithms under the action of the disturbance signal were compared in the experiment.

[0172] The results show that different degrees of overshoot occurred in the 4 control algorithms under the action of the disturbance signal, but the improved black-winged kite algorithm-based fuzzy neural network PID (IBKA-FNN-PID) of the present invention shows the best anti-interference ability. The overshoot amount after the disturbance of this method is only 2.3%, which is reduced by 12.5%, 8.4% and 3.7% compared with the traditional PID, fuzzy PID and fuzzy neural network PID respectively; the adjustment time is 26 seconds, which is shortened by 55.2%, 48% and 43.5% compared with 58 seconds, 50 seconds and 46 seconds of other control methods respectively. The IBKA-FNN-PID control method can restore the system to a stable state in a shorter time, and the liquid level fluctuation amplitude is the smallest, further reflecting its excellent stability and fast response ability.

[0173] Comparison table of the dynamic performance of 4 control algorithms after interference 2

[0174]

[0175] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A fuzzy neural network PID pressure control method based on an improved black kite algorithm, characterized in that: The following steps are involved: S1. Pressure modeling of the outlet pipe of the ozone water tank The dynamic characteristics of the water supply system are studied and a mathematical model is established. The water supply system is divided into the following three parts: magnetic levitation pump speed control link, pipeline pressure control link and other control and detection links. Finally, the transfer functions of each part are integrated through series-parallel relationship to obtain the overall system model. The operating characteristics of the magnetic levitation pump are expressed as a first-order inertia link, and its transfer function is: In the formula, G1(s) is the transfer function of the speed control part of the magnetic levitation pump; K1 is the gain of the magnetic levitation pump, which indicates the influence of the input signal on the output speed; T1 is the time constant, which reflects the dynamic response speed of the magnetic levitation pump; The pressure control part of the pipeline is determined by the dynamic relationship between flow and pressure. It is a first-order system with hysteresis characteristics. Its transfer function is: In the formula, G2(s) is the transfer function of the pipeline pressure control part; K2 is the pressure gain, which represents the impact of flow change on pipeline pressure; T2 is the time constant of the pressure control system, which reflects the inertia of the system; τ is the time delay, which represents the delay characteristics of the pump flow change to the pipeline pressure response; In the control system, signal conversion, gain adjustment and signal preprocessing are proportional links, and their transfer function is: G3(s)=K3 Where G3(s) is the transfer function of the signal detection and method link; K3 is the gain of the system detection and control link; Combining the magnetic suspension pump speed control part, pipeline pressure control part and other detection links, the transfer function of the overall system is: G(s)=G1(s)·G2(s)·G3(s) Substituting the transfer functions of each part into the equation, we get: After sorting: In the formula, K = K1·K2·K3. According to experimental measurements, T1 = 0.58, T2 = 10, τ = 6, K = 24. Substituting the parameters into the formula, we get: S2. Improved IBKA design of black-winged kite optimization algorithm The following three improvements are made to BKA in the population initialization, individual interaction and migration stages to form an improved black kite algorithm: S3. Design of fuzzy neural network PID controller A fuzzy neural network PID controller based on the improved black kite algorithm IBKA is designed, which includes three parts: IBKA algorithm module, fuzzy neural network module and PID controller module: S4. Pressure control system simulation experiment and performance verification In order to verify the performance of the fuzzy neural network PID controller IBKA-FNN-PID based on the improved black-winged kite algorithm in the pipeline pressure control system of the ozone dissolving tank, a simulation experimental environment was built on the MATLAB / Simulink platform.

2. The fuzzy neural network PID pressure control method based on the improved black kite algorithm according to claim 1 is characterized in that: In S2, the design of the improved black kite optimization algorithm IBKA includes the following steps: (1) Lens imaging reverse learning When the Black Kite Algorithm (BKA) is initialized, for the current individual, a "reverse solution" is constructed within its feasible definition domain; if the reverse solution has better fitness after lens mapping, the original solution is replaced, otherwise the original solution is retained. The mathematical form of lens imaging is expressed as: In the formula, x i is the current individual in the initial population, For x i The reverse solution space, n is the adjustment factor, BK lb represents the lower bound of the solution, BK ub represents the upper bound of the solution, f(·) is the fitness function; In the formula, t is the current iteration number, T is the maximum iteration number; (2) Vertical and horizontal cross strategy The horizontal cross operation formula is as follows: MS hc (i,n)=r1×x(i,n)+(1-r1)×x(j,n)+c1×(x(i,n)-x(j,n)) MS hc (j,n)=r2×x(j,n)+(1-r2)×x(i,n)+c2×(x(j,n)-x(i,n)) In the formula, MS hc (i,n) and MS hc (j,n) represent the positions of the new individuals generated by the previous generation black-winged kites i and j, respectively, x(i,n) and x(j,n) represent the positions of the previous generation black-winged kites in n-dimensions, respectively; r1 and r2 are random numbers in [0,1], c1 and c2 are random numbers in [-1,1]; The vertical cross operation formula is as follows: MS vc (i,n1)=r×x(i,n1)+(1-r)×x(i,n2) In the formula, MS vc (i,n1) represents the offspring individuals obtained by the vertical crossover between the n1th dimension and the n2th dimension of x(i), and r is a random number in [0,1]; (3) Levy flight Combined with the Levy flight strategy, it is used to explore the long-distance area in the space during the migration phase of the black kite algorithm. When θ approaches 0, the tangent slope becomes smaller, that is, the step size changes and becomes smaller. The final solution is close to the current solution, which is suitable for local search. When , the tangent slope becomes larger, that is, the step size changes and becomes larger, and the final solution is far away from the current solution, which is suitable for global search. The position update formula is: Where Levy(λ) is the Levy flight function, is the leading scorer of the j-th black-winged kite at the current position in the t-th iteration, i.e., the current optimal solution, is the updated value of the jth dimension of the ith individual at time t+1; the Levy flight probability density function and the formula for generating random steps are as follows: Levy~u=t -λ ,1≤λ≤3 In the formula, when updating, Levy(λ) is represented by S; when calculating, the parameter β is taken as 1.

5. The value of σ is:

3. The fuzzy neural network PID pressure control method based on the improved black kite algorithm according to claim 1 is characterized in that: In step S3, the fuzzy neural network PID controller is designed, and the IBKA algorithm module, the fuzzy neural network module and the PID controller module are respectively as follows: (1) Controller design First, the PID controller proportional factor CK is adjusted by the IBKA algorithm. p , CK i , CK d Perform global optimization and determine the initial parameter K based on the ZN tuning method and actual debugging results. p0 , K i0 , K d0 Get the optimal initial parameters; then, the fuzzy neural network dynamically adjusts the PID parameter increment ΔK according to the pressure error e and its change rate ec p , ΔK i , ΔK d ; Finally, the PID controller generates a control signal u(t) based on the real-time adjusted parameters, drives the magnetic suspension pump to adjust the water supply flow rate, and realizes stable pressure control; (2) Fuzzy control reasoning Fuzzy control rules based on pressure error e and error change rate ec, a total of 49 rules, are used to dynamically adjust the PID control parameter ΔK p , ΔK i , ΔK d , the input variables and output variables adopt 7 fuzzy subsets {NB, NM, NS, ZO, PS, PM, PB}; (3) Fuzzy Neural Network The topological structure of the fuzzy neural network includes the input layer, fuzzification layer, fuzzy reasoning layer, normalization layer and output layer. In the fuzzy neural network PID controller, the input signals e and ec are processed in each layer in turn, and finally the three adjustable parameters ΔK of the PID controller are generated in the output layer. p , ΔK i , ΔK d ; The first layer is the input layer, which has two nodes, error and error change rate, which is used to convert the input vector x i =[x1,x2] T The components of are transmitted to the next layer, and the input and output are: In the formula, is the input value of the first layer node, is the output value of the first layer node; The second layer is the fuzzification layer, which contains 2 inputs, each of which corresponds to 7 linguistic variable values. Its function is to calculate the membership function of the fuzzy set of each linguistic variable value to which each component of the input vector belongs, and map it to the fuzzy subset. The input and output are: In the formula, is the input value of the second layer node, is the output value of the second layer node, c ij is the central value of the membership function; σ ij is the width of the function curve, b ij is the shape parameter; The third layer is the fuzzy reasoning layer. Each node of this 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: Wherein, l = 1, 2, ..., 49; i1=i2=1,2,…,7; is the input value of the third layer node; is the output value of the third layer node; The fourth layer is the normalization layer. The number of nodes in this layer is the same as that in the third layer. The input and output are: In the formula, is the input value of the 4th layer node; is the output value of the 4th layer node; The fifth layer is the output layer, which performs weighted summation of the defuzzified output. Each node in this layer represents an output variable. There are three nodes in total, namely, ΔK P , ΔK I , ΔK D , the input and output are: Where k = 1, 2, 3; ω ij is the network weight of the output layer; is the input value of the 5th layer node; is the output value of the 5th layer node; (4) Parameter Adaptive Adjustment The fuzzy neural network PID controller is completed through forward propagation calculation and outputs ΔK p , ΔK i , ΔK d These parameter changes act on the actuator through the PID controller to adjust the system output. By comparing it with the target value y(t), if the error does not meet the target requirement, it enters the parameter adaptive adjustment process, which adjusts the central parameter C of the membership function in the fuzzy neural network through the error signal. ij , width parameter σ ij , and the membership shape parameter w ij , so that the error signal is reduced, and the objective function of error correction is defined as: In the formula, r(t) is the expected pressure of the given system, and y(t) is the actual pressure of the system; In order to minimize the objective function E, the fuzzy layer parameters are dynamically adjusted based on error feedback, including the center, width and shape parameters of the membership function. The iterative update formula of each parameter is as follows: Where n is the iteration step of the network; λ is the inertia coefficient, which is used to balance historical information and current updates; η is the learning rate, which controls the parameter update speed; Δc ij (n), Δσ ij (n), Δω ij (n) represent the change of each parameter, which is calculated based on the current error feedback.

4. The fuzzy neural network PID pressure control method based on the improved black kite algorithm according to claim 1 is characterized in that: In step S4, the pressure control system simulation experiment and performance verification include the following steps: S41, select several typical unimodal functions and multimodal functions to evaluate the performance of the improved black-winged kite optimization algorithm IBKA; S42. Observe its global optimization ability and convergence speed in the high-dimensional complex search space; in the pipeline pressure control simulation model, traditional PID, fuzzy PID, fuzzy neural network PID and fuzzy neural network PID of improved Black Kite algorithm are used for control, and their response time, overshoot and steady-state error indicators in the pressure regulation process are compared.

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