A Finite-Time Control Method for Dissolved Oxygen Based on Self-Organizing Fuzzy Terminal Sliding Mode Control

Abstract

The present invention proposes a finite-time control method for dissolved oxygen based on self-organizing fuzzy terminal sliding mode control, which realizes the precise control of the dissolved oxygen concentration. This method designs a self-organizing fuzzy neural network based on rule density and importance to predict the dynamic changes of the dissolved oxygen concentration in the biochemical reaction process, and establishes a terminal sliding mode controller based on the integral terminal sliding mode surface to achieve finite-time precise control of the dissolved oxygen concentration; by designing an adaptive law and a robust control term to reduce the influence of uncertainties and prediction errors on the control performance, the problem of low control accuracy of dissolved oxygen is solved. The experimental results show that this method can achieve precise control of the dissolved oxygen concentration within a finite time.

Description

Technical Field

[0001] The present invention realizes the precise control of the dissolved oxygen concentration in the sewage treatment process based on the finite-time control method of self-organizing fuzzy terminal sliding mode. The dissolved oxygen concentration is one of the key control parameters in the sewage biochemical reaction process and has an important impact on the effluent quality of the sewage treatment process. This invention belongs to both the water research field and the intelligent control field. Background Technique

[0002] With the acceleration of the urbanization process and the improvement of people's living standards, the pollution of various domestic garbage to water resources is becoming more and more serious. The establishment of sewage treatment plants is of great significance for improving the urban environment. At present, the activated sludge method has been widely used in sewage treatment processes. In sewage treatment plants, the dissolved oxygen concentration will directly affect the growth and activity of microorganisms in the aerobic zone, and at the same time, the dissolved oxygen concentration will have a certain impact on the effluent quality and operating costs. In addition, the dissolved oxygen concentration is a key factor affecting the removal rates of ammonia nitrogen and nitrate nitrogen in sewage treatment plants. Accurately controlling it within a reasonable range is a prerequisite for the normal operation of the sewage treatment process. Therefore, the research results of the present invention are of great significance for ensuring the stable operation of sewage treatment plants.

[0003] In actual sewage treatment plants, if the dissolved oxygen concentration cannot be adjusted in time to meet the needs of biochemical reactions, it will affect the normal operation of the sewage treatment process. Therefore, in order to ensure the stable operation of the sewage treatment process, the designed dissolved oxygen control method needs to respond quickly to external changes. However, although the existing dissolved oxygen control methods can better handle the dynamic changes of the dissolved oxygen concentration in the biochemical reaction process and external disturbances such as influent flow rate and weather changes, they ignore the response time of the dissolved oxygen concentration, resulting in poor control effects. Therefore, how to achieve the precise control of the dissolved oxygen concentration within a finite time is the key to ensuring the stable operation of the sewage treatment process. Self-organizing fuzzy terminal sliding mode control ensures the finite-time control of the dissolved oxygen concentration through the design of an integral terminal sliding mode surface; at the same time, this technology expresses prior knowledge through fuzzy rules, has strong learning and fuzzy information processing capabilities, and has good practical application value.

[0004] The present invention designs a finite-time control method for dissolved oxygen based on self-organizing fuzzy terminal sliding mode control, mainly by designing a self-organizing strategy without setting pruning thresholds to update the network structure and parameters, improving the approximation performance of the neural network for the dynamic changes of the dissolved oxygen concentration in the biochemical reaction process; in order to achieve the finite-time control of the dissolved oxygen concentration, an integral terminal sliding mode control law is designed. The present invention not only reduces the influence of external disturbances such as influent flow rate and weather changes on the control performance during the sewage treatment operation process, but also realizes a rapid response to external changes, enables the dissolved oxygen concentration to meet the needs of biochemical reactions, and ensures the safe and stable operation of the sewage treatment process. Summary of the Invention

[0005] The present invention obtains a finite-time control method for dissolved oxygen based on self-organizing fuzzy terminal sliding mode control. This method designs an integral terminal sliding mode surface using the tracking error of the dissolved oxygen concentration, and simultaneously designs a terminal sliding mode control law to ensure the finite-time control of the dissolved oxygen concentration under the condition of reducing the influence of disturbances. The self-organizing fuzzy neural network approximates the dynamic change process of the dissolved oxygen concentration in the biochemical reaction process according to the current dissolved oxygen concentration, the terminal sliding mode surface, the tracking error, and the oxygen transfer coefficient, improving the control performance to a certain extent. The controller controls the dissolved oxygen concentration according to the detected value of the oxygen transfer coefficient, and realizes the precise control of the dissolved oxygen concentration within a finite time to meet the demand of the biochemical reaction for the dissolved oxygen concentration.

[0006] The present invention adopts the following technical solutions and implementation steps:

[0007] 1. A self-organizing fuzzy terminal sliding mode control method for dissolved oxygen concentration, characterized in that: a prediction model for the dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment based on a self-organizing fuzzy neural network is established, and a self-organizing fuzzy terminal sliding mode controller based on an integral terminal sliding mode surface is designed to achieve finite-time precise control of the dissolved oxygen concentration; it includes the following steps:

[0008] (1) Extract the change characteristics of the dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment:

[0009] The dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment fluctuates greatly with time. The control model of the dissolved oxygen concentration in the fifth partition of the biochemical reaction tank is:

[0010]

[0011] Among them, S O,5 (t) represents the dissolved oxygen concentration in the fifth partition of the biochemical reaction tank at time t, S O,4 (t) represents the dissolved oxygen concentration in the fourth partition of the biochemical reaction tank at time t, g(S O,5 (t)) represents the change amount of the dissolved oxygen concentration in the fifth partition of the biochemical reaction tank at time t, K L a5(t) represents the oxygen transfer coefficient in the fifth partition of the biochemical reaction tank at time t;

[0012] (2) Establish a prediction model for the dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment:

[0013] Design a self-organizing fuzzy neural network prediction model to realize the prediction of the change amount g(S O,5 (t)) of the dissolved oxygen concentration in the fifth partition of the biochemical reaction process. The self-organizing fuzzy neural network is divided into four layers: an input layer, a membership function layer, a rule layer, and an output layer. The network structure is 4-l-l-1, where l is a positive integer greater than 1 and the initial value is 6; specifically:

[0014] Input layer: The input layer consists of 4 neurons, h(t) = [h1(t), h2(t), h3(t), h4(t)] T which is the input vector of the fuzzy neural network at time t, h1(t) = S O,5 (t), h2(t) = K L a5(t), h3(t) = e(t), where e(t) is the error between the set value S O,5d (t) and the actual value S O,5 (t) at time t, h4(t) = s(t), and s(t) is the terminal sliding mode surface at time t. T represents the transpose of the vector;

[0015] e(t) = S O,5d (t) - S O,5 (t) (2)

[0016]

[0017] Membership function layer: The membership function layer has l neurons, and the Gaussian function is used as the membership function. The output of the membership function layer is:

[0018]

[0019] where, μ ij (t) represents the output value of the j-th neuron in the membership function layer at time t, i = 1, 2, 3, 4, j = 1, 2, …, l, h i (t) is the i-th variable in the input vector h(t) of the input layer, c ij (t) represents the central value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t, a ij (t) represents the width value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t;

[0020] Rule layer: The rule layer has l neurons, and the output of each neuron in the rule layer is:

[0021]

[0022] where, is the output value of the j-th neuron in the rule layer at time t;

[0023] Output layer: The output of the output layer is the predicted value of the change in dissolved oxygen concentration in the fifth partition at time t

[0024]

[0025] where, w(t) = [w1(t), …, wl \((t)\) is the output weight vector of the fuzzy neural network at time \(t\), \(w_1(t)\) is the output weight of the first neuron in the rule layer of the fuzzy neural network at time \(t\), \(w\) l (t) is the output weight of the \(l\)-th neuron in the rule layer of the fuzzy neural network at time \(t\), is the output vector of the neurons in the rule layer of the fuzzy neural network at time \(t\), is the output value of the first neuron in the rule layer of the fuzzy neural network at time \(t\), is the output value of the \(l\)-th neuron in the rule layer of the fuzzy neural network at time \(t\);

[0026] Neuron growth stage in the rule layer: Calculate the tracking error threshold \(k\) of the control system at time \(t\) e (t):

[0027] \(k\) e (t) = max(0.95 t ×0.1, 0.02) (7)

[0028] where, max() is the function to find the maximum value;

[0029] Calculate the Mahalanobis distance threshold \(k\) between the input vector of the input layer and the center of the neurons in the membership function layer at time \(t\) d (t):

[0030] \(k\) d (t) = max(0.98 t , 0.2) (8)

[0031] Calculate the Mahalanobis distance \(M\) between the input vector of the input layer and the center of the neurons in the membership function layer at time \(t\) j (t):

[0032]

[0033] where, \(c\) j (t) = [c 1j (t), …, c 4j (t)] T is the center vector of the input layer neurons and the \(j\)-th neuron in the membership function layer at time \(t\), \(c\) 1j (t) is the center value of the first neuron in the input layer and the \(j\)-th neuron in the membership function layer at time \(t\), \(c\) 4j (t) is the center value of the fourth neuron in the input layer and the \(j\)-th neuron in the membership function layer at time \(t\), \(a\) 1j (t) represents the width value of the first neuron in the input layer and the \(j\)-th neuron in the membership function layer at time \(t\); When the tracking error \(e(t)\) of the control system at time \(t\) satisfies \(\|e(t)\|>k\) e(t) and the Mahalanobis distance M between the input vector of the input layer and the centers of the neurons in the membership function layer j (t) satisfies M j (t) > k d (t), add a neuron in the membership function layer and a neuron in the rule layer, and update the number of neurons in the membership function layer and the rule layer to N1 = l + 1; when the tracking error e(t) of the control system at time t does not satisfy ||e(t)|| > k e (t) or the Mahalanobis distance M between the input vector of the input layer and the centers of the neurons in the membership function layer j (t) does not satisfy M j (t) > k d (t), do not adjust the structure of the self-organizing fuzzy neural network, N1 = l;

[0034] Neuron deletion stage in the rule layer: Calculate the maximum density value d J (t) of the neurons in the rule layer at time t:

[0035]

[0036] where J represents the J-th neuron with the maximum rule density value in the rule layer, and update the density value of the J-th neuron in the rule layer at time t + 1 to d J (t + 1) = d J (t) + 0.1. After 5 iterations, calculate the set D of neurons in the rule layer with a density value less than 0.5:

[0037] D = {j|d j (t) < 0.5, 1 ≤ j ≤ l} (11)

[0038] where d j (t) is the density value of the j-th neuron in the rule layer at time t; then calculate the rule importance values of the neurons in D:

[0039]

[0040] where q o (t) is the importance value of the o-th neuron in the rule layer at time t, is the output value of the o-th neuron in the rule layer at time t, o ∈ D. Delete the neuron in the rule layer with the smallest rule importance value in D, and update the number of neurons in the membership function layer and the rule layer N2 = N1 - 1;

[0041] Design the parameter adaptation law of the self-organizing fuzzy neural network:

[0042]

[0043]

[0044]

[0045] Among them, w j (t) represents the output weight of the j-th neuron in the rule layer of the fuzzy neural network at time t, and w j (t + 1) represents the output weight of the j-th neuron in the rule layer of the fuzzy neural network at time t + 1, and c ij (t + 1) represents the center value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t + 1, and a ij (t + 1) represents the width value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t + 1;

[0046] (3) Design the self-organizing fuzzy terminal sliding mode control law:

[0047] ① At the initial moment t = 1 of the control action, randomly generate the initial values of the fuzzy neural network parameters;

[0048] ② Calculate the predicted value of the change in dissolved oxygen concentration in the fifth partition according to formula (6)

[0049] ③ Adjust the structure of the self-organizing fuzzy neural network according to formulas (7)-(12);

[0050] ④ Solve the self-organizing fuzzy neural network parameter adaptation law according to formulas (13)-(15);

[0051] ⑤ Calculate the control law u(t) at time t:

[0052] u(t) = u e (t) + u s (t) (16)

[0053] Among them, u e (t) is the equivalent component of the control law at time t, and u s (t) is the switching component of the control law at time t:

[0054]

[0055]

[0056] Among them, tanh(20s(t)) is the hyperbolic tangent function in the saturation function, is the change rate of the set value of the dissolved oxygen concentration at time t;

[0057] ⑥ Increase the time t by 1. If t < 200, return to step ②. If t = 200, end the loop;

[0058] (4) Use the obtained u(t) to perform tracking control on the dissolved oxygen concentration in the fifth sub-region of the biochemical reaction process of urban sewage treatment within a finite time of 5167 seconds. Here, u(t) is the oxygen transfer coefficient of the controller at time t, and the output of the control system is the actual dissolved oxygen concentration value. Description of the Drawings

[0059] Figure 1 is the structural block diagram of the dissolved oxygen finite-time control method based on self-organizing fuzzy terminal sliding mode control of the present invention;

[0060] Figure 2 is the topological diagram of the structural adjustment of the self-organizing fuzzy neural network of the present invention;

[0061] Figure 3 is the control effect diagram and error diagram of the fixed set-point dissolved oxygen concentration of the present invention;

[0062] Figure 4 is the control effect diagram and error diagram of the variable set-point dissolved oxygen concentration of the present invention. Detailed Implementation Manner

[0063] 1. A self-organizing fuzzy terminal sliding mode control method for dissolved oxygen concentration, characterized in that: a prediction model for the dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment based on a self-organizing fuzzy neural network is established, and a self-organizing fuzzy terminal sliding mode controller based on an integral terminal sliding mode surface is designed to achieve finite-time precise control of the dissolved oxygen concentration; it includes the following steps:

[0064] (1) Extract the change characteristics of the dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment:

[0065] The dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment fluctuates greatly with time. The control model for the dissolved oxygen concentration in the fifth sub-region of the biochemical reaction tank is:

[0066]

[0067] Among them, S O,5 (t) represents the dissolved oxygen concentration in the fifth sub-region of the biochemical reaction tank at time t, S O,4 (t) represents the dissolved oxygen concentration in the fourth sub-region of the biochemical reaction tank at time t, g(S O,5 (t)) represents the change amount of the dissolved oxygen concentration in the fifth sub-region of the biochemical reaction tank at time t, K L a5(t) represents the oxygen transfer coefficient in the fifth sub-region of the biochemical reaction tank at time t;

[0068] (2) Establish a prediction model for the dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment:

[0069] Design a self-organizing fuzzy neural network prediction model to realize the change amount g(S of the dissolved oxygen concentration in the fifth sub-region of the biochemical reaction processO,5 (t)), the self-organizing fuzzy neural network is divided into four layers: an input layer, a membership function layer, a rule layer, and an output layer. The network structure is 4-l-l-1, where l is a positive integer greater than 1 and the initial value is 6. Specifically:

[0070] Input layer: The input layer includes 4 neurons, h(t) = [h1(t), h2(t), h3(t), h4(t)] T is the input vector of the fuzzy neural network at time t, h1(t) = S O,5 (t), h2(t) = K L a5(t), h3(t) = e(t), where e(t) is the error between the set value S O,5d (t) and the actual value S O,5 (t) at time t, h4(t) = s(t), and s(t) is the terminal sliding mode surface at time t. T represents the transpose of the vector;

[0071] e(t) = S O,5d (t) - S O,5 (t) (2)

[0072]

[0073] Membership function layer: The membership function layer has l neurons, and the Gaussian function is used as the membership function. The output of the membership function layer is:

[0074]

[0075] where, μ ij (t) represents the output value of the j-th neuron in the membership function layer at time t, i = 1, 2, 3, 4, j = 1, 2,..., l, h i (t) is the i-th variable in the input vector h(t) of the input layer, c ij (t) represents the center value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t, a ij (t) represents the width value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t;

[0076] Rule layer: The rule layer has l neurons, and the output of each neuron in the rule layer is:

[0077]

[0078] where, is the output value of the j-th neuron in the rule layer at time t;

[0079] Output layer: The output of the output layer is the predicted value of the change in dissolved oxygen concentration in the fifth partition at time t

[0080]

[0081] Among them, w(t) = [w1(t), …, w l (t)] is the output weight vector of the fuzzy neural network at time t, w1(t) is the output weight of the first neuron in the rule layer of the fuzzy neural network at time t, w l (t) is the output weight of the l-th neuron in the rule layer of the fuzzy neural network at time t, is the output vector of the neurons in the rule layer of the fuzzy neural network at time t, is the output value of the first neuron in the rule layer of the fuzzy neural network at time t, is the output value of the l-th neuron in the rule layer of the fuzzy neural network at time t;

[0082] Neuron growth stage in the rule layer: Calculate the tracking error threshold k e (t) of the control system at time t:

[0083] k e (t) = max(0.95 t ×0.1, 0.02) (7)

[0084] Among them, max() is the function to find the maximum value;

[0085] Calculate the Mahalanobis distance threshold k d (t) between the input vector of the input layer and the center of the neurons in the membership function layer at time t:

[0086] k d (t) = max(0.98 t , 0.2) (8)

[0087] Calculate the Mahalanobis distance M j (t) between the input vector of the input layer and the center of the neurons in the membership function layer at time t:

[0088]

[0089] Among them, c j (t) = [c 1j (t), …, c 4j (t)] T is the center vector of the neurons in the input layer and the j-th neuron in the membership function layer at time t, c 1j (t) is the center value of the first neuron in the input layer and the j-th neuron in the membership function layer at time t, c 4j (t) is the center value of the fourth neuron in the input layer and the j-th neuron in the membership function layer at time t, a 1j(t) represents the width value of the first neuron in the input layer and the j-th neuron in the membership function layer at time t; when the tracking error e(t) of the control system at time t satisfies ||e(t)|| > k e (t) and the Mahalanobis distance M j (t) between the input vector of the input layer and the center of the neuron in the membership function layer satisfies M j (t) > k d (t), add a neuron in the membership function layer and a neuron in the rule layer, and update the number of neurons in the membership function layer and the rule layer to N1 = l + 1; when the tracking error e(t) of the control system at time t does not satisfy ||e(t)|| > k e (t) or the Mahalanobis distance M j (t) between the input vector of the input layer and the center of the neuron in the membership function layer does not satisfy M j (t) > k d (t), do not adjust the structure of the self-organizing fuzzy neural network, N1 = l;

[0090] Neuron pruning stage in the rule layer: Calculate the maximum density value d J (t) of the neurons in the rule layer at time t:

[0091]

[0092] where J represents the J-th neuron in the rule layer with the maximum rule density value, and update the density value of the J-th neuron in the rule layer at time t + 1 to d J (t + 1) = d J (t) + 0.1. After 5 iterations, calculate the set D of neurons in the rule layer whose density values are less than 0.5:

[0093] D = {j|d j (t) < 0.5, 1 ≤ j ≤ l} (11)

[0094] where d j (t) is the density value of the j-th neuron in the rule layer at time t; then calculate the rule importance value of the neurons in D:

[0095]

[0096] where q o (t) is the importance value of the o-th neuron in the rule layer at time t, is the output value of the o-th neuron in the rule layer at time t, o ∈ D. Delete the neuron in the rule layer with the smallest rule importance value in D, and update the number of neurons in the membership function layer and the rule layer N2 = N1 - 1;

[0097] Design the parameter adaptive law of the self-organizing fuzzy neural network:

[0098]

[0099]

[0100]

[0101] where, w j (t) represents the output weight of the j-th neuron in the rule layer of the fuzzy neural network at time t, w j (t + 1) represents the output weight of the j-th neuron in the rule layer of the fuzzy neural network at time t + 1, c ij (t + 1) represents the center value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t + 1, a ij (t + 1) represents the width value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t + 1;

[0102] (3) Design the self-organizing fuzzy terminal sliding mode control law:

[0103] ① At the initial moment t = 1 of the control action, randomly generate the initial values of the fuzzy neural network parameters;

[0104] ② Calculate the predicted value of the change in dissolved oxygen concentration in the fifth partition according to formula (6)

[0105] ③ Adjust the structure of the self-organizing fuzzy neural network according to formulas (7)-(12);

[0106] ④ Solve the self-organizing fuzzy neural network parameter adaptation law according to formulas (13)-(15);

[0107] ⑤ Calculate the control law u(t) at time t:

[0108] u(t) = u e (t) + u s (t) (16)

[0109] where, u e (t) is the equivalent component of the control law at time t, u s (t) is the switching component of the control law at time t:

[0110]

[0111]

[0112] where, tanh(20s(t)) is the hyperbolic tangent function in the saturation function, is the change rate of the set value of the dissolved oxygen concentration at time t;

[0113] ⑥Increment t by 1. If t < 200, return to step ②; if t = 200, end the loop.

[0114] (4) Use the obtained u(t) to perform tracking control on the dissolved oxygen concentration in the fifth zone of the biochemical reaction process for urban sewage treatment within a finite time of 5167 seconds. Here, u(t) is the oxygen transfer coefficient of the controller at time t, and the output of the control system is the actual dissolved oxygen concentration value. Figure 1 It is the structural block diagram of the dissolved oxygen finite-time control method based on self-organizing fuzzy terminal sliding mode control of the present invention; Figure 2 It is the topological diagram of the structural adjustment of the self-organizing fuzzy neural network of the present invention; Figure 3 It is the control effect diagram and tracking error diagram of the dissolved oxygen concentration when the set point is fixed in the present invention; Figure 4 It is the control effect diagram and tracking error diagram of the dissolved oxygen concentration when the set point is variable in the present invention. X-axis: time, unit is day; Y-axis: effluent dissolved oxygen concentration value and dissolved oxygen concentration tracking error value, unit is mg / L. The blue solid line is the actual dissolved oxygen concentration value, the black solid line is the dissolved oxygen concentration set value, and the blue dashed line is the dissolved oxygen concentration tracking error value.

Claims

1. A self-organizing fuzzy terminal sliding mode control method for dissolved oxygen concentration, characterized in that: Establish a prediction model for the dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment based on a self-organizing fuzzy neural network, and design a self-organizing fuzzy terminal sliding mode controller based on an integral terminal sliding surface to achieve finite-time precise control of the dissolved oxygen concentration; the steps are as follows: (1) Extract the variation characteristics of the dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment: The dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment fluctuates greatly with time, and the control model of the dissolved oxygen concentration in the fifth partition of the biochemical reaction tank is: Among them, S O,5 (t) represents the dissolved oxygen concentration in the fifth partition of the biochemical reaction pool at time t, and S O,4 (t) represents the dissolved oxygen concentration in the fourth partition of the biochemical reaction pool at time t. g(S O,5 (t)) represents the change in the dissolved oxygen concentration in the fifth partition of the biochemical reaction pool at time t, and K L a5(t) represents the oxygen transfer coefficient in the fifth partition of the biochemical reaction pool at time t; (2) Establish a prediction model for the dissolved oxygen concentration in the biochemical reaction process of urban sewage treatment: Design a self-organizing fuzzy neural network prediction model to realize the prediction of the change amount g(S O,5 (t)) of the dissolved oxygen concentration in the fifth partition of the biochemical reaction process. The self-organizing fuzzy neural network is divided into four layers: the input layer, the membership function layer, the rule layer, and the output layer. The network structure is 4-l-l-1, where l is a positive integer greater than 1 and the initial value is 6. Specifically: Input layer: The input layer consists of 4 neurons, h(t) = [h1(t), h2(t), h3(t), h4(t)] T is the input vector of the fuzzy neural network at time t, h1(t) = S O,5 (t), h2(t) = K L a5(t), h3(t) = e(t), where e(t) is the error between the set value S O,5d (t) and the actual value S O,5 (t) at time t, h4(t) = s(t), where s(t) is the terminal sliding mode surface at time t, and T represents the transpose of the vector; e(t) = S O,5d (t) - S O,5 (t) (2) Membership function layer: The membership function layer has l neurons, and the Gaussian function is used as the membership function. The output of the membership function layer is: where, μ ij (t) represents the output value of the j-th neuron in the membership function layer at time t, i = 1, 2, 3, 4, j = 1, 2, …, l, h i (t) is the i-th variable in the input vector h(t) of the input layer, c ij (t) represents the center value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t, a ij (t) represents the width value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t; Rule layer: The rule layer has l neurons, and the output of each neuron in the rule layer is: Among them, is the output value of the j-th neuron in the rule layer at time t; Output layer: The output of the output layer is the predicted value of the change in dissolved oxygen concentration in the fifth partition at time t where, w(t) = [w1(t), …, w l (t)] is the output weight vector of the fuzzy neural network at time t, w1(t) is the output weight of the first neuron in the rule layer of the fuzzy neural network at time t, w l (t) is the output weight of the l-th neuron in the rule layer of the fuzzy neural network at time t, is the output vector of the neurons in the rule layer of the fuzzy neural network at time t, is the output value of the first neuron in the rule layer of the fuzzy neural network at time t, is the output value of the l-th neuron in the rule layer of the fuzzy neural network at time t; Rule layer neuron growth stage: Calculate the tracking error threshold k of the control system at time t e (t): k e (t) = max(0.95 t ×0.1, 0.02) (7) Among them, max() is the function to find the maximum value; Calculate the Mahalanobis distance threshold k between the input vector of the input layer at time t and the center of the neurons in the membership function layer d (t): k d (t) = max(0.98 t , 0.2) (8) Calculate the Mahalanobis distance \(M\) between the input vector of the input layer at time \(t\) and the centers of the neurons in the membership function layer j (t): where, c j (t) = [c 1j (t), …, c 4j (t)] T is the center vector of the input layer neuron and the j-th neuron of the membership function layer at time t, c 1j (t) is the center value of the first neuron of the input layer and the j-th neuron of the membership function layer at time t, c 4j (t) is the center value of the fourth neuron of the input layer and the j-th neuron of the membership function layer at time t, a 1j (t) represents the width value of the first neuron of the input layer and the j-th neuron of the membership function layer at time t; when the tracking error e(t) of the control system at time t satisfies ||e(t)|| > k e (t) and the Mahalanobis distance M j (t) between the input vector of the input layer and the center of the neuron in the membership function layer satisfies M j (t) > k d (t), add a neuron in the membership function layer and a neuron in the rule layer, and update the number of neurons in the membership function layer and the rule layer to N1 = l + 1; when the tracking error e(t) of the control system at time t does not satisfy ||e(t)|| > k e (t) or the Mahalanobis distance M j (t) between the input vector of the input layer and the center of the neuron in the membership function layer does not satisfy M j (t) > k d (t), do not adjust the structure of the self-organizing fuzzy neural network, N1 = l; Rule layer neuron pruning stage: Calculate the maximum density value d of the rule layer neurons at time t J (t): Among them, J represents the J-th neuron with the maximum rule density value in the rule layer, and the density value of the J-th neuron in the rule layer at time t + 1 is updated to d J (t + 1) = d J (t) + 0.

1. After 5 iterations, the set D of rule layer neurons with rule layer neuron density values less than 0.5 is calculated: D = {j | d j (t) < 0.5, 1 ≤ j ≤ l} (11) where d j (t) is the density value of the j-th neuron in the rule layer at time t; then calculate the rule importance value of the neurons in D: where q o (t) is the importance value of the o-th neuron in the rule layer at time t, is the output value of the o-th neuron in the rule layer at time t, o ∈ D. Delete the neuron in the rule layer with the smallest rule importance value in D, and update the number of neurons in the membership function layer and the rule layer N2 = N1 - 1; Design the parameter adaptive law of the self-organizing fuzzy neural network: Among them, w j (t) represents the output weight of the j-th neuron in the rule layer of the fuzzy neural network at time t, w j (t + 1) represents the output weight of the j-th neuron in the rule layer of the fuzzy neural network at time t + 1, c ij (t + 1) represents the center value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t + 1, a ij (t + 1) represents the width value of the i-th neuron in the input layer and the j-th neuron in the membership function layer at time t + 1; (3) Design the self-organizing fuzzy terminal sliding mode control law: ① At the initial moment t = 1 of the control action, randomly generate the initial values of the parameters of the fuzzy neural network; ② Calculate the predicted value of the change in dissolved oxygen concentration in the fifth partition according to formula (6). ③ Adjust the structure of the self-organizing fuzzy neural network according to formulas (7)-(12); ④ Solve the parameter adaptive law of the self-organizing fuzzy neural network according to formulas (13)-(15); ⑤ Calculate the control law u(t) at time t: u(t) = u e (t) + u s (t) (16) where, u e (t) is the equivalent component of the control law at time t, and u s (t) is the switching component of the control law at time t: where, tanh(20s(t)) is the hyperbolic tangent function in the saturation function, is the change rate of the set value of the dissolved oxygen concentration at time t; ⑥ Increase the time t by 1. If t < 200, return to step ②. If t = 200, end the loop; (4) Use the solved u(t) to perform tracking control on the dissolved oxygen concentration in the fifth partition of the biochemical reaction process of urban sewage treatment within a finite time of 5167 seconds. u(t) is the oxygen transfer coefficient of the controller at time t, and the output of the control system is the actual dissolved oxygen concentration value.

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