Asymmetric Constrained Control Method for Multiple Equipment in Urban Wastewater Treatment Process Based on Neural Network

Abstract

The asymmetric constrained control method of multiple devices in the urban sewage treatment process based on neural networks involves the field of artificial intelligence. This paper aims to achieve transient and steady-state control performance of multiple devices in the case where actuator saturation is prone to occur in sewage treatment plants. Due to the long treatment process and frequent interference in sewage treatment plants, a self-organizing fuzzy neural network is used to accurately estimate the dynamic nonlinearity. Due to the limitation of peak power, a unified model of peristaltic pumps and saturated air pumps is established, which is more suitable for the operation requirements of sewage treatment plants. Due to the serious fluctuations in water quality, an asymmetric barrier Lyapunov function is introduced to constrain the control indicators of aeration pumps and return pumps within the expected asymmetric boundaries.

Description

Technical Field

[0001] The present invention is applied to the sewage treatment process, and an asymmetric constraint control method based on artificial intelligence is combined with an actuator saturation processing technology to realize asymmetric constraint control of multiple devices. Background Art

[0002] In recent years, due to the implementation of green production and environmental protection, the control technology of urban sewage treatment process has attracted the attention of various countries. The activated sludge method is currently the most widely used sewage purification method, and the aeration pump and return pump are the main equipment of this method. Due to the mutual influence between different treatment units, there are problems such as uncertainty, nonlinearity, and equipment operation saturation in the sewage treatment process.

[0003] In order to meet the standards and regulations for effluent quality, the dissolved oxygen concentration and nitrate nitrogen concentration must be quickly controlled when the aeration pump and return pump are saturated. In order to solve the strong nonlinearity and uncertainty in the sewage treatment process, many artificial intelligence methods based on neural networks have been proposed, and controllers such as self-organizing fuzzy neural networks have been designed to improve the control performance based on time-varying dynamic characteristics. However, in engineering applications, almost all equipment has peak power limitations, among which controller saturation is an important factor limiting system performance. This is rarely considered in the research and design of sewage treatment processes. In addition, in actual operation, many equipment are restricted by performance requirements, safety regulations and environmental factors. If the operating variables exceed the specified constraint boundaries, the control performance will decrease. The asymmetric barrier Lyapunov function is an effective tool that can constrain the control input and output results to ensure better tracking performance. In order to overcome the problem that the nonlinear function results need to be linearly parameterized, the neural network is combined with the asymmetric barrier Lyapunov function as an identifier. At present, there is no application of this method in sewage treatment. Summary of the invention

[0004] Aiming at the sewage treatment plant where the equipment is prone to saturation, this paper proposes a multi-equipment asymmetric constrained control method (FAACC) for sewage treatment process based on neural network to achieve transient and steady-state regulation of aeration pumps and return pumps. Firstly, a self-organizing fuzzy neural network is used to accurately identify the dynamic nonlinearity of the sewage treatment plant. Then, the control variables K of the aeration pump and return pump are analyzed. L a5(t) and Q c (t), a unified saturation model is established to ensure the reliability of the system. Finally, an asymmetric Lyapunov candidate function is introduced to keep the controlled object within the expected asymmetric range.

[0005] The specific technical solution of the present invention is:

[0006] Step 2.1: Design a fuzzy neural network as the identifier:

[0007] Fuzzy neural network consists of input layer, RBF layer, normalization layer and output layer, and has been widely used in system identification process. Therefore, fuzzy neural network is used to identify the unknown dynamics of each link in the sewage treatment process online. The output result L(t) of the identifier is as follows:

[0008]

[0009] where x i (t) is the input vector of the ith neuron in the input layer, c ij (t) is the jth activation function center, σ ij (t) is the width of the jth activation function, is the actual output value of the lth neuron in the regular layer at each iteration, is the weight vector of the lth neuron, and p is the total number of neurons in the current regular layer.

[0010] Step 2.2: Self-organizing structure adjustment mechanism:

[0011] In the sewage treatment process, since the existing mean square error criterion is difficult to solve the non-stationary and nonlinear problems caused by disturbances, the maximum relevant entropy criterion is used to improve the online identification ability of the long sewage treatment process:

[0012]

[0013] Where y(t) is the actual concentration of dissolved oxygen or nitrate nitrogen, which can be measured by sensors during sewage treatment. d (t) is the desired concentration of dissolved oxygen or nitrate nitrogen, set according to the International Water Quality Association Charter, σ r is the kernel width.

[0014] (1) Initial moment: Establish the structure of the network model based on the initial data and parameters.

[0015] (2) Growth stage: The rule growth criterion in the fuzzy neural network is designed based on the relevant entropy.

[0016] θ(t)<J1&θ(t)>J2 (3)

[0017] Where J1 and J2 represent the preset rule growth thresholds of the upper and lower limits of the relevant entropy respectively. If the above conditions are met, the newly added neuron parameter c p+1 =x i (t),σ p+1 =μ0||x i (t)||, c p+1 is the center of the newly added neuron, σ p+1is the width of the newly added neuron, w p+1 is the weight of the newly added neuron, ||·|| is the norm, μ0>0 represents the overlap coefficient, which is generally taken in the interval [0.5 1], with a step size of 0.02. The recognition result is used as the evaluation standard, and the overlap coefficient value corresponding to the minimum recognition error is selected as the identifier parameter. And the number of rules is updated to p=p+1.

[0018] (3) Pruning stage: When the conditions are met

[0019]

[0020] Where J3 is the pre-set correlation entropy threshold, J4 is the rule layer activation strength threshold, then c p =0,σ p =0,w p =0, where c p is the center of the pruned neuron, σ p is the width of the pruned neuron, w p is the weight of the deleted neuron, and the total number of rules is updated to p=p-1.

[0021] (4) Stop updating: Set the network structure stop condition

[0022] θ(t)>J5 (5)

[0023] Where J5 is a constant. If the network performance meets the above requirements, the structure will stop adjusting. At this time, the total number of neurons in the regular layer r = p.

[0024] Step 2.3: Design the device asymmetric constraint controller

[0025] The equivalent model of denitrification and aeration process in the biochemical reaction process is:

[0026]

[0027] Where S O,m (t), m = 4, 5 is the dissolved oxygen concentration in the mth area of ​​the biochemical reaction tank, S NO,n (t), n = 1, 2, 5 is the nitrate nitrogen concentration in the nth late biochemical reaction area, X B,H (t) is the heterotrophic biomass concentration, Y H =0.67 represents the heterotrophic biomass yield coefficient, μ(t) is the growth respiration coefficient, K L a5(t) is the oxygen transfer coefficient of the last aerobic zone, Q c (t) is the internal reflux flow, Q i(t), i = 1, 2, 4, 5 is the flow rate of the ith pool, V5 = 1333 is the volume of the fifth zone biochemical reaction pool, V2 = 1333 is the volume of the second zone biochemical reaction pool, k O =0.2 is the saturation coefficient of aerobic respiration of heterotrophic bacteria, S O,S =8 is the saturation value of dissolved oxygen concentration.

[0028] 1. Design of aeration pump controller

[0029] (1) Saturation processing of the control signal:

[0030] K L a5(t)=γ 11 v O (t)+γ 12 (v O (t)) (7)

[0031] where v O (t) is the input signal of the controller, function γ 11 is an arbitrary non-zero constant, v mo is the maximum input signal allowed by the controller, function π=3.14, x can be any non-zero real number.

[0032] (2) Define the tracking error of the controller:

[0033] z O (t) = S O,5 (t)-S O,set (t) (8)

[0034] Where S O,5 (t) is the actual concentration of dissolved oxygen, S O,set (t) is the set value of dissolved oxygen concentration, which is set in accordance with the charter of the International Water Quality Association.

[0035] (4) Derivative of controller tracking error for:

[0036]

[0037] in is the derivative of the set point value of dissolved oxygen concentration.

[0038] (5) Define the symbol q(z O (t)) is:

[0039]

[0040] (6) Construct asymmetric barrier Lyapunov candidate function:

[0041]

[0042] There are two constants η1 and η2 that satisfy the condition -η1≤z NO (t)≤η2, η1 and η2 are predefined parameters.

[0043] (7) Derivatives of asymmetric Lyapunov functions We can get:

[0044]

[0045] in is the difference between the current value and the expected optimal value of the width value, center value, weight value, and saturation processing value; It is the current width value, center value, weight value, and saturation processing value of the identifier each time it goes through a loop iteration; It is the expected optimal width value, center value, weight value, and saturation processing value obtained after the identifier undergoes cyclic iterative structural adjustment. They will be obtained after the identifier structure stops adjusting when the maximum correlation entropy is 1 or greater than the threshold J5; is the adaptive rate of width value, center value, weight value, and saturation processing value. In addition, the variable and

[0046] (8) The dynamic nonlinear equation of the sewage treatment process can be defined as follows:

[0047]

[0048] Based on the recognition ability of self-organizing fuzzy neural network, unknown dynamic function Can be replaced by

[0049]

[0050] in is the current actual output value of the normalization layer of the fuzzy neural network after the structure and parameters are adjusted, are constants obtained by the identifier during the identification process, which will be obtained after the identifier structure stops adjusting when the maximum correlation entropy is 1 or greater than the threshold J5. Define variables in It is the result of subtracting the actual rule layer output value at each iteration from the expected rule layer output after the identifier structure adjustment is completed; is the actual rule layer output value at each iteration.

[0051] (9) Based on formulas (13)-(14), formula (12) can be further rewritten as:

[0052]

[0053] (10) According to Young’s inequality, we can get:

[0054]

[0055] in is any non-zero constant.

[0056] (11) Then substitute formula (16) into formula (15):

[0057]

[0058] (12) Order in and They are The first and second values ​​of the matrix, and They are The first and second values ​​of the matrix, and They are The first and second values ​​of the matrix. Carry out Taylor expansion, we can get:

[0059]

[0060] in are the higher-order terms of the Taylor expansion.

[0061] (13) Controller input can be designed:

[0062]

[0063] Where k1 is the controller coefficient, is the actual weight of the identifier at each iteration, is the actual rule layer output value of the identifier at each iteration, ε1=1.

[0064] The four adaptive rates are designed as:

[0065]

[0066]

[0067]

[0068]

[0069] Where a1, b1, c1, δ1 are adaptive rate coefficients, which are fixed constants.

[0070] (14) Substituting (19)-(23) into (18), we obtain:

[0071]

[0072] in is an arbitrary non-zero constant, ρ=0.2785.

[0073] (15) According to Young’s inequality, we can get:

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] in and is any non-zero constant.

[0080] (16) Substituting (25)-(29) into formula (24), we can obtain:

[0081]

[0082] 2. Design of reflux pump controller

[0083] (1) After saturation treatment, the reflux pump controller can be obtained

[0084] Q c (t) = γ 21 v NO (t)+γ 22 (v NO (t)) (31)

[0085] where v NO (t) is the input signal of the controller, function γ 21 is an arbitrary non-zero constant, the function v mn is the maximum input signal allowed by the controller, π=3.14, and x can be any non-zero real number.

[0086] (2) Since the design of the return pump controller is the same as that of the aeration pump, the design process of the return pump controller is simplified. The tracking error of the nitrate nitrogen concentration is defined as

[0087] z NO (t) = SNO,2 (t)-S NO,set (t) (32)

[0088] Where S NO,2 (t) is the actual concentration of nitrate nitrogen in the second zone; S NO,set (t) is the desired set point for the nitrate-nitrogen concentration.

[0089] (3) The candidate Lyapunov function for the asymmetric barrier is

[0090]

[0091] Among them, if z NO (t)>0, then q(z NO (t))=1; if z NO (t)≤0, then q(z NO (t)) = 0. There are two constants η3 and η4 that can satisfy the condition -η3≤z NO (t)≤η4, η3 and η4 are predefined parameters.

[0092] (4) Taking the derivative of formula (33), we can get

[0093]

[0094] in is the difference between the current value and the expected optimal value of the width value, center value, weight value, and saturation processing value; It is the current width value, center value, weight value, and saturation processing value of the identifier each time it goes through a loop iteration; It is the expected optimal width value, center value, weight value, and saturation processing value obtained after the identifier undergoes cyclic iterative structural adjustment. They will be obtained after the identifier structure stops adjusting when the maximum correlation entropy is 1 or greater than the threshold J5; is the adaptive rate of width value, center value, weight value, and saturation processing value. In addition, the variable and

[0095] (5) Based on the self-organizing fuzzy neural network, the dynamic nonlinear equation R NO (t) as follows

[0096]

[0097] in is the current actual output value of the normalization layer of the fuzzy neural network after the structure and parameters are adjusted, are constants obtained by the identifier during the identification process, which will be obtained after the identifier structure stops adjusting when the maximum correlation entropy is 1 or greater than the threshold J5. Define variables in It is the result of subtracting the actual rule layer output value at each iteration from the expected rule layer output after the identifier structure adjustment is completed; is the actual rule layer output value at each iteration.

[0098] (6) According to Young’s inequality, we can further obtain:

[0099]

[0100] in is any non-zero constant.

[0101] (7) Design the controller as

[0102]

[0103] The corresponding four adaptive laws are as follows

[0104]

[0105]

[0106]

[0107]

[0108] Where k2 is the controller coefficient, is the actual weight of the identifier at each iteration, is the actual rule layer output value of the identifier at each iteration, ε2=1; a2, b2, c2, δ2 are adaptive rate coefficients, which are fixed constants.

[0109] (8) Substituting (37)-(41) into (36) and combining with Young’s inequality, we can obtain

[0110]

[0111] in and is any non-zero constant.

[0112] Step 2.4: Proof of controller stability

[0113] Theorem 1: Considering that the aeration pump subsystem in (6) is affected by saturation, if S O,set (t) is within the constraint interval, If continuous and bounded, the adaptive controller based on artificial intelligence technology designed in (19) and the corresponding adaptive rates in (20)-(23) can ensure satisfactory control performance. At the same time, the constraint of dissolved oxygen concentration is strictly observed to achieve the stability of the closed-loop system.

[0114] Proof: (30) can be further organized as:

[0115]

[0116] Then we can get:

[0117]

[0118] Finally, you can get

[0119]

[0120] in

[0121] Δ 11 =min{2k1γ 11 ,a1,b1,c1,δ1} (46)

[0122]

[0123] Multiply both sides by And take the integral to get:

[0124]

[0125] It can be seen that the stability of the aeration pump controller is established.

[0126] Theorem 2: Considering that the reflux pump subsystem in (6) is affected by saturation, if S NO,set (t) is within the constraint interval, If continuous and bounded, the adaptive controller based on artificial intelligence technology designed in (37) and the adaptive laws in (38)-(41) can ensure satisfactory control performance. At the same time, the nitrate nitrogen concentration constraint is strictly observed, and the stability of the closed-loop system is achieved.

[0127] Proof: The proof process is similar to Theorem 1, so it is simplified. By arranging, we can get

[0128]

[0129] in

[0130] Δ 21 =min{2k2γ 21 ,a2,b2,c2,δ2} (50)

[0131]

[0132] Multiply both sides by We can get:

[0133]

[0134] Then the stability of the reflux pump controller is established.

[0135] 3. Control performance evaluation:

[0136] In order to fairly evaluate the control performance, the integrated square error (ISE), integrated absolute error (IAE) and maximum absolute error (Dev max ) as the evaluation index.

[0137]

[0138]

[0139] Dev max =max{|y(t)-y d (t)|} (55)

[0140] Where Τ is the total number of samples. y(t) is the actual concentration of dissolved oxygen or nitrate nitrogen, which can be measured by the sensor during the sewage treatment process. d (t) is the desired dissolved oxygen or nitrate concentration. BRIEF DESCRIPTION OF THE DRAWINGS

[0141] Figure 1 Schematic diagram of FFAAC used in wastewater treatment process

[0142] Figure 2 Control results for fixed set point concentration

[0143] Figure 3 Fixed set point tracking error

[0144] Figure 4 Changes in the number of identifier rules

[0145] Figure 5 Oxygen transfer coefficient and internal recirculation coefficient

[0146] Figure 6 Control results for dynamic set point concentration

[0147] Figure 7 Tracking error of dynamic set point

[0148] Figure 8 Changes in the number of identifier rules

[0149] Fig. 9 Oxygen transfer coefficient and internal recirculation coefficient DETAILED DESCRIPTION

[0150] (1) Case 1: Fixed setpoint tracking control

[0151] The wastewater treatment plant is tracked and controlled on the baseline simulation model 1 (BSM1) with sunny weather as the background. The fixed set value of dissolved oxygen concentration is 2 mg / L, and the fixed set value of nitrate nitrogen concentration is 1 mg / L.

[0152] In order to evaluate the control performance of FAACC, it is compared with the self-organizing fuzzy neural network (SOFNN) controller, proportional differential integral (PID) controller and model predictive control (MPC) controller. Figures (2A) and (2B) plot the trajectories of the set values ​​of dissolved oxygen concentration and nitrate nitrogen concentration under different control modes. The tracking control errors of dissolved oxygen concentration and nitrate nitrogen concentration are shown in Figures (3A) and (3B). The changes in the number of identifier rules are shown in Figures (4A) and (4B). Figures (5A) and (5B) plot the evolution curves of oxygen transfer coefficient and internal recirculation coefficient. Based on the response curve and tracking error curve, it can be clearly seen that the proposed FAACC can obtain better transient and steady-state tracking performance. In addition, it can be seen that the proposed FAACC can guarantee the original control performance when considering actuator saturation.

[0153] (2) Case 2: Dynamic setpoint tracking control

[0154] In the baseline simulation model 1 (BSM1), the sewage treatment plant is dynamically set to track and control the rainstorm weather. The dynamic set point of dissolved oxygen concentration is 2 mg / L at the initial setting, which increases to 2.1 mg / L on the 4th day, decreases to 1.95 mg / L on the 8th day, and increases to 2 mg / L on the 12th day. The dynamic set point of nitrate nitrogen concentration is 1 mg / L at the initial setting, which increases to 1.2 mg / L on the 4th day, decreases to 0.85 mg / L on the 8th day, and increases to 1 mg / L on the 12th day.

[0155] The comparison results are as follows Figure 6-Figure 9As shown. The set value tracking trajectories of dissolved oxygen concentration and nitrate nitrogen concentration are shown in Figure (6A) and Figure (6B). It can be clearly seen that under FAACC control, not only the control effect at the inflection point is better than that of FNN, but also the control accuracy is better than that of MPC and PID. The tracking error trajectory is shown in Figure (7A) and Figure (7B), which verifies that the proposed control method can obtain the minimum convergence range. It can be seen from Figure (8A) and Figure (8B) that with the dynamic change of the set value, the identifier can adjust the number of rules in time to obtain the current state value of each indicator. Figure (9A) and Figure (9B) plot the evolution curves of the oxygen transfer coefficient and the internal recirculation coefficient. When the water inlet suddenly increases and the expected set point suddenly changes, the identifier of the designed method can quickly identify and dynamically adjust. It can be seen that FAACC has faster adaptive adjustment capability than FNN and higher control accuracy than MPC and PID.

Claims

1. A multi-device asymmetric constraint control method for urban sewage treatment process based on neural network, characterized by: For the dynamic uncertainties in sewage treatment, define the unknown function and The approximation characteristics of the fuzzy neural network are used to identify the unknown function; the output result L(t) of the identifier is as follows: where x i (t) is the input vector of the ith neuron in the input layer, c ij (t) is the jth activation function center, σ ij (t) is the width of the jth activation function, is the actual output value of the lth neuron in the regular layer at each iteration, is the weight vector of the lth neuron, and p is the total number of neurons in the current regular layer; Design the identifier structure adjustment mechanism. The specific steps are: In the sewage treatment process, since the existing mean square error criterion is difficult to solve the non-stationary and nonlinear problems caused by disturbances, the maximum relevant entropy criterion is used to improve the online identification ability of the long sewage treatment process: Where y(t) is the actual concentration of dissolved oxygen or nitrate nitrogen, which can be measured by sensors during sewage treatment. d (t) is the desired concentration of dissolved oxygen or nitrate nitrogen, set according to the International Water Quality Association Charter, σ r is the kernel width; 1) Initial moment: Establish the structure of the network model based on the initial data and parameters; 2) Growth stage: The rule growth criterion in the fuzzy neural network is designed based on the relevant entropy. θ(t)<J1&θ(t)>J2 (3) Where J1 and J2 represent the preset rule growth thresholds of the upper and lower limits of the relevant entropy respectively; if the above conditions are met, the newly added neuron parameter c p+1 =x i (t), σ p+1 =μ0||x i (t)||, c p+1 is the center of the newly added neuron, σ p+1 is the width of the newly added neuron, w p+1 is the weight of the newly added neuron, ||·|| is the norm, μ0>0 represents the overlap coefficient, which is generally taken in the interval [0.51], with a step size of 0.

02. The recognition result is used as the evaluation standard, and the overlap coefficient value corresponding to the minimum recognition error is selected as the identifier parameter; and the number of rules is updated to p=p+1; 3) Pruning stage: When the conditions are met Where J3 is the pre-set correlation entropy threshold, J4 is the rule layer activation strength threshold, then c p =0,σ p =0,w p =0, where c p is the center of the pruned neuron, σ p is the width of the pruned neuron, w p is the weight of the deleted neuron, and the total number of rules is updated to p = p-1; 4) Stop updating: set the network structure stop condition θ(t)>J5 (5) Where J5 is a constant; if the network performance meets the above requirements, the structure will stop adjusting; at this time, the total number of neurons in the regular layer r = p; J1, J2, J3, J4, J5 will define specific parameter values ​​according to the identifiers of the aeration pump and the return pump. 11 ,J 12 ,J 13 ,J 14 ,J 15 and J 21 ,J 22 ,J 23 ,J 24 ,J 25 ; The design steps of the control method are as follows: (1) First, establish an equivalent model of denitrification and aeration process in the biochemical reaction process: Where S O,m (t), m = 4, 5 is the dissolved oxygen concentration in the mth area of ​​the biochemical reaction tank, S NO,n (t), n = 1, 2, 5 is the nitrate nitrogen concentration in the nth late biochemical reaction area, X B,H (t) is the heterotrophic biomass concentration, Y H =0.67 represents the heterotrophic biomass yield coefficient, μ(t) is the growth respiration coefficient, K L a5(t) is the oxygen transfer coefficient of the last aerobic zone, Q c (t) is the internal reflux flow, Q i (t), i = 1, 2, 4, 5 is the flow rate of the ith pool, V5 = 1333 is the volume of the fifth zone biochemical reaction pool, V2 = 1333 is the volume of the second zone biochemical reaction pool, k O =0.2 is the saturation coefficient of aerobic respiration of heterotrophic bacteria, S O,S =8 is the saturation value of dissolved oxygen concentration; (2) Design of aeration pump controller: ①Saturation processing of the control signal: K L a5(t)=γ 11 v O (t)+γ 12 (v O (t)) (7) where v O (t) is the input signal of the controller, function γ 11 is an arbitrary non-zero constant, v mo is the maximum input signal allowed by the controller, function π=3.14, x can be any non-zero real number; ② Calculate the dissolved oxygen concentration tracking error as: z O (t)=S O,5 (t)-S O,set (t) (8) Where S O,5 (t) is the actual concentration of dissolved oxygen, S O,set (t) is the set value of dissolved oxygen concentration, which is set in accordance with the charter of the International Water Quality Association; ③ Calculate the time derivative of dissolved oxygen concentration tracking error for: in is the derivative of the set value of dissolved oxygen concentration; define the symbol q(z O (t)) is: ④Construct asymmetric barrier Lyapunov candidate function: There are two constants η1 and η2 that satisfy the condition -η1≤z NO (t)≤η2, η1 and η2 are predefined parameters; ⑤ Derivatives of asymmetric Lyapunov functions have to: in is the difference between the current value and the expected optimal value of the width value, center value, weight value, and saturation processing value; It is the current width value, center value, weight value, and saturation processing value of the identifier each time it goes through a loop iteration; It is the expected optimal width value, center value, weight value, and saturation processing value obtained after the identifier undergoes cyclic iterative structural adjustment. They will be obtained after the identifier structure stops adjusting when the maximum correlation entropy is 1 or greater than the threshold J5; is the adaptive rate of width value, center value, weight value, and saturation processing value; in addition, the variable and ⑥The dynamic nonlinear equation of the sewage treatment process can be defined as follows: Based on the recognition ability of self-organizing fuzzy neural network, unknown dynamic function Can be replaced by in is the current actual output value of the normalization layer of the fuzzy neural network after the structure and parameters are adjusted, are constants obtained by the identifier during the identification process. They will be obtained after the identifier structure stops adjusting when the maximum correlation entropy is 1 or greater than the threshold J5; define the variable in It is the result of subtracting the actual rule layer output value at each iteration from the expected rule layer output after the identifier structure adjustment is completed; is the actual rule layer output value at each iteration; then formula (12) is rewritten as: There exists Young's inequality: in is any non-zero constant; ⑦ Then substitute formula (16) into (15) to obtain ⑧ Order in and They are The first and second values ​​of the matrix, and They are The first and second values ​​of the matrix, and They are The first and second values ​​of the matrix; then Carry out Taylor expansion, we can get: in are the higher-order terms of the Taylor expansion. ⑨Then design the controller input: Where k1 is the controller coefficient, is the actual weight of the identifier at each iteration, is the actual rule layer output value of the identifier at each iteration, ε1 = 1; The four adaptive rates are designed as: Where a1, b1, c1, δ1 are adaptive rate coefficients, which are fixed constants; (3) Design of reflux pump controller: ①Saturation processing of the control signal: Q c (t)=γ 21 v NO (t)+γ 22 (v NO (t)) (24) where v NO (t) is the input signal of the controller, function γ 21 is an arbitrary non-zero constant, the function v mn is the maximum input signal allowed by the controller, π=3.14, x can be any non-zero real number; ② Calculate the dissolved oxygen concentration tracking error as: z NO (t)=S NO,2 (t)-S NO,set (t) (25) Where S NO,2 (t) is the actual concentration of nitrate nitrogen in the second zone; S NO,set (t) is the desired set point for nitrate-nitrogen concentration; ③Construct asymmetric barrier Lyapunov candidate function: in, If z NO (t)>0, then q(z NO (t))=1; if z NO (t)≤0, then q(z NO (t))=0; there are two constants η3 and η4 that can satisfy the condition -η3≤z NO (t)≤η4, η3 and η4 are predefined parameters; ④ Derivative of asymmetric Lyapunov function have to: in is the difference between the current value and the expected optimal value of the width value, center value, weight value, and saturation processing value; It is the current width value, center value, weight value, and saturation processing value of the identifier each time it goes through a loop iteration; It is the expected optimal width value, center value, weight value, and saturation processing value obtained after the identifier undergoes cyclic iterative structural adjustment. They will be obtained after the identifier structure stops adjusting when the maximum correlation entropy is 1 or greater than the threshold J5; is the adaptive rate of width value, center value, weight value, and saturation processing value; in addition, the variable and ⑤ Based on self-organizing fuzzy neural network, dynamic nonlinear equation R NO (t) as follows in is the current actual output value of the normalization layer of the fuzzy neural network after the structure and parameters are adjusted, are constants obtained by the identifier during the identification process. They will be obtained after the identifier structure stops adjusting when the maximum correlation entropy is 1 or greater than the threshold J5; define the variable in It is the result of subtracting the actual rule layer output value at each iteration from the expected rule layer output after the identifier structure adjustment is completed; is the actual rule layer output value at each iteration; ⑥According to Young's inequality, we can further obtain: in is any non-zero constant; ⑦Then design the controller input: The corresponding four adaptation rates are designed as: Where k2 is the controller coefficient, is the actual weight of the identifier at each iteration, is the actual rule layer output value of the identifier at each iteration, ε2=1; a2, b2, c2, δ2 are adaptive rate coefficients, which are fixed constants; (4) The identifier parameters of the aeration pump are set as: r =0.6, the upper limit of the growth threshold of the relevant entropy preset rule J 11 =0.995, related entropy preset rule growth threshold lower limit J 12 =0.6, related entropy preset rule deletion threshold J 13 =0.99995, rule layer activation intensity threshold J 14 =0.2, stop updating the threshold J 15 =0.999995, The identifier parameters of the reflux pump are set as: r =0.6, the upper limit of the growth threshold of the relevant entropy preset rule J 21 =0.995, related entropy preset rule growth threshold lower limit J 22 =0.6, related entropy preset rule deletion threshold J 23 =0.99995, rule layer activation intensity threshold J 24 =0.2, stop updating the threshold J 25 =0.999995, The controller parameters are set as follows: k1=8, k2=1995, ε1=1, ε2=1, a1=0.1, b1=0.1, c1=0.1, δ1=0.1, a2=0.1, b2=0.1, c2=0.1, δ2=0.1, η1=0.01, η2=0.02, η3=0.03, η4=0.04.

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