A multi-equipment fault-tolerant optimal control method for urban sewage treatment process based on specified performance

Abstract

The present invention provides a multi-device fault-tolerant optimal control method for an urban sewage treatment process based on specified performance, which solves the problem of reduced equipment operating capacity and sewage purification efficiency due to actuator failures in the sewage treatment process. By accurately controlling the parameters in the sewage treatment process, the equipment is ensured to operate with optimal energy efficiency. First, a specified performance control method based on error transformation is introduced to achieve stable tracking control of the controller during the treatment process. Secondly, a fault-tolerant control method based on fault approximation is adopted to solve the problem of unknown faults of aeration pumps and peristaltic pumps. Then, a neural network optimal controller is constructed to improve the control accuracy while ensuring the minimum energy consumption of equipment operation. Finally, the steady-state and transient performance of the system are analyzed, and the optimality and effectiveness of the control system are verified.

Description

Technical Field

[0001] The present invention is applied to the process of urban sewage treatment, based on the specified performance constraints, taking into account the accuracy and energy consumption of the controller, and realizing the optimal control of multiple devices. Background Art

[0002] With the rapid advancement of industrialization and urbanization, sewage treatment has become a huge challenge facing the world. The efficient, energy-saving and environmentally friendly operation mode of the sewage treatment industry is of great significance to the coordinated development of the economy, society and environment. Sewage treatment involves: (1) nitrification and denitrification reactions. (2) The continuous changes in the equipment operating environment. (3) Inevitable actuator failures. (4) Strong disturbances in influent flow and pollutant load. Therefore, it is urgent to develop reliable and efficient fault-tolerant optimal control solutions for urban sewage treatment process equipment to provide strong guarantees for the sustainable development of the energy economy.

[0003] Actuator failure is a common phenomenon in actual industrial applications. Generally speaking, actuator failures can be divided into two categories, namely, failure failures and bias failures, which often lead to system performance degradation and instability. Therefore, designing a fault-tolerant control method for actuator failure problems can maintain the normal operation of the system. In the control process of actual engineering fields, the designed control schemes often need to meet the transient and steady-state performance specified by the system. Therefore, it is necessary to design a strategy to meet the expected control performance of sewage treatment plant equipment to cope with the negative effects of environmental changes and actuator failures. The constraint control method based on the specified performance can achieve the expected tracking control performance through error transformation and ensure the stable operation of the system. In addition, the control mechanism based on long-term tracking error update can obtain more stable control performance in the sewage treatment process. Therefore, introducing reinforcement learning into the controller can reduce energy consumption while ensuring control accuracy. Summary of the invention

[0004] This paper designs a fault-tolerant optimal controller based on specified performance to achieve stable tracking control in the sewage treatment process. First, the specified performance constraint method based on error transformation is used to achieve the stable tracking control problem in the sewage treatment process. Secondly, the fault-tolerant method based on error approximation is considered in the design process to solve the problem of unknown actuator failure in the control of aeration pumps and peristaltic pumps. Then, an optimal controller based on the judgment-execution network structure is designed to ensure the effluent quality and energy consumption. Finally, the stability of the sewage treatment process system is demonstrated using the Lyapunov stability analysis theory. The superiority of the controller is proved by comparison with other methods.

[0005] Step 2.1: Determine the control system dynamics model:

[0006] In order to more intuitively describe the dynamic characteristics of the sewage treatment process, the kinetic model is as follows:

[0007]

[0008] and:

[0009]

[0010] 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 area of ​​the biochemical reaction pool, 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, Q c (t) is the internal reflux flow, Q q (t), q = 1, 2, 4, 5 is the flow rate of the ith pool, V5 = 1333 m 3 is the volume of the fifth zone biochemical reaction pool, V2 = 1333m 3 is the volume of the second zone biochemical reaction pool, S O,S =8g / m 3 is the dissolved oxygen concentration saturation value, μ H =4 is the maximum specific growth rate of heterotrophic bacteria, η g =0.8 is the correction factor for heterotrophic growth, k O =0.2 is the saturation coefficient of aerobic respiration of heterotrophic bacteria, k NO =0.5 is the nitrate nitrogen saturation coefficient of heterotrophic bacteria.

[0011] Step 2.2: Determine the aeration pump controller:

[0012] In order to ensure that the controller meets the specified performance requirements during the sewage treatment process, a controller design based on the error conversion function method is proposed. The error conversion variable of dissolved oxygen concentration is designed as follows:

[0013]

[0014] Where tan(·) is the tangent function. To simplify the formula, the constrained term Ξ1(t) is defined as:

[0015]

[0016] The function and For z O (t) boundary, π is the circumference of a circle, l o1 , lu1 , s1, ω1 are positive constants, and l u1 ∈(0.5,1],l o1 ∈(0,0.5],s1∈(0,1],ω1∈(0,2]. Tracking error z O (t) = S O,5 (t)-S O,set (t), S O,set (t) is the set value of dissolved oxygen concentration. The recommended setting range is [1.8,2.2].

[0017] Then, the time derivative of formula (4) can be obtained:

[0018]

[0019] To simplify the formula, the constant term G1(t) after error conversion is defined as:

[0020]

[0021] Define the actual error coefficient g after error conversion ψ1 (t) is:

[0022]

[0023] Then the derivative of the error Rewritten as:

[0024]

[0025] The final value of the fault It will be iteratively calculated in the subsequent control design process, and the fault change value is the current identification value. There is an unknown constant satisfy Unknown constant It will be obtained in the subsequent design. κ1(t)∈(0,1] represents the effectiveness of equipment control, and v1(t) is the aeration pump controller, which will be obtained in the subsequent control design process.

[0026] 1. Design a cumulative error approximation strategy based on the judgment network

[0027] In the iterative learning phase, by providing rewards or penalties to the judgment network, the current control strategy can be adjusted according to the error between the expected and actual operating cost functions. The long-term cost function is defined as follows

[0028]

[0029] Where ζ1>0 represents the constant for calculating the future loss function, τ1 is the integral term, and its value range is [t,∞). The instantaneous cost function is expressed as:

[0030]

[0031] Due to its self-learning ability, a fuzzy neural network consisting of a neural network and fuzzy logic is introduced to approximate the long-term cost function:

[0032]

[0033] in The final weight of the network (obtained when the network stops adjusting) value), F1(t) is the output value of the rule layer of the fuzzy neural network, To judge the final approximate error value of the network boundary, the current judgment network identification output function ∈1(t) is the approximate error value of the current judgment network boundary, x p1 (t) = [η O (t) Δη O (t)] T is the input value of the judgment network, Δη O (t) is the conversion error change rate of dissolved oxygen concentration, is the current evaluation network weight, c pr1 (t) and σ pr1 (t) are the center value and width value of the evaluation network respectively, P1=2 is the total number of neurons in the evaluation network input layer, R1=6 is the total number of neurons in the evaluation network membership layer and rule layer, and the evaluation network output layer is 1.

[0034] The estimated error of the function is defined as:

[0035]

[0036] As time accumulates, t goes from 0 to ∞, then the constant ζ1 of the future loss function will go from 0 to ∞ in a linear relationship. Therefore, the cost function for judging the network at time t is defined as:

[0037]

[0038] in is η O Therefore, the weight update rule of the evaluation network is designed as

[0039]

[0040] Where 0<b1<1 is the learning rate.

[0041] 2. Design an adaptive optimal controller based on execution network identification

[0042] Consider the following Lyapunov function:

[0043]

[0044] The execution network weight changes are: To execute the final weight of the network (obtained when the network stops adjusting ), To execute the current weight of the network, the fault estimation function changes Estimating the current value of a function Used to estimate

[0045] The time derivative of formula (15) is:

[0046]

[0047] In the wastewater treatment process, the unknown nonlinear dynamics can be determined by the execution network:

[0048]

[0049] Where F2(t) is the output of the execution network rule layer composed of fuzzy neural network. is the final approximate error value of the execution network boundary, F2(t) is the rule layer output of the fuzzy neural network, x p2 (t) = [η O (t) Δη O (t)] T Input value for executing network, currently executing network identification output function ∈2(t) is the approximate error of the current execution network boundary, c pr2 (t) and σ pr2 (t) is the center value and width value of the execution network, P2=2 is the total number of neurons in the input layer of the execution network, R2=6 is the total number of neurons in the membership layer and rule layer of the execution network, and the output layer of the execution network is 1.

[0050] Combining formula (17) and formula (18), we can get:

[0051]

[0052] According to Young's inequality, we have:

[0053]

[0054]

[0055] in yes is the maximum bound of , which is a nonzero constant.

[0056] Then we can further get:

[0057]

[0058] The inputs to the aeration pump controller are designed to be:

[0059]

[0060] The controller executes the network weight adaptive law and the fault adaptive law, respectively, which are designed as:

[0061]

[0062]

[0063] Where γ1 is the control coefficient, κ 1 is a 0≤ κ The constant 1<κ1(t)<1, 0<b2<1 and 0<a1<1 are the learning rates.

[0064] Based on formulas (14), (22)-(24), and Young's inequality, formula (21) can be rewritten as:

[0065]

[0066] According to the gradient descent algorithm, the following inequality can be obtained:

[0067]

[0068] The bias function And n1(t) is bounded, that is, the norm ||n1(t)||≤n 1,max , n 1,max is a non-zero constant and m1(t) is a bias function.

[0069] From formula (21), we can get:

[0070]

[0071] Substituting formulas (27) and (28) into formula (26), and using Young's inequality again, ||·|| represents the second norm of the corresponding function, we can obtain:

[0072]

[0073] in

[0074]

[0075] Proof: Multiply both sides of formula (28) by And integrate over [0,t]

[0076]

[0077] Therefore, based on formulas (28) and (31), we know that V O The boundedness of (t) is achieved, which means that η O (t) and is bounded. is bounded, so and The boundedness of can also be obtained. In addition, since S O,set (t) is known and bounded, we can get S O,5 (t) is also bounded. According to the above analysis and the expression of v1(t) in formula (22), the controller input v1(t) is bounded. In addition, based on the above analysis, the transformation error η of dissolved oxygen concentration can also be obtained. O (t) is bounded, proving that the tracking error z O (t) can satisfy the constraints. Therefore, the transient performance is guaranteed. By selecting appropriate parameters, the tracking error z O (t) converges to the neighborhood of zero, which means that the steady-state performance is guaranteed.

[0078] Step 2.3: Identify the peristaltic pump controller:

[0079] Based on formulas (4) and (6), the tracking transformation error of nitrate nitrogen concentration is obtained as:

[0080]

[0081] To simplify the formula, the constrained term Ξ2(t) is defined as:

[0082]

[0083] The function and For z NO (t) boundary, π is the circumference of a circle, l o2 , l u2 , s2, ω2 are positive constants, and l u2 ∈(0.5,1],l o2 ∈(0,0.5],s2∈(0,1],ω2∈(0,2]. Tracking error z NO (t) = S NO,2 (t)-S NO,set (t), S NO,set(t) is the set value of nitrate nitrogen concentration. The recommended setting range is [0.75,1.25].

[0084] Taking the time derivative of formula (32), we get:

[0085]

[0086]

[0087]

[0088] Where G2(t) is the constant term after error conversion, g ψ2 (t) is the actual error coefficient after error conversion, the final value of the fault It will be iteratively calculated in the subsequent control design process, and the fault change value is the current identification value. There is an unknown constant satisfy Unknown constant It will be obtained in the subsequent design. κ2(t) represents the effectiveness of equipment control, ranging from (0,1]. 1. Design a cumulative error approximation strategy based on the judgment network.

[0089] The long-term loss function of nitrate nitrogen concentration is defined as:

[0090]

[0091] Where ζ2>0 represents the constant for calculating the future loss function. As time accumulates, t changes from 0→∞, then ζ2 will change from 0→∞ in a linear relationship. τ2 is the integral term, and its value range is [t,∞). The instantaneous cost function is expressed as:

[0092]

[0093] The long-term cost function is approximated by a fuzzy neural network:

[0094]

[0095] in To judge the final network weight (the network stops adjusting when the value), F3(t) is the rule layer output of the fuzzy neural network, To judge the final approximate error value of the network boundary, the current judgment network output function ∈3(t) is the approximate error value of the current judgment network boundary, is the current evaluation network weight, x p3 (t) = [η NO (t) Δη NO(t)] T is the input value of the judgment network, Δη NO (t) is the conversion error change rate of nitrate nitrogen concentration, c pr3 (t) and σ pr3 (t) is the network center value and width value, P3=2 is the total number of neurons in the input layer of the network, R3=6 is the total number of neurons in the membership layer and rule layer of the network, and the output layer of the network is 1.

[0096] The estimated error of the function can be described as:

[0097]

[0098] in To e NO The gradient of (t). Let the effective function of the evaluation network be The weight update rule of the evaluation network is designed as:

[0099]

[0100] Where 0<b3<1 is the learning rate.

[0101] 2. Design an adaptive optimal tracking controller based on execution network identification.

[0102] Consider the following Lyapunov function:

[0103]

[0104] The execution network weight changes are: To execute the final weight of the network (obtained when the network stops adjusting ), To execute the current weight of the network, the fault estimation function changes Estimating the current value of a function Used to estimate

[0105] Taking the time derivative of formula (42), we get:

[0106]

[0107] In the wastewater treatment process, the dynamic nonlinear equations can be identified by executing the network:

[0108]

[0109] Where F4(t) is the output of the execution network rule layer composed of fuzzy neural network. To execute the final approximate error value of the network boundary, the current execution network identification output function ∈4(t) is the approximate error value of the current execution network boundary, x p4 (t) = [η NO (t) Δη NO (t)] T Input value for executing the network, Δη NO (t) is the conversion error change rate of nitrate nitrogen concentration, c pr4 (t) and σ pr4 (t) is the center value and width value of the execution network, P=2 is the total number of neurons in the input layer of the execution network, R=6 is the total number of neurons in the membership layer and rule layer of the execution network, and the output layer of the execution network is 1.

[0110] According to formulas (43), (44) and Young’s inequality, we can further obtain:

[0111]

[0112] in Is for The maximum value of is a non-zero constant.

[0113] The input to the peristaltic pump controller is designed to be:

[0114]

[0115] The controller executes the network weight adaptive law and the fault adaptive law, respectively, which are designed as:

[0116]

[0117]

[0118] Where γ2 is the control coefficient, F4(t) is the rule layer output of the fuzzy neural network, κ 2 is a 0≤ κ 2<κ2(t)<1, 0<b4<1 and 0<a2<1 are the learning rates.

[0119] According to the gradient descent algorithm, we can get:

[0120]

[0121] The bias function And n2(t) is bounded, that is, ||n2(t)||≤n 2,max , n 2,max is a non-zero constant and m2(t) is a bias function.

[0122] From formula (41), we can get:

[0123]

[0124] Based on formulas (43), (48)-(50), formula (47) can be transformed into

[0125]

[0126] in

[0127]

[0128]

[0129] Proof: Multiply both sides of formula (51) by And the integral over [0,t].

[0130]

[0131] Therefore, based on formulas (50) and (54), we know that V NO The boundedness of (t) is achieved, which means that η NO (t) and is bounded. is bounded, so and The boundedness of can also be obtained. In addition, since S NO,set (t) is known and bounded, we can get S NO,2 (t) is also bounded. According to the above analysis and the expression of v2(t) in formula (45), the controller input v2(t) is bounded. In addition, based on the above analysis, the transformation error η of nitrate nitrogen concentration can also be obtained NO (t) is bounded, proving that the tracking error z NO (t) can satisfy the constraints. Therefore, the transient performance is guaranteed. By selecting appropriate parameters, the tracking error z NO (t) converges to the neighborhood of zero, which means that the steady-state performance is guaranteed.

[0132] Step 2.4: Control performance evaluation

[0133] In order to fairly evaluate the control performance, the integrated square error (ISE), integrated absolute error (IAE) and maximum absolute error (Dev m ) as the evaluation index.

[0134]

[0135]

[0136] Dev m =max{|S(t)-Sd (t)|} (57)

[0137] Where U is the total number of samples, S(t) is the dissolved oxygen concentration S O,5 (t) or nitrate nitrogen concentration S NO,2 (t) value, S d (t) is the set value of dissolved oxygen concentration S O,set (t) or nitrate nitrogen concentration setting value S NO,set The value of (t). BRIEF DESCRIPTION OF THE DRAWINGS

[0138] Figure 1 Schematic diagram of fault-tolerant optimal controller

[0139] Figure 2 Aeration pump control result diagram under condition 1

[0140] Figure 3 Peristaltic pump control result diagram under condition 1

[0141] Figure 4 Change diagram of aeration pump and peristaltic pump control variables under condition 1

[0142] Figure 5 Aeration pump control result diagram under situation 2

[0143] Figure 6 Peristaltic pump control result diagram under situation 2

[0144] Figure 7 Change diagram of aeration pump and peristaltic pump control variables under situation 2 DETAILED DESCRIPTION

[0145] (1) Case 1: Fixed setpoint tracking control

[0146] The simulation experiment was carried out on a sunny day, with the tracking setting value of dissolved oxygen concentration being 2 mg / L and the tracking setting value of nitrate nitrogen concentration being 1 mg / L.

[0147] In order to prove the superiority of the designed PFOFC control method, it is compared with fuzzy neural network (FNN) control, proportional integral derivative (PID) control and adaptive dynamic programming (ADP) control. Using the same BSM1 system parameters, the control results of different control methods are shown in Figure 2. Figures 2 to 4 The variation trend of dissolved oxygen concentration is shown in Figure (2A), and the tracking error of the aeration pump controller is shown in Figure (2B). At the same time, the variation trend of nitrate nitrogen concentration is shown in Figure (3A), and the tracking error of the peristaltic pump controller is shown in Figure (3B). It can be seen that PFOFC has better control accuracy than FNN, PID and ADP. Oxygen transfer coefficient K La5(t) is shown in Figure (4A), the internal reflux flow Q c (t) is shown in Figure (4B), it can be seen that PFOFC can achieve better steady-state and transient tracking performance. Therefore, the proposed PFOFC can guarantee the original control performance in the presence of actuator faults.

[0148] (2) Case 2: Dynamic setpoint tracking control

[0149] A simulation experiment was conducted under heavy rain weather, and the dissolved oxygen concentration (S O,set (t)) and nitrate (S NO,set The dynamic set points of (t)) concentration are as follows:

[0150] For S O,set (t): When 0≤t<3, its value is 2.0mg / L; when 3≤t<6, the value becomes 2.1mg / L; when 6≤t<8, the value returns to 2.0mg / L; when 8≤t<10, the value drops to 1.9mg / L; when 10≤t<14, the value continues to drop to 1.8mg / L.

[0151] For S NO,set (t): When 0≤t<3, its value is 1.0mg / L; when 3≤t<6, the value becomes 1.2mg / L; when 6≤t<8, the value drops to 1.1mg / L; when 8≤t<10, the value continues to drop to 0.9mg / L; when 10≤t<14, the value drops to 0.8mg / L.

[0152] The simulation results of the four methods, PFOFC, FNN, ADP and PID, in BSM1 are compared. Figure 5-7 The trend of dissolved oxygen concentration is shown in Figure (5A), and the tracking error of the aeration pump controller is shown in Figure (5B). At the same time, the trend of nitrate nitrogen concentration is shown in Figure (6A), and the tracking error of the peristaltic pump controller is shown in Figure (6B). Oxygen transfer coefficient K L The variation of a5(t) is shown in Figure (7A). The internal reflux flow Q c The variation of (t) is shown in Figure (7B). The results show that the PFOFC method can achieve the smallest convergence range and better control accuracy.

Claims

1. A multi-device fault-tolerant optimal control method for a municipal sewage treatment process based on specified performance, characterized in that the steps are as follows: 1.1 Determine the control system dynamics model: In order to intuitively describe the dynamic characteristics of the sewage treatment process, the kinetic model is as follows: and: 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 area of ​​the biochemical reaction pool, 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, Q c (t) is the internal reflux flow, Q q (t), q = 1, 2, 4, 5 is the flow rate of the ith pool, V5 = 1333 m 3 is the volume of the fifth zone biochemical reaction pool, V2 = 1333m 3 is the volume of the second zone biochemical reaction pool, S O,S =8g / m 3 is the dissolved oxygen concentration saturation value, μ H =4 is the maximum specific growth rate of heterotrophic bacteria, η g =0.8 is the correction factor for heterotrophic growth, k O =0.2 is the saturation coefficient of aerobic respiration of heterotrophic bacteria, k NO =0.5 is the saturation coefficient of heterotrophic nitrate nitrogen; 1.2 Determine the aeration pump controller: In order to ensure that the controller meets the specified performance requirements during the sewage treatment process, a controller design based on the error conversion function method is proposed; the error conversion variable of the dissolved oxygen concentration is designed as follows: Where tan(·) is the tangent function. To simplify the formula, the constrained term Ξ1(t) is defined as: The function and For z O (t) boundary, π is the circumference of a circle, l o1 , l u1 , s1, ω1 are positive constants, and l u1 ∈(0.5,1],lo1 ∈(0,0.5],s1∈(0,1],ω1∈(0,2];tracking error z O (t) = S O,5 (t)-S O,set (t), S O,set (t) is the set value of dissolved oxygen concentration. The recommended setting range is [1.8, 2.2]; Then, the time derivative of formula (4) is: To simplify the formula, the constant term G1(t) after error conversion is defined as: Define the actual error coefficient g after error conversion ψ1 (t) is: Then the derivative of the error Rewritten as: The final value of the fault It will be iteratively calculated in the subsequent control design process, and the fault change value is the current identification value; there is an unknown constant satisfy Unknown constant It will be obtained in the subsequent design; κ1(t)∈(0,1] represents the effectiveness of equipment control, and v1(t) is the aeration pump controller, which will be calculated in the subsequent control design process; 1) Design a cumulative error approximation strategy based on the judgment network In the iterative learning phase, the current control strategy is adjusted according to the error between the expected and actual operating cost functions by providing rewards or penalties to the judgment network; the long-term cost function is defined as follows Where ζ1>0 represents the constant for calculating the future loss function, τ1 is the integral term, and its value range is [t,∞); the instantaneous cost function is expressed as: Due to its self-learning ability, a fuzzy neural network consisting of a neural network and fuzzy logic is introduced to approximate the long-term cost function: in To finally judge the weight of the network, the network stops adjusting and gets The value of; F1(t) is the output value of the rule layer of the fuzzy neural network, To judge the final approximate error value of the network boundary, the current judgment network identification output function ∈1(t) is the approximate error value of the current judgment network boundary, x p1 (t) = [η O (t) Δη O (t)] T is the input value of the judgment network, Δη O (t) is the conversion error change rate of dissolved oxygen concentration, is the current evaluation network weight, c pr1 (t) and σ pr1 (t) are the center value and width value of the evaluation network, P1=2 is the total number of neurons in the evaluation network input layer, R1=6 is the total number of neurons in the evaluation network membership layer and rule layer, and the evaluation network output layer is 1; The estimated error of the function is defined as: As time accumulates, t goes from 0 to ∞, then the constant ζ1 of the future loss function will go from 0 to ∞ in a linear relationship; therefore, the cost function for judging the network at time t is defined as: in is η O (t); therefore, the weight update rule of the evaluation network is designed as Where 0<b1<1 is the learning rate; 2) Design an adaptive optimal controller based on execution network identification Consider the following Lyapunov function: The execution network weight changes are: To implement the final weight of the network, the network stops adjusting and obtains The value of To execute the current weight of the network, the fault estimation function changes Estimating the current value of a function Used to estimate The time derivative of formula (15) is: In the wastewater treatment process, the unknown nonlinear dynamics are determined by the execution network: Where F2(t) is the output of the execution network rule layer composed of fuzzy neural network. is the final approximate error value of the execution network boundary, F2(t) is the rule layer output of the fuzzy neural network, x p2 (t) = [η O (t) Δη O (t)] T Input value for executing network, currently executing network identification output function ∈2(t) is the approximate error value of the current execution network boundary, c pr2 (t) and σ pr2 (t) is the center value and width value of the execution network, P2=2 is the total number of neurons in the input layer of the execution network, R2=6 is the total number of neurons in the membership layer and rule layer of the execution network, and the output layer of the execution network is 1; Combining formula (17) and formula (18), we get: According to Young's inequality, we have: in yes The maximum limit value of , which is a non-zero constant; Then further get: The inputs to the aeration pump controller are designed to be: The controller executes the network weight adaptive law and the fault adaptive law, respectively, which are designed as: Where γ1 is the control coefficient, κ1 is a constant 0≤κ1<κ1(t)<1, 0<b2<1 and 0<a1<1 are the learning rates; Based on formulas (14), (22)-(24), and Young's inequality, formula (21) can be rewritten as: According to the gradient descent algorithm, we get the following inequality: The bias function And n1(t) is bounded, that is, the norm ||n1(t)||≤n 1,max , n 1,max is a non-zero constant, m1(t) is a bias function; From formula (21), we get: Substituting formulas (27) and (28) into formula (26), and using Young's inequality again, where ||·|| represents the second norm of the corresponding function, we obtain: in 1.3 Determine the peristaltic pump controller: Based on formulas (4) and (6), the tracking transformation error of nitrate nitrogen concentration is obtained as: To simplify the formula, the constrained term Ξ2(t) is defined as: The function and For z NO (t) boundary, π is the circumference of a circle, l o2 , l u2 , s2, ω2 are positive constants, and l u2 ∈(0.5,1],l o2 ∈(0,0.5],s2∈(0,1],ω2∈(0,2];tracking error z NO (t) = S NO,2 (t)-S NO,set (t), S NO,set (t) is the set value of nitrate nitrogen concentration. The recommended setting range is [0.75,1.25]; Taking the time derivative of formula (32), we get: Where G2(t) is the constant term after error conversion, g ψ2 (t) is the actual error coefficient after error conversion, the final value of the fault It will be iteratively calculated in the subsequent control design process, and the fault change value is the current identification value; there is an unknown constant satisfy Unknown constant It will be obtained in the subsequent design; κ2(t) represents the effectiveness of equipment control, ranging from (0,1]; 1) Design a cumulative error approximation strategy based on the judgment network; The long-term loss function of nitrate nitrogen concentration is defined as: Where ζ2>0 represents the constant for calculating the future loss function. As time accumulates, t changes from 0→∞, then ζ2 will change from 0→∞ in a linear relationship; τ2 is the integral term, and its value range is [t,∞); the instantaneous cost function is expressed as: The long-term cost function is approximated by a fuzzy neural network: in To finally judge the network weight, the network stops adjusting and gets The value of; F3(t) is the rule layer output of the fuzzy neural network, To judge the final approximate error value of the network boundary, the current judgment network output function ∈3(t) is the approximate error value of the current judgment network boundary, is the current evaluation network weight, x p3 (t) = [η NO (t) Δη NO (t)] T is the input value of the judgment network, Δη NO (t) is the conversion error change rate of nitrate nitrogen concentration, c pr3 (t) and σ pr3 (t) is the central value and width value of the evaluation network, P3=2 is the total number of neurons in the evaluation network input layer, R3=6 is the total number of neurons in the evaluation network membership layer and rule layer, and the evaluation network output layer is 1; The estimated error of the function is described as: in To e NO (t) gradient; let the judgment network effective function The weight update rule of the evaluation network is designed as: Where 0<b3<1 is the learning rate; 2) Design an adaptive optimal tracking controller based on execution network identification; Consider the following Lyapunov function: The execution network weight change is To execute the final weight of the network (obtained when the network stops adjusting ), To execute the current weight of the network, the fault estimation function changes Estimation function current value Used to estimate Taking the time derivative of formula (41), we get: In the wastewater treatment process, the dynamic nonlinear equations are identified by executing the network: Where F4(t) is the output of the execution network rule layer composed of fuzzy neural network. To execute the final approximate error value of the network boundary, the current execution network identification output function ∈4(t) is the approximate error value of the current execution network boundary, x p4 (t) = [η NO (t) Δη NO (t)] T Input value for executing the network, Δη NO (t) is the conversion error change rate of nitrate nitrogen concentration, c pr4 (t) and σ pr4 (t) is the center value and width value of the execution network, P = 2 is the total number of neurons in the input layer of the execution network, R = 6 is the total number of neurons in the membership layer and rule layer of the execution network, and the output layer of the execution network is 1; According to formulas (42), (43) and Young's inequality, we can further obtain: in Is for The maximum value of is a non-zero constant; The input to the peristaltic pump controller is designed to be: The controller executes the network weight adaptive law and the fault adaptive law, respectively, which are designed as: Where γ2 is the control coefficient, F4(t) is the rule layer output of the fuzzy neural network, κ 2 is a 0≤ κ 2<κ2(t)<1 is a constant, 0<b4<1 and 0<a2<1 are learning rates; According to the gradient descent algorithm, we get: The bias function And n2(t) is bounded, that is, ||n2(t)||≤n 2,max , n 2,max is a non-zero constant, m2(t) is a bias function; From formula (40), we get: Based on formulas (42), (47)-(49), formula (46) is transformed into in 1.4 The parameters are set as follows: 1) The aeration pump controller evaluation network parameter values ​​are set as follows: The initial weight value is Learning rate b1 = 0.1, width value σ = [3.8, 3.3, 4.3, 4.6, 5.4, 4.2; -7.1, -5.3, -4.6, -3.8, 6.2, -6.8], center value c = [-0.1, -0.2, -0.3, -0.4, -0.6, -0.7; -0.6, -0.4, -0.3, -0.2, -0.5, -0.4]; the aeration pump controller execution network parameter values ​​are set as follows: the initial weight value is Learning rate b2 = 0.1, width value σ = [3.8, 3.3, 4.3, 4.6, 5.4, 4.2; -7.1, -5.3, -4.6, -3.8, -6.2, 6.8], center value c = [-0.1, -0.2, -0.3, -0.4, -0.6, -0.7; -0.6, -0.4, -0.3, -0.2, -0.5, -0.4], fault κ1(t) = 0.78 + 0.22sin(t), learning rate a1 = 0.1; controller parameters: γ1 = 365; 2) The parameters of the reflux pump controller evaluation network are set as follows: The initial weight value is Learning rate b3 = 0.1, width value σ = [3.8, 3.3, 4.3, 4.6, 5.4, 4.2; -7.1, -5.3, -4.6, -3.8, -6.2, 6.8], center system c = [-0.4, -0.6, -0.7, -0.4, -0.9, -0.5; -0.4, -0.8, -0.6, -0.7, -0.4, -0.9]; the execution network parameter values ​​of the reflux pump controller are set as follows: the initial value of the weight is Learning rate b4=0.1, width value σ=[3.8,3.3,4.3,4.6,-5.44.2;-7.1,-5.3,-4.6,-3.8,-6.2,-6.8], center value c=[-0.1,-0.2,-0.3,-0.4,-0.6,-0.7;-0.6,-0.4,-0.3,-0.2,-0.5,-0.4], fault κ2(t)=0.82+0.18sin(t), learning rate a2=0.1; controller parameters: γ2=395.

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