Self-adaptive neural network control method for sewage treatment process with time-varying asymmetric constraint

Abstract

The invention provides a sewage treatment process adaptive neural network control method with time-varying asymmetric constraints, is used for a sewage treatment process with unknown parameters, and belongs to the technical field of urban sewage treatment process intelligent control. A controller is designed by adopting a self-adaptive control method, and the concentration of dissolved oxygen and the concentration of nitrate nitrogen in the sewage treatment process are accurately controlled. Firstly, due to the fact that the fuzzy neural network has excellent robustness, unknown dynamics appearing in a sewage treatment plant can be effectively approached. Secondly, control input is designed by constructing a time-varying asymmetric obstacle type Lyapunov function, and a fault-tolerant control method is designed in consideration of an actuator fault condition. And finally, performing a simulation experiment by using the reference simulation model 1, and verifying the effectiveness of the proposed method by a simulation result.

Description

Technical Field

[0001] The present invention belongs to the research field of sewage treatment process control, and particularly relates to a sewage treatment process constraint control method for realizing asymmetric constraint control of multiple variables. Background Art

[0002] Municipal sewage treatment plants are complex dynamic systems involving intertwined and interacting physical, chemical, and biological processes. One of the most common and effective biological sewage treatment methods is the activated sludge process, which operates based on the anaerobic / anoxic / aerobic (A 2 / O) process. The biochemical reactor based on the anaerobic / anoxic / aerobic (A 2 / O) process has a unique structure, including an anaerobic tank, an anoxic tank, and three aerobic tanks. The anaerobic tank and the anoxic tank create an anoxic environment where some microorganisms carry out specific metabolic reactions. For example, denitrifying bacteria use nitrate nitrogen to remove nitrogen. The aerobic tanks provide oxygen to meet the needs of aerobic microorganisms, and the respiration of these aerobic microorganisms can decompose organic pollutants, which is very important for reducing the biochemical oxygen demand (BOD) and chemical oxygen demand (COD). Therefore, maintaining appropriate dissolved oxygen concentration and nitrate nitrogen concentration plays an extremely crucial role. Among them, the dissolved oxygen concentration in the fifth tank and the nitrate nitrogen concentration in the second tank are the most important controlled variables in the sewage treatment process and are also the key factors affecting the efficiency of municipal sewage treatment plants. Moreover, the dissolved oxygen concentration is regulated by the oxygen transfer coefficient, and the nitrate nitrogen concentration is regulated by the internal circulation return flow rate. Summary of the Invention

[0003] The object of the present invention is to achieve good control of the dissolved oxygen concentration and nitrate nitrogen concentration during the sewage treatment process. The present invention proposes a sewage treatment process control method. The sewage treatment process is based on a biochemical reactor, including five sequentially connected reaction tanks. The first reaction tank is an anaerobic tank, the second reaction tank is an anoxic tank, and the third to fifth reaction tanks are all aerobic tanks;

[0004] Design the control input υ O and the adaptation rate to control the dissolved oxygen concentration S o,5 (t) in the fifth reaction tank;

[0005] Design the control input υ NO and the adaptation rate to control the nitrate nitrogen concentration S no,2 (t) in the second reaction tank.

[0006] Furthermore, establish an equivalent model for the dissolved oxygen concentration and nitrate nitrogen concentration in the kth reaction tank:

[0007]

[0008] Among them, k = 2, 5 are the second reaction tank and the fifth reaction tank. In the first equation of formula (1), k = 5, and in the second equation, k = 2; S o,k (t) is the dissolved oxygen concentration in the k-th reaction tank, S no,k (t) is the nitrate nitrogen concentration in the k-th reaction tank, S o,S (t) is the saturated dissolved oxygen concentration, Q k (t) is the flow rate of the k-th reaction tank, V k is the volume of the k-th reaction tank, γ k is the biological reaction rate of the k-th reaction tank, K La,k is the oxygen transfer rate of the k-th reaction tank, Q A (t) is the external circulation flow rate, Q a (t) is the internal circulation return flow rate;

[0009] Furthermore, the process of designing the control input υ O and the adaptation rate of the dissolved oxygen concentration in the fifth reaction tank is as follows:

[0010] Step 1.1, design the error variable of the dissolved oxygen concentration in the fifth reaction tank as:

[0011] e o (t) = S o,5 (t) - S o,set (t) (2)

[0012] S o,5 (t) represents the dissolved oxygen concentration in the fifth reaction tank, S o,set (t) is the set value of the dissolved oxygen concentration;

[0013] Step 1.2, construct the time-varying asymmetric Lyapunov function V D (t), as follows:

[0014]

[0015] Among them, p1 is a positive constant, is the estimated value of the ideal weight of the first fuzzy neural network , is the estimation error, and satisfies Λ1 is a constant gain matrix to be designed, and satisfies

[0016] θ a1 and θ b1 are time-varying barrier functions, defined as:

[0017]

[0018] q O (e o ) is defined as

[0019]

[0020] θ a1 , and θ b1 are all constants and satisfy and

[0021] Introduce the error coordinate transformation as follows:

[0022]

[0023] According to the definition in (6), the time-varying asymmetric Lyapunov function V D (t) is further written as:

[0024]

[0025] Step 1.3, define an unknown function P O (E1) as

[0026]

[0027] where, is the input vector of the first fuzzy neural network, V5 represents the volume of the 5th reaction tank, Q4(t) represents the flow rate of the 4th reaction tank, Q5(t) represents the flow rate of the 5th reaction tank, and γ5 is the biological reaction rate of the 5th reaction tank;

[0028] Use the first fuzzy neural network to approximate P O (E1) as

[0029]

[0030] where, is the approximation error and satisfies S(t) is the Gaussian basis function vector of the first neural network, is the ideal weight of the first fuzzy neural network, represents the maximum value of;

[0031] Step 1.4, the derivative of the time-varying asymmetric Lyapunov function V D (t) with respect to time is expressed as:

[0032]

[0033] Among them,

[0034] Step 1.5, the control input υ of the dissolved oxygen concentration O and the adaptation rate are designed as

[0035]

[0036] Among them, μ1, ο1, and φ1 are all positive parameters, and there exists

[0037] Furthermore, considering the actuator fault, the oxygen transfer rate K of the fifth reaction tank is designed La,5 , expressed as:

[0038] K La,5 (t) = ε1(t ε,1 , t)υ O +τ1(t τ,1 , t) (13)

[0039] Among them, υ O is the control input of the dissolved oxygen concentration;

[0040] ε1(t ε,1 , t) represents the "health index" of the dissolved oxygen concentration control, reflecting the effectiveness of the aeration equipment;

[0041] τ1(t τ,1 , t) represents the uncertain control partition where the aeration equipment is completely out of control;

[0042] t ε,1 represents the moment when the additive fault occurs in the aeration equipment;

[0043] t τ,1 represents the moment when the fault occurs in the aeration equipment;

[0044] Furthermore, the derivative of the time-varying asymmetric Lyapunov function with respect to time is written as:

[0045]

[0046] Furthermore, the control input υ of the nitrate nitrogen concentration in the second reaction tank and the adaptation rate NO and the adaptation rate The process is as follows:

[0047] Step 2.1, calculate the error variable of the nitrate nitrogen concentration as:

[0048] eno S(t) = S no,2 S(t) - S no,set S(t)(15)

[0049] where S no,set (t) is the set value of the nitrate nitrogen concentration, and S no,2 (t) is the concentration of nitrate nitrogen in the second reaction tank, obtaining as follows:

[0050]

[0051] Step 2.2, design the unknown function P NO (E2), defined as:

[0052]

[0053] is the input vector of the second fuzzy neural network, V2 represents the volume of the second reaction tank, Q2(t) represents the flow rate of the second reaction tank, Q1(t) represents the flow rate of the first reaction tank, and γ2 is the biological reaction rate of the second reaction tank;

[0054] By using the second fuzzy neural network, the unknown function P NO (E2) is approximated as:

[0055]

[0056] where is a constant function representing the approximation error of the second fuzzy neural network, and D(t) is the Gaussian basis function vector of the second fuzzy neural network, is the optimal weight of the second fuzzy neural network, satisfying the error is the estimated value of;

[0057] Step 2.3, define the Lyapunov function of the nitrate nitrogen concentration as:

[0058]

[0059] where, if e no > 0, then q NO (e no ) = 1, if e no ≤ 0, then q NO (e no ) = 0, p2 is a positive constant, Λ2 is a constant gain matrix, and satisfies the condition θ no,a2 and θ no,b2 are time-varying barrier functions, and the following definitions are given:

[0060]

[0061] Among them, θ no,a2 , and θ no,b2 are constants and satisfy and

[0062] Step 2.4, the derivative of the Lyapunov function V N (t) becomes:

[0063]

[0064] Among them,

[0065] Step 2.5, design the control input υ NO and the corresponding adaptation rate as:

[0066]

[0067] Among them, μ2, ο2, and φ2 are all positive parameters, and ο2 > 0 and Furthermore, considering the case of reflux equipment failure, the derivative of the Lyapunov function becomes:

[0068]

[0069] Furthermore, considering the case of actuator failure, design the internal loop reflux flow rate Q a (t), let

[0070] Q a (t) = ε2(t ε,2 , t)υ NO + τ2(t τ,2 , t) (25)

[0071] Among them, υ NO is the control input of the nitrate nitrogen concentration,

[0072] ε2(t ε,2 , t) represents the "health index" of the nitrate nitrogen concentration control, reflecting the effectiveness of the reflux equipment;

[0073] τ2(t τ,2 , t) represents the uncertain control partition of the complete out-of-control of the reflux equipment;

[0074] tε,2 Indicates the moment when an additive failure occurs in the reflux device;

[0075] t τ,2 Indicates the moment when a failure occurs in the reflux device.

[0076] Beneficial effects:

[0077] 1. For the sewage treatment process with strong nonlinearity, strong uncertainty, and complex time-varying characteristics, this invention approximates the unknown function by using a fuzzy neural network during the design process;

[0078] 2. This invention considers potential actuator failure problems for the reflux device and aeration device in the sewage treatment plant and proposes a fault-tolerant method that can effectively eliminate the impact of faults;

[0079] 3. This invention uses a time-varying asymmetric barrier Lyapunov function to ensure that the dissolved oxygen concentration and nitrate nitrogen concentration always meet the constraint boundary conditions and remain within the specified constraint range. By designing the dynamic ideal set concentration, the control strategy can more closely match the actual operation requirements of the sewage treatment plant. Description of the drawings

[0080] Figure 1 is a schematic diagram of this invention for the sewage treatment process;

[0081] Figure 2 is the tracking trajectory diagram of the dissolved oxygen concentration of this invention;

[0082] Figure 3 is the control tracking error diagram of the dissolved oxygen concentration of this invention;

[0083] Figure 4 is the trajectory diagram of the oxygen transfer coefficient of this invention;

[0084] Figure 5 is the tracking trajectory diagram of the nitrate nitrogen concentration of this invention;

[0085] Figure 6 is the control tracking error diagram of the nitrate nitrogen concentration of this invention;

[0086] Figure 7 is the trajectory diagram of the internal circulation return flow rate of this invention. Detailed implementation manners

[0087] As Figure 1 shown, the sewage treatment process includes a primary treatment stage, a secondary treatment stage, and a tertiary treatment stage. In the secondary treatment stage, based on anaerobic / anoxic / aerobic (A 2The biochemical reactor of the / O) process includes five reaction tanks connected in sequence, an anaerobic tank, an anoxic tank, and three aerobic tanks; the 1st reaction tank is an anaerobic tank, the 2nd reaction tank is an anoxic tank, and the 3rd to 5th reaction tanks are all aerobic tanks. The method of the present invention is used in the secondary treatment stage;

[0088] The self - adaptive neural network control method for sewage treatment process with time - varying asymmetric constraints of the present invention includes the following steps:

[0089] Step 1: Select a fuzzy neural network as an identifier to identify the unknown variables in the sewage treatment process. The fuzzy neural network includes an input layer, a membership function layer, a rule layer, and an output layer.

[0090] Regarding the uncertain factors existing in the sewage treatment process, define the unknown functions P O (E1) and P NO (E2), and use two fuzzy neural networks to approximate the unknown functions P O (E1) and P NO (E2) respectively. Each fuzzy neural network consists of four layers;

[0091] The first layer: the input layer, which is used for data transmission. This layer consists of n neurons, representing the number of input variables in the fuzzy neural network. The formula of the input layer is:

[0092] s i (t) = x i (t) (26)

[0093] where i = 1, 2, …, n, s i (t) is the output of the i - th neuron in the input layer, and the output variable is x(t)=[x1(t), x2(t)] Τ ;

[0094] The second layer: the membership function layer, which is used for fuzzifying the input. The membership function layer consists of p neurons, and the Gaussian function is selected as the membership function. The output of the j - th neuron in the membership function layer is:

[0095]

[0096] where j = 1, 2, …, p, c ij (t) and σ ij (t) are the center and width of the i - th membership function of the j - th neuron respectively;

[0097] The third layer: the rule layer, which is used to define fuzzy rules and calculate the normalized value of the output. The rule layer includes p neurons, and the formula for the output of the l - th neuron in the rule layer is:

[0098]

[0099] where \(l = 1, 2, \ldots, p, v\) l \((t)\) represents the \(l\)-th output;

[0100] The fourth layer: the output layer, which is used for defuzzification and outputting the exact value. The weighted factor method is adopted, and its formula is:

[0101]

[0102] In summary, the output of the fuzzy neural network can be expressed as

[0103]

[0104] where \(W(t)=[w_1(t), w_2(t), \ldots, w\) l \((t)]\) Τ is the weight matrix connecting the rule layer and the output layer, and \(v(t)=[v_1(t), v_2(t), \ldots, v\) l \((t)]\) Τ is the normalized output vector of the rule layer, representing the rule activation intensity. \(w\) l \((t)\) represents the connection weight between the \(l\)-th neuron in the rule layer and the neuron in the output layer, and \(y\) q \((t)\) represents the output of the fuzzy neural network;

[0105] In a sewage treatment plant, unexpected actuator failures may occur during the long-term operation of equipment. Consider the following actuator anomaly model:

[0106] \(u\) i \(=\varepsilon\) i \((t\) ε,i ,t)\(\upsilon+\tau\) i \((t\) τ,i ,t) (31)

[0107] where \(i = 1, 2\), \(u\) represents the actual input, \(\upsilon\) represents the designed control input, \(\varepsilon(t\) ε,i ,t)\) is the "health index", which reflects the effectiveness of the actuator, and \(\tau\) i \((t\) τ,i ,t)\(\in R\) is the completely out-of-control uncertain control partition, and \(t\) ε,i represents the moment when the additive actuator failure occurs, and \(t\) τ,i represents the moment when the actuator failure occurs. \(\varepsilon\) i \((\cdot)\) and \(\tau\) i \((\cdot)\) are unknown time-varying functions but are bounded. \(\varepsilon\) i and are two positive constants that satisfy \(0\lt\varepsilon\) i \lt\varepsilon\) i \((t\)ε,i , t) ≤ 1 and

[0108] Step 2: Establish an equivalent model for the aeration process and the denitrification process

[0109] Establish an equivalent model for the dissolved oxygen concentration and the nitrate nitrogen concentration:

[0110]

[0111] In the formula, k = 2, 5 are the second reaction tank and the fifth reaction tank, S o,k (t) is the concentration of dissolved oxygen in the k-th reaction tank, S no,k (t) is the concentration of nitrate nitrogen in the k-th reaction tank, S o,S (t) is the saturation concentration of dissolved oxygen, Q k (t) is the flow rate of the k-th reaction tank, V k is the volume of the k-th reaction tank, γ k is the biological reaction rate of the k-th reaction tank, K La,k is the oxygen transfer rate of the k-th reaction tank, Q A (t) is the external circulation flow rate, Q a (t) is the internal circulation return flow rate. In the mechanism model of the sewage treatment system, as Figure 1 shown, the internal circulation refers to the circulation of the mixed liquid flowing back from the aerobic tank to the anoxic tank. The external circulation is the sludge circulation flowing back from the secondary sedimentation tank to the anaerobic tank or the anoxic tank.

[0112] The key variables in the sewage treatment process are the nitrate nitrogen concentration S no,2 (t) in the second reaction tank and the dissolved oxygen concentration S o,5 (t) in the fifth reaction tank, S o,5 (t) and S no,2 (t) are the key factors affecting the performance of the urban sewage treatment plant. The oxygen transfer rate K La,5 in the fifth reaction tank and the internal circulation return flow rate Q a (t) are the operating variables.

[0113] Step 3: Design the time-varying asymmetric constraint control input for the aeration process

[0114] Step 3.1: Design the error variable e o (t) for the dissolved oxygen concentration as: e o (t) = S o,5 (t) - S o,set (t), where S o,set (t) is the set value of the dissolved oxygen concentration.

[0115] Step 3.2: Construct the following time-varying asymmetric Lyapunov function V D(t):

[0116] where p1 is a positive constant, is the estimated value of the ideal weight of the fuzzy neural network , is the estimation error and satisfies Λ1 is a constant gain matrix to be designed and satisfies

[0117] Step 3.3: θ a1 and θ b1 are time-varying barrier functions defined as:

[0118]

[0119] and q O (e o ) is defined as

[0120]

[0121] θ a1 , and θ b1 are both constants and satisfy and

[0122] Step 3.4: Introduce the following error coordinate transformation:

[0123]

[0124] According to the definition in (36), the time-varying asymmetric Lyapunov function V D (t) is further written as:

[0125]

[0126] Step 3.5: Define an unknown function P O (E1) as

[0127]

[0128] where is the input vector.

[0129] Step 3.6: Use the fuzzy neural network to approximate P O (E1) as

[0130]

[0131] where is the approximation error and satisfies S(t) is a Gaussian function vector, and the input layer of the fuzzy neural network consists of 2 neurons.

[0132] Step 3.7: Differentiate Equation (12), the derivative of the Lyapunov function Obtain:

[0133]

[0134] where

[0135] Step 3.8: Considering the case of aeration equipment failure, the designed operating variable oxygen transfer rate K La,5 (t) is:

[0136] K La,5 (t) = ε1(t ε,1 , t)υ O + τ1(t τ,1 , t) (41)

[0137] where υ O is the control input of the dissolved oxygen concentration, ε1(t ε,1 , t) and τ1(t τ,1 , t) are two variables. There is the Young's inequality:

[0138]

[0139] Step 3.9: The control input υ O of the dissolved oxygen concentration and the adaptation rate are designed as:

[0140]

[0141] where μ1, μ1, ο1 and φ1 are all positive parameters, and μ1 = μ1·ε1, there is

[0142] Parameters such as the weights of the fuzzy neural network can be part of the controller parameters. The fuzzy neural network is selected as the identifier, and the adaptation rate determines the speed and manner of updating the identifier parameters. Since the fuzzy neural network needs to continuously adjust its own parameters to adapt to the changes in complex working conditions, and the adjustment of the adaptation rate will directly affect the change of the controller parameters, thus affecting the control input.

[0143] The design adaptation rate is to enhance the flexibility and robustness of the control system, enabling it to dynamically adjust control parameters according to real-time data, thereby coping with uncertainties and external disturbances in the system. The adaptation rate can optimize control performance, ensure the best control effect under different working conditions, and improve the stability and reliability of the system. Especially in complex and variable environments, such as sewage treatment systems, it can automatically adapt and maintain efficient and stable operation.

[0144] Step 4: Design the time-varying asymmetric constraint control input for the denitrification process

[0145] Step 4.1: Calculate the error variable e of the nitrate nitrogen concentration no (t) = S no,2 (t) - S no,set (t), where S no,set (t) is the set value of the nitrate nitrogen concentration, and S no,2 (t) is the actual output value of the nitrate nitrogen concentration control, obtaining as:

[0146]

[0147] Step 4.2: The unknown function P NO (E2) is defined as:

[0148]

[0149] where, is the input vector.

[0150] Step 4.3: By using a fuzzy neural network, the unknown function is approximated as:

[0151]

[0152] where, is a constant function, and D(t) is a vector of Gaussian basis functions, is the optimal weight of the fuzzy neural network, satisfying the error is the estimated value of, and the input layer of the fuzzy neural network consists of 2 neurons.

[0153] Step 4.4: Define the Lyapunov function V N (t) as:

[0154]

[0155] where, if e no > 0, then q NO (e no ) = 1, if e no≤ 0, then q NO (e no ) = 0. p2 is a positive constant, Λ2 is a constant gain matrix, and satisfies the condition θ no,a2 and θ no,b2 are time-varying barrier functions, and the following definitions are given:

[0156]

[0157] Among them, θ no,a2 , and θ no,b2 are constants and satisfy and

[0158] Step 4.5: The derivative of V N (t) becomes:

[0159]

[0160] Among them,

[0161] Step 4.6: Considering the case of reflux equipment failure, becomes:

[0162]

[0163] Considering the case of actuator failure, let Q a (t) = ε2(t ε,2 , t)υ NO + τ2(t τ,2 , t), where υ NO is the control input of nitrate nitrogen concentration, ε2(t ε,2 , t) and τ2(t τ,2 , t) are two variables.

[0164] Step 4.7: Using Young's inequality, the following inequality is obtained:

[0165]

[0166] Step 4.8: Design the control input υ NO and the corresponding adaptation rate as:

[0167]

[0168] Among them, μ2 and φ2 are both positive parameters, and ο2 > 0 and

[0169] On the benchmark simulation No. 1 model, with dry and rainy weather as the background, dynamic set-point tracking control is carried out on the dissolved oxygen concentration and nitrate nitrogen concentration in the sewage treatment process. The initial set value of the dynamic set-point of the dissolved oxygen concentration is S o,set (t) = 2.05 + 0.05sin(t), that is, in the range of 2mg / L to 2.1mg / L, and the set range of fluctuations is 1.98mg / L to 2.13mg / L. The dynamic set-point of the nitrate nitrogen concentration is the initial set value of S no,set (t) = 1 + 0.1cos(t), that is, in the range of 0.9mg / L to 1.1mg / L, and the set dynamic range is 0.87mg / L to 1.13mg / L.

[0170] The present invention designs an adaptive fuzzy neural network method using fault-tolerant control for the sewage treatment process, so that the sewage treatment system can still control the dissolved oxygen concentration and nitrate nitrogen concentration well in the case of possible actuator failures, and ensure that all closed-loop signals in the system are bounded and do not violate the time-varying asymmetric constraint range.

[0171] The present invention focuses on the adaptive constraint control problem in the nonlinear sewage treatment process. When the complex and dynamic sewage treatment process faces actuator failures and controller overloads, it can effectively cope with time-varying unknown disturbances and harsh working conditions, meeting the actual needs and solving control problems.

[0172] Figures 2 - 7 The simulation results using the control method are shown. Figure 2 It shows that the output of the dissolved oxygen concentration control can well track the desired signal and does not exceed the time-varying asymmetric constraint boundary under different working conditions, where the different working conditions refer to the dry condition and the rainy condition. In addition, considering that the aeration equipment may fail, the proposed fault-tolerant control method can compensate for the failure to ensure the stability of the dissolved oxygen concentration control system. The tracking error results of the dissolved oxygen concentration are as Figure 3 shown, indicating that under the control of the constraint method of the present invention, the errors under different working conditions are small. The change trajectory of the oxygen transfer coefficient is as Figure 4 shown. Figure 5 It shows that the nitrate nitrogen concentration can effectively track the set output that dynamically fluctuates with time and does not exceed the designed time-varying asymmetric constraint range. In addition, considering that the reflux equipment may fail, the proposed fault-tolerant control method can compensate for the failure, thereby ensuring the stable operation of the nitrate nitrogen concentration control system. The error trajectory of the nitrate nitrogen concentration is as Figure 6 shown, and the error is small when the constraint control method is adopted under different weather conditions with large fluctuations. The trajectory of the internal circulation return flow is as Figure 7As shown. Thus, the simulation experiment verifies the effectiveness of the proposed method under dry and rainy conditions.

Claims

1. A sewage treatment process control method, characterized in that, The sewage treatment process is based on a biochemical reactor, including five reaction pools connected in sequence. The first reaction pool is an anaerobic pool, the second reaction pool is an anoxic pool, and the third to fifth reaction pools are all aerobic pools. Control input υ for the dissolved oxygen concentration of the fifth reaction tank O and the adaptation rate to control the dissolved oxygen concentration S o,5 (t) in the fifth reaction tank; Control input υ for the nitrate nitrogen concentration in the second reaction tank NO and the adaptation rate to control the nitrate nitrogen concentration S no,2 (t) in the second reaction tank.

2. The method for controlling a sewage treatment process according to claim 1, wherein, Establish an equivalent model for the dissolved oxygen concentration and nitrate nitrogen concentration in the k-th reaction pool: Among them, k = 2, 5 are the second reaction tank and the fifth reaction tank. k = 5 in the first equation of formula (1), and k = 2 in the second equation; S o,k (t) is the dissolved oxygen concentration in the k-th reaction tank, S no,k (t) is the nitrate nitrogen concentration in the k-th reaction tank, S o,S (t) is the saturated dissolved oxygen concentration, Q k (t) is the flow rate of the k-th reaction tank, V k is the volume of the k-th reaction tank, γ k is the biological reaction rate of the k-th reaction tank, K La,k is the oxygen transfer rate of the k-th reaction tank, Q A (t) is the external circulation flow rate, Q a (t) is the internal circulation return flow rate.

3. The method for controlling a sewage treatment process according to claim 1, wherein Control input υ for the dissolved oxygen concentration of the fifth reaction tank in the design O and the adaptation rate The process is as follows: Step 1.1, design the error variable of the dissolved oxygen concentration in the fifth reaction pool as: e o e(t) = S o,5 e(t) - S o,set e(t) (2) S o,5 S(t) represents the dissolved oxygen concentration in the fifth reaction tank o,set S(t) is the set value of the dissolved oxygen concentration; Step 1.2, construct a time-varying asymmetric Lyapunov function \(V \) D (t) as follows: where p1 is a positive constant, is the estimated value of the ideal weight of the first fuzzy neural network , is the estimation error and satisfies Λ1 is a constant gain matrix to be designed and satisfies θ a1 and θ b1 are time-varying barrier functions, defined as: q O (e o ) is defined as θ a1 , and θ b1 are all constants and satisfy and Introduce the following error coordinate transformation: According to the definition in (6), the time-varying asymmetric Lyapunov function V D (t) is further written as: Step 1.3, define an unknown function P O (E1) is Among them, is the input vector of the first fuzzy neural network, V5 represents the volume of the 5th reaction tank, Q4(t) represents the flow rate of the 4th reaction tank, Q5(t) represents the flow rate of the 5th reaction tank, and γ5 is the biological reaction rate of the 5th reaction tank; Use the first fuzzy neural network to approximate P O (E1) is wherein, is the approximation error and satisfies S(t) is the Gaussian basis function vector of the first neural network, is the ideal weight of the first fuzzy neural network, denotes the maximum value of; Step 1.4, the derivative of the time-varying asymmetric Lyapunov function V D (t) with respect to time is expressed as: Among them, Step 1.5, control input υ of dissolved oxygen concentration O and adaptation rate are designed as Among them, μ1, ο1, and φ1 are all positive parameters, and there exists 4. The method for controlling a sewage treatment process according to claim 1, characterized in that, Considering the actuator failure, design the oxygen transfer rate K of the fifth reaction tank La,5 , expressed as: K La,5 (t) = ε1(t ε,1 , t)υ O + τ1(t τ,1 , t) (13) where υ O is the control input of the dissolved oxygen concentration; ε1(t ε,1 ,t) represents the "health index" for dissolved oxygen concentration control, reflecting the effectiveness of the aeration equipment; τ1(t τ,1 , t) represents the uncertain control partition where the aeration equipment is completely out of control; t ε,1 Indicates the moment when an additive fault occurs in the aeration equipment; t τ,1 Indicates the moment when the aeration equipment failure occurs.

5. The method for controlling a sewage treatment process according to claim 3, wherein The derivative of the time-varying asymmetric Lyapunov function with respect to time It can be further written as:

6. The method for controlling a sewage treatment process according to claim 1, wherein The control input υ of the nitrate nitrogen concentration in the second reaction tank of the design NO and the adaptation rate The process is as follows: Step 2.1, calculate the error variable of the nitrate nitrogen concentration as: e no S(t) = S no,2 S(t) - S no,set S(t)(15) Among them, S no,set (t) is the set value of the nitrate nitrogen concentration, and S no,2 (t) is the concentration of nitrate nitrogen in the second reaction tank, and it is obtained that as follows: Step 2.2, design the unknown function P NO (E2), which is defined as: is the input vector of the second fuzzy neural network, V2 represents the volume of the second reaction tank, Q2(t) represents the flow rate of the second reaction tank, Q1(t) represents the flow rate of the first reaction tank, and γ2 is the biological reaction rate of the second reaction tank; By using a second fuzzy neural network, the unknown function P NO (E2) is approximated as: Among them, is a constant function, representing the approximation error of the second fuzzy neural network, and D(t) is the Gaussian basis function vector of the second fuzzy neural network, is the optimal weight of the second fuzzy neural network, satisfying the error is the estimated value of Step 2.3, define the Lyapunov function of the nitrate nitrogen concentration as: where, if e no > 0, then q NO (e no ) = 1, if e no ≤ 0, then q NO (e no ) = 0, p2 is a positive constant, Λ2 is a constant gain matrix, and satisfies the condition θ no,a2 and θ no,b2 are time-varying barrier functions, and the following definitions are given: Among them, θ no,a2 , and θ no,b2 are constants and satisfy and Step 2.4, the derivative of the Lyapunov function V N (t) becomes: Among them, Step 2.5, design the control input υ NO and the corresponding adaptation rate as follows: wherein, μ2, ο2, and φ2 are all positive parameters, and ο2 > 0 and 7. The method for controlling a sewage treatment process according to claim 6, characterized in that, Considering the case of the reflux equipment failure, the derivative of the Lyapunov function becomes:

8. The method for controlling a sewage treatment process according to claim 6, wherein, Considering the case of actuator failure, the internal circulation reflux flow rate Q a (t) is designed, and let Q a (t) = ε2(t ε,2 , t) υ NO + τ2(t τ,2 , t) (25) where υ NO is the control input of the nitrate nitrogen concentration, ε2(t ε,2 , t) represents the "health index" for controlling the nitrate nitrogen concentration, reflecting the effectiveness of the reflux device; τ2(t τ,2 , t) represents the uncertain control partition of the complete out-of-control of the reflux device; t ε,2 Indicates the moment when an additive failure occurs in the reflux device; t τ,2 Indicates the moment when the reflux equipment failure occurs.

9. The method for controlling a sewage treatment process according to claim 3 or 6, characterized in that, The structures of the first fuzzy neural network and the second fuzzy neural network are the same, both including an input layer, a membership function layer, a rule layer, and an output layer connected in sequence.

10. The method for controlling a sewage treatment process according to claim 3 or 6, characterized in that, The number of neurons in the rule layer of the two fuzzy neural networks is set to 7; The experimental parameters for dissolved oxygen concentration control are set as follows: the volume of the second reaction tank V2 = 1000 m 3 , and the set value of the dissolved oxygen concentration is S o,set (t) = 2.05 + 0.05sin(t). The parameters of the control input are designed as μ1 = 3590, p1 = 3, and φ1 = 500. The adaptive rate parameters are set as ο1 = 0.1 and Λ1 = 0.

5. The constraint bounds are designed as θ c1 (t) = 2 - 0.02sin(-t) and The parameters of the actuator fault are designed as ε1(t ε,1 ,t) = 0.6 - 0.2sin(2t) and τ1(t τ,1 ,t) = 22.8sin(0.3t) + 0.3; The experimental parameter settings for nitrate nitrogen concentration control are as follows: the parameters of the control input are designed as μ2 = 9896, p2 = 4, and φ2 = 2000, the parameters of the adaptation rate are set as ο2 = 0.1 and Λ2 = 0.3, and the constraint bounds are designed as θ c2 (t) = 0.9 + 0.03cos(-t) and The nitrate nitrogen concentration is set to S no,set (t) = 1 + 0.1cos(t), and the parameters of the actuator fault are designed as ε2(t ε,2 ,t) = 0.8 + 0.1cos(3t) and τ2(t τ,2 ,t) = 30830cos(t) + 10060.

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