Dissolved oxygen concentration robust fault-tolerant control method in urban sewage treatment process
By constructing a dissolved oxygen concentration control system, designing a nonlinear observer and fuzzy neural network, and combining it with a robust fault-tolerant controller based on adaptive dynamic programming, the problem of dissolved oxygen concentration deviation caused by actuator failure and external disturbances is solved, and stable control of the urban sewage treatment process is achieved.
Patent Information
- Application Number
- CN202510825823.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-19
- Publication Date
- 2025-09-16
AI Technical Summary
Existing technologies are unable to effectively deal with the problem of dissolved oxygen concentration deviating from the set value caused by actuator failure and external disturbances during urban sewage treatment, especially in complex and changing environments, where it is difficult to achieve accurate dissolved oxygen concentration control.
A dissolved oxygen concentration control system is constructed. A nonlinear observer is designed to estimate actuator failures and external disturbances. A fuzzy neural network is used to estimate unknown nonlinear functions. A robust fault-tolerant controller is designed through adaptive dynamic programming. The neural network parameters are updated in combination with the experience replay method to achieve stable control of dissolved oxygen concentration.
The system achieves stable control of dissolved oxygen concentration in the presence of actuator failure and external disturbance, thereby improving the operating efficiency of the urban sewage treatment process and the rate of compliance of effluent water quality.
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Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of urban sewage treatment, and in particular relates to a robust fault-tolerant control method for dissolved oxygen concentration in an urban sewage treatment process. Background Art
[0002] With the acceleration of urbanization, water shortage and water pollution are becoming increasingly serious. The urban sewage treatment process, mainly based on the activated sludge method, plays a positive role in solving water pollution problems and is of great significance to alleviating water shortage. In the sewage treatment process, dissolved oxygen concentration is a key control parameter for maintaining the metabolic activity of microorganisms. Its stable control directly affects the compliance of effluent water quality standards and system operation efficiency. However, due to the complex and changeable environment of the urban sewage treatment process and the long-term operation of equipment in harsh environments, the actuator (aeration pump) is prone to failure, which leads to insufficient oxygen supply, causing the dissolved oxygen concentration to deviate from the set value, making it difficult to achieve precise tracking control. In addition, external disturbances inevitably affect the urban sewage treatment process, further increasing the difficulty of controlling the dissolved oxygen concentration.
[0003] As an advanced intelligent control technology for industrial processes, adaptive dynamic programming has been widely used in fault-tolerant control of nonlinear systems. However, wastewater treatment processes involve complex biological, chemical, and physical reactions, exhibiting more complex dynamic characteristics and significant time-varying and uncertainties. This makes it difficult for existing fault-tolerant control methods based on adaptive dynamic programming to directly address these challenges. Summary of the Invention
[0004] The object of the present invention is to provide a method for robust fault-tolerant control of dissolved oxygen concentration in a municipal sewage treatment process, aiming to solve the technical problems existing in the prior art identified in the background technology.
[0005] The present invention is implemented as follows: a method for robust fault-tolerant control of dissolved oxygen concentration in a municipal sewage treatment process, comprising:
[0006] (1) Constructing a dissolved oxygen concentration control system
[0007] Establish a dynamic model of the dissolved oxygen concentration control system with actuator failure and external interference:
[0008] x(k+1)=f(x(k))+g(x(k))(u(k)+w(k))+d(k)
[0009] Where x(k+1) represents the dissolved oxygen concentration at time k+1, x(k) represents the dissolved oxygen concentration at time k, f(x(k)) represents the unknown nonlinear function at time k, g(x(k)) represents the coefficient of the control input at time k, u(k) represents the control input of the oxygen transfer coefficient at time k, w(k) represents the fault input of the oxygen transfer coefficient at time k, and d(k) represents the external disturbance at time k.
[0010] (2) Estimation of actuator failure and external disturbance
[0011] Construct a nonlinear observer:
[0012]
[0013] in, represents the estimated value of x(k+1) at time k+1, e o (k) represents the estimated error of x(k) at time k, f(x(k)) represents the estimated value of the unknown nonlinear function at time k, represents the estimated value of d(k) at time k, represents the estimated value of ρ(k) at time k, k1(e o (k)) represents the state observation coefficient at time k, k2(e o (k)) represents the fault observation coefficient at time k, k3(e o (k)) represents the disturbance observation coefficient at time k.
[0014] (3) Fuzzy neural network estimation of nonlinear functions
[0015] The output expression of the fuzzy neural network is:
[0016]
[0017] Among them, T represents the transpose of the matrix, α l (k) represents the lth input of the fuzzy neural network model at time k, ω r (k) represents the connection weight between the rth regular layer neuron and the output layer neuron of the fuzzy neural network model at time k, c lr (k) represents the central value of the rth radial base layer neuron corresponding to the lth input layer neuron of the fuzzy neural network model at time k, σ lr (k) represents the width of the rth radial base layer neuron corresponding to the lth input layer neuron of the fuzzy neural network model at time k, b represents the number of input layer neurons of the fuzzy neural network model, a represents the number of radial base layer neurons and rule layer neurons of the fuzzy neural network model, ω r (k), c lr (k), σ lr (k) is randomly assigned a value within [0, 1].
[0018] (4) Design a robust fault-tolerant controller
[0019] ①Strategy iteration to find the optimal input:
[0020] Minimize the cost function:
[0021]
[0022] Solve the optimal control input and maximum fault input through strategy iteration;
[0023] Control input at time k+1:
[0024] u(k+1)=u(k)+Δu * (k)
[0025] Δu * (k)=ε * (k)u * (k)+(1-ε * (k))u w * (k)
[0026] ②Neural network implementation:
[0027] Evaluation network:
[0028] Input [α1(k), α2(k), α3(k)] T =[e(k),u i (k), w i (k)] T , output Use the parameter update strategy to update the neural network parameters. The loss function formula is:
[0029] E(k)=1 / 2e c(i) 2 (k)
[0030] Control input execution network: input α1(k)=e(k), each iteration step outputs Use the parameter update strategy to update the neural network parameters. The loss function formula is:
[0031] E(k)=1 / 2e u(i) 2 (k)
[0032] Fault input execution network: input α1(k)=e(k), each iteration step outputs Use parameter update strategies (6)-(8) to update the neural network parameters. The loss function formula is:
[0033] E(k)=1 / 2e w(i)2 (k)
[0034] ③Experience replay update parameters:
[0035] Construct the experience replay area B(k):
[0036] Calculate the data importance index ξ(kj):
[0037]
[0038] Where D(kj) represents the disturbance amplitude of the data sample b(kj) at time k, and δ(kj) represents the time series difference error of the data sample b(kj) at time k;
[0039] Dynamically select the first N(k) groups of data to update network parameters.
[0040] (5) Execute fault-tolerant control
[0041] The control law u(k+1) is used as the input of the oxygen transfer coefficient. The frequency of the inverter is adjusted by the programmable logic controller to control the blower speed to adjust the aeration volume and achieve stable control of the dissolved oxygen concentration.
[0042] The beneficial effects of the present invention are:
[0043] The present invention designs a nonlinear observer to estimate actuator faults and external disturbances, and constructs a fuzzy neural network to estimate unknown nonlinear functions, providing necessary information for the cost function design of a robust fault-tolerant controller based on adaptive dynamic programming.
[0044] To address the problem of dissolved oxygen concentration deviating from the set value due to actuator failure and external disturbances, the present invention designs a robust fault-tolerant control method based on adaptive dynamic programming. By constructing and training an evaluation network and an execution network, and combining an improved experience replay method to select specific data to further update the evaluation network, stable control of dissolved oxygen concentration is achieved. BRIEF DESCRIPTION OF THE DRAWINGS
[0045] Figure 1 is a control result diagram of a set point of dissolved oxygen concentration according to the present invention;
[0046] Figure 2 is a control result error diagram of a set point of dissolved oxygen concentration according to the present invention;
[0047] Figure 3 This is a control result diagram of the dissolved oxygen concentration varying the set point of the present invention;
[0048] Figure 4 It is an error diagram of the control result of the dissolved oxygen concentration changing set point of the present invention. DETAILED DESCRIPTION
[0049] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.
[0050] A robust fault-tolerant control method for dissolved oxygen concentration in a municipal sewage treatment process is disclosed. The method comprises the following steps: constructing a dissolved oxygen concentration control system for a municipal sewage treatment process in the presence of actuator failures and external disturbances; establishing a nonlinear observer to estimate actuator failures and external disturbances; constructing a fuzzy neural network model to estimate unknown nonlinear functions; and designing a robust fault-tolerant controller based on adaptive dynamic programming to achieve fault-tolerant control of dissolved oxygen concentration.
[0051] S1. Construct a dissolved oxygen concentration control system for a municipal sewage treatment process with actuator failure and external interference.
[0052] The dynamic model of the dissolved oxygen concentration control system in the municipal sewage treatment process with actuator failure and external interference is:
[0053] x(k+1)=f(x(k))+g(x(k))(u(k)+w(k))+d(k)
[0054] Where x(k+1) represents the dissolved oxygen concentration at time k+1, x(k) represents the dissolved oxygen concentration at time k, f(x(k)) represents the unknown nonlinear function at time k, g(x(k)) = 8 - x(k) represents the coefficient of the control input at time k, u(k) represents the control input of the oxygen transfer coefficient at time k, w(k) = -ρ(k)u(k) represents the fault input of the oxygen transfer coefficient at time k, ρ(k) represents the actuator fault coefficient at time k, 0 ≤ ρ(k) < 1, and d(k) represents the external disturbance at time k.
[0055] S2. Establish a nonlinear observer to estimate actuator faults and external disturbances
[0056] A nonlinear observer is constructed to estimate the actuator fault coefficient ρ(k) and external disturbance d(k), specifically:
[0057]
[0058] in, represents the estimated value of x(k+1) at time k+1, represents the estimation error of x(k) at time k, f(x(k)) represents the estimated value of the unknown nonlinear function at time k, represents the estimated value of d(k) at time k, represents the estimated value of ρ(k) at time k, k1(e o(k))=2(1.5+Δk0(k)) represents the state observation coefficient at time k, k2(e o (k))=(1.5+Δk0(k))2 represents the fault observation coefficient at time k, k3(e o (k))=(1.5+Δk0(k))2 represents the disturbance observation coefficient at time k, is the increment of k0, is a variable constant;
[0059] S3. Construct a fuzzy neural network model to estimate unknown nonlinear functions
[0060] The input of the fuzzy neural network model is [α1(k),α2(k),…,α b (k)] T , the output expression of the fuzzy neural network model is:
[0061]
[0062] Among them, T represents the transpose of the matrix, α l (k) represents the lth input of the fuzzy neural network model at time k, ω r (k) represents the connection weight between the rth regular layer neuron and the output layer neuron of the fuzzy neural network model at time k, c lr (k) represents the central value of the rth radial base layer neuron corresponding to the lth input layer neuron of the fuzzy neural network model at time k, σ lr (k) represents the width of the rth radial base layer neuron corresponding to the lth input layer neuron of the fuzzy neural network model at time k, b represents the number of input layer neurons of the fuzzy neural network model, a represents the number of radial base layer neurons and rule layer neurons of the fuzzy neural network model, ω r (k), c lr (k), σ lr (k) is randomly assigned a value within [0, 1];
[0063] The parameter updating strategy of the fuzzy neural network model is designed as follows:
[0064]
[0065]
[0066] Among them, E(k) represents the loss function number of the fuzzy neural network at time k;
[0067] The unknown term in the nonlinear observer is estimated using a fuzzy neural network. The number of radial base layer neurons and regular layer neurons in the fuzzy neural network model is a=10, the number of input layer neurons in the fuzzy neural network model is b=6, and the input is [α1(k),α2(k),…,α6(k)] T , where each element is defined as α z (k) = x(k-(z-1))(z = 1, 2, .., 6), which represents the dissolved oxygen concentration at the time k-(z-1). The output is The loss function is in is the estimation error, x d (k) represents the set value of dissolved oxygen concentration at time k;
[0068] S4. Design a robust fault-tolerant controller based on adaptive dynamic programming, specifically:
[0069] ① Design a robust fault-tolerant control law based on the adaptive dynamic programming method, specifically:
[0070] For the robust fault-tolerant control problem, the goal is to find a suitable control input and fault input to minimize the cost function. The cost function is expressed as follows:
[0071]
[0072] Where τ=k,k+1,k+2,… represents any time on and after k;
[0073]
[0074] U(e(k),u(k),w(k))=e T (k)e(k)+u
[0075] T (k)u(k)-w T (k)w(k) is the utility function at time k, e(k)=x(k)-x d (k) is the tracking error of dissolved oxygen concentration at time k;
[0076] According to the Bellman optimality principle, the optimal cost function satisfies the following discrete-time HJB equation:
[0077]
[0078] The optimal control input and the maximum allowed fault input are solved by the following formula:
[0079]
[0080] Construct a policy iterative adaptive dynamic programming framework to solve the optimal control input and the maximum allowed fault input, assuming i=0,1,2,...i max Indicates the number of iteration steps, i max It means that given the maximum number of iteration steps, the iteration process starts from u0(k) = 0 and w0(k) = 0 at each moment to solve the iterative cost function:
[0081]
[0082] Update iterative control input and fault input:
[0083]
[0084] The above iterative process is expressed as
[0085] u0(k),w0(k)→Q0(e(k),u(k),w(k))→u1(k),w1(k)→...→u i (k),w i (k)→Q i+1 (e(k),u(k),w(k))→...
[0086] When || Q i+1 (e(k),u(k),w(k))-Q i (e(k),u(k),w(k))||<10 -3 Or i reaches the maximum number of iterations i max When , stop the iteration and output the approximate optimal control input u*(k) and the maximum allowed fault input w*(k); otherwise, set the iteration step i=i+1, and repeat the above steps to continue the iteration process;
[0087] Therefore, the control input at time k+1 is calculated as follows:
[0088] u(k+1)=u(k)+Δu * (k)
[0089] Δu * (k)=ε * (k)u * (k)+(1-ε * (k))u w * (k)
[0090] in, is the weight coefficient;
[0091] ② Carry out the neural network implementation of strategy iteration adaptive dynamic programming, specifically:
[0092] First, since the cost function cannot be obtained directly, an evaluation network is constructed based on a fuzzy neural network to estimate the cost function. The number of radial base layer neurons and regular layer neurons in the fuzzy neural network model is a=10, the number of input layer neurons in the fuzzy neural network model is b=3, and the input is [α1(k), α2(k), α3(k)] T =[e(k),u i (k),w i (k)] T , the output of each iteration step is Use the parameter update strategy to update the neural network parameters, the loss function E(k) = 1 / 2e c(i) 2 (k), where e c(i) (k) is the estimation error, expressed as follows:
[0093]
[0094] Then, the execution network estimation control input is constructed based on the fuzzy neural network. Let the number of radial base layer neurons and regular layer neurons of the fuzzy neural network model be a=6, the number of input layer neurons of the fuzzy neural network model be b=1, the input is α1(k)=e(k), and the output of each iterative step is Use the parameter update strategy to update the neural network parameters, and the loss function is E(k) = 1 / 2e u(i) 2 (k), where is the estimation error;
[0095] Finally, the execution network is constructed based on the fuzzy neural network to estimate the fault input. Let the number of radial base layer neurons and regular layer neurons of the fuzzy neural network model be a=6, the number of input layer neurons of the fuzzy neural network model be b=1, the input be α1(k)=e(k), and the output of each iteration step be Use parameter update strategies (6)-(8) to update the neural network parameters, and the loss function is E(k) = 1 / 2e w(i) 2 (k), where is the estimation error;
[0096] In the neural network implementation process of iterative adaptive dynamic programming algorithm, when the iterative algorithm meets the convergence requirements, there is and The approximate optimal control input can be obtained and the maximum allowable fault input
[0097] ③ Design an experience replay mechanism to further update the neural network parameters, specifically:
[0098] The experience replay area B(k) is constructed at time k as follows:
[0099] B(k)={b(kM),...,b(k-2),b(k-1)}
[0100] Where M is the size of the experience playback area, b(kj) (j=1,..,M) is the sample at time kj, which is specifically expressed as:
[0101]
[0102] e(kj-1) is the tracking error of the dissolved oxygen concentration at time kj-1, u(kj-1) is the control input of the oxygen transfer coefficient at time kj-1, w(kj-1) is the fault input of the oxygen transfer coefficient at time kj-1, U(kj-1)=U(e(kj-1),u(kj-1),w(kj-1)) is the utility function at time kj-1, represents the estimated value of the disturbance d(kj-1) at time kj-1, e(kj) is the tracking error of the dissolved oxygen concentration at time kj, u(kj) is the control input of the oxygen transfer coefficient at time kj, and w(kj) is the fault input of the oxygen transfer coefficient at time kj;
[0103] Define ξ(kj) as the importance index for evaluating each set of data b(kj) in the experience playback area B(k), specifically:
[0104]
[0105] D(kj) represents the disturbance amplitude of the data sample b(kj) at time k, specifically:
[0106] D(kj)=||e(k)-e(kj)||
[0107] δ(kj) represents the time series difference error of the data sample b(kj) at time k, specifically:
[0108]
[0109] in It is an approximate cost function recalculated by combining e(kj), u(kj) and w(kj) in the data sample b(kj) with the evaluation network parameters at time k;
[0110] The average importance of all data in the experience replay area B(k) is designed to be:
[0111]
[0112] According to ξ avg (k) Dynamically adjust the number of groups of data selected from B(k), specifically:
[0113]
[0114] Among them, N max and N min is the maximum and minimum value of the selected data groups, h max and h min are the maximum and minimum values of the threshold used to adjust N(k), Indicates the rounding symbol; when rounded up, it is N max When the value is forced to N max -1;
[0115] According to the importance index, the data samples of the top N(k) groups in the experience replay area B(k) are stored in a new experience replay area B′(k), which is expressed as follows:
[0116] B'(k)={b(kj)|j∈{τ1,τ2,...,τ N(k)}}
[0117] in, is the historical moment corresponding to the first N(k) groups of data samples of the importance index in B(k), satisfying
[0118] Each time a set of data samples b(kj) is selected from B′(k), the estimation errors of the three networks are calculated as follows:
[0119]
[0120] in, It is calculated by combining e(kj), u(kj) and w(kj) in the data sample b(kj) in B′(k) with the evaluation network parameters at time k. It is calculated by combining e(kj-1), u(kj-1) and w(kj-1) in the data sample b(kj) in B′(k) with the evaluation network parameters at time k;
[0121] Use the parameter update strategy to update the evaluation network and execution network parameters, and the loss functions are E(k)=1 / 2e c 2 (k), E(k)=1 / 2e u 2 (k) and E(k)=1 / 2e w 2(k), and then use the next set of data samples to continue updating the parameters of the evaluation network and the execution network. After N(k) updates, the experience replay process ends, and the approximate optimal cost function at time k is finally obtained. Optimal control input and the maximum allowable fault input
[0122] Finally, calculate the optimal fault-tolerant control law u(k+1) at time k+1;
[0123] S5. Execute fault-tolerant control
[0124] The control law u(k+1) represents the oxygen transfer coefficient required to handle actuator failures and suppress external disturbances at time k+1. The frequency of the inverter is adjusted through a programmable logic controller, and ultimately robust fault-tolerant control of the municipal sewage treatment process is achieved by regulating the dissolved oxygen concentration.
[0125] Figure 1 Displays the tracking control results of the dissolved oxygen concentration set point, X-axis: time, unit is day, Y-axis: dissolved oxygen concentration value, unit is mg / L;
[0126] Figure 2 Displays the error between the actual dissolved oxygen concentration and the set value of dissolved oxygen concentration under the condition of a set set point. X-axis: time, unit is day; Y-axis: dissolved oxygen concentration error value, unit is mg / L.
[0127] Figure 3 Displays the tracking control results of dissolved oxygen concentration changing set point, X axis: time, unit is day, Y axis: dissolved oxygen concentration value, unit is mg / L,
[0128] Figure 4 The error between the actual dissolved oxygen concentration and the set value of dissolved oxygen concentration under the condition of variable set point is displayed. The X-axis is time in days, and the Y-axis is the dissolved oxygen concentration error value in mg / L. The results prove the effectiveness of this method.
[0129] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0130] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.
[0131] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.
Claims
1. A robust fault-tolerant control method for dissolved oxygen concentration in a municipal sewage treatment process, characterized in that: The method comprises: S1. Construct a dissolved oxygen concentration control system for a municipal sewage treatment process with actuator failure and external interference. S2, establish a nonlinear observer to estimate the actuator fault coefficient and external disturbance; S3, construct a fuzzy neural network model to estimate unknown nonlinear functions; S4. Design a robust fault-tolerant controller based on adaptive dynamic programming, including designing control laws, neural network implementation, and experience replay mechanism; S5. Calculate the oxygen transfer coefficient according to the control law, adjust the aeration volume through the programmable logic controller and frequency converter, and control the dissolved oxygen concentration robustly and fault-tolerantly.
2. The method according to claim 1, characterized in that The kinetic model of the dissolved oxygen concentration control system in the municipal sewage treatment process is: x(k+1)=f(x(k))+g(x(k))(u(k)+w(k))+d(k) Where x(k+1) represents the dissolved oxygen concentration at time k+1, x(k) represents the dissolved oxygen concentration at time k, f(x(k)) represents the unknown nonlinear function at time k, g(x(k)) represents the coefficient of the control input at time k, u(k) represents the control input of the oxygen transfer coefficient at time k, w(k) represents the fault input of the oxygen transfer coefficient at time k, and d(k) represents the external disturbance at time k.
3. The method according to claim 1, characterized in that The expression for establishing the nonlinear observer to estimate the actuator fault coefficient and external disturbance is: in, represents the estimated value of x(k+1) at time k+1, represents the estimated value of x(k) at time k, e o (k) represents the estimation error of x(k) at time k, represents the estimated value of the unknown nonlinear function at time k, represents the estimated value of d(k) at time k, represents the estimated value of ρ(k) at time k, κ1(e o (k)) represents the state observation coefficient at time k, κ2(e o (k)) represents the fault observation coefficient at time k, κ3(e o (k)) represents the disturbance observation coefficient at time k.
4. The method according to claim 1, wherein The fuzzy neural network model is constructed to estimate the unknown nonlinear function, and the output expression of the fuzzy neural network model is: Among them, T represents the transpose of the matrix, α l (k) represents the lth input of the fuzzy neural network model at time k, ω r (k) represents the connection weight between the rth regular layer neuron and the output layer neuron of the fuzzy neural network model at time k, c lr (k) represents the central value of the rth radial base layer neuron corresponding to the lth input layer neuron of the fuzzy neural network model at time k, σ lr (k) represents the width of the rth radial base neuron corresponding to the lth input layer neuron of the fuzzy neural network model at time k, b represents the number of input layer neurons of the fuzzy neural network model, a represents the number of radial base neurons and regular layer neurons of the fuzzy neural network model, ω r (k), c lr (k), σ lr (k) is randomly assigned a value within [0, 1].
5. The method according to claim 1, wherein The parameter updating strategy of the fuzzy neural network described in S3 is: Among them, E(k) represents the loss function of the fuzzy neural network at time k, Represents the loss function E(k) versus weight ω r (k) Find the partial derivative, Represents the loss function E(k) for the center value c lr (k) Find the partial derivative, Represents the loss function E(k) versus width σ lr (k) Find the partial derivative.
6. The method according to claim 1, characterized in that The design is based on a robust fault-tolerant controller using adaptive dynamic programming, specifically including: S41. Design of control law based on adaptive dynamic programming: Objective function: Minimize the cost function: Solve the optimal control input and maximum fault input through strategy iteration; Where, e(k) is the tracking error of dissolved oxygen concentration at time k, is the gradient of the cost function at time k, and U(e(k),u(k),w(k)) is the utility function at time k; Control input at time k+1: u(k+1)=u(k)+Δu * (k) Thu * (k)=e * (k)u * (k)+(1-e * (k))u w * (k) S42. Use the evaluation network and execution network to perform policy iteration: Evaluation network: Input [α1(k), α2(k), α3(k)] T =[e(k),u i (k), w i (k)] T , output Use the parameter update strategy to update the neural network parameters. The loss function formula is: where e c(i) (k) is the estimation error, expressed as: in, represents the approximate cost function of the i-th iteration obtained at time k based on the control input and fault input of the i-th iteration, represents the approximate cost function obtained by solving the control input and fault input at the k-1 moment used in the i-th iteration, represents the estimated value of the fault at time k-1, represents the gradient of the approximate cost function used at time k-1 in the i-th iteration, and U(e(k-1),u(k-1),w(k-1)) is the utility function at time k-1; Control input execution network: Input α1(k)=e(k), each iteration step outputs Use the parameter update strategy to update the neural network parameters. The loss function formula is: in is the estimation error; Fault input execution network: Input α1(k)=e(k), each iteration step outputs Use parameter update strategies (6)-(8) to update the neural network parameters. The loss function formula is: in is the estimation error; S43. Update network parameters through experience replay mechanism: Construct the experience replay area B(k): B(k)={b(kM),...,b(k-2),b(k-1)} Where M is the size of the experience replay area, b(kj) (j=1, .., M) is the sample at time kj; Calculate the data importance index ξ(kj): Where D(kj) represents the disturbance amplitude of the data sample b(kj) at time k, δ(kj) represents the time series difference error of the data sample b(kj) at time k, D(kp) represents the disturbance amplitude of the data sample b(kp) at time k, δ(kp) represents the time series difference error of the data sample b(kp) at time k, and the value of p ranges from 1 to M. Dynamically select the first N(k) groups of data to update network parameters.
7. The method according to claim 3, characterized in that In S5, the optimal fault-tolerant control law u(k+1) at time k+1 is converted into a frequency converter signal through a programmable logic controller to control the blower speed to adjust the aeration volume.