Robust model-free fault-tolerant control method for dissolved oxygen concentration in urban sewage treatment process

Abstract

The invention provides a robust model-free fault-tolerant control method for dissolved oxygen concentration in an urban sewage treatment process, aiming at the problem that the system stability in the urban sewage treatment process is influenced by insufficient aeration caused by a fault of a dissolved oxygen sensor in the urban sewage treatment process. The method comprises the following steps: firstly, designing a robust fault detection threshold value based on an extended state observer, and timely and accurately detecting the fault of the dissolved oxygen sensor; secondly, estimating a fault through a fuzzy neural network; and finally, based on fault estimation information, a robust model-free fault-tolerant control strategy is designed by considering the dissolved oxygen concentration tracking error variation, the dissolved oxygen concentration measurement deviation caused by the fault of the dissolved oxygen sensor is dynamically compensated, the stable control of the dissolved oxygen concentration is realized, and the reliable operation of the urban sewage treatment process is ensured.

Description

Technical Field

[0001] The present invention proposes a robust model-free fault-tolerant control method for dissolved oxygen concentration in a municipal sewage treatment process, which can compensate for dissolved oxygen concentration measurement deviations caused by dissolved oxygen sensor failures in real time, achieve stable regulation of dissolved oxygen concentration, and ensure the reliable operation of the municipal sewage treatment process. This invention belongs to both the field of intelligent control and the field of water treatment. Background Art

[0002] The municipal sewage treatment process is a key link in safeguarding public health and achieving water resource recycling. Dissolved oxygen concentration is an important parameter that affects the activity of aerobic microorganisms and the efficiency of ammonia nitrogen removal. Its precise control is crucial for the stable operation of the municipal sewage treatment process. To achieve closed-loop control, dissolved oxygen sensors are usually used to monitor the dissolved oxygen concentration in sewage in real time, and the measurement results are fed back to the control system to adjust the operating status of the blower and maintain an appropriate dissolved oxygen level. However, as a core monitoring device, the dissolved oxygen sensor needs to work in the sewage environment for a long time. Its probe is easily affected by the deposition of sludge and suspended matter, resulting in measurement data deviation, which in turn causes the control system to misjudge the aeration equipment, resulting in insufficient oxygen supply, reducing sewage treatment efficiency and affecting system stability. Therefore, it is urgent to design a fault-tolerant control method that is robust and does not rely on an accurate system model to improve the reliability of the system under sensor failure conditions. It has important engineering practical value and application promotion prospects.

[0003] Traditional passive fault-tolerant control approaches for sensor failures typically pre-define possible fault types during the system design phase and employ fixed control strategies. This approach is difficult to address in complex and variable fault scenarios during actual operation and presents certain limitations. In contrast, active fault-tolerant control offers real-time fault detection and online estimation capabilities, allowing for dynamic adjustment of control strategies to rapidly respond to faults and minimize their impact on system performance. Furthermore, among various control strategies, model-free adaptive control is more suitable for the dynamic, complex, and nonlinear urban sewage treatment process due to its simple structure, low computational complexity, and lack of reliance on precise system models. This process exhibits significant nonstationarity and is significantly affected by external disturbances such as influent flow rate and pollutant concentration. These disturbances significantly reduce the accuracy of fault detection. To improve fault detection accuracy, an extended state observer is introduced to construct a robust fault detection threshold and is combined with a fuzzy neural network for online fault estimation. Furthermore, existing model-free adaptive fault-tolerant control approaches only consider the effects of dissolved oxygen concentration tracking error and oxygen transfer coefficient increment, ignoring the impact of the dissolved oxygen concentration tracking error variation on controller performance. Incorporating the dissolved oxygen concentration tracking error variation into the control algorithm can more accurately reflect the system's dynamic characteristics, reduce overall tracking error, and improve system stability. Therefore, it is urgent to design a robust model-free fault-tolerant control strategy with fault detection, estimation and dynamic compensation capabilities to ensure the stable operation of the urban sewage treatment process.

[0004] The present invention proposes a robust model-free fault-tolerant control strategy. First, the strategy transforms the dissolved oxygen concentration control system of the municipal sewage treatment process into a tight-form dynamic linearization system of the dissolved oxygen concentration in the municipal sewage treatment process. Second, a robust fault detection threshold is designed based on an extended state observer, and a fuzzy neural network is used to estimate the fault. Finally, based on the fault estimation information, a robust model-free fault-tolerant control strategy is designed taking into account the variation of the dissolved oxygen concentration tracking error. This achieves stable control of the dissolved oxygen concentration and ensures the reliable operation of the municipal sewage treatment process. Summary of the Invention

[0005] This paper proposes a robust, model-free, fault-tolerant control method for dissolved oxygen concentration in a municipal sewage treatment process. This method constructs a robust fault detection threshold based on an extended state observer to enable timely and accurate detection of dissolved oxygen sensor faults. It also utilizes a fuzzy neural network to estimate faults online. Furthermore, it introduces the variation in dissolved oxygen concentration tracking error to design a robust, model-free, fault-tolerant control strategy. By adjusting the oxygen transfer coefficient, it achieves stable tracking control of dissolved oxygen concentration, effectively compensating for interference caused by sensor failures and ensuring stable operation of the municipal sewage treatment process.

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

[0007] 1. A robust model-free fault-tolerant control method for dissolved oxygen concentration in a municipal sewage treatment process, characterized by establishing a compact dynamic linearization system for dissolved oxygen concentration in the municipal sewage treatment process, constructing a dissolved oxygen sensor fault detection threshold based on an extended state observer, estimating dissolved oxygen sensor faults, and designing a robust model-free fault-tolerant controller that takes into account the variation in dissolved oxygen concentration tracking error. The method comprises the following steps:

[0008] (1) Establish a tight-form dynamic linearization system for dissolved oxygen concentration in urban sewage treatment process

[0009] Dissolved oxygen sensors in municipal sewage treatment processes are used to monitor dissolved oxygen concentrations in real time. Due to long-term exposure to sewage, the probe surfaces of these sensors are prone to fouling, which can lead to measurement deviations. This can affect the accuracy of aeration control, cause insufficient dissolved oxygen supply, and reduce the stability of the municipal sewage treatment process. Therefore, a robust model-free fault-tolerant controller is designed to compensate for measurement deviations caused by dissolved oxygen sensor failures in real time, achieve stable control of dissolved oxygen concentration, and ensure reliable operation of the municipal sewage treatment process.

[0010] The input of the dissolved oxygen concentration control system in the municipal sewage treatment process is the oxygen transfer coefficient, and the output is the dissolved oxygen concentration. The expression of the system is:

[0011] y(k+1)=f(y(k),u(k),d(k)) (1)

[0012] Where y(k+1) represents the dissolved oxygen concentration measurement value at time k+1, in mg / L; y(k) represents the dissolved oxygen concentration measurement value at time k, in mg / L; u(k) represents the oxygen transfer coefficient at time k, in 1 / s; d(k) represents the external disturbance at time k; and f(.) represents the nonlinear mapping.

[0013] The compact dynamic linearization system of dissolved oxygen concentration in the municipal sewage treatment process is:

[0014] y(k+1)=y(k)+φ(k)Δu(k)+w(k) (2)

[0015] in, represents the pseudo partial derivative of dissolved oxygen concentration with respect to the oxygen transfer coefficient, Δu(k)=u(k)-u(k-1) represents the increment of oxygen transfer coefficient at time k, in units of 1 / second, and w(k) represents the residual disturbance at time k:

[0016] w(k)=f(y(k),u(k-1),u(k-1),u(k),d(k))-f(y(k-1),u(k-1),d(k-1)) (3)

[0017] Where u(k-1) represents the oxygen transfer coefficient at time k-1, the unit is 1 / second, and d(k-1) represents the external disturbance at time k-1;

[0018] Build a dissolved oxygen sensor failure model:

[0019] y f (k)=y(k)+f s (k) (4)

[0020] Among them, f s (k) represents the dissolved oxygen sensor failure at time k, y f (k) represents the dissolved oxygen concentration measurement value affected by the fault at time k, in mg / L;

[0021] Combining the compact dynamic linearization system (2) of dissolved oxygen concentration in the municipal sewage treatment process and the dissolved oxygen sensor failure model (4), a compact dynamic linearization system of dissolved oxygen concentration in the municipal sewage treatment process affected by dissolved oxygen sensor failure is established:

[0022] y(k+1)=y(k)+φ(k)Δu(k)+w(k)+f s (k) (5)

[0023] (2) Constructing a fault detection threshold for dissolved oxygen sensors based on an extended state observer

[0024] Introducing the residual disturbance as a state variable, the system (2) is transformed into an extended form of a compact dynamic linear system of dissolved oxygen concentration in the urban sewage treatment process:

[0025] x(k+1)=Ax(k)+B(k)Δu(k)+Dξ(k) (6)

[0026] where x(k) = [y(k), w(k)] T represents the state vector at time k, which consists of the dissolved oxygen concentration measurement value y(k) and the residual disturbance w(k) at time k, x(k+1)=[y(k+1),w(k+1)] T represents the state vector at time k+1, which consists of the dissolved oxygen concentration measurement value y(k+1) at time k+1 and the residual disturbance w(k+1), B(k)=[φ(k),0] T Denotes the pseudo partial derivative vector at time k, D = [0, 1] T represents the constant vector, ξ(k)=w(k+1)-w(k)) represents the residual disturbance increment at time k+1, represents a constant matrix;

[0027] Design an extended state observer:

[0028]

[0029] in, represents the estimated value of x(k+1), represents the estimated value of x(k), in represents the estimated value of φ(k), represents the estimated value of y(k);

[0030] Designing the Dissolved Oxygen Sensor Fault Detection Threshold:

[0031] Calculate the state observation error:

[0032]

[0033] Among them, ε(k+1) represents the state observation error at time k+1;

[0034] Construct a Lyapunov function:

[0035] V(k)=0.005ε T (k)ε(k) (9)

[0036] Among them, ε(k) represents the state observation error at time k;

[0037] Compute the difference of the Lyapunov function (9):

[0038]

[0039] in, represents a constant matrix;

[0040] Using the differential condition of the Lyapunov function ΔV(k+1)≤0, the fault detection threshold of the dissolved oxygen sensor is obtained:

[0041]

[0042] Where σ(k) represents the fault detection threshold of the dissolved oxygen sensor at time k, represents the maximum value of C(0), C(1),…, C(k-1), represents the auxiliary variable for constructing σ(k), express 2-norm of Δ|u(k)| 2 represents the square increment of u(k);

[0043] The dissolved oxygen sensor fault detection criteria are established as follows: if |ε(k)|≤σ(k), no dissolved oxygen sensor fault has occurred; if |ε(k)|>σ(k), a dissolved oxygen sensor fault has occurred;

[0044] (3) Estimation of dissolved oxygen sensor failure

[0045] Introducing fuzzy neural network to estimate dissolved oxygen sensor fault on-line

[0046] Design the output expression of the fuzzy neural network:

[0047]

[0048] Among them, l (k) represents the connection weight between the first rule layer neuron and the output layer neuron of the fuzzy neural network at time k, Ψ l (k) takes a random value in the range [0,1], β j (k) represents the jth input of the fuzzy neural network at time k, and β1(k)=y r (k), β2(k)=y(k), β3(k)=f s (k-1), y r (k) represents the set value of dissolved oxygen concentration at time k, f s (k-1) indicates that the dissolved oxygen sensor fails at time k-1, c jl (k) represents the center value of the jth input layer neuron corresponding to the lth radial base layer neuron of the fuzzy neural network at time k, c jl (k) takes a random value in the range [0,1], θ jl (k) represents the width of the jth input layer neuron corresponding to the lth radial base layer neuron of the fuzzy neural network at time k, θ jl (k) takes a random value in the range of [0,1], l = 1, 2, ..., 10 represents the number of radial base layer neurons and regular layer neurons of the fuzzy neural network, j = 1, 2, 3 represents the number of input layer neurons of the fuzzy neural network

[0049] Calculate the dissolved oxygen concentration tracking error:

[0050] z(k)=y r (k)-y(k) (13)

[0051] Among them, y r (k) represents the dissolved oxygen concentration set value at time k, in mg / L; z(k) represents the dissolved oxygen concentration tracking error at time k, in mg / L;

[0052] Design cost function:

[0053]

[0054] Using the gradient descent method, the fuzzy neural network parameters are updated according to the cost function (14):

[0055]

[0056] Among them, α(k)=[Ψ1(k),…,Ψ 10 (k),c1(k),…,c3(k),θ1(k),…,θ3(k)] T represents the parameter vector of the fuzzy neural network at time k, Ψ1(k) represents the connection weight between the first regular layer neuron and the output layer neuron of the fuzzy neural network at time k, 10 (k) represents the connection weight between the 10th regular layer neuron and the output layer neuron of the fuzzy neural network at time k, Ψ1(k) and Ψ 10 (k) takes a random value in the range [0,1], c1(k)=[c 11 (k),…,c 110 (k)] T represents the center vector of the first radial basis neuron of the fuzzy neural network at time k, c 11 (k),…,c 110 (k) are randomly selected in the range [0,1], θ1(k)=[θ 11 (k),…,θ 110 (k)] T Represents the width vector of the first radial basis neuron of the fuzzy neural network at time k, θ 11 (k),…,θ 110 (k) are all randomly selected in the range [0,1]. Denotes the Jacobian matrix of the fuzzy neural network at time k, α(k+1)=[Ψ1(k+1),…,Ψ 10 (k+1),c1(k+1),…,c3(k+1),θ1(k+1),…,θ3(k+1)] T represents the parameter vector of the fuzzy neural network at time k+1, Ψ1(k+1) represents the connection weight between the first regular layer neuron and the output layer neuron of the fuzzy neural network at time k+1, Ψ 10 (k+1) represents the connection weight between the 10th regular layer neuron and the output layer neuron of the fuzzy neural network at time k+1, Ψ1(k+1) and Ψ 10 (k+1) takes a random value in the range [0,1], c1(k+1)=[c 11 (k+1),…,c 110 (k+1)] T represents the center vector of the first radial basis neuron of the fuzzy neural network at time k+1, c 11 (k),…,c 110 (k) are all randomly selected in the range [0,1], θ1(k+1)=[θ 11 (k+1),…,θ 110 (k+1)] TRepresents the width vector of the first radial basis neuron of the fuzzy neural network at time k+1, θ 11 (k),…,θ 110 (k) are all randomly selected in the range [0,1], and I represents the 70-dimensional identity matrix;

[0057] (4) Design a robust model-free fault-tolerant controller that considers the variation of dissolved oxygen concentration tracking error

[0058] According to the optimal control principle, an improved oxygen transfer coefficient cost function is designed:

[0059] J(u(k))=(z(k+1)) 2 +101(△u(k)) 2 +0.85(△z(k+1)) 2 (16)

[0060] Where z(k+1) represents the tracking error of dissolved oxygen concentration at time k+1, in mg / L, and Δz(k+1)=z(k+1)-z(k), in mg / L;

[0061] For the unknown pseudo partial derivative φ(k), design the cost function:

[0062]

[0063] in, represents the estimated value of φ(k), represents the estimated value of φ(k-1);

[0064] According to the optimal conditions And the fuzzy neural network output (12), to obtain the robust model-free fault-tolerant control law:

[0065]

[0066] in, represents the estimated value of w(k), y r (k+1) represents the set value of dissolved oxygen concentration at time k+1, in mg / L;

[0067] Real-time fault detection is achieved through the dissolved oxygen sensor fault detection threshold (11), and the fault is dynamically estimated using the fuzzy neural network output (12). According to the robust model-free fault-tolerant control law (18), the measurement deviation caused by the dissolved oxygen sensor fault is compensated in real time. Specifically, u(k) represents the inverter input signal at time k. The inverter adjusts the motor speed to control the blower operation, thereby achieving stable control of the dissolved oxygen concentration and ensuring the stable operation of the urban sewage treatment process.

[0068] The creativity of the present invention is mainly reflected in:

[0069] (1) This invention addresses the problem of decreased fault detection accuracy in urban sewage treatment processes due to external interference. By using an extended state observer to design a robust fault detection threshold, the invention effectively improves the detection capability and response speed of fault-tolerant control, provides an innovative solution for fault detection and control under external interference conditions, and enhances system stability.

[0070] (2) The present invention addresses the problem of insufficient aeration caused by dissolved oxygen sensor failure, which affects the stable operation of the urban sewage treatment process system. Based on fault estimation information and considering the variation of dissolved oxygen concentration tracking error, a robust model-free fault-tolerant control strategy is designed to achieve stable tracking control of dissolved oxygen concentration and ensure the reliable operation of the urban sewage treatment process. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a fault detection result diagram of the present invention;

[0072] Figure 2 This is a fault estimation result diagram of the present invention;

[0073] Figure 3 This is a diagram showing the results of the dissolved oxygen concentration tracking control of the present invention;

[0074] Figure 4 It is an error diagram of the dissolved oxygen concentration tracking control result of the present invention. DETAILED DESCRIPTION

[0075] A robust model-free fault-tolerant control method for dissolved oxygen concentration in a municipal sewage treatment process is characterized by establishing a compact dynamic linearization system for dissolved oxygen concentration in the municipal sewage treatment process, constructing a dissolved oxygen sensor fault detection threshold based on an extended state observer, estimating dissolved oxygen sensor faults, and designing a robust model-free fault-tolerant controller that takes into account the variation of dissolved oxygen concentration tracking error. The method comprises the following steps:

[0076] (1) Establish a tight-form dynamic linearization system for dissolved oxygen concentration in urban sewage treatment process

[0077] Dissolved oxygen sensors in municipal sewage treatment processes are used to monitor dissolved oxygen concentrations in real time. Due to long-term exposure to sewage, the probe surfaces of these sensors are prone to fouling, which can lead to measurement deviations. This can affect the accuracy of aeration control, cause insufficient dissolved oxygen supply, and reduce the stability of the municipal sewage treatment process. Therefore, a robust model-free fault-tolerant controller is designed to compensate for measurement deviations caused by dissolved oxygen sensor failures in real time, achieve stable control of dissolved oxygen concentration, and ensure reliable operation of the municipal sewage treatment process.

[0078] The input of the dissolved oxygen concentration control system in the municipal sewage treatment process is the oxygen transfer coefficient, and the output is the dissolved oxygen concentration. The expression of the system is:

[0079] y(k+1)=f(y(k),u(k),d(k)) (19)

[0080] Where y(k+1) represents the dissolved oxygen concentration measurement value at time k+1, in mg / L; y(k) represents the dissolved oxygen concentration measurement value at time k, in mg / L; u(k) represents the oxygen transfer coefficient at time k, in 1 / s; d(k) represents the external disturbance at time k; and f(.) represents the nonlinear mapping.

[0081] The compact dynamic linearization system of dissolved oxygen concentration in the municipal sewage treatment process is:

[0082] y(k+1)=y(k)+φ(k)Δu(k)+w(k) (20)

[0083] in, represents the pseudo partial derivative of dissolved oxygen concentration with respect to the oxygen transfer coefficient, Δu(k)=u(k)-u(k-1) represents the increment of oxygen transfer coefficient at time k, in units of 1 / second, and w(k) represents the residual disturbance at time k:

[0084] w(k)=f(y(k),u(k-1),u(k-1),u(k),d(k))-f(y(k-1),u(k-1),d(k-1)) (21)

[0085] Where u(k-1) represents the oxygen transfer coefficient at time k-1, the unit is 1 / second, and d(k-1) represents the external disturbance at time k-1;

[0086] Build a dissolved oxygen sensor failure model:

[0087] y f (k)=y(k)+f s (k) (22)

[0088] Among them, f s (k) represents the dissolved oxygen sensor failure at time k, y f (k) represents the dissolved oxygen concentration measurement value affected by the fault at time k, in mg / L;

[0089] Combining the compact dynamic linearization system (20) of dissolved oxygen concentration in urban sewage treatment process and the dissolved oxygen sensor failure model (22), a compact dynamic linearization system of dissolved oxygen concentration in urban sewage treatment process affected by dissolved oxygen sensor failure is established.

[0090] y(k+1)=y(k)+φ(k)Δu(k)+w(k)+fs (k) (23)

[0091] (2) Constructing a fault detection threshold for dissolved oxygen sensors based on an extended state observer

[0092] Introducing the residual disturbance as a state variable, the system (20) is transformed into an extended form of a compact dynamic linear system of dissolved oxygen concentration in the urban sewage treatment process:

[0093] x(k+1)=Ax(k)+B(k)Δu(k)+Dξ(k) (24)

[0094] where x(k) = [y(k), w(k)] T represents the state vector at time k, which consists of the dissolved oxygen concentration measurement value y(k) and the residual disturbance w(k) at time k, x(k+1)=[y(k+1),w(k+1)] T represents the state vector at time k+1, which consists of the dissolved oxygen concentration measurement value y(k+1) at time k+1 and the residual disturbance w(k+1), B(k)=[φ(k),0] T Denotes the pseudo partial derivative vector at time k, D = [0, 1] T represents the constant vector, ξ(k)=w(k+1)-w(k)) represents the residual disturbance increment at time k+1, represents a constant matrix;

[0095] Design an extended state observer:

[0096]

[0097] in, represents the estimated value of x(k+1), represents the estimated value of x(k), in represents the estimated value of φ(k), represents the estimated value of y(k);

[0098] Designing the Dissolved Oxygen Sensor Fault Detection Threshold:

[0099] Calculate the state observation error:

[0100]

[0101] Among them, ε(k+1) represents the state observation error at time k+1;

[0102] Construct a Lyapunov function:

[0103] V(k)=0.005ε T (k)ε(k) (27)

[0104] Among them, ε(k) represents the state observation error at time k;

[0105] Compute the difference of the Lyapunov function (27):

[0106]

[0107] in, represents a constant matrix;

[0108] Using the differential condition of the Lyapunov function ΔV(k+1)≤0, the fault detection threshold of the dissolved oxygen sensor is obtained:

[0109]

[0110] Where σ(k) represents the fault detection threshold of the dissolved oxygen sensor at time k, represents the maximum value of C(0), C(1),…, C(k-1), represents the auxiliary variable for constructing σ(k), express 2-norm of Δ|u(k)| 2 represents the square increment of u(k);

[0111] The dissolved oxygen sensor fault detection criteria are established as follows: if |ε(k)|≤σ(k), no dissolved oxygen sensor fault has occurred; if |ε(k)|>σ(k), a dissolved oxygen sensor fault has occurred;

[0112] (3) Estimation of dissolved oxygen sensor failure

[0113] Introducing fuzzy neural network to estimate dissolved oxygen sensor fault on-line

[0114] Design the output expression of the fuzzy neural network:

[0115]

[0116] Among them, l (k) represents the connection weight between the first rule layer neuron and the output layer neuron of the fuzzy neural network at time k, Ψ l (k) takes a random value in the range [0,1], β j (k) represents the jth input of the fuzzy neural network at time k, and β1(k)=y r (k), β2(k)=y(k), β3(k)=f s (k-1), y r (k) represents the set value of dissolved oxygen concentration at time k, f s (k-1) indicates that the dissolved oxygen sensor fails at time k-1, c jl(k) represents the center value of the jth input layer neuron corresponding to the lth radial base layer neuron of the fuzzy neural network at time k, c jl (k) takes a random value in the range [0,1], θ jl (k) represents the width of the jth input layer neuron corresponding to the lth radial base layer neuron of the fuzzy neural network at time k, θ jl (k) takes a random value in the range [0,1], l = 1, 2, ..., 10 represents the number of radial base layer neurons and regular layer neurons of the fuzzy neural network, j = 1, 2, 3 represents the number of input layer neurons of the fuzzy neural network;

[0117] Calculate the dissolved oxygen concentration tracking error:

[0118] z(k)=y r (k)-y(k) (31)

[0119] Among them, y r (k) represents the dissolved oxygen concentration set value at time k, in mg / L; z(k) represents the dissolved oxygen concentration tracking error at time k, in mg / L;

[0120] Design cost function:

[0121]

[0122] Using the gradient descent method, the fuzzy neural network parameters are updated according to the cost function (32):

[0123]

[0124] Among them, α(k)=[Ψ1(k),…,Ψ 10 (k),c1(k),…,c3(k),θ1(k),…,θ3(k)] T represents the parameter vector of the fuzzy neural network at time k, Ψ1(k) represents the connection weight between the first regular layer neuron and the output layer neuron of the fuzzy neural network at time k, 10 (k) represents the connection weight between the 10th regular layer neuron and the output layer neuron of the fuzzy neural network at time k, Ψ1(k) and Ψ 10 (k) takes a random value in the range [0,1], c1(k)=[c 11 (k),…,c 110 (k)] T represents the center vector of the first radial basis neuron of the fuzzy neural network at time k, c 11 (k),…,c 110 (k) are randomly selected in the range [0,1], θ1(k)=[θ 11 (k),…,θ 110 (k)]T Represents the width vector of the first radial basis neuron of the fuzzy neural network at time k, θ 11 (k),…,θ 110 (k) are all randomly selected in the range [0,1]. Denotes the Jacobian matrix of the fuzzy neural network at time k, α(k+1)=[Ψ1(k+1),…,Ψ 10 (k+1),c1(k+1),…,c3(k+1),θ1(k+1),…,θ3(k+1)] T represents the parameter vector of the fuzzy neural network at time k+1, Ψ1(k+1) represents the connection weight between the first regular layer neuron and the output layer neuron of the fuzzy neural network at time k+1, Ψ 10 (k+1) represents the connection weight between the 10th regular layer neuron and the output layer neuron of the fuzzy neural network at time k+1, Ψ1(k+1) and Ψ 10 (k+1) takes a random value in the range [0,1], c1(k+1)=[c 11 (k+1),…,c 110 (k+1)] T represents the center vector of the first radial basis neuron of the fuzzy neural network at time k+1, c 11 (k),…,c 110 (k) are all randomly selected in the range [0,1], θ1(k+1)=[θ 11 (k+1),…,θ 110 (k+1)] T Represents the width vector of the first radial basis neuron of the fuzzy neural network at time k+1, θ 11 (k),…,θ 110 (k) are all randomly selected in the range [0,1], and I represents the 70-dimensional identity matrix;

[0125] (4) Design a robust model-free fault-tolerant controller that considers the variation of dissolved oxygen concentration tracking error

[0126] According to the optimal control principle, an improved oxygen transfer coefficient cost function is designed:

[0127] J(u(k))=(z(k+1)) 2 +101(△u(k)) 2 +0.85(△z(k+1)) 2 (34)

[0128] Where z(k+1) represents the tracking error of dissolved oxygen concentration at time k+1, in mg / L, and Δz(k+1)=z(k+1)-z(k), in mg / L;

[0129] For the unknown pseudo partial derivative φ(k), design the cost function:

[0130]

[0131] in, represents the estimated value of φ(k), represents the estimated value of φ(k-1);

[0132] According to the optimal conditions And the fuzzy neural network output (30) is used to obtain the robust model-free fault-tolerant control law:

[0133]

[0134] in, represents the estimated value of w(k), y r (k+1) represents the set value of dissolved oxygen concentration at time k+1, in mg / L;

[0135] Real-time fault detection is achieved through the dissolved oxygen sensor fault detection threshold (29), and the fault is dynamically estimated using the fuzzy neural network output (30). According to the robust model-free fault-tolerant control law (36), the measurement deviation caused by the dissolved oxygen sensor fault is compensated in real time. Specifically, u(k) represents the inverter input signal at time k. The inverter adjusts the motor speed to control the blower operation, thereby achieving stable control of the dissolved oxygen concentration and ensuring the stable operation of the urban sewage treatment process.

Claims

1. A robust model-free fault-tolerant control method for dissolved oxygen concentration in a municipal sewage treatment process, characterized in that: A compact dynamic linearization system for dissolved oxygen concentration in a municipal sewage treatment process is established. A fault detection threshold for the dissolved oxygen sensor based on an extended state observer is constructed. The dissolved oxygen sensor fault is estimated. A robust model-free fault-tolerant controller that considers the variation of the dissolved oxygen concentration tracking error is designed. The following steps are involved: (1) Establish a tight-form dynamic linearization system for dissolved oxygen concentration in urban sewage treatment process The input of the dissolved oxygen concentration control system in the municipal sewage treatment process is the oxygen transfer coefficient, and the output is the dissolved oxygen concentration. The expression of the system is: y(k+1)=f(y(k),u(k),d(k)) (1) Where y(k+1) represents the dissolved oxygen concentration measurement value at time k+1, in mg / L; y(k) represents the dissolved oxygen concentration measurement value at time k, in mg / L; u(k) represents the oxygen transfer coefficient at time k, in 1 / s; d(k) represents the external disturbance at time k; and f(.) represents the nonlinear mapping. The compact dynamic linearization system of dissolved oxygen concentration in the municipal sewage treatment process is: y(k+1)=y(k)+φ(k)Δu(k)+w(k) (2) in, represents the pseudo partial derivative of dissolved oxygen concentration with respect to the oxygen transfer coefficient, Δu(k)=u(k)-u(k-1) represents the increment of oxygen transfer coefficient at time k, in units of 1 / second, and w(k) represents the residual disturbance at time k: w(k)=f(y(k),u(k-1),u(k-1),u(k),d(k))-f(y(k-1),u(k-1),d(k-1)) (3) Where u(k-1) represents the oxygen transfer coefficient at time k-1, the unit is 1 / second, and d(k-1) represents the external disturbance at time k-1; Build a dissolved oxygen sensor failure model: y f (k)=y(k)+f s (k) (4) Among them, f s (k) represents the dissolved oxygen sensor failure at time k, y f (k) represents the dissolved oxygen concentration measurement value affected by the fault at time k, in mg / L; Combining the compact dynamic linearization system (2) of dissolved oxygen concentration in the municipal sewage treatment process and the dissolved oxygen sensor failure model (4), a compact dynamic linearization system of dissolved oxygen concentration in the municipal sewage treatment process affected by dissolved oxygen sensor failure is established: y(k+1)=y(k)+φ(k)△u(k)+w(k)+f s (k) (5) (2) Constructing a fault detection threshold for dissolved oxygen sensors based on an extended state observer Introducing the residual disturbance as a state variable, the system (2) is transformed into an extended form of a compact dynamic linear system of dissolved oxygen concentration in the urban sewage treatment process: x(k+1)=Ax(k)+B(k)Δu(k)+Dξ(k) (6) where x(k) = [y(k), w(k)] T represents the state vector at time k, which consists of the dissolved oxygen concentration measurement value y(k) and the residual disturbance w(k) at time k, x(k+1)=[y(k+1),w(k+1)] T represents the state vector at time k+1, which consists of the dissolved oxygen concentration measurement value y(k+1) at time k+1 and the residual disturbance w(k+1), B(k)=[φ(k),0] T Denotes the pseudo partial derivative vector at time k, D = [0,1] T represents the constant vector, ξ(k)=w(k+1)-w(k)) represents the residual disturbance increment at time k+1, represents a constant matrix; Design an extended state observer: in, represents the estimated value of x(k+1), represents the estimated value of x(k), in represents the estimated value of φ(k), represents the estimated value of y(k); Designing the Dissolved Oxygen Sensor Fault Detection Threshold: Calculate the state observation error: Among them, ε(k+1) represents the state observation error at time k+1; Construct a Lyapunov function: V(k)=0.005ε T (k)e(k) (9) Among them, ε(k) represents the state observation error at time k; Compute the difference of the Lyapunov function (9): in, represents a constant matrix; Using the differential condition of the Lyapunov function ΔV(k+1)≤0, the fault detection threshold of the dissolved oxygen sensor is obtained: Where σ(k) represents the fault detection threshold of the dissolved oxygen sensor at time k, represents the maximum value of C(0), C(1),…, C(k-1), represents the auxiliary variable for constructing σ(k), express 2-norm of Δ|u(k)| 2 represents the square increment of u(k); The dissolved oxygen sensor fault detection criteria are established as follows: if |ε(k)|≤σ(k), no dissolved oxygen sensor fault has occurred; if |ε(k)|>σ(k), a dissolved oxygen sensor fault has occurred; (3) Estimation of dissolved oxygen sensor failure Introducing fuzzy neural network to estimate dissolved oxygen sensor fault on-line Design the output expression of the fuzzy neural network: Among them, l (k) represents the connection weight between the lth rule layer neuron and the output layer neuron of the fuzzy neural network at time k, Ψ l (k) takes a random value in the range [0,1], β j (k) represents the jth input of the fuzzy neural network at time k, and β1(k)=y r (k), β2(k)=y(k), β3(k)=f s (k-1), y r (k) represents the set value of dissolved oxygen concentration at time k, f s (k-1) indicates that the dissolved oxygen sensor fails at time k-1, c jl (k) represents the center value of the jth input layer neuron corresponding to the lth radial base layer neuron of the fuzzy neural network at time k, c jl (k) takes a random value in the range [0,1], θ jl (k) represents the width of the jth input layer neuron corresponding to the lth radial base layer neuron of the fuzzy neural network at time k, θ jl (k) takes a random value in the range [0,1], l = 1, 2, ..., 10 represents the number of radial base layer neurons and regular layer neurons of the fuzzy neural network, j = 1, 2, 3 represents the number of input layer neurons of the fuzzy neural network; Calculate the dissolved oxygen concentration tracking error: z(k)=y r (k)-y(k) (13) Among them, y r (k) represents the dissolved oxygen concentration set value at time k, in mg / L; z(k) represents the dissolved oxygen concentration tracking error at time k, in mg / L; Design cost function: Using the gradient descent method, the fuzzy neural network parameters are updated according to the cost function (14): Among them, α(k)=[Ψ1(k),…,Ψ 10 (k),c1(k),…,c3(k),θ1(k),…,θ3(k)] T represents the parameter vector of the fuzzy neural network at time k, Ψ1(k) represents the connection weight between the first regular layer neuron and the output layer neuron of the fuzzy neural network at time k, 10 (k) represents the connection weight between the 10th regular layer neuron and the output layer neuron of the fuzzy neural network at time k, Ψ1(k) and Ψ 10 (k) takes a random value in the range [0,1], c1(k)=[c 11 (k),…,c 110 (k)] T represents the center vector of the first radial basis neuron of the fuzzy neural network at time k, c 11 (k),…,c 110 (k) are randomly selected in the range [0,1], θ1(k)=[θ 11 (k),…,θ 110 (k)] T Represents the width vector of the first radial basis neuron of the fuzzy neural network at time k, θ 11 (k),…,θ 110 (k) are all randomly selected in the range [0,1]. Denotes the Jacobian matrix of the fuzzy neural network at time k, α(k+1)=[Ψ1(k+1),…,Ψ 10 (k+1),c1(k+1),…,c3(k+1),θ1(k+1),…,θ3(k+1)] T represents the parameter vector of the fuzzy neural network at time k+1, Ψ1(k+1) represents the connection weight between the first regular layer neuron and the output layer neuron of the fuzzy neural network at time k+1, 10 (k+1) represents the connection weight between the 10th regular layer neuron and the output layer neuron of the fuzzy neural network at time k+1, Ψ1(k+1) and Ψ 10 (k+1) takes a random value in the range [0,1], c1(k+1)=[c 11 (k+1),…,c 110 (k+1)] T represents the center vector of the first radial basis neuron of the fuzzy neural network at time k+1, c 11 (k),…,c 110 (k) are all randomly selected in the range [0,1], θ1(k+1)=[θ 11 (k+1),…,θ 110 (k+1)] T Represents the width vector of the first radial basis neuron of the fuzzy neural network at time k+1, θ 11 (k),…,θ 110 (k) are all randomly selected in the range [0,1], and I represents the 70-dimensional identity matrix; (4) Design a robust model-free fault-tolerant controller that considers the variation of dissolved oxygen concentration tracking error According to the optimal control principle, an improved oxygen transfer coefficient cost function is designed: J(u(k))=(z(k+1)) 2 +101(△u(k)) 2 +0.85(△z(k+1)) 2 (16) Where z(k+1) represents the tracking error of dissolved oxygen concentration at time k+1, in mg / L, and Δz(k+1)=z(k+1)-z(k), in mg / L; For the unknown pseudo partial derivative φ(k), design the cost function: in, represents the estimated value of φ(k), represents the estimated value of φ(k-1); According to the optimal conditions And the fuzzy neural network output (12), to obtain the robust model-free fault-tolerant control law: in, represents the estimated value of w(k), y r (k+1) represents the set value of dissolved oxygen concentration at time k+1, in mg / L; Real-time fault detection is achieved through the dissolved oxygen sensor fault detection threshold (11), and the fault is dynamically estimated using the fuzzy neural network output (12). According to the robust model-free fault-tolerant control law (18), the measurement deviation caused by the dissolved oxygen sensor fault is compensated in real time; u(k) represents the inverter input signal at time k. The inverter adjusts the motor speed to control the blower operation and achieve stable control of the dissolved oxygen concentration.

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