Fixed-time fault-tolerant control method for urban sewage treatment process

Abstract

The invention provides a fixed-time fault-tolerant control method so as to quickly respond to blower faults and solve the problems that in the urban sewage treatment process based on the blower faults, the concentration of dissolved oxygen cannot be stabilized within a preset range and a set value is difficult to track quickly, and it is ensured that the dissolved oxygen reaches an ideal tracking control effect and does not exceed a constraint range at the same time. The method comprises the following steps: firstly, directly constraining the dissolved oxygen concentration by using an asymmetric integral barrier Lyapunov function; secondly, aiming at the blower fault, considering a self-adaptive compensation item, estimating an unknown boundary of a blower bias fault parameter on line, and quickly responding and compensating the deviation caused by the blower fault; finally, a fixed time stability criterion is introduced, a fixed time fault-tolerant control strategy is provided, and the problem that the system stability in the urban sewage treatment process is affected due to the fact that convergence time based on asymptotic stability control is slow and the dissolved oxygen concentration deviates from a set value due to blower faults at present is solved.

Description

Technical field

[0001] The present invention proposes a fixed time fault-tolerant control method for urban sewage treatment, so as to ensure that when the blower fails, the deviation caused by the blower is dynamically compensated, thereby maintaining the stability of the dissolved oxygen concentration. In the urban sewage treatment process, the dissolved oxygen concentration is maintained. Playing a crucial role, this invention not only promotes innovation in urban sewage treatment technology, but is also closely related to the core issues of urban sewage treatment processes. It belongs to both the field of intelligent control and the field of water treatment. Background technology

[0002] Urban sewage treatment is not only about public health, but also the key to the continuous supply of water resources. This invention focuses on responding to the challenges of blower failures in urban sewage treatment processes, and is of great significance to environmental protection, resource conservation and efficient management of water resources. With the help of cutting-edge engineering technology and innovative technology, the invention has the potential to achieve major breakthroughs in the field of environmental science, promote the improvement of public health and water quality supervision, and provide new energy for the country's scientific and technological innovation strategy. Therefore, the application prospects of this technology are very broad.

[0003] In the daily operation of urban sewage treatment process, due to the blower's motor wear or aging, the actual aeration capacity is deviated from the required aeration capacity, which in turn is insufficient oxygen supply, affecting the stability of the urban sewage treatment process system. In response to blower failures, traditional asymptotic stability fault tolerance control is difficult to meet strict time requirements, and the convergence speed is slow, resulting in poorer processing results. In addition, the longer the fault-tolerant treatment time, the more serious the damage caused by the fault to urban sewage treatment plants. Therefore, in order to enhance the adaptability of urban sewage treatment plants control systems and enable them to remain stable in the event of blower failure, it is particularly critical and valuable to study and implement a fault-tolerant control strategy based on fixed time stability. In addition, excessively high dissolved oxygen concentration will lead to oxygen poisoning or energy waste in aquatic organisms, while low dissolved oxygen concentration will affect the oxidative degradation of organic waste. Ignoring the constraint control problem of dissolved oxygen concentration will lead to the control system dealing with different loads and water quality The performance is unstable during changes, and even the system is unstable. A typical asymmetric constraint range of dissolved oxygen concentration is two positive values, and new control methods must be sought to meet the needs of asymmetric constraint control of dissolved oxygen concentration in wastewater treatment. Therefore, considering the asymmetric constraint of dissolved oxygen concentration in urban sewage treatment process and fixed-time fault tolerance control strategy, and thus improving the control efficiency of dissolved oxygen concentration based on blower failure is an urgent problem.

[0004] The present invention proposes a fixed-time fault-tolerant control strategy based on the asymmetric integral type barrier Lyapunov function and the fixed-time stability criterion. The radial basis function neural network is used to approximate unknown terms of the system, and the blower failure is quickly responded to the fixed-time fault-tolerant control method, and the dissolved oxygen concentration is constrained within a predetermined safe range using the asymmetric integral barrier Liyapunov function. Contents of invention

[0005] The present invention obtains a fixed-time fault-tolerant control method for handling blower failures. The controller is based on the asymmetric integral obstacle Liyapunov function and fixed-time stability criterion, quickly responds to compensate blower failures, accurately tracks and controls dissolved oxygen concentration, and ensures that It improves the control performance of the sewage treatment process within a reasonable range; approximates unknown terms of the system through the radial basis function neural network; solves the slow convergence speed in the current asymptotic stability control method, and the blower failure, resulting in the dissolving oxygen concentration. Low, problem beyond the constraint boundary. By adjusting the oxygen transfer coefficient of the sewage treatment process, even in the event of a blower failure, tracking and controlling dissolved oxygen can be achieved to ensure the normal operation of the sewage treatment process;

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

[0007] 1. A fixed time fault-tolerant control method for urban sewage treatment process, characterized by constructing a dissolved oxygen dynamic model of urban sewage treatment process based on blower failure, and designing a fixed time fault-tolerant control for urban sewage treatment process based on radial basis function neural network To achieve safe and stable operation of urban sewage treatment process, including the following steps:

[0008] (1) Construct a dissolved oxygen dynamics model of urban sewage treatment process based on blower failure

[0009] During urban sewage treatment, the blower provides the oxygen required for metabolism to aerobic organisms to remove pollutants; however, the blower has problems such as motor wear or aging, resulting in a deviation from the required aeration capacity. In turn, insufficient oxygen supply affects the stability of the urban sewage treatment process system; by building a fixed-time fault-tolerant controller, dynamically compensates for the deviation caused by blower failure, thereby maintaining the stability of dissolved oxygen concentration;

[0010] Establish a dynamic model of dissolved oxygen concentration in urban sewage treatment process:

[0011]

[0012] Among them, S 5 (t) indicates the dissolved oxygen concentration in the fifth section of the biochemical reaction tank, S 4 (t) indicates the dissolved oxygen concentration in the fourth section of the biochemical reaction tank, K L a 5 (t) represents the oxygen transfer coefficient in the fifth section of the biochemical reaction tank, R s (t) indicates the microbial reaction rate in the fifth section of the biochemical reaction pool, V 5 Indicates the 5th partition volume, S s Indicates the saturation concentration of dissolved oxygen, Q 4 (t) indicates the flow rate of the fourth section of the biochemical reaction tank, Q 5 (t) represents the flow rate of the 5th section of the biochemical reaction tank, and the dissolved oxygen concentration constraint is 1.95<S 5 (t)<2.05; At the same time, an oxygen transfer coefficient model with blower failure was established:

[0013] K L a 5 (t)=0.5u(t)+A(t),t≥t f ; (2)

[0014] Where u(t) represents the actual control input, A(t) represents the unmeasurable time-varying additive fault and the boundary is |A(t)|≤1, t f ≥0 indicates an unknown moment when the fault occurs;

[0015] Combining the dissolved oxygen concentration kinetic model (1) of urban sewage treatment process and the oxygen transfer coefficient model (2) with blower failure, a dissolved oxygen concentration kinetic model based on blower failure is designed:

[0016]

[0017] Where, G(t)=-Q 5 (t)S 5 (t) / V 5 +Q 4 (t)S 4 (t) / V 5 +R s (t) represents an unknown nonlinear function of dissolved oxygen concentration in the fifth section of the biochemical reaction cell, M(t)=S s -S 5 (t) represents the difference between the dissolved oxygen concentration in the fifth partition and its saturation concentration;

[0018] (2) Design a fixed time fault-tolerant controller for urban sewage treatment process based on radial basis function neural network

[0019] ① Calculate the tracking error of dissolved oxygen concentration:

[0020]

[0021] in, It represents the set value of dissolved oxygen concentration at time t, and the time derivative of the tracking error of dissolved oxygen concentration can be obtained;

[0022]

[0023] ②Construct the Liyapunov function of asymmetric integral type barrier:

[0024]

[0025] in,

[0026]

[0027] (e I (t)) T Indicates e I Transpose of (t), e I (t)=I ～ (t)-I(t), where I(t) represents the radial basis function neural network weight vector, I ～ (t) represents the estimation of the weight vector of the radial basis function neural network, e I (t) indicates the error between the estimate and the actual value; (e A (t)) T Indicates e A Transpose of (t), e A (t)=A ～ (t)-A(t), where A ～ (t) represents the estimate of unmeasurable time-varying additive fault A(t), e A (t) indicates the error between the estimate and the actual value;

[0028] ③ Calculate the derivative of the Liyapunov function of the asymmetric integral type barrier:

[0029]

[0030] in,

[0031]

[0032] π(t) represents an unknown nonlinear term, and a 1 (t)=S 5 (t)-1.95 represents the difference between the dissolved oxygen concentration in the fifth partition and its restricted lower limit, a 2 (t)=2.05-S 5 (t) indicates the difference between the dissolved oxygen concentration in the fifth partition and its upper limit, Indicates the difference between the set value of dissolved oxygen concentration and its upper limit of constraints. It represents the difference between the set value of dissolved oxygen concentration and its constraint lower limit, and ln(.) represents a natural logarithmic function;

[0033] ④ Establish a radial basis function neural network estimator:

[0034] The output expression of a radial basis function neural network is as follows:

[0035]

[0036] in,

[0037]

[0038] π ～ (t) represents the estimated value of the unknown nonlinear term π(t) at time t, S 0i (t) represents the output of the i-th hidden layer neuron, x j (t) represents the jth input at the radial basis function neural network at t time, where x 1 (t)=S 5 (t), w i (t) Randomly take the value in the interval [0,1], c ji (t) represents the central value of the i-th hidden layer neuron corresponding to the jth input neuron at the radial basis function neural network, c ji (t) Randomly take the value in the interval [0,1], ξ ji (t) represents the center width value of the i-th hidden layer neuron corresponding to the j-th input neuron at the radial basis function neural network, ξ ji (t) Randomly take the value in the interval [0,1], e (·)Represents an exponential function;

[0039] Design the weight adaptive update strategy for radial basis function neural network:

[0040]

[0041] Among them, I ～ (t) represents the estimation of the weight vector I(t) of the radial basis function neural network, I(t)=[w 1 (t),w 2 (t),…,w 10 (t)] T ,S 0 (x j (t))=[S 01 (t),S 02 (t),…,S 010 (t)] T Represents the output vector of hidden layer neurons;

[0042] ⑤ Design fixed time fault-tolerant controller

[0043] Based on the derivative of the asymmetric integral type barrier Lyapunov function (8) and the weight adaptive update strategy of the radial basis function neural network (12), a fixed time fault tolerance control law is obtained:

[0044]

[0045] Among them (I ～ (t)) T Indicates I ～ Transpose of (t);

[0046] Estimation of unmeasurable time-varying additive faults in fixed-time fault tolerance control law (13) A ～ (t), design adaptive compensation terms:

[0047]

[0048] According to the fixed-time fault tolerance control law (13) and the designed adaptive compensation term (14), the system can quickly respond and compensate for deviations caused by blower failure to ensure the normal operation of the urban sewage treatment process; specifically, u(t) Indicates the input signal of the inverter at time t. The inverter controls the blower by adjusting the motor speed to ensure accurate tracking of dissolved oxygen concentration within the constraint range, so as to achieve stable operation of the urban sewage treatment process under blower failure;

[0049] The creativity of the present invention is mainly reflected in:

[0050] (1) The present invention constructs an asymmetric integral type barrier, the Lyapnov function directly constrains the dissolved oxygen concentration, ensuring that it does not exceed the asymmetric constraint range, and has a significant effect on improving water quality and enhancing the effectiveness of urban sewage treatment plants. Control problems under complex environmental conditions provide an innovative solution;

[0051] (2) The present invention proposes a fixed time fault-tolerant control method for the blower failure in urban sewage treatment process, adaptive compensation in the controller, which will affect the activity of microbials and affect the stability of urban sewage treatment process system. It estimates the unknown boundary of blower bias faults online, quickly compensates blower faults, has the characteristics of strong adaptability, and improves system safety; Attached description of the drawings

[0052] Figure 1 It is the radial basis function neural network topology structure of the present invention;

[0053] Figure 2 It is the result diagram of the dissolved oxygen concentration control of the present invention;

[0054] Figure 3 It is the error chart of the dissolved oxygen concentration control result of the present invention. Specific implementation methods

[0055] The present invention obtains a fixed time fault-tolerant control method for urban sewage treatment. The controller is based on the asymmetric integral obstacle Liyapunov function and fixed time stability criterion, quickly responds to compensate blower failure, accurately tracks and controls dissolved oxygen concentration, and ensures that Within a predetermined range, it improves the control performance of urban sewage treatment process and maintains the stability of dissolved oxygen concentration; approximates unknown terms of the system through the radial basis function neural network; solves the slow convergence speed existing in the current asymptotic stability control method, And the problem of blower failure resulting in the low dissolved oxygen concentration, which exceeds the constraint range, which in turn affects the stability of the urban sewage treatment process system. By adjusting the oxygen transfer coefficient of the urban sewage treatment process, the desired control of dissolved oxygen can be achieved even in the event of a blower failure to ensure the normal operation of the sewage treatment process;

[0056] The present invention adopts the following technical solutions and implementation steps:

[0057] 1. A fixed time fault-tolerant control method for urban sewage treatment process, characterized by constructing a dissolved oxygen dynamic model of urban sewage treatment process based on blower failure, and designing a fixed time fault-tolerant control for urban sewage treatment process based on radial basis function neural network To achieve safe and stable operation of urban sewage treatment process, including the following steps:

[0058] (1) Construct a dissolved oxygen dynamics model of urban sewage treatment process based on blower failure

[0059] During urban sewage treatment, the blower provides the oxygen required for metabolism to aerobic organisms to remove pollutants; however, the blower has problems such as motor wear or aging, resulting in a deviation from the required aeration capacity. In turn, insufficient oxygen supply affects the stability of the urban sewage treatment process system; by building a fixed-time fault-tolerant controller, dynamically compensates for the deviation caused by blower failure, thereby maintaining the stability of dissolved oxygen concentration:

[0060] Establish a dynamic model of dissolved oxygen concentration in urban sewage treatment process:

[0061]

[0062] Among them, S 5 (t) indicates the dissolved oxygen concentration in the fifth section of the biochemical reaction tank, S 4 (t)表示生化反应池第4分区溶解氧浓度,K L a 5 (t) represents the oxygen transfer coefficient in the fifth section of the biochemical reaction tank, R s (t) indicates the microbial reaction rate in the fifth section of the biochemical reaction pool, V 5 =1333 cubic meters represent the 5th partition volume, S s =8 mg / L indicates the saturation concentration of dissolved oxygen, Q 4 (t) indicates the flow rate of the fourth section of the biochemical reaction tank, Q 5 (t) represents the flow rate of the 5th section of the biochemical reaction tank, and the dissolved oxygen concentration constraint is 1.95<S 5 (t)<2.05; At the same time, an oxygen transfer coefficient model with blower failure was established:

[0063] K L a 5 (t)=0.5u(t)+A(t),t≥t f ; (16)

[0064] Where u(t) represents the actual control input, A(t) represents the unmeasurable time-varying additive fault and the boundary is |A(t)|≤1, t f = 6 days indicates an unknown moment when the failure occurs;

[0065] Combining the dissolved oxygen concentration kinetic model (15) of urban sewage treatment process and the oxygen transfer coefficient model (16) with blower failure, a dissolved oxygen concentration kinetic model based on blower failure is designed:

[0066]

[0067] Where, G(t)=-Q 5 (t)S 5 (t) / V 5 +Q 4 (t)S 4 (t) / V 5 +R s (t)表示生化反应池第5分区关于溶解氧浓度的未知非线性函数,M(t)=S s -S 5 (t) represents the difference between the dissolved oxygen concentration in the fifth partition and its saturation concentration;

[0068] (2) Design a fixed time fault-tolerant controller for urban sewage treatment process based on radial basis function neural network

[0069] ① Calculate the tracking error of dissolved oxygen concentration:

[0070]

[0071] in, Indicates the set value of dissolved oxygen concentration at time t, the time derivative of the dissolved oxygen concentration tracking error can be obtained:

[0072]

[0073] ②Construct the Liyapunov function of asymmetric integral type barrier:

[0074]

[0075] in,

[0076]

[0077] (e I (t)) T Indicates e I Transpose of (t), e I (t)=I ～ (t)-I(t), where I(t) represents the radial basis function neural network weight vector, I ～ (t) represents the estimation of the weight vector of the radial basis function neural network, e I (t) indicates the error between the estimate and the actual value; (e A (t)) T Indicates e A Transpose of (t), e A (t)=A ～ (t)-A(t), where A ～ (t) represents the estimate of unmeasurable time-varying additive fault A(t), e A (t) indicates the error between the estimate and the actual value;

[0078] ③ Calculate the derivative of the Liyapunov function of the asymmetric integral type barrier:

[0079]

[0080] in,

[0081]

[0082] π(t) represents an unknown nonlinear term, and a 1 (t)=S 5 (t)-1.95 represents the difference between the dissolved oxygen concentration in the fifth partition and its restricted lower limit, a 2 (t)=2.05-S 5 (t) indicates the difference between the dissolved oxygen concentration in the fifth partition and its upper limit, Indicates the difference between the set value of dissolved oxygen concentration and its upper limit of constraints. It represents the difference between the set value of dissolved oxygen concentration and its constraint lower limit, and ln(.) represents a natural logarithmic function;

[0083] ④ Establish a radial basis function neural network estimator:

[0084] The output expression of a radial basis function neural network is as follows:

[0085]

[0086] in,

[0087]

[0088] π ～ (t) represents the estimated value of the unknown nonlinear term π(t) at time t, S 0i (t) represents the output of the i-th hidden layer neuron, x j (t) represents the jth input at the radial basis function neural network at t time, where x 1 (t)=S 5 (t), w i (t) Randomly take the value in the interval [0,1], c ji (t) represents the central value of the i-th hidden layer neuron corresponding to the jth input neuron at the radial basis function neural network, c ji (t) Randomly take the value in the interval [0,1], ξ ji (t) represents the center width value of the i-th hidden layer neuron corresponding to the j-th input neuron at the radial basis function neural network, ξ ji (t) Randomly take the value in the interval [0,1], e (·) Represents an exponential function;

[0089] Design the weight adaptive update strategy for radial basis function neural network:

[0090]

[0091] Among them, I ～ (t) represents the estimation of the weight vector I(t) of the radial basis function neural network, I(t)=[w 1 (t),w 2 (t),…,w 10 (t)] T ,S 0 (x j (t))=[S 01 (t),S 02 (t),…,S 010 (t)] T Represents the output vector of hidden layer neurons;

[0092] ⑤ Design fixed time fault-tolerant controller

[0093] Based on the derivative of the asymmetric integral type barrier Lyapunov function (22) and the weight adaptive update strategy of the radial basis function neural network (26), a fixed time fault tolerance control law is obtained:

[0094]

[0095] Among them (I ～ (t)) T Indicates I ～ Transpose of (t);

[0096] Estimation of unmeasurable time-varying additive faults in fixed-time fault tolerance control law (27) A ～ (t), design adaptive compensation terms:

[0097]

[0098] (3) Realize the tracking and control of dissolved oxygen concentration

[0099] According to the fixed-time fault tolerance control law (27) and the designed adaptive compensation term (28), the system can quickly respond and compensate for deviations caused by blower failure to ensure the normal operation of the urban sewage treatment process; specifically, u(t) Indicates the input signal of the inverter at t time. The inverter controls the blower by adjusting the motor speed to ensure that the dissolved oxygen concentration is accurately tracked within the constraint range, so as to achieve stable operation of the urban sewage treatment process under blower failure; the actual output dissolved oxygen concentration value is as follows Figure 2 , X-axis: time, unit is day, Y-axis: dissolved oxygen concentration, unit is milligram / liter, the black solid line is the expected dissolved oxygen concentration value, and the blue dotted line is the actual dissolved oxygen output concentration value; the actual output dissolved oxygen concentration and The error of the desired dissolved oxygen concentration is as follows Figure 3 , X-axis: time, unit is day, Y-axis: dissolved oxygen concentration error value, unit is milligram / liter, the result proves the effectiveness of this method.

Claims

1. A fixed-time fault-tolerant control method for a municipal sewage treatment process, characterized in that: The following steps are involved: (1) Constructing a dissolved oxygen dynamics model for urban sewage treatment based on blower failure Establish a kinetic model of dissolved oxygen concentration in the urban sewage treatment process: Among them, S5(t) represents the dissolved oxygen concentration in the 5th partition of the biochemical reaction tank, S4(t) represents the dissolved oxygen concentration in the 4th partition of the biochemical reaction tank, and K L a5(t) represents the oxygen transfer coefficient in the 5th partition of the biochemical reaction tank, and R s (t) represents the microbial reaction rate in the 5th partition of the biochemical reaction tank, V5 represents the volume of the 5th partition, and S s represents the dissolved oxygen saturation concentration, Q4(t) represents the flow rate in the 4th partition of the biochemical reaction tank, Q5(t) represents the flow rate in the 5th partition of the biochemical reaction tank, and the dissolved oxygen concentration constraint condition is 1.95 < S5(t) < 2.05; meanwhile, an oxygen transfer coefficient model with blower failure is established: K L a5(t)=0.5u(t)+A(t),t≥t f ; (2) Where u(t) represents the actual control input, A(t) represents the unmeasurable time-varying additive fault and the limit is |A(t)|≤1, t f ≥0 indicates an unknown time when the fault occurred; Combining the dissolved oxygen concentration kinetic model of the urban sewage treatment process (1) and the oxygen transfer coefficient model with blower failure (2), a dissolved oxygen concentration kinetic model based on blower failure is designed: Where G(t) = -Q5(t)S5(t) / V5+Q4(t)S4(t) / V5+R s (t) represents the unknown nonlinear function of dissolved oxygen concentration in the fifth partition of the biochemical reaction tank, M(t) = S s -S5(t) represents the difference between the dissolved oxygen concentration in the 5th zone and its saturation concentration; (2) Design of a fixed-time fault-tolerant controller for urban sewage treatment process based on radial basis function neural network ① Calculate the dissolved oxygen concentration tracking error: in, Represents the set value of dissolved oxygen concentration at time t, and the time derivative of dissolved oxygen concentration tracking error can be obtained: ②Construct an asymmetric integral barrier Lyapunov function: in, (e I (t)) T Indicates e I The transpose of (t), e I (t) = I ～ (t)-I(t), where I(t) represents the weight vector of the radial basis function neural network, I ～ (t) represents the estimation of the weight vector of the radial basis function neural network, e I (t) represents the error between the estimate and the actual value; (e A (t)) T Indicates e A The transpose of (t), e A (t) = A ～ (t)-A(t), where A ～ (t) represents the estimate of the unmeasurable time-varying additive fault A(t), e A (t) represents the error between the estimate and the actual value; ③ Calculate the derivative of the asymmetric integral barrier Lyapunov function: in, π(t) represents the unknown nonlinear term, and a1(t)=S5(t)-1.95 represents the difference between the dissolved oxygen concentration in the fifth partition and its lower constraint limit, a2(t)=2.05-S5(t) represents the difference between the dissolved oxygen concentration in the fifth partition and its upper constraint limit, Represents the difference between the set value of dissolved oxygen concentration and its upper constraint limit, represents the difference between the set value of dissolved oxygen concentration and its lower limit, and ln(.) represents the natural logarithmic function; ④ Establish a radial basis function neural network estimator: The output expression of the radial basis function neural network is as follows: in, π ～ (t) represents the estimated value of the unknown nonlinear term π(t) at time t, S 0i (t) represents the output of the i-th hidden layer neuron, x j (t) represents the jth input of the radial basis function neural network at time t, where x1(t) = S5(t), w i (t) represents the connection weight between the i-th hidden layer neuron and the output neuron of the radial basis function neural network at time t, w i (t) takes a random value in the interval [0,1], c ji (t) represents the central value of the jth input neuron corresponding to the i-th hidden layer neuron at time t in the radial basis function neural network, c ji (t) takes a random value in the interval [0,1], ξ ji (t) represents the central width value of the jth input neuron corresponding to the i-th hidden layer neuron of the radial basis function neural network at time t, ξ ji (t) takes a random value in the interval [0,1], e (·) represents the exponential function; Design a weight adaptive update strategy for radial basis function neural networks: Among them, I ～ (t) represents the estimation of the radial basis function neural network weight vector I(t), I(t) = [w1(t), w2(t), …, w 10 (t)] T ,S0(x j (t))=[S 01 (t),S 02 (t),…,S 010 (t)] T Represents the output vector of hidden layer neurons; ⑤Design a fixed-time fault-tolerant controller According to the derivative of the asymmetric integral barrier Lyapunov function (8) and the weight adaptive update strategy of the radial basis function neural network (12), the fixed-time fault-tolerant control law is obtained: Among them (I ～ (t)) T Indicates I ～ The transpose of (t); Estimation of unmeasurable time-varying additive faults in fixed-time fault-tolerant control law (13) ～ (t), design the adaptive compensation term: According to the fixed-time fault-tolerant control law (13) and the designed adaptive compensation term (14), the deviation caused by the blower failure is compensated. The frequency converter controls the blower by adjusting the motor speed, thereby achieving stable operation of the urban sewage treatment process under the blower failure.

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