Constrained urban sewage treatment process anti-interference control method

Abstract

The invention provides an anti-interference control method for a constrained urban sewage treatment process. Stable control over the urban sewage treatment process with input and output constraints is achieved under challenging working conditions. A disturbance observer is designed, and lumped disturbance is accurately estimated according to related variables in the urban sewage treatment process; a nominal prediction model is designed, and necessary input is provided for a model prediction controller; an anti-interference control strategy comprising a compensation controller and a model prediction controller is designed, constraints can be comprehensively considered, and system disturbance can be effectively processed. Experimental results show that the method can realize stable control of the urban sewage treatment process with input and output constraints under challenging working conditions.

Description

Technical Field

[0001] The present invention designs a constrained urban sewage treatment process anti-disturbance control method, which realizes stable control of the urban sewage treatment process with input and output constraints under challenging working conditions. The sewage treatment process control belongs to both the field of intelligent control and the field of water treatment. Background Art

[0002] With the acceleration of urbanization, the demand for water resources has increased dramatically, and the amount of sewage discharged has increased significantly, which has brought tremendous pressure to sewage treatment plants. The activated sludge method has been widely used in major sewage treatment plants because of its efficient purification effect, good economy and stable operation. In the wastewater treatment process of the activated sludge method, in order to ensure sewage efficiency and system stability, it is crucial to effectively control the concentration of dissolved oxygen and nitrate nitrogen. However, sewage treatment systems face many challenges, including frequent fluctuations in influent flow and water quality, the complexity and nonlinear characteristics of the biological treatment process, and constraints on inputs and outputs. Therefore, it is of great significance to develop intelligent control strategies to ensure the efficient and stable operation of urban sewage treatment processes.

[0003] The municipal sewage treatment process controls the dissolved oxygen concentration and nitrate nitrogen concentration in the aeration tank by operating the oxygen transfer coefficient and the internal recirculation flow, which involves complex biological, chemical and physical processes and is a typical nonlinear control system. Due to the physical characteristics of the equipment and the system operation performance requirements, the input and output constraints of the system need to be considered in the sewage treatment process to ensure the feasibility of the control strategy. The model predictive control method can achieve optimal control of system performance while considering physical and safety constraints by solving the optimization problem containing explicit constraints. However, due to the uncertainty of environmental factors, the complexity of biochemical reactions and the dynamic characteristics of the system, the control of dissolved oxygen concentration in the sewage treatment process is susceptible to disturbances and uncertainties. In this case, the original constraints of the system may be too strict, making the optimization problem infeasible, thereby reducing the flexibility and response speed of the controller.

[0004] The soft-constrained model predictive control method allows the system to slightly violate the constraints at a certain cost when subject to disturbances and uncertainties to improve the adaptability of the controller. This enables the soft-constrained model predictive control method to provide a more flexible and practical control strategy in practical applications. Since it does not directly deal with disturbances and uncertainties, the simple soft-constrained model predictive control method cannot fully guarantee that the sewage treatment process control system can achieve stable tracking control of dissolved oxygen concentration to the desired set value under complex and challenging working conditions. The anti-disturbance control strategy can directly deal with disturbances and uncertainties to ensure the stability and tracking accuracy of the system. Its core idea is to treat all factors that may affect the performance of the system, including dynamic changes within the system and external disturbances, as lumped disturbances, and estimate and offset these disturbances by designing control strategies. Therefore, the introduction of anti-disturbance strategies in the soft-constrained model predictive control method can ensure the feasibility and robustness of the constraints of the urban sewage treatment process control system under various challenging environments.

[0005] The present invention designs a constrained anti-disturbance control method for urban sewage treatment process, constructs a disturbance observer to estimate the lumped disturbance using process variables, constructs a nominal prediction model to provide necessary input for the controller, designs an anti-disturbance control strategy, uses a compensation controller to compensate for matching disturbances, and uses a model predictive controller to handle non-matching disturbances and constraints, so as to achieve stable control of the urban sewage treatment process under challenging working conditions. Summary of the invention

[0006] The present invention proposes a constrained anti-disturbance control method for urban sewage treatment process, constructs a disturbance observer to estimate the lumped disturbance using process variables, constructs a nominal prediction model to provide necessary input for the controller, and designs an anti-disturbance control strategy including a compensation controller and a model predictive controller to handle disturbances and constraints, thereby solving the tracking control problem of the urban sewage treatment process under challenging working conditions.

[0007] The present invention adopts the following technical solutions and implementation steps:

[0008] 1. A constrained anti-disturbance control method for a municipal sewage treatment process, characterized by: constructing a municipal sewage treatment process control system, constructing a disturbance observer and a nominal prediction model based on a fuzzy neural network, designing an anti-disturbance controller to regulate the dissolved oxygen concentration and the nitrate nitrogen concentration, and realizing stable control of the municipal sewage treatment process; comprising the following steps:

[0009] (1) Construction of urban sewage treatment process control system

[0010] The input of the urban sewage treatment process control system is the oxygen transfer coefficient and the internal recirculation flow, and the output is the dissolved oxygen concentration and the nitrate nitrogen concentration. The system expression is:

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

[0012] Where x(k+1)=[x DO (k+1),x NO (k+1)] T , x DO (k+1) represents the actual value of dissolved oxygen concentration at time k+1, x NO (k+1) represents the actual value of nitrate nitrogen concentration at time k+1, T represents the transpose of the vector, x(k)=[x DO (k),x NO (k)] T , x DO (k) represents the actual value of dissolved oxygen concentration at time k, x NO (k) represents the actual value of nitrate nitrogen concentration at time k, u(k) = [u KLa (k),u Qa (k)] T ,u KLa (k) represents the oxygen transfer coefficient at time k, u Qa (k) represents the reflux at time k, d(k) represents the system disturbance at time k, and f(·) represents the unknown nonlinear function;

[0013] The input and output constraints of the urban sewage treatment process control system are set as:

[0014] 40≤u KLa (k)≤240 (2)

[0015] 0≤u Qa (k)≤92230 (3)

[0016]

[0017]

[0018] in, represents the lower bound of dissolved oxygen concentration at time k, represents the upper bound of dissolved oxygen concentration at time k, represents the lower bound of nitrate nitrogen concentration at time k, represents the upper bound of nitrate nitrogen concentration at time k, r DO (k) represents the set value of dissolved oxygen concentration at time k, r DO (k) Assign a value in the range [1.8,2.2], r NO (k) represents the set value of nitrate nitrogen concentration at time k, r NO (k) Assign values ​​in the range [0.8,1.2];

[0019] (2) Constructing a disturbance observer based on fuzzy neural network

[0020] The input of the fuzzy neural network disturbance observer is Wherein z1(k) represents the sample vector of dissolved oxygen concentration at time k, z2(k) represents the sample vector of chemical oxygen demand at time k, z3(k) represents the sample vector of biological oxygen demand at time k, z4(k) represents the sample vector of ammonia nitrogen concentration at time k, z5(k) represents the sample vector of oxygen transfer coefficient at time k, z6(k) represents the sample vector of total nitrogen concentration at time k, z7(k) represents the sample vector of sludge concentration at time k, and z8(k) represents the sample vector of influent flow at time k. The above sample vectors contain n samples;

[0021] The output of the fuzzy neural network disturbance observer is the disturbance estimate at time k, expressed as:

[0022]

[0023] Among them, w h (k) represents the connection weight between the hth normalized layer neuron and the output layer neuron of the fuzzy neural network at time k, w h (k) is randomly assigned a value in the range [0,1], z j (k) represents the jth input vector of the fuzzy neural network at time k, ε jh (k) represents the central value of the jth input layer neuron corresponding to the hth radial base layer neuron of the fuzzy neural network at time k, ε jh (k) is randomly assigned a value in the range [0,1], I n represents a vector of all 1s with 1 row and n columns, θ jh (k) represents the width value of the jth input layer neuron corresponding to the hth radial base layer neuron of the fuzzy neural network at time k, θ jh (k) is randomly assigned in the range of [0,3.5], j = 1, 2, ..., 8 represents the number of input feature variables of the fuzzy neural network, and h = 1, 2, ..., 10 represents the number of radial base layer neurons and normalization layer neurons of the fuzzy neural network;

[0024] The weight w of the fuzzy neural network disturbance observer h (k), center ε jh (k), and width θ jh The update strategy of (k) is designed as:

[0025]

[0026]

[0027]

[0028] Among them, e c (k) = 1 / 2(e DO (k)+e NO (k)), e DO (k) = r DO (k)-x DO (k) represents the tracking error of dissolved oxygen concentration at time k, e NO (k) = r NO (k)-x NO (k) represents the tracking error of nitrate nitrogen concentration at time k;

[0029] (3) Constructing a nominal prediction model based on fuzzy neural network

[0030] The input of the fuzzy neural network nominal prediction model is in represents the nominal value of dissolved oxygen concentration at time k-1, represents the nominal value of nitrate nitrogen concentration at time k-1, represents the nominal value of oxygen transfer coefficient at time k-1, It represents the nominal value of the reflux flow at time k-1;

[0031] The output of the fuzzy neural network nominal prediction model is the nominal prediction vector at time k in represents the nominal predicted value of dissolved oxygen concentration at time k, Represents the nominal predicted value of nitrate nitrogen concentration at time k, and the output expression is:

[0032]

[0033] Among them, v β (k)=[v β1 (k),v β2 (k)] T represents the connection weight vector of the βth normalized layer neuron and the output layer neuron of the fuzzy neural network at time k, v β1 (k) and v β2 (k) is randomly assigned a value in the range [0,1], s α (k) represents the αth input of the fuzzy neural network at time k, c αβ (k) represents the central value of the αth input layer neuron corresponding to the βth radial base neuron of the fuzzy neural network at time k, c αβ (k) is randomly assigned a value in the range [0,3], b αβ (k) represents the width value of the αth input layer neuron corresponding to the βth radial base neuron of the fuzzy neural network at time k, b αβ(k) is randomly assigned a value in the range of [0,3], α = 1, 2, ..., 4 represents the number of neurons in the input layer of the fuzzy neural network, and β = 1, 2, ..., 8 represents the number of neurons in the radial base layer and the normalization layer of the fuzzy neural network;

[0034] Weights v of the fuzzy neural network nominal prediction model β (k), center c αβ (k), and width b αβ The update strategy of (k) is designed as:

[0035]

[0036]

[0037]

[0038] in, represents the prediction error at time k, in represents the nominal value of dissolved oxygen concentration at time k, represents the nominal value of nitrate nitrogen concentration at time k;

[0039] The fuzzy neural network nominal prediction model is used to obtain the three-step prediction output at time k. The specific process is as follows:

[0040] Let the prediction model input be Get prediction output in represents the nominal predicted value of dissolved oxygen concentration at time k+1, represents the nominal predicted value of nitrate nitrogen concentration at time k+1 at time k;

[0041] Let the prediction model input be Get prediction output in represents the nominal predicted value of dissolved oxygen concentration at time k+2, represents the nominal predicted value of nitrate nitrogen concentration at time k+2 at time k;

[0042] Let the prediction model input be Get prediction output in represents the nominal predicted value of dissolved oxygen concentration at time k+3, represents the nominal predicted value of nitrate nitrogen concentration at time k+3 at time k;

[0043] (4) Design of anti-disturbance controller

[0044] The disturbance d(k) estimated by the disturbance observer is decomposed into matching disturbance and non-matching disturbance. The matching disturbance is expressed as:

[0045] d1(k)=g(x)g + (x)d(k) (14)

[0046] Where g(x)=[g DO (x),g NO (x)] T , g DO (x) = 8 - x DO (k), g NO (x) = x NO (k) / 1000, g + (x) = (g T (x)g(x)) -1 g T (x) represents the MP generalized inverse of g(x), and the non-matching perturbation is expressed as:

[0047] d2(k)=(Ig(x)g + (x))d(k) (15)

[0048] Where I represents a 2nd-order identity matrix;

[0049] Design compensation controller u for matching disturbance d1(k) DOB (k) is:

[0050] u DOB (k) = -d1(k) (16)

[0051] The reconstruction constraint formulas (4) and (5) for the non-matching disturbance d2(k) are:

[0052]

[0053]

[0054] Model Predictive Controller MPC The objective function of (k) is designed as:

[0055]

[0056] Where, σ(i|k)=[σ DO (i|k),σ NO (i|k)] T , where σ DO (i|k) represents the relaxation variable of dissolved oxygen concentration at time k+i calculated at time k, σ NO (i|k) represents the relaxation variable of the nitrate nitrogen concentration at time k+i calculated at time k, represents the tracking error of the system nominal output at time k+i calculated at time k, r(k+i)=[r DO (k+i),r NO (k+i)] T , where r DO (k+i) represents the set value of dissolved oxygen concentration at time k+i, r NO (k+i) represents the set value of nitrate nitrogen concentration at time k+i, in represents the nominal predicted value of dissolved oxygen concentration at time k+i at time k, represents the nominal predicted value of nitrate nitrogen concentration at time k+i at time k, Δu MPC (i|k)=u MPC (i|k)-u MPC (i|k-1) represents the increment of the model predictive control law at time k+i calculated at time k, u MPC (i|k) represents the model predictive control law at time k+i calculated at time k, u MPC (i|k-1) represents the model predictive control law at time k-1+i calculated at time k-1, i=0,...,3 represents the number of prediction steps;

[0057] The nonlinear programming method is used to solve the constrained optimization problem consisting of constraint condition formula (2), formula (3), formula (17), formula (18) and objective function formula (19) to obtain the model predictive control law at time k:

[0058]

[0059] Among them, arg min represents the decision variable that calculates the minimum value of the objective function;

[0060] Combined with compensation controller u DOB (k) and the model predictive controller u MPC (k), the disturbance rejection controller expression is:

[0061] u(k)=u DOB (k)+u MPC (k) (21)

[0062] (5) Stable control of urban sewage treatment process

[0063] The control law u(k) includes the oxygen transfer coefficient and the internal recirculation volume at time k. The programmable logic controller controls the frequency of the frequency converter according to the calculated oxygen transfer coefficient. The frequency converter controls the aeration volume by adjusting the speed of the blower. The electric regulating valve controls the internal recirculation by adjusting the valve opening according to the calculated internal recirculation volume. Finally, stable control of the constrained urban sewage treatment process is achieved by regulating the dissolved oxygen concentration and the nitrate nitrogen concentration.

[0064] The creativity of the present invention is mainly reflected in:

[0065] (1) The present invention designs a disturbance observer based on a fuzzy neural network to estimate the lumped disturbance, and estimates the lumped disturbance of the system according to the data change characteristics of the process variables, thereby solving the problem that it is difficult to accurately measure unknown disturbances in the urban sewage treatment process;

[0066] (2) The present invention designs an anti-disturbance control strategy, which uses a compensation controller to handle matching disturbances and a model predictive controller to suppress non-matching disturbances, thereby ensuring efficient and stable operation of the constrained urban sewage treatment process under challenging working conditions;

[0067] Special attention: The present invention is also applicable to the control of nitrogen removal and phosphorus removal in sewage treatment processes, nitrification processes and denitrification processes. Without departing from the core of the present invention, any simple deformation, modification or equivalent substitution shall fall within the protection scope of the claims of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 This is the controlled variable tracking control result diagram of the present invention.

[0069] Figure 2 This is the result diagram of the operating variables of the present invention.

[0070] Figure 3 is the relaxation variable result diagram of the present invention DETAILED DESCRIPTION

[0071] A constrained anti-disturbance control method for a municipal sewage treatment process is characterized by: constructing a municipal sewage treatment process control system, constructing a disturbance observer and a nominal prediction model based on a fuzzy neural network, designing an anti-disturbance controller to regulate the concentration of dissolved oxygen and the concentration of nitrate nitrogen, and realizing stable control of the municipal sewage treatment process; comprising the following steps:

[0072] (1) Construction of urban sewage treatment process control system

[0073] The input of the urban sewage treatment process control system is the oxygen transfer coefficient and the internal recirculation flow, and the output is the dissolved oxygen concentration and the nitrate nitrogen concentration. The system expression is:

[0074] x(k+1)=f(x(k),u(k),d(k)) (22)

[0075] Where x(k+1)=[x DO (k+1),x NO (k+1)] T , x DO (k+1) represents the actual value of dissolved oxygen concentration at time k+1, x NO (k+1) represents the actual value of nitrate nitrogen concentration at time k+1, T represents the transpose of the vector, x(k)=[x DO (k),x NO (k)] T , x DO (k) represents the actual value of dissolved oxygen concentration at time k, x NO (k) represents the actual value of nitrate nitrogen concentration at time k, u(k) = [u KLa (k),u Qa (k)] T ,u KLa (k) represents the oxygen transfer coefficient at time k, u Qa (k) represents the reflux at time k, d(k) represents the system disturbance at time k, and f(·) represents the unknown nonlinear function;

[0076] The input and output constraints of the urban sewage treatment process control system are set as:

[0077] 40≤u KLa (k)≤240 (23)

[0078] 0≤u Qa (k)≤92230 (24)

[0079]

[0080]

[0081] in, represents the lower bound of dissolved oxygen concentration at time k, represents the upper bound of dissolved oxygen concentration at time k, represents the lower bound of nitrate nitrogen concentration at time k, represents the upper bound of nitrate nitrogen concentration at time k, r DO (k) represents the set value of dissolved oxygen concentration at time k, r DO (k) Assign a value in the range [1.8,2.2], r NO (k) represents the set value of nitrate nitrogen concentration at time k, r NO (k) Assign values ​​in the range [0.8,1.2];

[0082] (2) Constructing a disturbance observer based on fuzzy neural network

[0083] The input of the fuzzy neural network disturbance observer is Wherein z1(k) represents the sample vector of dissolved oxygen concentration at time k, z2(k) represents the sample vector of chemical oxygen demand at time k, z3(k) represents the sample vector of biological oxygen demand at time k, z4(k) represents the sample vector of ammonia nitrogen concentration at time k, z5(k) represents the sample vector of oxygen transfer coefficient at time k, z6(k) represents the sample vector of total nitrogen concentration at time k, z7(k) represents the sample vector of sludge concentration at time k, and z8(k) represents the sample vector of influent flow at time k. The above sample vectors contain n samples;

[0084] The output of the fuzzy neural network disturbance observer is the disturbance estimate at time k, expressed as:

[0085]

[0086] Among them, w h (k) represents the connection weight between the hth normalized layer neuron and the output layer neuron of the fuzzy neural network at time k, w h (k) is randomly assigned a value in the range [0,1], z j (k) represents the jth input vector of the fuzzy neural network at time k, ε jh (k) represents the central value of the jth input layer neuron corresponding to the hth radial base layer neuron of the fuzzy neural network at time k, ε jh (k) is randomly assigned a value in the range [0,1], I n represents a vector of all 1s with 1 row and n columns, θ jh (k) represents the width value of the jth input layer neuron corresponding to the hth radial base layer neuron of the fuzzy neural network at time k, θ jh (k) is randomly assigned in the range of [0,3.5], j = 1, 2, ..., 8 represents the number of input feature variables of the fuzzy neural network, and h = 1, 2, ..., 10 represents the number of radial base layer neurons and normalization layer neurons of the fuzzy neural network;

[0087] The weight w of the fuzzy neural network disturbance observer h (k), center ε jh (k), and width θ jh The update strategy of (k) is designed as:

[0088]

[0089]

[0090]

[0091] Among them, e c(k) = 1 / 2(e DO (k)+e NO (k)), e DO (k) = r DO (k)-x DO (k) represents the tracking error of dissolved oxygen concentration at time k, e NO (k) = r NO (k)-x NO (k) represents the tracking error of nitrate nitrogen concentration at time k;

[0092] (3) Constructing a nominal prediction model based on fuzzy neural network

[0093] The input of the fuzzy neural network nominal prediction model is in represents the nominal value of dissolved oxygen concentration at time k-1, represents the nominal value of nitrate nitrogen concentration at time k-1, represents the nominal value of oxygen transfer coefficient at time k-1, It represents the nominal value of the reflux flow at time k-1;

[0094] The output of the fuzzy neural network nominal prediction model is the nominal prediction vector at time k in represents the nominal predicted value of dissolved oxygen concentration at time k, Represents the nominal predicted value of nitrate nitrogen concentration at time k, and the output expression is:

[0095]

[0096] Among them, v β (k)=[v β1 (k),v β2 (k)] T represents the connection weight vector of the βth normalized layer neuron and the output layer neuron of the fuzzy neural network at time k, v β1 (k) and v β2 (k) is randomly assigned a value in the range [0,1], s α (k) represents the αth input of the fuzzy neural network at time k, c αβ (k) represents the central value of the αth input layer neuron corresponding to the βth radial base neuron of the fuzzy neural network at time k, c αβ (k) is randomly assigned a value in the range [0,3], b αβ (k) represents the width value of the αth input layer neuron corresponding to the βth radial base neuron of the fuzzy neural network at time k, b αβ(k) is randomly assigned a value in the range of [0,3], α = 1, 2, ..., 4 represents the number of neurons in the input layer of the fuzzy neural network, and β = 1, 2, ..., 8 represents the number of neurons in the radial base layer and the normalization layer of the fuzzy neural network;

[0097] Weights v of the fuzzy neural network nominal prediction model β (k), center c αβ (k), and width b αβ The update strategy of (k) is designed as:

[0098]

[0099]

[0100]

[0101] in, represents the prediction error at time k, in represents the nominal value of dissolved oxygen concentration at time k, represents the nominal value of nitrate nitrogen concentration at time k;

[0102] The fuzzy neural network nominal prediction model is used to obtain the three-step prediction output at time k. The specific process is as follows:

[0103] Let the prediction model input be Get prediction output in represents the nominal predicted value of dissolved oxygen concentration at time k+1, represents the nominal predicted value of nitrate nitrogen concentration at time k+1 at time k;

[0104] Let the prediction model input be Get prediction output in represents the nominal predicted value of dissolved oxygen concentration at time k+2, represents the nominal predicted value of nitrate nitrogen concentration at time k+2 at time k;

[0105] Let the prediction model input be Get prediction output in represents the nominal predicted value of dissolved oxygen concentration at time k+3, represents the nominal predicted value of nitrate nitrogen concentration at time k+3 at time k;

[0106] (4) Design of anti-disturbance controller

[0107] The disturbance d(k) estimated by the disturbance observer is decomposed into matching disturbance and non-matching disturbance. The matching disturbance is expressed as:

[0108] d1(k)=g(x)g + (x)d(k) (35)

[0109] Where g(x)=[g DO (x),g NO (x)] T , g DO (x) = 8 - x DO (k), g NO (x) = x NO (k) / 1000, g + (x) = (g T (x)g(x)) -1 g T (x) represents the MP generalized inverse of g(x), and the non-matching perturbation is expressed as:

[0110] d2(k)=(Ig(x)g + (x))d(k) (36)

[0111] Where I represents a 2nd-order identity matrix;

[0112] Design compensation controller u for matching disturbance d1(k) DOB (k) is:

[0113] u DOB (k)=-d1(k) (37)

[0114] The reconstruction constraint formulas (4) and (5) for the non-matching disturbance d2(k) are:

[0115]

[0116]

[0117] Model Predictive Controller MPC The objective function of (k) is designed as:

[0118]

[0119] Where, σ(i|k)=[σ DO (i|k),σ NO (i|k)] T , where σ DO (i|k) represents the relaxation variable of dissolved oxygen concentration at time k+i calculated at time k, σ NO (i|k) represents the relaxation variable of the nitrate nitrogen concentration at time k+i calculated at time k, represents the tracking error of the system nominal output at time k+i calculated at time k, r(k+i)=[r DO (k+i),r NO (k+i)] T , where r DO (k+i) represents the set value of dissolved oxygen concentration at time k+i, r NO (k+i) represents the set value of nitrate nitrogen concentration at time k+i, in represents the nominal predicted value of dissolved oxygen concentration at time k+i at time k, represents the nominal predicted value of nitrate nitrogen concentration at time k+i at time k, Δu MPC (i|k)=u MPC (i|k)-u MPC (i|k-1) represents the increment of the model predictive control law at time k+i calculated at time k, u MPC (i|k) represents the model predictive control law at time k+i calculated at time k, u MPC (i|k-1) represents the model predictive control law at time k-1+i calculated at time k-1, i=0,...,3 represents the number of prediction steps;

[0120] The nonlinear programming method is used to solve the constrained optimization problem consisting of constraint condition formula (2), formula (3), formula (17), formula (18) and objective function formula (19) to obtain the model predictive control law at time k:

[0121]

[0122] Among them, arg min represents the decision variable that calculates the minimum value of the objective function;

[0123] Combined with compensation controller u DOB (k) and the model predictive controller u MPC (k), the disturbance rejection controller expression is:

[0124] u(k)=u DOB (k)+u MPC (k) (42)

[0125] (5) Stable control of urban sewage treatment process

[0126] The control law u(k) includes the oxygen transfer coefficient and the internal recirculation volume at time k. The programmable logic controller controls the frequency of the frequency converter according to the calculated oxygen transfer coefficient. The frequency converter controls the aeration volume by adjusting the speed of the blower. The electric regulating valve controls the internal recirculation by adjusting the valve opening according to the calculated internal recirculation volume. Finally, the stable control of the constrained urban sewage treatment process is achieved by regulating the dissolved oxygen concentration and the nitrate nitrogen concentration. Figure 1 Display the tracking results of dissolved oxygen concentration and nitrate nitrogen concentration, X-axis: time, the unit is day, Y-axis: dissolved oxygen concentration value and nitrate nitrogen concentration value, the unit is mg / L; Figure 2 Display oxygen transfer coefficient and internal recirculation volume, X-axis: time, unit is day, Y-axis: oxygen transfer coefficient and internal recirculation volume; Figure 3 The relaxation variable values ​​are displayed, X-axis: time, in days, Y-axis: relaxation variable values. The results prove the effectiveness of this method for controlling dissolved oxygen concentration and nitrate nitrogen concentration under challenging working conditions.

Claims

1. A constrained anti-disturbance control method for a municipal sewage treatment process, characterized by: Construct a control system for the urban sewage treatment process, construct a disturbance observer and a nominal prediction model based on a fuzzy neural network, design an anti-disturbance controller to regulate the dissolved oxygen concentration and nitrate nitrogen concentration, and achieve stable control of the urban sewage treatment process; including the following steps: (1) Construction of urban sewage treatment process control system The input of the urban sewage treatment process control system is the oxygen transfer coefficient and the internal recirculation flow, and the output is the dissolved oxygen concentration and the nitrate nitrogen concentration. The system expression is: x(k+1)=f(x(k),u(k),d(k)) (1) Where x(k+1)=[x DO (k+1),x NO (k+1)] T , x DO (k+1) represents the actual value of dissolved oxygen concentration at time k+1, x NO (k+1) represents the actual value of nitrate nitrogen concentration at time k+1, T represents the transpose of the vector, x(k)=[x DO (k),x NO (k)] T , x DO (k) represents the actual value of dissolved oxygen concentration at time k, x NO (k) represents the actual value of nitrate nitrogen concentration at time k, u(k) = [u KLa (k),u Qa (k)] T ,u KLa (k) represents the oxygen transfer coefficient at time k, u Qa (k) represents the reflux at time k, d(k) represents the system disturbance at time k, and f(·) represents the unknown nonlinear function; The input and output constraints of the urban sewage treatment process control system are set as: 40≤u KLa (k)≤240 (2) 0≤u Qa (k)≤92230 (3) in, x DO (k) = r DO (k)-0.1 represents the lower bound of dissolved oxygen concentration at time k, represents the upper bound of dissolved oxygen concentration at time k, x NO (k) = r NO (k)-0.05 represents the lower bound of nitrate nitrogen concentration at time k. represents the upper bound of nitrate nitrogen concentration at time k, r DO (k) represents the set value of dissolved oxygen concentration at time k, r DO (k) Assign a value in the range [1.8,2.2], r NO (k) represents the set value of nitrate nitrogen concentration at time k, r NO (k) Assign values ​​in the range [0.8,1.2]; (2) Constructing a disturbance observer based on fuzzy neural network The input of the fuzzy neural network disturbance observer is Wherein z1(k) represents the sample vector of dissolved oxygen concentration at time k, z2(k) represents the sample vector of chemical oxygen demand at time k, z3(k) represents the sample vector of biological oxygen demand at time k, z4(k) represents the sample vector of ammonia nitrogen concentration at time k, z5(k) represents the sample vector of oxygen transfer coefficient at time k, z6(k) represents the sample vector of total nitrogen concentration at time k, z7(k) represents the sample vector of sludge concentration at time k, and z8(k) represents the sample vector of influent flow at time k. The above sample vectors contain n samples; The output of the fuzzy neural network disturbance observer is the disturbance estimate at time k, expressed as: Among them, w h (k) represents the connection weight between the hth normalized layer neuron and the output layer neuron of the fuzzy neural network at time k, w h (k) is randomly assigned a value in the range [0,1], z j (k) represents the jth input vector of the fuzzy neural network at time k, ε jh (k) represents the central value of the jth input layer neuron corresponding to the hth radial base layer neuron of the fuzzy neural network at time k, ε jh (k) is randomly assigned a value in the range [0,1], I n represents a vector of all 1s with 1 row and n columns, θ jh (k) represents the width value of the jth input layer neuron corresponding to the hth radial base layer neuron of the fuzzy neural network at time k, θ jh (k) is randomly assigned in the range of [0,3.5], j = 1, 2, ..., 8 represents the number of input feature variables of the fuzzy neural network, and h = 1, 2, ..., 10 represents the number of radial base layer neurons and normalization layer neurons of the fuzzy neural network; The weight w of the fuzzy neural network disturbance observer h (k), center ε jh (k), and width θ jh The update strategy of (k) is designed as: Among them, e c (k) = 1 / 2(e DO (k)+e NO (k)), e DO (k) = r DO (k)-x DO (k) represents the tracking error of dissolved oxygen concentration at time k, e NO (k) = r NO (k)-x NO (k) represents the tracking error of nitrate nitrogen concentration at time k; (3) Constructing a nominal prediction model based on fuzzy neural network The input of the fuzzy neural network nominal prediction model is in represents the nominal value of dissolved oxygen concentration at time k-1, represents the nominal value of nitrate nitrogen concentration at time k-1, represents the nominal value of oxygen transfer coefficient at time k-1, It represents the nominal value of the reflux flow at time k-1; The output of the fuzzy neural network nominal prediction model is the nominal prediction vector at time k in represents the nominal predicted value of dissolved oxygen concentration at time k, Represents the nominal predicted value of nitrate nitrogen concentration at time k, and the output expression is: Among them, v β (k)=[v β1 (k),v β2 (k)] T represents the connection weight vector of the βth normalized layer neuron and the output layer neuron of the fuzzy neural network at time k, v β1 (k) and v β2 (k) is randomly assigned a value in the range [0,1], s α (k) represents the αth input of the fuzzy neural network at time k, c αβ (k) represents the central value of the αth input layer neuron corresponding to the βth radial base neuron of the fuzzy neural network at time k, c αβ (k) is randomly assigned a value in the range [0,3], b αβ (k) represents the width value of the αth input layer neuron corresponding to the βth radial base neuron of the fuzzy neural network at time k, b αβ (k) is randomly assigned a value in the range of [0,3], α = 1, 2, ..., 4 represents the number of neurons in the input layer of the fuzzy neural network, and β = 1, 2, ..., 8 represents the number of neurons in the radial base layer and the normalization layer of the fuzzy neural network; Weights v of the fuzzy neural network nominal prediction model β (k), center c αβ (k), and width b αβ The update strategy of (k) is designed as: in, represents the prediction error at time k, in represents the nominal value of dissolved oxygen concentration at time k, represents the nominal value of nitrate nitrogen concentration at time k; The fuzzy neural network nominal prediction model is used to obtain the three-step prediction output at time k. The specific process is as follows: Let the prediction model input be Get prediction output in represents the nominal predicted value of dissolved oxygen concentration at time k+1, represents the nominal predicted value of nitrate nitrogen concentration at time k+1 at time k; Let the prediction model input be Get prediction output in represents the nominal predicted value of dissolved oxygen concentration at time k+2, represents the nominal predicted value of nitrate nitrogen concentration at time k+2 at time k; Let the prediction model input be Get prediction output in represents the nominal predicted value of dissolved oxygen concentration at time k+3, represents the nominal predicted value of nitrate nitrogen concentration at time k+3 at time k; (4) Design of anti-disturbance controller The disturbance d(k) estimated by the disturbance observer is decomposed into matching disturbance and non-matching disturbance. The matching disturbance is expressed as: d1(k)=g(x)g + (x)d(k) (14) Where g(x)=[g DO (x),g NO (x)] T , g DO (x) = 8 - x DO (k), g NO (x) = x NO (k) / 1000, g + (x) = (g T (x)g(x)) -1 g T (x) represents the MP generalized inverse of g(x), and the non-matching perturbation is expressed as: d2(k)=(I-g(x)g + (x))d(k) (15) Where I represents a 2nd-order identity matrix; Design compensation controller u for matching disturbance d1(k) DOB (k) is: in DOB (k)=-d1(k) (16) The reconstruction constraint formulas (4) and (5) for the non-matching disturbance d2(k) are: Model Predictive Controller MPC The objective function of (k) is designed as: Where, σ(i|k)=[σ DO (i|k),σ NO (i|k)] T , where σ DO (i|k) represents the relaxation variable of dissolved oxygen concentration at time k+i calculated at time k, σ NO (i|k) represents the relaxation variable of the nitrate nitrogen concentration at time k+i calculated at time k, represents the tracking error of the system nominal output at time k+i calculated at time k, r(k+i)=[r DO (k+i),r NO (k+i)] T , where r DO (k+i) represents the set value of dissolved oxygen concentration at time k+i, r NO (k+i) represents the set value of nitrate nitrogen concentration at time k+i, in represents the nominal predicted value of dissolved oxygen concentration at time k+i at time k, represents the nominal predicted value of nitrate nitrogen concentration at time k+i at time k, Δu MPC (i|k)=u MPC (i|k)-u MPC (i|k-1) represents the increment of the model predictive control law at time k+i calculated at time k, u MPC (i|k) represents the model predictive control law at time k+i calculated at time k, u MPC (i|k-1) represents the model predictive control law at time k-1+i calculated at time k-1, i=0,...,3 represents the number of prediction steps; The nonlinear programming method is used to solve the constrained optimization problem consisting of constraint condition formula (2), formula (3), formula (17), formula (18) and objective function formula (19) to obtain the model predictive control law at time k: Among them, arg min represents the decision variable that calculates the minimum value of the objective function; Combined with compensation controller u DOB (k) and the model predictive controller u MPC (k), the disturbance rejection controller expression is: u(k)=u DOB (k)+u MPC (k) (21) (5) Stable control of urban sewage treatment process The control law u(k) includes the oxygen transfer coefficient and the internal recirculation volume at time k. The programmable logic controller controls the frequency of the frequency converter according to the calculated oxygen transfer coefficient. The frequency converter controls the aeration volume by adjusting the speed of the blower. The electric regulating valve controls the internal recirculation by adjusting the valve opening according to the calculated internal recirculation volume. Finally, stable control of the constrained urban sewage treatment process is achieved by regulating the dissolved oxygen concentration and the nitrate nitrogen concentration.

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