Multi-random sampling interval model prediction control method in urban sewage treatment process

Abstract

The invention provides a multi-random-sampling-interval model prediction control method in the urban sewage treatment process. Stable control over the dissolved oxygen concentration and the nitrate nitrogen concentration with the multi-random-sampling-interval characteristic is achieved. The multi-random sampling interval characteristic of a controlled system is considered, a fuzzy neural network model with different prediction step lengths is established, a prediction data interpolation algorithm is designed to reduce the calculation complexity of multi-model prediction, and an adaptive nominal prediction node updating mechanism is designed to ensure the interpolation prediction precision. Therefore, predicted output values of the dissolved oxygen concentration and the nitrate nitrogen concentration at the next possible sampling moment are calculated, an objective function based on predicted output is constructed, and a model prediction control law is calculated by minimizing the objective function. The problem that due to the multi-random sampling interval characteristic, the dissolved oxygen concentration and the nitrate nitrogen concentration are stably controlled in the urban sewage treatment process is solved. Experimental results show that the method can ensure the control precision of the dissolved oxygen concentration and the nitrate nitrogen concentration.

Description

Technical Field

[0001] The present invention designs a multi-random sampling interval model predictive controller, which realizes the random sampling control of dissolved oxygen concentration and nitrate nitrogen concentration in the process of urban sewage treatment. The control of dissolved oxygen concentration and nitrate nitrogen concentration is an important link in the process of urban sewage treatment and an important branch of the field of advanced manufacturing technology. It belongs to both the field of intelligent control and the field of water treatment. Background Art

[0002] With the continuous development of my country's economy and the accelerating urbanization, the discharge of urban sewage is increasing, and the problem of urban water shortage is becoming more and more serious. As a stable freshwater resource, the treatment and reuse of urban sewage can improve the utilization rate of water resources and improve the quality of urban water ecological environment in my country. It has become a strategic measure for my country to promote the construction of ecological civilization. In the process of urban sewage treatment, the dissolved oxygen concentration in the aerobic zone and the nitrate nitrogen concentration in the anoxic zone directly affect the progress of nitrification and denitrification reactions. Stable control of their concentrations will directly affect the sewage treatment effect. Therefore, in order to ensure the sewage treatment effect, it is very important to stably control the dissolved oxygen concentration and nitrate nitrogen concentration.

[0003] However, due to the complex biochemical reactions involved in the urban sewage treatment process, the large changes in influent flow and composition, and the influence of weather, operating conditions and other interferences, the urban sewage treatment process always operates in an unstable state. At the same time, due to the harsh sewage treatment environment, the physical equipment of the control system is easily randomly attached and blocked by sludge, resulting in multiple random sampling intervals in the sampling process of dissolved oxygen concentration and nitrate nitrogen concentration. Traditional control methods such as PID control and nonlinear model predictive control are mainly designed for periodic sampling, which is difficult to deal with such situations and cannot achieve stable control of dissolved oxygen concentration and nitrate nitrogen concentration. Therefore, it is of great application value to design an effective control method to achieve stable control of dissolved oxygen concentration and nitrate nitrogen concentration in the urban sewage treatment process under multiple random sampling intervals.

[0004] The present invention proposes a multi-random sampling interval model predictive control method for an urban sewage treatment process. By establishing a fuzzy neural network with different prediction step sizes, designing a prediction data interpolation algorithm and an adaptive nominal prediction node update mechanism, a real-time prediction model is obtained, and a multi-random sampling interval model predictive controller is designed to achieve stable control of the dissolved oxygen concentration and the nitrate nitrogen concentration in the sewage treatment process under multi-random sampling intervals. Summary of the invention

[0005] The present invention obtains a multi-random sampling interval model predictive control method for urban sewage treatment process. A fuzzy neural network with different prediction step sizes is established, a prediction data interpolation algorithm and an adaptive nominal prediction node update mechanism are designed, thereby obtaining a real-time prediction model and constructing a multi-random sampling interval model predictive controller, solving the problem of stable control of dissolved oxygen concentration and nitrate nitrogen concentration with multiple random sampling intervals in the urban sewage treatment process;

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

[0007] 1. A multi-random sampling interval model predictive control method for a municipal sewage treatment process, characterized in that it comprises the following steps:

[0008] (1) Establish multiple fuzzy neural network prediction models

[0009] The kth sampling interval of dissolved oxygen (DO) concentration and nitrate nitrogen (NOx-N) concentration is Δt k =t k+1 -t k , where t k represents the kth sampling time, t k+1 represents the k+1th sampling time, Δt k The possible value set is {6, 12, 15, 21, 30} minutes, and the probabilities are p1, p2, p3, p4 and p5 respectively. Five fuzzy neural network prediction models are constructed according to the five random sampling intervals of the system, which are denoted as model l, where l = 1, 2, 3, 4, 5. The prediction step length h of each model l is l Corresponding to the respective sampling intervals, i.e., h1=6, h2=12, h3=15, h4=21 and h5=30, the unit is minutes; the structure of each model includes 4 input layer neurons, 6 membership function layer neurons, 6 normalization layer neurons, and 2 output layer neurons; the output of model l is calculated as follows:

[0010]

[0011] in f l (·) is the mapping function of the input-output relationship of the system represented by model l. Prediction output at time T is the transpose of the formula, Prediction for model l DO concentration value at the time, Prediction for model l NOx-N concentration value at the moment, Yes k The input of model l at time instant, is the qth normalization layer neuron and output layer neuron of model l at t k The connection weight at the moment, whose elements are initialized to random values ​​in the range [0,1], t k The center vector of the neuron in the qth membership function layer of the model at time l, whose elements are initialized to random values ​​in the range [0,1], t k The neuron width vector of the qth membership function layer of the model at time l is also initialized to a random value in the range [0,1];

[0012] (2) Online correction of parameters of multiple prediction models

[0013] ①Let l = 1;

[0014] ②Calculate Δt k-1 =t k -t k-1 , t k-1 Indicates the k-1th sampling time of DO concentration and NOx-N concentration, and determines Δt k-1 =h l Minutes are established?

[0015] ③If not, increase l by 1 and return to step ②;

[0016] ④If it is established, then according to the model l at t k System prediction output at time With t k The actual system output y(t k ) Perform parameter correction, where Error Vector Expressed as in For model l in t k The error in predicting DO concentration at any moment, For model l in t k The error in predicting NOx-N concentration at any moment is corrected by the following formula:

[0017]

[0018] Where I represents the identity matrix, t k-1 The parameter vector of the model l at time Contains three types of parameters: model l at t k-1 The connection weight between the qth normalized layer neuron and the output layer neuron at the moment Model l in t k-1 The center vector of the qth membership function layer neuron at the moment Model l in tk-1 The width vector of the qth membership function layer neuron at time The calculation formula is:

[0019]

[0020] End the loop;

[0021] (3) Solving the model predictive control law

[0022] ① Use five prediction models to predict the first prediction step t k+1 All possible sampling times for system DO concentration values ​​and NOx-N concentration values. There are five possible sampling times: Indicated by t k The sampling time that may be reached based on the time of the first prediction step, where It represents five possible sampling intervals for 1-step prediction, and its value set is {6, 12, 15, 21, 30} minutes; the input of model l is unified as: t k The DO concentration of the system at the moment, t k NOx-N concentration at the time, t k Aeration volume at any time, t k The internal recirculation flow at the time, the output of model l is the corresponding Predicted values ​​of DO concentration and NOx-N concentration at the time for Predicted DO concentration at the time, for NOx-N concentration prediction value at the moment;

[0023] ② Design the prediction data interpolation algorithm and the adaptive nominal prediction node update mechanism to obtain the predicted values ​​of all possible DO concentrations and NOx-N concentrations within the set prediction domain of 3, and perform multi-step prediction, specifically:

[0024] For the p-th prediction step t k+p , p = 2,3, there are 5 possible combinations of sampling times p kind: l (i) It can take values ​​in the set {1,2,3,4,5}, i = 1,…,p, which represents the sampling time that may be reached in the p-th prediction step, where Represents the five possible sampling intervals for the i-th prediction step, and their value sets are all {6, 12, 15, 21, 30}

[0025] Minutes; the prediction output corresponding to the sampling time is recorded as The sampling time The predicted value of DO concentration, The sampling time The predicted value of NOx-N concentration;

[0026] In order to facilitate the subsequent calculation of the nominal prediction node, the following recursive multi-step prediction method is adopted:

[0027]

[0028] in is the input vector of model l at the p-th prediction step, t k The control vector u(t k )=[u1(t k ),u2(t k )] T ,u1(t k ) indicates t k The aeration volume at the time, u2(t k ) indicates t k The internal reflux at the time, Prediction output at time Represents prediction DO concentration value at the time, Represents prediction NOx-N concentration value at the moment, is the function approximated by the prediction model l in the p-th prediction step, indicating and Specifically, if p = 2, let the model input for The predicted DO concentration at the time, for NOx-N concentration prediction value at time, According to formula (1), we can get Prediction output at time For prediction DO concentration value at the time, For prediction NOx-N concentration value at the time; if p = 3, let the model input According to formula (1), we can get Prediction output at time For prediction DO concentration value at the time, For prediction NOx-N concentration value at the moment;

[0029] The adaptive nominal prediction node update mechanism is designed as follows: According to the change of prediction step, the number of nominal prediction nodes is calculated as follows

[0030]

[0031] in is the ceiling function, s p is the number of nominal prediction nodes in the p-th prediction step, p = 2, 3; at the same time, the nominal prediction nodes are calculated The horizontal axis t a as follows

[0032] t a =σ D(l) (B a ),a=1,...,s p (6)

[0033]

[0034] D(l)=max{l (p) -l (1)}(8)

[0035] where σ D(l) (B a ) represents the set B a The elements that satisfy the condition D(l) in represents one of the possible sampling moments of the p-th prediction step, and max{·} represents the maximum value function; according to formula (4), is the pth prediction step t a The predicted DO concentration at the time, is the pth prediction step t a The predicted value of NOx-N concentration at the time;

[0036] The Lagrange interpolation polynomial is constructed using the nominal prediction node as follows

[0037]

[0038] According to formula (9), the predicted values ​​of all possible DO concentrations and NOx-N concentrations are calculated in a multi-step prediction range of 3. Indicates prediction DO concentration value at the moment, Indicates prediction NOx-N concentration value at the moment, p = 2,3;

[0039] ③Calculate the mathematical expectation of the predicted output:

[0040]

[0041] in is the mth prediction step t k+m The mathematical expectation of the predicted DO concentration in is the mth prediction step t k+m The mathematical expectation of the predicted value of NOx-N concentration, m = 1, 2, 3; p1 = 0.63, p2 = 0.049, p3 = 0.27, p4 = 0.042, p5 = 0.009 are the probabilities of sampling intervals h1, h2, h3, h4, h5 respectively; Time prediction output Represents prediction DO concentration value at the time, Represents prediction NOx-N concentration value at the moment, l(1 ) =1,2,3,4,5; Time prediction output Represents prediction DO concentration value at the time, Represents prediction NOx-N concentration value at time, l (i) =1, 2, 3, 4, 5, i = 1,..., p;

[0042] ④Design objective function:

[0043]

[0044] Where r(t k )=[r(t k+1 ) T , r(t k+2 ) T , r(t k+3 ) T ] T , r(t k+μ )=[r1(t k+μ ), r2(t k+μ )] T , r1(t k+μ )=2 mg / L, indicating t k+μ Reference value of DO concentration at time r2(t k+μ )=1 mg / L, indicating t k+μ Reference value of NOx-N concentration at the moment, μ=1, 2, 3; Δu(t k )=[Δu1(t k ), Δu2(tk )] T , Δu1(t k ) is t k Aeration adjustment at each moment, Δu2(t k ) is t k The reflux adjustment amount within the time, where:

[0045] Δu(t k )=u(t k+1 )-u(t k ) (12)

[0046] |Δu(t k )|≤Δu max (13)

[0047] u(t k ) is t k The control vector at time is represented by u(t k )=[u1(t k ), u2(t k )] T ,u(t k+1 )=[u1(t k+1 ), u2(t k+1 )] T t k+1 The control vector at time, u1(t k+1 ) is t k+1 The aeration volume at the time, u2(t k+1 ) is t k+1 Internal recirculation at time, Δu max =[ΔK L a 5max , ΔQ amax ] T is the maximum adjustment vector allowed by the controller, ΔK L a 5max =100 liters / minute, indicating the maximum aeration adjustment allowed by the controller, ΔQ amax =50000L / min, indicating the maximum internal reflux adjustment allowed by the controller;

[0048] ⑤Minimize the cost function J(t k ) Calculate the output of the model predictive controller

[0049]

[0050] Adjust t k Aeration volume and internal recirculation volume at each moment:

[0051] u(t k+1 )=u(t k )+Δu(t k) (15)

[0052] (4) Achieve stable control of DO concentration and NOx-N concentration

[0053] Using the calculated control vector u(t k+1 ) can precisely control the DO concentration and NOx-N concentration, where u(t k+1 )=[u1(t k+1 ), u2(t k+1 )] T Including inverter input u1(t k+1 ) and sensor input u2(t k+1 ) The frequency converter adjusts the motor speed and controls the blower to adjust the aeration volume. At the same time, the sensor adjusts the internal reflux by adjusting the instrument opening control valve. The output of the system is the actual value of DO concentration and NOx-N concentration y(t k+1 )=[y1(t k+1 ), y2(t k+1 )] T , where y1(t k+1 ) represents the actual value of DO concentration, y2(t k+1 ) represents the actual value of NOx-N concentration.

[0054] The creativity of the present invention is mainly reflected in:

[0055] (1) In view of the challenge of multiple random sampling intervals in the sewage treatment process, it is difficult to establish an accurate model to predict the dissolved oxygen concentration and nitrate nitrogen concentration in real time. A fuzzy neural network model with different prediction step sizes is established, a prediction data interpolation algorithm and an adaptive nominal prediction node update mechanism are designed, and the predicted output of the dissolved oxygen concentration and nitrate nitrogen concentration at the next possible sampling moment is obtained, which provides the necessary information for the design of the controller.

[0056] (2) In order to solve the problem that multiple random sampling intervals are difficult to achieve stable control of dissolved oxygen concentration and nitrate nitrogen concentration in the sewage treatment process, the present invention designs a multi-random sampling interval model predictive controller based on the established real-time prediction model, which achieves stable control of dissolved oxygen concentration and nitrate nitrogen concentration.

[0057] It should be noted that the present invention is only for the convenience of description and adopts the control of dissolved oxygen concentration and nitrate nitrogen concentration. Similarly, the present invention can also be used to control ammonia nitrogen in sewage treatment processes, etc. As long as the principle of the present invention is used for control, it should fall within the scope of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a dissolved oxygen concentration control result diagram of the present invention;

[0059] Figure 2 This is the error diagram of the dissolved oxygen concentration control result of the present invention.

[0060] Figure 3 This is the nitrate nitrogen concentration control result diagram of the present invention

[0061] Figure 4 This is the error diagram of the nitrate nitrogen concentration control result of the present invention. DETAILED DESCRIPTION

[0062] 1. A multi-random sampling interval model predictive control method for a municipal sewage treatment process, characterized in that it comprises the following steps:

[0063] (1) Establish multiple fuzzy neural network prediction models

[0064] The kth sampling interval of dissolved oxygen (DO) concentration and nitrate nitrogen (NOx-N) concentration is Δt k =t k+1 -t k , where t k represents the kth sampling time, t k+1 represents the k+1th sampling time, Δt k The possible value set is {6, 12, 15, 21, 30} minutes, and the probabilities are p1, p2, p3, p4 and p5 respectively. Five fuzzy neural network prediction models are constructed according to the five random sampling intervals of the system, which are denoted as model l, where l = 1, 2, 3, 4, 5. The prediction step length h of each model l is l Corresponding to the respective sampling intervals, i.e., h1=6, h2=12, h3=15, h4=21 and h5=30, the unit is minutes; the structure of each model includes 4 input layer neurons, 6 membership function layer neurons, 6 normalization layer neurons, and 2 output layer neurons; the output of model l is calculated as follows:

[0065]

[0066] in f l (·) is the mapping function of the input-output relationship of the system represented by model l. Prediction output at time T is the transpose of the formula, Prediction for model l DO concentration value at the time, Prediction for model l NOx-N concentration value at the moment, Yes k The input of model l at time instant, is the qth normalization layer neuron and output layer neuron of model l at t kThe connection weight at the moment, whose elements are initialized to random values ​​in the range [0,1], t k The center vector of the neuron in the qth membership function layer of the model at time l, whose elements are initialized to random values ​​in the range [0,1], t k The neuron width vector of the qth membership function layer of the model at time instant l is also initialized to a random value in the range of [0,1];

[0067] (2) Online correction of parameters of multiple prediction models

[0068] ①Let l = 1;

[0069] ②Calculate Δt k-1 =t k -t k-1 , t k-1 Indicates the k-1th sampling time of DO concentration and NOx-N concentration, and determines Δt k-1 =h l Minutes are established?

[0070] ③If not, increase l by 1 and return to step ②;

[0071] ④If it is established, then according to the model l at t k System prediction output at time With t k The actual system output y(t k ) Perform parameter correction, where Error Vector Expressed as in For model l in t k The error in predicting DO concentration at any moment, For model l in t k The error in predicting NOx-N concentration at any moment is corrected by the following formula:

[0072]

[0073] Where I represents the identity matrix, t k-1 The parameter vector of the model l at time Contains three types of parameters: model l in t k-1 The connection weight between the qth normalized layer neuron and the output layer neuron at the moment Model l in t k-1 The center vector of the qth membership function layer neuron at the moment Model l in t k-1 The width vector of the qth membership function layer neuron at time The calculation formula is:

[0074]

[0075] End the loop;

[0076] (3) Solving the model predictive control law

[0077] ① Use five prediction models to predict the first prediction step t k+1 All possible sampling times for system DO concentration values ​​and NOx-N concentration values. There are five possible sampling times: Indicated by t k The sampling time that may be reached based on the time of the first prediction step, where It represents five possible sampling intervals for 1-step prediction, and its value set is {6, 12, 15, 21, 30} minutes; the input of model l is unified as: t k The DO concentration of the system at the moment, t k NOx-N concentration at the time, t k Aeration volume at any time, t k The internal recirculation flow at the time, the output of model l is the corresponding Predicted values ​​of DO concentration and NOx-N concentration at the time for Predicted DO concentration at the time, for NOx-N concentration prediction value at the moment;

[0078] ② Design the prediction data interpolation algorithm and the adaptive nominal prediction node update mechanism to obtain the predicted values ​​of all possible DO concentrations and NOx-N concentrations within the set prediction domain of 3, and perform multi-step prediction, specifically:

[0079] For the p-th prediction step t k+p , p = 2,3, there are 5 possible combinations of sampling times p kind: h l(p) , l (i) It can take values ​​in the set {1,2,3,4,5}, i = 1,…,p, which represents the sampling time that may be reached in the p-th prediction step, where represents the five possible sampling intervals for the i-th prediction step, and their value sets are all {6, 12, 15, 21, 30} minutes; the prediction output corresponding to the sampling time is recorded as The sampling time The predicted value of DO concentration, The sampling time The predicted value of NOx-N concentration;

[0080] In order to facilitate the subsequent calculation of the nominal prediction node, the following recursive multi-step prediction method is adopted:

[0081]

[0082] in is the input vector of model l at the p-th prediction step, t k The control vector u(t k )=[u1(t k ),u2(t k )] T ,u1(t k ) indicates t k The aeration volume at the time, u2(t k ) indicates t k The internal reflux at the time, Prediction output at time Indicates prediction DO concentration value at the time, Indicates prediction NOx-N concentration value at the time, is the function approximated by the prediction model l in the p-th prediction step, indicating and Specifically, if p = 2, let the model input for The predicted DO concentration at the time, for NOx-N concentration prediction value at time, According to formula (1), we can get Prediction output at time For prediction The DO concentration value at the time, For prediction NOx-N concentration value at the time; if p = 3, let the model input According to formula (1), we can get Prediction output at time For prediction The DO concentration value at the time, For prediction NOx-N concentration value at the moment;

[0083] The adaptive nominal prediction node update mechanism is designed as follows: According to the change of prediction step, the number of nominal prediction nodes is calculated as follows

[0084]

[0085] in is the ceiling function, s p is the number of nominal prediction nodes in the p-th prediction step, p = 2, 3; at the same time, the nominal prediction nodes are calculated The horizontal axis t a as follows

[0086] t a =σ D(l) (B a ),a=1,...,s p (6)

[0087]

[0088] D(l)=max{l (p) -l (1)} (8)

[0089] Where σD(l)(B a ) represents the set B a The elements that satisfy the condition D(l) in represents one of the possible sampling moments in the p-th prediction step, and max{·} represents the maximum value function, which is calculated according to formula (4) is the pth prediction step t a The predicted DO concentration at the time, is the pth prediction step t a The predicted value of NOx-N concentration at the time;

[0090] The Lagrange interpolation polynomial is constructed using the nominal prediction node as follows

[0091]

[0092] According to formula (9), the predicted values ​​of all possible DO concentrations and NOx-N concentrations are calculated in a multi-step prediction range of 3. Indicates prediction DO concentration value at the moment, Indicates prediction NOx-N concentration value at time, p = 2, 3;

[0093] ③Calculate the mathematical expectation of the predicted output:

[0094]

[0095] in is the mth prediction step t k+m The mathematical expectation of the predicted DO concentration in is the mth prediction step t k+m Mathematical expectation of the predicted value of NOx-N concentration, m = 1, 2, 3; p1 = 0.63, p2 = 0.049, p3 = 0.27, p4 = 0.042, p5 = 0.009 are the probabilities of sampling intervals h1, h2, h3, h4, h5 respectively; Time prediction output Represents prediction DO concentration value at the time, Represents prediction NOx-N concentration value at time, l (1) =1,2,3,4,5; Time prediction output Represents prediction DO concentration value at the time, Represents prediction NOx-N concentration value at time, l (i) =1, 2, 3, 4, 5, i = 1,..., p;

[0096] ④Design objective function:

[0097]

[0098] Where r(t k )=[r(t k+1 ) T , r(t k+2 ) T , r(t k+3 ) T ] T , r(t k+μ )=[r1(t k+μ ), r2(t k+μ )] T , r1(t k+μ )=2 mg / L, indicating t k+μ Reference value of DO concentration at time r2(t k+μ )=1 mg / L, indicating t k+μ Reference value of NOx-N concentration at the moment, μ=1, 2, 3; Δu(t k )=[Δu1(t k ), Δu2(t k )] T , Δu1(t k) is t k Aeration adjustment at each moment, Δu2(t k ) is t k The reflux adjustment amount within the time, where:

[0099] Δu(t k )=u(t k+1 )-u(t k ) (12)

[0100] |Δu(t k )|≤Δu max (13)

[0101] u(t k ) is t k The control vector at time is represented by u(t k )=[u1(t k ), u2(t k )] T ,u(t k+1 )=[u1(t k+1 ), u2(t k+1 )] T t k+1 The control vector at time, u1(t k+1 ) is t k+1 The aeration volume at the time, u2(t k+1 ) is t k+1 Internal recirculation at time, Δu max =[ΔK L a 5max , ΔQ amax ] T is the maximum adjustment vector allowed by the controller, ΔK L a 5max =100 liters / minute, indicating the maximum aeration adjustment allowed by the controller, ΔQ amax =50000L / min, indicating the maximum internal reflux adjustment allowed by the controller;

[0102] ⑤Minimize the cost function J(t k ) Calculate the output of the model predictive controller

[0103]

[0104] Adjust t k Aeration volume and internal recirculation volume at each moment:

[0105] u(t k+1 )=u(t k )+Δu(t k ) (15)

[0106] (4) Achieve stable control of dissolved oxygen concentration and nitrate nitrogen concentration

[0107] Using the calculated control vector u(t k+1 ) can precisely control the DO concentration and NOx-N concentration, where u(t k+1 )=[u1( t k +1 ), u2(t k+1 )] T Including inverter input u1(t k+1 ) and sensor input u2(t k+1 ) The frequency converter adjusts the motor speed and controls the blower to adjust the aeration volume. At the same time, the sensor adjusts the internal reflux by adjusting the instrument opening control valve. The output of the system is the actual value of DO concentration and NOx-N concentration y(t k+1 )=[y1(t k+1 ), y2(t k+1 )] T , where y1( t k +1 ) represents the actual value of DO concentration, y2(t k+1 ) represents the actual value of NOx-N concentration. Figure 1 Displays the dissolved oxygen concentration value of the system, X-axis: time, unit is day, Y-axis: dissolved oxygen concentration value, unit is mg / L, the solid line is the set value of dissolved oxygen concentration, and the dotted line is the actual dissolved oxygen concentration value; the error between the set value of dissolved oxygen concentration and the actual value of dissolved oxygen concentration is as follows: Figure 2 , X-axis: time, the unit is day, Y-axis: dissolved oxygen concentration error value, the unit is mg / L; Figure 3 The system displays the nitrate nitrogen concentration value. The X-axis is time in days, and the Y-axis is the nitrate nitrogen concentration value in mg / L. The solid line is the set nitrate nitrogen concentration value, and the dotted line is the actual nitrate nitrogen concentration value. The error between the set nitrate nitrogen concentration value and the actual nitrate nitrogen concentration value is as follows: Figure 4 ,X-axis: time, the unit is day, Y-axis: NOx-N concentration error value, the unit is mg / L, the results prove the effectiveness of this method.

Claims

1. A multi-random sampling interval model predictive control method for urban sewage treatment process, characterized in that: The following steps are involved: (1) Establish multiple fuzzy neural network prediction models The kth sampling interval of dissolved oxygen (DO) concentration and nitrate nitrogen (NOx-N) concentration is Δt k =t k+1 -t k , where t k represents the kth sampling time, t k+1 represents the k+1th sampling time, Δt k The possible value set is {6, 12, 15, 21, 30} minutes, and the probabilities are p1, p2, p3, p4 and p5 respectively. Five fuzzy neural network prediction models are constructed according to the five random sampling intervals of the system, which are denoted as model l, where l = 1, 2, 3, 4, 5. The prediction step length h of each model l is l Corresponding to the respective sampling intervals, i.e., h1=6, h2=12, h3=15, h4=21 and h5=30, the unit is minutes; the structure of each model includes 4 input layer neurons, 6 membership function layer neurons, 6 normalization layer neurons, and 2 output layer neurons; the output of model l is calculated as follows: in f l (·) is the mapping function of the input-output relationship of the system represented by model l. Prediction output at time T is the transpose of the formula, Prediction for model l DO concentration value at the time, Prediction for model l NOx-N concentration value at the moment, Yes k The input of model l at time instant, is the qth normalization layer neuron and output layer neuron of model l at t k The connection weight at the moment, whose elements are initialized to random values ​​in the range [0,1], t k The center vector of the neuron in the qth membership function layer of the model at time l, whose elements are initialized to random values ​​in the range [0,1], t k The neuron width vector of the qth membership function layer of the model at time instant l is also initialized to a random value in the range of [0,1]; (2) Online correction of parameters of multiple prediction models ①Let l = 1; ②Calculate Δt k-1 =t k -t k-1 , t k-1 Indicates the k-1th sampling time of DO concentration and NOx-N concentration, and determines Δt k-1 =h l Minutes are established? ③If not, increase l by 1 and return to step ②; ④If it is established, then according to the model l at t k System prediction output at time With t k The actual system output y(t k ) Perform parameter correction, where Error Vector Expressed as in For model l in t k The error in predicting DO concentration at any moment, For model l in t k The error in predicting NOx-N concentration at any moment is corrected by the following formula: Where I represents the identity matrix, t k-1 The parameter vector of the model l at time Contains three types of parameters: model l in t k-1 The connection weight between the qth normalized layer neuron and the output layer neuron at the moment Model l in t k-1 The central vector of the qth membership function layer neuron at the moment Model l in t k-1 The width vector of the qth membership function layer neuron at time The calculation formula is: End the loop; (3) Solving the model predictive control law ① Use five prediction models to predict the first prediction step t k+1 All possible sampling times for system DO concentration values ​​and NOx-N concentration values. There are five possible sampling times: l (1) =1,2,3,4,5, indicating that t k The sampling time that may be reached based on the time of the first prediction step, where h l(1) It represents five possible sampling intervals for 1-step prediction, and its value set is {6, 12, 15, 21, 30} minutes; the input of model l is unified as: t k The DO concentration of the system at the moment, t k NOx-N concentration at the time, t k Aeration volume at any time, t k The internal recirculation flow at the time, the output of model l is the corresponding Predicted values ​​of DO concentration and NOx-N concentration at the time for Predicted DO concentration at the time, for NOx-N concentration prediction value at the moment; ② Design the prediction data interpolation algorithm and the adaptive nominal prediction node update mechanism to obtain the predicted values ​​of all possible DO concentrations and NOx-N concentrations within the set prediction domain of 3, and perform multi-step prediction, specifically: For the p-th prediction step t k+p , p = 2,3, there are 5 possible combinations of sampling times p kind: l (i) It can take values ​​in the set {1,2,3,4,5}, i = 1,…,p, indicating the sampling time that may be reached in the p-th prediction step, where h l(i) , i=1,…,p represents the five possible sampling intervals for the i-th prediction step, and their value sets are all {6, 12, 15, 21, 30} minutes; the prediction output corresponding to the sampling time is recorded as The sampling time The predicted value of DO concentration, The sampling time The predicted value of NOx-N concentration; In order to facilitate the subsequent calculation of the nominal prediction node, the following recursive multi-step prediction method is adopted: in is the input vector of model l at the p-th prediction step, t k The control vector u(t k )=[u1(t k ),u2(t k )] T ,u1(t k ) indicates t k The aeration volume at the time, u2(t k ) indicates t k The internal reflux at the time, Prediction output at time Indicates prediction DO concentration value at the time, Indicates prediction NOx-N concentration value at the moment, is the function approximated by the prediction model l in the p-th prediction step, indicating and Specifically, if p = 2, let the model input for The predicted DO concentration at the time, for NOx-N concentration prediction value at time, According to formula (1), we can get Prediction output at time For prediction DO concentration value at the time, For prediction NOx-N concentration value at the time; if p = 3, let the model input According to formula (1), we can get Prediction output at time For prediction DO concentration value at the time, For prediction NOx-N concentration value at the moment; The adaptive nominal prediction node update mechanism is designed as follows: According to the change of prediction step, the number of nominal prediction nodes is calculated as follows in is the ceiling function, s p is the number of nominal prediction nodes in the pth prediction step, p = 2, 3; At the same time, the nominal prediction node is calculated a=1,…,s p The horizontal axis t a as follows t a =s D(l) (B a ),a=1,...,s p (6) D(l)=max{l (p) -l (1) } (8) where σ D(l) (B a ) represents the set B a The elements that satisfy the condition D(l) in p = 2, 3, represents one of the possible sampling moments of the p-th prediction step, and max{·} represents the maximum value function, which is calculated according to formula (4) is the pth prediction step t a The predicted DO concentration at the time, is the pth prediction step t a The predicted value of NOx-N concentration at the time; The Lagrange interpolation polynomial is constructed using the nominal prediction node as follows According to formula (9), the predicted values ​​of all possible DO concentrations and NOx-N concentrations are calculated in a multi-step prediction range of 3. Indicates prediction DO concentration value at the moment, Indicates prediction NOx-N concentration value at the moment, p = 2,3; ③Calculate the mathematical expectation of the predicted output: in is the mth prediction step t k+m The mathematical expectation of the predicted DO concentration in is the mth prediction step t k+m The mathematical expectation of the predicted value of NOx-N concentration, m = 1, 2, 3; p1 = 0.63, p2 = 0.049, p3 = 0.27, p4 = 0.042, p5 = 0.009 are the probabilities of sampling intervals h1, h2, h3, h4, h5 respectively; Time prediction output Indicates prediction DO concentration value at the time, Indicates prediction NOx-N concentration value at time l (1) =1,2,3,4,5; Time prediction output Indicates prediction DO concentration value at the time, Indicates prediction NOx-N concentration value at time l (i) =1,2,3,4,5,i=1,…,p; ④Design objective function: Where r(t k )=[r(t k+1 ) T ,r(t k+2 ) T ,r(t k+3 ) T ] T , r(t k+μ )=[r1(t k+μ ),r2(t k+μ )] T , r1(t k+μ )=2 mg / L, indicating t k+μ Reference value of DO concentration at time, r2(t k+μ )=1 mg / L, indicating t k+μ Reference value of NOx-N concentration at the moment, μ=1,2,3; Δu(t k )=[Δu1(t k ),Δu2(t k )] T , Δu1(t k ) is t k Aeration adjustment at each moment, Δu2(t k ) is t k The reflux adjustment amount within the time, where: Δu(t k )=u(t k+1 )-u(t k ) (12) |Δu(t k )|≤Δu max (13)u(t k ) is t k The control vector at time is represented by u(t k )=[u1(t k ),u2(t k )] T ,u(t k+1 )=[u1(t k+1 ),u2(t k+1 )] T t k+1 The control vector at time, u1(t k+1 ) is t k+1 The aeration volume at the time, u2(t k+1 ) is t k+1 Internal recirculation at time, Δu max =[ΔK L a 5max ,ΔQ amax ] T is the maximum adjustment vector allowed by the controller, ΔK L a 5max =100 liters / minute, indicating the maximum aeration adjustment allowed by the controller, ΔQ amax =50000L / min, indicating the maximum internal reflux adjustment allowed by the controller; ⑤Minimize the cost function J(t k ) Calculate the output of the model predictive controller Adjust t k Aeration volume and internal recirculation volume at each moment: u(t k+1 )=u(t k )+Δu(t k ) (15) (4) Achieve stable control of DO concentration and NOx-N concentration Using the calculated control vector u(t k+1 ) can precisely control the DO concentration and NOx-N concentration, where u(t k+1 )=[u1(t k+1 ),u2(t k+1 )] T Including inverter input u1(t k+1 ) and sensor input u2(t k+1 ) The frequency converter adjusts the motor speed and controls the blower to adjust the aeration volume; at the same time, the sensor adjusts the internal reflux by adjusting the instrument opening to control the valve; the output of the system is the actual value of DO concentration and NOx-N concentration y(t k+1 )=[y1(t k+1 ),y2(t k+1 )] T , where y1(t k+1 ) represents the actual value of DO concentration, y2(t k+1 ) represents the actual value of NOx-N concentration.

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