CN114527656B - Nitrate nitrogen concentration control method based on time-lag compensation strategy - Google Patents
Nitrate nitrogen concentration control method based on time-lag compensation strategy Download PDFInfo
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- 210000002569 neuron Anatomy 0.000 claims description 51
- 238000005192 partition Methods 0.000 claims description 20
- 238000010992 reflux Methods 0.000 claims description 16
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 claims description 11
- 241000894006 Bacteria Species 0.000 claims description 10
- 229910052760 oxygen Inorganic materials 0.000 claims description 9
- 239000001301 oxygen Substances 0.000 claims description 9
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 claims description 6
- 238000005842 biochemical reaction Methods 0.000 claims description 4
- FDWIKIIKBRJSHK-UHFFFAOYSA-N 2-(2-methyl-4-oxochromen-5-yl)acetic acid Chemical compound C1=CC=C2OC(C)=CC(=O)C2=C1CC(O)=O FDWIKIIKBRJSHK-UHFFFAOYSA-N 0.000 claims description 3
- 239000002028 Biomass Substances 0.000 claims description 3
- 229910002651 NO3 Inorganic materials 0.000 claims description 3
- NHNBFGGVMKEFGY-UHFFFAOYSA-N Nitrate Chemical compound [O-][N+]([O-])=O NHNBFGGVMKEFGY-UHFFFAOYSA-N 0.000 claims description 3
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- 238000004062 sedimentation Methods 0.000 claims description 3
- 230000004888 barrier function Effects 0.000 abstract description 3
- IJGRMHOSHXDMSA-UHFFFAOYSA-N Atomic nitrogen Chemical compound N#N IJGRMHOSHXDMSA-UHFFFAOYSA-N 0.000 description 2
- 101100436077 Caenorhabditis elegans asm-1 gene Proteins 0.000 description 2
- 101100204282 Neurospora crassa (strain ATCC 24698 / 74-OR23-1A / CBS 708.71 / DSM 1257 / FGSC 987) Asm-1 gene Proteins 0.000 description 2
- 230000001580 bacterial effect Effects 0.000 description 2
- 230000018109 developmental process Effects 0.000 description 2
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- 206010021143 Hypoxia Diseases 0.000 description 1
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- 230000008929 regeneration Effects 0.000 description 1
- 238000011069 regeneration method Methods 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
- 239000010802 sludge Substances 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
- 238000003911 water pollution Methods 0.000 description 1
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Abstract
A nitrate nitrogen concentration control method based on a time lag compensation strategy belongs to the field of control. Aiming at the problem that the nitrate nitrogen concentration is difficult to effectively control due to time-varying time lag in the denitrification process, a time-varying time lag model of the denitrification process is established through mechanism analysis and time lag tracing, unknown parts in the model are identified by adopting a fuzzy neural network, the influence of the Lyapunov-Ke-Lawski functional compensation time lag on the control performance is utilized, and the design of the barrier Lyapunov function ensures that the nitrate nitrogen concentration does not exceed a preset range. The result shows that the control method effectively eliminates the influence of time lag, ensures the designated tracking control performance and improves the stability of the sewage treatment process.
Description
Technical Field
Aiming at the problem that the nitrate nitrogen concentration is difficult to accurately control due to time-varying time-lag in a denitrification link in the urban sewage treatment process, the invention provides a nitrate nitrogen concentration control method based on a time-lag compensation strategy. The method can eliminate the influence of time-varying time lag on the control precision of nitrate nitrogen, ensure the expected control performance, realize the stable and efficient operation of the sewage treatment process, belongs to the control field and also belongs to the technical field of sewage treatment.
Background
Fresh water resources become one of global risks due to excessive development, improper drainage and unbalanced surface runoff distribution, and severely restrict the bottleneck of sustainable development of the economic society. With rapid expansion of urban scale and increased population density, municipal sewage has become a major source of pollution. The urban sewage regeneration and reuse is a direct and effective means for solving the water resource shortage and relieving the water pollution. The nitrate nitrogen concentration is used as an important operation parameter of the whole flow of urban sewage treatment, and the stability of the sewage treatment process and the standard reaching rate of the effluent quality are directly restricted by the control effect. Therefore, the research result of the invention has important theoretical significance and wide application prospect.
The nitrate nitrogen concentration is used as an important control variable for sewage treatment, and directly influences the microbial activity, the effluent quality, the sewage treatment process stability and the treatment efficiency. The sewage treatment process by the activated sludge process is a complex dynamic system and comprises a series of physical, chemical and biological reaction processes. Meanwhile, each biochemical reaction unit changes the time-varying plug flow time lag due to the change of the inflow water flow, and the time-varying circulation time lag is caused by the internal and external circulation flow velocity, which also brings great control difficulty to the nitrate nitrogen concentration control. The traditional control scheme ignores the existence of plug flow time lag and circulation time lag, which is obviously inconsistent with the actual sewage treatment process. Therefore, how to integrate plug flow time lag and backflow time lag into an ASM1 standard mechanism model, eliminate the influence of time-varying time lag on system control performance, improve the stability of the sewage treatment process, and become a problem to be solved in the field of urban sewage treatment control, and have very important practical application significance.
Aiming at the problem that nitrate nitrogen concentration is difficult to control due to plug flow time lag and circulation time lag in a denitrification link, the invention provides a nitrate nitrogen concentration control method based on a time lag compensation strategy, which is characterized in that a time lag mechanism model of the nitrate nitrogen concentration is established by analyzing an ASM1 standard mechanism model and tracing the plug flow time lag and the circulation time lag, unknown parts in a system are identified by using a fuzzy neural network, the influence of the Liapunov-kelasofos functional on control performance is compensated by using a barrier Liapunov function, and the nitrate nitrogen concentration and tracking error thereof are ensured to be always kept in a specified interval, so that the specified tracking control performance is realized.
Disclosure of Invention
Aiming at the problem that the nitrate nitrogen concentration is difficult to accurately control due to time-varying time delay in the denitrification link in the urban sewage treatment process, the invention provides a nitrate nitrogen concentration control method based on a time-delay compensation strategy, which mainly comprises the following steps:
The nitrate nitrogen concentration control method based on the time lag compensation strategy is characterized by being used for eliminating the influence of time lag on the accurate control of the nitrate nitrogen concentration and realizing the designated tracking control performance, and mainly comprises the following steps:
(1) Determining a time lag mechanism model: according to the characteristics of an anaerobic-anoxic-oxygen consumption process for urban sewage treatment, a time-lag mechanism model of a denitrification process is established:
wherein, the heterotrophic bacteria growth coefficient at the time t S NO,1(t),SNO,2 (t) and S NO,5 (t) are respectively actual nitrate nitrogen concentration values of the first partition, the second partition and the fifth partition at the moment t, S o,2 (t) is a dissolved oxygen concentration value of the second partition, mu H is a maximum growth rate of heterotrophic bacteria, K NO is a nitrate half-saturation coefficient, K OH is a heterotrophic bacteria oxygen half-saturation coefficient, Y H is a heterotrophic bacteria yield coefficient at the moment t, and parameters Y H,μH,KNO and K OH are determined according to an international water society release municipal sewage treatment biochemical reaction mechanism model; x (t) is the biomass concentration at time t; time-varying time lags τ1(t)＝VQa/Qa(t)+V2/Q1(t),τ2(t)＝VS/Q5(t)+VQr/Qr(t)+V2/Q1(t)+V1/(Qin(t)+Qr(t)),Qa(t) and Q r (t) represent the internal reflux amount and the external reflux amount at the moment t, Q 1(t),Q2 (t) and Q 5 (t) are the flow amounts of the first, second and fifth partitions at the moment t, V 1 and V 2 are the volumes of the first and second partitions, and V S,VQa,VQr is the volume of the secondary sedimentation tank, the internal circulation pipeline and the external circulation pipeline; τ i (t), i=1, 2 and its derivativeSatisfies τ i(t)≤τmax andThe constant τ max＝max{τ1(t),τ2 (t); determining the constraint condition of nitrate nitrogen concentration asK NO,s As for the nitrate nitrogen concentration constraint boundary, the value ranges are 98% and 102% of nitrate nitrogen concentration set values, and the BSM1 model is developed according to the combination of International water and European Union science and technology and cooperation organization, the range of the second partition nitrate nitrogen concentration set value is 0.8mg/L-1.2mg/L.
(2) The method for controlling the nitrate nitrogen concentration based on the time-lag compensation strategy is designed and comprises the following specific steps:
① Initializing the parameter quantity of the time lag compensation controller, the weight, the center and the width of the neural network, and setting the limit of the nitrate nitrogen concentration constraint and the limit of the tracking error constraint.
② The nitrate nitrogen concentration tracking error is calculated as follows:
zNO,2(t)＝SNO,2(t)-SNO,set(t) (2)
Wherein S NO,set (t) is a set value of nitrate nitrogen concentration at the moment t.
③ Calculating the time derivative of the tracking error of the nitrate nitrogen concentration
Wherein,Is the derivative of the nitrate nitrogen concentration error at the time t,Is the derivative of the nitrate nitrogen concentration at time t,And the derivative of the nitrate nitrogen concentration set value at the time t.
④ Design of Lyapunov function to ensure nitrate nitrogen concentration and tracking error not exceeding specified constraint range
Where e is a natural constant, log (-) is a natural logarithm, q NO (-) is an unknown function, Is the optimal weight vectorK NO,z is the nitrate nitrogen tracking error constraint boundary, and the value is 2% of the nitrate nitrogen concentration set value. Calculating the derivative of the Lyapunov function:
Wherein, τmax＝max{τ1(t),τ2(t)}。
⑤ A fuzzy neural network approximator designed for identifying unknown dynamic of a system comprises the following specific steps of
For the uncertainty term existing in the formula (5), an unknown function P NO(ZNO (t)) is defined, and the unknown function P NO(ZNO (t)) is identified by utilizing the approximation characteristic of the fuzzy neural network, wherein the fuzzy neural network is divided into four layers: the device comprises an input layer, RBF layers, a rule layer and an output layer, wherein the number of neurons of the input layer is 3, the number of neurons of the RBF layer is L, the number of neurons of the rule layer is P, and the number of neurons of the output layer is 1; the weights between the input layer and the RBF layer and between the RBF and the rule layer are 1, and the weights between the rule layer and the output layer are assigned in the interval of [ -1,1 ]; let the input of the fuzzy neural network at the time t be Z NO(t)＝[x1(t),x2(t),x3(t)],x1 (t) expressed as the nitrate nitrogen concentration at the time t S NO,2(t),x2 (t) expressed as the nitrate nitrogen set value at the time t S NO,set(t),x3 (t) expressed as the nitrate nitrogen concentration derivative at the time tThe fuzzy neural network output is denoted q (t); the fuzzy neural network identification process is as follows:
Input layer: the layer consists of 3 neurons, the output of each neuron is
hj(t)＝xj(t),j＝1,2,3 (6)
Wherein h j (t) represents the output of the jth neuron of the input layer at time t, and x j (t) represents the input of the jth neuron of the input layer at time t.
RBF layer: the layer is composed of L neurons, a positive integer L epsilon [5,15], and the output of each neuron is
Wherein, in the RBF layer, c ji (t) is the central value of the j-th membership function of the i-th neuron at the moment t, n ji is the width value of the j-th membership function of the i-th neuron at the moment t,Representing the output of the ith neuron of the RBF layer at time t.
Rule layer: the layer is composed of P neurons, the positive integer P E [5,15], the output of each neuron is
Wherein,Is the output value of the ith neuron at the t-th iteration.
Output layer: the output of the layer is as follows:
wherein w i (t) is the connection weight between the ith neuron of the t-time normalization layer and the output layer, and q (t) is the output of the t-time output layer. The unknown function identification process by using the fuzzy neural network is as follows
Wherein,For the fuzzy neural network input vector, the T symbol is transposed,For the fuzzy neural network to be an optimal weight vector,Representing the activation function vector, and according to the approximation characteristic of the fuzzy neural network, the normal number existsSo that the recognition error ε NO(ZNO (t)) satisfies
Updating the fuzzy neural network weight:
Wherein the normal number sigma 1 has a value range of (0, 2).
⑥ Calculating the internal reflux quantity at the moment t, wherein the output value of the internal reflux quantity consists of an adaptive control function u a (t) and a fuzzy neural network compensation function u Fnn (t)
o1(t)＝uFnn(t)+ua(t) (12)
Wherein, the positive constant c 1 is selected so that the tracking error of the nitrate nitrogen concentration does not exceed the range of the set value of the nitrate nitrogen concentration by 2 percent
⑦ Calculating the actual output of nitrate nitrogen concentration based on time-lag compensation strategy
Wherein, Q a,max is the maximum internal reflux amount allowed by the system, and Q a,min is the daily average water inflow.
(3) And (3) tracking and controlling the nitrate nitrogen concentration by using the solved Q a (t), eliminating the influence of time-varying time lag on control performance, and ensuring that the nitrate nitrogen concentration is always kept in the constraint range appointed in the step (1).
The invention mainly comprises the following steps:
Aiming at the problem that the nitrate nitrogen concentration is difficult to accurately control due to time-varying time lag in the denitrification link in the urban sewage treatment process, the invention utilizes the fuzzy neural network to identify nonlinear dynamics in the sewage treatment process, adopts the Lyapunov-kelasofos functional to eliminate the influence of time-varying time lag on control precision, uses the barrier Lyapunov function to ensure the appointed control performance, and realizes the stable and efficient operation of the sewage treatment process
Drawings
FIG. 1 control method architecture diagram
FIG. 2 shows a graph of plug flow and cycle time lag analysis
FIG. 3 is a graph showing the effect of controlling nitrogen in the Chi Xiao-state of oxygen deficiency
FIG. 4 is a graph of the results of tracking errors of nitrate nitrogen
Detailed Description
Aiming at the problem that the nitrate nitrogen concentration is difficult to accurately control due to time lag in a denitrification link in the urban sewage treatment process, the invention provides a nitrate nitrogen concentration control method based on a time lag compensation strategy, wherein the nitrate nitrogen concentration is used as a control variable, the internal flow is used as an operation quantity, the frame of the nitrate nitrogen concentration time lag compensation control method is shown in figure 1, and the plug flow time lag and circulation time lag analysis is shown in figure 2. In order to realize the accurate control of the nitrate nitrogen concentration in the sewage treatment process, the provided nitrate nitrogen concentration control method based on the time lag compensation strategy comprises the following steps:
The nitrate nitrogen concentration control method based on the time lag compensation strategy is characterized by being used for eliminating the influence of time lag on the accurate control of the nitrate nitrogen concentration and realizing the designated tracking control performance, and mainly comprises the following steps:
(1) Determining a time lag mechanism model: according to the characteristics of an anaerobic-anoxic-oxygen consumption process for urban sewage treatment, the sampling period of each component sensor of the urban sewage is 15min, and a time lag mechanism model of a denitrification process is established:
wherein, the heterotrophic bacteria growth coefficient at the time t S NO,1(t),SNO,2 (t) and S NO,5 (t) are respectively the actual values of nitrate nitrogen concentration of the first partition, the second partition and the fifth partition at the moment t, S O,2 (t) is the value of dissolved oxygen concentration of the second partition, mu H is the maximum growth rate of heterotrophic bacteria, K NO is a nitrate half-saturation coefficient, K OH is a heterotrophic bacterial oxygen half-saturation coefficient, Y H is a t-moment heterotrophic bacterial yield coefficient, a parameter Y H＝0.67,μH =4/day is determined according to an international water society release municipal sewage treatment biochemical reaction mechanism model, K NO =0.5 g/cubic meter, K OH =0.2 g/cubic meter, X (t) is the biomass concentration at time t; Time-varying lags τ1(t)＝VQa/Qa(t)+V2/Q1(t),τ2(t)＝VS/Q5(t)+V2/Q2(t)+V1/(Qin(t)+Qr(t))+VQr/Qr(t),Qa(t) and Q r (t) represent the inner and outer reflux amounts at time t, Q 1 (t) and Q 2 (t) are the first and second reflux amounts at time t, V 1 and V 2 are the volumes of the first and second partitions, V 2＝1000m3,VS,VQa,VQr are the volumes of the secondary sedimentation tank, the internal circulation and the external circulation pipeline, V S＝6000m3,VQa＝4167m3 and V Qr＝3535.5m3;τi (t), i=1, 2 and their derivatives, respectively Satisfies τ i(t)≤τmax andConstant τ max＝max{τ1(t),τ2 (t) }, constantThe range of the value of (0, 1) is determined as the constraint condition of the nitrate nitrogen concentrationWherein, the nitrate nitrogen set value of K NO,S =98% and K NO,S =102% is known from the BSM1 model developed by the combination of the international water company, the European Union science and the cooperation organization, and the concentration set value of the nitrate nitrogen of the second partition ranges from 0.8mg/L to 1.2mg/L. In order to verify the effectiveness of the method, the set value of the nitrate nitrogen concentration of the second subarea is 1mg/L when t is less than 4, 0.8mg/L when t is more than or equal to 4 and less than 6 days, 1.2mg/L when t is more than or equal to 6 and less than 11, and 1mg/L when t is more than or equal to 11 and less than or equal to 14.
(2) The method for controlling the nitrate nitrogen concentration based on the time-lag compensation strategy is designed and comprises the following specific steps:
① Initializing the parameter quantity of the time lag compensation controller, the weight, the center and the width of the neural network, and setting the limit of the nitrate nitrogen concentration constraint and the limit of the tracking error constraint.
② The nitrate nitrogen concentration tracking error is calculated as follows:
zNO,2(t)＝SNO,2(t)-SNO,set(t) (2)
Wherein S NO,set (t) is a set value of nitrate nitrogen concentration at the moment t.
③ Calculating the time derivative of the tracking error of the nitrate nitrogen concentration
Wherein,Is the derivative of the nitrate nitrogen concentration error at the time t,Is the derivative of the nitrate nitrogen concentration at time t,And the derivative of the nitrate nitrogen concentration set value at the time t.
④ Design of Lyapunov function to ensure nitrate nitrogen concentration and tracking error not exceeding specified constraint range
Where e is a natural constant, log (-) is a natural logarithm, q NO (-) is an unknown function, Is the optimal weight vectorK NO,z is the nitrate nitrogen tracking error constraint, k NO,2＝0.02SNO,set (t). Calculating the derivative of the Lyapunov function:
Wherein, τmax＝max{τ1(t),τ2(t)}。
⑤ A fuzzy neural network approximator designed for identifying unknown dynamic of a system comprises the following specific steps of
For the uncertainty term existing in the formula (5), an unknown function P NO(ZNO (t)) is defined, and the unknown function P NO(ZNO (t)) is identified by utilizing the approximation characteristic of the fuzzy neural network, wherein the fuzzy neural network is divided into four layers: the device comprises an input layer, RBF layers, a rule layer and an output layer, wherein the number of neurons of the input layer is 3, the number of neurons of the RBF layer is 10, the number of neurons of the rule layer is 10, and the number of neurons of the output layer is 1; the weights between the input layer and the RBF layer and between the RBF and the rule layer are 1, and the weights between the rule layer and the output layer are assigned in the interval of [ -1, 1]; let the input of the fuzzy neural network at the time t be Z NO(t)＝[x1(t),x2(t),x3(t)],x1 (t) expressed as the nitrate nitrogen concentration at the time t S NO,2(t),x2 (t) expressed as the nitrate nitrogen set value at the time t S NO,set(t),x3 (t) expressed as the nitrate nitrogen concentration derivative at the time tThe fuzzy neural network output is denoted q (t); the fuzzy neural network identification process is as follows:
Input layer: the layer consists of 3 neurons, the output of each neuron is
hj(t)＝xj(t),j＝1,2,3 (6)
Wherein h j (t) represents the output of the jth neuron of the input layer at time t, and x j (t) represents the input of the jth neuron of the input layer at time t.
RBF layer: the RBF layer consists of 10 neurons, each neuron outputting as
Wherein the natural constant e=2.71828, in the RBF layer, c ji (t) is the center value of the j-th membership function of the i-th neuron at the time t, n ji is the width value of the j-th membership function of the i-th neuron at the time t,Representing the output of the ith neuron of the RBF layer at time t.
Rule layer: the layer consists of 10 neurons, each neuron outputting as
Wherein,Is the output value of the ith neuron at the t-th iteration.
Output layer: the output of the layer is as follows:
wherein w i (t) is the connection weight between the ith neuron of the t-time normalization layer and the output layer, and q (t) is the output of the t-time output layer. The unknown function identification process by using the fuzzy neural network is as follows
Wherein,For the fuzzy neural network input vector, the T symbol is transposed,For the fuzzy neural network to be an optimal weight vector,Representing the activation function vector, and according to the approximation characteristic of the fuzzy neural network, the normal number existsSo that the recognition error ε NO(ZNO (t)) satisfiesThe initial parameters of the neural network are selected asThe width η 1 =2, the central value ranges are [ -2,2] × [ -15,20] × [ -1,3].
Updating the fuzzy neural network weight:
Wherein the constant σ 1 =0.15.
⑥ Calculating the internal reflux quantity at the moment t, wherein the output value o 1 (t) of the internal reflux quantity consists of an adaptive control function u a (t) and a fuzzy neural network compensation function u Fnn (t)
o1(t)＝uFnn(t)+ua(t) (12)
Where, given c 1 = 1572,
⑦ Calculating the actual output of nitrate nitrogen concentration based on time-lag compensation strategy
Wherein Q a,max＝5Q0,stab,Qa,min＝Q0,stab,Q0,stab＝19106m3/d is daily average water inflow.
(3) And (3) tracking and controlling the nitrate nitrogen concentration by using the solved Q a (t), eliminating the influence of time-varying time lag on control performance, and ensuring that the nitrate nitrogen concentration is always kept in the constraint range appointed in the step (1).
The provided self-adaptive fuzzy neural network control method solves the problem that the plug flow time lag and the circulation time lag precisely affect the nitrate nitrogen control, takes the reflux quantity in the moment t as an operation variable, and takes the nitrate nitrogen concentration in the moment t as a system output value, thereby realizing precise tracking of the nitrate nitrogen concentration in the moment t. FIG. 3 shows the nitrate nitrogen concentration set point and tracking control results for the system, X axis: time, in days, Y-axis: the nitrate nitrogen concentration value is in milligrams per liter, the solid line is a nitrate nitrogen concentration set value, the dotted line is a nitrate nitrogen concentration tracking value, and the dotted line represents the upper/lower limit of the nitrate nitrogen concentration constraint; FIG. 4 shows the results of nitrate nitrogen concentration tracking error, X-axis: time, in days, Y-axis: the internal reflux quantity is in milligrams per liter, the solid line is the nitrate nitrogen concentration tracking error, and the dotted line is the upper/lower bound of the nitrate nitrogen concentration tracking error.
Claims (1)
1. The nitrate nitrogen concentration control method based on the time lag compensation strategy is characterized by comprising the following steps of:
(1) Determining a time lag mechanism model: according to the characteristics of an anaerobic-anoxic-oxygen consumption process for urban sewage treatment, a time-lag mechanism model of a denitrification process is established:
wherein, the heterotrophic bacteria growth coefficient at the time t S NO,1(t),SNO,2 (t) and S NO,5 (t) are respectively actual nitrate nitrogen concentration values of the first partition, the second partition and the fifth partition at the moment t, S O,2 (t) is a dissolved oxygen concentration value of the second partition, mu H is a maximum growth rate of heterotrophic bacteria, K NO is a nitrate half-saturation coefficient, K OH is a heterotrophic bacteria oxygen half-saturation coefficient, Y H is a heterotrophic bacteria yield coefficient at the moment t, and parameters Y H,μH,KNO and K OH are determined according to an international water society release municipal sewage treatment biochemical reaction mechanism model; x (t) is the biomass concentration at time t; time-varying time lags τ1(t)＝VQa/Qa(t)+V2/Q1(t),τ2(t)＝VS/Q5(t)+VQr/Qr(t)+V2/Q1(t)+V1/(Qin(t)+Qr(t)),Qa(t) and Q r (t) represent the internal reflux amount and the external reflux amount at the moment t, Q l(t),Q2 (t) and Q 5 (t) are the flow amounts of the first, second and fifth partitions at the moment t, V 1 and V 2 are the volumes of the first and second partitions, and V S,VQa,VQr is the volume of the secondary sedimentation tank, the internal circulation pipeline and the external circulation pipeline; τ i (t), i=1, 2 and its derivativeSatisfies τ i(t)≤τmax andThe constant τ max＝max{τ1(t),τ2 (t); determining the constraint condition of nitrate nitrogen concentration asK NO,s As for the nitrate nitrogen concentration constraint boundary, the value ranges are 98% and 102% of nitrate nitrogen concentration set values, and the BSM1 model is developed according to the combination of international water and European Union science and technology and cooperation organization, the range of the second partition nitrate nitrogen concentration set value is 0.8mg/L-1.2mg/L;
(2) The method for controlling the nitrate nitrogen concentration based on the time-lag compensation strategy is designed and comprises the following specific steps:
① Initializing the parameter quantity of a time lag compensation controller, the weight, the center and the width of a neural network, and setting a nitrate nitrogen concentration constraint limit and a tracking error constraint limit;
② The nitrate nitrogen concentration tracking error is calculated as follows:
zNO,2(t)＝SNO,2(t)-SNO,set(t) (2)
s NO,set (t) is a set value of nitrate nitrogen concentration at the moment t;
③ Calculating the time derivative of the tracking error of the nitrate nitrogen concentration
Wherein,Is the derivative of the nitrate nitrogen concentration error at the time t,Is the derivative of the nitrate nitrogen concentration at time t,The derivative of the nitrate nitrogen concentration set value at the time t;
④ Design of Lyapunov function to ensure nitrate nitrogen concentration and tracking error not exceeding specified constraint range
Where e is a natural constant, log (-) is a natural logarithm, q NO (-) is an unknown function, Is the optimal weight vectorK NO,z is a nitrate nitrogen tracking error constraint boundary, and the value is 2% of a nitrate nitrogen concentration set value; calculating the derivative of the Lyapunov function:
Wherein, The constant τ max＝max{τ1(t),τ2 (t);
⑤ A fuzzy neural network approximator designed for identifying unknown dynamic of a system comprises the following specific steps of
For the uncertainty term existing in the formula (5), an unknown function P NO(ZNO (t)) is defined, and the unknown function P NO(ZNO (t)) is identified by utilizing the approximation characteristic of the fuzzy neural network, wherein the fuzzy neural network is divided into four layers: the device comprises an input layer, RBF layers, a rule layer and an output layer, wherein the number of neurons of the input layer is 3, the number of neurons of the RBF layer is L, the number of neurons of the rule layer is P, and the number of neurons of the output layer is 1; the weights between the input layer and the RBF layer and between the RBF and the rule layer are 1, and the weights between the rule layer and the output layer are assigned in the interval of [ -1,1 ]; let the input of the fuzzy neural network at the time t be Z NO(t)＝[x1(t),x2(t),x3(t)],x1 (t) expressed as the nitrate nitrogen concentration at the time t S NO,2(t),x2 (t) expressed as the nitrate nitrogen set value at the time t S NO,set(t),x3 (t) expressed as the nitrate nitrogen concentration derivative at the time tThe fuzzy neural network output is denoted q (t); the fuzzy neural network identification process is as follows:
Input layer: the layer consists of 3 neurons, the output of each neuron is
hj(t)＝xj(t),j＝1,2,3 (6)
Wherein h j (t) represents the output of the jth neuron t of the input layer, and x j (t) represents the input of the jth neuron t of the input layer;
RBF layer: the layer is composed of L neurons, a positive integer L epsilon [5,15], and the output of each neuron is
Wherein, in the RBF layer, c ji (t) is the central value of the j-th membership function of the i-th neuron at the moment t, n ji is the width value of the j-th membership function of the i-th neuron at the moment t,The output of the ith neuron of the RBF layer at the moment t is represented;
rule layer: the layer is composed of P neurons, a positive integer P E [5,15], each neuron outputs as
Wherein,The output value of the ith neuron at the t-th iteration;
Output layer: the output of the layer is as follows:
Wherein w i (t) is the connection weight between the ith neuron of the t moment rule layer and the output layer, and q (t) is the output of the t moment output layer; the unknown function identification process by using the fuzzy neural network is as follows
Wherein,For the fuzzy neural network input vector, the T symbol is transposed,For the fuzzy neural network to be an optimal weight vector,Representing the activation function vector, and according to the approximation characteristic of the fuzzy neural network, the normal number existsSo that the recognition error ε NO(ZNO (t)) satisfies
Updating the fuzzy neural network weight:
Wherein, the value range of the normal number sigma 1 is (0, 2);
⑥ Calculating the internal reflux quantity at the moment t, wherein the output value of the internal reflux quantity consists of an adaptive control function u a (t) and a fuzzy neural network compensation function u Fnn (t)
o1(t)＝uFnn(t)+ua(t) (12)
Wherein, the positive constant c 1 is selected so that the tracking error of the nitrate nitrogen concentration does not exceed the range of the set value of the nitrate nitrogen concentration by 2 percent
⑦ Calculating the actual output of nitrate nitrogen concentration based on time-lag compensation strategy
Wherein Q a,max is the maximum internal reflux quantity allowed by the system, and Q a,min is the daily average water inflow;
(3) And (3) tracking and controlling the nitrate nitrogen concentration by using the solved Q a (t), eliminating the influence of time-varying time lag on control performance, and ensuring that the nitrate nitrogen concentration is always kept in the constraint range appointed in the step (1).
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