Adaptive fuzzy echo state network control method for denitrification process

Abstract

The invention provides an adaptive fuzzy echo state network control method for a denitrification process, and the method comprises the steps: simulating the whole sewage treatment process, simplifying a nitrate nitrogen concentration kinetic model, and obtaining a simplified kinetic model; derivation is carried out on the defined time-delay-error-free signal; fitting an unknown function by using a fuzzy echo state network, and designing an output weight adaptive updating law comprising error information for the fuzzy echo state network; deducing a delay-free control law by using the delay-free error signal, extracting the internal reflux quantity at the current moment, and performing nitrate nitrogen concentration control by taking the internal reflux quantity as the control input of a sewage treatment system; and carrying out stability verification on the time-delay-error-free signal, and carrying out convergence proving on an output weight self-adaptive updating law. Accurate finite time tracking control of nitrate nitrogen concentration in the denitrification process is achieved, and the control problem caused by water quality fluctuation and backflow delay is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent water treatment, in particular to a self-adaptive fuzzy echo state network control method for a denitrification process. BACKGROUND

[0002] Water pollution is a serious challenge to ecological security and human health. In the wastewater treatment process, the concentration of nitrate nitrogen is a key indicator affecting water quality. When the concentration of nitrate nitrogen is too high, it will inhibit the denitrification reaction in the anoxic zone, resulting in excessive nitrate nitrogen and total nitrogen in the effluent; when the concentration of nitrate nitrogen is too low, it will lead to insufficient denitrification substrate in the anoxic section, also causing insufficient removal of nitrate nitrogen and total nitrogen in the effluent. Currently, the control of nitrate nitrogen concentration relies mainly on traditional PID control strategies. However, the wastewater treatment system exhibits high nonlinearity and large time-varying characteristics, making traditional control schemes often have low control accuracy and large overshoot.

[0003] On the other hand, the synergy of nitrification and denitrification in the wastewater treatment process highly depends on the closed-loop flow of internal circulation (nitrification liquid reflux) and external circulation (sludge reflux), and these two circulation processes have uncertainty and time delay characteristics. The design logic of traditional control schemes often implies the "no time delay" assumption, which cannot adapt to the current high-precision and high-stability water quality requirements. With the increasing demand for control performance, how to offset the unknown time delay of internal circulation in the nitrification and denitrification process has become a popular research field. SUMMARY

[0004] In order to overcome the shortcomings of the prior art, the purpose of the present application is to provide a self-adaptive fuzzy echo state network control method for a denitrification process, which realizes precise finite time tracking control of the concentration of nitrate nitrogen in the denitrification process, solves the control problems caused by water quality fluctuations and reflux delay, and provides a high-performance intelligent control solution for energy saving optimization and stable operation of wastewater treatment plants.

[0005] To achieve the above purpose, the present application provides the following scheme: a self-adaptive fuzzy echo state network control method for a denitrification process, comprising: Based on BSM1, the whole wastewater treatment process is simulated to obtain a denitrification process, based on the denitrification process, a nitrate nitrogen concentration dynamics model under the multi-zone structure of the biological reaction tank is constructed, and a controller state variable is introduced to simplify the nitrate nitrogen concentration dynamics model to obtain a simplified dynamics model; Based on the simplified dynamics model, a tracking error, an integral type compensation signal and a filtering error are defined, a time delay error signal is constructed using the integral type compensation signal, and the derivative of the time delay error signal is obtained by using the Lyapunov function to derive the time delay error signal; Based on the non-time delay error signal, an unknown function is fitted by using a fuzzy echo state network, and then an output weight adaptive updating law including error information is designed for the fuzzy echo state network; Based on the output weight adaptive updating law, a non-delay control law is derived by using the non-time delay error signal, an internal recycle flow at the current time is extracted according to the non-delay control law, and the internal recycle flow is taken as a control input of the sewage treatment system to control the nitrate nitrogen concentration. The defined first Lyapunov function and the second Lyapunov function are summed to obtain a total function, the stability of the non-time delay error signal is verified by using the total function, and the convergence of the output weight adaptive updating law is proved by using the defined third Lyapunov function.

[0006] Optionally, the expression of the nitrate nitrogen concentration dynamic model is: ; Among them, is the flow of the first partition in the biological reaction tank, is the flow of the second partition in the biological reaction tank, is the nitrate nitrogen concentration of the first partition in the biological reaction tank, is the change rate of the nitrate nitrogen concentration of the first partition in the biological reaction tank; is the nitrate nitrogen concentration of the second partition in the biological reaction tank, is the change rate of the nitrate nitrogen concentration of the second partition in the biological reaction tank, is the volume of the first partition in the biological reaction tank, is the volume of the second partition in the biological reaction tank, represents the internal recycle flow, is the influent flow in the biological reaction tank, is the sludge recycle flow, is the nitrate nitrogen concentration in the internal cycle, is the nitrate nitrogen concentration in the influent, is the nitrate nitrogen concentration in the sludge recycle liquid, is the heterotrophic bacteria yield coefficient, is the autotrophic bacteria yield coefficient, is the heterotrophic bacteria anoxic growth rate in the first partition in the biological reaction tank, is the heterotrophic bacteria anoxic growth rate in the second partition in the biological reaction tank, is the autotrophic bacteria aerobic growth rate in the first reaction zone in the biological reaction tank, is the autotrophic bacteria aerobic growth rate in the second reaction tank in the biological reaction tank; The controller state variable includes a first variable and a second variable, and the expression of the simplified dynamic model is: , , ; ; wherein, is a first derivative of the variable , is a first derivative of the variable , is a measurable non-zero constant, is a delayed control input at time , is an unknown time delay, is an unknown nonlinear function existing in tracking control of nitrate nitrogen concentration, is a first derivative of the heterotrophic anoxic growth rate of the bacteria in the second partition of the bioreactor, is a second derivative of the autotrophic aerobic growth rate of the bacteria in the second reactor of the bioreactor.

[0007] Optionally, the expression of the tracking error is: ; wherein, is a tracking error of nitrate nitrogen concentration, is an expected concentration of nitrate nitrogen; the expression of the integral type compensation signal is: ; wherein, is a control input at time , is a first derivative of the control input, is an integral variable; the expression of the filter error is: , ; wherein, is a filter error, is a normal number, is a derivative of the tracking error; the expression of the time delay free error signal is: , ; wherein, is a first derivative of the filter error, is a control gain; the expression of the Lyapunov function is: ; the derivative expression of the time delay free error signal is: ; ; , wherein, is a first derivative of the time delay-free error, is a first derivative of the unknown nonlinear function, is an auxiliary variable, is an increasing constant positive function, is a system error state vector, is a modulo operator.

[0008] Optionally, based on the time delay-free error signal, a fuzzy echo state network is used to fit the unknown function, comprising: based on the time delay-free error signal, a new unknown function is set for the unknown nonlinear function, a fuzzy echo state network is used to perform real-time approximation on the new unknown function to obtain an approximation result; an expression of the approximation result is: , ; wherein, is an ideal output weight matrix, is a bounded approximation error, is a reservoir state vector, and an update formula of the reservoir state vector is: ; ; wherein, is a fuzzy basis function vector generated by fuzzy processing of input variables using a Gaussian membership function, is a total number of fuzzy rules, is a first derivative of the reservoir state vector, is an input weight matrix, is a reservoir weight matrix, is an arctangent function.

[0009] Optionally, for the fuzzy echo state network, an output weight adaptive update law including error information is designed, comprising: for the fuzzy echo state network, a low-pass filter is introduced to filter process the first derivatives of the reservoir state vector, the time delay-free error signal, the auxiliary variable, the control input, and the filtering error to obtain a filtering variable; Based on the filter variable, an auxiliary matrix is defined, and an estimation error information of the ideal output weight matrix is extracted in combination with the auxiliary matrix; an expression of the estimation error information is: , ; ; ; ; wherein, is an auxiliary signal containing error information, is a fitting error of the fuzzy echo state network, is an estimation value of the weight matrix, is an estimation error of the weight matrix, is a first derivative of , is a transpose of a filter vector , is a filter coefficient, is a filter factor; a leakage term containing the estimation error information is designed, and an adaptive update law of the estimation value of the ideal output weight matrix is obtained by using the leakage term; an expression of the leakage term is: wherein, is a learning gain; an expression of the adaptive update law is: , wherein, is a learning gain, is a projection operator used for ensuring that the adaptive law is bounded within a preset convex set.

[0010] Optionally, an expression of the delay-free control law is: , ; wherein, is a feedback gain.

[0011] Optionally, an expression of the first Lyapunov function is: ; derivation is performed on the first Lyapunov function to obtain: ; wherein, is a first derivative of , The first derivative of the delay control input By using Young's inequality, a first inequality relationship can be obtained, and an expression of the first inequality relationship is as follows: ; The inequality relationship is substituted into the first derivative of the first Lyapunov function to obtain a first function, and an expression of the first function is as follows: .

[0012] Optionally, an expression of the second Lyapunov function is as follows: ; ; Derivation is performed on the second Lyapunov function to obtain: ; ; wherein, is the first derivative of , , is a normal number, is a second inequality relationship, and the second inequality relationship is substituted into the first derivative of the second Lyapunov function to obtain a second function, and an expression of the second function is as follows: ; ; ; wherein, , is a normal number, and are the maximum value and the minimum value of singular values of a matrix, is a constant and satisfies .

[0013] Optionally, an expression of the total function is as follows: ; ; wherein, is a normal number; By using Cauchy-Schwarz inequality, a third inequality relationship can be obtained, and an expression of the third inequality relationship is as follows: ; Scaling is performed on the third inequality relationship to obtain a first scaling, and an expression of the first scaling is as follows: ; to scaling, a second scaling is obtained, and an expression of the second scaling is: ; The first scaling and the second scaling are substituted into the total function, and the following is obtained: ; wherein, , to Simultaneous integration on both sides obtains: ; According to the Lyapunov stability theorem, a bounded error signal is obtained, and the stability verification of the non-time-lag error signal is completed.

[0014] Optionally, an expression of the third Lyapunov function is: ; Derivation of the third Lyapunov function obtains: ; wherein, , , a third inequality relationship is obtained, and an expression of the third inequality relationship is: ; The third inequality relationship is substituted into the third Lyapunov function, and the following is obtained: ; The convergence of the output weight adaptive update law is proved.

[0015] The present application provides an adaptive fuzzy echo state network control method for a denitrification process, and the following technical effects are disclosed: 1. Precise control of nitrate nitrogen concentration: The fuzzy echo state network is used to approximate unknown nonlinearity, and an adaptive law is used for online updating, so that real-time compensation of complex biochemical reactions and nonlinear disturbances is realized, and the effluent nitrate nitrogen more accurately tracks the set value.

[0016] 2. Effectively handle unknown time lag problems: By constructing an integral type compensation signal and a non-time-lag error signal, the internal circulation reflux time lag is "absorbed" in the control law design, avoiding the control failure caused by the traditional assumption of "no time lag", and more in line with the internal circulation and external reflux time lag characteristics in actual wastewater treatment.

[0017] 3. Efficient and stable self-adaptive intelligent control: the echo state network uses a fixed random reservoir, mainly trains the output weight, and has high training efficiency; the fuzzy processing enhances the local approximation ability, and the self-adaptive law guarantees the convergence of the weight, so as to realize online learning under the premise of ensuring performance and adapt to water quality fluctuations.

[0018] 4. Theoretically provable stability: through the system proof of Lyapunov method and parameter update self-adaptive law, it is guaranteed that the error and parameter estimation are bounded, and the unpredictable risk brought by "black box control" is avoided; the coupling of the controller, neural network approximation and self-adaptive law is considered in the proof, so that the whole closed loop has complete theoretical guarantee.

[0019] The technical solutions of the present application will be further described in detail below with the help of the accompanying drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the accompanying drawings needed to be used in the embodiments will be briefly introduced. Obviously, the accompanying drawings in the following description are only some embodiments of the present application, and other accompanying drawings can be obtained by those skilled in the art without creative labor under the premise of the accompanying drawings.

[0021] Figure 1 The method flowchart provided for the embodiments of the present application is shown in the figure; Figure 2 The tracking result graph of the effluent nitrate nitrogen concentration under the dynamic set value provided for the embodiments of the present application is shown in the figure; Figure 3 The tracking error graph of the effluent nitrate nitrogen concentration under the dynamic set value provided for the embodiments of the present application is shown in the figure; Figure 4 The result graph of the internal return flow under the dynamic set value provided for the embodiments of the present application is shown in the figure; Figure 5 The tracking result graph of the effluent nitrate nitrogen concentration under the fixed set value provided for the embodiments of the present application is shown in the figure; Figure 6 The tracking error graph of the effluent nitrate nitrogen concentration under the fixed set value provided for the embodiments of the present application is shown in the figure; Figure 7 The result graph of the internal return flow under the fixed set value provided for the embodiments of the present application is shown in the figure. DETAILED DESCRIPTION

[0022] With reference to the accompanying drawings: clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the scope of the present application.

[0023] In order to make the above-mentioned purposes, features and advantages of the present application more apparent and easy to understand, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] As shown in Figure 1 The present application provides an adaptive fuzzy echo state network control method for a denitrification process, comprising: Based on BSM1, the whole wastewater treatment process is simulated to obtain a denitrification process, based on the denitrification process, a nitrate nitrogen concentration kinetic model under a multi-partition structure of a biological reaction tank is constructed, a controller state variable is introduced, the nitrate nitrogen concentration kinetic model is simplified to obtain a simplified kinetic model; Based on the simplified kinetic model, a tracking error, an integral type compensation signal and a filtering error are defined, a time-lag-free error signal is constructed using the integral type compensation signal, and the derivative of the time-lag-free error signal is obtained by using the Lyapunov function to derive the time-lag-free error signal; Based on the time-lag-free error signal, a fuzzy echo state network is used to fit an unknown function, and an output weight adaptive updating law including error information is designed for the fuzzy echo state network; Based on the output weight adaptive updating law, a time-delay-free control law is derived using the time-lag-free error signal, the internal return flow at the current time is extracted according to the time-delay-free control law, and the internal return flow is used as the control input of the wastewater treatment system to control the nitrate nitrogen concentration; The first Lyapunov function and the second Lyapunov function are summed to obtain a total function, the stability of the time-lag-free error signal is verified using the total function, and the convergence of the output weight adaptive updating law is proved using the third Lyapunov function.

[0025] Specifically, BSM1 is used to simulate a 14-day wastewater treatment process to evaluate the control performance of the present application on the dissolved oxygen concentration. The actual observation data under sunny weather is used to verify the nitrate nitrogen concentration control experiment on the BSM1 simulation model. The data used is the sampling data of a 14-day actual wastewater treatment plant, and the sampling period is 15 minutes.

[0026] Step 1: Construct a nitrate nitrogen concentration kinetic model based on BSM1: wherein, represents the flow rate of the first zone in the biological reaction tank; represents the flow rate of the second zone in the biological reaction tank; represents the nitrate nitrogen concentration of the first zone in the biological reaction tank; represents the rate of change of the nitrate nitrogen concentration of the first zone in the reaction tank; represents the nitrate nitrogen concentration of the second zone in the biological reaction tank; represents the rate of change of the nitrate nitrogen concentration of the second zone in the biological reaction tank; represents the volume of the first zone in the biological reaction tank; represents the volume of the second zone in the biological reaction tank; represents the internal recycle flow rate; represents the influent flow rate in the biological reaction tank; represents the sludge return flow rate; represents the nitrate nitrogen concentration in the internal recycle; represents the nitrate nitrogen concentration in the influent; represents the nitrate nitrogen concentration in the sludge return flow; represents the heterotrophic bacteria yield coefficient; represents the autotrophic bacteria yield coefficient; represents the heterotrophic bacteria anoxic growth rate in the first zone in the biological reaction tank; represents the heterotrophic bacteria anoxic growth rate in the second zone in the biological reaction tank; represents the autotrophic bacteria aerobic growth rate in the first zone in the biological reaction tank; represents the autotrophic bacteria aerobic growth rate in the second zone in the biological reaction tank.

[0027] Step 2: Define controller variables Define variables and variables , the original kinetic model is simplified to obtain the simplified kinetic model: wherein represents the first derivative of the variable , represents the first derivative of the variable , can be regarded as a measurable non-zero constant, is the delayed control input at the moment , is an unknown time delay, which is taken as , is an unknown nonlinear function existing in tracking control of the nitrate nitrogen concentration, wherein The first derivative represents the anaerobic growth rate of heterotrophic bacteria in the second zone of the bioreactor. The second derivative represents the aerobic growth rate of autotrophic bacteria in the second reaction tank of the bioreactor.

[0028] Step 3: Construct a time-delay-free error signal using time-delay characteristics. like Figures 2-7 As shown, firstly, the tracking error is defined as... ,in This indicates the tracking error of nitrate nitrogen concentration. This represents the desired concentration of nitrate nitrogen, and is typically taken as a fixed setpoint. When setting a value dynamically, it is generally taken as... Define the integral compensation signal. ,in Representative moment The control input, The first derivative represents the control input. It is the integral variable.

[0029] Then, the filtering error is defined as ,in For filtering error, It is a positive number. This represents the derivative of the tracking error. Here, we take... .

[0030] Finally, an error signal without time delay can be constructed using an integral compensation signal. ,in The first derivative representing the filtering error. To control the gain, we take [the value here]. .

[0031] Step 4: Construct the Lyapunov function based on the error signal. Constructing Lyapunov functions Taking the derivative of the Lyapunov function yields the derivative of the signal without time delay error: in The first derivative represents the error without time delay. Representing an unknown nonlinear function The first derivative, Representing an auxiliary variable and satisfying ,in It represents a strictly increasing, always positive function. Let be the system error state vector. This represents the modulo operator.

[0032] Step 5: Fitting unknown function with fuzzy echo state network 5.1 Fitting unknown function with fuzzy echo state network First, for the above unknown function , let , it is obvious that is still an unknown function. The present application uses fuzzy echo state network to approximate in real time, and the approximation result can be expressed as: where is the ideal output weight matrix, is the bounded approximation error, is the reservoir state vector. The update formula of the state vector is: where represents the fuzzy basis function vector generated by fuzzying the input variable using the Gaussian membership function, is the total number of fuzzy rules, represents the first derivative of the reservoir vector, is the input weight matrix, is the reservoir weight matrix, represents the inverse tangent function. Here , the center point of the membership function is selected as , the width is , the number of reservoir nodes is 20, and are randomly generated, and their values are distributed on , and it is ensured that the sparsity is and the spectral radius is less than 1.

[0033] 5.2 Designing output weight adaptive update law containing error information for fuzzy echo state network First, introduce a low-pass filter to filter the reservoir state vector , the error signal without time lag , the auxiliary variable , the first derivative of the control input , and the filtering error . Get the filtered variable , , , , where represents the filtering result of , represents the filtering result of , the filtered result of , the filtered result of , the filtered result of .

[0034] Then, define the auxiliary matrix , and to extract the estimation error information of the output weight matrix , which is given by where is the auxiliary signal containing the error information, represents the fitting error of the fuzzy echo state network, represents the estimated value of the weight matrix, represents the estimation error of the weight matrix, is the first derivative of the auxiliary matrix , is the first derivative of the auxiliary matrix , represents the filtered variable of , represents the first derivative of , represents the transpose of the filtered vector , is the filter coefficient, is the filter factor, which is taken as , here. Using the above auxiliary matrix, a leakage term containing error information is designed, where is the learning gain. Here is taken.

[0035] Finally, using the leakage term with error information, the adaptive law of the estimated value of the optimal weight matrix is obtained as where is the learning gain, represents the projection operator, which can ensure to be bounded within a certain pre-set convex set. Here Step 6: Derive the delay-free control law using the time-lag-free error signal In order to make the time-lag-free error signal converge, design , where is the feedback gain. Here we take the feedback gain . Integrating the above equation, we can get the implementable control law: Therefore, we can take the internal return flow at the current time as the control input of the sewage treatment system.

[0036] Step 7: Proof of closed-loop system stability and finite-time convergence 7.1 Verification of system stability Construct Lyapunov function , where the first Lyapunov function is , and the second Lyapunov function is .

[0037] First, take the derivative of , we can get: where is the first derivative of , and represents the first derivative of the delayed control input . Using Young's inequality, we can get the following first inequality relationship: Using the above first inequality relationship into , we can get: In , and and are represented as follows: Take the derivative of , we can get: where is the first derivative of . From the adaptive law of , we know that is bounded, so we can get the second inequality relationship , where and are normal numbers. Bringing the second inequality relationship into the above equation, we can get: where , are normal numbers, and represent the maximum and minimum values of the singular values of the matrix, is a constant and satisfies .

[0038] Using and , one can calculate : where is a positive constant. Using the Cauchy-Schwarz inequality, one can obtain the third inequality Taking the derivative of the third inequality, one obtains the first scaling, whose expression is Meanwhile, scaling , one obtains the second scaling, whose expression is Substituting the above formula into , one obtains where , , taking the integral of both sides of , one obtains According to the Lyapunov stability theorem, the proposed control method can make the error signal , , , bounded, so the system is stable.

[0039] 7.2 Convergence proof of the output weight adaptive law of the fuzzy echo state network First, define the third Lyapunov function as Taking the derivative of , one obtains where . Obviously, , so one can obtain the following inequality: Substituting the above inequality into , one obtains According to the above formula, when the learning gain L is large enough, there is , so one can obtain , where is a constant. According to Lyapunov stability theorem, when the parameter is updated using the proposed adaptive law , the weight parameter error converges to a minimal compact set, and thus the parameter estimation capability can be achieved.

[0040] Therefore, the present application provides an adaptive fuzzy echo state network control method for denitrification process, which realizes the precise finite time tracking control of nitrate nitrogen concentration in the denitrification process, solves the control problem caused by water quality fluctuation and reflux delay, and provides a high-performance intelligent control solution for energy saving optimization and stable operation of the sewage treatment plant.

[0041] The various embodiments are described in a progressive manner in the specification, and each embodiment focuses on the differences from other embodiments, and the same or similar parts between the various embodiments can be referred to each other.

[0042] The principles and implementation modes of the present application are described by applying specific examples in this paper, and the above description of the embodiments is only used to help understand the method of the present application and its core idea; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed. In view of the above, the content of the specification should not be understood as a limitation of the present application.

Claims

1. An adaptive fuzzy echo state network control method for denitrification process, characterized in that, The method comprises the following steps: Based on the BSM1, the whole process of sewage treatment is simulated to obtain a denitrification process, and based on the denitrification process, a nitrate nitrogen concentration dynamic model under a multi-partition structure of a biological reaction tank is constructed, a controller state variable is introduced to simplify the nitrate nitrogen concentration dynamic model, and a simplified dynamic model is obtained; Based on the simplified dynamic model, a tracking error, an integral type compensation signal and a filter error are defined, a time lag error signal is constructed by using the integral type compensation signal, and a derivative of the time lag error signal is obtained by using a Lyapunov function to derive the time lag error signal; Based on the time lag error signal, a fuzzy echo state network is used to fit an unknown function, and an output weight adaptive updating law including error information is designed for the fuzzy echo state network; Based on the output weight adaptive updating law, a time delay control law is derived by using the time lag error signal, the internal return flow at the current time is extracted according to the time delay control law, and the internal return flow is taken as a control input of the sewage treatment system to control the nitrate nitrogen concentration; The first Lyapunov function and the second Lyapunov function are summed to obtain a total function, the stability of the time lag error signal is verified by using the total function, and the convergence of the output weight adaptive updating law is proved by using the third Lyapunov function.

2. The adaptive fuzzy echo state network control method for denitrification process according to claim 1, wherein, The expression of the nitrate nitrogen concentration dynamic model is: ； wherein, is the flow rate in the first zone of the biological reaction tank, is the flow rate in the second zone of the biological reaction tank, is the nitrate nitrogen concentration in the first zone of the biological reaction tank, is the rate of change of the nitrate nitrogen concentration in the first zone of the reaction tank; is the nitrate nitrogen concentration in the second zone of the biological reaction tank, is the rate of change of the nitrate nitrogen concentration in the second zone of the biological reaction tank, is the volume of the first zone of the biological reaction tank, is the volume of the second zone of the biological reaction tank, denotes the internal recycle flow rate, is the influent flow rate in the biological reaction tank, is the sludge return flow rate, is the nitrate nitrogen concentration in the internal recycle, is the nitrate nitrogen concentration in the influent, is the nitrate nitrogen concentration in the sludge return flow, is the heterotrophic bacteria yield coefficient, is the autotrophic bacteria yield coefficient, is the rate of anoxic growth of heterotrophic bacteria in the first zone of the biological reaction tank, is the rate of anoxic growth of heterotrophic bacteria in the second zone of the biological reaction tank, is the rate of aerobic growth of autotrophic bacteria in the first reaction zone of the biological reaction tank, is the rate of aerobic growth of autotrophic bacteria in the second reaction zone of the biological reaction tank; The controller state variable includes a first variable and a second variable, and the expression of the simplified dynamic model is: ， ， ； ； wherein is the first derivative of the variable , is the first derivative of the variable , is a measurable non-zero constant, is the delayed control input at time instant is the unknown time delay, is an unknown nonlinear function existing in the tracking control of the nitrate nitrogen concentration, is the first derivative of the heterotrophic anoxic growth rate of the heterotrophic bacteria in the second partition of the bioreactor, is the second derivative of the autotrophic aerobic growth rate of the autotrophic bacteria in the second reactor of the bioreactor.

3. The adaptive fuzzy echo state network control method for the denitrification process according to claim 2, characterized in that: The expression of the tracking error is: ； wherein, is the nitrate nitrogen concentration tracking error, is the desired concentration of nitrate nitrogen; The expression of the integral type compensation signal is: ； wherein is the control input at time is the first derivative of the control input, is the first derivative of the control input, is the integral variable; The expression of the filter error is: ， ； wherein, is a filtered error, is a constant, is a derivative of the tracking error; The expression of the time lag error signal is: ， ； wherein, is a first derivative of the filtered error, is a control gain; The expression of the Lyapunov function is: ； The derivative expression of the time lag error signal is: ； ； ， wherein, is a first derivative of the time-lag term error, is a first derivative of the unknown nonlinear function, is an auxiliary variable, is an increasing constant positive function, is a system error state vector, is a modulo operator.

4. The adaptive fuzzy echo state network control method for denitrification process according to claim 3, wherein, Based on the time lag error signal, a fuzzy echo state network is used to fit an unknown function, including: Based on the time lag error signal, a new unknown function is set for the unknown nonlinear function, a fuzzy echo state network is used to realize real-time approximation of the new unknown function to obtain an approximation result; the expression of the approximation result is: ， ； wherein, is the ideal output weight matrix, is a bounded approximation error, is the reservoir state vector, whose update formula is: ； ； wherein, is a fuzzy basis function vector generated by fuzzifying the input variable using a Gaussian membership function, is the total number of fuzzy rules, is the first derivative of the reservoir state vector, is the input weight matrix, is the reservoir weight matrix, is an arc tangent function.

5. The adaptive fuzzy echo state network control method for denitrification process according to claim 4, wherein, For the fuzzy echo state network, an output weight adaptive updating law including error information is designed, including: For the fuzzy echo state network, a low-pass filter is introduced to filter the reserve pool state vector, the time lag error signal, the auxiliary variable, the first derivative of the control input and the filter error to obtain a filtering variable; Based on the filtering variable, an auxiliary matrix is defined, and the estimation error information of the ideal output weight matrix is extracted in combination with the auxiliary matrix; the expression of the estimation error information is: ， ； ； ； ； in, This is an auxiliary signal that contains error information. The fitting error of the fuzzy echo state network. This is an estimate of the weight matrix. The estimation error of the weight matrix, Auxiliary matrix The first derivative, Auxiliary matrix The first derivative, for The filter variable, for The first derivative, filter vector transpose, These are the filter coefficients. The filter factor; A leakage term containing the estimation error information is designed, and the adaptive updating law of the estimation value of the ideal output weight matrix is obtained by using the leakage term; The expression of the leakage term is: wherein, is the learning gain; The expression of the adaptive updating law is: ， wherein, is the learning gain, is a projection operator used to guarantee that the adaptive law is bounded within a pre-specified convex set.

6. The adaptive fuzzy echo state network control method for denitrification process according to claim 5, wherein, The expression of the time delay control law is: ， ； wherein is the feedback gain.

7. The adaptive fuzzy echo state network control method for denitrification process according to claim 6, wherein, An expression of the first Lyapunov function is: ； Derivation is performed on the first Lyapunov function to obtain: ； wherein is the first derivative of is the first derivative of the delay control input the first derivative of the delay control input using Young's inequality, a first inequality relationship can be obtained, the expression of which is: ； The inequality relationship is substituted into the first-order derivative of the first Lyapunov function to obtain a first function, and an expression of the first function is: 。 8. The adaptive fuzzy echo state network control method for denitrification process according to claim 7, wherein, An expression of the second Lyapunov function is: ； ； Derivation is performed on the second Lyapunov function to obtain: ； ； wherein is a first derivative of , is a normal number, is a second inequality relationship, substituting the second inequality relationship into the first derivative of the second Lyapunov function to obtain a second function, and an expression of the second function is ； ； ； wherein , is a normal number, and is the maximum and minimum of the singular values of the matrix, is a constant and satisfies .

9. The adaptive fuzzy echo state network control method for denitrification process according to claim 8, wherein, An expression of the total function is: ； ； wherein is a constant; A third inequality relationship is obtained by using the Cauchy-Schwarz inequality, and an expression of the third inequality relationship is: ； A first scaling is obtained by scaling the third inequality relationship, and an expression of the first scaling is: ； to scaling, to obtain a second scaling, an expression of which is: ； The first scaling and the second scaling are substituted into the total function to obtain: ； wherein , , to both sides simultaneously integrating gives: ； According to the Lyapunov stability theorem, a bounded error signal conclusion is obtained, and the stability verification of the non-time-lag error signal is completed.

10. The adaptive fuzzy echo state network control method for denitrification process according to claim 9, wherein, An expression of the third Lyapunov function is: ； Derivation is performed on the third Lyapunov function to obtain: ； wherein , , obtaining a third inequality, the expression of which is: ； The third inequality relationship is substituted into the third Lyapunov function to obtain: ； The convergence of the output weight adaptive updating law is proved.

Images