A sewage treatment adaptive adjustable multi-device optimal control method based on a constraint framework

Abstract

The application provides a sewage treatment adaptive adjustable multi-device optimal control method based on a constraint framework, and relates to the technical field of sewage treatment. The method comprises the following steps: constructing a first and a second dynamic model, and then establishing corresponding first and second asymmetric obstacle Lyapunov functions; creating a first and a second execution network based on a fuzzy neural network framework; designing an initial aeration pump and a backflow pump adaptive controller; constructing a corresponding long-term loss function and a first and a second evaluation network, and optimizing and updating the execution network and the adaptive controller to realize optimal control. The method effectively solves the problems of index exceeding, concentration tracking not in time and high equipment power consumption in conventional control.

Description

Technical Field

[0001] This invention relates to the field of wastewater treatment technology, and in particular to an adaptive and adjustable multi-device optimal control method for wastewater treatment based on a constraint framework. Background Technology

[0002] Water resource protection and wastewater recycling have long been considered top priorities for global sustainable development. To meet the ever-growing demand for clean water, urban wastewater treatment has been widely implemented as a key method. However, in complex and dynamic environments, monitored wastewater indicators are frequently affected by constant fluctuations. Challenges including high energy consumption and system instability highlight the urgent need for adaptive optimal control technologies. Therefore, developing adaptive optimal control strategies to ensure both reduced equipment operating energy consumption and guaranteed equipment reliability under good effluent quality conditions has become a pressing research area in engineering.

[0003] Activated sludge process technology is widely used, and precise control of dissolved oxygen and nitrate nitrogen concentrations is crucial for improving wastewater treatment efficiency. Currently, adaptive control methods are designed to address the complex and uncertain environments in wastewater treatment, dynamically responding to environmental changes and ensuring system stability. Neural network-based adaptive control methods can more precisely control dissolved oxygen and nitrate nitrogen concentrations. However, these methods cannot solve the problem of control indicators easily exceeding limits. Constraint control methods, by incorporating constraints such as physical limitations, safety regulations, and performance requirements into the design of control strategies, can effectively avoid safety hazards and performance degradation caused by control variable deviations and have been widely used. However, although the control target and tracking error are kept within the expected range during the control process, the operating energy consumption of the equipment remains high, failing to meet the needs of current energy economic development. Therefore, optimal control technology based on reinforcement learning structures can achieve a dynamic balance between operating energy consumption and control performance through continuous interaction with the surrounding environment. However, the problem of peak values ​​of some key indicators easily exceeding limits remains unresolved. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, the purpose of this invention is to provide an adaptive and adjustable multi-device optimal control method for wastewater treatment based on a constraint framework. This invention solves the problems of key indicator peak values ​​easily exceeding the standard, indicator concentration tracking not being timely, and high equipment power consumption caused by strictly ensuring effluent quality in conventional tracking control methods in the prior art.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] An adaptive and adjustable multi-device optimal control method for wastewater treatment based on a constraint framework includes:

[0007] Construct the first dynamic model and the second dynamic model respectively;

[0008] Construct the corresponding first asymmetric barrier Lyapunov function and second asymmetric barrier Lyapunov function based on the first dynamic model and the second dynamic model;

[0009] The current first and second execution networks are constructed based on the fuzzy neural network framework;

[0010] Based on the first asymmetric barrier Lyapunov function and the second asymmetric barrier Lyapunov function, respectively construct the initial aeration pump adaptive controller and the initial reflux pump adaptive controller corresponding to the first execution network and the second execution network.

[0011] Construct the first long-term loss function, the second long-term loss function, and their corresponding first and second evaluation networks, respectively;

[0012] The initial aeration pump adaptive controller and the initial return pump adaptive controller are updated using the first evaluation network, the second evaluation network, the first execution network and the second execution network to obtain the optimal aeration pump adaptive controller and the optimal return pump adaptive controller.

[0013] The wastewater treatment process is controlled using the optimal aeration pump adaptive controller and the optimal return pump adaptive controller.

[0014] Preferably, the initial aeration pump adaptive controller and the initial return pump adaptive controller are updated using the first evaluation network, the second evaluation network, the first execution network, and the second execution network to obtain the optimal aeration pump adaptive controller and the optimal return pump adaptive controller, including:

[0015] Calculate the adaptive weight law corresponding to the evaluation network and the execution network;

[0016] The evaluation network and the execution network are updated using the aforementioned weight adaptation law;

[0017] The initial aeration pump adaptive controller and the initial return pump adaptive controller are updated using the updated evaluation network and the execution network to obtain the optimal aeration pump adaptive controller and the optimal return pump adaptive controller.

[0018] Preferably, the expressions corresponding to the first dynamic model and the second dynamic model are as follows:

[0019] ;

[0020] in, This refers to the dissolved oxygen concentration in the fourth zone of the biochemical reaction tank. This refers to the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank. The concentration of nitrate nitrogen in the first zone of the biochemical reaction tank; The concentration of nitrate nitrogen in the second zone of the biochemical reaction tank; The concentration of nitrate nitrogen in the fifth zone of the biochemical reaction tank; This represents the saturation value of dissolved oxygen concentration. Dissolved oxygen concentration is the operating variable; The operating variable is the concentration of nitrate nitrogen; Microbial respiration coefficient; The flow rate of the first section of the biochemical reaction tank; The flow rate of the second section of the biochemical reaction tank; The flow rate of the fourth section of the biochemical reaction tank; The flow rate of the fifth section of the biochemical reaction tank; The concentration of heterotrophic biomass; Heterotrophic biomass; This refers to the volume of the second section of the biochemical reaction tank. This refers to the volume of the fifth section of the biochemical reaction tank; This is the dissolved oxygen concentration saturation coefficient.

[0021] Preferably, the expression for the first asymmetric barrier Lyapunov function is:

[0022] ;

[0023] in, For the tracking error of dissolved oxygen concentration, and Dissolved oxygen concentration tracking error The upper and lower thresholds that are constrained.

[0024] Preferably, the expression for the second asymmetric barrier Lyapunov function is:

[0025] ;

[0026] in, This is the tracking error for nitrate nitrogen concentration. and It is the tracking error of nitrate nitrogen concentration. The upper and lower thresholds that are constrained.

[0027] Preferably, the expression for the first long-term loss function is:

[0028]

[0029] in, The first discount cost, This is the first instantaneous cost item.

[0030] Preferably, the expression for the second long-term loss function is:

[0031]

[0032] in, For the second discount cost, This is the second instantaneous cost item.

[0033] Preferably, the expression for the optimal aeration pump adaptive controller is:

[0034] ;

[0035] in, It is the adaptive controller coefficient of the aeration pump. This is the output of the first normalization layer. It is the current weight value of the network.

[0036] Preferably, the expression for the optimal reflux pump adaptive controller is:

[0037] ;

[0038] in, These are the coefficients of the adaptive controller for the reflux pump. It is the output of the second normalization layer. It is the second weight value of the current network execution.

[0039] The present invention discloses the following technical effects:

[0040] This invention provides an adaptive and adjustable multi-device optimal control method for wastewater treatment based on a constraint framework, comprising: constructing a first dynamic model and a second dynamic model respectively; constructing corresponding first and second asymmetric barrier Lyapunov functions based on the first and second dynamic models; constructing a first and second execution network based on a fuzzy neural network framework; constructing an initial aeration pump adaptive controller and an initial return pump adaptive controller corresponding to the first and second execution networks respectively based on the first and second asymmetric barrier Lyapunov functions; constructing a first long-term loss function, a second long-term loss function, and their corresponding first and second evaluation networks respectively; updating the initial aeration pump adaptive controller and the initial return pump adaptive controller using the first and second evaluation networks to obtain the optimal aeration pump adaptive controller and the optimal return pump adaptive controller; and controlling the wastewater treatment process using the optimal aeration pump adaptive controller and the optimal return pump adaptive controller. This invention, through an optimal control framework with an evaluation-execution network structure, not only achieves precise tracking of the set values ​​of dissolved oxygen and nitrate nitrogen concentrations, but also reduces equipment operating energy consumption while ensuring that the effluent water quality meets standards. By introducing an asymmetric barrier Lyapunov function into the control framework, it ensures that the concentrations of dissolved oxygen and nitrate nitrogen, as well as the tracking error, are within the desired range. By designing a dynamic adjustment mechanism in the optimal framework, it effectively avoids the problem of key indicators easily exceeding the standard, further ensuring strict effluent water quality. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 A flowchart of an adaptive and adjustable multi-device optimal control method for wastewater treatment based on a constraint framework, provided by an embodiment of the present invention;

[0043] Figure 2 A schematic diagram of the first comparative simulation results provided for an embodiment of the present invention;

[0044] Figure 3 This is a schematic diagram of the second comparative simulation results provided for an embodiment of the present invention. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] like Figure 1 As shown, this invention provides an adaptive and adjustable multi-device optimal control method for wastewater treatment based on a constraint framework, comprising:

[0048] Step 100: Construct the first dynamic model and the second dynamic model respectively;

[0049] Step 200: Construct the corresponding first asymmetric barrier Lyapunov function and second asymmetric barrier Lyapunov function based on the first dynamic model and the second dynamic model;

[0050] Step 300: Construct the first and second execution networks based on the fuzzy neural network framework;

[0051] Step 400: Construct the initial aeration pump adaptive controller and the initial reflux pump adaptive controller corresponding to the first execution network and the second execution network respectively, based on the first asymmetric barrier Lyapunov function and the second asymmetric barrier Lyapunov function.

[0052] Step 500: Construct the first long-term loss function, the second long-term loss function, and their corresponding first and second evaluation networks, respectively;

[0053] Step 600: Update the initial aeration pump adaptive controller and the initial return pump adaptive controller using the first evaluation network, the second evaluation network, the first execution network and the second execution network to obtain the optimal aeration pump adaptive controller and the optimal return pump adaptive controller.

[0054] Step 700: The wastewater treatment process is controlled using the optimal aeration pump adaptive controller and the optimal return pump adaptive controller.

[0055] Furthermore, the initial aeration pump adaptive controller and the initial return pump adaptive controller are updated using the first evaluation network, the second evaluation network, the first execution network, and the second execution network to obtain the optimal aeration pump adaptive controller and the optimal return pump adaptive controller, including:

[0056] Calculate the adaptive weight law corresponding to the evaluation network and the execution network;

[0057] The evaluation network and the execution network are updated using the aforementioned weight adaptation law;

[0058] The initial aeration pump adaptive controller and the initial return pump adaptive controller are updated using the updated evaluation network and the execution network to obtain the optimal aeration pump adaptive controller and the optimal return pump adaptive controller.

[0059] Furthermore, the expressions corresponding to the first dynamic model and the second dynamic model are as follows:

[0060] ;

[0061] in, This refers to the dissolved oxygen concentration in the fourth zone of the biochemical reaction tank. This refers to the dissolved oxygen concentration in the fifth zone of the biochemical reaction tank. The concentration of nitrate nitrogen in the first zone of the biochemical reaction tank; The concentration of nitrate nitrogen in the second zone of the biochemical reaction tank; The concentration of nitrate nitrogen in the fifth zone of the biochemical reaction tank; This represents the saturation value of dissolved oxygen concentration. Dissolved oxygen concentration is the operating variable; The operating variable is the concentration of nitrate nitrogen; Microbial respiration coefficient; The flow rate of the first section of the biochemical reaction tank; The flow rate of the second section of the biochemical reaction tank; The flow rate of the fourth section of the biochemical reaction tank; The flow rate of the fifth section of the biochemical reaction tank; The concentration of heterotrophic biomass; Heterotrophic biomass; This refers to the volume of the second section of the biochemical reaction tank. This refers to the volume of the fifth section of the biochemical reaction tank; This is the dissolved oxygen concentration saturation coefficient.

[0062] Furthermore, (1) firstly, an adaptive optimal controller for the aeration pump is designed under the constraint framework, and the tracking error of dissolved oxygen concentration is defined as:

[0063] ;

[0064] in, This is the set value for dissolved oxygen concentration;

[0065] The derivative of the tracking error is then calculated as follows:

[0066] ;

[0067] Define the first long-term loss function in the process of controlling dissolved oxygen concentration as:

[0068]

[0069] in, This is the discounted cost. Based on the detected current water quality indicators, the instantaneous cost term is designed as follows:

[0070] ;

[0071] in, and There are two switching thresholds. This represents the proportional adjustment coefficient.

[0072] Therefore, the first long-term loss function is approximated by the first evaluator network based on the fuzzy neural network, namely:

[0073] ;

[0074] in It is the optimal output weight. It is the first output of the normalization layer. This is the boundary approximation error. Therefore, the current output function of the network is used to evaluate it. ,in It is currently the number one weight in the network.

[0075] The approximation error of the evaluation network is defined as:

[0076] ;

[0077] The cost function of this evaluation network is then defined as follows: Then the adaptive law can be derived. for:

[0078] ;

[0079] in, The first parameter is the self-learning rate. .

[0080] Define a symbolic function as follows:

[0081] ;

[0082] Then, the first asymmetric barrier Lyapunov function is constructed as follows:

[0083] ;

[0084] in, and These are the upper and lower thresholds that constrain the dissolved oxygen concentration tracking error, ensuring that the dissolved oxygen concentration tracking error is within a certain range. Within the range.

[0085] Then, differentiating this first asymmetric barrier Lyapunov function yields:

[0086] ;

[0087] Among them, the change in weight , , and These are the optimal weights for the corresponding evaluation network and execution network, respectively. and The current actual value. In addition, the variable... , .

[0088] Define the first unknown dynamic information that is difficult to obtain during wastewater treatment:

[0089] ;

[0090] At this point, an execution network is used to approximate this unknown information. ;in It is the optimal output weight. It is the second output of the normalization layer. This is the estimation error. Define the weight change. , It is the current weight value of the network.

[0091] Based on the approximation information of the execution network mentioned above, the differentiated first Lyapunov function can be further obtained as follows:

[0092] ;

[0093] According to Young's inequality, we have:

[0094] ;

[0095] in It is a positive constant. Therefore, we can obtain:

[0096] ;

[0097] Therefore, the adaptive optimal controller input of the aeration pump Designed as follows:

[0098] ;

[0099] in It is the controller coefficient.

[0100] Based on the output of the evaluation network, the estimation error of the execution network is defined as:

[0101] ;

[0102] Subsequently, the cost function of the execution network is defined as follows: Then the adaptive law It is deduced as:

[0103] ;

[0104] in It is the parameter self-learning rate.

[0105] The differentiated Lyapunov function can be obtained as follows:

[0106] ;

[0107] As reinforcement learning theory is iteratively updated, the cost function can be continuously reduced to a minimum range. Therefore, at some point, there will exist a small constant function. To ensure Then there are:

[0108] ;

[0109] in , It is bounded, that is... .

[0110] According to Young's inequality, we have:

[0111] ;

[0112] ;

[0113] ;

[0114] in , and They are three positive constants.

[0115] because Furthermore, based on the above inequalities and Young's inequality, we can obtain:

[0116] ;

[0117] in, ;

[0118] ;

[0119] exist Based on this, we can further obtain the following:

[0120] ;

[0121] This proves that the control system is stable.

[0122] (2) Next, design an adaptive optimal controller for the reflux pump under the constraint framework:

[0123] The tracking error for nitrate nitrogen concentration is defined as:

[0124] ;

[0125] in, This is the set value for the nitrate nitrogen concentration;

[0126] The derivative of the tracking error is:

[0127] ;

[0128] Define the long-term loss function for controlling nitrate nitrogen concentration as:

[0129]

[0130] The instantaneous cost term is designed as follows:

[0131] ;

[0132] in It is the discounted cost. and There are two switching thresholds. This represents the proportional adjustment coefficient.

[0133] Therefore, a second evaluation network based on a fuzzy neural network is used to approximate this long-term loss function, namely:

[0134] ;

[0135] in It is the optimal output weight. It is the third output of the normalization layer. This is the boundary approximation error. Therefore, the current output function of the network is used to evaluate it. ,in It represents the current network weight.

[0136] The approximation error of the evaluation network is defined as:

[0137] ;

[0138] The cost function for evaluating the network is then defined as follows: Then the adaptive law can be derived. for:

[0139] ;

[0140] in It is the parameter self-learning rate. .

[0141] Define a symbolic function as follows:

[0142] ;

[0143] Then, the second asymmetric barrier Lyapunov function is constructed as follows:

[0144] ;

[0145] in, and These are the upper and lower thresholds that constrain the tracking error of nitrate nitrogen concentration, i.e., ensuring that the tracking error of nitrate nitrogen concentration is within a certain range. Within the range. Then, differentiating this asymmetric barrier Lyapunov function yields:

[0146] ;

[0147] Among them, the change in weight , , and These are the optimal weights for the corresponding evaluation network and execution network, respectively. and The current estimated value. In addition, the variable... , .

[0148] The second unknown dynamic information, which is difficult to obtain during processing, is approximated using an execution network:

[0149] ;

[0150] in It is the optimal output weight. It is the fourth output of the normalization layer. This is the estimation error. Define the weight change. , This is the current network weight value.

[0151] Based on the approximation information of the execution network mentioned above, the differentiated second Lyapunov function can be further obtained as follows:

[0152] ;

[0153] Therefore, the adaptive optimal controller input for the return pump Designed as follows:

[0154] ;

[0155] in It is the controller coefficient.

[0156] Based on the output of the evaluation network, the network cost function is as follows: The estimation error Then the adaptive law Designed as follows:

[0157] ;

[0158] in, It is the parameter self-learning rate.

[0159] The differentiated second Lyapunov function can be further obtained as follows:

[0160] ;

[0161] There exists a small constant function. and ensure Then we can obtain:

[0162] ;

[0163] in , It is bounded, that is... .

[0164] ;

[0165] in,

[0166] ;

[0167] in , , and It is a positive constant.

[0168] exist Based on this, we can further obtain the following:

[0169] ;

[0170] This proves that the control system is stable.

[0171] Furthermore, the control effect of the actual controller with optimal parameters is evaluated using the combined square error and the combined absolute error to obtain the evaluation result; the formula for calculating the combined square error is:

[0172] ;

[0173] The formula for calculating the comprehensive absolute error is as follows:

[0174] 2 ;

[0175] in, The total squared error; This refers to the overall absolute error; The total number of samples.

[0176] Specifically, to demonstrate the superiority of the designed control method (CAFOC), Figure 2 and Figure 3 The simulation results are shown in comparison with proportional-integral-derivative (PID), fuzzy neural network (FNN) and adaptive dynamic programming (ADP) control methods. Figure 2 (a) and Figure 2 (b) The tracking control curve and control error curve of dissolved oxygen concentration are presented, and the results show that the CAFOC control method can achieve the best tracking performance. Figure 3 (a) and Figure 3 (b) The tracking control curve and control error curve of nitrate nitrogen concentration are presented, and the results show that the CAFOC control method can achieve the highest control accuracy. Therefore, it can be concluded that compared with PID, FNN and ADP methods, the CAFOC proposed in this paper can achieve the best control accuracy and tracking response speed under stormy weather conditions.

[0177] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0178] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A sewage treatment adaptive adjustable multi-device optimal control method based on a constraint framework, characterized in that, The method comprises the following steps: constructing a first dynamic model and a second dynamic model respectively; constructing a first asymmetric barrier Lyapunov function and a second asymmetric barrier Lyapunov function corresponding to the first dynamic model and the second dynamic model respectively; constructing a current first execution network and a current second execution network based on a fuzzy neural network framework; constructing an initial aeration pump adaptive controller and an initial reflux pump adaptive controller corresponding to the first execution network and the second execution network respectively according to the first asymmetric barrier Lyapunov function and the second asymmetric barrier Lyapunov function; constructing a first long-term loss function and a second long-term loss function and first and second judgment networks corresponding to the first long-term loss function and the second long-term loss function respectively; updating the initial aeration pump adaptive controller and the initial reflux pump adaptive controller by using the first and second judgment networks, the first and second execution networks to obtain an optimal aeration pump adaptive controller and an optimal reflux pump adaptive controller; controlling a sewage treatment process by using the optimal aeration pump adaptive controller and the optimal reflux pump adaptive controller; updating the initial aeration pump adaptive controller and the initial reflux pump adaptive controller by using the first and second judgment networks, the first and second execution networks to obtain an optimal aeration pump adaptive controller and an optimal reflux pump adaptive controller, which comprises the following steps: calculating a weight value adaptive law corresponding to the judgment network and the execution network; updating the judgment network and the execution network by using the weight value adaptive law; updating the initial aeration pump adaptive controller and the initial reflux pump adaptive controller by using the updated judgment network and the execution network to obtain the optimal aeration pump adaptive controller and the optimal reflux pump adaptive controller; an expression of the first asymmetric barrier Lyapunov function is as follows: ； wherein, is a tracking error of the dissolved oxygen concentration, and is a tracking error of the dissolved oxygen concentration upper and lower thresholds constrained; an expression of the second asymmetric barrier Lyapunov function is as follows: ； wherein, is a tracking error of the nitrate nitrogen concentration, and is a tracking error of the nitrate nitrogen concentration upper and lower thresholds constrained; an expression of the optimal aeration pump adaptive controller is as follows: ； wherein, is an aeration pump adaptive controller coefficient, is an output of a first normalization layer, is a current execution network first weight value; an expression of the optimal reflux pump adaptive controller is as follows: ； wherein, is a reflux pump adaptive controller coefficient, is an output of a second normalization layer, is a current execution network second weight value.

2. The self-adaptive adjustable multi-device optimal control method for sewage treatment based on a constraint framework according to claim 1, characterized in that, expressions of the first dynamic model and the second dynamic model are as follows respectively: ； wherein, is the dissolved oxygen concentration of the fourth zone of the biochemical reaction tank; is the dissolved oxygen concentration of the fifth zone of the biochemical reaction tank; is the nitrate nitrogen concentration of the first zone of the biochemical reaction tank; is the nitrate nitrogen concentration of the second zone of the biochemical reaction tank; is the nitrate nitrogen concentration of the fifth zone of the biochemical reaction tank; is the operating variable for the dissolved oxygen concentration; is the operating variable for the nitrate nitrogen concentration; is the coefficient of microbial respiration; is the flow rate of the first zone of the biochemical reaction tank; is the flow rate of the second zone of the biochemical reaction tank; is the flow rate of the fourth zone of the biochemical reaction tank; is the flow rate of the fifth zone of the biochemical reaction tank; is the concentration of the heterotrophic biomass; is the heterotrophic biomass; is the volume of the second zone of the biochemical reaction tank; is the volume of the fifth zone of the biochemical reaction tank; is the saturation coefficient for the dissolved oxygen concentration.

3. The adaptive adjustable multi-device optimal control method for sewage treatment based on a constraint framework according to claim 1, characterized in that, an expression of the first long-term loss function is as follows: ； wherein is the first discounted cost, is the first instantaneous cost term.

4. The adaptive adjustable multi-device optimal control method for sewage treatment based on a constraint framework according to claim 3, characterized in that, an expression of the second long-term loss function is as follows: ； wherein, is a second discounted cost, is a second instantaneous cost term.

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