Self-adaptive collaborative optimal tracking control method for sewage treatment based on dynamic event triggering

Abstract

The invention belongs to the technical field of sewage treatment, and provides a sewage treatment adaptive collaborative optimal tracking control method based on dynamic event triggering. The method comprises the steps of simplified dynamical model construction, Lyapunov function construction, optimal controller construction based on an execution network, evaluation network construction, weight adaptive law construction, dynamic event trigger mechanism setting and tracking control. According to the invention, the parameters of the evaluation network and the execution network are selectively updated through the weight adaptive law, so that the burden of large information communication traffic and insufficient computing power of the water plant is relieved; through an adaptive controller of the execution network, the set values of the dissolved oxygen concentration and the nitrate nitrogen concentration can be accurately tracked, and effective and rapid control is realized; and the execution network and the controller are optimized through the evaluation network, so that the operation energy consumption of the equipment is effectively reduced while the effluent quality is ensured to reach the standard.

Description

Technical Field

[0001] The present invention relates to the technical field of sewage treatment, and in particular to a sewage treatment adaptive collaborative optimal tracking control method based on dynamic event triggering. Background Art

[0002] The application of sewage treatment technology can significantly reduce the discharge of water pollutants and promote the recycling and reuse of water resources. At present, the activated sludge method is widely used in sewage treatment processes. This process involves numerous physical and biochemical reactions and exhibits complex time-varying dynamic characteristics. Therefore, there is an urgent need to develop efficient control technologies to ensure that the energy consumption of equipment operation is effectively reduced while meeting strict effluent water quality standards. At present, there has been a lot of research on the implementation of adaptive tracking control for sewage treatment processes, such as model predictive control, neural network control, proportional-integral-differential control methods, etc.

[0003] However, the above-mentioned methods rely solely on instantaneous tracking errors for iterative parameter updates, which can only guarantee effluent water quality but cannot reduce the energy consumption of equipment operation. Due to the feedback, reward and penalty mechanisms, adaptive optimal control methods based on reinforcement learning are able to interact with the environment over the long term and have been widely studied and applied. However, this technology requires complex calculations and can easily impose a communication burden on real-time control in actual industry. Currently, in the sewage treatment process of reclaimed water plants, most of the trigger control methods used are fixed thresholds, which are prone to delays or over-triggering. Summary of the Invention

[0004] In order to overcome the shortcomings of the existing technology, the purpose of the present invention is to provide an adaptive collaborative optimal tracking control method for sewage treatment based on dynamic event triggering, which solves the problems of excessive communication and computing power burden, untimely concentration tracking, and high equipment power consumption due to the need to ensure water quality in conventional tracking control methods.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] An adaptive collaborative optimal tracking control method for sewage treatment based on dynamic event triggering, comprising:

[0007] Construct a simplified kinetic model for dissolved oxygen concentration and nitrate nitrogen concentration;

[0008] constructing a Lyapunov function according to the simplified dynamic model;

[0009] Constructing an execution network based on a fuzzy neural network, and constructing an optimal controller based on the execution network according to the Lyapunov function;

[0010] Constructing a long-term loss function, and constructing an evaluation network based on the fuzzy neural network according to the long-term loss function;

[0011] Constructing a weight adaptive law for the execution network and the evaluation network;

[0012] Setting two sets of dynamic trigger thresholds, and setting a dynamic event trigger mechanism according to the dynamic trigger thresholds;

[0013] The dynamic event triggering mechanism and the weight adaptive law are updated to the execution network and the evaluation network, and the updated execution network and the evaluation network are used to update the optimal controller of the target device.

[0014] Preferably, a simplified kinetic model for dissolved oxygen concentration and nitrate nitrogen concentration is constructed, including:

[0015] An original kinetic model is established; the expression of the original kinetic model is:

[0016]

[0017] Among them, S O,4 (t) is the dissolved oxygen concentration in the fourth partition of the biochemical reaction tank; S O,5 (t) is the dissolved oxygen concentration in the fifth partition of the biochemical reaction tank; S NO,1 (t) is the nitrate nitrogen concentration in the first partition of the biochemical reaction tank; S NO,2 (t) is the nitrate nitrogen concentration in the second partition of the biochemical reaction tank; S NO,5 (t) is the nitrate nitrogen concentration in the fifth zone of the biochemical reaction tank; S O,S is the saturation value of dissolved oxygen concentration; K L a5(t) is the manipulated variable of dissolved oxygen concentration; Q r (t) is the manipulated variable of nitrate nitrogen concentration; μ(t) is the microbial respiration coefficient; ψ1(t) is the flow rate of the first partition of the biochemical reaction tank; ψ2(t) is the flow rate of the second partition of the biochemical reaction tank; ψ4(t) is the flow rate of the fourth partition of the biochemical reaction tank; ψ5(t) is the flow rate of the fifth partition of the biochemical reaction tank; X b,h (t) is the concentration of heterotrophic biomass; Y h is the heterotrophic biomass; V2 is the volume of the second partition of the biochemical reaction tank; V5 is the volume of the fifth partition of the biochemical reaction tank; a1 is the first constant; a2 is the second constant;

[0018] Define a first unknown function and a second unknown function; the expression of the first unknown function is:

[0019]

[0020] Among them, D1(t) is the unknown dynamic information of the environment when tracking and controlling the dissolved oxygen concentration;

[0021] The expression of the second unknown function is:

[0022]

[0023] Among them, D2(t) is the unknown dynamic information of the environment when tracking and controlling the nitrate nitrogen concentration;

[0024] The original kinetic model is simplified using the first unknown function and the second unknown function to obtain the simplified kinetic model; the expression of the simplified kinetic model is:

[0025]

[0026] Where P1(t)=S O,S -S O,5 (t); P2(t) = S NO,5 (t) / V2; For S O,5 (t); P1(t) is the result of subtracting the current dissolved oxygen concentration from the dissolved oxygen saturation value; P2(t) is the result of dividing the current concentration of nitrate nitrogen by the volume of the second partition of the biochemical reaction tank.

[0027] Preferably, constructing a Lyapunov function according to the simplified dynamics model comprises:

[0028] The dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error are set according to the simplified kinetic model; the expression of the dissolved oxygen concentration tracking error is: O (t) = S O,5 (t)-S O,set (t); where e O (t) is the dissolved oxygen concentration tracking error; S O,set (t) is the dissolved oxygen concentration set value; the expression of the nitrate nitrogen concentration tracking error is: e NO (t) = S NO,2 (t)-S NO,set (t); where e NO (t) is the nitrate nitrogen concentration tracking error; S NO,set (t) is the set value of nitrate nitrogen concentration;

[0029] The Lyapunov function is constructed according to the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the Lyapunov function based on the error is: Among them, V z (t) is the Lyapunov function based on the error; e(t) is the tracking control error; T represents the transposition operation.

[0030] Preferably, constructing an optimal controller based on an execution network according to the Lyapunov function includes:

[0031] Deriving the Lyapunov function to obtain a Lyapunov derivative function;

[0032] Extract the unknown dynamic information part in the Lyapunov derivative function; the expression of the unknown dynamic information part is: Where D(t) = [D1(t), D2(t)] T ; D(t) is the matrix formed by vertically concatenating D1(t) and D2(t);

[0033] The execution network is constructed according to the unknown part of the dynamic information; the expression of the execution network based on the fuzzy neural network is:

[0034]

[0035] in, is the optimal output weight of the execution network; U a (t) is the output of the normalization layer of the execution network; θ a (t) is the estimated error of the execution network; is the input of the execution network; is the center of the execution network; is the width of the execution network; m is the number of neurons in the input layer; l is the number of neurons in the RBF layer and the normalization layer.

[0036] Preferably, constructing an optimal controller based on an execution network according to the Lyapunov function includes:

[0037] Construct an optimal controller; the expression of the optimal controller is:

[0038]

[0039] Among them, v * is the output of the optimal controller; ζ is the control coefficient vector; is the transpose of the optimal output weight;

[0040] The actual controller is constructed according to the optimal controller; the expression of the actual controller is:

[0041]

[0042] Wherein, v(t) is the output of the actual controller; for The transpose of the current value of ;

[0043] The actual controller is iteratively updated according to the updated execution network to obtain the updated optimal controller.

[0044] Preferably, constructing a long-term loss function, and constructing an evaluation network of the fuzzy neural network based on the long-term loss function, includes:

[0045] An instantaneous loss function is constructed according to the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the instantaneous loss function is:

[0046]

[0047] Wherein, R(t) is the output value of the instantaneous loss function;

[0048] Integrate the instantaneous loss function to obtain the long-term loss function; the expression of the long-term loss function is: in, is the output value of the long-term loss function; ι is the integral variable;

[0049] The evaluation network is constructed according to the long-term loss function; the expression of the evaluation network based on the fuzzy neural network is:

[0050]

[0051] in, is the optimal output weight of the evaluation network; U c (t) is the output of the normalization layer of the judgment network; θ c (t) is the estimated error of the judgment network; is the input of the judgment network; is the center of the judging network; is the width of the evaluation network.

[0052] Preferably, constructing the weight adaptive law of the execution network and the evaluation network includes:

[0053] Set the first estimated error of the evaluation network and the second estimated error of the execution network; the expression of the first estimated error is:

[0054]

[0055] Where η1(t) is the first estimation error; ξ is the discounted future cost; is the output function of the evaluation network;

[0056] The expression of the second estimation error is:

[0057]

[0058] Wherein, η2(t) is the second estimation error;

[0059] A first cost function of the evaluation network is constructed based on the first estimated error, and a second cost function of the execution network is constructed based on the second estimated error. The expression of the first cost function is: Among them, E c (t) is the first cost function;

[0060] The expression of the second cost function is: Among them, E a (t) is the second cost function;

[0061] The weight adaptive law of the execution network and the evaluation network is constructed according to the first cost function and the second cost function respectively; the expression of the weight adaptive law includes:

[0062]

[0063] in, for The transpose of the current value of β c is the first adaptive rate coefficient; for The current value of β a is the second adaptive rate coefficient; is the rule layer change value of the evaluation network.

[0064] Preferably, setting a dynamic trigger threshold, and setting a dynamic event trigger mechanism according to the dynamic trigger threshold, includes:

[0065] Construct the dynamic trigger threshold; the expression of the dynamic trigger threshold includes:

[0066] and

[0067]

[0068] Wherein, τ1 is the first dynamic threshold; δ1 is the first positive definite parameter; λ is the Puschitz constant; τ2 is the second dynamic threshold; δ2 is the second positive definite parameter;

[0069] A dynamic event triggering mechanism is set according to the dynamic triggering threshold; the expression of the dynamic event triggering mechanism is: in, M1 is the first event; For the second event; is the tracking error based on event sampling; is the long-term cost function.

[0070] The present invention discloses the following technical effects:

[0071] The present invention provides a sewage treatment adaptive collaborative optimal tracking control method based on dynamic event triggering. The parameters of the evaluation network and the execution network are selectively updated through the weight adaptive law, which solves the problems of excessive communication and computing power burden in conventional tracking control methods, and reduces the information communication volume and computing power burden of the water plant; through the adaptive controller of the execution network, the problem of untimely concentration tracking in conventional tracking control methods is solved, and accurate tracking of the set values ​​of dissolved oxygen concentration and nitrate nitrogen concentration is achieved; through the evaluation network, the execution network and the controller are optimized, which solves the problem of high equipment power consumption in conventional tracking control methods in order to ensure water quality, and reduces the operating energy consumption of the equipment while ensuring that the effluent water quality meets the standards. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0073] Figure 1 A schematic diagram of the adaptive collaborative optimal tracking control process for sewage treatment based on dynamic event triggering provided by an embodiment of the present invention;

[0074] Figure 2 A schematic diagram of comparative simulation results provided by an embodiment of the present invention, Figure 2 (a) is a schematic diagram of the dissolved oxygen concentration control results; Figure 2 (b) is a schematic diagram of the nitrate nitrogen concentration control results;

[0075] Figure 3 The control error curves of the two methods provided in the embodiment of the present invention are: Figure 3 (a) is a schematic diagram of the control error curve of dissolved oxygen, Figure 3 (b) is a schematic diagram of the control error curve of nitrate nitrogen;

[0076] Figure 4 The change curve of the control variable provided by the embodiment of the present invention is Figure 4 (a) is K L Schematic diagram of the change curve of a5(t), Figure 4 (b) is Q r (t) Schematic diagram of the change curve;

[0077] Figure 5Schematic diagram of parameter update intervals of the dissolved oxygen concentration controller and the nitrate nitrogen concentration controller under two triggering conditions provided in an embodiment of the present invention. Figure 5 (a) is a schematic diagram of the parameter update interval of the dissolved oxygen concentration controller. Figure 5 (b) is a schematic diagram of the parameter update interval of the nitrate nitrogen concentration controller. DETAILED DESCRIPTION

[0078] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0079] The purpose of the present invention is to provide an adaptive collaborative optimal tracking control method for sewage treatment based on dynamic event triggering, which solves the problems of excessive communication and computing power burden, untimely concentration tracking, and high equipment power consumption due to the need to ensure water quality in conventional tracking control methods.

[0080] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0081] Figure 1 The schematic diagram of the adaptive collaborative optimal tracking control process of sewage treatment based on dynamic event triggering provided by the embodiment of the present invention is as follows: Figure 1 As shown, the present invention provides a sewage treatment adaptive collaborative optimal tracking control method based on dynamic event triggering, comprising:

[0082] Step 100: constructing a simplified kinetic model for dissolved oxygen concentration and nitrate nitrogen concentration;

[0083] Step 200: constructing a Lyapunov function according to the simplified dynamics model;

[0084] Step 300: constructing an execution network based on a fuzzy neural network, and constructing an optimal controller based on the execution network according to the Lyapunov function;

[0085] Step 400: constructing a long-term loss function, and constructing an evaluation network based on the fuzzy neural network according to the long-term loss function;

[0086] Step 500: constructing a weight adaptive law for the execution network and the evaluation network;

[0087] Step 600: setting two sets of dynamic trigger thresholds, and setting a dynamic event trigger mechanism according to the dynamic trigger thresholds;

[0088] Step 700: updating the dynamic event triggering mechanism and the weight adaptive law into the execution network and the evaluation network, and using the updated execution network and the evaluation network to update the optimal controller of the target device.

[0089] Furthermore, a simplified kinetic model for dissolved oxygen concentration and nitrate nitrogen concentration was constructed, including:

[0090] An original kinetic model is established; the expression of the original kinetic model is:

[0091]

[0092] Among them, S O,4 (t) is the dissolved oxygen concentration in the fourth partition of the biochemical reaction tank; S O,5 (t) is the dissolved oxygen concentration in the fifth partition of the biochemical reaction tank; S NO,1 (t) is the nitrate nitrogen concentration in the first partition of the biochemical reaction tank; S NO,2 (t) is the nitrate nitrogen concentration in the second partition of the biochemical reaction tank; S NO,5 (t) is the nitrate nitrogen concentration in the fifth zone of the biochemical reaction tank; S O,S is the saturation value of dissolved oxygen concentration; K L a5(t) is the manipulated variable of dissolved oxygen concentration; Q r (t) is the manipulated variable of nitrate nitrogen concentration; μ(t) is the microbial respiration coefficient; ψ1(t) is the flow rate of the first partition of the biochemical reaction tank; ψ2(t) is the flow rate of the second partition of the biochemical reaction tank; ψ4(t) is the flow rate of the fourth partition of the biochemical reaction tank; ψ5(t) is the flow rate of the fifth partition of the biochemical reaction tank; X b,h (t) is the concentration of heterotrophic biomass; Y h is the heterotrophic biomass; V2 is the volume of the second partition of the biochemical reaction tank; V5 is the volume of the fifth partition of the biochemical reaction tank; a1 is the first constant; a2 is the second constant;

[0093] Define a first unknown function and a second unknown function; the expression of the first unknown function is:

[0094]

[0095] Among them, D1(t) is the unknown dynamic information of the environment when tracking and controlling the dissolved oxygen concentration;

[0096] The expression of the second unknown function is:

[0097]

[0098] Among them, D2(t) is the unknown dynamic information of the environment when tracking and controlling the nitrate nitrogen concentration;

[0099] The original kinetic model is simplified using the first unknown function and the second unknown function to obtain the simplified kinetic model; the expression of the simplified kinetic model is:

[0100]

[0101] Where P1(t)=S O,S -S O,5 (t); P2(t) = S NO,5 (t) / V2; For S O,5 (t); P1(t) is the result of subtracting the current dissolved oxygen concentration from the dissolved oxygen saturation value; P2(t) is the result of dividing the current concentration of nitrate nitrogen by the volume of the second partition of the biochemical reaction tank.

[0102] Preferably, constructing a Lyapunov function according to the simplified dynamics model comprises:

[0103] The dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error are set according to the simplified kinetic model; the expression of the dissolved oxygen concentration tracking error is: O (t) = S O,5 (t)-S O,set (t); where e O (t) is the dissolved oxygen concentration tracking error; S O,set (t) is the dissolved oxygen concentration set value; the expression of the nitrate nitrogen concentration tracking error is: e NO (t) = S NO,2 (t)-S NO,set (t); where e NO (t) is the nitrate nitrogen concentration tracking error; S NO,set (t) is the set value of nitrate nitrogen concentration;

[0104] The Lyapunov function is constructed according to the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the Lyapunov function based on the error is: Among them, V z (t) is the Lyapunov function based on the error; e(t) is the tracking control error; T represents the transposition operation.

[0105] Specifically, constructing an optimal controller based on an execution network according to the Lyapunov function includes:

[0106] Deriving the Lyapunov function to obtain a Lyapunov derivative function;

[0107] Extract the unknown dynamic information part in the Lyapunov derivative function; the expression of the unknown dynamic information part is: Where D(t) = [D1(t), D2(t)] T ; D(t) is the matrix formed by vertically concatenating D1(t) and D2(t);

[0108] The execution network is constructed according to the unknown part of the dynamic information; the expression of the execution network based on the fuzzy neural network is:

[0109]

[0110] in, is the optimal output weight of the execution network; U a (t) is the output of the normalization layer of the execution network; θ a (t) is the estimated error of the execution network; is the input of the execution network; is the center of the execution network; is the width of the execution network; m is the number of neurons in the input layer; l is the number of neurons in the RBF layer and the normalization layer.

[0111] Furthermore, an optimal controller based on an execution network is constructed according to the Lyapunov function, including:

[0112] Construct an optimal controller; the expression of the optimal controller is:

[0113]

[0114] Among them, v * is the output of the optimal controller; ζ is the control coefficient vector; is the transpose of the optimal output weight;

[0115] The actual controller is constructed according to the optimal controller; the expression of the actual controller is:

[0116]

[0117] Wherein, v(t) is the output of the actual controller; for The transpose of the current value of ;

[0118] The actual controller is iteratively updated according to the updated execution network to obtain the updated optimal controller.

[0119] Specifically, constructing a long-term loss function, and constructing an evaluation network of the fuzzy neural network based on the long-term loss function, includes:

[0120] An instantaneous loss function is constructed according to the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the instantaneous loss function is:

[0121]

[0122] Wherein, R(t) is the output value of the instantaneous loss function;

[0123] Integrate the instantaneous loss function to obtain the long-term loss function; the expression of the long-term loss function is: in, is the output value of the long-term loss function; ι is the integral variable;

[0124] The evaluation network is constructed according to the long-term loss function; the expression of the evaluation network based on the fuzzy neural network is:

[0125]

[0126] in, is the optimal output weight of the evaluation network; U c (t) is the output of the normalization layer of the judgment network; θ c (t) is the estimated error of the judgment network; is the input of the judgment network; is the center of the judging network; is the width of the evaluation network.

[0127] Furthermore, constructing the weight adaptive law of the execution network and the evaluation network includes:

[0128] Set the first estimated error of the evaluation network and the second estimated error of the execution network; the expression of the first estimated error is:

[0129]

[0130] Where η1(t) is the first estimation error; ξ is the discounted future cost; is the output function of the evaluation network;

[0131] The expression of the second estimation error is:

[0132]

[0133] Wherein, η2(t) is the second estimation error;

[0134] A first cost function of the evaluation network is constructed based on the first estimated error, and a second cost function of the execution network is constructed based on the second estimated error. The expression of the first cost function is: Among them, E c (t) is the first cost function;

[0135] The expression of the second cost function is: Among them, E a (t) is the second cost function;

[0136] The weight adaptive law of the execution network and the evaluation network is constructed according to the first cost function and the second cost function respectively; the expression of the weight adaptive law includes:

[0137] and

[0138]

[0139] in, for The transpose of the current value of β c is the first adaptive rate coefficient; for The current value of β a is the second adaptive rate coefficient; is the change value of the rule layer of the evaluation network.

[0140] Specifically, setting a dynamic trigger threshold, and setting a dynamic event trigger mechanism according to the dynamic trigger threshold, includes:

[0141] Construct the dynamic trigger threshold; the expression of the dynamic trigger threshold includes:

[0142] and

[0143]

[0144] Wherein, τ1 is the first dynamic threshold; δ1 is the first positive definite parameter; λ is the Puschitz constant; τ2 is the second dynamic threshold; δ2 is the second positive definite parameter;

[0145] A dynamic event triggering mechanism is set according to the dynamic triggering threshold; the expression of the dynamic event triggering mechanism is: in, For the first event; For the second event; is the tracking error based on event sampling; is the long-term cost function.

[0146] Specifically, a kinetic model for dissolved oxygen concentration and nitrate nitrogen concentration was established:

[0147]

[0148] Furthermore, for the above dynamic model, the following two unknown functions are defined:

[0149]

[0150]

[0151] Then, the dynamic model can be reformulated as:

[0152]

[0153] Preferably, the tracking errors of dissolved oxygen concentration and nitrate nitrogen concentration are defined as:

[0154] e O (t) = S O,5 (t)-S O,set (t)

[0155] e NO (t) = S NO,2 (t)-S NO,set (t)

[0156] The time derivative of the tracking error of dissolved oxygen concentration and nitrate nitrogen concentration is calculated as:

[0157]

[0158] in, is the derivative of the set point dissolved oxygen concentration, is the derivative of the set value of nitrate-nitrogen concentration.

[0159] Furthermore, the Lyapunov function based on tracking error is designed as:

[0160]

[0161] The derivative of the Lyapunov function yields:

[0162]

[0163] Where, e(t)=[e O (t),e NO (t)] T , P(t)=[P1(t),P2(t)] T , D(t)=[D1(t),D2(t)] T ,

[0164] Specifically, for the dynamic information of sewage treatment process Due to the unknown nature, an execution network based on fuzzy neural network is designed to approximate

[0165]

[0166] in, is the optimal output weight, represents the input of the fuzzy neural network, γ(t) represents the center of the fuzzy neural network, b(t) represents the width of the fuzzy neural network, Γ(t) represents the width weight of the fuzzy neural network; m represents the number of neurons in the input layer of the fuzzy neural network, l represents the number of neurons in the RBF layer and the normalization layer of the fuzzy neural network; U a (t) is the output of the normalization layer of the fuzzy neural network, θ a (t) is the estimation error, and the weight change is in yes The current value of .

[0167] Furthermore, the optimal controller can be designed as:

[0168]

[0169] The control coefficient vector is ζ = [ζ1ζ2]. Therefore, the actual controller can be expressed as:

[0170]

[0171] Preferably, based on the current state of the execution network identification, the long-term loss function is calculated using the cumulative tracking control error of the sewage treatment process. First, the instantaneous loss function is designed as:

[0172]

[0173] Therefore, the long-term loss function can be expressed as follows:

[0174]

[0175] Here, ξ>0 represents discounted future costs.

[0176] A fuzzy neural network-based evaluation network is used to approximate the long-term cost function and is designed as follows:

[0177]

[0178] in, is the optimal output weight, x(t) represents the input of the fuzzy neural network, γ(t) represents the center of the fuzzy neural network, b(t) represents the width of the fuzzy neural network, Γ(t) represents the width weight of the fuzzy neural network; m represents the number of neurons in the input layer of the fuzzy neural network, l represents the number of neurons in the RBF layer and normalization layer of the fuzzy neural network; U c (t) is the output of the normalization layer of the fuzzy neural network, θ c (t) is the boundary approximation error. The weight change is in yes The current value of . Therefore, the output function of the review network is

[0179] Furthermore, the estimation error based on the critic network and the execution network can be defined as:

[0180]

[0181] The cost functions of the judgment network and the execution network are defined as and Therefore, the weight adaptation laws of the two networks are designed as follows:

[0182]

[0183] Among them, β c >0,β a >0 is the adaptive rate coefficient, and

[0184] Specifically, we design a dynamic event triggering mechanism: In the absence of event triggering, the final controller is as shown above. We use the event sampling time to reconstruct the adaptive event triggering optimization controller:

[0185]

[0186] in, When t∈[t k ,t k+1 ), where Represents a monotonically increasing sequence of triggering times when events occur. Assume that the first event occurs at the initial time.

[0187] The trigger mechanism ET is expressed as:

[0188]

[0189] Among them, the event and for

[0190]

[0191] Among them, the dynamic trigger thresholds τ1 and τ2 are defined as

[0192]

[0193] where λ is the known Puschitz constant of the Gaussian function, and δ1 and δ2 are positive definite parameters.

[0194] This event is triggered in the following cases: 1) If the current error e(t) reaches the threshold τ1, the weight parameters of the evaluator network and the actor network are updated simultaneously; 2) If the long-term cost function When the threshold τ2 is reached, the weight parameter of the evaluator network is updated, and Reset to zero and re-accumulate; 3) If the above deviation conditions are not met, it means that the current model can meet the control accuracy requirements and no update is required.

[0195] Specifically, for the tracking control problem of the sewage treatment process, the dynamic collaborative optimal controller and parameter adaptive update method are adopted, which can not only obtain good transient and steady-state performance, but also strictly comply with and The boundedness of the flow ensures the stability of the sewage treatment process system.

[0196] Furthermore, the Lyapunov candidate function is introduced as:

[0197]

[0198] The time derivative of the above function is:

[0199]

[0200] Further we get:

[0201]

[0202] As the iterative process based on reinforcement learning proceeds, the cost function continues to decrease and eventually converges to the minimum boundary. Therefore, there is a small constant function Right now therefore:

[0203]

[0204] in, And ρ(t) is bounded, that is

[0205] According to Young's inequality

[0206]

[0207]

[0208] in, and is a positive constant.

[0209] The previous formula can be further written as:

[0210]

[0211] From this we get:

[0212]

[0213] in,

[0214]

[0215] exist On this basis, we can further obtain the following:

[0216]

[0217] Therefore, we can know that:

[0218] 1) All signals in the sewage treatment process system are bounded:

[0219] Based on the previous formula, the boundedness of V(t) is completed, which represents the change of weight and The tracking error e(t) is bounded. is bounded, so we can get and In addition, S set is known and bounded. Therefore, S O,5 (t) and S NO,2 (t) is bounded. From the above analysis and the definition of υ(t), we can see that υ * It is bounded.

[0220] 2) Ensure the transient and steady-state tracking performance of dissolved oxygen concentration and nitrate nitrogen concentration:

[0221] From the above stability analysis, it can be seen that the boundedness of dissolved oxygen concentration, nitrate nitrogen concentration and tracking error is strictly satisfied, which means that the transient performance is effectively maintained. It can be concluded that:

[0222]

[0223] By selecting appropriate parameters, the minimum value of the tracking error e(t) is converged to a smaller range, thus achieving accurate tracking of the dissolved oxygen concentration and nitrate nitrogen concentration.

[0224] Based on the above theoretical discussion, the stability of the control system is proved.

[0225] Furthermore, the control effect of the actual controller with the optimal parameters is evaluated using the comprehensive square error and the comprehensive absolute error to obtain an evaluation result; the calculation formula of the comprehensive square error is:

[0226]

[0227] The calculation formula of the comprehensive absolute error is:

[0228]

[0229] Wherein, IAE is the integrated square error; ISE is the integrated absolute error; is the total number of samples.

[0230] Specifically, to prove the superiority of the designed control method, Figure 2 and Figure 3 The comparative simulation results with the proportional-integral-derivative control method (PID), fuzzy neural network control method (FNN) and adaptive dynamic programming control method (ADP) are shown. Figure 2 (a) and Figure 2 (b) The tracking curves of dissolved oxygen concentration and nitrate nitrogen concentration are presented respectively. The results show that the DECOC control method can achieve the optimal tracking performance. Figure 3 (a) and Figure 3 (b) The control error curves of the two methods are plotted, confirming that the proposed scheme can achieve the highest control accuracy. Therefore, it can be concluded that compared with the PID, FNN, and ADP methods, the DECOC proposed in this paper can achieve the best control accuracy and tracking response speed under stormy weather conditions. Figure 3 (a) and Figure 3 (b) further gives the change curve of the control variable, and Figure 4 (a) and Figure 4 (b) shows the parameter update interval of the dissolved oxygen concentration controller and the nitrate nitrogen concentration controller under two trigger conditions. Figure 5 (a) Schematic diagram of the parameter update interval of the nitrate nitrogen concentration controller. Figure 5 (b).

[0231] The beneficial effects of the present invention are as follows:

[0232] The present invention selectively updates the parameters of the evaluation network and the execution network through the weight adaptive law, thereby reducing the burden of large information communication volume and insufficient computing power in the water plant; through the adaptive controller of the execution network, it can accurately track the set values ​​of dissolved oxygen concentration and nitrate nitrogen concentration, and achieve effective and rapid control; through the evaluation network, the execution network and controller are optimized, while ensuring that the water quality of the effluent meets the standards, the operating energy consumption of the equipment is effectively reduced.

[0233] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0234] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A sewage treatment adaptive collaborative optimal tracking control method based on dynamic event triggering, characterized in that: include: Construct a simplified kinetic model for dissolved oxygen concentration and nitrate nitrogen concentration; constructing a Lyapunov function according to the simplified dynamic model; Constructing an execution network based on a fuzzy neural network, and constructing an optimal controller based on the execution network according to the Lyapunov function; Constructing a long-term loss function, and constructing an evaluation network based on the fuzzy neural network according to the long-term loss function; Constructing a weight adaptive law for the execution network and the evaluation network; Setting two sets of dynamic trigger thresholds, and setting a dynamic event trigger mechanism according to the dynamic trigger thresholds; The dynamic event triggering mechanism and the weight adaptive law are updated to the execution network and the evaluation network, and the updated execution network and the evaluation network are used to update the optimal controller of the target device.

2. The method for adaptive collaborative optimal tracking control of sewage treatment based on dynamic event triggering according to claim 1 is characterized in that: A simplified kinetic model for dissolved oxygen and nitrate concentrations was constructed, including: An original kinetic model is established; the expression of the original kinetic model is: Among them, S O,4 (t) is the dissolved oxygen concentration in the fourth partition of the biochemical reaction tank; S O,5 (t) is the dissolved oxygen concentration in the fifth partition of the biochemical reaction tank; S NO,1 (t) is the nitrate nitrogen concentration in the first partition of the biochemical reaction tank; S NO,2 (t) is the nitrate nitrogen concentration in the second partition of the biochemical reaction tank; S NO,5 (t) is the nitrate nitrogen concentration in the fifth zone of the biochemical reaction tank; S O,S is the saturation value of dissolved oxygen concentration; K L a5(t) is the manipulated variable of dissolved oxygen concentration; Q r (t) is the manipulated variable of nitrate nitrogen concentration; μ(t) is the microbial respiration coefficient; ψ1(t) is the flow rate of the first partition of the biochemical reaction tank; ψ2(t) is the flow rate of the second partition of the biochemical reaction tank; ψ4(t) is the flow rate of the fourth partition of the biochemical reaction tank; ψ5(t) is the flow rate of the fifth partition of the biochemical reaction tank; X b,h (t) is the concentration of heterotrophic biomass; Y h is the heterotrophic biomass; V2 is the volume of the second partition of the biochemical reaction tank; V5 is the volume of the fifth partition of the biochemical reaction tank; a1 is the first constant; a2 is the second constant; Define a first unknown function and a second unknown function; the expression of the first unknown function is: Among them, D1(t) is the unknown dynamic information of the environment when tracking and controlling the dissolved oxygen concentration; The expression of the second unknown function is: Among them, D2(t) is the unknown dynamic information of the environment when tracking and controlling the nitrate nitrogen concentration; The original kinetic model is simplified using the first unknown function and the second unknown function to obtain the simplified kinetic model; the expression of the simplified kinetic model is: Where P1(t)=S O,S -S O,5 (t); P2(t) = S NO,5 (t) / V2; For S O,5 (t); P1(t) is the result of subtracting the current dissolved oxygen concentration from the dissolved oxygen saturation value; P2(t) is the result of dividing the current concentration of nitrate nitrogen by the volume of the second partition of the biochemical reaction tank.

3. The method for adaptive collaborative optimal tracking control of sewage treatment based on dynamic event triggering according to claim 2 is characterized in that: The Lyapunov function is constructed according to the simplified dynamic model, including: The dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error are set according to the simplified kinetic model; the expression of the dissolved oxygen concentration tracking error is: O (t) = S O,5 (t)-S O,set (t); where e O (t) is the dissolved oxygen concentration tracking error; S O,set (t) is the dissolved oxygen concentration set value; the expression of the nitrate nitrogen concentration tracking error is: e NO (t) = S NO,2 (t)-S NO,set (t); where e NO (t) is the nitrate nitrogen concentration tracking error; S NO,set (t) is the set value of nitrate nitrogen concentration; The Lyapunov function is constructed according to the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the Lyapunov function based on the error is: Among them, V z (t) is the Lyapunov function based on the error; e(t) is the tracking control error; T represents the transposition operation.

4. The method for adaptive collaborative optimal tracking control of sewage treatment based on dynamic event triggering according to claim 3 is characterized in that: According to the Lyapunov function, an optimal controller based on an execution network is constructed, including: Deriving the Lyapunov function to obtain a Lyapunov derivative function; Extract the unknown dynamic information part in the Lyapunov derivative function; the expression of the unknown dynamic information part is: Where D(t) = [D1(t), D2(t)] T ; D(t) is the matrix formed by vertically concatenating D1(t) and D2(t); The execution network is constructed according to the unknown part of the dynamic information; the expression of the execution network based on the fuzzy neural network is: in, is the optimal output weight of the execution network; U a (t) is the output of the normalization layer of the execution network; θ a (t) is the estimated error of the execution network; is the input of the execution network; is the center of the execution network; is the width of the execution network; m is the number of neurons in the input layer; l is the number of neurons in the RBF layer and the normalization layer.

5. The method for adaptive collaborative optimal tracking control of sewage treatment based on dynamic event triggering according to claim 4 is characterized in that: According to the Lyapunov function, an optimal controller based on an execution network is constructed, including: Construct an optimal controller; the expression of the optimal controller is: Among them, v * is the output of the optimal controller; ζ is the control coefficient vector; is the transpose of the optimal output weight; The actual controller is constructed according to the optimal controller; the expression of the actual controller is: Wherein, v(t) is the output of the actual controller; for The transpose of the current value of ; The actual controller is iteratively updated according to the updated execution network to obtain the updated optimal controller.

6. The method for adaptive collaborative optimal tracking control of sewage treatment based on dynamic event triggering according to claim 5 is characterized in that: Constructing a long-term loss function, and constructing an evaluation network of the fuzzy neural network according to the long-term loss function, including: An instantaneous loss function is constructed according to the dissolved oxygen concentration tracking error and the nitrate nitrogen concentration tracking error; the expression of the instantaneous loss function is: Wherein, R(t) is the output value of the instantaneous loss function; Integrate the instantaneous loss function to obtain the long-term loss function; the expression of the long-term loss function is: in, is the output value of the long-term loss function; ι is the integral variable; The evaluation network is constructed according to the long-term loss function; the expression of the evaluation network based on the fuzzy neural network is: in, is the optimal output weight of the evaluation network; U c (t) is the output of the normalization layer of the judgment network; θ c (t) is the estimated error of the judgment network; is the input of the judgment network; is the center of the judging network; is the width of the evaluation network.

7. The method for adaptive collaborative optimal tracking control of sewage treatment based on dynamic event triggering according to claim 6 is characterized in that: Constructing the weight adaptive law of the execution network and the evaluation network, including: Set the first estimated error of the evaluation network and the second estimated error of the execution network; the expression of the first estimated error is: Where η1(t) is the first estimation error; ξ is the discounted future cost; is the output function of the evaluation network; The expression of the second estimation error is: Wherein, η2(t) is the second estimation error; A first cost function of the evaluation network is constructed based on the first estimated error, and a second cost function of the execution network is constructed based on the second estimated error. The expression of the first cost function is: Among them, E c (t) is the first cost function; The expression of the second cost function is: Among them, E a (t) is the second cost function; The weight adaptive law of the execution network and the evaluation network is constructed according to the first cost function and the second cost function respectively; the expression of the weight adaptive law includes: in, for The transpose of the current value of β c is the first adaptive rate coefficient; for The current value of β a is the second adaptive rate coefficient; is the change value of the rule layer of the evaluation network.

8. The method for adaptive collaborative optimal tracking control of sewage treatment based on dynamic event triggering according to claim 7 is characterized in that: Setting a dynamic trigger threshold, and setting a dynamic event trigger mechanism according to the dynamic trigger threshold, including: Construct the dynamic trigger threshold; the expression of the dynamic trigger threshold includes: Wherein, τ1 is the first dynamic threshold; δ1 is the first positive definite parameter; λ is the Puschitz constant; τ2 is the second dynamic threshold; δ2 is the second positive definite parameter; A dynamic event triggering mechanism is set according to the dynamic triggering threshold; the expression of the dynamic event triggering mechanism is: in, For the first event; For the second event; is the tracking error based on event sampling; is the long-term cost function.

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