A flue gas oxygen content control method based on interval type-2 fuzzy width PID

Abstract

The application provides a flue gas oxygen content control method based on interval type-2 fuzzy-width PID, and relates to the technical field of solid waste incineration. The method comprises the following steps: obtaining a control variable, a disturbance variable and a flue gas oxygen content set value at a preset time; designing a double ET mechanism, inputting the control variable, the disturbance variable and the flue gas oxygen content set value at the preset time into a first controller and a second controller according to the double ET mechanism to obtain a first control variable increment and a second control variable increment, wherein the first controller is a complex controller based on IT2FBLS, and the second controller is a simple controller based on adaptive PID; determining an output control variable at the preset time according to the first control variable increment and the second control variable increment; and determining an actual output value of the flue gas oxygen content at the preset time according to the output control variable at the preset time. The application solves the problems of poor real-time performance, large calculation amount and resource consumption in the combustion state control of the municipal solid waste incineration (MSWI) process in the prior art.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of solid waste incineration, in particular to a flue gas oxygen content control method based on interval type-2 fuzzy width PID. BACKGROUND

[0002] MSW incineration (MSWI) has become the main way of MSW treatment due to its advantages of harmless, resource and reduction. Limited by the differences of MSW component fluctuation range, operation personnel operation ability and MSWI equipment operation and maintenance level, the automatic combustion control (ACC) technology developed by developed countries is not suitable for developing countries, which mainly use manual control mode, and it is difficult to maintain the stable operation of MSWI process for a long period of time, which is easy to cause pollution emission exceeding standard. Flue gas oxygen content is the characterization of peroxide air coefficient, which has a strict control range in the process. When the flue gas oxygen content is low, the incomplete combustion of MSW will lead to the increase of incomplete heat loss and the generation of toxic and harmful gases such as dioxin (DXN) and sulfur dioxide (SO2); when the flue gas oxygen content is too high, the increase of heat loss will lead to the reduction of incineration efficiency. Studies have shown that when the flue gas oxygen content at the outlet of the waste heat boiler is controlled at 6%-9%, MSW and flammable flue gas can be fully combusted.

[0003] Flue gas oxygen content can represent the combustion state of municipal solid waste incineration (MSWI) process to a certain extent, and its accurate control is crucial to ensure the efficient and stable operation of the system. The process control of MSWI has strong nonlinearity and complex uncertainty, and the traditional PID control and neural network control (NNC) have poor robustness. Fuzzy NNC has problems of poor real-time performance, large calculation amount and resource consumption, and cannot guarantee the running stability and rapid convergence to the set value at the initial control time. SUMMARY

[0004] In order to overcome the shortcomings of the prior art, the purpose of the present application is to provide a flue gas oxygen content control method based on interval type-2 fuzzy width PID, which solves the problems of poor real-time performance, large calculation amount and resource consumption in the combustion state control of municipal solid waste incineration (MSWI) process in the prior art.

[0005] To achieve the above purpose, the present application provides the following scheme:

[0006] A flue gas oxygen content control method based on interval type-2 fuzzy width PID, comprising:

[0007] obtaining a control variable, a disturbance variable and a flue gas oxygen content set value at a preset time;

[0008] A double ET mechanism is designed, and the control variable, the disturbance variable and the preset time oxygen content of flue gas set value are input into the first controller and the second controller according to the double ET mechanism, so as to obtain the first control variable increment and the second control variable increment, wherein the first controller is an IT2FBLS-based complex controller, and the second controller is a simple controller of adaptive PID.

[0009] The output control variable at the preset time is determined according to the first control variable increment and the second control variable increment.

[0010] The actual output value of the oxygen content of flue gas at the preset time is determined according to the output control variable at the preset time.

[0011] Preferably, the double ET mechanism comprises:

[0012] The first trigger condition and the second trigger condition are set;

[0013] If the first trigger condition is met, the parameters of the first controller are not updated;

[0014] If the second trigger condition is met, the first controller does not work;

[0015] The first trigger condition is:

[0016] δ2≤|e o (t)|≤δ1 and|e o (t)|≤|e o (t-1)|;

[0017] Wherein, δ2 represents a set threshold for triggering the condition of using only the second controller, δ1 represents a set threshold for not triggering the condition of not updating the parameters of the first controller, e o (t) represents the system error at time t;

[0018] The second trigger condition is:

[0019] |e o (t)|<δ2 and|e o (t)|≤|e o (t-1)|.

[0020] Preferably, the first controller comprises:

[0021] An IT2FNN layer and a data input layer, an enhancement layer and an output layer connected with the IT2FNN layer;

[0022] The enhancement layer is connected with the output layer;

[0023] The data input layer is used to transmit control variables, interference variables, preset time oxygen content set value of flue gas and e = [e1, e2] T o p T ; wherein, e represents the input of the data input layer, e o = e1 represents the system error, i.e. the difference between the expected value and the actual value, e p = e2 represents the proportional term incremental error, i.e. the difference between the current time error and the next time error, the IT2FNN layer is used to fuzz the input data to obtain a first output, the enhancement layer is used to perform nonlinear transformation on the first output to obtain a second output, and the output layer is used to linearly combine the first output and the second output to obtain a first control variable increment, wherein e o (t) = y r (t) - y(t), e p (t) = e o (t) - e o (t-1), wherein e p (t) represents the proportional term incremental error at time t, y r (t) represents the oxygen content set value of flue gas at time t, and the expression of the first control variable increment is:

[0024]

[0025] wherein w f (t) = [w f1 ,…, w fK ] T is the connection weight value between the IT2FNN layer output and the output layer, h = [h1, h2, …, h L ] T is the enhancement layer output vector, w e (t) = [w e1 ,…, w eL ] T is the connection weight value between the enhancement layer output and the output layer, wherein Δu1(t) represents the output of the IT2FBLS controller at time t, i.e. the first control variable increment, hl(t) is the output of the output layer at time t, i.e. the second output, z(t) is the first output, K is a natural number, w fk represents the connection weight value between the output of the kth IT2FNN subsystem and the output layer, and w el represents the connection weight value between the output of the lth enhancement node and the output layer, K is a natural number.

[0026] Preferably, the IT2FNN layer comprises:

[0027] ​​​K IT2FNN subsystems, wherein the IT2FNN subsystem comprises:

[0028] an antecedent network, a consequent network and a defuzzification algorithm network;

[0029] wherein the antecedent network is configured to fuzz the input by using uncertain Gaussian type interval type-2 membership functions, lower and upper bounds of the membership values of the input, and determine lower and upper bounds of the activation strength of each rule according to the lower and upper bounds of the membership values, the defuzzification algorithm network is configured to obtain lower and upper bounds of the output values of the subsystem by using BMM algorithm to defuzzify the lower and upper bounds of the activation strength of each rule, and the consequent network is configured to obtain a first output according to the lower and upper bounds of the output values of the subsystem, and expressions of the lower and upper bounds of the membership values are respectively:

[0030]

[0031] wherein e i is the i-th element of e, i = 1, 2; and respectively represent the lower and upper bounds of the membership values of the i-th input corresponding to the j-th fuzzy rule in the k-th IT2FNN subsystem, j = 1, …, J, and J represents the number of fuzzy rules of the IT2FNN subsystem; respectively represent the lower and upper bounds of the uncertain center of the j-th membership function corresponding to the i-th input; is the width of the j-th membership function corresponding to the i-th input;

[0032] expressions of the lower and upper bounds of the activation strength are respectively:

[0033]

[0034] wherein, and respectively represent the lower and upper bounds of the activation strength of the j-th fuzzy rule in the k-th IT2FNN subsystem;

[0035] expressions of the lower and upper bounds of the output values of the subsystem are respectively:

[0036]

[0037] z k and respectively represent the lower and upper bounds of the output of the k-th IT2FNN subsystem; is the consequent output weight of the j-th rule;

[0038] expression of the first output is:

[0039] z = [z 1 ,…,z K ].

[0040] Preferably, the expression of the second control variable increment is:

[0041] Δu2(t) = K p (t) * e p (t) + K i (t) * e o (t) + K d (t) * e d (t).

[0042] where Δu2(t) is the second control variable increment, K p , K i and K d are the proportional gain, integral time constant and derivative time constant respectively, and e d (t) represents the incremental error of the derivative term at time t.

[0043] Preferably, the expression of the output control variable at the preset time is:

[0044] u(t) = u(t-1) + Δu1(t) + Δu2(t).

[0045] Preferably, it further comprises:

[0046] setting an enhancement condition and a reduction condition;

[0047] if the enhancement condition is met, increasing the enhancement nodes of the enhancement layer;

[0048] if the reduction condition is met, reducing the enhancement nodes of the enhancement layer.

[0049] Preferably, the enhancement condition is:

[0050]

[0051] where G th is the judgment threshold of structure expansion, h L+1 = [h1, h2, …, h L , h L+1 ] T represents the output vector of the enhancement layer after structure expansion, and w e,L+1 = [w e1 , w e2 , …, w eL , w e(L+1) ] T represents the connection weight between the output of the enhancement layer after structure expansion and the output layer.

[0052] Preferably, the reduction condition is:

[0053]

[0054] wherein Rate_useless m Rate_useless d R m Rate_useless

[0055] The present application discloses the following technical effects:

[0056] The present application provides a flue gas oxygen content control method based on interval type 2 fuzzy width PID, comprising: obtaining a control variable, a disturbance variable and a flue gas oxygen content set value at a preset time; designing a double ET mechanism, inputting the control variable, the disturbance variable and the flue gas oxygen content set value at the preset time into a first controller and a second controller according to the double ET mechanism to obtain a first control variable increment and a second control variable increment, wherein the first controller is a complex controller based on IT2FBLS, and the second controller is a simple controller of adaptive PID; determining an output control variable at the preset time according to the first control variable increment and the second control variable increment; and determining a flue gas oxygen content actual output value at the preset time according to the output control variable at the preset time. The present application reduces the calculation amount and resource consumption while ensuring the control precision, and proposes a DET mechanism for the controller. The present application has strong stability, robustness and adaptability, and can accurately control the combustion state of the municipal solid waste incineration (MSWI) process. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0058] Figure 1 A flue gas oxygen content control method flow chart based on interval type 2 fuzzy width PID provided by the embodiment of the present application;

[0059] Figure 2 A flue gas oxygen content control method strategy schematic diagram based on interval type 2 fuzzy width PID provided by the embodiment of the present application;

[0060] Figure 3 A structure schematic diagram of IT2FBLS provided by the embodiment of the present application;

[0061] Figure 4 The constant set value tracking experiment curve schematic diagram of the experimental results provided for the embodiment of the present application is shown in the following table:

[0062] Figure 5 The constant set value tracking experiment error curve schematic diagram of the experimental results provided for the embodiment of the present application is shown in the following table:

[0063] Figure 6 The constant set value tracking experiment primary air volume increment curve schematic diagram of the experimental results provided for the embodiment of the present application is shown in the following table:

[0064] Figure 7 The constant set value tracking experiment primary air volume change curve schematic diagram of the experimental results provided for the embodiment of the present application is shown in the following table:

[0065] Figure 8 The constant set value tracking experiment enhanced node change curve schematic diagram of the experimental results provided for the embodiment of the present application is shown in the following table:

[0066] Figure 9 The constant set value tracking experiment Δu1 and Δu2 change curve schematic diagram of the experimental results provided for the embodiment of the present application is shown in the following table. DETAILED DESCRIPTION

[0067] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0068] In order to make the above objectives, characteristics and advantages of the present application more apparent, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0069] As shown in the following table, the present application provides a flue gas oxygen content control method based on interval type 2 fuzzy width PID, comprising: Figure 1

[0070] Step 100: obtaining a control variable, a disturbance variable and a flue gas oxygen content set value at a preset time;

[0071] Step 200: designing a double ET mechanism, inputting the control variable, the disturbance variable and the flue gas oxygen content set value at the preset time into a first controller and a second controller according to the double ET mechanism, obtaining a first control variable increment and a second control variable increment, wherein the first controller is a complex controller based on IT2FBLS, and the second controller is a simple controller of adaptive PID;

[0072] ​Step 300: determining the output control variable at the preset time according to the first control variable increment and the second control variable increment;

[0073] Step 400: determining the flue gas oxygen content actual output value at the preset time according to the output control variable at the preset time.

[0074] Specifically, the process flow of a typical grate furnace MSWI mainly includes six process stages of storage fermentation, solid waste combustion, waste heat exchange, steam power generation, flue gas treatment, and flue gas emission.

[0075] (1) Storage fermentation stage: the original MSW is continuously fermented in the solid waste storage pool for 3-7 days to improve the calorific value, and is put into the hopper by the grab bucket.

[0076] (2) Solid waste combustion stage: under the coupling action of solid-gas-liquid and thermal flow force, the fermented MSW is converted into high-temperature flue gas and solid residues, which can be divided into three sub-processes: drying, combustion, and afterburning.

[0077] ① Drying sub-process: surface moisture gradually evaporates as the temperature rises, and is completely evaporated when the temperature rises to 100℃; at the same time, internal moisture is gradually separated and absorbs a large amount of heat energy.

[0078] ② Combustion sub-process: from the ignition of MSW to strong light heating, and finally ending with oxidation reaction. From the perspective of chemical reaction mechanism, this sub-process involves strong oxidation, pyrolysis, and atomic group collision reaction. Among them, the strong oxidation reaction represents the complete combustion reaction of combustible components with oxygen; the pyrolysis reaction represents that under the condition of no oxygen or close to no oxygen, thermal radiation energy breaks the chemical bonds between carbon-containing polymer compounds or recombines them, and then the volatile matter is separated and oxidized; the atomic group collision reaction represents the transition of atomic group electron energy, molecular rotation and vibration, etc. to produce infrared thermal radiation, visible light and ultraviolet light, and then form the shape of flame. From the perspective of combustion position, it can be divided into solid-phase combustion on the grate and gas-phase combustion in the hearth. It can be seen that this sub-process is closely related to the oxygen content.

[0079] ③ Afterburning sub-process: the residual combustible components after combustion are mainly composed of coke. Under high temperature conditions, coke reacts with O2 in the primary air, and reacts with CO2, water vapor, etc. Further, inert substances gradually accumulate until MSW is all converted into ash, and then the combustion is weakened until it completely stops. Prolonging the afterburning sub-process can effectively improve the loss on ignition of MSW and improve the level of reduction.

[0080] (3) Residual heat exchange stage: First, the high-temperature flue gas is initially cooled by the water-cooled wall. Second, the heat energy is transferred to the boiler by radiation and convection using superheater, evaporator and economizer, etc. Then, in the boiler, water is converted into high-pressure superheated steam, which enters the steam power generation stage. Finally, the flue gas temperature at the boiler outlet drops rapidly to 200°C.

[0081] (4) Steam power generation stage: The high-temperature steam generated by the waste heat boiler drives the steam turbine generator, which can convert mechanical energy into electrical energy.

[0082] (5) Flue gas treatment stage: First, the selective non-catalytic reduction (SNCR) system removes NOx in the temperature range of 850°C to 1100°C. Second, the semi-dry deacidification process is used to neutralize the acid gases, including HCl, HF, SO2 and heavy metals, by injecting lime and water. Then, activated carbon is used to adsorb DXN and heavy metals present in the flue gas. Finally, the particulate matter, neutralization reaction products and activated carbon adsorbents in the flue gas are removed by a bag filter, thus completing the purification process.

[0083] (6) Flue gas emission stage: The flue gas that meets the national emission standard (GB18485-2014) is drawn by the induced draft fan and discharged into the atmosphere through the chimney.

[0084] As can be seen from the above, in the combustion sub-process, the combustible components undergo a strong oxidation reaction with oxygen; in the afterburning sub-process, the coke undergoes an oxidation reaction with oxygen under the action of high temperature and primary air; generally, the oxygen content of the flue gas at the outlet of the waste heat boiler is taken as the key controlled variable of the MSWI process. Only by controlling the oxygen content of the flue gas within the process set range, it is possible to make the solid-phase MSW on the grate and the combustible flue gas in the furnace burn fully, thereby ensuring that the flue gas emission meets the standard. Therefore, accurate control of the oxygen content of the flue gas is of great significance to the stable operation of the combustion process.

[0085] The five key variables related to the oxygen content of the flue gas are the primary air volume, the secondary air volume, the feeder uniform speed, the drying grate uniform speed and the ammonia water injection volume. Except for the ammonia water injection volume, the PCC absolute value of the secondary air volume and the primary air volume with the oxygen content of the flue gas is large, considering the actual MSWI process, the primary air volume is selected as the manipulated variable, and the remaining key variables are selected as the disturbance variables.

[0086] Further, BLS is an important research field of machine learning, the original input is transferred and placed in the feature node as "mapping feature", the structure is expanded in width in the form of "enhanced node", BLS consists of four main parts: input, feature neuron, enhanced neuron and output four main parts, which can be represented as:

[0087] Y(t) = [Z(t) | H(t)] W(t) (1)

[0088] wherein Z(t) and H(t) represent outputs of the feature neuron and the enhancement neuron respectively, and W(t) represents a connection weight value of the feature neuron and the enhancement neuron to the output neuron.

[0089] Further, as shown in Figure 2 , the functions of the modules are as follows: (1) IT2FBLS-PID control module: used for constructing the IT2FBLS complex controller and the adaptive PID simple controller; (2) DET mechanism module: used for reducing the update and use frequency of the IT2FBLS complex controller, so as to reduce the calculation amount and resource consumption; (3) structure self-organizing module: used for adjusting the structure of the IT2FBLS controller when the condition is met.

[0090] Further, as shown in Figure 3 , the first controller comprises:

[0091] an IT2FNN layer, a data input layer, an enhancement layer and an output layer which are all connected with the IT2FNN layer;

[0092] the enhancement layer is connected with the output layer;

[0093] the data input layer is used for transmitting a control variable, a disturbance variable, a flue gas oxygen content set value at a preset time and e = [e1, e2] T = [e o ,e p ] T ; wherein e represents an input of the data input layer, e o = e1 represents a system error, i.e. a difference between an expected value and an actual value, and e p = e2 represents a proportional term incremental error, i.e. a difference between an error at a current time and an error at a next time, the IT2FNN layer is used for fuzzifying the input data to obtain a first output, the enhancement layer is used for performing a nonlinear transformation on the first output to obtain a second output, and the output layer is used for performing a linear combination on the first output and the second output to obtain a first control variable increment, wherein e o (t) = y r (t) - y(t), e p (t) = e o (t) - e o (t-1), wherein e p (t) represents a proportional term incremental error at a time t, y r (t) represents a flue gas oxygen content set value at the time t,

[0094] Further, the IT2FNN layer comprises:

[0095] K IT2FNN subsystems, wherein the IT2FNN subsystems comprise:

[0096] an antecedent network, a consequent network and a defuzzification algorithm network;

[0097] wherein the antecedent network is configured to fuzz the input by using an uncertain Gaussian type interval type-2 membership function, lower and upper bounds of a membership value of the input, and determine lower and upper bounds of an activation strength of each rule according to the lower and upper bounds of the membership value, the defuzzification algorithm network is configured to obtain lower and upper bounds of an output value of the subsystem by using a BMM algorithm to defuzz the lower and upper bounds of the activation strength of each rule, and the consequent network is configured to obtain a first output according to the lower and upper bounds of the output value of the subsystem.

[0098] (1) Data input layer: for information transmission, receiving input e = [e1, e2] T o p T , e o = e1 represents a system error, i.e. a difference between an expected value and an actual value; e p = e2 represents a proportional term incremental error, i.e. a difference between an error at a current time and an error at a next time; this representation is used for subsequent formula expression and derivation. e o and e p are calculated as follows:

[0099] e o (t) = y r (t) - y(t) (2)

[0100] e p (t) = e o (t) - e o (t-1) (3)

[0101] (2) IT2FNN layer: the layer comprises K IT2FNN subsystems. Each IT2FNN subsystem is composed of an antecedent network, a consequent network and a defuzzification algorithm.

[0102] The antecedent network mainly fuzzes the input by using an uncertain Gaussian type interval type-2 membership function, as follows:

[0103]

[0104] wherein e i is an i-th element of e, i = 1, 2; and ​​​respectively represent the lower bound and upper bound of the membership value of the ith input corresponding to the jth fuzzy rule in the kth IT2FNN subsystem; j = 1, …, J, J represents the number of fuzzy rules of the IT2FNN subsystem; respectively represent the lower bound and upper bound of the uncertainty center of the jth membership function corresponding to the ith input; is the width of the jth membership function corresponding to the ith input.

[0105] Then, the lower bound and upper bound of the activation strength of each rule are calculated as follows:

[0106]

[0107] where, and respectively represent the lower bound and upper bound of the activation strength of the jth fuzzy rule in the kth IT2FNN subsystem.

[0108] The lower bound and upper bound of the output value of the subsystem are obtained by using the Begian-melek-mendel (BMM) algorithm reduction, as follows:

[0109]

[0110] where, z k and respectively represent the lower bound and upper bound of the output of the kth IT2FNN subsystem; is the consequent output weight of the jth rule, which is obtained by the consequent network, and its calculation is as follows:

[0111]

[0112] where, represents the jth rule of the jth input corresponding to the consequent connection weight.

[0113] Further, the output of the kth subsystem is obtained as follows:

[0114]

[0115] Finally, the output of the IT2FNN layer is obtained by K subsystems as follows:

[0116] z = [z 1 ,…, z K ](11)

[0117] (3) Enhancement layer: the output of the IT2FNN layer is nonlinearly transformed, and the output of the lth enhancement node is calculated as follows:

[0118] h l = tanh(zwl +β l (12)

[0119] Among them, w l =[w 1l ,…,w Kl ] T β represents the connection weight between the IT2FNN layer and the l-th augmentation node. l The bias term coefficients between the IT2FNN layer and the l-th enhancement node are given.

[0120] (4) Output layer: The outputs of the IT2FNN layer and the enhancement layer are linearly combined to obtain the final output Δu1(t), as follows:

[0121]

[0122] Among them, w f (t)=[w f1 ,…,w fK ] T The connection weights between the output and output layers of the IT2FNN layer are given by h = [h1, h2, ..., h]. L ] T To enhance the output vector of the layer, w e (t)=[w e1 ,…,w eL ] T To enhance the connection weights between the output layer and the output layer, Δu1(t) represents the output of the IT2FBLS controller at time t, i.e., the increment of the first control variable, where K is a natural number. fk w represents the connection weight between the output of the k-th IT2FNN subsystem and the output layer. el h represents the connection weight between the output of the l-th augmentation node and the output layer. l z(t) is the output of the l-th augmentation node at time t (second output), z(t) is the output of the IT2FNN layer at time t (first output), and K is a natural number.

[0123] Parameter w f and w e The initial values ​​are obtained using the ridge regression approximation algorithm, as follows:

[0124]

[0125] in, I is the identity matrix, and λ is the regularization coefficient. This is a matrix consisting of the actual output values ​​of all samples.

[0126] Furthermore, the input of the gradient descent-based adaptive incremental PID controller is... eo and e p The calculation of e d is shown in equation (2) (3), e d The calculation is as follows:

[0127] e o (t) = e o (t-1) + e o (t-2) (15)

[0128] Further, the output value Δu2(t) of the adaptive PID controller can be obtained as follows:

[0129] Δu2(t) = K p (t) * e p (t) + K i (t) * e o (t) + K d (t) * e d (t) (16)

[0130] where Δu2(t) is the second control variable increment, K p , K i and K d are the proportional gain, integral time constant and derivative time constant respectively, and e d (t) represents the differential term increment error at time t.

[0131] The parameter update process based on gradient descent is as follows:

[0132] First, define the performance function as shown in equation (15).

[0133] Then, calculate the gradient of the performance function with respect to each parameter as follows:

[0134]

[0135]

[0136] where, is approximated as follows:

[0137]

[0138] According to equation (31), consider starting to update the parameters at t≥2.

[0139] Finally, update the parameters based on gradient descent as follows:

[0140]

[0141] where η p , η iand η d respectively represent K p , K i and K d three parameters learning rate.

[0142] Parallel controller manipulated variable increment includes the output of IT2FBLS controller and the output of PID controller, as follows:

[0143] Δu(t) = Δu1(t) + Δu2(t) (24)

[0144] Further, the manipulated variable is obtained as follows:

[0145] u(t) = u(t-1) + Δu1(t) + Δu2(t) (25)

[0146] Further, the dual ET mechanism includes:

[0147] Set the first trigger condition and the second trigger condition;

[0148] If the first trigger condition is met, the parameters of the first controller are not updated;

[0149] If the second trigger condition is met, the first controller does not work;

[0150] The IT2FBLS controller can quickly reduce the system error, and its complex structure can improve the steady-state performance of the control system to some extent. However, as a complex controller, it has large computational load, high computational complexity, and large resource consumption of the computer. Therefore, this paper combines the event-driven idea and introduces the DET mechanism, aiming to reduce the update frequency and usage times of the IT2FBLS complex controller while ensuring control accuracy, thereby reducing computational complexity and resource consumption.

[0151] First, set the trigger condition as follows:

[0152] δ2≤|e o (t)|≤δ1 and|e o (t)|≤|e o (t-1)| (26)

[0153] δ2 represents the set threshold for triggering the "only use adaptive PID simple controller" condition, and δ1 represents the set threshold for not triggering the "IT2FBLS parameter does not update" condition.

[0154] When the trigger condition is met, the parameters of IT2FBLS are not updated, that is:

[0155] Δu1(t) = Δu1(t-1) (27)

[0156] Then, the trigger condition is set as follows:

[0157] |e o (t)|≤δ2 and|e o (t)|≤|e o (t-1)| (28)

[0158] When the trigger condition is satisfied, only the adaptive PID simple controller is used, and the IT2FBLS complex controller is no longer used, i.e.

[0159] Δu1(t)=0 (29)

[0160] Further, it also includes:

[0161] Set the enhancement condition and the reduction condition;

[0162] If the enhancement condition is satisfied, the enhancement node of the enhancement layer is increased;

[0163] If the reduction condition is satisfied, the enhancement node of the enhancement layer is reduced.

[0164] Specifically, taking t time as an example, the system error e o As a judgment index of structure expansion, when the following rules are satisfied, an enhancement node is added:

[0165]

[0166] Wherein, G th is the judgment threshold of structure expansion, h L+1 =[h1,h2,…,h L ,h L+1 ] T represents the output vector of the enhancement layer after structure expansion, w e,L+1 =[w e1 ,w e2 ,…,w eL ,w e(L+1) ] T represents the connection weight between the output of the enhancement layer after structure expansion and the output layer, and the calculation of h L+1 (t+1) is as follows:

[0167] h L+1 (t)=tanh(z(t)w L+1 (t)+β L+1 (t)) (31)

[0168] Wherein, w L+1 represents the connection weight between the IT2FNN layer and the enhancement node added by structure expansion, and β L+1Bias term coefficient between IT2 FNN layer and the added enhanced node of structure expansion.

[0169] The initial value of each parameter is set as follows for the added enhanced node:

[0170]

[0171] Where rand(a, b) function generates an array of a x b size composed of random numbers uniformly distributed between 0 and 1, a and b have no actual meaning.

[0172] Take the reduction of the mth enhanced node at the tth moment as an example.

[0173] This paper uses the useless rate as the judgment index of structure reduction, and the useless rate is calculated as follows:

[0174]

[0175] Where Rate_useless m represents the useless rate of the mth enhanced node, T d is the judgment period of structure reduction, R m represents the number of times the mth enhanced node is marked as useless, which is calculated as follows:

[0176]

[0177] Where R m is defined as 0, R th is the judgment threshold of the enhanced node being marked as having an important role.

[0178] The specific rules of structure reduction are as follows:

[0179]

[0180] Where D th is the judgment threshold of structure reduction, h L-1 represents the output vector of the enhanced layer after structure reduction, w e,L-1 represents the connection weight between the enhanced layer output after structure reduction and the output layer.

[0181] Finally, in order to avoid the impact of structure reduction on the network and ensure the stability of the network output, further compensation is made to the network parameters. Assuming that the Euclidean distance between the nth enhanced node and the deleted mth enhanced node is the smallest, the parameters are compensated as follows:

[0182]

[0183] Where, ​denotes the connection weight between the IT2 FNN layer and the reduced structure enhanced layer, is the bias term coefficient between the IT2 FNN layer and the reduced structure enhanced layer, denotes the connection weight between the reduced structure of the first enhanced node and the output layer.

[0184] Further, the experimental demonstration corresponding to the current scheme of the embodiment is as follows:

[0185] In this experiment, the control performance is analyzed by using the integral of squared error (ISE), the integral of absolute error (IAE) and the maximum deviation of set value (Devmax) control indicators. The calculation is as follows:

[0186]

[0187] Dev max = max{|e o (t)|} (70)

[0188] Wherein, ISE is the integral of squared error, IAE is the integral of absolute error, and Devmax is the maximum deviation of set value.

[0189] In this embodiment, the operation data of a certain MSWI plant in Beijing from 8:00 to 24:00 on a certain day is selected. The preprocessed data set consists of 857 samples, including 4 disturbance variables (secondary air volume, feeder uniform speed, drying grate uniform speed, ammonia injection volume), 1 manipulated variable (primary air volume) and 1 controlled variable (flue gas oxygen content). The flue gas oxygen content model is constructed based on the main supplement set integration strategy based on BO.

[0190] In this experiment, the parallel control based on IT2FBLS-PID is used to control the flue gas oxygen content of the actual MSWI plant, and two experiments of constant reference value (6.8) and variable set reference value (6.4-7.05) of flue gas oxygen content are designed to evaluate the control performance, wherein a 60dbw Gaussian white noise is applied as a disturbance variable during the experiment.

[0191] Table 1 is the hyperparameter table based on IT2FBLS-PID control, and Table 1 is as follows:

[0192] Table 1 Hyperparameters based on IT2FBLS-PID control

[0193]

[0194] Wherein, in this paper, η = η e = η f = η l = η βTo further illustrate the performance of the controller proposed in this paper, PID control, IT2FBLS control, TSFNN-PID control, IT2FBLS-PID control (without ET) and IT2FBLS-PID control (single ET) are set as comparative experiments, and the comparative experiment parameters are set as follows: PID control: K p = 0.6, K i = 0.2, K d = 0.02; IT2FBLS control: η = 0.2, G th = 0.005, R th = 0.0005, D th = 0.6; TSFNN-PID control: K p = 0.7, K i = 0.5, K d = 0.001, η c = 0.01, η b = 0.01, η a = 0.2, wherein, η c , η b and η a represent the learning rate of the center, width and consequent coefficient of TSFNN respectively; IT2FBLS-PID control (without ET) has the same super parameter settings as this paper except that there are no super parameters δ1 and δ2; IT2FBLS-PID control (single ET): δ = 0.002 in constant set value experiment and δ = 0.01 in variable set value experiment, and the rest of the parameters are the same as this paper.

[0195] The reference value of flue gas oxygen content is set to 6.8, and the constant set reference value tracking control experiment is carried out, and the iteration number is set to 1000. The experimental results are shown in Figures 4-8 .

[0196] According to Figures 4-8 , the controller proposed in this paper can effectively control the flue gas oxygen content, and can quickly respond to the change of primary air volume in the control process. At the same time, when facing disturbance, the control error of the controller is always within a small range (±0.22) fluctuation, which reflects that the controller has strong stability and robustness.

[0197] In the constant set value tracking experiment, the comparison of performance indicators of different controllers is shown in Table 2, and Table 2 is a comparison table of performance indicators of constant set value tracking experiment, and Table 2 is as follows:

[0198] Table 2 Comparison table of performance indicators of constant set value tracking experiment

[0199]

[0200] From Table 2, it can be seen that the ISE, IAE and Devmax of the controller proposed in this paper are smaller than those of the PID control and the TSFNN-PID control, i.e. the performances are better, which proves the effectiveness of the IT2FBLS controller submodule in this paper; by comparison with the IT2FBLS control, the ISE, IAE and Devmax of the controller proposed in this paper are smaller, which proves the effectiveness of the adaptive PID controller submodule in this paper; in addition, the controller proposed in this paper is compared with the IT2FBLS-PID control (without ET) and the IT2FBLS-PID control (single ET), and the comparison results show that the DET not only improves the control performance, but also effectively reduces the update and use frequency of the IT2FBLS controller, thereby reducing the calculation amount and computer resource consumption. At the same time, by comparison with the IT2FBLS-PID control (without ET), the experimental time is also shortened, which occupies a certain advantage in time performance, and it is proved that the use of the DET mechanism module plays an important role in the performance improvement of the control system.

[0201] During the constant set value tracking experiment, the change curves of Δu1 and Δu2 are as shown in Figure 9

[0202] According to Figure 9 it can be seen that during the constant set value tracking experiment, formula (27) and (29) are satisfied at many places as T increases, which shows that the introduction of the error-based DET mechanism can greatly reduce the update and use frequency of the IT2FBLS to achieve the purpose of reducing the calculation amount and resource consumption.

[0203] Each of the embodiments in the specification is described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same or similar parts between the embodiments can be referred to each other.

[0204] The principles and implementation manners of the present application are described by using 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 manner and application range will be changed. In conclusion, the content of the specification should not be understood as a limitation of the present application.​

Claims

1. A flue gas oxygen content control method based on interval type-2 fuzzy width PID, characterized in that, The method comprises the following steps: obtaining a control variable, a disturbance variable and a preset time point of a flue gas oxygen content set value; designing a double ET mechanism, inputting the control variable, the disturbance variable and the preset time point of the flue gas oxygen content set value into a first controller and a second controller according to the double ET mechanism, obtaining a first control variable increment and a second control variable increment, wherein the first controller is a complex controller based on an IT2FBLS, and the second controller is a simple controller based on an adaptive PID; determining an output control variable at a preset time point according to the first control variable increment and the second control variable increment; determining an actual output value of the flue gas oxygen content at the preset time point according to the output control variable at the preset time point; the double ET mechanism comprises the following steps: setting a first trigger condition and a second trigger condition; if the first trigger condition is met, the parameters of the first controller are not updated; if the second trigger condition is met, the first controller does not work; wherein the first trigger condition is: ； wherein, represents a set threshold for triggering the second controller only condition, represents a set threshold for the parameter not updating condition of not triggering the first controller, represents time system error; the second trigger condition is: ； the first controller comprises the following steps: an IT2FNN layer and a data input layer, an enhancement layer and an output layer connected with the IT2FNN layer; the enhancement layer is connected with the output layer; The data input layer is used for transmitting control variables, interference variables, preset time flue gas oxygen content set values and their transmission is performed, wherein, represents the input of the data input layer, represents the system error, i.e. the difference between the expected value and the actual value, represents the proportional term incremental error, i.e. the difference between the current time error and the next time error; the IT2FNN layer is used for fuzzy processing of the input data to obtain a first output, the enhancement layer is used for nonlinear transformation of the first output to obtain a second output, and the output layer is used for linear combination of the first output and the second output to obtain a first control variable increment, wherein the , wherein, represents the proportional term incremental error at the current time, represents the flue gas oxygen content set value at the current time, and the expression of the first control variable increment is: ； in, The connection weights between the output and output layers of the IT2FNN layer. To enhance the output vector of the layer, To enhance the connection weights between the output layer and the output layer, where, express The output of the IT2FBLS controller at time step, i.e., the increment of the first control variable, Indicates the first The connection weights between the output and output layer of each IT2FNN subsystem Indicates the first The connection weights between the output of each enhancement node and the output layer. For time t, the first The output of each enhancement node, z(t) is The output of the IT2FNN layer at time k, where K is a natural number.

2. The flue gas oxygen content control method based on interval type-2 fuzzy width PID according to claim 1, characterized in that, the IT2FNN layer comprises the following steps: K IT2FNN subsystems, wherein the IT2FNN subsystem comprises the following steps: an antecedent network, a consequent network and a defuzzification algorithm network; wherein the antecedent network is used to fuzz the input by an uncertain Gaussian type interval type-2 membership function, the lower bound and the upper bound of the membership value of the input, the lower bound and the upper bound of the activation strength of each rule are determined according to the lower bound and the upper bound of the membership value, the defuzzification algorithm network is used to obtain the lower bound and the upper bound of the output value of the subsystem by adopting a BMM algorithm to reduce the lower bound and the upper bound of the activation strength of each rule, the consequent network is used to obtain a first output according to the lower bound and the upper bound of the output value of the subsystem, and the expressions of the lower bound and the upper bound of the membership value are respectively: ； Among them, for The One element, ; and They represent the first The IT2FNN subsystem of the first The input corresponds to the first The lower and upper bounds of the membership degree values ​​of a fuzzy rule; , This represents the number of fuzzy rules in the IT2FNN subsystem; They represent the first The input corresponds to the first Lower and upper bounds of the uncertainty centers of membership functions; For the first The input corresponds to the first The width of each membership function; the expressions of the lower bound and the upper bound of the activation strength are respectively: ； ； wherein, and respectively represent the lower bound and the upper bound of the activation strength of the th fuzzy rule in the th IT2FNN subsystem. the expressions of the lower bound and the upper bound of the output value of the subsystem are respectively: ； ； and denote the lower and upper bounds of the output of the th IT2FNN subsystem, respectively; is the consequent output weight of the th rule. the expression of the first output is: 。 3. The flue gas oxygen content control method based on interval type-2 fuzzy width PID according to claim 2, characterized in that, the expression of the second control variable increment is: ； wherein, is a second control variable increment, , and are a proportional gain, an integral time constant, and a derivative time constant, respectively, denotes a differential term increment error at the instant 4. The flue gas oxygen content control method based on interval type-2 fuzzy width PID according to claim 3, characterized in that, the expression of the output control variable at the preset time point is: 。 5. The flue gas oxygen content control method based on interval type-2 fuzzy width PID according to claim 3, characterized in that, the method further comprises the following steps: setting an enhancement condition and a reduction condition; if the enhancement condition is met, the enhancement layer is increased by an enhancement node; if the reduction condition is met, the enhancement layer is reduced by an enhancement node.

6. The flue gas oxygen content control method based on interval type-2 fuzzy width PID according to claim 5, characterized in that, the enhancement condition is: ； wherein is a threshold for the structure expansion, denotes the output vector of the enhancement layer after structure expansion, denotes the connection weight between the enhancement layer output after structure expansion and the output layer.

7. The flue gas oxygen content control method based on interval type-2 fuzzy width PID according to claim 5, characterized in that, the reduction condition is: ； wherein, represents the number of times the enhancement node is marked as useless, is the judgment period of structure reduction, represents the number of times the enhancement node is marked as useless.

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