Anti-interference control method for pemfc air management system considering dead-time effect

Abstract

The application provides a kind of PEMFC air management system anti-interference control method considering dead zone effect, and relates to fuel cell technical field.Firstly, according to the mathematical model of PEMFC air management system, single-input single-output PEMFC nonlinear system is obtained;Based on the mechanism of dead zone effect, the input voltage dead zone model of air compressor is established, and then the state space model of PEMFC air management system is established;Based on the state space model, controllable standard PEMFC nonlinear system is obtained;Then, a tracking differentiator is designed to estimate the system output and its derivative variable;Then, a single neural network is used to approximate the lumped uncertainty in the system;Design a neural network hybrid adaptive learning rate to speed up the convergence of the neural network, realize the rapid and stable control of air flow;Considering the composite disturbance composed of dead zone and external disturbance, a nonlinear disturbance observer is constructed to estimate the composite disturbance, and the anti-interference control of PEMFC air management system is realized.

Description

Technical Field

[0001] This invention relates to the field of fuel cell technology, and in particular to an anti-interference control method for a PEMFC air management system that takes into account the dead zone effect. Background Technology

[0002] With the emergence of energy shortages and global warming, PEMFCs have seen rapid development due to their advantages such as low operating temperature, high power, and fast response. To maintain maximum net output power, airflow in the PEMFC air management system needs to be regulated. However, when the fuel cell system is affected by disturbances, insufficient airflow to the stack cathode can easily occur, damaging the fuel cell and shortening its lifespan. Therefore, reasonable anti-interference control methods can reduce the impact of external disturbances on the fuel cell and improve system durability.

[0003] In terms of anti-interference control of fuel cell systems, the paper "Observer-based adaptive neural network control for PEMFC air-feed subsystem" (Yunlong Wang, Yongfu Wang, Jing Zhao and Jianfeng Xu, Applied Soft Computing, Vol. 113, 2021) uses a tracking error observer to reconstruct unknown variables, and then uses a neural network and an interference observer to compensate for uncertainties and external disturbances in the PEMFC air management system.

[0004] While the above control methods achieve stable control of the PEMFC air management system under external disturbances, the reconstruction process of unknown variables is complex, requiring more computational resources and reducing the effectiveness of disturbance compensation. On the other hand, these anti-interference control methods only compensate for external disturbances caused by load current, neglecting the dead-zone effect of the control input. Furthermore, using multiple radial basis function neural networks to approximate system uncertainties online also increases the computational load. Therefore, the controller designed above fails to achieve good anti-interference control performance when the control input has a dead-zone effect and the gas flow rate changes rapidly. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the shortcomings of the prior art by providing an anti-interference control method for a PEMFC air management system that considers the dead zone effect. This method takes into account the dead zone effect of the control input and designs a tracking differentiator, an adaptive neural network, and an interference observer to achieve stable airflow control, thereby solving the technical problem of insufficient practicality of existing PEMFC air systems.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by this invention is as follows: An anti-interference control method for a PEMFC air management system considering the dead-zone effect is proposed. Based on the mathematical model of the PEMFC air management system, a single-input, single-output PEMFC nonlinear system is obtained. Based on the dead-zone effect mechanism, a dead-zone model of the air compressor input voltage is established. Based on the dead-zone model and the PEMFC nonlinear system, a state-space model of the PEMFC air management system is established. Based on the state-space model, a controllable standard PEMFC nonlinear system is obtained through coordinate transformation. Based on the controllable standard PEMFC nonlinear system, a tracking differentiator is designed to estimate the system output and its derivative variables. Considering the lumped uncertainty in the system, a single neural network is used to approximate the lumped uncertainty, reducing the complexity of the controller design and facilitating engineering implementation. By introducing the modeling error of the identification model and the tracking error of the system output, a hybrid adaptive learning rate of the neural network is designed to accelerate the convergence speed of the neural network, achieving rapid and stable control of airflow. Considering the composite interference composed of the dead zone and external disturbances, a nonlinear disturbance observer is constructed to estimate the composite disturbance, thereby realizing anti-interference control of the PEMFC air management system.

[0007] Specifically, the following steps are included:

[0008] Step 1: Construct a controllable standard PEMFC nonlinear system;

[0009] The mathematical model of the PEMFC air management system is established as shown in the following formula:

[0010]

[0011] Where, p ca p represents the cathode pressure of the fuel cell. sm ω represents the pressure in the supply pipeline. cp The angular velocity of the air compressor is represented by μ1 to μ4 and c1 to c8, which represent the system parameters of the PEMFC air management system, respectively. st Represents the load current, h(ω) cp ,p sm () represents airflow rate, and u represents the air compressor input voltage;

[0012] The output of the PEMFC air management system is as follows:

[0013]

[0014] Where y represents the oxygen ratio of the PEMFC air management system. This indicates the airflow rate in the fuel cell stack. Indicates the pipe pressure, c9 and c 10 This indicates the system parameters of the PEMFC air management system;

[0015] Therefore, the PEMFC air management system can be represented as a single-input single-output affine nonlinear system in the following form:

[0016]

[0017] Where x = [x1, x2, x3] T =[p ca ,ω cp ,p sm ] T The state variables of the system are represented by f(x), g(x), and d, which are known terms obtained from the PEMFC air management system mathematical model (1).

[0018] By using coordinate transformation, the affine nonlinear system 3) is transformed into the following controllable canonical nonlinear system:

[0019]

[0020] Where z1 and z2 represent the output and derivative of the PEMFC air management system, respectively, α(x), β(x), and γ(x, I) st ) are complex expressions for f(x), g(x), and d, respectively;

[0021] Since there is a dead zone voltage in the input voltage of the air compressor, based on the dead zone effect mechanism, the dead zone mechanism model of the air compressor input voltage is established as shown in the following formula:

[0022]

[0023] Wherein, λ, b r b l U represents an unknown constant. v Indicates the controller input variables;

[0024] Combining systems (4)-(5), the state-space model of the PEMFC air management system considering the dead-zone effect is expressed as:

[0025]

[0026] Where, β new (x)=λβ(x), Represented as:

[0027]

[0028] Step 2: Based on the controllable standard PEMFC nonlinear system, design a tracking differentiator to estimate the system output and derivative variables of the PEMFC air management system;

[0029] The design of the tracking differentiator is as follows:

[0030]

[0031] Where R>0, a i >0, b i >0 represents the design parameters of the tracking differentiator, i = 1, 2, 3; π0, π1, π2 are the state variables of the tracking differentiator, representing the system state variables z1, z2, respectively. Estimate Right now

[0032] Step 3: Design a composite neural network based on a tracking differentiator to approximate the system uncertainty;

[0033] For the unknown function β in the state-space model of the PEMFC air management system new (x) is approximated using a neural network, as shown in the following formula:

[0034]

[0035] in, For the unknown function β new The estimated value of (x), It is an estimate of the optimal weight vector of the neural network, θ a (x) represents the basis function vector of the neural network;

[0036] Define modeling errors ζ1 and ζ2:

[0037]

[0038] in, It is obtained from the following identification model:

[0039]

[0040] Where ζ = [ζ1, ζ2] T To model the error vector, k F To identify the gain coefficient vector of the model, This is the output value of the interference observer;

[0041] Estimation of the optimal weight vector of a neural network The update law is designed as follows:

[0042]

[0043] Where σ1 is the neural network learning rate, B = [0,1], P and P F All are positive definite symmetric matrices. To estimate the tracking error, ym The desired superoxide ratio;

[0044] Step 4: Design an interference observer to estimate and compensate for actuator dead zones and external system interference;

[0045] Design an interference observer:

[0046]

[0047] Where, k s The gain coefficient of the interference observer. The following formula can be used to calculate:

[0048]

[0049] Among them, A F Design the coefficient matrix;

[0050] Step 5: Design the controller input variables;

[0051] Design the following controller input variables:

[0052]

[0053] Where k is the gain coefficient vector of the controller;

[0054] Step 6: Substitute the obtained tracking differentiator (8), the estimated value of the optimal weight vector of the neural network (12), the disturbance observer (13) and the controller input variable (15) into the state space model (6) of the PEMFC air management system to perform tracking control of the air flow of the PEMFC air management system.

[0055] The beneficial effects of adopting the above technical solution are as follows: The anti-interference control method of PEMFC air management system considering dead zone effect provided by the present invention (1) converts the affine nonlinear PEMFC air management system form into a controllable standard system form, and at the same time models the dead zone mechanism of the air compressor input voltage, thereby obtaining the lumped uncertainty expression of the system, which is convenient for handling uncertainty, input voltage dead zone and external interference.

[0056] (2) For the PEMFC air management system with unmeasurable variables, the tracking differentiator is used to realize the effective estimation of unmeasurable variables, which reduces the complexity of the control system, reduces the impact of noise, and improves the performance of the system.

[0057] (3) Considering system uncertainty, input voltage dead zone and external interference, construct a single neural network and a nonlinear interference observer. In the design of the neural network adaptive learning rate, introduce modeling error and tracking error to achieve fast and stable control of air flow.

[0058] In summary, the method of this invention considers the dead-time effect of the input voltage and incorporates it as a system uncertainty factor in the controller design process, thereby improving the robustness of the PEMFC air management system. By designing a tracking differentiator to estimate unmeasurable system variables, the impact of noise is reduced without increasing system cost, simplifying controller design and reducing the complexity of the control system. By introducing modeling error and tracking error, a neural network composite adaptive learning law is designed to achieve effective estimation of unknown uncertainties. An interference observer is designed to estimate and compensate for the input voltage dead-time and external interference, improving the system's anti-interference capability. Attached Figure Description

[0059] Figure 1 A flowchart of an anti-interference control method for a PEMFC air management system considering dead-zone effect provided in an embodiment of the present invention;

[0060] Figure 2 A control comparison diagram of different anti-interference control methods provided in the embodiments of the present invention. Detailed Implementation

[0061] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0062] In this embodiment, the anti-interference control method of the PEMFC air management system considering the dead zone effect is as follows: Figure 1 As shown, it includes the following steps:

[0063] Step 1: Establish the mathematical model of the PEMFC air management system:

[0064]

[0065] Where, p ca p represents the cathode pressure of the fuel cell. sm ω represents the pressure in the supply pipeline. cp The angular velocity of the air compressor is represented by μ1 to μ4 and c1 to c8, which represent the system parameters of the PEMFC air management system, respectively. st Represents the load current, h(ω) cp ,p sm () represents airflow rate, and u represents the air compressor input voltage;

[0066] In this embodiment, the selected parameters for the PEMFC air management system are: μ1 = 36.16, μ2 = 31.69, μ3 = 18953, μ4 = 289.72, c1 = 5.59, c2 = 7483.6, c3 = 101325, c4 = 0.2857, c5 = 365.7, and c6 = 4.27 × 10⁻⁶.6 c7 = 1.25, c8 = 3.62 × 10 -6 ;

[0067] The output of the PEMFC air management system is as follows:

[0068]

[0069] Where y represents the oxygen ratio of the PEMFC air management system. This indicates the airflow rate in the fuel cell stack. Indicates the pipe pressure, c9 and c 10 This indicates the system parameters of the PEMFC air management system;

[0070] In this embodiment, the parameters selected for the PEMFC air management system are c9 = 7.25 × 10⁻⁶. -7 and c 10 =3.15×10 -5 ;

[0071] The PEMFC air management system can be represented as a single-input, single-output affine nonlinear system as follows:

[0072]

[0073] Where x = [x1, x2, x3] T =[p ca ,ω cp ,p sm ] T The state variables of the system are represented by f(x), g(x), and d, which are known terms obtained from the PEMFC air management system mathematical model (1).

[0074] By using coordinate transformation, the affine nonlinear system (3) is transformed into the following controllable canonical nonlinear system:

[0075]

[0076] Where z1 and z2 represent the output and derivative of the PEMFC air management system, respectively, α(x), β(x), and γ(x, I) st ) are complex expressions for f(x), g(x), and d, respectively;

[0077] Since there is a dead zone voltage in the input voltage of the air compressor, a dead zone mechanism model for the air compressor input voltage is established based on the dead zone effect mechanism:

[0078]

[0079] Wherein, λ, b r b lU represents an unknown constant. v Indicates the controller input variables;

[0080] The state-space model of the PEMFC air management system considering the dead-zone effect is expressed as follows:

[0081]

[0082] Where, β new (x)=λβ(x), Represented as:

[0083]

[0084] Step 2: Design a tracking differentiator to estimate the output and derivative variables of the PEMFC air management system:

[0085]

[0086] Where R>0, a i >0, b i >0 represents the design parameters of the tracking differentiator, i = 1, 2, 3; π0, π1, π2 are the state variables of the tracking differentiator, representing the system state variables z1, z2, respectively. Estimate Right now

[0087] In this embodiment, the tracking differentiator parameters R = 40, a1 = 4, a2 = 5, a3 = 4, b1 = 4, b5 = 4, b3 = 4 are selected as the tracking differentiator design parameters, and the expression sig(·) is:

[0088] Step 3: Design a composite neural network based on a tracking differentiator to approximate the system uncertainty;

[0089] For the unknown function β in the PEMFC air management system model new (x), approximated using a neural network:

[0090]

[0091] in, For the unknown function β new The estimated value of (x), It is an estimate of the optimal weight vector of the neural network, θ a (x) represents the basis function vector of the neural network;

[0092] In this embodiment, a single-hidden-layer radial basis function neural network is selected, with 5 hidden layer nodes. The i-th vector of the basis function is selected as... Where c a,i =[0,0.25,0.5,0.75,1] T and σ a,i =0.5 represents the center value vector and standard deviation of the Gaussian function.

[0093] Define modeling errors ζ1 and ζ2:

[0094]

[0095] in, It is obtained from the following identification model:

[0096]

[0097] Where ζ = [ζ1, ζ2] T To model the error vector, k F To identify the gain coefficient vector of the model, This is the output value of the interference observer;

[0098] In this embodiment, the gain coefficient vector of the identification model is selected as k. F =[1,2] T ;

[0099] Estimation of the optimal weight vector of a neural network The update law is designed as follows:

[0100]

[0101] Where σ1 is the neural network learning rate, B = [0,1], P and P F All are positive definite symmetric matrices. To estimate the tracking error, y m The desired superoxide ratio;

[0102] In this embodiment, the neural network learning rate is selected as σ1 = 100, and the positive definite symmetric matrix is... The desired superoxide ratio is y m =2;

[0103] Step 4: Design the following interference observer:

[0104]

[0105] Where, k s For the gain coefficient of the interference observer, this embodiment selects the interference observer gain coefficient k. s =10, The following formula can be used to calculate:

[0106]

[0107] Among them, A F Design the coefficient matrix;

[0108] This embodiment selects the design coefficient matrix.

[0109] Step 5: Design the following controller input variables:

[0110]

[0111] Where k is the gain coefficient vector of the controller;

[0112] In this embodiment, the gain coefficient vector of the controller is selected as k = [1,2]. T ;

[0113] Step 6: Substitute the obtained tracking differentiator (8), the estimated value of the optimal weight vector of the neural network (12), the disturbance observer (13) and the controller input variable (15) into the state space model (6) of the PEMFC air management system to perform tracking control of the air flow of the PEMFC air management system.

[0114] This embodiment also compares the control method of the present invention with the control method of a classic PID controller through simulation, and the simulation results of the control effect comparison are as follows: Figure 2 As shown in the simulation diagram comparing the control effects, it can be seen that, under external disturbances, the method of this invention, compared with the control effect of the classic PID controller, can ensure that the excess oxygen ratio quickly and stably converges to the ideal excess oxygen ratio. The results demonstrate that the method of this invention has a good anti-interference effect against dead zone effect and external disturbances.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. An anti-interference control method for a PEMFC air management system considering dead-zone effect, characterized in that: Based on the mathematical model of the PEMFC air management system, a single-input single-output PEMFC nonlinear system is obtained; Based on the dead zone effect mechanism, a dead zone model of the air compressor input voltage is established; based on the dead zone model and the PEMFC nonlinear system, a state-space model of the PEMFC air management system is established. Based on the state-space model, a controllable canonical PEMFC nonlinear system is obtained by coordinate transformation. Based on the controllable canonical PEMFC nonlinear system, a tracking differentiator is designed to estimate the system output and its derivative variables. Considering the lumped uncertainty in the system, a single neural network is used to approximate the lumped uncertainty in the system, reducing the complexity of the controller design. By introducing the modeling error of the identification model and the tracking error of the system output, a hybrid adaptive learning rate of the neural network is designed to accelerate the convergence speed of the neural network and achieve rapid and stable control of air flow. Considering the composite interference composed of dead zone and external interference, a nonlinear interference observer is constructed to estimate the composite interference and realize the anti-interference control of the PEMFC air management system. The method includes the following steps: Step 1: Construct a controllable standard PEMFC nonlinear system; The mathematical model of the PEMFC air management system is established as shown in the following formula: (1)； in, Indicates the cathode pressure of the fuel cell. Indicates the pressure of the supply pipeline. Indicates the angular velocity of the air compressor. and ~ These represent the system parameters of the PEMFC air management system. Indicates the load current. Indicates airflow. Indicates the input voltage of the air compressor; The output of the PEMFC air management system is as follows: (2)； in, This indicates the oxygen ratio in the PEMFC air management system. This indicates the airflow rate in the fuel cell stack. Indicates the pressure in the pipeline. and This indicates the system parameters of the PEMFC air management system; Therefore, the PEMFC air management system can be represented as a single-input single-output affine nonlinear system in the following form: (3)； in, Represents the system's state variables. , , These are known terms obtained from the PEMFC air management system mathematical model (1); By using coordinate transformation, the affine nonlinear system (3) is transformed into the following controllable canonical nonlinear system: (4)； in, , Let represent the output and derivative of the PEMFC air management system, respectively. , , They are respectively about , , Complex expressions; Since there is a dead zone voltage in the input voltage of the air compressor, based on the dead zone effect mechanism, the dead zone mechanism model of the air compressor input voltage is established as shown in the following formula: (5)； in, , , Represents an unknown constant. Indicates the controller input variables; Combining systems (4)-(5), the state-space model of the PEMFC air management system considering the dead-zone effect is expressed as: (6)； in, , , Represented as: (7)； Step 2: Based on the controllable standard PEMFC nonlinear system, design a tracking differentiator to estimate the system output and derivative variables of the PEMFC air management system; Step 3: Design a composite neural network based on a tracking differentiator to approximate the system uncertainty; Step 4: Design an interference observer to estimate and compensate for actuator dead zones and external system interference; Step 5: Design the controller input variables; Step 6: Substitute the obtained tracking differentiator, the estimated value of the optimal weight vector of the neural network, the input variables of the disturbance observer and the controller into the state space model of the PEMFC air management system to perform tracking control of the air flow of the PEMFC air management system.

2. The anti-interference control method for PEMFC air management system considering dead zone effect according to claim 1, characterized in that: The tracking differentiator designed in step 3 is as follows: (8)； in, , , To track the design parameters of the differentiator, ; These are the state variables of the tracking differentiator, representing the state variables of the system respectively. Estimate , , ,Right now .

3. The anti-interference control method for PEMFC air management system considering dead zone effect according to claim 2, characterized in that: Step 3 involves addressing the unknown functions in the state-space model of the PEMFC air management system. The approximation is achieved using a neural network, as shown in the following formula: (9)； in, For unknown functions The estimated value, It is an estimate of the optimal weight vector of the neural network. The basis function vectors of the neural network; Define modeling error , : (10)； in, , It is obtained from the following identification model: (11)； in, To model the error vector, To identify the gain coefficient vector of the model, This is the output value of the interference observer; Estimation of the optimal weight vector of a neural network The update law is designed as follows: (12)； in, For the neural network learning rate, , and All are positive definite symmetric matrices. To estimate the tracking error, This represents the desired superoxide ratio.

4. The anti-interference control method for PEMFC air management system considering dead zone effect according to claim 3, characterized in that: The interference observer designed in step 4 is shown in the following formula: (13)； in, The gain coefficient of the interference observer. The following formula can be used to calculate: (14)； in, To design the coefficient matrix.

5. The anti-interference control method for PEMFC air management system considering dead zone effect according to claim 4, characterized in that: Step 5 involves designing the following controller input variables: (15)； in, This is the gain coefficient vector of the controller.

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