Air flow control method for fuel cell system

Abstract

The invention relates to the technical field of fuel cell air system control, in particular to an air flow control method for a fuel cell system. The method comprises the following steps: firstly, analyzing the structure and working principle of a fuel cell flow supply subsystem, and establishing a mathematical model of a centrifugal air compressor model, an air supply pipeline and an exhaust pipeline according to energy conversion, a mass conservation law and air thermodynamic characteristics; establishing a fourth-order nonlinear equation of the fuel cell air system according to the mathematical model; secondly, establishing a feedback linearization controller according to the fourth-order nonlinear equation, converting a nonlinear model into a linear model, and designing an extended state observer to observe unknown environmental disturbance to obtain an observation value; and finally, establishing a super-torsion nonsingular terminal sliding mode control law according to the linear model, and substituting the observed value into the super-torsion nonsingular terminal sliding mode control law to realize tracking control of the cathode pressure and the peroxide ratio.

Description

Technical Field

[0001] The present invention relates to the technical field of fuel cell air system control, and in particular to an air flow control method for a fuel cell system. Background Art

[0002] With the rapid development of new energy vehicles, fuel cells have attracted widespread attention as an efficient and environmentally friendly energy conversion technology. In particular, proton exchange membrane fuel cells are considered to be one of the important technologies for the development of new energy vehicles due to their high power density, high energy conversion efficiency, low temperature start-up capability and environmental friendliness. In the fuel cell system, the air supply system is one of the key auxiliary subsystems, and its energy consumption accounts for 20% to 30% of the output power, which has a vital impact on the performance and efficiency of the entire fuel cell system.

[0003] The air system has obvious strong nonlinearity, strong coupling and uncertainty characteristics, which make it complicated to accurately control it under variable load conditions. If the air flow is not adjusted properly, it may cause oxygen starvation inside the fuel cell stack, reduce working efficiency and shorten service life; and improper air pressure adjustment may cause air compressor surge, blockage and other problems. Therefore, achieving accurate control of air flow is crucial to ensure stable and efficient operation of the fuel cell system.

[0004] In the prior art, the control strategies for fuel cell air systems mainly focus on the application of linear controllers, such as using feedforward, dynamic feedforward and PI feedback control schemes to adjust the oxygen ratio. However, these methods have limitations in dealing with nonlinear and strong coupling problems, especially when they deviate far from the operating point, the control effect will be significantly reduced. In addition, the single oxygen ratio parameter control cannot fully meet the system's dual requirements for cathode flow and pressure.

[0005] In recent years, although some studies have begun to focus on the coupling of air flow and pressure and have tried to improve system performance through decoupling control, these methods still face problems such as model mismatch and environmental disturbance in practical applications. Therefore, developing an air flow control method that can effectively handle nonlinearity, strong coupling, and has good robustness is of great significance for improving the overall performance of the fuel cell system. In view of the above problems, the present invention proposes an air flow control method for a fuel cell system, which aims to improve the efficiency and service life of the fuel cell system by accurately controlling the air flow. Summary of the invention

[0006] The present invention provides an air flow control method for a fuel cell system, which is used to solve the above technical problems. First, the structure and working principle of the fuel cell flow supply subsystem are analyzed, and according to the energy conversion, mass conservation law and air thermodynamic characteristics, a centrifugal air compressor model and a mathematical model of the air supply and exhaust pipelines are established, and the fourth-order nonlinear equation of the fuel cell air system is established according to the mathematical model; secondly, according to the fourth-order nonlinear equation, a feedback linearization controller is designed to convert the nonlinear model into a linear model, and an extended state observer is designed to observe the unknown environmental disturbance to obtain the observed value; finally, a super-torsion non-singular terminal sliding mode control law is designed according to the linear model, and the observed value is substituted into the super-torsion non-singular terminal sliding mode control law to achieve accurate tracking control of the cathode pressure and the oxygen ratio, so that the fuel cell system can more efficiently utilize air resources during operation, reduce energy loss, improve energy conversion efficiency, and at the same time improve the efficiency and service life of the fuel cell system.

[0007] An air flow control method for a fuel cell system comprises the following steps:

[0008] S1. Analyze the structure and working principle of the fuel cell flow supply subsystem, establish a centrifugal air compressor model, a mathematical model of the air supply pipeline and the exhaust pipeline according to energy conversion, the law of conservation of mass and the thermodynamic characteristics of air, and establish the fourth-order nonlinear equation of the fuel cell air system according to the mathematical model;

[0009] S2. According to the fourth-order nonlinear equation, a feedback linearization controller is established to convert the nonlinear model into a linear model, and an extended state observer is designed to observe the unknown environmental disturbance to obtain an observation value;

[0010] S3. Establish a super-twist non-singular terminal sliding mode control law according to the linear model, and substitute the observed value into the super-twist non-singular terminal sliding mode control law to obtain a non-singular terminal sliding mode anti-interference control law.

[0011] Furthermore, a mathematical model of the centrifugal air compressor is established according to the law of energy conversion, and the specific formula is:

[0012]

[0013] Among them, ω cp represents the rotation speed of the centrifugal air compressor rotor, t is the time constant, Indicates ω cp The first-order differential of cm is the torque output by the motor, τ cp The torque required to drive the compressor;

[0014] Among them, τcm and τ cp The formula is:

[0015]

[0016] Among them, η cm is the motor mechanical efficiency, k t is the motor torque constant, R cm is the internal resistance of the motor armature, k v is the back electromotive force constant of the motor, V cm is the motor voltage; C p is the specific heat capacity of air, T atm is the atmospheric temperature, η cp is the air compressor efficiency, p sm is the supply manifold pressure, p atm is the atmospheric pressure, γ is the air specific heat coefficient, W cp is the mass flow rate;

[0017] Among them, W cp The formula is:

[0018] W cp =p1ω cp 2 p sm +p2ω cp 2 +p3ω cp p sm 2 +p4ω cp p sm +p5ω cp +p6p sm 2 +p7p sm +p8;

[0019] Among them, p1, p2, ... p8 are fitting parameters.

[0020] Furthermore, according to the law of conservation of mass and the thermodynamic characteristics of gas, a mathematical model of the gas supply pipeline and the gas exhaust pipeline is established, and the specific formula is:

[0021]

[0022]

[0023] Among them, p sm is the air pressure in the air supply pipeline, γ is the air specific heat coefficient, R a is the air gas constant, V sm is the volume of the gas supply pipeline, T sm is the gas temperature in the gas supply pipeline, W cp is the mass flow rate, Tcp,out is the air compressor outlet gas temperature, W sm,out is the outlet flow of the intake pipe; p rm is the exhaust pipe pressure, T rm is the gas temperature in the exhaust duct, V rm is the exhaust duct volume, W rm,out is the exhaust pipe outlet flow rate, W ca,out is the cathode outlet air flow rate; is the peroxygen ratio, The oxygen flow rate supplied to the cathode, is the actual required oxygen flow;

[0024] Among them, T cp,out and W rm,out Respectively expressed as:

[0025]

[0026] Among them, T atm is the atmospheric temperature, η is is the electrochemical conversion efficiency, p atm is the atmospheric pressure; θ is the opening of the back pressure valve in the exhaust pipe, C d is the back pressure valve flow coefficient, A T is the back pressure valve area, p ca is the cathode pressure, R is the ideal gas constant, T st is the cathode temperature of the battery stack.

[0027] Furthermore, a fourth-order nonlinear equation of the fuel cell air system is established according to the mathematical model, and the specific formula is:

[0028]

[0029] Among them, x and y are state variables, is the first-order differential of x, u1 and u2 are the control inputs, h1(x) and h2(x) are the output variables, and x, u1, u2, h1(x) and h2(x) are expressed as follows:

[0030] x=[ω cp p sm p ca p rm ] T ;

[0031] y1=V cm ;

[0032]

[0033] h1(x)=p ca ;

[0034]

[0035] Among them, ω cp Indicates the rotation speed of the centrifugal air compressor rotor, p sm is the air supply pipeline pressure, p ca is the cathode pressure, p rm V is the air pressure of the exhaust pipe; cm is the motor voltage; θ is the opening of the back pressure valve in the exhaust pipe; is the peroxygen ratio; g1(x), g2(x) and f(x) are intermediate variables, and the formula is:

[0036] g1(x)=[c1 0 0 0] T ;

[0037] g2(x)=[0 0 0c 16 x4] T ;

[0038]

[0039] Among them, x1, x2, x3 and x4 are intermediate variables, expressed as x1 = ω cp , x2=p sm , x3=p ca , x4=p rm , c i (i=1,...16) is the air system model constant, i is a subscript, and the specific formula of the air system model constant is:

[0040]

[0041] c4=p atm ;

[0042]

[0043] c7=-K sm,out ;

[0044]

[0045]

[0046] Among them, J cp is the air compressor rotation inertia; K sm,out is the inlet and outlet flow coefficient; is the oxygen gas constant, is the nitrogen gas constant, is the state of oxygen in the atmosphere, n is the number of cells in the battery stack, F is the Faraday constant, V cais the volume of the cathode of the battery stack; K ca,out is the cathode outlet flow coefficient, k is the average molar constant; p sat is the saturation pressure.

[0047] Furthermore, according to the fourth-order nonlinear equation, the feedback linearization controller is designed, and the acquisition process of the feedback linearization controller is:

[0048] Design a new virtual input v as:

[0049] v=[v1 v2] T ;

[0050] Wherein, v is a virtual control input vector, v1 is a virtual control input vector for cathode pressure, and v2 is a virtual control input vector for the excess oxygen ratio;

[0051] The feedback control variable can be obtained as:

[0052]

[0053] Among them, u1 and u2 are the actual control input vectors, A(x) is the system state matrix, and b(x) is the intermediate variable, which is expressed as:

[0054]

[0055] Among them, L f h1(x),L f h2(x) is the Lie derivative along the vector directions g1(x) and g2(x);

[0056] The coordinate transformation is defined as:

[0057]

[0058] Among them, j=1,2 is the intermediate variable, and To accurately feedback the linearized state variables;

[0059] The feedback linearization controller is obtained by using the pole placement method:

[0060]

[0061] Among them, v j is a virtual input, j=1, 2 are intermediate variables, and the virtual inputs v1 and v2 respectively control the cathode pressure p ca and the peroxygen ratio c 11 、c 12 、c 21 and c 22are the feedback linearization controller parameters, is the desired cathode pressure, is the desired peroxygen ratio.

[0062] Furthermore, according to the feedback linearization controller, the nonlinear model is converted into the linear model, and the acquisition process of the linear model is:

[0063] According to the feedback linearization controller, appropriate coordinate transformation and feedback are performed to obtain the linear model:

[0064]

[0065] in, They are The first-order differential of j is a virtual input, j=1,2 is an intermediate variable, and the virtual inputs v1 and v2 respectively control the cathode pressure p ca and the peroxygen ratio y is the output variable.

[0066] Furthermore, according to the linear model, the extended state observer is established to observe the unknown environmental disturbance, and the acquisition process of the extended state observer is:

[0067] Introducing unknown environmental disturbances into the linear model, the formula is:

[0068]

[0069] Among them, d j The unknown environmental disturbance;

[0070] The extended state observer is:

[0071]

[0072] Among them, j=1,2 is the intermediate variable, System Status The estimated value of System Status The estimated value of is the unknown environmental disturbance d j The estimated value of They are The first-order differential of are the parameters of the extended state observer.

[0073] Furthermore, according to the linear model and the extended state observer, the super-torsion non-singular terminal sliding mode control law is established, and the acquisition process of the super-torsion non-singular terminal sliding mode control law is:

[0074] Tracking error is defined as:

[0075]

[0076] in, is the tracking error, are the desired cathode pressure and the excess oxygen ratio, respectively, and satisfy in for The first-order derivative of ; the designed sliding surface is:

[0077]

[0078] Among them, s j is the sliding surface, λ j , γ j is the sliding surface coefficient, s j , j and γ j is a positive constant, and the super-torsion non-singular terminal sliding mode control law is established as:

[0079]

[0080]

[0081] Among them, sign(*) is the saturation function, L 1j and L 2j is the control law parameter, L 1j >0,L 2j >0, substituting the observed value into the super-torsion non-singular terminal sliding mode control law to achieve tracking control of the cathode pressure and the excess oxygen ratio.

[0082] Compared with the prior art, the present invention has the following beneficial effects:

[0083] 1. The present invention adopts feedback linearization technology to transform the inherent nonlinear characteristics of the fuel cell air system into an easy-to-handle linear system, significantly reducing the impact of nonlinearity on control accuracy. Compared with traditional linear controllers, this method exhibits superior control performance and ensures stable operation of the system under various working conditions, thereby improving the efficiency and service life of the fuel cell system.

[0084] 2. The present invention introduces an extended state observer to monitor the external disturbances and internal uncertainties in the system in real time. The extended state observer can compensate for the interference factors in the system in a timely manner through accurate observation of the disturbances, thereby enhancing the anti-disturbance ability of the system. In complex environments and variable working conditions, the fuel cell system can maintain efficient and stable operation, thereby improving the efficiency and service life of the fuel cell system.

[0085] 3. By adopting the super-torque non-singular sliding mode control strategy, the present invention avoids the chattering problem in traditional sliding mode control while ensuring the system control accuracy. This method improves the accuracy of air flow regulation and significantly improves the response speed of the system, so that the fuel cell system can quickly adjust the air supply under different working conditions, ensuring that the dual requirements of excess oxygen ratio, air flow and pressure are met, thereby improving the overall performance and service life of the fuel cell system. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 It is a schematic diagram of the process of the present invention;

[0087] Figure 2 It is a schematic diagram of the structure of the fuel cell flow supply subsystem provided by the present invention;

[0088] Figure 3 It is a system control block diagram provided by the present invention. DETAILED DESCRIPTION

[0089] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0090] Commonly used fuel cell systems generate electricity and a large amount of waste heat through the electrochemical reaction of the fuel cell stack. If the air flow cannot be effectively controlled, it will lead to a decrease in the combustion efficiency of the fuel cell and thermal management problems, thereby affecting the overall performance and life of the battery. In the prior art, although flow sensors and regulating valves are used for air flow control, their control accuracy and response speed are still insufficient when dealing with dynamic loads and complex environmental changes. In order to improve the accuracy and response speed of air flow control in fuel cell systems, the present invention proposes an air flow control method for fuel cell systems. In order to verify the effectiveness of the present invention, it will be described in detail through the following two specific embodiments.

[0091] Embodiment 1

[0092] In the present application example, an air flow control method for a fuel cell system is adopted; the specific implementation process is as follows Figure 1As shown, first, the structure and working principle of the fuel cell flow supply subsystem are analyzed, and according to the energy conversion, mass conservation law and air thermodynamic characteristics, the centrifugal air compressor model and the mathematical model of the air supply and exhaust pipelines are established, and the fourth-order nonlinear equation of the fuel cell air system is established according to the mathematical model; secondly, according to the fourth-order nonlinear equation, a feedback linearization controller is designed to convert the nonlinear model into a linear model, and an extended state observer is designed to observe the unknown environmental disturbance to obtain the observed value; finally, a super-torsion non-singular terminal sliding mode control law is designed according to the linear model, and the observed value is substituted into the super-torsion non-singular terminal sliding mode control law to achieve accurate tracking control of the cathode pressure and the oxygen ratio. The purpose of this embodiment is to develop an adaptive control strategy that can automatically adjust the control parameters according to the real-time working condition changes to achieve a better control effect. At the same time, the air flow is controlled more accurately to adapt to the rapidly changing working condition requirements, reduce energy waste, and improve the system's adaptability to unknown disturbances. This method effectively improves the air flow control performance, robustness and energy efficiency of the fuel cell system.

[0093] The fuel cell flow supply subsystem consists of two parts: the hydrogen system and the air system. The structure of the fuel cell flow supply subsystem is as follows: Figure 2 As shown in the figure, the system drives the air compressor from the motor, compresses the air and enters the intercooler for cooling, and then passes through the membrane humidifier to adjust the humidity. The compressed air enters the fuel cell stack through the ventilation inlet, and the hydrogen enters the stack through the electronic throttle adjustment from the hydrogen bottle on the right. Inside the stack, the oxygen in the air reacts electrochemically with the hydrogen to generate electricity. After the reaction, the air is discharged through the cathode outlet, and the air pressure is adjusted by the back pressure valve after passing the mixing point to ensure the balance of air flow and pressure inside the system, and finally discharged from the system through the ventilation outlet.

[0094] Furthermore, the parameters are selected as follows: R a =286.9J·(kg·K) -1 , V sm =0.02m 3 , T rm =353K, C d =0.0124, R=8.3145J·(mol·K) -1 , T st =353K, A T =0.002m 2 ; Among them, R a is the air gas constant, V sm is the volume of the intake pipe, T rm is the exhaust pipe temperature, C d is the throttle coefficient, R is the ideal gas constant, T st is the cathode temperature of the battery stack, AT is the throttle area; the expected cathode pressure and excess oxygen ratio are set to be the optimal working cathode pressure and excess oxygen ratio, namely Expected excess oxygen ratio

[0095] The mathematical model of the centrifugal air compressor is established according to the law of energy conversion, and the specific formula is:

[0096]

[0097] Among them, ω cp represents the rotation speed of the centrifugal air compressor rotor, t is the time constant, Indicates ω cp The first-order differential of cm is the torque output by the motor, τ cp The torque required to drive the compressor;

[0098] Among them, τ cm and τ cp The formula is:

[0099]

[0100]

[0101] Among them, η cm is the motor mechanical efficiency, k t is the motor torque constant, R cm is the internal resistance of the motor armature, k v is the back electromotive force constant of the motor, V cm is the motor voltage; C p is the specific heat capacity of air, T atm is the atmospheric temperature, η cp is the air compressor efficiency, p sm is the supply manifold pressure, p atm is the atmospheric pressure, γ is the air specific heat coefficient, W cp is the mass flow rate;

[0102] Among them, W cp The formula is:

[0103] W cp =p1ω cp 2 p sm +p2ω cp 2 +p3ω cp p sm 2 +p4ω cp p sm +p5ω cp+p6p sm 2 +p7p sm +p8;

[0104] Among them, p1, p2, ... p8 are fitting parameters.

[0105] In the embodiments of the present application, the structure and working principle of the fuel cell flow supply subsystem are analyzed, and a mathematical model of the centrifugal air compressor is established based on energy conversion, thereby achieving precise control of the air compressor speed and torque, improving the control accuracy and efficiency of the system, and ensuring efficient energy transfer and precise regulation of air supply, avoiding over-regulation and energy loss, and significantly improving the performance of the fuel cell system.

[0106] Furthermore, according to the law of conservation of mass and the thermodynamic characteristics of gas, a mathematical model of the gas supply pipeline and the gas exhaust pipeline is established, and the specific formula is:

[0107]

[0108] Among them, p sm is the air pressure in the air supply pipeline, γ is the air specific heat coefficient, R a is the air gas constant, V sm is the volume of the gas supply pipeline, T sm is the gas temperature in the gas supply pipeline, W cp is the mass flow rate, T cp,out is the air compressor outlet gas temperature, W sm,out is the outlet flow of the intake pipe; p rm is the exhaust pipe pressure, T rm is the gas temperature in the exhaust duct, V rm is the exhaust duct volume, W rm,out is the exhaust pipe outlet flow rate, W ca,out is the cathode outlet air flow rate; is the peroxygen ratio, The oxygen flow rate supplied to the cathode, is the actual required oxygen flow rate; where T cp,out and W rm,out Respectively expressed as:

[0109]

[0110]

[0111] Among them, T atm is the atmospheric temperature, η is is the electrochemical conversion efficiency, p atm is the atmospheric pressure; θ is the opening of the back pressure valve in the exhaust pipe, C d is the back pressure valve flow coefficient, AT is the back pressure valve area, p ca is the cathode pressure, R is the ideal gas constant, T st is the cathode temperature of the battery stack.

[0112] In the embodiments of the present application, the thermodynamic characteristics of air in the air supply and exhaust ducts are further analyzed, and a mathematical model of the air supply and exhaust ducts is established based on the law of conservation of mass. The model comprehensively considers parameters such as the air gas constant, duct volume and temperature to ensure that the cathode oxygen ratio is always maintained within the optimal range, effectively preventing the occurrence of oxygen starvation. At the same time, the response speed and stability of the air system are further improved, thereby significantly improving the overall operating efficiency and service life of the fuel cell system.

[0113] Furthermore, a fourth-order nonlinear equation of the fuel cell air system is established according to the mathematical model, and the specific formula is:

[0114]

[0115] Among them, x and y are state variables, is the first-order differential of x, u1 and u2 are the control inputs, h1(x) and h2(x) are the output variables, and x, u1, u2, h1(x) and h2(x) are expressed as follows:

[0116] x=[ω cp p sm p ca p rm ] T ;

[0117] u1=V cm ;

[0118]

[0119] h1(x)=p ca =200;

[0120]

[0121] Among them, ω cp Indicates the rotation speed of the centrifugal air compressor rotor, p sm is the air supply pipeline pressure, p ca is the cathode pressure, p rm V is the air pressure of the exhaust pipe; cm is the motor voltage; θ is the opening of the back pressure valve in the exhaust pipe; is the peroxygen ratio; g1(x), g2(x) and f(x) are intermediate variables, and the formula is:

[0122] g1(x)=[c1 0 0 0] T ;

[0123] g2(x)=[0 0 0c 16 x4] T ;

[0124]

[0125] Among them, x1, x2, x3 and x4 are intermediate variables, expressed as x1 = ω cp , x2=p sm , x3=p ca , x4=p rm , c i (i=1,...16) is the air system model constant, i is a subscript, and the specific formula of the air system model constant is:

[0126]

[0127] c4=p atm =101325;

[0128]

[0129] c7=-K sm,out =-3.629×10 -6 ;

[0130]

[0131]

[0132] Among them, J cp K is the air compressor rotation inertia; sm,out is the inlet and outlet flow coefficient; is the oxygen gas constant, is the nitrogen gas constant, is the state of oxygen in the atmosphere, n is the number of cells in the battery stack, F is the Faraday constant, V ca is the volume of the cathode of the battery stack; K ca,out is the cathode outlet flow coefficient, k is the average molar constant; p sat is the saturation pressure.

[0133] In the embodiment of the present application, a nonlinear control system is established to meet the needs of controlling the cathode pressure and excess oxygen ratio of the fuel cell. By reasonably selecting the control input and output, the air supply and exhaust process are optimized to ensure the precise regulation of the cathode excess oxygen ratio. This nonlinear model can not only handle the strong coupling and nonlinear problems in the air system, but also improve the robustness and response speed of the system, thereby improving the overall efficiency and stability of the fuel cell system and extending the service life of the system.

[0134] Furthermore, according to the fourth-order nonlinear equation, the feedback linearization controller is designed, and the acquisition process of the feedback linearization controller is:

[0135] Design a new virtual input v as:

[0136] v=[v1 v2] T ;

[0137] Wherein, v is a virtual control input vector, v1 is a virtual control input vector for cathode pressure, and v2 is a virtual control input vector for the excess oxygen ratio;

[0138] The feedback control variable can be obtained as:

[0139]

[0140] Among them, u1 and u2 are the actual control input vectors, A(x) is the system state matrix, and b(x) is the intermediate variable, which is expressed as:

[0141]

[0142] Among them, L f h1(x),L f h2(x) is the Lie derivative along the vector directions g1(x) and g2(x);

[0143] The coordinate transformation is defined as:

[0144]

[0145] Among them, j=1,2 is the intermediate variable, and To accurately feedback the linearized state variables;

[0146] The feedback linearization controller is obtained by using the pole placement method:

[0147]

[0148] Among them, v j is a virtual input, j=1, 2 are intermediate variables, and the virtual inputs v1 and v2 respectively control the cathode pressure pca and the peroxygen ratio c 11 、c 12 、c 21 and c 22 are the feedback linearization controller parameters, is the desired cathode pressure, is the desired peroxygen ratio.

[0149] In the embodiment of the present application, the nonlinear characteristics in the air system are converted into a linear system through feedback linearization technology, which significantly reduces the impact of nonlinearity on control accuracy. Compared with the traditional linear controller, this method has better control effect in dealing with the strong nonlinearity and coupling of the fuel cell air system, especially under variable load conditions, it can ensure the stable operation of the system.

[0150] Furthermore, according to the feedback linearization controller, the nonlinear model is converted into the linear model, and the acquisition process of the linear model is:

[0151] According to the feedback linearization controller, appropriate coordinate transformation and feedback are performed to obtain the linear model:

[0152]

[0153] in, They are The first-order differential of j is a virtual input, j=1,2 is an intermediate variable, and the virtual inputs v1 and v2 respectively control the cathode pressure p ca and the peroxygen ratio y is the output variable.

[0154] In an embodiment of the present application, a complex nonlinear model of the fuel cell air system is converted into a linear model by applying a feedback linearization controller, thereby achieving simplified control of the system. Through coordinate transformation and feedback, the nonlinear relationship in the model is decoupled, making the virtual input for controlling the cathode pressure and the peroxygen ratio more intuitive, and facilitating the design and implementation of precise control. The linearized model effectively reduces the complexity of the control system, allowing the traditional linear control algorithm to run efficiently on the model, improving the response speed and robustness of the system, thereby significantly improving the operating efficiency and stability of the fuel cell system.

[0155] Furthermore, according to the linear model, the extended state observer is established to observe the unknown environmental disturbance, and the acquisition process of the extended state observer is:

[0156] Introducing unknown environmental disturbances into the linear model, the formula is:

[0157]

[0158] Among them, d j The unknown environmental disturbance;

[0159] The extended state observer is:

[0160]

[0161] Among them, j=1,2 is the intermediate variable, System Status The estimated value of System Status The estimated value of is the unknown environmental disturbance d j The estimated value of They are The first-order differential of are the parameters of the extended state observer.

[0162] In an embodiment of the present application, an extended state observer is introduced to monitor the external disturbances and internal uncertainties in the system in real time. Through accurate observation of the disturbances, the interference factors in the system can be compensated in time, thereby enhancing the anti-disturbance capability of the system, so that the fuel cell system can still maintain efficient and stable operation in a complex environment.

[0163] Furthermore, according to the linear model and the extended state observer, the super-torsion non-singular terminal sliding mode control law is established, and the acquisition process of the super-torsion non-singular terminal sliding mode control law is:

[0164] Tracking error is defined as:

[0165]

[0166] in, is the tracking error, are the desired cathode pressure and the excess oxygen ratio, respectively, and satisfy in for The first-order derivative of ; the designed sliding surface is:

[0167]

[0168] Among them, s j is the sliding surface, λ j , γ j is the sliding surface coefficient, s j , j and γ j is a positive constant, and the super-torsion non-singular terminal sliding mode control law is established as:

[0169]

[0170] Among them, sign(*) is the saturation function, L 1j and L 2j is the control law parameter, L 1j >0,L 2j >0, substituting the observed value into the super-torsion non-singular terminal sliding mode control law to achieve tracking control of the cathode pressure and the excess oxygen ratio.

[0171] In the embodiment of the present application, by adopting the super-torque non-singular sliding mode control strategy, the present invention avoids the chattering problem in the traditional sliding mode control while ensuring the control accuracy of the system. This method improves the accuracy of air flow regulation and significantly improves the response speed of the system, so that the fuel cell system can quickly adjust the air supply under different working conditions to ensure that the dual requirements of excess oxygen ratio, air flow and pressure are met, thereby improving the overall performance and service life of the fuel cell system. By avoiding the chattering problem and improving the control accuracy, the present invention helps to reduce the wear caused by system instability and extend the service life of the fuel cell system. For example, after long-term operation, the fuel cell vehicle using this control strategy remains as good as new in performance, reducing the maintenance and replacement costs required due to performance degradation.

[0172] Super-twist non-singular terminal sliding mode control is a means to improve the accuracy and robustness of air systems. To a certain extent, it can make up for the poor control problems of feedback linearization under model uncertainty and environmental interference conditions. The design block diagram of super-twist non-singular terminal sliding mode controller based on feedback linearization is as follows: Figure 3 shown.

[0173] Embodiment 2

[0174] In this application example, the parameters of the fuel cell system are the same as those in Example 1, in order to further verify and demonstrate the effectiveness and superiority of the super torque non-singular sliding mode control strategy in practical applications. By setting the expected cathode pressure and the oxygen excess ratio to be the optimal working cathode pressure and oxygen excess ratio of the system, that is, Expected excess oxygen ratio This embodiment aims to ensure that the fuel cell system can achieve better operating results under various operating conditions.

[0175] Furthermore, a mathematical model of the centrifugal air compressor is established according to the law of energy conversion, and the specific formula is:

[0176]

[0177] Among them, ω cp represents the rotation speed of the centrifugal air compressor rotor, t is the time constant, Indicates ω cp The first-order differential of cm is the torque output by the motor, τ cp The torque required to drive the compressor;

[0178] Among them, τ cm and τ cp The formula is:

[0179]

[0180] Among them, η cm is the motor mechanical efficiency, k t is the motor torque constant, R cm is the internal resistance of the motor armature, k v is the back electromotive force constant of the motor, V cm is the motor voltage; C p is the specific heat capacity of air, T atm is the atmospheric temperature, η cp is the air compressor efficiency, p sm is the supply manifold pressure, p atm is the atmospheric pressure, γ is the air specific heat coefficient, W cp is the mass flow rate;

[0181] Among them, W cp The formula is:

[0182] W cp =p1ω cp 2 p sm +p2ω cp 2 +p3ω cp p sm 2 +p4ω cp p sm +p5ω cp +p6p sm 2 +p7p sm +p8;

[0183] Among them, p1, p2, ... p8 are fitting parameters.

[0184] Furthermore, according to the law of conservation of mass and the thermodynamic characteristics of gas, a mathematical model of the gas supply pipeline and the gas exhaust pipeline is established, and the specific formula is:

[0185]

[0186] Among them, p sm is the air pressure in the air supply pipeline, γ is the air specific heat coefficient, R ais the air gas constant, V sm is the volume of the gas supply pipeline, T sm is the gas temperature in the gas supply pipeline, W cp is the mass flow rate, T cp,out is the air compressor outlet gas temperature, W sm,out is the outlet flow of the intake pipe; p rm is the exhaust pipe pressure, T rm is the gas temperature in the exhaust duct, V rm is the exhaust duct volume, W rm,out is the exhaust pipe outlet flow rate, W ca,out is the cathode outlet air flow rate; is the peroxygen ratio, The oxygen flow rate supplied to the cathode, is the actual required oxygen flow;

[0187] Among them, T cp,out and W rm,out Respectively expressed as:

[0188]

[0189] Among them, T atm is the atmospheric temperature, η is is the electrochemical conversion efficiency, p atm is the atmospheric pressure; θ is the opening of the back pressure valve in the exhaust pipe, C d is the back pressure valve flow coefficient, A T is the back pressure valve area, p ca is the cathode pressure, R is the ideal gas constant, T st is the cathode temperature of the battery stack.

[0190] Furthermore, a fourth-order nonlinear equation of the fuel cell air system is established according to the mathematical model, and the specific formula is:

[0191]

[0192] Among them, x and y are state variables, is the first-order differential of x, u1 and u2 are the control inputs, h1(x) and h2(x) are the output variables, and x, u1, u2, h1(x) and h2(x) are expressed as follows:

[0193] x=[ω cp p sm p ca p rm ] T ;

[0194] u1=V cm ;

[0195]

[0196] h1(x)=p ca =200;

[0197]

[0198] Among them, ω cp Indicates the rotation speed of the centrifugal air compressor rotor, p sm is the air supply pipeline pressure, p ca is the cathode pressure, p rm V is the exhaust pipe pressure; cm is the motor voltage; θ is the opening of the back pressure valve in the exhaust pipe; is the peroxygen ratio; g1(x), g2(x) and f(x) are intermediate variables, and the formula is:

[0199] g1(x)=[c1 0 0 0] T ;

[0200] g2(x)=[0 0 0 c 16 x4] T ;

[0201]

[0202] Among them, x1, x2, x3 and x4 are intermediate variables, expressed as x1 = ω cp , x2=p sm , x3=p ca , x4=p rm , c i (i=1,...16) is the air system model constant, i is a subscript, and the specific formula of the air system model constant is:

[0203]

[0204] c4=p atm =101325;

[0205]

[0206] c7=-K sm,out =-3.629×10 -6 ;

[0207]

[0208] Among them, J cp K is the air compressor rotation inertia; sm,out is the inlet and outlet flow coefficient; is the oxygen gas constant, is the nitrogen gas constant, is the state of oxygen in the atmosphere, n is the number of cells in the battery stack, F is the Faraday constant, V ca is the volume of the cathode of the battery stack; K ca,out is the cathode outlet flow coefficient, k is the average molar constant; p sat is the saturation pressure.

[0209] Furthermore, according to the fourth-order nonlinear equation, the feedback linearization controller is designed, and the acquisition process of the feedback linearization controller is:

[0210] Design a new virtual input v as:

[0211] v=[v1v2] T ;

[0212] Wherein, v is a virtual control input vector, v1 is a virtual control input vector for cathode pressure, and v2 is a virtual control input vector for the excess oxygen ratio;

[0213] The feedback control variable can be obtained as:

[0214]

[0215] Among them, u1 and u2 are the actual control input vectors, A(x) is the system state matrix, and b(x) is the intermediate variable, which is expressed as:

[0216]

[0217] Among them, L f h1(x),L f h2(x) is the Lie derivative along the vector directions g1(x) and g2(x);

[0218] The coordinate transformation is defined as:

[0219]

[0220] Among them, j=1,2 is the intermediate variable, and To accurately feedback the linearized state variables;

[0221] The feedback linearization controller is obtained by using the pole placement method:

[0222]

[0223] Among them, v j is a virtual input, j=1, 2 are intermediate variables, and the virtual inputs v1 and v2 respectively control the cathode pressure p ca and the peroxygen ratio c 11 、c 12 、c 21 and c 22 are the feedback linearization controller parameters, is the desired cathode pressure, is the desired peroxygen ratio.

[0224] Furthermore, according to the feedback linearization controller, the nonlinear model is converted into the linear model, and the acquisition process of the linear model is:

[0225] According to the feedback linearization controller, appropriate coordinate transformation and feedback are performed to obtain the linear model:

[0226]

[0227] in, They are The first-order differential of j is a virtual input, j=1,2 is an intermediate variable, and the virtual inputs v1 and v2 respectively control the cathode pressure p ca and the peroxygen ratio y is the output variable.

[0228] Furthermore, according to the linear model, the extended state observer is established to observe the unknown environmental disturbance, and the acquisition process of the extended state observer is:

[0229] Introducing unknown environmental disturbances into the linear model, the formula is:

[0230]

[0231] Among them, d j The unknown environmental disturbance;

[0232] The extended state observer is:

[0233]

[0234] Among them, j=1,2 is the intermediate variable, System Status The estimated value of System Status The estimated value of is the unknown environmental disturbance d j The estimated value of They are The first-order differential of are the parameters of the extended state observer.

[0235] Furthermore, according to the linear model and the extended state observer, the super-torsion non-singular terminal sliding mode control law is established, and the acquisition process of the super-torsion non-singular terminal sliding mode control law is:

[0236] Tracking error is defined as:

[0237]

[0238] in, is the tracking error, are the desired cathode pressure and the excess oxygen ratio, respectively, and satisfy in for The first-order derivative of ; the designed sliding surface is:

[0239]

[0240] Among them, s j is the sliding surface, λ j , γ j is the sliding surface coefficient, s j , j and γ j is a positive constant, and the super-torsion non-singular terminal sliding mode control law is established as:

[0241]

[0242] Among them, sign(*) is the saturation function, L 1j and L 2j is the control law parameter, L 1j >0,L 2j >0, substituting the observed value into the super-torsion non-singular terminal sliding mode control law to achieve tracking control of the cathode pressure and the excess oxygen ratio.

[0243] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. An air flow control method for a fuel cell system, characterized in that: The following steps are involved: S1. Analyze the structure and working principle of the fuel cell flow supply subsystem, establish a mathematical model of a centrifugal air compressor, an air supply pipeline and an exhaust pipeline according to energy conversion, the law of conservation of mass and the thermodynamic characteristics of air, and establish a fourth-order nonlinear equation of the fuel cell air system according to the mathematical model; S2. According to the fourth-order nonlinear equation, a feedback linearization controller is established to convert the nonlinear model into a linear model, and an extended state observer is designed to observe the unknown environmental disturbance to obtain an observation value; S3. Establish a super-twist non-singular terminal sliding mode control law according to the linear model, and substitute the observed value into the super-twist non-singular terminal sliding mode control law to obtain a non-singular terminal sliding mode anti-interference control law.

2. The air flow control method for a fuel cell system according to claim 1, characterized in that: The mathematical model of the centrifugal air compressor is established according to the law of energy conversion, and the specific formula is: Among them, ω cp represents the rotation speed of the centrifugal air compressor rotor, t is the time constant, Indicates ω cp The first-order differential of cm is the torque output by the motor, τ cp The torque required to drive the compressor; Among them, τ cm and τ cp The formula is: Among them, η cm is the motor mechanical efficiency, k t is the motor torque constant, R cm is the internal resistance of the motor armature, k v is the back electromotive force constant of the motor, V cm is the motor voltage; C p is the specific heat capacity of air, T atm is the atmospheric temperature, η cp is the air compressor efficiency, p sm is the supply manifold pressure, p atm is the atmospheric pressure, γ is the air specific heat coefficient, W cp is the mass flow rate; Among them, W cp The formula is: W cp =p1ω cp 2 p sm +p2ω cp 2 +p3ω cp p sm 2 +p4ω cp p sm +p5ω cp +p6p sm 2 +p7p sm +p8; Among them, p1, p2, ...p8 are fitting parameters.

3. The air flow control method for a fuel cell system according to claim 2, characterized in that: According to the law of conservation of mass and the thermodynamic characteristics of gas, a mathematical model of the gas supply pipeline and the gas exhaust pipeline is established, and the specific formula is: Among them, p sm is the air pressure in the air supply pipeline, γ is the air specific heat coefficient, R a is the air gas constant, V sm is the volume of the gas supply pipeline, T sm is the gas temperature in the gas supply pipeline, W cp is the mass flow rate, T cp，out is the air compressor outlet gas temperature, W sm，out is the outlet flow of the intake pipe; p rm is the exhaust pipe pressure, T rm is the gas temperature in the exhaust duct, V rm is the exhaust duct volume, W rm，out is the exhaust pipe outlet flow rate, W ca，out is the cathode outlet air flow rate; is the peroxygen ratio, The oxygen flow rate supplied to the cathode, is the actual required oxygen flow; Among them, T cp，out and W rm，out Respectively expressed as: Among them, T atm is the atmospheric temperature, η is is the electrochemical conversion efficiency, p atm is the atmospheric pressure; θ is the opening of the back pressure valve in the exhaust pipe, C d is the back pressure valve flow coefficient, A T is the back pressure valve area, p ca is the cathode pressure, R is the ideal gas constant, T st is the cathode temperature of the battery stack.

4. The air flow control method for a fuel cell system according to claim 3, characterized in that: The fourth-order nonlinear equation of the fuel cell air system is established according to the mathematical model, and the specific formula is: Among them, x and y are state variables, is the first-order differential of x, u1 and u2 are the control inputs, h1(x) and h2(x) are the output variables, and x, u1, u2, h1(x) and h2(x) are expressed as follows: x=[ω cp p sm p ca p rm ] T ; u1=V cm ; h1(x)=p ca ; Among them, ω cp Indicates the rotation speed of the centrifugal air compressor rotor, p sm is the air supply pipeline pressure, p ca is the cathode pressure, p rm V is the air pressure of the exhaust pipe; cm is the motor voltage; θ is the opening of the back pressure valve in the exhaust pipe; is the peroxygen ratio; g1(x), g2(x) and f(x) are intermediate variables, and the formula is: g1(x)=[c1 0 0 0] T ; g2(x)=[000c 16 x4] T ; Among them, x1, x2, x3 and x4 are intermediate variables, expressed as x1 = ω cp , x2=p sm , x3=p ca , x4=p rm , c i (i=1, ...16) are air system model constants, i is a subscript.

5. The air flow control method for a fuel cell system according to claim 4, characterized in that: According to the fourth-order nonlinear equation, the feedback linearization controller is designed, and the acquisition process of the feedback linearization controller is: Design a new virtual input v as: v=[v1 v2] T ; Wherein, v is a virtual control input vector, v1 is a virtual control input vector for cathode pressure, and v2 is a virtual control input vector for the excess oxygen ratio; The feedback control variable can be obtained as: Among them, u1 and u2 are the actual control input vectors, A(x) is the system state matrix, and b(x) is the intermediate variable, which is expressed as: Among them, L f h1(x),L f h2(x) is the Lie derivative along the vector directions g1(x) and g2(x); The coordinate transformation is defined as: Among them, j=1,2 is the intermediate variable, and To accurately feedback the linearized state variables; The feedback linearization controller is obtained by using the pole placement method: Among them, v j is a virtual input, j=1, 2 are intermediate variables, and the virtual inputs v1 and v2 respectively control the cathode pressure p ca and the peroxygen ratio c 11 、c 12 、c 21 and c 22 are the feedback linearization controller parameters, is the desired cathode pressure, is the desired peroxygen ratio.

6. The air flow control method for a fuel cell system according to claim 5, characterized in that: According to the feedback linearization controller, the nonlinear model is converted into the linear model, and the acquisition process of the linear model is: According to the feedback linearization controller, appropriate coordinate transformation and feedback are performed to obtain the linear model: in, They are The first-order differential of j is a virtual input, j=1, 2 are intermediate variables, and the virtual inputs v1 and v2 respectively control the cathode pressure p ca and the peroxygen ratio y is the output variable.

7. The air flow control method for a fuel cell system according to claim 6, characterized in that: According to the linear model, the extended state observer is established to observe the unknown environmental disturbance. The acquisition process of the extended state observer is: Introducing unknown environmental disturbances into the linear model, the formula is: Among them, d j The unknown environmental disturbance; The extended state observer is: Among them, j=1, 2 are intermediate variables, System Status The estimated value of System Status The estimated value of is the unknown environmental disturbance d j The estimated value of They are The first-order differential of are the parameters of the extended state observer.

8. The air flow control method for a fuel cell system according to claim 7, characterized in that: According to the linear model and the extended state observer, the super-torsion non-singular terminal sliding mode control law is established, and the acquisition process of the super-torsion non-singular terminal sliding mode control law is: Tracking error is defined as: in, is the tracking error, are the desired cathode pressure and the excess oxygen ratio, respectively, and satisfy in for The first-order derivative of ; the designed sliding surface is: Among them, s j is the sliding surface, λ j , γ j is the sliding surface coefficient, s j , j and γ j is a positive constant, and the super-torsion non-singular terminal sliding mode control law is established as: Among them, sign(*) is the saturation function, L 1j and L 2j is the control law parameter, L 1j >0,L 2j >0, the observed value is substituted into the super-torsion non-singular terminal sliding mode control law to achieve tracking control of the cathode pressure and the excess oxygen ratio.

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