Flexible performance control method for hydrogen supply system of proton exchange membrane fuel cell

Abstract

The invention discloses a method for controlling the flexible performance of a hydrogen supply system of a proton exchange membrane fuel cell, and the method comprises the following steps: S1, constructing a control-oriented kinetic model for components of the hydrogen supply system of the proton exchange membrane fuel cell according to gas dynamics and a motor rotating speed equation; s2, establishing an error dynamic model of the hydrogen ratio and the anode pressure of the system; s3, according to the error dynamic model of the system, establishing a self-adaptive system for detecting flow interference of the drain valve, designing a flexible performance function by introducing a correction signal of the self-adaptive system, and converting tracking errors of the hydrogen passing ratio and the anode pressure; s4, designing a push-back controller, selecting a proper Lyapunov function to prove the stability of the system, and proving that the hydrogen passing ratio and the anode pressure tracking error of the system meet the flexible performance constraint; according to the method, the limitation of performance constraint control on the hydrogen supply system of the proton exchange membrane fuel cell under the condition that the flow of the drain valve jumps is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of proton exchange membrane fuel cell hydrogen supply system control, and more specifically, to a flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system. Background Art

[0002] In the global fossil energy crisis, hydrogen energy has attracted widespread attention due to its abundant reserves, high calorific value and low environmental impact. Proton exchange membrane fuel cells (PEMFC) promote electrochemical energy conversion through the reaction of hydrogen and oxygen and have become a promising technology. The hydrogen supply system of the proton exchange membrane fuel cell consists of the following components: Figure 2 As shown in Figure 1, PEMFCs directly convert chemical energy into electrical energy through electrochemical reactions, offering advantages such as high efficiency, environmental sustainability, and clean energy production. In applications such as aviation and maritime, PEMFCs are increasingly being used as power generation systems to improve the endurance of aircraft and seafaring vessels. However, as these applications continue to expand, the operating environment of PEMFCs has become more complex, placing greater emphasis on extending lifespan and safety performance. The PEMFC control system is a key component for hydrogen and oxygen regulation, thermal management, and water management. The hydrogen supply control system plays a crucial role in ensuring continuous and stable hydrogen delivery to the fuel cell stack. To optimize hydrogen utilization, a circulation device is typically integrated at the anode outlet of the hydrogen supply system. However, the inherent complexity of the hydrogen supply system, characterized by numerous auxiliary components and strong nonlinear dynamics, presents significant challenges. Issues such as delayed response time and unreliable control performance remain key bottlenecks, limiting the wider application of PEMFCs in engineering. Addressing these challenges is crucial to unleashing the full potential of PEMFC technology in practical environments.

[0003] Based on the above analysis, current research on PEMFC hydrogen supply system control, both domestically and internationally, focuses on linearized PEMFC hydrogen supply system control. In reality, model linearization can vary significantly under different operating conditions, especially in environments with large temperature or humidity fluctuations. Errors introduced by the model can affect the control accuracy of the control system. Summary of the Invention

[0004] The purpose of the present invention is to provide a flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system, which solves the problem that drainage valve flow interference may cause tracking error constraint control to fail.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for controlling the flexible performance of a proton exchange membrane fuel cell hydrogen supply system comprises the following steps:

[0007] S1. Based on the gas dynamics and motor speed equations, a control-oriented dynamic model is constructed for the components of the proton exchange membrane fuel cell hydrogen supply system.

[0008] S2. Establish error dynamics model of system hydrogen ratio and anode pressure;

[0009] S3. Based on the system's error dynamics model, an adaptive system for detecting drain valve flow disturbances is established. By introducing correction signals from the adaptive system and designing a flexible performance function, the tracking errors of the hydrogen excess ratio and anode pressure are converted.

[0010] S4. Design a pushback controller, select a suitable Lyapunov function to prove the stability of the system, and prove that the system hydrogen ratio and anode pressure tracking error meet the flexible performance constraints.

[0011] Furthermore, in step S1, the kinetic model of the proton exchange membrane fuel cell hydrogen supply system is as follows:

[0012]

[0013] Where x1 = ω cp is the circulating pump speed, x2=p sm is the total pressure of the gas supply manifold, is the hydrogen partial pressure in the gas supply manifold, x4=p an is the total pressure of the anode flow field, is the hydrogen partial pressure in the anode flow field, x6=p rm is the total return manifold pressure, is the hydrogen partial pressure returning to the manifold; W cp and W sv,max are the gas output flow rate leaving the circulation pump and the maximum proportional valve output flow rate; d1 = I st is the stack current interference, d2=W purge is the flow disturbance of the drain valve, which is a known system disturbance; M r 、M s 、M a are the mass fractions of hydrogen in the supply manifold, anode flow field and return manifold respectively; m r 、m s 、m a are the mass ratios of hydrogen in the supply manifold, anode flow field, and return manifold respectively; u1=v cp is the circulating pump voltage, u2=α sm is the proportional valve opening; c i (i=1,2,...,18) is the system parameter, which is expressed as follows:

[0014]

[0015] Among them, η cp is the mechanical efficiency of the circulating pump, k t is the motor coefficient, J cp is the moment of inertia of the circulating pump, k v is the circulation pump coefficient, C p is the specific heat capacity of the circulating pump, T cp is the circulating pump temperature, γ is the circulating pump heat ratio, R is the gas constant, T sm is the air supply manifold temperature, k sm,out is the flow coefficient of the air supply manifold, V sm is the volume of the air supply manifold, is the molar mass of hydrogen, T an is the anode flow field temperature, V an is the anode flow field volume, k an,out is the anode flow field flow coefficient, n is the number of stacks, α net is the net water coefficient, M v is the molar mass of water vapor, F is the Faraday constant, T rm is the return manifold temperature, k rm,out is the return manifold flow coefficient, V rm is the return manifold volume;

[0016] The control targets of the system are the total pressure of the anode flow field x4 and the hydrogen ratio Hydrogen ratio The expression is as follows:

[0017]

[0018] Among them, c 19 is a system parameter, which is expressed as follows:

[0019]

[0020] Furthermore, in step S2, the error dynamics model is established as follows:

[0021] Define the error variable:

[0022]

[0023] in, is the desired hydrogen excess ratio, is the expected pressure of the anode flow field; and is the virtual control law;

[0024] The dynamic equation about the error variable is established as follows:

[0025]

[0026] Among them, g1 and g2 are non-singular system functions that are smooth in the feasible domain, and f1 and f2 are nonlinear functions that are smooth in the feasible domain. The specific expressions are as follows:

[0027]

[0028]

[0029] in,

[0030]

[0031] Furthermore, step S3 includes:

[0032] S3.1. Establish flexible performance constraints, convert hydrogen ratio and anode pressure tracking error, and introduce the following preset performance function:

[0033]

[0034] Where i = 1, 2; ρ 0,i , ρ ∞,i and a i are the preset performance function parameters, all of which are positive and satisfy: ρ 0,i >ρ ∞,i ;

[0035] The constraints that the tracking error needs to satisfy are as follows:

[0036]

[0037] Where 0<δ i <1、 is the flexible performance boundary parameter; Ω l,i (t) = ρ i (t)+ω l,i (t),Ω u,i (t) = ρ i (t)+ω u,i (t),ω l,i (t) and ω u,i (t) corrections provided to the adaptive system;

[0038] The initial value conditions of the flexible performance constraint are as follows:

[0039]

[0040] The error constraint can be further transformed into:

[0041]

[0042] S3.2. Establish an adaptive system for detecting flow disturbances in drain valves as follows:

[0043]

[0044] φ 1,i (t) = g i ω 2,i (t)

[0045] φ 2,i (t) = g i ω 1,i (t)

[0046] φ 3,i (t)=|r i (x)|(d2-τ w ) +

[0047] φ 4,i (t)=|r i (x)|(d2-τ w ) +

[0048] Among them, ω l,i 、ω u,i 、ω 1,i and ω 2,i is the state of the adaptive system; h 1,i >0,h 2,i >0 is the adaptive system parameter; operator f + =max{f,0};τ w represents the threshold for detecting flow disturbance in the drain valve;

[0049] r i (x) is a system function, and its specific form is as follows:

[0050]

[0051] r2=-c 10 c 16 M r M a .

[0052] Furthermore, step S4 includes:

[0053] S4.1. Design a virtual control law for the error dynamics equation of the established proton exchange membrane fuel cell hydrogen supply system and the error conversion of flexible performance. And the control laws u1 and u2 are as follows:

[0054]

[0055] Among them, k1>0, k2>0, k3>0 and k4>0 are controller parameters;

[0056] S4.2. Based on the error system model, select an appropriate Lyapunov function to prove the stability of the system and prove that the system hydrogen ratio and anode pressure errors meet the flexible performance constraints;

[0057] Select the following candidate Lyapunov function:

[0058]

[0059] After taking the derivative of V, when the initial value constraint is satisfied, The tracking errors z1, z2, e1 and e2 are bounded; according to the Russell invariance theorem, when The error system is asymptotically stable under the action of the controller, and the system tracking error is always within the set flexible constraint boundary.

[0060] The beneficial effects of the present invention are as follows:

[0061] 1. The present invention directly utilizes the nonlinear components of the model to design the controller, ensuring the global asymptotic stability of the tracking error and having higher tracking performance.

[0062] 2. The present invention introduces flexible performance constraints to ensure that the system hydrogen ratio and anode pressure tracking error have good convergence speed and steady-state accuracy.

[0063] 3. The present invention establishes an adaptive correction system to detect the drainage valve flow interference in real time and compensate for the preset performance function boundary. When the system encounters a strong interference similar to the drainage valve flow, the constraint controller can safely manage the hydrogen ratio and the anode pressure, ensuring the effectiveness of the controller design in the event of strong interference and improving the safety of the control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0065] Figure 1 This is a flow chart of the flexible performance control method of the proton exchange membrane fuel cell hydrogen supply system of the present invention.

[0066] Figure 2 Schematic diagram of the hydrogen supply system for proton exchange membrane fuel cells.

[0067] Figure 3 This is a schematic diagram of a hydrogen excess ratio error curve in a flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system according to an embodiment of the present invention.

[0068] Figure 4This is a schematic diagram of an anode pressure error curve in a flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system according to an embodiment of the present invention.

[0069] Figure 5 This is a schematic diagram of the stack current curve in the flexible performance control method of the proton exchange membrane fuel cell hydrogen supply system according to an embodiment of the present invention.

[0070] Figure 6 This is a schematic diagram of a drain valve opening curve in a flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0071] In order to more clearly illustrate the present invention, the present invention is further described below in conjunction with preferred embodiments and drawings. Those skilled in the art should understand that the following specific description is illustrative rather than restrictive and should not be used to limit the scope of protection of the present invention.

[0072] This embodiment provides a flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system, which solves the problem of drain valve flow interference causing tracking error constraint control to fail. Figure 1 As shown, the control method includes the following steps:

[0073] S1. Based on the gas dynamics and motor speed equations, a control-oriented dynamic model is constructed for the components of the proton exchange membrane fuel cell hydrogen supply system.

[0074] S2. Establish error dynamics model of system hydrogen ratio and anode pressure;

[0075] S3. Based on the system's error dynamics model, an adaptive system for detecting drain valve flow disturbances is established. By introducing correction signals from the adaptive system and designing a flexible performance function, the tracking errors of the hydrogen excess ratio and anode pressure are converted.

[0076] S4. Design a pushback controller and select a suitable Lyapunov function to prove the stability of the system and prove that the system hydrogen ratio and anode pressure tracking error meet the flexible performance constraints.

[0077] The following describes each step in detail.

[0078] In step S1, the kinetic model of the proton exchange membrane fuel cell hydrogen supply system is as follows:

[0079]

[0080] Where x1 = ω cp is the circulating pump speed, x2=p sm is the total pressure of the gas supply manifold, is the hydrogen partial pressure in the gas supply manifold, x4=p an is the total pressure of the anode flow field, is the hydrogen partial pressure in the anode flow field, x6=p rm is the total return manifold pressure, is the hydrogen partial pressure returning to the manifold; W cp and W sv,max are the gas output flow rate leaving the circulation pump and the maximum proportional valve output flow rate; d1 = I st is the stack current interference, d2=W purge is the flow disturbance of the drain valve, which is a known system disturbance; M r 、M s 、M a are the mass fractions of hydrogen in the supply manifold, anode flow field and return manifold respectively; m r 、m s 、m a are the mass ratios of hydrogen in the supply manifold, anode flow field, and return manifold respectively; u1=v cp is the circulating pump voltage, u2=α sm is the proportional valve opening, the circulating pump voltage and the proportional valve opening are the control inputs of the system; c i (i=1,2,...,18) is the system parameter, which is expressed as follows:

[0081]

[0082] Among them, η cp is the mechanical efficiency of the circulating pump, k t is the motor coefficient, J cp is the moment of inertia of the circulating pump, k v is the circulation pump coefficient, C p is the specific heat capacity of the circulating pump, T cp is the circulating pump temperature, γ is the circulating pump heat ratio, R is the gas constant, T sm is the air supply manifold temperature, k sm,out is the flow coefficient of the air supply manifold, V sm is the volume of the air supply manifold, is the molar mass of hydrogen, T an is the anode flow field temperature, V an is the anode flow field volume, k an,out is the anode flow field flow coefficient, n is the number of stacks, α net is the net water coefficient, M v is the molar mass of water vapor, F is the Faraday constant, T rm is the return manifold temperature, k rm,out is the return manifold flow coefficient, V rm For the return manifold volume, the above coefficients are all constants;

[0083] The control targets of the system are the total pressure of the anode flow field x4 and the hydrogen ratio Hydrogen ratio The expression is as follows:

[0084]

[0085] Among them, c 19 is a system parameter, which is expressed as follows:

[0086]

[0087] In step S2, the error dynamics model of the proton exchange membrane fuel cell hydrogen supply system is established as follows:

[0088] Define the error variable:

[0089]

[0090] in, is the desired hydrogen excess ratio, is the expected pressure of the anode flow field; and It is a virtual control law, which is specifically designed in step S4;

[0091] The dynamic equation about the error variable is established as follows:

[0092]

[0093] Among them, g1 and g2 are non-singular system functions that are smooth enough in the feasible domain, and f1 and f2 are nonlinear functions that are smooth enough in the feasible domain. The specific expressions are as follows:

[0094]

[0095] in,

[0096]

[0097] Step S3 further includes the following sub-steps:

[0098] S3.1. Establish flexible performance constraints, convert hydrogen ratio and anode pressure tracking error, and introduce the following preset performance function:

[0099]

[0100] Where i = 1, 2; ρ 0,i , ρ ∞,i and a i are the preset performance function parameters, all of which are positive and satisfy: ρ 0,i >ρ ∞,i .

[0101] The constraints that the tracking error needs to satisfy are as follows:

[0102]

[0103] Where 0<δ i <1、 is the flexible performance boundary parameter; Ω l,i (t) = ρ i (t)+ω l,i (t),Ω u,i (t) = ρ i (t)+ω u,i (t),ω l,i (t) and ω u,i (t) Correction terms provided for the adaptive system, which are subsequently designed in S3.2;

[0104] The initial value conditions of the flexible performance constraint are as follows:

[0105]

[0106] The error constraint is further transformed into:

[0107]

[0108] S3.2. Establish an adaptive system for detecting flow disturbances in drain valves as follows:

[0109]

[0110] φ 1,i (t) = g i ω 2,i (t)

[0111] φ 2,i (t) = g i ω 1,i (t)

[0112] φ 3,i (t)=|r i (x)|(d2-τ w ) +

[0113] φ 4,i (t)=|r i (x)|(d2-τ w ) +

[0114] Among them, ω l,i 、ω u,i 、ω 1,i and ω 2,iis the state of the adaptive system; h 1,i >0,h 2,i >0 is the adaptive system parameter; operator f + =max{f,0};τ w is a positive constant, representing the threshold for detecting flow disturbance of the drain valve;

[0115] r i (x) is a system function, and its specific form is as follows:

[0116]

[0117] r2=-c 10 c 16 M r M a .

[0118] Step S4 further includes the following sub-steps:

[0119] S4.1. Design a virtual control law for the error dynamics equation of the established proton exchange membrane fuel cell hydrogen supply system and the error conversion of flexible performance. And the control laws u1 and u2 are as follows:

[0120]

[0121] Among them, k1>0, k2>0, k3>0 and k4>0 are controller parameters;

[0122] S4.2. Based on the error system model, select an appropriate Lyapunov function to prove the stability of the system and prove that the system hydrogen ratio and anode pressure errors meet the flexible performance constraints;

[0123] Select the following Lyapunov candidate function:

[0124]

[0125] After taking the derivative of V, it is found that when the initial value constraint is satisfied, This shows that the tracking errors z1, z2, e1 and e2 are bounded; according to Russell’s invariance theorem, when The error system is asymptotically stable under the action of the controller, and the system tracking error is always within the set flexible constraint boundary.

[0126] In order to verify the effectiveness of the flexible performance control method for the proton exchange membrane fuel cell hydrogen supply system provided in this embodiment, a simulation experiment was conducted using MATLAB, and a detailed description is given below.

[0127] Select the adaptive system parameter h 1,i=5,h 2,i =10, flexible performance boundary parameter δ i =0.8, Controller parameters k1=2, k2=2, k3=5 and k4=5, preset performance function parameter ρ 0,1 =200,ρ 0,2 =20000,ρ ∞,1 =10,ρ ∞,2 =5, a1=10, a2=5, and the control strategy proposed by the present invention is simulated and verified. Figure 3-Figure 6 ;

[0128] in, Figure 3 、 Figure 4 A schematic diagram showing the curves of hydrogen ratio error and anode pressure error in the flexible performance control method of the proton exchange membrane fuel cell hydrogen supply system. Figure 5 、 Figure 6 A schematic diagram of the stack current and drain valve opening curves in the flexible performance control method for the proton exchange membrane fuel cell hydrogen supply system is shown. It can be seen that the flexible performance controller proposed in this embodiment has good transient and steady-state performance, and the hydrogen overload ratio and anode pressure tracking error are constrained within the flexible performance boundary, which proves the effectiveness of the flexible performance control method for the proton exchange membrane fuel cell hydrogen supply system provided in this embodiment.

[0129] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not limitations on the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for controlling the flexible performance of a proton exchange membrane fuel cell hydrogen supply system, characterized in that: The steps include: S1. Based on the gas dynamics and motor speed equations, a control-oriented dynamic model is constructed for the components of the proton exchange membrane fuel cell hydrogen supply system. S2. Establish error dynamics model of system hydrogen ratio and anode pressure; S3. Based on the system's error dynamics model, an adaptive system for detecting drain valve flow disturbances is established. By introducing correction signals from the adaptive system and designing a flexible performance function, the tracking errors of the hydrogen excess ratio and anode pressure are converted. S4. Design a pushback controller, select a suitable Lyapunov function to prove the stability of the system, and prove that the system hydrogen ratio and anode pressure tracking error meet the flexible performance constraints.

2. The flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system according to claim 1, characterized in that: In step S1, the kinetic model of the proton exchange membrane fuel cell hydrogen supply system is as follows: Where x1 = ω cp is the circulating pump speed, x2=p sm is the total pressure of the gas supply manifold, is the hydrogen partial pressure in the gas supply manifold, x4=p an is the total pressure of the anode flow field, is the hydrogen partial pressure in the anode flow field, x6=p rm is the total return manifold pressure, is the return manifold hydrogen partial pressure; W cp and W sv,max are the gas output flow rate leaving the circulation pump and the maximum proportional valve output flow rate; d1 = I st is the stack current interference, d2=W purge is the flow disturbance of the drain valve, which is a known system disturbance; M r 、M s 、M a are the mass fractions of hydrogen in the supply manifold, anode flow field and return manifold respectively; m r 、m s 、m a are the mass ratios of hydrogen in the supply manifold, anode flow field, and return manifold respectively; u1=v cp is the circulating pump voltage, u2=α sm is the proportional valve opening; c i (i=1,2,...,18) is the system parameter, which is expressed as follows: Among them, η cp is the mechanical efficiency of the circulating pump, k t is the motor coefficient, J cp is the moment of inertia of the circulating pump, k v is the circulation pump coefficient, C p is the specific heat capacity of the circulating pump, T cp is the circulating pump temperature, γ is the circulating pump heat ratio, R is the gas constant, T sm is the air supply manifold temperature, k sm,out is the flow coefficient of the air supply manifold, V sm is the volume of the air supply manifold, is the molar mass of hydrogen, T an is the anode flow field temperature, V an is the anode flow field volume, k an,out is the anode flow field flow coefficient, n is the number of stacks, α net is the net water coefficient, M v is the molar mass of water vapor, F is the Faraday constant, T rm is the return manifold temperature, k rm,out is the return manifold flow coefficient, V rm is the return manifold volume; The control targets of the system are the total pressure of the anode flow field x4 and the hydrogen ratio Hydrogen ratio The expression is as follows: Among them, c 19 is a system parameter, which is expressed as follows:

3. The flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system according to claim 2, characterized in that: In step S2, the error dynamics model is established as follows: Define the error variable: in, is the desired hydrogen excess ratio, is the expected pressure of the anode flow field; and is the virtual control law; The dynamic equation about the error variable is established as follows: Among them, g1 and g2 are non-singular system functions that are smooth in the feasible domain, and f1 and f2 are nonlinear functions that are smooth in the feasible domain. The specific expressions are as follows: in, 4. The flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system according to claim 3, characterized in that: Step S3 includes: S3.

1. Establish flexible performance constraints, convert hydrogen ratio and anode pressure tracking error, and introduce the following preset performance function: Where i = 1, 2; ρ 0,i , ρ ∞,i and a i are the preset performance function parameters, all of which are positive and satisfy: ρ 0,i >ρ ∞,i ; The constraints that the tracking error needs to satisfy are as follows: Where 0<δ i <1、 is the flexible performance boundary parameter; Ω l,i (t) = ρ i (t)+ω l,i (t),Ω u,i (t) = ρ i (t)+ω u,i (t),ω l,i (t) and ω u,i (t) correction terms provided for the adaptive system; The initial value conditions of the flexible performance constraint are as follows: The error constraint can be further transformed into: S3.

2. Establish an adaptive system for detecting flow disturbances in drain valves as follows: Among them, ω l,i 、ω u,i 、ω 1,i and ω 2,i is the state of the adaptive system; h 1,i >0,h 2,i >0 is the adaptive system parameter; operator f + =max{f,0};τ w represents the threshold for detecting flow disturbance in the drain valve; r i (x) is a system function, and its specific form is as follows:

5. The flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system according to claim 4, characterized in that: Step S4 includes: S4.

1. Design a virtual control law for the error dynamics equation of the established proton exchange membrane fuel cell hydrogen supply system and the error conversion of flexible performance. And the control laws u1 and u2 are as follows: Among them, k1>0, k2>0, k3>0 and k4>0 are controller parameters; S4.

2. Based on the error system model, select an appropriate Lyapunov function to prove the stability of the system and prove that the system hydrogen ratio and anode pressure errors meet the flexible performance constraints; Select the following candidate Lyapunov function: After taking the derivative of V, when the initial value constraint is satisfied, The tracking errors z1, z2, e1 and e2 are bounded; according to the Russell invariance theorem, when The error system is asymptotically stable under the action of the controller, and the system tracking error is always within the set flexible constraint boundary.

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