Flexible performance control methods for proton exchange membrane fuel cell hydrogen supply systems

Abstract

This invention discloses a flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system, comprising the following steps: S1, constructing a control-oriented dynamic model for the components of the proton exchange membrane fuel cell hydrogen supply system based on gas dynamics and motor speed equations; S2, establishing error dynamic models for the system's hydrogen overload ratio and anode pressure; S3, establishing an adaptive system for detecting flow disturbances in the drain valve based on the system's error dynamic model, and designing a flexible performance function by introducing a correction signal from the adaptive system to convert the tracking errors of the hydrogen overload ratio and anode pressure; S4, designing a push-back controller, selecting a suitable Lyapunov function to prove the system's stability, and proving that the tracking errors of the system's hydrogen overload ratio and anode pressure satisfy the flexible performance constraints; this invention solves the limitations of performance constraint control of the proton exchange membrane fuel cell hydrogen supply system when the drain valve flow rate jumps.

Description

Technical Field

[0001] This invention relates to the field of proton exchange membrane fuel cell hydrogen supply system control technology, and more specifically, to a flexible performance control method for proton exchange membrane fuel cell hydrogen supply systems. Background Technology

[0002] Amid the global fossil fuel crisis, hydrogen energy has garnered widespread attention due to its abundant reserves, high calorific value, and minimal environmental impact. Proton exchange membrane fuel cells (PEMFCs), which promote electrochemical energy conversion through the reaction of hydrogen and oxygen, have emerged as a promising technology. The hydrogen supply system of a PEMFC consists of... Figure 2 As shown, 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 in aviation and maritime fields, PEMFCs are increasingly being used as power generation systems to improve the endurance of aircraft and ships. However, with the continuous expansion of application scenarios, the operating environment of PEMFCs is becoming more complex, placing greater emphasis on extended lifespan and safety performance. The control system of a PEMFC is a key component for hydrogen and oxygen regulation, thermal management, and water management. Among these, the hydrogen supply control system plays a crucial role in ensuring a continuous and stable supply of hydrogen to the fuel cell stack. To optimize hydrogen utilization, the recirculation unit 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 critical bottlenecks, limiting the wider engineering application of PEMFCs. Addressing these challenges is essential to unlocking the full potential of PEMFC technology in real-world environments.

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

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

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

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

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

[0008] S2. Establish error kinetic models for the system's hydrogen permeation ratio and anode pressure;

[0009] S3. Based on the error dynamics model of the system, an adaptive system for detecting flow disturbance of the drain valve is established. By introducing the correction signal of the adaptive system, a flexible performance function is designed to convert the tracking errors of hydrogen ratio and anode pressure.

[0010] S4. Design a push-back controller, select a suitable Lyapunov function to prove the stability of the system, and prove that the system's hydrogen ratio and anode pressure tracking error meet the flexibility 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 x2 = p, where p is the speed of the circulating pump. sm For the total pressure of the gas supply manifold, For the partial pressure of hydrogen in the gas supply manifold, x4 = p an The total pressure of the anode flow field is... For the hydrogen partial pressure in the anolyte flow field, x6 = p rm To return the total manifold pressure, To return the partial pressure of hydrogen in the manifold; W cp and W sv,max These are the gas output flow rate leaving the circulating pump and the maximum proportional valve output flow rate, respectively; d1 = I st For the interference of the fuel cell current, d2 = W purge The interference is from the drain valve flow rate, and all of these are known system interferences; M r M s M a These represent the mass fraction of hydrogen in the supply manifold, anode flow field, and return manifold, respectively; m r m s m a These represent the mass ratios of hydrogen in the supply manifold, the anode flow field, and the return manifold, respectively; u1 = v cp For the circulating pump voltage, u2 = α sm c is the proportional valve opening. i (i = 1, 2, ..., 18) are system parameters, specifically expressed as follows:

[0014]

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

[0016] The system's control objectives are the total pressure of the anode flow field x4 and the hydrogen permeation ratio. hydrogen permeability The expression is as follows:

[0017]

[0018] Among them, c 19 These are system parameters, 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, To achieve the desired hydrogen peroxide ratio, The desired pressure for the anode flow field; and For virtual control laws;

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

[0025]

[0026] Where g1 and g2 are smooth nonsingular system functions within the feasible region, and f1 and f2 are smooth nonlinear functions within the feasible region, specifically expressed as follows:

[0027]

[0028]

[0029] in,

[0030]

[0031] Further, step S3 includes:

[0032] S3.1 Establish flexible performance constraints, convert the 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 The preset performance function parameters are all positive values, satisfying: ρ 0,i >ρ ∞,i ;

[0035] The constraints that the tracking error needs to satisfy are shown below:

[0036]

[0037] Where, 0 < δ i <1, Ω is the boundary parameter for flexible performance. 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) represents the correction term provided by the adaptive system;

[0038] The initial conditions for the flexibility performance constraints 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 the drain valve 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] Where, ω l,i ω u,i ω 1,i and ω 2,i The state of the adaptive system; h 1,i >0, h 2,i >0 represents the adaptive system parameter; operator f + =max{f,0};τ w The threshold representing the detection of flow disturbances in the drain valve;

[0049] r i (x) is a system function, with the following specific form:

[0050]

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

[0052] Further, step S4 includes:

[0053] S4.1. Based on the established error kinetic equations of the proton exchange membrane fuel cell hydrogen supply system and the error conversion of flexible performance, design a virtual control law. The control laws u1 and u2 are as follows:

[0054]

[0055] Where 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 at the same time prove that the system's hydrogen ratio and anode pressure error satisfy the flexibility performance constraints.

[0057] Select the following Lyapunov candidate functions:

[0058]

[0059] After differentiating with respect to V, when the initial value constraints are satisfied, 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 boundaries.

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

[0061] 1. This invention directly utilizes the nonlinear components of the model for controller design, ensuring global asymptotic stability of the tracking error and exhibiting high tracking performance.

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

[0063] 3. This invention establishes an adaptive correction system that detects flow disturbances in the drain valve in real time and compensates for the preset performance function boundary. When strong disturbances similar to those in the drain valve flow occur, the system constrains the controller to safely manage the hydrogen ratio and anode pressure, ensuring the effectiveness of the controller design under strong disturbances and improving the safety of the control system. Attached Figure Description

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

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

[0066] Figure 2 This is a schematic diagram of the hydrogen supply system for a proton exchange membrane fuel cell.

[0067] Figure 3 This is a schematic diagram of the hydrogen permeate ratio error 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.

[0068] Figure 4This is a schematic diagram of the anode pressure error 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.

[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 the drain valve opening 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. Detailed Implementation

[0071] To more clearly illustrate the present invention, the following description, in conjunction with preferred embodiments and accompanying drawings, further clarifies the invention. Those skilled in the art should understand that the specific description below is illustrative rather than restrictive and should not be construed as limiting 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 that flow interference from the drain valve can cause tracking error constraint control to fail. Figure 1 As shown, the control method includes the following steps:

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

[0074] S2. Establish error kinetic models for the system's hydrogen permeability and anode pressure;

[0075] S3. Based on the error dynamics model of the system, an adaptive system for detecting flow disturbance of the drain valve is established. By introducing the correction signal of the adaptive system, a flexible performance function is designed to convert the tracking errors of hydrogen ratio and anode pressure.

[0076] S4. Design a push-back controller, select a suitable Lyapunov function to prove the stability of the system, and prove that the system's hydrogen ratio and anode pressure tracking error meet the flexibility performance constraints.

[0077] The following details each step.

[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 x2 = p, where p is the speed of the circulating pump. sm For the total pressure of the gas supply manifold, For the partial pressure of hydrogen in the gas supply manifold, x4 = p an The total pressure of the anode flow field is... For the hydrogen partial pressure in the anolyte flow field, x6 = p rm To return the total manifold pressure, To return the partial pressure of hydrogen in the manifold; W cp and W sv,max These are the gas output flow rate leaving the circulating pump and the maximum proportional valve output flow rate, respectively; d1 = I st For the interference of the fuel cell current, d2 = W purge The interference is from the drain valve flow rate, and all of these are known system interferences; M r M s M a These represent the mass fraction of hydrogen in the supply manifold, anode flow field, and return manifold, respectively; m r m s m a These represent the mass ratios of hydrogen in the supply manifold, the anode flow field, and the return manifold, respectively; u1 = v cp For the circulating pump voltage, u2 = α sm The proportional valve opening, the circulating pump voltage, and the proportional valve opening are the system control inputs; c i (i = 1, 2, ..., 18) are system parameters, specifically expressed as follows:

[0081]

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

[0083] The system's control objectives are the total pressure of the anode flow field x4 and the hydrogen permeation ratio. hydrogen permeability The expression is as follows:

[0084]

[0085] Among them, c 19 These are system parameters, expressed as follows:

[0086]

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

[0088] Define the error variable:

[0089]

[0090] in, To achieve the desired hydrogen peroxide ratio, The desired pressure for the anode flow field; and The virtual control law is designed in detail in step S4;

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

[0092]

[0093] Where g1 and g2 are sufficiently smooth nonsingular system functions within the feasible region, and f1 and f2 are sufficiently smooth nonlinear functions within the feasible region, specifically expressed as follows:

[0094]

[0095] in,

[0096]

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

[0098] S3.1 Establish flexible performance constraints, convert the 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 The preset performance function parameters are all positive values, satisfying: ρ 0,i >ρ ∞,i .

[0101] The constraints that the tracking error needs to satisfy are shown below:

[0102]

[0103] Where, 0 < δ i <1, Ω is the boundary parameter for flexibility performance. 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) represents the correction term provided by the adaptive system, which will be used for subsequent design in S3.2;

[0104] The initial conditions for the flexibility performance constraints 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 the drain valve 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] Where, ω l,i ω u,i ω 1,i and ω 2,iThe state of the adaptive system; h 1,i >0, h 2,i >0 represents the adaptive system parameter; operator f + =max{f,0};τ w This is a normal number, representing the threshold for detecting flow interference in the drain valve;

[0115] r i (x) is a system function, with the following specific form:

[0116]

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

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

[0119] S4.1. Based on the established error kinetic equations of the proton exchange membrane fuel cell hydrogen supply system and the error conversion of flexible performance, design a virtual control law. The control laws u1 and u2 are as follows:

[0120]

[0121] Where 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 at the same time prove that the system's hydrogen ratio and anode pressure error satisfy the flexibility performance constraints;

[0123] Select the following Lyapunov candidate functions:

[0124]

[0125] Taking the derivative with respect to V, we find that when the initial value constraints are satisfied, This indicates 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 boundaries.

[0126] To verify the effectiveness of the flexible performance control method for the proton exchange membrane fuel cell hydrogen supply system provided in this embodiment, MATLAB was used for simulation experiments, which are described in detail below.

[0127] Selecting adaptive system parameters h 1,i=5, h 2,i =10, flexibility 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. Through simulation verification of the control strategy proposed in this invention, the results are obtained. Figure 3-Figure 6 ;

[0128] in, Figure 3 , Figure 4 The diagram shows the curves of hydrogen permeate ratio error and anode pressure error in the flexible performance control method of a proton exchange membrane fuel cell hydrogen supply system. Figure 5 , Figure 6 The diagram shows the stack current and drain valve opening curves in the flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system. 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 a 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 intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for flexible performance control of a proton exchange membrane fuel cell hydrogen supply system, characterized in that, Includes the following steps: S1. Based on gas dynamics and motor speed equations, construct control-oriented dynamic models for the components of the proton exchange membrane fuel cell hydrogen supply system. S2. Establish error kinetic models for the system's hydrogen permeation ratio and anode pressure; S3. Based on the error dynamics model of the system, an adaptive system for detecting flow disturbance of the drain valve is established. By introducing the correction signal of the adaptive system, a flexible performance function is designed to convert the tracking errors of hydrogen ratio and anode pressure. S4. Design a push-back controller, select an appropriate Lyapunov function to prove the stability of the system, and prove that the system's hydrogen ratio and anode pressure tracking error satisfy the flexibility performance constraints. In step S1, the kinetic model of the proton exchange membrane fuel cell hydrogen supply system is as follows: ， in, The speed of the circulating pump. For the total pressure of the gas supply manifold, To provide hydrogen partial pressure in the gas supply manifold, The total pressure of the anode flow field is... The hydrogen partial pressure in the anolyte flow field. To return the total manifold pressure, To return the partial pressure of hydrogen in the manifold; and These are the gas output flow rate leaving the circulating pump and the maximum proportional valve output flow rate, respectively. For fuel cell current interference, The interference is due to the flow rate of the drain valve, and all of these are known system interferences. , , These represent the mass fraction of hydrogen in the supply manifold, the anode flow field, and the return manifold, respectively. , , These represent the mass ratios of hydrogen in the supply manifold, anode flow field, and return manifold, respectively. This is the voltage of the circulating pump. This refers to the proportional valve opening. These are system parameters, specifically expressed as follows: ， in, For the mechanical efficiency of the circulating pump, For motor coefficients, The moment of inertia of the circulating pump. For the circulating pump coefficient, For the specific heat capacity of the circulating pump, For the temperature of the circulating pump, For the heat ratio of the circulating pump, The gas constant is For the gas supply manifold temperature, For the gas supply manifold flow coefficient, For the volume of the gas supply manifold, The molar mass of hydrogen gas is... The temperature of the anode flow field is... For the anode flow field volume, The flow coefficient of the anode flow field is... For stack number, The water purification coefficient is... The molar mass of water vapor. It is Faraday's constant. To return the manifold temperature, To return the manifold flow coefficient, To return the manifold volume; The system's control objective is the total pressure of the anode flow field. and hydrogen peroxide ratio hydrogen peroxide ratio The expression is as follows: ， in, These are system parameters, expressed as follows: 。 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 S2, the error dynamics model is established as follows: Define the error variable: ， ， ， ， in, To achieve the desired hydrogen peroxide ratio, The desired pressure for the anode flow field; and For virtual control laws; The dynamic equation for the error variable is established as follows: ， in, , It is a smooth, non-singular system function within the feasible region. , It is a smooth nonlinear function within the feasible region, specifically expressed as follows: ， ， ， ， in, 。 3. The flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system according to claim 2, characterized in that, Step S3 includes: S3.1 Establish flexible performance constraints, convert the hydrogen ratio and anode pressure tracking error, and introduce the following preset performance function: ， in, ; , and The preset performance function parameters are all positive values, satisfying the following: ; The constraints that the tracking error needs to satisfy are shown below: ， in, , These are the boundary parameters for flexible performance; , , and Correction terms provided for adaptive systems; The initial conditions for the flexibility performance constraints are as follows: ， The error constraint is further transformed into: ； S3.2, Establish an adaptive system for detecting flow disturbances in the drain valve as follows: ， ， ， ， ， ， ， ， in, , , and The state of the adaptive system; , For adaptive system parameters; operators ; The threshold representing the detection of flow disturbances in the drain valve; It is a system function, and its specific form is as follows: ， 。 4. The flexible performance control method for a proton exchange membrane fuel cell hydrogen supply system according to claim 3, characterized in that, Step S4 includes: S4.

1. Based on the established error kinetic equations of the proton exchange membrane fuel cell hydrogen supply system and the error conversion of flexible performance, design a virtual control law. , and control laws , as follows: ， ， in, , , and For controller parameters; S4.2 Based on the error system model, select an appropriate Lyapunov function to prove the stability of the system, and at the same time prove that the system's hydrogen ratio and anode pressure error satisfy the flexibility performance constraints. Select the following Lyapunov candidate functions: ， right After differentiation, when the initial value constraints are satisfied, Tracking error , , and It is 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 boundaries.

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