A multivariable high-coupling hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells

Abstract

This invention discloses a multivariable, highly coupled hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells, comprising the following steps: S1, establishing a nonlinear high-order system model with flow rate and pressure coupling based on the cathode and anode gas dynamic equations of the fuel cell system; S2, designing a multivariable coordinated backstepping controller with the excess oxygen ratio, excess hydrogen ratio, and anode-cathode pressure difference as control objectives; S3, considering the influence of load changes and model uncertainties on the hydrogen-oxygen dual loop, introducing an adaptive control method and designing control commands for the air compressor, circulating pump, and solenoid valve; S4, selecting a suitable Lyapunov function to prove the stability of the system and completing the adaptive backstepping control of the anode-cathode pressure difference and gas flow rate; This invention solves the problem of multivariable, highly coupled coordinated control of the hydrogen-oxygen dual loop in fuel cells, and can maintain the transient and steady-state performance of the system under sudden load changes, improving the safety and reliability of system operation.

Description

Technical Field

[0001] This invention relates to the field of fuel cell technology, and more specifically, to a multivariable, highly coupled hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells. Background Art

[0002] Proton exchange membrane fuel cells (PEMFCs), as a highly efficient and clean energy technology, meet society's urgent need for zero-emission energy. Their system composition is as follows: Figure 1 As shown. Especially in the aerospace and transportation fields, PEMFCs are applied to unmanned aerial vehicles (UAVs), underwater vehicles (UVs), and lightweight traction systems, offering longer range and higher energy density compared to lithium-ion batteries. PEMFCs are characterized by high energy conversion efficiency and environmental friendliness; their chemical reaction produces only water, eliminating greenhouse gas emissions. These characteristics make them a key technology for achieving carbon neutrality. A PEMFC system integrates four interdependent subsystems: hydrogen and oxygen supply management, thermal management, water management, and power management. These subsystems are strongly interdependent. Therefore, the entire system faces the challenge of strong multivariate coupling; the dynamic interactions of airflow, pressure, humidity, temperature, and current are highly nonlinear, and any imbalance among these variables can lead to performance degradation or system instability. Solving this problem requires designing efficient multivariate coordinated control strategies to optimize the matching of gas flow and pressure dynamics, thereby improving fuel cell efficiency.

[0003] Based on the above analysis, there is already a wealth of literature on PEMFC systems both domestically and internationally. However, research using the anode-cathode pressure difference as the control objective still has limitations, and the decoupling and coordinated control of multivariable high-order nonlinear models urgently needs to be addressed. Therefore, this invention proposes a multivariable, highly coupled hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells. This method effectively solves the problem of severe pressure fluctuations across the proton exchange membrane when the load changes, avoids membrane damage caused by mechanical stress, and thus significantly improves operational safety and reliability. Summary of the Invention

[0004] The purpose of this invention is to provide a multivariable, highly coupled hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells, which solves the problem of severe pressure fluctuations on both sides of the proton exchange membrane when the load changes.

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

[0006] A multivariable, highly coupled hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells, characterized by the following steps:

[0007] S1. Based on the gas dynamic equations of the cathode and anode of the fuel cell system, establish a nonlinear high-order system model that couples flow rate and pressure.

[0008] S2. Using the oxygen ratio, hydrogen ratio and anode-cathode pressure difference as control targets, design a multivariable coordinated backstepping controller.

[0009] S3. Considering the impact of load changes and model uncertainties on the hydrogen-oxygen dual loop, an adaptive control method is introduced and control commands for the air compressor, circulating pump and solenoid valve are designed.

[0010] S4. Select a suitable Lyapunov function to verify the stability of the fuel cell system and complete the adaptive backstepping control of the anode-cathode pressure difference and gas flow.

[0011] Furthermore, step S1 specifically includes:

[0012] Establish information about the cathode field pressure P ca Oxygen supply manifold pressure air compressor angular speed Ω acp Circulating pump angular speed Ω hcp Hydrogen supply manifold pressure Anode field pressure P an and the return manifold pressure P rm Nonlinear high-order system model:

[0013]

[0014] in, For system state variables, For x i The first derivative, I st For the fuel cell load current, u acp The input voltage for the air compressor, u hcp α is the input voltage for the circulating pump. sv W is the solenoid valve opening control command. acp (x2, x3) represents the air compressor outlet gas flow rate, W hcp (x4, x5, x7) represents the outlet gas flow rate of the air compressor, W sv W represents the maximum gas flow rate at the outlet of the solenoid valve. purge k is the outlet flow rate of the drain valve. an The anode inlet flow coefficient is... The flow coefficient M at the inlet of the hydrogen supply manifold s M a and M r These represent the average molar mass fractions of the mixed gas in the hydrogen supply manifold, anode field, and return manifold, respectively. i (i = 1, ..., 21) are the parameters of the nonlinear high-order system model;

[0015] When the parameters of the air compressor and circulating pump motor change, or when there is gas leakage from the manifold, the output flow rate will change. Therefore, the nonlinear high-order system model has uncertainties, as detailed below:

[0016]

[0017] in, and ΔW1 and ΔW2 are the changes in the parameters of the air compressor and circulating pump motors, respectively, and the changes in the output flow rates of the air compressor and circulating pump when gas leaks from the manifold, respectively.

[0018] Further, step S2 includes the following sub-steps:

[0019] S2.1. Using the excess oxygen ratio as the control target of the oxygen circuit, and based on the dynamic characteristics of the oxygen supply system, the oxygen circuit error equation is constructed as follows:

[0020]

[0021] in, and These are the superoxygen ratio and the reference superoxygen ratio, respectively, with e1 representing the superoxygen ratio tracking error. and To track the first and second derivatives of the error e1, Due to the uncertainty of air compressors, f is a function that includes the uncertainties of the air compressor and the state variable x. 1,i and g 1,i (i = 1, 2) is the positive smooth system function, specifically represented as follows:

[0022]

[0023] in, Let x1 be the second derivative of the state variable. and For reference peroxy ratio The first and second derivatives, For W acp The partial derivative with respect to x2, For W acp Partial derivative with respect to x3;

[0024] S2.2. Using the pressure difference between the anode and cathode and the hydrogen overload ratio as the control targets for this part, and based on the dynamic characteristics of the hydrogen supply system, the hydrogen loop error equation is constructed as follows:

[0025]

[0026] Where, ΔP=Pan -P ca and ΔP * These are the pressure difference between the anode and cathode and the reference pressure difference, respectively. and These represent the hydrogen excess ratio and the reference hydrogen excess ratio, respectively; e2 is the pressure difference tracking error; e3 is the oxygen excess ratio tracking error; α = M s (x5-x6) is an intermediate variable. Due to the uncertainty of the circulating pump, for Control input α sv The coupling term with the state variable x, The derivative of the coupling term, Let x be a function that includes the uncertainty of the circulating pump and the state variable x. and For tracking error e i The first and second derivatives; f i,j and g i,j (j=1,2) is the positive smooth system function, specifically represented as follows:

[0027]

[0028] Where, m s The mass fraction of hydrogen in the hydrogen supply manifold. and For m s The first and second partial derivatives with respect to x5, For M s The first-order partial derivative with respect to x5, For M a The first-order partial derivative with respect to x6, For M r The first-order partial derivative with respect to x7, and For the first and second derivatives of the reference pressure difference ΔP, and For reference hydrogen ratio The first and second derivatives, For W hcp The partial derivative with respect to x4, For W hcp The partial derivative with respect to x5, For W hcp The partial derivative with respect to x7.

[0029] Furthermore, step S3 includes the following sub-steps:

[0030] S3.1 Construct the following virtual control law based on the backstepping method:

[0031]

[0032] in, α * and Corresponding to control input W acp α sv and W hcp The virtual control law, k i,1 >0 represents the control gain to be designed, i = 1, 2, 3;

[0033] S3.2. Make an upper bound estimate for the uncertainties of the air compressor and circulating pump:

[0034]

[0035] Where θ1 and θ2 are uncertain parameters, and sup(·) is the upper bound of the uncertainty of the air compressor and the circulating pump;

[0036] S3.3, The design adaptive law is as follows:

[0037]

[0038] Where z1 and z3 are error variables, and ε1 and ε2 are auxiliary variables. For θ i The estimated quantity, for The derivative of the scalar ψ i >0, σ i >0 represents the adaptive control gain to be designed, i = 1, 2;

[0039] S3.4 Based on the above steps, design the control commands for the air compressor, solenoid valve, and circulating pump:

[0040]

[0041] in, and Corresponding to virtual control laws α * and The derivative of S k (k = 1, ..., 4) represents intermediate computational quantities, z i k is the error variable. i,2 >0 represents the control gain to be designed, i = 1, 2, 3.

[0042] Furthermore, step S4 includes the following sub-steps:

[0043] S4.1. Regarding the oxygen ratio tracking error e1, the following Lyapunov candidate function is selected, and the derivative is obtained:

[0044]

[0045] in, To estimate the error, scaling is performed according to Young's inequality. get:

[0046]

[0047] in, For positive integers, For the residual term, γ1 > 0 is a positive design constant. According to Russell's invariance theorem, the oxygen ratio tracking error e1 can converge to an arbitrarily small residual set, and all signals are uniformly bounded, i.e., the oxygen ratio... It can track a given reference signal;

[0048] S4.2. For the differential pressure tracking error e2, the following Lyapunov candidate function is selected, and the derivative is obtained:

[0049]

[0050] This reveals that when the gain k 2,1 ,k 2,2 When >0, This indicates that the differential pressure tracking error e2 can converge to zero and is globally asymptotically stable, meaning that the differential pressure between the anode and cathode can track a given reference signal.

[0051] S4.3. Regarding the hydrogen ratio tracking error e3, the following Lyapunov candidate function is selected, and the derivative is obtained:

[0052]

[0053] in, To estimate the error, scaling is performed according to Young's inequality. get:

[0054]

[0055] in, For positive integers, For the residual term, γ2 > 0 is a positive design constant. According to Russell's invariance theorem, the hydrogen over-ratio tracking error e3 can converge to an arbitrarily small residual set, and all signals are uniformly bounded, i.e., the hydrogen over-ratio... It can track a given reference signal.

[0056] The beneficial effects of this invention are as follows:

[0057] 1. To address the nonlinear strong coupling between gas flow rate and pressure in proton exchange membrane fuel cell systems, a multi-input multi-output nonlinear dynamic model was established. This model overcomes the limitations of traditional methods in handling nonlinear coupling relationships, effectively solves the control deviation problem caused by insufficient decoupling, and significantly improves the control accuracy of the system.

[0058] 2. Considering the pressure difference between the cathode and anode as the control target, the gas flow rate is adjusted in real time to suppress pressure fluctuations across the membrane, effectively preventing membrane rupture caused by excessive pressure difference fluctuations, and improving the operational safety and reliability of the fuel cell system.

[0059] 3. Compared with general linearization techniques, adaptive compensation is used to handle the model uncertainties of air compressor and circulating pump, reducing model errors caused by parameter fitting and modeling of air compressor and circulating pump, and improving the accuracy of the control system. Attached Figure Description

[0060] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings:

[0061] Figure 1 A system composition diagram of an existing proton exchange membrane fuel cell is shown.

[0062] Figure 2 A flowchart is shown for a multivariable, highly coupled hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells.

[0063] Figure 3 A schematic diagram of the load current request according to an embodiment of the present invention is shown.

[0064] Figure 4 The graph shows the performance results of the oxygen ratio tracking in an embodiment of the present invention.

[0065] Figure 5 The diagram shows the tracking performance results of the pressure difference between the anode and cathode in an embodiment of the present invention.

[0066] Figure 6 The graph shows the hydrogen peroxide ratio tracking performance results of an embodiment of the present invention. Detailed Implementation

[0067] 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.

[0068] like Figure 1As shown, the system components of a proton exchange membrane fuel cell include: a hydrogen tank, a solenoid valve, a supply manifold, an anode field, a return manifold, a circulation pump, a drain valve, an air compressor, and a cathode field. The hydrogen tank stores hydrogen; the solenoid valve controls the on / off flow and flow regulation of hydrogen; the supply manifold distributes gas to the anode and cathode flow fields; the anode field guides hydrogen to flow uniformly through the catalyst bed; the return manifold collects unreacted gas for recycling or direct venting to the atmosphere; the circulation pump drives the hydrogen circulation flow on the anode side; the drain valve discharges water generated during the reaction; the air compressor provides oxygen to the cathode side; and the cathode field guides oxygen to flow uniformly through the catalyst bed.

[0069] The multivariable, highly coupled hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells provided in this embodiment achieves efficient and stable operation of the hydrogen-oxygen fuel cell system under complex operating conditions, such as... Figure 2 As shown, the control method includes the following steps:

[0070] S1. Based on the gas dynamic equations of the cathode and anode of the fuel cell system, establish a nonlinear high-order system model that couples flow rate and pressure.

[0071] S2. Using the oxygen ratio, hydrogen ratio and anode-cathode pressure difference as control targets, design a multivariable coordinated backstepping controller.

[0072] S3. Considering the impact of load changes and model uncertainties on the hydrogen-oxygen dual loop, an adaptive control method is introduced and control commands for the air compressor, circulating pump and solenoid valve are designed.

[0073] S4. Select a suitable Lyapunov function to prove the stability of the system and complete the adaptive backstepping control of the anode-cathode pressure difference and gas flow rate.

[0074] Specifically, step S1 includes:

[0075] Establish information about the cathode field pressure P ca Oxygen supply manifold pressure air compressor angular speed Ω acp Circulating pump angular speed Ω hcp Hydrogen supply manifold pressure Anode field pressure P an and the return manifold pressure P rm Nonlinear high-order system model:

[0076]

[0077] Assumptions: Neglecting changes in water vapor during the fuel cell reaction, with saturation pressure P sat Replaces the partial pressure of water vapor; among which, For system state variables, For x iThe first derivative, I st For the fuel cell load current, u acp The input voltage for the air compressor, u hcp α is the input voltage for the circulating pump. sv W is the solenoid valve opening control command. acp (x2, x3) represents the air compressor outlet gas flow rate, W hcp (x4, x5, x7) represents the outlet gas flow rate of the air compressor, W sv W represents the maximum gas flow rate at the outlet of the solenoid valve. purge k is the outlet flow rate of the drain valve. an The anode inlet flow coefficient is... The flow coefficient M at the inlet of the hydrogen supply manifold s M a and M r These represent the average molar mass fractions of the mixed gas in the hydrogen supply manifold, anode field, and return manifold, respectively. i (i = 1, ..., 21) are the parameters of the nonlinear high-order system model;

[0078] As crucial driving structures in the hydrogen-oxygen dual-loop system, the air compressor and circulating pump experience changes in output flow rate due to aging and frictional wear of their mechanical components, as well as variations in motor parameters and manifold leaks. Therefore, the nonlinear high-order system model exhibits uncertainties, as detailed below:

[0079]

[0080] in, and ΔW1 and ΔW2 are the changes in the parameters of the air compressor and circulating pump motors, respectively, and the changes in the output flow rates of the air compressor and circulating pump when gas leaks from the manifold, respectively.

[0081] Step S2 further includes the following sub-steps:

[0082] S2.1. Using the excess oxygen ratio as the control target of the oxygen circuit, and based on the dynamic characteristics of the oxygen supply system, the oxygen circuit error equation is constructed as follows:

[0083]

[0084] in, and These are the superoxygen ratio and the reference superoxygen ratio, respectively, with e1 representing the superoxygen ratio tracking error. and To track the first and second derivatives of the error e1, Due to the uncertainty of air compressors, f is a function that includes the uncertainties of the air compressor and the state variable x.1,i and g 1,i (i = 1, 2) is the positive smooth system function, specifically represented as follows:

[0085]

[0086] in, Let x1 be the second derivative of the state variable. and For reference peroxy ratio The first and second derivatives, For W acp The partial derivative with respect to x2, For W acp Partial derivative with respect to x3;

[0087] S2.2. Using the pressure difference between the anode and cathode and the hydrogen overload ratio as the control targets for this part, and based on the dynamic characteristics of the hydrogen supply system, the hydrogen loop error equation is constructed as follows:

[0088]

[0089] Where, ΔP=P an -P ca and ΔP * These are the pressure difference between the anode and cathode and the reference pressure difference, respectively. and These represent the hydrogen excess ratio and the reference hydrogen excess ratio, respectively; e2 is the pressure difference tracking error; e3 is the oxygen excess ratio tracking error; α = M s (x5-x6) is an intermediate variable. Due to the uncertainty of the circulating pump, for Control input α sv The coupling term with the state variable x, The derivative of the coupling term, Let x be a function that includes the uncertainty of the circulating pump and the state variable x. and For tracking error e i The first and second derivatives; f i,j and g i,j (j=1,2) is the positive smooth system function, specifically represented as follows:

[0090]

[0091] Where, m s The mass fraction of hydrogen in the hydrogen supply manifold. and For m s The first and second partial derivatives with respect to x5, For Ms The first-order partial derivative with respect to x5, For M a The first-order partial derivative with respect to x6, For M r The first-order partial derivative with respect to x7, and For the first and second derivatives of the reference pressure difference ΔP, and For reference hydrogen ratio The first and second derivatives, For W hcp The partial derivative with respect to x4, For W hcp The partial derivative with respect to x5, For W hcp The partial derivative with respect to x7.

[0092] Step S3 further includes the following sub-steps:

[0093] S3.1 Construct the following virtual control law based on the backstepping method:

[0094]

[0095] in, α * and Corresponding to control input W acp α sv and W hcp The virtual control law, k i,1 >0 represents the control gain to be designed, i = 1, 2, 3;

[0096] S3.2. Make an upper bound estimate for the model uncertainty:

[0097]

[0098] Where θ1 and θ2 are uncertain parameters, and sup(·) is the upper bound of the uncertainty of the air compressor and the circulating pump;

[0099] S3.3, The design adaptive law is as follows:

[0100]

[0101] Where z1 and z3 are error variables, and ε1 and ε2 are auxiliary variables. For θ i The estimated quantity, for The derivative of the scalar ψ i >0, σ i >0 represents the adaptive control gain to be designed, i = 1, 2;

[0102] S3.4 Based on the above steps, design the control commands for the air compressor, solenoid valve, and circulating pump:

[0103]

[0104] in, and Corresponding to virtual control laws α * and The derivative of

[0105] S k (k = 1, ..., 4) represents intermediate computational quantities, z i k is the error variable. i,2 >0 represents the control gain to be designed, i = 1, 2, 3.

[0106] Step S4 further includes the following sub-steps:

[0107] S4.1. For the oxygen ratio tracking error e1, the following Lyapunov candidate function is selected, and the derivative is obtained:

[0108]

[0109] in, To estimate the error, scaling is performed according to Young's inequality. get:

[0110]

[0111] in, For positive integers, For the residual term, γ1 > 0 is a positive design constant. According to Russell's invariance theorem, the oxygen ratio tracking error e1 can converge to an arbitrarily small residual set, and all signals are uniformly bounded, i.e., the oxygen ratio... It can track a given reference signal;

[0112] S4.2. For the differential pressure tracking error e2, the following Lyapunov candidate function is selected, and the derivative is obtained:

[0113]

[0114] This reveals that when the gain k 2,1 ,k 2,2 When >0, This indicates that the differential pressure tracking error e2 can converge to zero and is globally asymptotically stable, meaning that the differential pressure between the anode and cathode can track a given reference signal.

[0115] S4.3. Regarding the hydrogen ratio tracking error e3, the following Lyapunov candidate function is selected, and the derivative is obtained:

[0116]

[0117] in, To estimate the error, scaling is performed according to Young's inequality. get:

[0118]

[0119] in, For positive integers, For the residual term, γ2 > 0 is a positive design constant. According to Russell's invariance theorem, the hydrogen over-ratio tracking error e3 can converge to an arbitrarily small residual set, and all signals are uniformly bounded, i.e., the hydrogen over-ratio... It can track a given reference signal.

[0120] Example:

[0121] This embodiment takes a fuel cell oxygen and hydrogen supply system as an example and uses MATLAB for simulation experiments to verify the results. Considering the impact of load current changes and model uncertainties on the hydrogen-oxygen dual loop in actual operation, a multivariable highly coupled hydrogen-oxygen dual loop coordinated control method for hydrogen fuel cells is designed to ensure the reliability and safety of the hydrogen-oxygen fuel cell system under complex operating conditions.

[0122] To verify the effectiveness of the control method in this embodiment, the specific steps are as follows:

[0123] The first step involves establishing a high-order nonlinear system model that couples flow rate and pressure, based on the cathode and anode gas dynamic equations of the fuel cell system and the dynamic variation laws of key components such as the air compressor, circulating pump, and return manifold. Specific model parameters are shown in Table 1.

[0124] Table 1

[0125]

[0126] The second step is to determine the reference signal based on the control requirements of the PEMFC system for the oxygen ratio, hydrogen ratio, and anode-cathode voltage difference. and ΔP * =20kPa, define tracking error e i (i = 1, 2, 3), design a multivariable coordinated backstepping controller;

[0127] The third step is to use boundary estimation to determine the upper bound of the model uncertainty and design an adaptive control strategy. To compensate for its effects, a virtual control law is constructed based on the established multi-input multi-output nonlinear high-order system model. α * and Design control commands for air compressors, solenoid valves, and circulating pumps. acp α sv and

[0128] The fourth step involves using an adaptive estimation method to compensate for uncertainties based on the nonlinear high-order system model designed in the previous steps. The control law is then designed by recursion using the backstepping method. Taking into account the impact of load changes and uncertainties in the nonlinear high-order system model on the control accuracy of the hydrogen and oxygen supply system, a suitable Lyapunov function is selected to prove the stability of the system. Finally, the adaptive backstepping control of the anode-cathode pressure difference and gas flow rate is completed.

[0129] Based on the above parameters and the specific steps of the embodiments, the proposed multivariable highly coupled hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells was simulated and verified. Figure 3 , Figure 4 , Figure 5 and Figure 6 ;in, Figure 3 This diagram illustrates the changes in the load current request of a hydrogen-oxygen fuel cell. Figure 4 This diagram illustrates the performance results of the hydrogen-oxygen fuel cell over-oxygen ratio tracking. Figure 5 This diagram illustrates the performance of the pressure difference tracking between the anode and cathode of a hydrogen-oxygen fuel cell. Figure 6 A schematic diagram showing the hydrogen-to-oxygen ratio tracking performance results of a hydrogen-oxygen fuel cell is displayed. (Based on simulation illustration) Figure 3-6 It can be seen that the proposed multivariable, highly coupled hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells achieves simultaneous adjustment of multiple variables through nonlinear decoupling and employs an adaptive method to address model uncertainties. This method effectively suppresses excessive pressure fluctuations across the membrane and prevents membrane damage caused by mechanical stress, thereby significantly improving operational safety and reliability, and exhibiting excellent transient and steady-state performance.

[0130] The above analysis demonstrates the effectiveness of the multivariable, highly coupled hydrogen-oxygen dual-loop coordinated control method for hydrogen fuel cells provided in this embodiment.

[0131] 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 multivariable, highly coupled hydrogen-oxygen dual-loop coordinated control method for a hydrogen fuel cell, characterized in that, Includes the following steps: S1. Based on the gas dynamic equations of the cathode and anode of the fuel cell system, establish a nonlinear high-order system model that couples flow rate and pressure. S2. Using the oxygen ratio, hydrogen ratio and anode-cathode pressure difference as control targets, design a multivariable coordinated backstepping controller. S3. Considering the impact of load changes and model uncertainties on the hydrogen-oxygen dual loop, an adaptive control method is introduced and control commands for the air compressor, circulating pump and solenoid valve are designed. S4. Select an appropriate Lyapunov function to verify the stability of the fuel cell system and complete the adaptive backstepping control of the anode-cathode pressure difference and gas flow rate. Step S1 specifically includes: Establish information about cathode field pressure Oxygen supply manifold pressure Air compressor angular speed Circulating pump angular speed Hydrogen supply manifold pressure Anode field pressure and return manifold pressure Nonlinear high-order system model: ， in, For system state variables, for The first derivative, This is the load current of the fuel cell. This is the input voltage for the air compressor. Input voltage for the circulating pump, This is a control command for the opening degree of the solenoid valve. This refers to the outlet gas flow rate of the air compressor. This refers to the gas flow rate at the outlet of the circulating pump. This represents the maximum gas flow rate at the solenoid valve outlet. This refers to the outlet flow rate of the drain valve. The anode inlet flow coefficient is... The flow coefficient at the inlet of the hydrogen supply manifold. and These represent the average molar mass fraction of the mixed gas in the hydrogen supply manifold, anode field, and return manifold, respectively. These are the parameters for a nonlinear high-order system model. When the parameters of the air compressor and circulating pump motor change, or when there is gas leakage from the manifold, the output flow rate will change. Therefore, the nonlinear high-order system model has uncertainties, as detailed below: ， in, and These are the changes in parameters for the air compressor and circulating pump motors, respectively. and These represent the changes in output flow rates of the air compressor and circulating pump when gas leaks from the manifold.

2. The method for coordinated control of a multivariable highly coupled hydrogen-oxygen dual-loop system in a hydrogen fuel cell according to claim 1, characterized in that, Step S2 includes the following sub-steps: S2.

1. Using the excess oxygen ratio as the control target of the oxygen circuit, and based on the dynamic characteristics of the oxygen supply system, the oxygen circuit error equation is constructed as follows: ， in, and These are the superoxide ratio and the reference superoxide ratio, respectively. To account for the error in the oxygen ratio tracking, and For tracking error The first and second derivatives, Due to the uncertainty of air compressors, For air compressor uncertainties and state variables The function, and For a positive smooth system function, the specific representation is as follows: ， in, State variables The second derivative, and For reference peroxy ratio The first and second derivatives, for right The partial derivatives, for right The partial derivatives; S2.

2. Using the pressure difference between the anode and cathode and the hydrogen overload ratio as the control targets for this part, and based on the dynamic characteristics of the hydrogen supply system, the hydrogen loop error equation is constructed as follows: ， in, and These are the pressure difference between the anode and cathode and the reference pressure difference, respectively. and These are the hydrogen permeation ratio and the reference hydrogen permeation ratio, respectively. For differential pressure tracking error, To account for the error in the oxygen ratio tracking, As an intermediate variable, Due to the uncertainty of the circulating pump, for Central control input With state variables Coupling terms, The derivative of the coupling term, For including uncertainties and state variables of circulating pumps The function, and For tracking error The first and second derivatives; and For a positive smooth system function, the specific representation is as follows: ， in, The mass fraction of hydrogen in the hydrogen supply manifold. and for right The first and second partial derivatives, for right The first-order partial derivative, for right The first-order partial derivative, for right The first-order partial derivative, and Reference pressure difference The first and second derivatives, and For reference hydrogen ratio The first and second derivatives, for right The partial derivatives, for right The partial derivatives, for right The partial derivatives of .

3. The method for coordinated control of a multivariable highly coupled hydrogen-oxygen dual-loop system in a hydrogen fuel cell according to claim 2, characterized in that, Step S3 includes the following sub-steps: S3.1 Construct the following virtual control law based on the backstepping method: ， in, and Corresponding to control inputs, Virtual control law, For the control gain to be designed, ; S3.

2. Make an upper bound estimate for the uncertainties of the air compressor and circulating pump: ， in, For uncertain parameters, For the upper bound of the uncertainty of air compressors and circulating pumps; S3.3, The design adaptive law is as follows: ， in, For error variables, As an auxiliary variable, The estimated quantity, The derivative of the scalar The adaptive control gain to be designed, ; S3.4 Based on the above steps, design the control commands for the air compressor, solenoid valve, and circulating pump: ， in, Corresponding to virtual control laws, The derivative of This is for intermediate calculations. For error variables, For the control gain to be designed, .

4. The method for coordinated control of a multivariable highly coupled hydrogen-oxygen dual-loop system in a hydrogen fuel cell according to claim 3, characterized in that, Step S4 includes the following sub-steps: S4.1, Regarding the tracking error of the oxygen ratio Choosing the following Lyapunov candidate function and then taking the derivative, we get: ， in, To estimate the error, scaling is performed according to Young's inequality. ,get: ， in, For positive integers, For the residual term, As a positive design constant, according to Russell's invariance theorem, the oxygen ratio tracking error... It can converge to arbitrarily small residual sets, and all signals are uniformly bounded, i.e., the superoxide ratio. It can track a given reference signal; S4.2, Regarding differential pressure tracking error Choosing the following Lyapunov candidate function and then taking the derivative, we get: ， This reveals that when the gain hour, This indicates a pressure differential tracking error. It can converge to zero and is globally asymptotically stable, meaning that the pressure difference between the anode and cathode can track a given reference signal; S4.3, Regarding the tracking error of the hydrogen ratio Choosing the following Lyapunov candidate function and then taking the derivative, we get: ， in, To estimate the error, scaling is performed according to Young's inequality. ,get: ， in, For positive integers, For the residual term, As a positive design constant, according to Russell's invariance theorem, the hydrogen ratio tracking error... It can converge to arbitrarily small residual sets, and all signals are uniformly bounded, i.e., the hydrogen permeability ratio. It can track a given reference signal.

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