Method for decoupling control of air supply system of proton exchange membrane fuel cell

Abstract

The invention discloses a decoupling control method for an air supply system of a proton exchange membrane fuel cell. Comprising five parts of establishing a galvanic pile model and an air supply system model, determining a control target, designing an extended state observer-fractional order proportional-integral-derivative controller, and optimizing control parameters. With net power and system efficiency as targets, a Pareto solution set is obtained through a non-dominated sorting genetic algorithm, and target peroxide ratios and cathode pressures under different load currents are determined in combination with a TOPSIS algorithm. A fractional order operator is introduced to expand PID parameters, internal and external disturbance and coupling interference are compensated through an expansion state observer, and finally an integral time absolute error is used as a fitness function. Cooperative optimization of five parameters is realized by using a balance optimizer algorithm, and dual-channel independent decoupling control of the peroxide ratio and the cathode pressure is achieved. Compared with the current PID and FOPID, the control strategy provided by the invention obviously improves the net output power and the energy conversion efficiency of the PEMFC system.

Description

Technical Field

[0001] This invention belongs to the field of fuel cell technology, specifically relating to a method for decoupling control of an air supply system for a proton exchange membrane fuel cell. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs) have become a core research direction for new energy vehicle power systems due to their significant advantages of zero carbon emissions, low noise pollution, and high energy conversion efficiency. The cathode air supply system, as the core subsystem maintaining the electrochemical reaction, determines the fuel cell's output power density and overall energy efficiency through its dynamic characteristics. The excess oxygen ratio and cathode pressure are key control parameters of the air supply system. An excessively low excess oxygen ratio leads to cathode hypoxia, causing a sudden drop in battery voltage or even irreversible damage; an excessively high excess oxygen ratio increases the parasitic power of the air compressor, reducing the system's net output efficiency; and inappropriate cathode pressure slows down the electrochemical reaction rate and may also damage the proton exchange membrane, shortening the battery's lifespan.

[0003] In actual vehicle operating conditions, drastic fluctuations in load current lead to rapid changes in cathode air intake demand, while PEMFC air supply systems exhibit typical nonlinear characteristics. A strong coupling exists between the excess oxygen ratio and cathode pressure, making simultaneous and precise adjustment difficult, which becomes a core issue restricting the system's efficient operation. Currently, while third-, fourth-, and fifth-order lumped parameter models have been proposed for PEMFC air supply systems, these models neglect key factors such as multiphase transport and coupled changes in gas temperature and humidity during simplification. This results in significant deviations between the model's prediction accuracy and the dynamic response of the actual system, severely hindering the development and application of advanced control strategies.

[0004] Regarding control strategies, existing technologies have proposed various methods such as linearized input-output sliding mode control, deep reinforcement learning, and PID neural networks (proportional-integral-derivative control). While these methods have improved control performance to some extent, the complexity of these control strategies consumes significant computing power in the actual controllers of fuel cell vehicles, making them difficult to adapt to the real-time requirements of on-board scenarios. Currently, PID control, widely used in industrial applications, suffers from problems such as large overshoot, slow adjustment speed, and insufficient steady-state accuracy when facing the strong nonlinearity and strong coupling characteristics of PEMFC air supply systems due to fixed parameter adjustments. Although single fractional-order PID (FOPID) improves parameter adjustment flexibility by extending the integral and derivative orders, it cannot effectively compensate for internal and external disturbances and coupling interference, and its control effect still needs improvement.

[0005] In summary, current technology has not yet solved the technical challenges of high-precision modeling of PEMFC air supply systems, decoupling and adjusting coupled parameters, and balancing the accuracy and flexibility of control strategies. There is an urgent need for a decoupled control method for PEMFC air supply systems that can adapt to dynamic load conditions. This method would involve constructing a high-precision mechanistic model, determining the optimal control objective, and designing an efficient decoupled control strategy to achieve precise, rapid, and stable control of the oxygen ratio and cathode pressure, thereby improving the net output power and energy conversion efficiency of the PEMFC system. Summary of the Invention

[0006] The purpose of this invention is to address the technical problems of low modeling accuracy, strong coupling between oxygen ratio and cathode pressure, poor dynamic response of traditional control strategies, and inability to effectively compensate for disturbances in current PEMFC air supply systems, by providing a decoupled control method for proton exchange membrane fuel cell air supply systems.

[0007] This invention provides a precise foundation for control strategies by constructing a high-precision multiphysics mechanism model. A multi-objective optimization algorithm determines the optimal oxygen ratio and cathode pressure control targets under different load currents, balancing system net power and efficiency. By designing an ESO-FOPID decoupled control architecture and combining it with a balanced optimizer algorithm, optimal tuning of controller parameters is achieved, effectively compensating for internal and external disturbances and coupling interference. This enables independent decoupled control of the oxygen ratio and cathode pressure through dual channels, reducing control overshoot, shortening settling time, and improving the overall operating performance of the PEMFC system.

[0008] A method for decoupling control of the air supply system of a proton exchange membrane fuel cell, comprising the following steps:

[0009] (1) Establishing a fuel cell stack model: Constructing a fuel cell stack mechanism model, comprehensively considering electrochemical, fluid transport and thermophysical characteristics, and accurately characterizing the multi-physics coupling process inside the proton exchange membrane fuel cell;

[0010] (2) Establish an air supply system model: accurately characterize the dynamic characteristics of the fuel cell air supply system using a set of nonlinear differential equations;

[0011] (3) Determine the control target: taking into account the maximum net power and the highest efficiency of the gas supply system, the target oxygen ratio and cathode pressure under different currents are determined by non-dominated genetic algorithm;

[0012] (4) Design ESO-FOPID (Extended State Observer-Fractional Proportional-Integral-Derivative) Controller: Introduce fractional operators to extend proportional-integral-derivative control parameters, design an extended state observer to compensate for disturbances in the control quantity, and realize decoupled control of the two loops of the oxygen ratio control channel and the cathode pressure control channel.

[0013] (5) Optimization of control parameters: The FOPID (fractional proportional-integral-derivative) algorithm is implemented using the balanced optimizer algorithm to achieve coordinated optimization of five parameters: proportional gain, integral gain, derivative gain, integral order, and derivative order.

[0014] Furthermore:

[0015] (1) Construction of PEMFC stack mechanism model: A PEMFC stack mechanism model is constructed by coupling the cathode flow channel model, voltage model, membrane hydration model and anode flow channel model. The model comprehensively considers electrochemical, fluid transport and thermophysical characteristics to accurately characterize the multi-physics coupling process inside the PEMFC. Among them, the cathode and anode flow channel models follow the molar conservation law, the principle of mass flow continuity, the ideal gas law and the electrochemical reaction kinetic equation; the membrane hydration model considers two membrane water transport modes, namely electroosmotic drag and membrane water diffusion; the fuel cell operating voltage is jointly determined by the open circuit voltage, ohmic loss and activation loss.

[0016] (2) Construction of a multiphysics mechanism model for the PEMFC air supply system: Based on the fuel cell stack mechanism model, and combined with the air compressor model, air supply pipeline model, intercooler model, humidifier model, and exhaust pipeline model, a multiphysics mechanism model for the PEMFC air supply system containing six sub-models is constructed. The dynamic characteristics of the entire air supply system are accurately characterized by a set of nonlinear differential equations. Among them, the air compressor model represents the mass flow rate through angular velocity and air supply pipeline pressure, and the nonlinear curve fitting method is used to fit the air compressor MAP diagram to improve the model accuracy. The exhaust pipeline model is based on the isothermal gas equation, combines the critical pressure ratio to divide the gas flow characteristics, and correlates the back pressure valve opening with the mass flow rate at the exhaust pipeline outlet.

[0017] (3) Determine the optimal control objectives under different load currents: The net power and system efficiency of the PEMFC system are used as multi-objective optimization indicators, where net power is the difference between the fuel cell stack output power and the air compressor parasitic power, and system efficiency is the ratio of net power to fuel cell stack output power. The non-dominated sorting genetic algorithm (NSGA-II) is used to optimize the air compressor voltage and back pressure valve opening under different load currents to obtain the Pareto solution set of net power and system efficiency. Then, the TOPSIS algorithm (approximation ideal solution sorting method) is used to comprehensively evaluate the Pareto solution set and select the optimal solution. The oxygen ratio and cathode pressure corresponding to the optimal solution are the control objectives under the load current. After optimization in the 100~400A load current range with a fixed step size, the continuous target value curves of oxygen ratio and cathode pressure in the entire range are obtained by interpolation.

[0018] (4) Design of ESO-FOPID (Extended State Observer-Fractional Proportional-Integral-Derivative) Decoupling Controller: An ESO-FOPID decoupling control architecture combining an extended state observer and a fractional-order PID controller is designed. The PEMFC air supply system is deconstructed into two independent single-input single-output control units: an oxygen ratio control channel and a cathode pressure control channel. Each unit is equipped with an independent ESO-FOPID controller. The oxygen ratio is adjusted by the air compressor voltage, and the cathode pressure is adjusted by the back pressure valve opening. Based on the proportional, integral, and derivative elements of the current PID controller, the FOPID controller introduces the integral order λ and the derivative order μ (within the range [0,2]) to expand the parameter adjustment dimension. The extended state observer integrates the internal and external disturbances of the system and the coupling interference of the other channel into a total disturbance. The total disturbance is observed in real time through the feedback structure of a piecewise nonlinear function, and the observed total disturbance is compensated to the output control signal of the FOPID controller to offset the influence of the disturbance on the system and realize the decoupled independent control of the two channels.

[0019] (5) Cooperative optimization of FOPID parameters based on the balanced optimizer algorithm: The integral time absolute error (ITAE) is selected as the performance evaluation index of the control system and used as the fitness function of the balanced optimizer algorithm to optimize the proportional gain K of the FOPID controller. p Integral gain K i Differential gain K d The five parameters—integral order λ, derivative order μ, and total FOPID—are optimized collaboratively. Specifically, the optimization range for the FOPID parameters in the oxygen ratio control channel is set to be greater than 0, while the optimization range for the FOPID parameters in the cathode pressure control channel is set to be less than 0, adapting to the correlation between the actuator and the control objective. The balance optimizer algorithm achieves parameter optimization by simulating a mass balance model of the control volume, effectively avoiding local optima and achieving rapid and accurate tuning of the five FOPID parameters.

[0020] The specific implementation process of the TOPSIS algorithm in step 3 is as follows:

[0021] (1) Construct the original decision matrix consisting of the net power and system efficiency of the Pareto solution set.

[0022] (2) The decision matrix is ​​positiveized. Since net power and system efficiency are both extremely large indicators, the original data is directly retained.

[0023] (3) Normalize the normalized matrix to eliminate the difference in the dimensions of the indicators.

[0024] (4) Set the weights of net power and system efficiency to 0.5 and construct a weighted normalization matrix.

[0025] (5) Extract the optimal and worst values ​​of each index in the weighted standardized matrix to determine the ideal solution and the negative ideal solution.

[0026] (6) Calculate the Euclidean distance from each solution to the ideal solution and the negative ideal solution, calculate the relative proximity of each solution using the relative proximity formula, and select the solution with the largest relative proximity as the optimal solution.

[0027] The implementation process of the extended state observer in step 4 is as follows:

[0028] Taking the oxygen ratio control channel as an example, a system state-space equation is constructed, with the oxygen ratio as the system output, the air compressor voltage as the control input, and the total disturbance as the extended state variable. The observation gain and piecewise nonlinear function coefficients are set, and the observer equation is constructed using the fal piecewise nonlinear function to observe the observed value of the total disturbance in real time. The observed value of the total disturbance is compensated to the output of the FOPID controller to achieve disturbance suppression. The extended state observer for the cathode pressure control channel is constructed using the same logic, except that the cathode pressure is used as the system output and the back pressure valve opening is used as the control input.

[0029] The features of this invention and the significant beneficial effects it produces are as follows:

[0030] (1) High modeling accuracy: The constructed multi-physics mechanism model comprehensively considers multiple key influencing factors, providing an accurate model basis for control strategies.

[0031] (2) Optimal control objectives: By combining NSGA-II with the TOPSIS algorithm, multi-objective collaborative optimization of net power and system efficiency is achieved, and reasonable control objectives are formulated.

[0032] (3) The decoupling control effect is good. The ESO-FOPID architecture effectively compensates for disturbances and coupling interference. Compared with the traditional method, the overshoot is smaller and the adjustment time is shorter.

[0033] (4) The parameter tuning is efficient and accurate. The fitness function is ITAE (integral time absolute error). The five parameters of FOPID are automatically optimized through the balanced optimizer algorithm to avoid local optima and eliminate the need for manual parameter tuning. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the air supply system for the proton exchange membrane fuel cell in this invention.

[0035] Figure 2 This is the ESO-FOPID control structure diagram in this invention.

[0036] Figure 3 It is the Pareto solution set obtained by multi-objective optimization in the embodiments of the present invention.

[0037] Figure 4It is the TOPSIS score of each solution in the Pareto solution set in the embodiments of the present invention.

[0038] Figure 5 This is a graph showing the result of oxygen ratio control in an embodiment of the present invention.

[0039] Figure 6 This is a diagram showing the cathode pressure control results in an embodiment of the present invention. Detailed Implementation

[0040] The following specific calculation examples further illustrate the method steps of the present invention. It should be noted that this embodiment is descriptive rather than limiting, and is not intended to limit the scope of protection of the present invention.

[0041] The specific implementation process of this invention is divided into 5 parts:

[0042] (1) Establishing a fuel cell stack model: Constructing a fuel cell stack mechanism model, taking into account electrochemical, fluid transport and thermophysical characteristics, to accurately characterize the multi-physics coupling process inside the proton exchange membrane fuel cell.

[0043] (2) Establish an air supply system model: use a set of nonlinear differential equations to accurately characterize the dynamic characteristics of the fuel cell air supply system.

[0044] (3) Determine the control target: Taking into account the maximum net power and the highest efficiency of the gas supply system, the target oxygen ratio and cathode pressure under different currents are determined by non-dominated genetic algorithm.

[0045] (4) Design ESO-FOPID controller: Introduce fractional-order operators to extend proportional-integral-derivative control parameters, design extended state observer to perform disturbance compensation on control quantity, and realize decoupled control of the two loops.

[0046] (5) Optimization of control parameters: The five parameters of FOPID are optimized by using the balanced optimizer algorithm.

[0047] The details are as follows:

[0048] 1. Construction of the mechanism model of PEMFC stack and air supply system

[0049] 1.1 Stack Mechanism Model

[0050] A fuel cell stack mechanism model was constructed by coupling a cathode flow channel model, a voltage model, a membrane hydration model, and an anode flow channel model. This model comprehensively considers electrochemical, fluid transport, and thermophysical properties to accurately characterize the multi-physics coupling process inside the PEMFC.

[0051] Voltage model: The operating voltage of the fuel cell is:

[0052]

[0053] Where E fc η is the open-circuit voltage. ohm For Ohm loss, η act,a It is the activation loss of the anode; η act,c It is the activation loss of the cathode, measured in V.

[0054] Cathode channel model: Following the Mohr's law of conservation, the dynamic equilibrium equation is:

[0055]

[0056] Where, m O2,ca It is the mass of oxygen in the cathode flow field; m N2,ca It is the mass of nitrogen gas in the cathode flow field, m v,ca W is the mass of water vapor in the cathode flow field. O2,ca,in It is the mass flow rate of oxygen at the cathode inlet; W N2,ca,in It is the mass flow rate of nitrogen; W v,ca,in W is the mass flow rate of water vapor. O2,ca,out W is the mass flow rate of oxygen at the cathode outlet. N2,ca,out W is the mass flow rate of nitrogen gas at the cathode outlet. v,ca,out W is the mass flow rate of water vapor at the cathode outlet. O2,react W is the mass flow rate of oxygen consumed in the reaction. v,gen It is the mass flow rate of water vapor produced in the reaction. W v,mem This refers to the mass flow rate of water vapor migrating through the membrane. All mass flow rates mentioned above are in kg / s.

[0057] Anode flow channel model: It adopts the same theoretical framework as the cathode flow channel model, based on the principle of mass conservation, the ideal gas law and the electrochemical reaction kinetics equation, to characterize the mass change and consumption of hydrogen in the anode flow field.

[0058] Membrane hydration model: Simultaneously considering both electroosmotic drag and membrane water diffusion transport modes, the water vapor mass flow rate W across the electrolyte membrane to the cathode. v,mem satisfy:

[0059]

[0060] Where n is the number of batteries; F is Faraday's constant; n d It is the electroosmotic coefficient; D w This is the water diffusion coefficient, measured in cm. 2 / s;c v,an It is the water concentration on the anode-side membrane surface; c v,cnThis refers to the water concentration on the cathode-side membrane surface, expressed in mol / cm³. 3 A act It is the active area of ​​the battery, measured in meters (m²). 2 ;t m It is the thickness of the membrane, measured in meters (m).

[0061] 1.2 Air Supply System Model

[0062] Based on the fuel cell stack mechanism model, five sub-models—air compressor, air supply pipeline, intercooler, humidifier, and exhaust pipeline—are constructed, forming a six-sub-model multiphysics mechanism model of the PEMFC air supply system, with the structure as follows: Figure 1 As shown.

[0063] Air compressor model: The air compressor is the core component of the air supply system, and its angular velocity change satisfies:

[0064]

[0065] Among them, J cp The moment of inertia of an air compressor is expressed in kg·m. 2 ;τ cm It is the driving torque of the motor; τ cp It is the load torque of the air compressor, and the unit of both is N·m.

[0066] The MAP diagram of the air compressor is fitted using a nonlinear curve fitting method, with angular velocity ω. cp and gas supply line pressure p sm Characterizing mass flow rate W cp The fitting formula is a multivariate polynomial, and the fitting parameters are shown in Table 1. The goodness of fit R0 is... 2 =0.963, and the root mean square error is 0.0115.

[0067] Table 1. Parameters for Fitting Curves in the MAP Diagram of the Air Compressor

[0068] Air supply pipeline model: The pipeline between the air compressor outlet and the cathode inlet is simplified to an air supply pipeline, and the outlet mass flow rate expression is:

[0069]

[0070] The expression for the gas supply line pressure is:

[0071]

[0072] Among them, κ sm,outThis is the flow coefficient at the outlet of the supply pipeline, expressed in kg / (s·Pa); p ca This is the cathode pressure, measured in Pa. R air V is the gas constant of air; sm The volume of the supply pipeline is expressed in meters (m). 3 ;T cp,out It is the air compressor outlet temperature; T sm It refers to the temperature of the supply pipeline; both are in Kelvin (K).

[0073] Intercooler model: This model cools the high-temperature air compressed by the air compressor to prevent damage to the proton exchange membrane. It assumes constant gas mass flow rate and pressure, considering only the effect of temperature on humidity, with humidity changes satisfying the following:

[0074]

[0075] Where: Φ cl This refers to the relative humidity at the intercooler outlet; Φ sm This refers to the relative humidity at the outlet of the supply pipeline. cl This is the intercooler outlet pressure, in Pa; p sat (T cl ) is the saturated steam pressure at the intercooler outlet; p sat (T sm ) is the saturated water vapor pressure at the temperature inside the supply pipeline, and both are in Pa.

[0076] Humidifier model: It humidifies the air to prevent the membrane from drying out. The outlet mass flow rate is the sum of the mass flow rates of the dry air and the injected water vapor, and the pressure is the sum of the partial pressures of each gas.

[0077]

[0078] Among them, W da,cl It is the mass flow rate of the dry air at the humidifier inlet; W v,hm This refers to the mass flow rate of water vapor injected into the humidifier inlet; both are measured in kg / s. da,cl It is the partial pressure of the dry air at the humidifier inlet; p v,hm It is the partial pressure of water vapor at the humidifier outlet, and both are in Pa.

[0079] Exhaust pipe model: Characterizing pressure characteristics based on isothermal gas equations:

[0080]

[0081] Among them, T rm It is the temperature inside the exhaust pipe, measured in Kelvin (K); V rmThis refers to the volume of the exhaust pipe, measured in cubic meters (m³). 3 W ca,out This is the mass flow rate at the cathode outlet, expressed in kg / s; W rm,out It is the mass flow rate at the exhaust pipe outlet, measured in kg / s.

[0082] 2. Determination of the optimal control objective under different load currents

[0083] Determine the multi-objective optimization index: The system net power expression is:

[0084]

[0085] Among them, P st P is the output power of the fuel cell stack. cp This refers to the air compressor power, measured in kW.

[0086] The system efficiency expression is:

[0087]

[0088] To achieve P net and η sys Maximizing collaboration is the optimization objective.

[0089] NSGA-II Algorithm Optimization: This embodiment optimizes the load current range of 100~400A in 20A steps, using the air compressor voltage and back pressure valve opening as optimization variables. The NSGA-II algorithm is used to obtain P under each current condition. net and η sys The Pareto solution set is the optimal solution set for multi-objective optimization. Taking a 200 A current as an example, the Pareto solution set obtained by optimization using a non-dominated sorting genetic algorithm is as follows: Figure 3 As shown in the figure, the net output power of the system gradually decreases as the system efficiency increases, indicating a typical trade-off. Specifically, the variation in system efficiency is approximately 1%, while the variation in net power is approximately 2 kW, demonstrating that the oxygen excess ratio and cathode inlet pressure have a significant impact on the performance of the fuel cell system.

[0090] TOPSIS algorithm for selecting the optimal solution: setting P net and η sys The weights are all 0.5. Following the steps of constructing the decision matrix, positiveization, standardization, determining the ideal and negative ideal solutions, and calculating the relative closeness, the solution with the highest relative closeness is selected from the Pareto solution set. The corresponding oxygen ratio and cathode pressure are the control targets under that load current. Taking a 200 A current as an example, the solutions are numbered according to the system efficiency from low to high, and then the TOPSIS score of each solution is calculated. The results are as follows: Figure 4 As shown in the figure, it can be seen that from No. 1 to No. 8, the TOPSIS score shows a trend of first rising and then falling. No. 2 has the highest score and is the solution with the best overall performance. The oxygen ratio and cathode pressure corresponding to this solution are the control targets at 200A.

[0091] Continuous target value curve acquisition: Interpolation processing is performed on the control target at discrete current points to obtain continuous oxygen ratio and cathode pressure target value curves within the load current range of 100~400A. The optimal control target under some currents is shown in Table 2.

[0092] Table 2 Target oxygen ratio and cathode pressure at different currents

[0093] 3. Design and Parameter Optimization of ESO-FOPID Decoupling Controller

[0094] 3.1 FOPID Controller Design

[0095] The FOPID controller, based on the traditional PID controller, extends the integral and derivative orders from integers to non-integers. Its mathematical expression is:

[0096]

[0097] Where e(t) is the deviation between the actual value and the set value of the control target, and K p It is a ratio, K i It is an integral, K d It is the differential gain, λ∈[0,2] is the integral order, and μ∈[0,2] is the differential order. Based on the correlation between the actuator and the control objective, the optimization range of the FOPID parameters for the oxygen ratio control channel is set to be greater than 0, and the optimization range of the FOPID parameters for the cathode pressure control channel is set to be less than 0.

[0098] 3.2 Design of Extended State Observer

[0099] The extended state observer is used to observe internal and external disturbances and coupled interferences of the system in real time, and compensate them to the control output to achieve disturbance suppression; taking the oxygen ratio control channel as an example, the state-space equation is constructed as follows:

[0100]

[0101] Where x1 is the system output, i.e., the excess oxygen ratio; x2 is the rate of change of x1; x3 is the total disturbance; u is the control input, b is the control gain, and y is the system output; the ESO observer equation is constructed based on a piecewise nonlinear function:

[0102]

[0103] Where z1, z2, and z3 are the observed values ​​of x1, x2, and x3, respectively; e = x1 - z1 is the observation error; β1, β2, and β3 are the observation gains of the ESO; α1, α2, and α3 are the coefficients of the piecewise nonlinear function; δ is the width of the linear region of the piecewise nonlinear function; and the fal function is the piecewise nonlinear function, expressed as:

[0104]

[0105] The total disturbance observation value z3 observed by ESO is compensated to the FOPID output to obtain the final control signal. This achieves disturbance suppression. The meaning of each character in this formula is the same as that in formula (14).

[0106] 3.3 Decoupling Control Logic

[0107] like Figure 2 As shown, the ESO-FOPID controller divides the control system into two independent control channels, achieving decoupled control of the oxygen ratio and cathode pressure:

[0108] Oxygen ratio channel: The oxygen ratio setpoint is used as input and the air compressor voltage is used as output. The ESO monitors the coupling interference and current surge caused by the back pressure valve adjustment in real time, and compensates the total disturbance to the FOPID output to adjust the air compressor voltage to control the oxygen ratio.

[0109] Cathode pressure channel: The cathode pressure setpoint is used as input and the back pressure valve opening is used as output. The ESO monitors the coupling interference caused by the air compressor adjustment and the internal disturbance of the system in real time, and compensates the total disturbance to the FOPID output to adjust the back pressure valve opening to control the cathode pressure.

[0110] 3.4 FOPID Parameter Optimization Based on Balanced Optimizer Algorithm

[0111] The ITAE function is chosen as the fitness function, and its expression is:

[0112]

[0113] Minimizing ITAE is taken as the optimization objective, and a balanced optimizer algorithm is used to optimize the K-axis of FOPID. p K i K d The algorithm employs a coordinated optimization of five parameters: λ, μ, and μ. By simulating a mass balance model of the control volume, it updates the population position through initialization, exploration, and development phases until convergence to the optimal solution, effectively avoiding local optima and achieving rapid and accurate parameter tuning.

[0114] 4. Simulation Comparison

[0115] A simulation model of the PEMFC air supply system was built in Matlab / Simulink. The performance of the three control strategies of the present invention, ESO-FOPID, traditional PID and single FOPID was compared with the load current step disturbance as input. ITAE was used as the core evaluation index. The results are shown in Table 3.

[0116] Table 3 Comparison of ITAE indices for three control strategies

[0117] Simulation results show that the ITAE index of the ESO-FOPID control strategy proposed in this invention is reduced by 21.2% compared with traditional PID and by 9.9% compared with single FOPID.

[0118] The results of oxygen ratio control under different control methods and the application of step load current are as follows: Figure 5 As shown in the figure, when the load current increases, oxygen consumption immediately increases, leading to a sharp increase in the excess oxygen ratio; when the load current decreases, oxygen consumption immediately decreases, and the excess oxygen ratio subsequently drops sharply. All control methods can bring the excess oxygen ratio close to the target value within a certain time. The control effect at the 10th second shows that, because the ESO-FOPID controller can mitigate the impact of back pressure valve changes, it exhibits less fluctuation and a shorter settling time compared to the other two schemes.

[0119] The control results of cathode pressure under step load current under different control methods are as follows: Figure 6 As shown in the figure, when the load current undergoes a step change, all control methods can bring the cathode pressure to the target value within a certain time, but PID and FOPID control produce significant overshoot. The control effect at 15 seconds shows that, compared to the other two control methods, the ESO-FOPID controller has smaller overshoot and faster adjustment speed.

[0120] Simulation results show that ESO-FOPID can respond quickly to load changes, significantly reduce the overshoot of oxygen ratio and cathode pressure, greatly shorten the settling time, and has no obvious steady-state deviation. The decoupling control effect and dynamic response performance are significantly better than traditional PID and single FOPID control strategies.

[0121] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for decoupling control of the air supply system of a proton exchange membrane fuel cell, characterized by: The control method includes the following steps: (1) Establishing a fuel cell stack model: Constructing a fuel cell stack mechanism model, comprehensively considering electrochemical, fluid transport and thermophysical characteristics, and accurately characterizing the multi-physics coupling process inside the proton exchange membrane fuel cell; (2) Establish an air supply system model: accurately characterize the dynamic characteristics of the fuel cell air supply system using a set of nonlinear differential equations; (3) Determine the control target: taking into account the maximum net power and the highest efficiency of the gas supply system, the target oxygen ratio and cathode pressure under different currents are determined by non-dominated genetic algorithm; (4) Design of extended state observer-fractional order proportional-integral-derivative controller: Introduce fractional order operators to extend proportional-integral-derivative control parameters, design an extended state observer to perform disturbance compensation on the control quantity, and realize decoupled control of the two loops of the oxygen ratio control channel and the cathode pressure control channel. (5) Optimization of control parameters: The fractional-order proportional-integral-derivative (PII) algorithm is used to achieve coordinated optimization of five parameters: proportional gain, integral gain, derivative gain, integral order, and derivative order.

2. The method for decoupling control of the proton exchange membrane fuel cell air supply system according to claim 1, characterized in that: The fuel cell stack mechanism model in step (1) consists of four mutually coupled sub-models: cathode flow channel model, voltage model, membrane hydration model, and anode flow channel model. The cathode and anode flow channel models follow the principle of mass conservation, the ideal gas law, and the electrochemical reaction kinetics equation. The membrane hydration model considers two membrane water transport modes: electroosmotic drag and membrane water diffusion. The operating voltage of the fuel cell is determined by the open circuit voltage, ohmic loss, and activation loss.

3. The method for decoupling control of the proton exchange membrane fuel cell air supply system according to claim 1, characterized in that: The air supply system model in step (2) consists of an air compressor model, an air supply pipeline model, an intercooler model, a humidifier model, and an exhaust pipeline model.

4. The method for decoupling control of the proton exchange membrane fuel cell air supply system according to claim 1, characterized in that: Step (3) uses a non-dominated genetic algorithm to obtain the Pareto solution set with the maximum net power and the highest efficiency, and then uses the approximation ideal solution sorting method to select the most suitable control target from it.

5. The method for decoupling control of the proton exchange membrane fuel cell air supply system according to claim 1, characterized in that: In step (4), an extended state observer is designed to observe the internal and external disturbances of the model, calculate the total disturbance, and compensate the observed total disturbance to the fractional proportional-integral-derivative control output, thereby realizing the dual-channel decoupled control of the oxygen ratio control channel and the cathode pressure control channel.

6. The method for decoupling control of the air supply system of a proton exchange membrane fuel cell according to claim 1, characterized in that: Step (5) uses the integral time absolute error of the control result as the fitness function of the balanced optimizer algorithm to optimize five parameters: proportional coefficient, integral coefficient, derivative coefficient, derivative order, and integral order.

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