A method for fault-tolerant control of a proton exchange membrane fuel cell

Abstract

The application discloses a kind of proton exchange membrane fuel cell fault tolerance control methods, comprising: the system model is established to proton exchange membrane fuel cell system, and state equation is established based on system model;With fault value as extended state variable, make state equation extended to augmented state equation;Based on augmented state equation, high-order sliding mode observer for observing the internal state quantity of proton exchange membrane fuel cell in real time is established, and based on the state quantity estimation value of high-order sliding mode observer and sensor measurement value, fault state judgment model is established;Determine fault state based on fault state judgment model, and carry out fault tolerance control to proton exchange membrane fuel cell system in fault state or no fault state by fault tolerance controller.The method of the present application can make the system can quickly detect and implement control when sensor failure or reactant shortage occurs, so that the system can still maintain stable output performance, with fast convergence speed, small overshoot and other characteristics.

Description

Technical Field

[0001] This invention relates to the field of fuel cell technology, and in particular to a fault-tolerant control method for proton exchange membrane fuel cells. Background Technology

[0002] With economic globalization and the continuous development of modern technology, human demand for energy is increasing daily. Meanwhile, fossil fuels, upon which early industrial production relied, are facing depletion and constraining the development of human society. Hydrogen energy, as a clean energy source with high power generation efficiency, high calorific value, and diverse sources, has attracted much attention. Among them, proton exchange membrane fuel cells (PEMFCs) possess advantages such as high energy conversion efficiency, high power density, and fast start-up speed, occupying a leading position in the application market and possessing broad development prospects.

[0003] Currently, proton exchange membrane fuel cells (PEMFCs) have been applied to varying degrees across different industries. However, in actual operation, the output performance of PEMFC systems is affected by operational factors such as gas flow rate, temperature, and humidity, as well as various environmental factors. Furthermore, PEMFC systems are prone to malfunctions such as reactant shortages, which can impact their operational status. Additionally, sensors, as a crucial tool for monitoring the performance of PEMFC systems, can also affect their output performance if they malfunction.

[0004] Although there has been a wealth of research on fault-tolerant control of proton exchange membrane fuel cell systems both domestically and internationally, research on fault-tolerant control methods for sensor failures and reactant shortages in proton exchange membrane fuel cell systems remains lacking. Therefore, research on fault-tolerant control of proton exchange membrane fuel cell systems regarding sensor failures and reactant shortages is of great significance. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a fault-tolerant control method for proton exchange membrane fuel cells. This method enables the system to quickly detect and implement control when sensor failures or reactant shortages occur, allowing the system to maintain stable output performance. It features fast convergence speed and small overshoot.

[0006] The technical solution adopted in this invention is as follows:

[0007] A fault-tolerant control method for proton exchange membrane fuel cells includes:

[0008] A system model is established for a proton exchange membrane fuel cell system, and a state equation is established based on the system model; fault values ​​are used as extended state variables to extend the state equation into an augmented state equation.

[0009] A high-order sliding mode observer is established based on the augmented equation of state to observe the internal state variables of a proton exchange membrane fuel cell in real time, and a fault state judgment model is established based on the state variable estimates of the high-order sliding mode observer and the sensor measurements.

[0010] The fault state is determined based on the fault state judgment model, and the proton exchange membrane fuel cell system is subjected to fault-tolerant control in the fault state or the fault-free state through the fault-tolerant controller.

[0011] Furthermore, the system model established for the proton exchange membrane fuel cell system includes: an air compressor model, a cathode flow channel model, an anode flow channel model, a return pipe model, and a fuel cell stack model.

[0012] Furthermore, the air compressor model includes:

[0013]

[0014] In the formula, ω cp J is the rotational speed of the air compressor motor, J is the moment of inertia, and k is the rotational speed of the air t k v R cm η is a motor-related constant. cm η cp The efficiencies of the motor and air compressor, respectively, V cm For the input voltage, C p P is the specific heat capacity of air, γ is the specific heat ratio of air, and P is the specific heat capacity of air. sm To supply pipeline pressure, P atm For atmospheric pressure, T atm For atmospheric temperature, F cp This is the mass flow rate at the air compressor outlet.

[0015] Furthermore, the cathode flow channel model and the anode flow channel model include:

[0016]

[0017] In the formula, P sm To supply pipeline pressure, m sm For the air quality in the gas supply pipeline, m O2 m N2 These represent the mass of oxygen and nitrogen in the cathode channel, respectively, where γ is the specific heat ratio of air, and R... a V is the gas constant for air. sm For the volume of the gas supply pipeline, T cp T is the air temperature of the compressor. sm W represents the air temperature in the gas supply pipeline. cp W is the output mass flow rate of the air compressor. sm,out W is the output mass flow rate of the gas supply pipeline. O2,ca,inTo input the oxygen mass flow rate into the cathode channel, W O2,ca,out W represents the oxygen mass flow rate output from the cathode channel after the reaction. O2,react W represents the mass flow rate of oxygen consumed in the electrochemical reaction occurring in the cathode channel under the influence of the load current. N2,ca,in To input the nitrogen mass flow rate into the cathode channel, W N2,ca,out This represents the mass flow rate of nitrogen gas output from the cathode channel after the reaction.

[0018] Furthermore, the reflux pipe model includes:

[0019]

[0020] In the formula, P rm R is the pressure in the return pipe. a T is the gas constant of air. st V is the temperature of the fuel cell stack. rm W is the volume of the return pipe. ca,out W is the mass flow rate of the gas output from the cathode. rm,out This refers to the mass flow rate of the gas output from the return pipeline.

[0021] Furthermore, the fuel cell stack model includes:

[0022] V st =N(EV) act -V conc -V ohm )

[0023] In the formula, V st Where N is the stack voltage, E is the number of stacks, and V is the Nernst voltage. act For activation loss, V conc For concentration loss, V ohm For ohmic loss.

[0024] Furthermore, the establishment of state equations based on the system model includes:

[0025] The state variables of the system model are determined, including the air compressor speed, air supply pipeline pressure, air mass flow rate, air mass in the air supply pipeline, oxygen mass in the cathode channel, nitrogen mass in the cathode channel, and return pipeline pressure.

[0026] Determine the input variables of the system model, including the air compressor voltage and the fuel cell stack current;

[0027] Determine the output variables of the system model, including air compressor speed, air supply pipeline pressure, air mass flow rate, and return pipeline pressure;

[0028] Establish state equations based on the state variables, input variables, and output variables of the system model:

[0029]

[0030] In the formula, C = [1,1,1,0,0,0,1], ω cp F represents the air compressor motor speed. cp P is the mass flow rate at the air compressor outlet. sm To supply pipeline pressure, m sm For the air quality in the gas supply pipeline, m O2 m N2 These represent the mass of oxygen and nitrogen in the cathode channel, respectively, P rm V represents the pressure in the return pipe. cm For the input voltage, I st This represents the fuel cell current.

[0031] Furthermore, the step of using the fault value as an extended state variable to extend the state equation into an augmented state equation includes:

[0032] Sensor malfunction and reactant shortage are designated as b1 and b2 respectively, and the malfunction values ​​are used as extended state variables according to the established state equation to form an augmented state equation:

[0033]

[0034] In the formula, It is the identity matrix. To augment the state variables, Γ·v represents the effect of system noise on the system, and e represents the measurement noise, where:

[0035]

[0036] Furthermore, the determination of the fault state based on the fault state judgment model includes:

[0037]

[0038] In the formula, A is the judgment threshold.

[0039] Furthermore, the fault-tolerant control of the proton exchange membrane fuel cell system under faulty or fault-free conditions via a fault-tolerant controller includes:

[0040] When it is determined that the proton exchange membrane fuel cell system has not malfunctioned, the fault diagnosis and isolation module outputs the oxygen ratio measurement value, and the fault-tolerant controller adjusts the input voltage of the air compressor accordingly.

[0041] When a sensor failure is detected in the proton exchange membrane fuel cell system, the measurement variables are reconstructed using an established high-order sliding mode observer to replace the faulty sensor measurement values, and the input voltage of the air compressor is adjusted accordingly by the fault-tolerant controller.

[0042] When a reactant shortage fault is detected in the proton exchange membrane fuel cell system, the oxygen ratio measurement value is reconstructed through the fault diagnosis and isolation module, and the input voltage of the air compressor is adjusted accordingly through the fault-tolerant controller.

[0043] When a sensor failure and a reactant shortage failure are simultaneously detected in a proton exchange membrane fuel cell system, the peroxygen ratio measured by a high-order sliding mode observer is reconstructed through a fault diagnosis and isolation module, and the input voltage of the air compressor is adjusted accordingly through a fault-tolerant controller.

[0044] The beneficial effects of this invention are as follows:

[0045] 1. This invention establishes a state equation for the control of proton exchange membrane fuel cells, and based on this, establishes a high-order sliding mode observer that can accurately and in real time observe the changes in the internal state variables of the proton exchange membrane fuel cell.

[0046] 2. This invention proposes a fault state judgment model. Based on the judgment results of the fault state judgment model, the fault source can be quickly and accurately cut off and the operation of the proton exchange membrane fuel cell system can be restored, thereby achieving efficient and reliable operation of the proton exchange membrane fuel cell system.

[0047] 3. Based on the reference oxygen ratio trajectory, the present invention uses a sliding mode controller to ensure that the actual oxygen ratio is always near the reference oxygen ratio. This achieves efficient operation of the proton exchange membrane fuel cell system while having a faster response speed and lower overshoot. Attached Figure Description

[0048] Figure 1 This is a flowchart of a fault-tolerant control method for a proton exchange membrane fuel cell according to Embodiment 1 of the present invention.

[0049] Figure 2 This is a schematic diagram of the proton exchange membrane fuel cell system model of Embodiment 1 of the present invention.

[0050] Figure 3 This is a schematic diagram of a fault-tolerant control method for a proton exchange membrane fuel cell according to Embodiment 1 of the present invention. Detailed Implementation

[0051] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments are now described. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention; that is, the described embodiments are only a part of the embodiments of the invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0052] Example 1

[0053] like Figure 1 As shown, this embodiment provides a fault-tolerant control method for proton exchange membrane fuel cells, including:

[0054] A system model is established for a proton exchange membrane fuel cell system, and a state equation is established based on the system model; fault values ​​are used as extended state variables to extend the state equation into an augmented state equation.

[0055] A high-order sliding mode observer is established based on the augmented equation of state to observe the internal state variables of a proton exchange membrane fuel cell in real time, and a fault state judgment model is established based on the state variable estimates of the high-order sliding mode observer and the sensor measurements.

[0056] The fault state is determined based on the fault state judgment model, and the proton exchange membrane fuel cell system is subjected to fault-tolerant control in the fault state or the fault-free state through the fault-tolerant controller.

[0057] like Figure 2 As shown, the system model established for the proton exchange membrane fuel cell system includes an air compressor model, a cathode flow channel model, an anode flow channel model, a return pipe model, and a stack model.

[0058] Preferably, the air compressor model includes:

[0059]

[0060] In the formula, ω cp J is the rotational speed of the air compressor motor, J is the moment of inertia, and k is the rotational speed of the air t k v R cm η is a motor-related constant. cm η cp The efficiencies of the motor and air compressor, respectively, V cm For the input voltage, C p P is the specific heat capacity of air, γ is the specific heat ratio of air, and P is the specific heat capacity of air. sm To supply pipeline pressure, P atm For atmospheric pressure, T atm For atmospheric temperature, F cp This is the mass flow rate at the air compressor outlet.

[0061] It should be noted that the dynamic characteristics of the air mass flow rate output by the air compressor are determined by both the air compressor's speed and pressure ratio, as shown in the following formula:

[0062]

[0063] In the formula, F cp Let A be the mass flow rate of the air output from the air compressor, A be the flow area, and L be the pipe length. For the air compressor pressure ratio characteristics, P atm For atmospheric pressure, P sm To supply pipeline pressure.

[0064] Preferably, the cathode flow channel model and the anode flow channel model include:

[0065]

[0066] In the formula, P sm To supply pipeline pressure, m sm For the air quality in the gas supply pipeline, m O2 m N2 These represent the mass of oxygen and nitrogen in the cathode channel, respectively, where γ is the specific heat ratio of air, and R... a V is the gas constant for air. sm For the volume of the gas supply pipeline, T cp T is the air temperature of the compressor. sm W represents the air temperature in the gas supply pipeline. cp W is the output mass flow rate of the air compressor. sm,out W is the output mass flow rate of the gas supply pipeline. O2,ca,in To input the oxygen mass flow rate into the cathode channel, W O2,ca,out W represents the oxygen mass flow rate output from the cathode channel after the reaction. O2,react W represents the mass flow rate of oxygen consumed in the electrochemical reaction occurring in the cathode channel under the influence of the load current. N2,ca,in To input the nitrogen mass flow rate into the cathode channel, W N2,ca,out This represents the mass flow rate of nitrogen gas output from the cathode channel after the reaction.

[0067] Preferably, the reflux pipe model includes:

[0068]

[0069] In the formula, P rm R is the pressure in the return pipe. a T is the gas constant of air. st V is the temperature of the fuel cell stack. rm W is the volume of the return pipe. ca,outW is the mass flow rate of the gas output from the cathode. rm,out This refers to the mass flow rate of the gas output from the return pipeline.

[0070] Preferably, the fuel cell stack model includes:

[0071] V st =N(EV) act -V conc -V ohm )

[0072] In the formula, V st Where N is the stack voltage, E is the number of stacks, and V is the Nernst voltage. act For activation loss, V conc For concentration loss, V ohm For ohmic loss.

[0073] Preferably, establishing state equations based on the system model includes:

[0074] Determine the state variables of the system model, including air compressor speed, air supply pipeline pressure, air mass flow rate, air mass in the air supply pipeline, oxygen mass in the cathode channel, nitrogen mass in the cathode channel, and return pipeline pressure.

[0075] Determine the input variables of the system model, including the air compressor voltage and the fuel cell stack current;

[0076] Determine the output variables of the system model, including air compressor speed, air supply pipeline pressure, air mass flow rate, and return pipeline pressure;

[0077] Establish state equations based on the state variables, input variables, and output variables of the system model:

[0078]

[0079] In the formula, C = [1,1,1,0,0,0,1], ω cp F represents the air compressor motor speed. cp P is the mass flow rate at the air compressor outlet. sm To supply pipeline pressure, m sm For the air quality in the gas supply pipeline, m O2 m N2 These represent the mass of oxygen and nitrogen in the cathode channel, respectively, P rm V represents the pressure in the return pipe. cm For the input voltage, I st This represents the fuel cell current.

[0080] Preferably, the fault value is used as an extended state variable, thereby expanding the state equation into an augmented state equation, including:

[0081] Sensor malfunction and reactant shortage are designated as b1 and b2 respectively, and the malfunction values ​​are used as extended state variables according to the established state equation to form an augmented state equation:

[0082]

[0083] In the formula, It is the identity matrix. To augment the state variables, Γ·v represents the effect of system noise on the system, and e represents the measurement noise, where:

[0084]

[0085] Preferably, determining the fault state based on the fault state judgment model includes:

[0086]

[0087] In the formula, A is the judgment threshold.

[0088] Preferably, a fault state judgment model is established based on the state quantity estimates of a high-order sliding mode observer and sensor measurements, including:

[0089]

[0090] In the formula, For the fault state judgment model, ω cp ,F cp ,P sm ,P rm This refers to the output value of the sensor when actually monitoring the proton exchange membrane fuel cell system. is the output value of the higher-order sliding mode observer, and g() is a mapping relationship.

[0091] Preferably, such as Figure 3 As shown, fault-tolerant control of the proton exchange membrane fuel cell system under faulty or fault-free conditions is achieved through a fault-tolerant controller, including:

[0092] When it is determined that the proton exchange membrane fuel cell system has not malfunctioned, the oxygen ratio measurement value is output through the fault diagnosis and isolation module, and the decision variable will maintain the operation of the fault-tolerant controller 1.

[0093] When a sensor failure is detected in the proton exchange membrane fuel cell system, the measurement variables are reconstructed using the established high-order sliding mode observer to replace the sensor measurement values ​​that have failed. At the same time, the decision variables will maintain the operation of the fault-tolerant controller 2.

[0094] When a reactant shortage fault is detected in the proton exchange membrane fuel cell system, the oxygen ratio measurement value of the fault diagnosis and isolation module is reconstructed, and the decision variable will maintain the operation of the fault-tolerant controller 3.

[0095] When a sensor failure and a reactant shortage failure are simultaneously detected in a proton exchange membrane fuel cell system, the peroxy ratio measured by a high-order sliding mode observer is reconstructed through the fault diagnosis and isolation module, while the decision variables will maintain the operation of the fault-tolerant controller 3.

[0096] More preferably, when a reactant shortage is detected in the proton exchange membrane fuel cell system, the peroxy ratio is reconstructed and transmitted to the fault-tolerant controller 3, the specific expression of which is as follows:

[0097]

[0098] In the formula, This represents the predicted superoxide ratio at time (t+j). ΔV represents the measured value of the superoxide ratio at time t. cm (t+j-1) represents the future input setpoint of the system at time (t+j-1), E j ,F j All are polynomials uniquely determined by the shift operator polynomial A and the prediction length j, and B is the shift operator polynomial.

[0099] E j (q -1 ) = e j,0 +e j,1 q -1 +…+e j,j-1 q -(j-1)

[0100] F j (q -1 )=f j,0 +f j,1 q -1 +…+f j,j-1 q -(j-1)

[0101] B(q -1 )=b0+b1 q -1 +…+b n q -n

[0102] In the formula, t is the sampling time point, q is the shift operator, and n is the lag step size.

[0103] More preferably, the input signal of the fault-tolerant controller is the difference between the actual oxygen ratio and the reference oxygen ratio of the proton exchange membrane fuel cell system, and the output signal is the input voltage of the air compressor. The mathematical model of the fault-tolerant controller is as follows:

[0104]

[0105] In the formula, u s t is the input voltage of the air compressor, e1(t) is the difference between the reference oxygen ratio and the actual oxygen ratio, and W1 and W2 are both preset parameters.

[0106] Example 2

[0107] This embodiment is based on embodiment 1:

[0108] This embodiment provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the proton exchange membrane fuel cell fault-tolerant control method of Embodiment 1. The computer program can be in the form of source code, object code, executable file, or some intermediate form.

[0109] Example 3

[0110] This embodiment is based on embodiment 1:

[0111] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the proton exchange membrane fuel cell fault-tolerant control method of Embodiment 1. The computer program can be in the form of source code, object code, executable file, or some intermediate form. The storage medium includes any entity or device capable of carrying computer program code, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc. It should be noted that the content contained in the storage medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the storage medium does not include electrical carrier signals and telecommunication signals.

[0112] It should be noted that, for the sake of simplicity, the foregoing method embodiments are described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

Claims

1. A fault-tolerant control method for a proton exchange membrane fuel cell, characterized in that, include: A system model was established for a proton exchange membrane fuel cell system, and state equations were established based on the system model. By using the fault value as an extended state variable, the state equation is extended into an augmented state equation. A high-order sliding mode observer is established based on the augmented equation of state to observe the internal state variables of a proton exchange membrane fuel cell in real time, and a fault state judgment model is established based on the state variable estimates of the high-order sliding mode observer and the sensor measurements. The fault state is determined based on the fault state judgment model, and the fault-tolerant controller is used to perform fault-tolerant control on the proton exchange membrane fuel cell system in the fault state or the fault-free state. The establishment of state equations based on the system model includes: The state variables of the system model are determined, including the air compressor speed, air supply pipeline pressure, air mass flow rate, air mass in the air supply pipeline, oxygen mass in the cathode channel, nitrogen mass in the cathode channel, and return pipeline pressure. Determine the input variables of the system model, including the air compressor voltage and the fuel cell stack current; Determine the output variables of the system model, including air compressor speed, air supply pipeline pressure, air mass flow rate, and return pipeline pressure; Establish state equations based on the state variables, input variables, and output variables of the system model: In the formula, , , ω cp F represents the air compressor motor speed. cp P is the mass flow rate at the air compressor outlet. sm To supply pipeline pressure, m sm For the air quality in the gas supply pipeline, m O2 m N2 These represent the mass of oxygen and nitrogen in the cathode channel, respectively, P rm V represents the pressure in the return pipe. cm For the input voltage, I st This refers to the current in the fuel cell stack. The step of using fault values ​​as extended state variables to expand the state equations into augmented state equations includes: Sensor malfunction and reactant shortage are designated as b1 and b2 respectively, and the malfunction values ​​are used as extended state variables according to the established state equation to form an augmented state equation: In the formula, It is the identity matrix. To augment state variables, Let be the effect of system noise on the system, and e be the measurement noise, where: ； The fault state determination based on the fault state judgment model includes: In the formula, A is the judgment threshold.

2. The fault-tolerant control method for a proton exchange membrane fuel cell according to claim 1, characterized in that, The system model established for the proton exchange membrane fuel cell system includes: an air compressor model, a cathode flow channel model, an anode flow channel model, a return pipe model, and a fuel cell stack model.

3. The fault-tolerant control method for a proton exchange membrane fuel cell according to claim 2, characterized in that, The air compressor model includes: In the formula, ω cp J is the rotational speed of the air compressor motor, J is the moment of inertia, and k is the rotational speed of the air t k v R cm η is a motor-related constant. cm η cp The efficiencies of the motor and air compressor, respectively, V cm For the input voltage, C p P is the specific heat capacity of air, γ is the specific heat ratio of air, and P is the specific heat capacity of air. sm To supply pipeline pressure, P atm For atmospheric pressure, T atm For atmospheric temperature, F cp This is the mass flow rate at the air compressor outlet.

4. The fault-tolerant control method for a proton exchange membrane fuel cell according to claim 2, characterized in that, The cathode flow channel model and the anode flow channel model include: In the formula, P sm To supply pipeline pressure, m sm For the air quality in the gas supply pipeline, m O2 m N2 These represent the mass of oxygen and nitrogen in the cathode channel, respectively, where γ is the specific heat ratio of air, and R... a V is the gas constant for air. sm For the volume of the gas supply pipeline, T cp T is the air temperature of the compressor. sm W represents the air temperature in the gas supply pipeline. cp W is the output mass flow rate of the air compressor. sm,out W is the output mass flow rate of the gas supply pipeline. O2,ca,in To input the oxygen mass flow rate into the cathode channel, W O2,ca,out W represents the oxygen mass flow rate output from the cathode channel after the reaction. O2,react W represents the mass flow rate of oxygen consumed in the electrochemical reaction occurring in the cathode channel under the influence of the load current. N2,ca,in To input the nitrogen mass flow rate into the cathode channel, W N2,ca,out This represents the mass flow rate of nitrogen gas output from the cathode channel after the reaction.

5. The fault-tolerant control method for a proton exchange membrane fuel cell according to claim 2, characterized in that, The reflux pipe model includes: In the formula, P rm R is the pressure in the return pipe. a T is the gas constant of air. st V is the temperature of the fuel cell stack. rm W is the volume of the return pipe. ca,out W is the mass flow rate of the gas output from the cathode. rm,out This refers to the mass flow rate of the gas output from the return pipeline.

6. The fault-tolerant control method for a proton exchange membrane fuel cell according to claim 2, characterized in that, The fuel cell stack model includes: In the formula, V st Where N is the stack voltage, E is the number of stacks, and V is the Nernst voltage. act For activation loss, V conc For concentration loss, V ohm For ohmic loss.

7. A fault-tolerant control method for a proton exchange membrane fuel cell according to any one of claims 1-6, characterized in that, The fault-tolerant control of the proton exchange membrane fuel cell system under fault-tolerant or fault-free conditions via a fault-tolerant controller includes: When it is determined that the proton exchange membrane fuel cell system has not malfunctioned, the fault diagnosis and isolation module outputs the oxygen ratio measurement value, and the fault-tolerant controller adjusts the input voltage of the air compressor accordingly. When a sensor failure is detected in the proton exchange membrane fuel cell system, the measurement variables are reconstructed using an established high-order sliding mode observer to replace the faulty sensor measurement values, and the input voltage of the air compressor is adjusted accordingly by the fault-tolerant controller. When a reactant shortage fault is detected in the proton exchange membrane fuel cell system, the oxygen ratio measurement value is reconstructed through the fault diagnosis and isolation module, and the input voltage of the air compressor is adjusted accordingly through the fault-tolerant controller. When a sensor failure and a reactant shortage failure are simultaneously detected in a proton exchange membrane fuel cell system, the peroxygen ratio measured by a high-order sliding mode observer is reconstructed through a fault diagnosis and isolation module, and the input voltage of the air compressor is adjusted accordingly through a fault-tolerant controller.

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