CN117039069A - Water management fault-tolerant control method for proton exchange membrane fuel cell - Google Patents
Water management fault-tolerant control method for proton exchange membrane fuel cell Download PDFInfo
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- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 title claims abstract description 74
- 238000000034 method Methods 0.000 title claims abstract description 51
- 239000012528 membrane Substances 0.000 title claims abstract description 42
- 239000000446 fuel Substances 0.000 title claims abstract description 24
- 238000013178 mathematical model Methods 0.000 claims abstract description 25
- 230000036571 hydration Effects 0.000 claims abstract description 8
- 238000006703 hydration reaction Methods 0.000 claims abstract description 8
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 claims description 25
- 239000001301 oxygen Substances 0.000 claims description 25
- 229910052760 oxygen Inorganic materials 0.000 claims description 25
- IJGRMHOSHXDMSA-UHFFFAOYSA-N Atomic nitrogen Chemical compound N#N IJGRMHOSHXDMSA-UHFFFAOYSA-N 0.000 claims description 21
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 claims description 12
- 239000001257 hydrogen Substances 0.000 claims description 12
- 229910052739 hydrogen Inorganic materials 0.000 claims description 12
- 239000013598 vector Substances 0.000 claims description 12
- 229910052757 nitrogen Inorganic materials 0.000 claims description 9
- 230000008569 process Effects 0.000 claims description 8
- 238000006243 chemical reaction Methods 0.000 claims description 7
- 238000005457 optimization Methods 0.000 claims description 7
- MYMOFIZGZYHOMD-UHFFFAOYSA-N Dioxygen Chemical compound O=O MYMOFIZGZYHOMD-UHFFFAOYSA-N 0.000 claims description 6
- 229910001882 dioxygen Inorganic materials 0.000 claims description 6
- 239000007789 gas Substances 0.000 claims description 6
- 239000011159 matrix material Substances 0.000 claims description 6
- 238000012545 processing Methods 0.000 claims description 5
- 238000005096 rolling process Methods 0.000 claims description 4
- 239000000243 solution Substances 0.000 claims description 4
- 230000004913 activation Effects 0.000 claims description 3
- 238000009792 diffusion process Methods 0.000 claims description 3
- 229910001873 dinitrogen Inorganic materials 0.000 claims description 3
- 238000002347 injection Methods 0.000 claims description 3
- 239000007924 injection Substances 0.000 claims description 3
- 238000007726 management method Methods 0.000 claims 8
- 238000011160 research Methods 0.000 abstract description 7
- 230000007547 defect Effects 0.000 abstract description 4
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- 239000003054 catalyst Substances 0.000 description 1
- 238000011217 control strategy Methods 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
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- 230000008878 coupling Effects 0.000 description 1
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- 238000006731 degradation reaction Methods 0.000 description 1
- 238000007599 discharging Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000020169 heat generation Effects 0.000 description 1
- 235000003642 hunger Nutrition 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000013486 operation strategy Methods 0.000 description 1
- 125000000864 peroxy group Chemical group O(O*)* 0.000 description 1
- 239000000376 reactant Substances 0.000 description 1
- 230000037351 starvation Effects 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
- H01M8/00—Fuel cells; Manufacture thereof
- H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
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- H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
- H01M8/00—Fuel cells; Manufacture thereof
- H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
- H01M8/04291—Arrangements for managing water in solid electrolyte fuel cell systems
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- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract
The invention discloses a water management fault-tolerant control method of a proton exchange membrane fuel cell, which comprises the following steps: establishing a PEMFC mathematical model aiming at a PEMFC system, wherein the PEMFC mathematical model comprises a cathode model, an anode model, a membrane hydration model and a voltage model; according to the PEMFC mathematical model, a state equation facing PEMFC control is established; establishing a controller based on a discrete linearization model predictive control method; detecting the current fault state of the PEMFC system, adjusting parameters in a mathematical model of the system to corresponding states, and then performing fault-tolerant control on the system in a fault-free state, a membrane dry state and a flooding state by using a controller adopting a model prediction control method based on discrete linearization. The invention can keep stable output performance when the system has water management fault, has the advantages of high convergence speed, small overshoot and the like, and overcomes the defect of the conventional fuel cell fault-tolerant control in water management fault research.
Description
Technical Field
The invention belongs to the technical field of fuel cells, and particularly relates to a water management fault-tolerant control method for a proton exchange membrane fuel cell.
Background
Proton exchange membrane fuel cell (Proton Exchange Membrane Fuel Cell, PEMFC) systems are typically composed of a fuel supply system, an air supply system, a humidification system, a cooling system, a galvanic pile, etc., and the multi-auxiliary system structure and the multi-physical field coupling phenomenon involved in the operation of the cell itself place high demands on the control system thereof. The prior art has focused on controlling fuel cell systems in normal operating conditions with less control research in fault conditions. However, various faults such as water management, thermal management, reactant starvation and the like often occur in the operation of the PEMFC system, so that the aging of system components and the degradation of performance are caused, and the damage of the PEMFC stack is caused when the faults are serious, so that the reliability, the stability, the safety and the durability of the operation of the system are obviously limited. The fault-tolerant control technology is to determine control operation and control strategy based on the diagnosed faults, so as to achieve the effects of relieving system faults, improving system performance and prolonging system service life.
The existing fault-tolerant control research on the PEMFC system is mostly focused on the researches on an air supply system and a thermal management system. By taking supply manifold faults, exhaust manifold faults, sensor faults, thermal management faults and the like into consideration, a corresponding accurate mathematical model is established for the system, and methods such as PID control, fuzzy control, self-adaptive control and observer-based control are applied to adjust the air flow, the peroxy ratio, the cathode pressure and the temperature of the PEMFC system, so that the safe, stable and reliable operation of the system in a fault state is ensured. The research of the PEMFC fault-tolerant control often focuses on the subsystem of the PEMFC, but simplifies or ignores the water transmission mechanism in the system, and has certain limitation. Existing studies on the fault-tolerant control of the PEMFC system mostly consider air supply system faults, thermal management faults, and few studies on water management faults related to the internal water transfer mechanism of the fuel cell. Furthermore, studies have shown that water management faults are the most frequent type of faults occurring during PEMFC operation, including membrane drying and flooding. The membrane drying causes an increase in resistivity, resulting in an increase in heat generation, while flooding causes clogging of porous channels, a decrease in catalyst active area, and a decrease in reaction rate. It is important to study the fault-tolerant control of PEMFC water management faults.
The prior art has mainly the following disadvantages: (1) The existing research on PEMFC fault-tolerant control mostly considers air supply side faults, sensor faults and thermal management faults, and rarely considers the water management faults (2) to simplify or ignore the transmission mechanism of water in a battery in the process of establishing a mathematical model, so that larger errors exist between the water management faults and an actual system; (3) The prior art has the defects of long adjustment time, large overshoot and the like in the aspect of fault-tolerant control, and has the defects of accuracy and effectiveness.
Disclosure of Invention
In order to solve the problems, the invention provides a water management fault-tolerant control method for a proton exchange membrane fuel cell, which can ensure that a system can still maintain stable output performance when water management faults occur, has the advantages of high convergence speed, small overshoot and the like, and overcomes the defects of the conventional fuel cell fault-tolerant control in water management fault research.
In order to achieve the above purpose, the invention adopts the following technical scheme: a proton exchange membrane fuel cell water management fault-tolerant control method comprises the following steps:
establishing a PEMFC mathematical model aiming at a PEMFC system, wherein the PEMFC mathematical model comprises a cathode model, an anode model, a membrane hydration model and a voltage model;
according to the PEMFC mathematical model, a state equation facing PEMFC control is established;
a controller for establishing a model predictive control method based on discrete linearization, comprising the steps of: linearizing the state equation, discretizing, and finally solving a quadratic programming QP to obtain a control input; performing rolling optimization by using a model predictive control method based on discrete linearization to obtain control input at each moment;
detecting the current fault state of the PEMFC system, adjusting parameters in a mathematical model of the system to corresponding states, and then performing fault-tolerant control on the system in a fault-free state, a membrane dry state and a flooding state by using a controller adopting a model prediction control method based on discrete linearization.
Further, the anode and cathode mathematical models:
in the method, in the process of the invention,for the partial pressure of cathode oxygen, ">For cathode nitrogen partial pressure, p v,ca For the partial pressure of the water vapor of the cathode,for anode hydrogen partial pressure, p v,an For the partial pressure of the water vapor of the anode,/->Is oxygen gas constant, +.>Is the constant of nitrogen gas, R v Is water vapor gas constant, +.>Is oxygen gas constant, T is stack temperature, V ca/an For the cathode/anode volume of a single cell,W v,ca,in 、/>W v,an,in the mass flow rate of oxygen, nitrogen and water vapor flowing into the cathode and the mass flow rate of hydrogen and water vapor flowing into the anode are respectively +.>W v,ca,out 、/>W v,an,out The mass flow rates of oxygen, nitrogen and water vapor flowing out of the cathode and the mass flow rates of hydrogen and water vapor flowing out of the anode are respectively, the mass flow rates of oxygen and hydrogen consumed by the reaction are respectively W v,gen For the mass flow of the water vapor produced by the reaction, W v,mbr Is the mass flow rate of water vapor passing through the proton exchange membrane;
the membrane hydration model is:
wherein n is the number of the galvanic pile cells, M v Is the molar mass of water vapor, A f I is the current density of the galvanic pile, F is Faraday constant, D w Is the water diffusion coefficient of the film, t m Is the thickness of the proton exchange membrane; n is n d For the electroosmotic coefficient, c v,ca/an Is the concentration of water at the cathode/anode, both as a function of the water content;
the output voltage model is:
V st ＝n(E-v act -v conc -v ohm )；
wherein n is the number of cells in the stack, E is the Nernst voltage, v act V for activation loss conc Is concentration difference loss, v ohm Is ohmic loss.
Further, partial pressures of gases of the cathode and the anode are selected as state variables, a cathode-anode pressure difference and an oxygen partial pressure are selected as system output, air inflow of the cathode and the anode is selected as system input, and a state equation of the PEMFC system is obtained:
in the method, in the process of the invention,
u T ＝[p an,in ,p ca,in ] T ，/>
further, the linearization processing of the state equation includes: and obtaining the state equation after the linearization treatment of the PEMFC system by solving the jacobian matrix of the state equation at the current operation point.
Further, after the linearization of the state equation, discretization is performed, including: and integrating and simplifying the state equation after linearization processing to obtain the state equation after discretization processing.
Further, performing a quadratic programming QP solution includes: based on discrete linearization, the PEMFC system input is solved by a QP solver by establishing a cost function.
Further, by simplifying the cost function on the error vector and the control input vector, a state equation form which can be solved by the QP solver is obtained;
inputting a state equation matrix and constraint conditions in a QP solver to obtain a control sequence for minimizing a cost function, namely an input vector; and taking the first control input to be applied to the PEMFC system to finish the updating of the system parameters.
Further, the regulating parameter of the fault-free state is load current, the regulating parameter of the membrane dry state is load current and cathode inlet relative humidity, and the regulating parameter of the flooding state is load current and water injection flow of the humidifier.
The beneficial effect of adopting this technical scheme is:
the invention considers the transmission mechanism of water in the PEMFC in the establishment of the PEMFC mathematical model, so that the model is more accurate.
The invention provides a controller of a linearization model predictive control method based on discrete, and applies the controller to fault-tolerant control of a PEMFC system, and considers water management faults of membrane dry flooding which often occur in the PEMFC system. The proposed controller has a good control effect, has a smaller overshoot and a shorter adjustment time than the conventional method, and has stable output performance.
Drawings
FIG. 1 is a schematic flow diagram of a water management fault tolerant control method for a PEM fuel cell in accordance with the present invention;
FIG. 2 is a schematic diagram of a controller based on a discrete linearization model predictive control method in an embodiment of the invention;
FIG. 3 is a graph of a step load current signal in an embodiment of the invention;
FIG. 4 is a graph showing the control result of the cathode-anode pressure difference in the non-failure state according to the embodiment of the present invention;
FIG. 5 is a graph showing the control result of oxygen partial pressure in a fault-free state according to an embodiment of the present invention;
FIG. 6 is a graph showing the control result of the cathode-anode pressure difference in the dry state of the membrane according to the embodiment of the invention;
FIG. 7 shows the control result of oxygen partial pressure in the dry state of the membrane according to the embodiment of the invention;
FIG. 8 is a graph showing the control result of the cathode-anode pressure difference in the flooding state according to the embodiment of the present invention;
FIG. 9 is a graph showing the control result of oxygen partial pressure in a flooding state according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, in order to make the objects, technical solutions and advantages of the present invention more apparent.
In this embodiment, referring to fig. 1, the present invention provides a fault-tolerant control method for water management of a proton exchange membrane fuel cell, which includes the steps of:
establishing a PEMFC mathematical model aiming at a PEMFC system, wherein the PEMFC mathematical model comprises a cathode model, an anode model, a membrane hydration model and a voltage model;
according to the PEMFC mathematical model, a state equation facing PEMFC control is established;
a controller for establishing a model predictive control method based on discrete linearization, comprising the steps of: linearizing the state equation, discretizing, and finally solving a quadratic programming QP to obtain a control input; performing rolling optimization by using a model predictive control method based on discrete linearization to obtain control input at each moment;
detecting the current fault state of the PEMFC system, adjusting parameters in a mathematical model of the system to corresponding states, and then performing fault-tolerant control on the system in a fault-free state, a membrane dry state and a flooding state by using a controller adopting a model prediction control method based on discrete linearization.
As an optimization scheme of the above embodiment, a PEMFC mathematical model is established for a PEMFC system, the PEMFC mathematical model including a cathode, an anode model, a membrane hydration model, and a voltage model.
Wherein, the anode and cathode mathematical models:
in the method, in the process of the invention,for the partial pressure of cathode oxygen, ">For cathode nitrogen partial pressure, p v,ca For the partial pressure of cathodic water vapor,/-)>For anode hydrogen partial pressure, p v,an For the partial pressure of the water vapor of the anode,/->Is oxygen gas constant, +.>Is the constant of nitrogen gas, R v Is water vapor gas constant, +.>Is oxygen gas constant, T is stack temperature, V ca/an For the cathode/anode volume of a single cell,W v,ca,in 、/>W v,an,in the mass flow rate of oxygen, nitrogen and water vapor flowing into the cathode and the mass flow rate of hydrogen and water vapor flowing into the anode are respectively +.>W v,ca,out 、/>W v,an,out The mass flow rates of oxygen, nitrogen and water vapor flowing out of the cathode and the mass flow rates of hydrogen and water vapor flowing out of the anode are respectively, the mass flow rates of oxygen and hydrogen consumed by the reaction are respectively W v,gen For the mass flow of the water vapor produced by the reaction, W v,mbr Is the mass flow rate of water vapor passing through the proton exchange membrane;
wherein, the membrane hydration model is:
wherein n is the number of the galvanic pile cells, M v Is the molar mass of water vapor, A f I is the current density of the galvanic pile, F is Faraday constant, D w Is the water diffusion coefficient of the film, t m Is the thickness of the proton exchange membrane; n is n d For the electroosmotic coefficient, c v,ca/an Is the concentration of water at the cathode/anode, both as a function of the water content;
the output voltage model is as follows:
V st ＝n(E-v act -v conc -v ohm )；
wherein n is the number of cells in the stack, E is the Nernst voltage, v act V for activation loss conc Is concentration difference loss, v ohm Is ohmic loss.
As an optimization scheme of the above embodiment, according to the PEMFC mathematical model, a state equation facing PEMFC control is established:
the partial pressure of each gas of the cathode and the anode is selected as a state variable, the cathode-anode pressure difference and the oxygen partial pressure are selected as system output, the air inflow of the cathode and the anode is selected as system input, and a state equation of the PEMFC system is obtained:
in the method, in the process of the invention,
u T ＝[p an,in ,p ca,in ] T ，/>
as an optimization scheme of the above embodiment, a controller for establishing a model predictive control method based on discrete linearization includes the steps of: linearizing the state equation, discretizing, and finally solving a quadratic programming QP to obtain a control input; the control input at each moment is obtained by performing rolling optimization by using a model predictive control method based on discrete linearization, as shown in fig. 2.
Wherein the linearizing the state equation includes: and obtaining a state equation after the linearization treatment of the PEMFC system by solving a jacobian matrix of the state equation at the current operation point:
wherein A is L 、B L 、C L Jacobian submatrices of functions F and Z with respect to the derivatives at the state vector component and at the input vector component, respectively, i.eK is a constant term. X is x o 、u o Is the state quantity and input quantity at the current operating point.
After the linearization of the state equation, discretization is performed, including: and integrating and simplifying the state equation after linearization to obtain a discretized state equation:
in the method, in the process of the invention,C D ＝C L 。
wherein performing the quadratic programming QP solution includes: based on discrete linearization, the PEMFC system input is solved by a QP solver by establishing a cost function.
By simplifying the relation of error vectorsAnd control input vector +.>To obtain a state equation form that the QP solver can solve:
wherein M, N is Q, R, A D 、B D 、C D Q, R are weight matrices of error and input vectors, respectively, expressed as Wherein n is p For predicting the interval length, the present invention takes +.>
Constraint conditions: because the inlet pressure of the anode and the cathode of the PEMFC system is limited, the minimum inlet pressure of the anode and the cathode is set to be 100kPa, and the maximum inlet pressure is set to be 600kPa.
Inputting the state equation matrix M, N and constraints in the QP solver results in a control sequence that minimizes the cost function, i.e., the input vectorTaking the first control inputThe method is applied to the PEMFC system to finish the updating of the system parameters.
As an optimized discharging scheme of the above embodiment, the adjustment parameter of the non-fault state is a load current, the adjustment parameter of the dry state is a load current and a cathode intake relative humidity, and the adjustment parameter of the flooded state is a load current and a water injection flow of the humidifier.
Specific examples:
the present invention allows the PEMFC system to operate under a step load current signal as shown in fig. 3.
In the first case, control in a failure-free state.
The control results of the cathode-anode pressure difference and the oxygen partial pressure of the PEMFC system in the fault-free state are shown in fig. 4 and 5, respectively. It can be seen that the differential pressure between the cathode and anode and the partial pressure of oxygen can be maintained around the reference value under the control of the controller based on the discrete linearization model predictive control method.
And secondly, fault-tolerant control under the membrane dry fault state.
At 5s, the system failed dry film. The control results of the cathode pressure difference and the oxygen partial pressure in the dry state of the membrane are shown in fig. 6 and 7, respectively. It can be seen that under the control of the controller based on the discrete linearization model predictive control method, the cathode-anode pressure difference and the oxygen partial pressure can be maintained near the reference values even if the system suffers from a dry film failure.
And thirdly, fault-tolerant control under the flooding fault state.
At 5s, the system fails to flood. The control results of the cathode-anode pressure difference and the oxygen partial pressure in the flooding failure state are shown in fig. 8 and 9, respectively. It can be seen that under the control of the controller based on the discrete linearization model predictive control method, the cathode-anode pressure difference and the oxygen partial pressure can be maintained near the reference values even if the system fails to water flooding.
In all three cases, a traditional PID controller is introduced to compare the control performance with a controller based on a discrete linearization model predictive control method. Compared with the average overshoot of PID, the controller provided by the invention reduces the average adjustment time by about 83% and shortens the average adjustment time by about 87% for the cathode-anode pressure difference; for the oxygen partial pressure, the average overshoot of the controller provided by the invention is only about 2% of the PID, and the average adjustment time is only about 0.4% of the PID. Therefore, compared with the PID-based fault-tolerant control, the fault-tolerant control of the controller provided by the invention has shorter adjustment time and smaller overshoot, and particularly in the control of poor cathode-anode pressure under flooding faults, the controller provided by the invention has obvious advantages in controlling the overshoot.
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (8)
1. A proton exchange membrane fuel cell water management fault-tolerant control method is characterized by comprising the following steps:
establishing a PEMFC mathematical model aiming at a PEMFC system, wherein the PEMFC mathematical model comprises a cathode model, an anode model, a membrane hydration model and a voltage model;
according to the PEMFC mathematical model, a state equation facing PEMFC control is established;
a controller for establishing a model predictive control method based on discrete linearization, comprising the steps of: linearizing the state equation, discretizing, and finally solving a quadratic programming QP to obtain a control input; performing rolling optimization by using a model predictive control method based on discrete linearization to obtain control input at each moment;
detecting the current fault state of the PEMFC system, adjusting parameters in a mathematical model of the system to corresponding states, and then performing fault-tolerant control on the system in a fault-free state, a membrane dry state and a flooding state by using a controller adopting a model prediction control method based on discrete linearization.
2. The fault tolerant control method for water management of a proton exchange membrane fuel cell according to claim 1, wherein the mathematical models of anode and cathode:
in the method, in the process of the invention,for the partial pressure of cathode oxygen, ">For cathode nitrogen partial pressure, p v,ca For the partial pressure of cathodic water vapor,/-)>For anode hydrogen partial pressure, p v,an For the partial pressure of the water vapor of the anode,/->Is oxygen gas constant, +.>Is the constant of nitrogen gas, R v Is water vapor gas constant, +.>Is oxygen gas constant, T is stack temperature, V ca/an For the cathode/anode volume of a single cell,W v,ca,in 、/>W v,an,in the mass flow rate of oxygen, nitrogen and water vapor flowing into the cathode and the mass flow rate of hydrogen and water vapor flowing into the anode are respectively +.>W v,an,out The mass flow rates of oxygen, nitrogen and water vapor flowing out of the cathode and the mass flow rates of hydrogen and water vapor flowing out of the anode are respectively, the mass flow rates of oxygen and hydrogen consumed by the reaction are respectively W v,gen For the mass flow of the water vapor produced by the reaction, W v,mbr Is the mass flow rate of water vapor passing through the proton exchange membrane;
the membrane hydration model is:
wherein n is the number of the galvanic pile cells, M v Is the molar mass of water vapor, A f I is the current density of the galvanic pile, F is Faraday constant, D w Is the water diffusion coefficient of the film, t m Is the thickness of the proton exchange membrane; n is n d For the electroosmotic coefficient, c v,ca/an Is the concentration of water at the cathode/anode, both as a function of the water content;
the output voltage model is:
V st ＝n(E-v act -v conc -v ohm )；
wherein n is the number of cells in the stack, E is the Nernst voltage, v act V for activation loss conc Is concentration difference loss, v ohm Is ohmic loss.
3. The fault-tolerant control method for water management of a proton exchange membrane fuel cell according to claim 2, wherein partial pressures of each gas of a cathode and an anode are selected as state variables, a cathode-anode pressure difference and an oxygen partial pressure are selected as system outputs, air inflow of the cathode and the anode is selected as system inputs, and a state equation of a PEMFC system is obtained:
in the method, in the process of the invention,
4. the fault-tolerant control method for water management of a pem fuel cell according to claim 1, wherein said linearizing of said equation of state comprises: and obtaining the state equation after the linearization treatment of the PEMFC system by solving the jacobian matrix of the state equation at the current operation point.
5. The fault-tolerant control method for water management of a pem fuel cell of claim 4 wherein said linearizing of said equation of state is followed by discretizing said equation of state comprising: and integrating and simplifying the state equation after linearization processing to obtain the state equation after discretization processing.
6. The fault-tolerant control of proton exchange membrane fuel cell water management method as claimed in claim 5, wherein performing a quadratic programming QP solution comprises: based on discrete linearization, the PEMFC system input is solved by a QP solver by establishing a cost function.
7. The fault-tolerant control method for water management of a proton exchange membrane fuel cell according to claim 6, wherein the form of a state equation that can be solved by a QP solver is obtained by simplifying a cost function with respect to an error vector and a control input vector;
inputting a state equation matrix and constraint conditions in a QP solver to obtain a control sequence for minimizing a cost function, namely an input vector; and taking the first control input to be applied to the PEMFC system to finish the updating of the system parameters.
8. The fault-tolerant control method for water management of a proton exchange membrane fuel cell according to claim 1, wherein the adjustment parameter of the no-fault state is a load current, the adjustment parameter of the membrane dry state is a load current and a cathode intake relative humidity, and the adjustment parameter of the flooded state is a load current and a water injection flow of a humidifier.
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