Dual closed-loop control method for air supply system of proton exchange membrane fuel cell

By adopting a dual closed-loop control method in the fuel cell air supply system, and using the super-spiral algorithm and the preset time convergence algorithm, the problems of complex and low efficiency of existing systems are solved, and faster response speed and better anti-interference performance are achieved.

CN115295840BActive Publication Date: 2025-04-18HARBIN INST OF TECH
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Patent Information

Application Number
CN202111394217.1
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2021-11-23
Publication Date
2025-04-18
Estimated Expiration
2041-11-23

AI Technical Summary

Technical Problem

The existing fuel cell air supply system has problems such as complex calculations, large calculation volume and low efficiency, making it difficult to apply in real time.

Method used

A double closed-loop control method for air supply system of proton exchange membrane fuel cell is proposed. The outer ring controls the oxygen excess ratio based on the superspiral algorithm, and the inner ring controls the compressor flow through the preset time convergence algorithm to achieve the actual oxygen supply tracking the given value of the outer ring.

Benefits of technology

This method can cope with system parameter uncertainty, significantly improve response speed, and improve anti-interference performance and stability.

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Abstract

The double closed-loop control method of the air supply system of a proton exchange membrane fuel cell belongs to the field of fuel cell technology. The present invention is to solve the problem that the existing fuel cell air supply system has complex calculations, large amount of calculations, and low efficiency, which makes it difficult to apply in real time. It includes: the outer loop adjusts the oxygen supply by controlling the compressor flow, so that the control target of the air supply system is: the actual oxygen excess ratio can track the optimal oxygen excess ratio of the current state: represents the actual oxygen excess ratio, represents the optimal oxygen excess ratio of the current state; the control loop of the outer loop generates a reference compressor flow rate based on the oxygen excess ratio error through a super spiral algorithm; the inner loop controls the torque by controlling the compressor current, so that the actual oxygen supply tracks the given value of the outer loop; the control loop of the inner loop controls the actual speed according to the given reference compressor flow of the outer loop through a preset time convergence algorithm. The present invention is used for the air supply system of a fuel cell.
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Description

Technical Field

[0001] The invention relates to a double closed-loop control method for an air supply system of a proton exchange membrane fuel cell, belonging to the technical field of fuel cells. Background Art

[0002] Fuel cells are considered as a potential energy conversion technology with high efficiency and environmental protection. Among various types of fuel cells, proton exchange membrane fuel cells (PEMFC) are particularly suitable for the energy supply of electric vehicles due to their advantages such as low temperature, fast start-up and high energy density. However, PEMFC is a multi-input and multi-output system with strong nonlinearity, so precise control technology is required to ensure optimal performance. One of the most challenging tasks is the fuel cell air supply control, that is, regulating the oxygen flow in the cathode. When the load suddenly increases, it must be ensured that the amount of oxygen supplied by the air compressor does not drop below the critical level (oxygen excess ratio is less than 1), otherwise oxygen deficiency will occur, resulting in hot spots on the membrane surface and irreversible damage to the exchange membrane. On the other hand, since the intake system can consume up to 30% of the power of the fuel cell under high load conditions, it is necessary to reduce its energy consumption. In short, the control of the fuel cell air supply system is one of the key factors for optimizing the operating conditions of the fuel cell.

[0003] At the controller level, there are many model-based control strategies for fuel cell air supply systems, including linear state feedback control, model predictive control, intelligent control, and sliding mode control (SMC). The main disadvantage of using intelligent control methods is that the computational burden is too high and offline training is required, which makes their practical application difficult. In addition, models based on neural networks / fuzzy rules cannot provide explicit structural properties of the physical system. At the observer level, the key issue in fuel cell control design is the reconstruction of the oxygen excess ratio. Since this value depends on the oxygen flow entering the cathode and cannot be obtained by measurement, a state observer can be used to estimate the variable instead of a physical sensor. At present, many observation / estimation strategies related to fuel cell systems have been proposed, and a variety of Kalman filters have been applied to the state estimation of fuel cell systems. However, these methods are greatly affected by external disturbances, and the calculation of their Jacobian matrices is time-consuming and laborious. There is also a finite-time convergent state observer based on a high-order sliding mode, which satisfies the separation principle, which means that the controller and observer can be designed separately. However, this method relies on the calculation of a complex observability matrix, which is highly nonlinear and closely related to the state variables, making it difficult to apply in real time. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that the existing fuel cell air supply system has complex calculations, large amount of calculations, low efficiency and is difficult to apply in real time, and a dual closed-loop control method for a proton exchange membrane fuel cell air supply system is provided.

[0005] The double closed-loop control method of the air supply system of a proton exchange membrane fuel cell described in the present invention comprises:

[0006] The outer loop adjusts the oxygen supply by controlling the compressor flow, so that the control target of the air supply system is: the actual oxygen excess ratio can track the optimal oxygen excess ratio of the current state: represents the actual oxygen excess ratio, Indicates the optimal oxygen excess ratio in the current state; the control loop of the outer loop generates a reference compressor flow rate based on the oxygen excess ratio error through a super spiral algorithm;

[0007] The inner loop controls the torque by controlling the compressor current, so that the actual oxygen supply tracks the given value of the outer loop; the control loop of the inner loop controls the actual speed according to the reference compressor flow given by the outer loop through a preset time convergence algorithm.

[0008] Preferably, the actual oxygen excess ratio for:

[0009]

[0010] in: represents the oxygen inlet flow rate, represents the oxygen reaction flow rate,

[0011] k 18 and k 19 All represent constants;

[0012] ζ, ζ: = I st is the load change, i.e., stack current;

[0013] p sm represents the gas pressure in the supply manifold, the supply manifold volume being the lumped volume of the piping between the compressor and the manifold;

[0014] χ represents the cathode pressure.

[0015] Preferably, the optimal oxygen excess ratio in the current state Fitting to the stack current I st Function:

[0016]

[0017] Preferably, the optimal oxygen excess ratio in the current state Fluctuates within the range of 2 to 2.5.

[0018] Preferably, the specific method for obtaining the control target of the air supply system includes:

[0019] S1. Establishing the air supply system of the fuel cell according to the general fourth-order model of the fuel cell, and adding the water vapor partial pressure in the air supply system during the establishment process;

[0020] The state vector is:

[0021] x=[x1,x2,x3,x4,x5] T =[ω cp ,p sm ,P O2 ,P N2 ,P v,ca ] T ;

[0022] Among them, x1, x2, x3, x4, x5 are intermediate parameters, ω cp Indicates the speed of the intake duct compressor, p sm Indicates the air pressure in the air supply manifold, represents the dynamic partial pressure of oxygen, represents the dynamic partial pressure of nitrogen, P v,ca represents the dynamic partial pressure of water vapor;

[0023] S2, establish a compressor model;

[0024] Compressor mass flow W cp is the compressor speed ω cp The function of is denoted as h2;

[0025] Note: χ: = p ca =x3+x4+x5;

[0026] Where: p ca Defined as the fuel cell cathode pressure;

[0027] S3. Establish a nonlinear model for control:

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] Among them, u:=i q is the control input, function Indicates the flow rate at the cathode outlet; k1~k 17 All represent constants;

[0034] Measurable outputs:

[0035] Output voltage h1 = V st , compressor flow h2=W cp , manifold pressure p sm ;

[0036] S4, power optimization is equivalent to keeping the oxygen excess ratio at the optimal value in the current state

[0037] The control objectives of the fuel cell air supply system are:

[0038] The actual oxygen excess ratio Ability to track current optimal oxygen excess ratio

[0039] Preferably, the specific method for obtaining the cathode pressure χ is:

[0040] Use the extended state observer ESO to obtain;

[0041] According to formula (6), we can obtain:

[0042]

[0043] in, The system disturbance is d(t)=k8g1(x2)χ;

[0044] Let e1:=x2 and e2:=d(t), g1(x2) and χ are both differentiable, and Where b(t) is the rate of change of the system disturbance d(t);

[0045] Then the linear extended state observer ESO is expressed as:

[0046]

[0047] in: R 2 represents a two-dimensional space consisting of real numbers R, α1 and α2 represent the parameters to be designed, and the poles are located in the left half plane; g2(e1,h2)=g1(e1)(h2-k8e1);

[0048] The error of the extended state observer ESO is: and

[0049] The dynamic characteristics of the error are expressed as:

[0050]

[0051] g1(x2) is a bounded reversible function within the domain of definition. The estimated value of the cathode pressure χ can be inferred from the perturbation relationship in formula (7).

[0052] Preferably, the controller of the outer control loop is:

[0053] The oxygen excess ratio is:

[0054]

[0055] The outer ring sliding surface is

[0056] Take the first-order derivative of the sliding surface σ1(t):

[0057]

[0058] Among them, φ1 and γ1 represent design parameters, including system uncertainties;

[0059] The super spiral algorithm is used to solve the system to converge all solutions, that is, the compressor flow target value given by the outer loop to the inner loop:

[0060]

[0061] Among them, φ 10 represents the known part of φ1 as a function of nominal parameters, represents the known part of the function based on the nominal parameters in γ1, λ1 and β1 are the parameters to be adjusted, The real-time value of is obtained using the Levant integrator.

[0062] Preferably, to prevent excessive fluctuations in the given value, a linear first-order filter is added after the controller of the outer loop:

[0063]

[0064] Where μ is a selectable constant. represents the output of the linear first-order filter, which is the compressor flow command provided to the control loop.

[0065] Preferably, the controller of the inner control loop is:

[0066] The synovial surface of the inner ring is

[0067] Obtain the first-order derivative of σ2(t) with respect to time:

[0068]

[0069] Wherein: η υ-c represents the volumetric efficiency, V cpr / tr represents the volume of gas transported per revolution of the compressor, ρ a represents the air density;

[0070] Using feedback linearization:

[0071]

[0072] Substituting Equation (12) into Equation (13), we obtain:

[0073]

[0074] where d2(t) represents the uncertainty of the system. For an actual system, |d2(t)| < K, where K is a constant;

[0075] The controller for the inner loop is obtained as:

[0076]

[0077] The constant ε > 1; v, v nom 、v dis all represent intermediate variables.

[0078] Preferably, the convergence time is set to t f to obtain the sliding mode surface s as:

[0079] s = σ2 - σ2(0) - ∫v nom dτ;

[0080] σ2(0) represents the initial value of σ2.

[0081] Advantages of the present invention: The dual closed-loop control method for the air supply system of the proton exchange membrane fuel cell proposed by the present invention is a dual closed-loop structure: an oxygen excess ratio regulation loop (outer loop) based on ESO and a compressor flow control loop (inner loop). Under the control of the method of this invention, the system can cope with the uncertainty of system parameters, and the response speed has been significantly improved.

[0082] The present invention incorporates a sliding mode control technique into the cascaded controller based on ESO, which well improves the anti-interference performance and stability of the system. The extended state observer regards the external disturbance as a new system state and estimates and compensates it in a feedback manner. Such an observer is a very effective way to deal with system uncertainty and external disturbances.

[0083] High-order sliding mode control is very suitable for fuel cell air supply systems. It is essentially a special type of nonlinear control, and the nonlinearity is manifested as control discontinuity. This control strategy can change purposefully and continuously according to the current state of the system during the dynamic process, forcing the system to move according to the state trajectory of the predetermined "sliding mode". Since the sliding mode can be designed and is independent of the object parameters and disturbances, this makes the sliding mode control have the advantages of fast response, robustness to corresponding parameter changes and disturbances, no need for online identification of the system, and simple physical implementation. The preset time convergence can ensure that the selected state reaches stability at a certain set time, so that the inner loop tracks the outer loop given within a certain time, thereby ensuring the overall expected control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 is a schematic diagram of the system structure of the fuel cell of the present invention;

[0085] Figure 2 It is a flow chart of the double closed-loop control method of the air supply system of the proton exchange membrane fuel cell of the present invention;

[0086] Figure 3 is the output current under load changes in the experimental verification. In the figure: the horizontal axis is time, the vertical axis is output current, and the unit is (A);

[0087] Figure 4 is the flow rate of the compressor under load changes. In the figure: the horizontal axis is time, and the vertical axis is the compressor flow rate, the unit is (g / s);

[0088] Figure 5 It is the performance of oxygen excess ratio. In the figure: the horizontal axis is time, and the vertical axis is oxygen excess ratio;

[0089] Figure 6 It is the output voltage characteristic. In the figure: the horizontal axis is time, the vertical axis is output voltage, unit (V);

[0090] Figure 7 is the output power. In the figure: the horizontal axis is time, the vertical axis is power, unit (kW). DETAILED DESCRIPTION

[0091] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0092] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0093] Specific implementation method 1: The following is combined Figure 1 and Figure 2 The present embodiment is described. The dual closed-loop control method of the air supply system of the proton exchange membrane fuel cell described in the present embodiment comprises: the outer loop adjusts the oxygen supply by controlling the compressor flow, so that the control target of the air supply system is: the actual oxygen excess ratio can track the optimal oxygen excess ratio of the current state: represents the actual oxygen excess ratio, Indicates the optimal oxygen excess ratio in the current state; the control loop of the outer loop generates a reference compressor flow rate based on the oxygen excess ratio error through a super spiral algorithm;

[0094] The inner loop controls the torque by controlling the compressor current, so that the actual oxygen supply tracks the given value of the outer loop; the control loop of the inner loop controls the actual speed according to the reference compressor flow given by the outer loop through a preset time convergence algorithm.

[0095] Furthermore, the actual oxygen excess ratio for:

[0096]

[0097] in: represents the oxygen inlet flow rate, represents the oxygen reaction flow rate,

[0098] k 18 and k 19 All represent constants;

[0099] ζ, ζ: = I st is the load change, i.e., stack current;

[0100] p sm represents the gas pressure in the supply manifold, the supply manifold volume being the lumped volume of the piping between the compressor and the manifold;

[0101] χ represents the cathode pressure.

[0102] Furthermore, the optimal oxygen excess ratio in the current state Fitting to the stack current I st Function:

[0103]

[0104] Furthermore, the optimal oxygen excess ratio in the current state Fluctuates within the range of 2 to 2.5.

[0105] In this embodiment, under high load conditions, the air supply system can consume up to 30% of the fuel cell power. Therefore, it should be operated at the optimal point as much as possible to provide the most sufficient oxygen required for the hydrogen and oxygen reaction. Power optimization is equivalent to keeping the oxygen excess ratio at the optimal value. The value fluctuates in the range of 2-2.5.

[0106] Furthermore, the specific method of obtaining the control target of the air supply system includes:

[0107] S1. Establishing the air supply system of the fuel cell according to the general fourth-order model of the fuel cell, and adding the water vapor partial pressure in the air supply system during the establishment process;

[0108] The state vector is:

[0109] x=[x1,x2,x3,x4,x5] T =[ω cp ,p sm ,P O2 ,P N2 ,P v,ca ] T ;

[0110] Among them, x1, x2, x3, x4, x5 are intermediate parameters, ω cp Indicates the speed of the intake duct compressor, p sm Indicates the air pressure in the air supply manifold, represents the dynamic partial pressure of oxygen, represents the dynamic partial pressure of nitrogen, P v,ca represents the dynamic partial pressure of water vapor;

[0111] S2, establish a compressor model;

[0112] Compressor mass flow W cp is the compressor speed ω cp The function of is denoted as h2;

[0113] Note: χ: = p ca =x3+x4+x5;

[0114] Where: p ca Defined as the fuel cell cathode pressure;

[0115] S3. Establish a nonlinear model for control:

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] Among them, u:=i q is the control input, function Indicates the flow rate at the cathode outlet; k1~k 17 All represent constants;

[0122] Measurable outputs:

[0123] Output voltage h1 = V st , compressor flow h2=W cp , manifold pressure p sm ;

[0124] S4, power optimization is equivalent to keeping the oxygen excess ratio at the optimal value in the current state

[0125] The control objectives of the fuel cell air supply system are:

[0126] The actual oxygen excess ratio Ability to track current optimal oxygen excess ratio

[0127] Furthermore, the specific method for obtaining the cathode pressure χ is:

[0128] Use the extended state observer ESO to obtain;

[0129] According to formula (6), we can obtain:

[0130]

[0131] in, The system disturbance is d(t)=k8g1(x2)χ;

[0132] Let e1:=x2 and e2:=d(t), g1(x2) and χ are both differentiable, and Where b(t) is the rate of change of the system disturbance d(t);

[0133] Then the linear extended state observer ESO is expressed as:

[0134]

[0135] in: R 2represents a two-dimensional space consisting of real numbers R, α1 and α2 represent the parameters to be designed, and the poles are located in the left half plane; g2(e1,h2)=g1(e1)(h2-k8e1);

[0136] The error of the extended state observer ESO is: and

[0137] The dynamic characteristics of the error are expressed as:

[0138]

[0139] g1(x2) is a bounded reversible function within the domain of definition. The estimated value of the cathode pressure χ can be inferred from the perturbation relationship in formula (7).

[0140] Furthermore, the controller of the outer control loop is:

[0141] The oxygen excess ratio is:

[0142]

[0143] The outer ring sliding surface is

[0144] Take the first-order derivative of the sliding surface σ1(t):

[0145]

[0146] Among them, φ1 and γ1 represent design parameters, including system uncertainties;

[0147] The super spiral algorithm is used to solve the system to converge all solutions, that is, the compressor flow target value given by the outer loop to the inner loop:

[0148]

[0149] Among them, φ 10 represents the known part of φ1 as a function of nominal parameters, represents the known part of the function based on the nominal parameters in γ1, λ1 and β1 are the parameters to be adjusted, The real-time value of is obtained using the Levant integrator.

[0150] Furthermore, to prevent excessive fluctuations in the given value, a linear first-order filter is added after the controller of the outer loop:

[0151]

[0152] Where μ is a selectable constant. denotes the output of the linear first-order filter and is the compressor flow rate command provided to the control loop.

[0153] Furthermore, the controller of the inner loop control loop is:

[0154] The sliding surface of the inner loop is

[0155] Obtain the first derivative of σ2(t) with respect to time:

[0156]

[0157] Where: η υ-c denotes the volumetric efficiency, V cpr / tr denotes the volume of gas transported per revolution of the compressor, ρ a denotes the air density;

[0158] Use feedback linearization:

[0159]

[0160] Substitute Equation (12) into Equation (13) to obtain:

[0161]

[0162] where d2(t) represents the uncertainty of the system. For an actual system, |d2(t)| < K, where K is a constant;

[0163] Obtain the controller of the inner loop as:

[0164]

[0165] The constant ε > 1; v, v nom 、v dis all represent intermediate variables.

[0166] Furthermore, set the convergence time to t f to obtain the sliding surface s as:

[0167] s = σ2 - σ2(0) - ∫v nom dτ;

[0168] σ2(0) represents the initial value of σ2.

[0169] During the verification experiment of the present invention, the output current fluctuates within 100 - 350 A, as Figure 3 shown, and the corresponding compressor flow rate is as Figure 4 shown. The parameter values are shown in Table 1, the parameter uncertainties are shown in Table 2, and the parameter definitions are shown in Table 3:

[0170] Table 1

[0171]

[0172]

[0173] Table 2

[0174]

[0175]

[0176] Table 3

[0177]

[0178] like Figure 5 As shown in the figure, it can be seen that at t=10s, the load current suddenly increases (from 150 to 300A), resulting in a sudden decrease in the oxygen excess ratio (from 2.1 to 1.4). On the contrary, at t=20s, the sudden decrease in the load current (from 350 to 250A) causes a sudden increase in the oxygen excess ratio (from 2.1 to 2.9). However, it can basically be guaranteed that the optimal oxygen excess ratio will be readjusted within 2s.

[0179] The compressor flow reference value is generated by the outer regulation loop, which calculates the compressor flow reference value based on the error between the expected value of the oxygen excess ratio and its estimated value. The stack voltage and net power under the joint control of the inner and outer loops are shown as follows: Figure 6 and 7 As shown, according to the load current, when the net power of the fuel cell varies between 6 and 22 kW, the output voltage varies between 61 and 67 V. It can be seen that the controller of the present invention has a small overshoot and a fast adjustment speed.

[0180] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be used in other described embodiments.

Claims

1. A double closed-loop control method for an air supply system of a proton exchange membrane fuel cell, characterized in that: It includes: The outer loop adjusts the oxygen supply by controlling the compressor flow, so that the control target of the air supply system is: the actual oxygen excess ratio can track the optimal oxygen excess ratio of the current state: represents the actual oxygen excess ratio, Indicates the optimal oxygen excess ratio in the current state; the control loop of the outer loop generates a reference compressor flow rate based on the oxygen excess ratio error through a super spiral algorithm; The inner loop controls the torque by controlling the compressor current, so that the actual oxygen supply tracks the given value of the outer loop; the control loop of the inner loop controls the actual speed according to the given reference compressor flow of the outer loop through a preset time convergence algorithm; The actual oxygen excess ratio for: in: represents the oxygen inlet flow rate, represents the oxygen reaction flow rate, k 18 and k 19 All represent constants; ζ, ζ: = I st is the load change, i.e., stack current; p sm represents the gas pressure in the supply manifold, the supply manifold volume being the lumped volume of the piping between the compressor and the manifold; χ represents cathode pressure; The specific method for obtaining the control target of the air supply system includes: S1. Establishing the air supply system of the fuel cell according to the general fourth-order model of the fuel cell, and adding the water vapor partial pressure in the air supply system during the establishment process; The state vector is: Among them, x1, x2, x3, x4, x5 are intermediate parameters, ω cp Indicates the speed of the intake duct compressor, p sm Indicates the air pressure in the air supply manifold, represents the dynamic partial pressure of oxygen, represents the dynamic partial pressure of nitrogen, P v,ca represents the dynamic partial pressure of water vapor; S2, establish a compressor model; Compressor mass flow W cp is the compressor speed ω cp The function of is denoted as h2; Note: χ: = p ca =x3+x4+x5; Where: p ca Defined as the fuel cell cathode pressure; S3. Establish a nonlinear model for control: Among them, u:=i q is the control input, function Indicates the flow rate at the cathode outlet; k1~k 17 All represent constants; measurable output quantities: Output voltage h1 = V st , compressor flow h2=W cp , manifold pressure p sm ; S4, power optimization is equivalent to keeping the oxygen excess ratio at the optimal value in the current state The control objectives of the fuel cell air supply system are: The actual oxygen excess ratio Ability to track current optimal oxygen excess ratio The specific method for obtaining the cathode pressure χ is: Use the extended state observer ESO to obtain; According to formula (6), we can obtain: in, The system disturbance is d(t)=k8g1(x2)χ; Let e1:=x2 and e2:=d(t), g1(x2) and χ are both differentiable, and Where b(t) is the rate of change of the system disturbance d(t); Then the linear extended state observer ESO is expressed as: in: R 2 represents a two-dimensional space consisting of real numbers R, α1 and α2 represent the parameters to be designed, and the poles are located in the left half plane; g2(e1,h2)=g1(e1)(h2-k8e1); The error of the extended state observer ESO is: and The dynamic characteristics of the error are expressed as: g1(x2) is a bounded reversible function within the domain of definition. The estimated value of the cathode pressure χ can be inferred from the perturbation relationship in formula (7); The controller of the outer control loop is: The oxygen excess ratio is: The outer ring sliding surface is Take the first-order derivative of the sliding surface σ1(t): Among them, φ1 and γ1 represent design parameters, including system uncertainties; The super spiral algorithm is used to solve the system to converge all solutions, that is, the compressor flow target value given by the outer loop to the inner loop: Among them, φ 10 represents the known part of φ1 as a function of nominal parameters, represents the known part of the function based on the nominal parameters in γ1, λ1 and β1 are the parameters to be adjusted, The real-time value of is obtained using the Levant integrator; To prevent excessive fluctuations in the given value, a linear first-order filter is added after the controller of the outer loop: Where μ is a selectable constant. represents the output of the linear first-order filter, which is the compressor flow command provided to the control loop; The controller of the inner control loop is: The synovial surface of the inner ring is Obtain the first-order derivative of σ2(t) with respect to time: in: η υ-c Represents volumetric efficiency, V cpr / tr Indicates the volume of gas delivered per revolution of the compressor, ρ a Indicates the air density; Use feedback linearization: Substituting formula (12) into formula (13), we obtain: Where d2(t) represents the uncertainty of the system. For the actual system, |d2(t)|<K, K is a constant; The controller of the inner loop is obtained as: Constant ε>1; v, v nom 、v dis All represent intermediate variables; Set the convergence time to t f , the synovial surface s is obtained as: s=σ2(t)-σ2(0)-∫v nom dτ; σ2(0) represents the initial value of σ2(t).

2. The double closed-loop control method for the air supply system of a proton exchange membrane fuel cell according to claim 1, characterized in that: The best oxygen excess ratio in the current state Fitting to the stack current I st Function:

3. The double closed-loop control method for the air supply system of a proton exchange membrane fuel cell according to claim 2, characterized in that: The best oxygen excess ratio in the current state Fluctuates within the range of 2 to 2.5.

Citation Information

Patent Citations

  • Sliding-mode control method of proton exchange membrane fuel cell air supply system

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