CN113299951B - Method for observing cathode pressure and flow of proton exchange membrane fuel cell - Google Patents

Abstract

The invention provides a method for observing cathode pressure and flow of a proton exchange membrane fuel cell, which comprises the following steps: s1: establishing a lumped parameter model of a fuel cell air system; s2: based on the model, designing an adaptive observer to observe the pressure of a cathode cavity and the flow of a cathode inlet; s3: the observer design process considers the temperature difference between the inlet and the outlet of the manifold, which is caused by the intercooler, so as to ensure the convergence of the observer; s4: measurable signals of the fuel cell system are input into an observer, and real-time accurate observation of cathode flow and pressure is realized through real-time iterative operation. The method for observing the cathode pressure and the flow of the proton exchange membrane fuel cell has the advantages of convenient arrangement of a sensor for signal acquisition, strong realizability, effective increase of the observation precision and control effect of transient working conditions during high fuel cell power point migration.

Description

A method for observing the cathode pressure and flow rate of a proton exchange membrane fuel cell

technical field

The invention belongs to the technical field of fuel cells, and in particular relates to a method for observing the cathode pressure and flow of a proton exchange membrane fuel cell.

Background technique

With the increasingly severe energy and environmental problems, new energy vehicles have received widespread attention. Compared with pure electric vehicles, fuel cell vehicles have the advantages of shorter hydrogenation time and longer driving range. However, the current large-scale production and application of fuel cell vehicles are still restricted by many technical difficulties. For automotive products, reliability and durability are important indicators for evaluating vehicle performance, and fuel cells need to respond quickly under dynamic vehicle conditions. Rapid changes in power demand to ensure the power requirements of the car, and at the same time require precise control of the flow of hydrogen and air to ensure economical requirements. Insufficient air supply will lead to the phenomenon of "oxygen starvation", affecting life, and the cathode pressure is too low It will reduce the internal reaction efficiency. Therefore, in order to accurately control the cathode inlet air flow and the cathode cavity pressure, feedback control is required. However, the above physical quantities cannot be directly measured by sensors, and an observer needs to be designed to estimate them in real time.

SUMMARY OF THE INVENTION

In view of this, the purpose of the present invention is to realize the real-time accurate estimation of the cathode cavity pressure and the air flow rate of the stack inlet by designing an observer, and indirectly estimate the pressure according to the measurable signals such as the inlet flow rate of the intake manifold, the temperature of the inlet and outlet, and the pressure in the manifold. The flow in and out of the stack port and the pressure in the cathode cavity cannot be directly measured or difficult to measure by sensors. As important state parameters and control feedback quantities of fuel cells, the air flow rate at the inlet port and the cathode cavity pressure are crucial in key technical fields such as fault diagnosis, state detection and air system decoupling control.

In order to achieve the above object, the technical scheme created by the present invention is realized like this:

Real-time observation during driving is realized, providing a technical basis for state detection and precise control of fuel cells. The specific steps are as follows:

1) Establish a lumped parameter model of the fuel cell air system;

2) Based on this model, an adaptive observer is designed to observe the cathode cavity pressure and cathode inlet flow;

3) In the observer design process, the temperature difference between the inlet and outlet of the manifold caused by the intercooler is considered to improve the observation accuracy, and at the same time, the observer parameters are designed through the convergence analysis to ensure the convergence of the observer;

4) Input the measurable signals of the fuel cell system (including the air compressor outlet temperature and flow, the cathode inlet temperature and the pressure in the manifold) into the observer, and realize the real-time accurate observation of the cathode flow and pressure through real-time iterative operations.

In the step 1), a control-oriented lumped parameter model of the fuel cell air system is built according to the law of conservation of mass, the ideal gas equation and assumptions, and considering the temperature difference between the inlet and outlet of the manifold.

The model assumptions specifically include:

The air in the manifold is regarded as an ideal gas;

Uniform distribution of pressure, temperature and concentration of gas components;

The cathode inlet flow is proportional to the differential pressure;

The thermodynamic process is not considered, and it is regarded as an adiabatic system.

The construction of the fuel cell air system lumped parameter model needs to consider the temperature difference between the inlet and outlet of the manifold, and its state space equation is specifically:

x=P _sm y=P _sm

R为气体常数，V_sm为进气管体积，M_a为空气摩尔质量，

为阴极入口流量。Among them, P _sm is the state variable and output quantity, and u is the input quantity, including intake pipe inlet temperature T _sm,in , intake pipe outlet temperature T _sm,out and air compressor flow

R is the gas constant, V _sm is the volume of the intake pipe, _Ma is the air molar mass,

is the cathode inlet flow.

作为时变参数，阴极腔压力P_ca根据入口流量和进气管压力计算获得，具体观测器公式如下：In the described step 2), an adaptive observer is designed based on the model to observe the cathode cavity pressure and the cathode inlet flow rate, and the cathode inlet flow rate is

As a time-varying parameter, the cathode cavity pressure P _ca is calculated from the inlet flow rate and the intake pipe pressure. The specific observer formula is as follows:

where g _ca,in is the inlet flow coefficient, A, B, C and Φ are coefficient matrices, Y is an intermediate variable, L and Γ are observer gains, and Σ is an arbitrary positive definite diagonal matrix.

In the described step 3), the observer parameters are designed by the convergence analysis, and the specific steps of the state variable and the time-varying parameter estimation error convergence analysis are as follows:

与

的关系式：3) First need to define about

and

The relation of:

4) Derive the above formula to get:

求导后的共识可展开为如下形式：in

The consensus after derivation can be expanded into the following form:

According to the state space equation and the observer formula, it can be transformed into the following form:

Since the parameter θ changes relatively slowly, its derivative can be approximated to zero, and the above formula can be simplified to the following form:

If it can be guaranteed that A+LC<0, that is, L<0, then η converges to 0.

根据观测器公式，可推导出参数估计误差

的动态方程：3) Due to

According to the observer formula, the parameter estimation error can be deduced

The dynamic equation of :

收敛于0，同时Y为有界变量，能够保证

也收敛于0。Since ∑ is a positive definite diagonal matrix, if the observer gain Γ>0, then

Convergence to 0, and Y is a bounded variable, which can guarantee

also converges to 0.

Compared with the prior art, the method for observing the cathode pressure and flow rate of a proton exchange membrane fuel cell created by the present invention has the following advantages:

1) The present invention reduces the requirement for model accuracy by introducing the self-adaptation rate, and the model used for the observer design adopts the simplified air system model, which effectively improves the operation speed and thus meets the real-time requirement of control.

2) The observer designed in the present invention proposes a parameter range to ensure the convergence of the observer through convergence analysis, and can ensure the stability of the observation process under any working conditions through parameter design, and meets the safety requirements of the fuel cell system.

3) The observer designed in the present invention has less input, and the sensor used for signal acquisition is convenient to be arranged and highly implementable.

4) The present invention considers the temperature difference between the air compressor outlet of the air system and the inlet of the stack, and on the basis of collecting the temperature of the inlet of the stack, the collection of the outlet temperature of the air compressor is added, and the two are simultaneously used as the input of the observer, It can eliminate the observation bias based on a single temperature and effectively increase the observation accuracy.

5) The present invention conducts real-time observation of cathode pressure and cathode inlet flow rate through an observer, which provides technical support for the realization of functions such as fuel cell state detection and fault diagnosis.

6) The cathode pressure and the flow rate of the inlet port observed by the observer of the present invention can be used as feedback control quantities, thereby effectively improving the control effect of the transient working condition when the power point of the fuel cell is migrated.

Description of drawings

Fig. 1 is the schematic diagram of the observer system in the present invention;

2 is a schematic diagram of the internal algorithm structure of the observer in the present invention;

Fig. 3 is FCU controller hardware in the example of the present invention;

4 is a hardware-in-the-loop system architecture for testing an observer in the present invention;

Fig. 5 is the hardware-in-the-loop experiment platform control interface in the present invention;

Fig. 6 is the test condition of the example of the present invention;

Fig. 7 is the observation result of inlet flow rate in the example of the present invention;

Fig. 8 is the observation result of the cathode cavity pressure in the example of the present invention;

FIG. 9 shows the results of the observer-based peroxygen ratio control in the example of the present invention.

Detailed ways

Unless otherwise defined, technical terms used in the following embodiments have the same meanings as commonly understood by those skilled in the art to which the present invention belongs. The test reagents used in the following examples are conventional biochemical reagents unless otherwise specified; the experimental methods are conventional methods unless otherwise specified.

The present invention will be described in detail below with reference to the embodiments and the accompanying drawings.

Fig. 1 is a proton exchange membrane fuel cell cathode pressure and flow observation system constructed by an example of the present invention. The fuel cell air system in this example mainly includes an air compressor, an intercooler, a humidifier, a condenser, a back pressure valve and various This observation method requires that a temperature sensor, a pressure sensor and a flow sensor are installed in the fuel cell air system, and the flow sensor is installed at the inlet of the air compressor to measure the inlet air flow of the intake manifold, and the pressure sensor is installed at the inlet. The stack port is used to measure the pressure in the intake manifold, and two temperature sensors are installed at the air compressor outlet and the stack inlet to measure the temperature difference after the air passes through the intercooler, as shown in Figure 1. The device collects the measurement signals of each sensor, and calculates in real time through the internal operation to obtain the estimated value of the air flow rate of the inlet port and the pressure of the cathode cavity.

In this example, the fuel cell air system lumped parameter model needs to be built before designing the observer. This model is a control-oriented model. In order to meet the real-time requirements of the observer, the model needs to be simplified. The simplified process includes: The following assumptions:

1) The air in the manifold is regarded as an ideal gas;

2) The pressure, temperature and concentration of gas components are uniformly distributed;

3) The cathode inlet flow is proportional to the pressure difference;

4) The thermodynamic process is not considered, and it is regarded as an adiabatic system.

Based on the above assumptions, the fuel cell air system model is established, including the intake manifold model, the exhaust manifold model and the cathode cavity model. The intake manifold model also includes the air compressor sub-model, the stack inlet sub-model and the pressure in the manifold. The dynamic model, its state space equation can be described as:

为空压机出口流量(kg/s)，f_cp(·)代表空压机MAP，ω为空压机转速(rpm)，k为压力比，k＝P_a/P_sm，P_a为大气压(1.013×10⁵Pa)，P_sm为进气歧管压力(Pa)。

为入堆口流量，由于入堆口两侧压差较小，非线性模型可以简化为关于压差的线型方程(3)，g_ca,in为入堆口流量系数，可通过参数辨识确定，P_ca为阴极腔压力。V_sm为进气歧管体积(m³)，M_a为空气的摩尔质量(28.84g/mol)，R为气体常数(8.314J/(K·mol))，T_sm为进气歧管温度(K)。本发明在建立进气歧管模型时考虑进出口温差，将方程(1)转化为如下形式：in

is the air compressor outlet flow (kg/s), f _cp (·) represents the air compressor MAP, ω is the air compressor rotational speed (rpm), k is the pressure ratio, k=P _a /P _sm , and P _a is the atmospheric pressure (1.013×10 ⁵ Pa), and P _sm is the intake manifold pressure (Pa).

is the flow rate of the reactor inlet, because the pressure difference between the two sides of the reactor inlet is small, the nonlinear model can be simplified to the linear equation (3) about the pressure difference, g _ca,in is the inlet flow coefficient, which can be determined by parameter identification , P _ca is the cathode cavity pressure. V _sm is the intake manifold volume (m ³ ), Ma is the molar mass of air (28.84 _g /mol), R is the gas constant (8.314 J/(K·mol)), and T _sm is the intake manifold temperature (K). The present invention considers the inlet and outlet temperature difference when establishing the intake manifold model, and transforms equation (1) into the following form:

where T _sm,in is the intake manifold inlet temperature, and T _sm,out is the intake manifold outlet temperature.

The exhaust manifold model can be divided into a stack outlet sub-model, a back pressure valve model and a pressure dynamic sub-model in the manifold. The reactor outlet model is similar to the reactor inlet model, and is described by a linear equation about the pressure difference between the cathode cavity and the exhaust manifold; the structure of the back pressure valve is a butterfly valve, and its model can be a nozzle model with a variable effective cross-sectional area. describe. Its state space equation can be described as:

为出堆口流量，g_ca,out为出堆口流量系数，P_rm为排气歧管压力，

为背压阀流量，W为修正系数，T_rm为排气管温度，

为背压阀开度(rad)，a₁和a₂为开度系数，V_rm为排气歧管体积。in

is the outlet flow rate, g _ca,out is the outlet flow coefficient, P _rm is the exhaust manifold pressure,

is the back pressure valve flow, W is the correction coefficient, T _rm is the exhaust pipe temperature,

is the back pressure valve opening (rad), a ₁ and a ₂ are the opening coefficients, and V _rm is the exhaust manifold volume.

The cathode cavity model can describe the dynamic change of the cathode cavity pressure according to the reactor inlet submodel, the reactor outlet submodel and the oxygen consumption submodel. Its state space equation can be described as:

为每秒氧气消耗量，

为氧气摩尔质量(32g/mol)，n为膜电极数量，I_st为电堆电流(A)，F为法拉第常数(96485C/mol)。where T _ca is the cathode cavity temperature, V _ca is the cathode cavity volume,

is the oxygen consumption per second,

is the oxygen molar mass (32 g/mol), n is the number of membrane electrodes, I _st is the stack current (A), and F is the Faraday constant (96485 C/mol).

The state observer is designed according to the fuel cell air system model established in this example. For the convenience of description, the intake manifold model is first written in the form of a state space equation:

时变参数

A＝0，

C＝1。where the state variable x=P _sm , the input quantity

time-varying parameters

A=0,

C=1.

Figure 2 is a schematic diagram of the internal structure of the observer, and the specific structural form is:

where L and Γ are the observer gains, Σ is a positive definite diagonal matrix, and the state variable estimation error and parameter estimation error are defined as follows:

与

的关系式：In order to verify the convergence of the adaptive observer, first define the

and

The relation of:

Derive the above formula

Combining formulas (16) and (17), the above formula can be written in the following form:

Taking formulas (12), (13) and (15) into formula (21), we can get

Since the parameter changes relatively slowly, its derivative can be approximated to zero, and the above formula can be simplified to the following form:

根据公式(14)，参数估计误差的收敛性可以通过下式保证：If A+LC<0 can be guaranteed, then η converges to 0, and at the same time

According to formula (14), the convergence of parameter estimation error can be guaranteed by the following formula:

收敛于0，同时Y为有界变量，能够保证

也收敛于0。Since ∑ is a positive definite diagonal matrix, if the observer gain Γ>0, then

Convergence to 0, and Y is a bounded variable, which can guarantee

also converges to 0.

In order to verify the effect of the observer of the present invention, a fuel cell model is built by using MATLAB/Simulink, and verified by hardware-in-the-loop (HIL) experiments. The test environment is built based on NI's Veristand. The controller hardware is shown in Figure 3, using TC277D as the computing core, and integrating AD, CAN and other data communication modules, with PWM input and output, high and low side drive, high voltage acquisition and LIN communication, etc. Function, the hardware-in-the-loop test system architecture is shown in Figure 4, and the hardware-in-the-loop experimental platform control interface is shown in Figure 5. The fuel cell air system model and observer parameters are given in Table 1. The target current and cathode cavity pressure given by the experimental conditions are shown in Figure 6. The target current changes stepwise between 100-150A, and the target pressure is 2 The step change between -2.2bar, the corresponding observation results of the inlet flow are shown in Figure 7, and the observation results of the cathode cavity pressure are shown in Figure 8. The measured values of the flow and pressure sensors adopt the output value of the hardware-in-the-loop model Approximate representation, through the comparison with the estimated value of the observer, it can be seen that it has higher observation accuracy in both steady state and transient conditions, and has a higher observation accuracy than the observer based on a single temperature input. Higher transient accuracy. Under the transient conditions of the step change of target current from 140A to 130A and the step change of target pressure from 2.1bar to 2.05bar, it can be seen from the partial enlarged view that the observed value has a good follow-up effect. In order to further verify the beneficial effect of the observer on the control of the cathode air system, Figure 9 compares the control effect of the peroxygen ratio with and without the observer. Under the transient condition, the observer-based control method has better transient control precision.

Table 1 Model and observer parameters

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the within the scope of protection of the present invention.

Claims (3)

1. A method for observing the cathode pressure and flow of a proton exchange membrane fuel cell is characterized in that: the method comprises the following steps:

s1: establishing a lumped parameter model of the fuel cell air system;

s2: based on the model, designing an adaptive observer to observe the pressure of a cathode cavity and the flow of a cathode inlet;

s3: the observer design process considers the temperature difference between an inlet and an outlet of the manifold, which is caused by the intercooler, so that the convergence of the observer is ensured;

s4: inputting a measurable signal of the fuel cell system into an observer, and realizing real-time accurate observation of cathode flow and pressure through real-time iterative operation;

the construction of the fuel cell air system lumped parameter model needs to consider the temperature difference between an inlet and an outlet of a manifold, and the state space equation is as follows:

x＝P _sm y＝P _sm

wherein P is _sm Is the state variable and the output quantity, u is the input quantity,

T _sm,in is the inlet temperature of the air inlet pipe,

T _sm,out is the temperature at the outlet of the air inlet pipe,

is the flow rate of the air compressor,

r is the gas constant, and R is the gas constant,

V _sm is the volume of the air inlet pipe,

M _a the molar mass of the air is the mass of the air,

is the cathode inlet flow rate;

in S2, the adaptive observer is designed based on the model to observe the cathode cavity pressure and the cathode inlet flow rate, and the cathode inlet flow rate is measured

Cathode cavity pressure P as a time varying parameter _ca The observer is obtained by calculation according to the inlet flow and the pressure of the air inlet pipe, and the specific observer formula is as follows:

wherein g is _ca,in For the flux coefficient of the reactor inlet, A, B, C and phi are coefficient matrixes, Y is an intermediate variable, L and gamma are observer gains, and sigma is an arbitrary positive definite diagonal matrix;

in S3, the convergence analysis of the observer parameters, state variables, and time-varying parameter estimation errors is designed through convergence analysis, which includes the following specific steps:

1) first, it is necessary to define

And

the relation of (c):

2) the above formula is derived:

wherein

The derived consensus can be expanded into the following form:

according to the state space equation and the observer formula, the transformation and the adjustment can be in the following form:

since the parameter θ changes relatively slowly, its derivative can be approximated to zero, and the above equation can be simplified to the following form:

if the A + LC is less than 0, namely L is less than 0, then eta converges to 0;

due to the fact that

Deducing parameter estimation error according to observer formula

The dynamic equation of (c):

since sigma is a positive definite diagonal matrix, if observer gain gamma > 0, then

Convergence to 0, with Y being a bounded variable, can be guaranteed

Also converging to 0.

2. The method for observing the cathode pressure and flow of a proton exchange membrane fuel cell according to claim 1, wherein: in S1, the total parameter model builds a control-oriented fuel cell air system lumped parameter model according to the mass conservation law, the ideal gas equation and the assumed conditions, and according to the manifold inlet-outlet temperature difference, where the model assumed conditions specifically include: the air in the manifold is considered an ideal gas; the pressure, temperature and concentration of the gas component are uniformly distributed; the cathode inlet flow is proportional to the pressure differential; irrespective of the thermodynamic process, an adiabatic system is considered.

3. The method for observing the cathode pressure and flow of a proton exchange membrane fuel cell according to claim 1, wherein: the measurable signals in S4 include air compressor outlet temperature and flow, cathode inlet temperature, and manifold pressure.

Images