CN117199459A - Decoupling control method and control system for air supply system of proton exchange membrane fuel cell - Google Patents

Decoupling control method and control system for air supply system of proton exchange membrane fuel cell Download PDF

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CN117199459A
CN117199459A CN202311088332.5A CN202311088332A CN117199459A CN 117199459 A CN117199459 A CN 117199459A CN 202311088332 A CN202311088332 A CN 202311088332A CN 117199459 A CN117199459 A CN 117199459A
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air supply
supply system
feedforward
fuel cell
feedback controller
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高金武
陈林
尹海
胡云峰
陈虹
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Jilin University
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Jilin University
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    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • 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
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/30—Hydrogen technology
    • Y02E60/50—Fuel cells

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Abstract

The invention provides a decoupling control method and a control system for an air supply system of a proton exchange membrane fuel cell, which are used for collecting air flow and pressure data under different air compressor speeds and throttle opening; the method comprises the steps of performing linear interpolation and fitting on acquired data, establishing a feedforward lookup table, eliminating feedforward errors by means of a feedback controller constructed by a super Spiral Sliding Model (SSM), performing self-adaptive optimization on feedback controller parameters by utilizing Extremum Searching (ES), and loading the optimized parameters into the feedback controller.

Description

Decoupling control method and control system for air supply system of proton exchange membrane fuel cell
Technical Field
The invention belongs to the field of fuel cell decoupling control, in particular to a decoupling control method and a control system for an air supply system of a proton exchange membrane fuel cell, and more particularly relates to air flow and pressure decoupling control.
Background
Proton Exchange Membrane (PEM) fuel cells are widely used in various fields such as automobiles, manned aerospace, underwater submarines, distributed power generation and the like due to the advantages of high efficiency, high power density, low working temperature, almost zero emission and the like. As an important component of the fuel cell, the air supply system provides sufficient fresh air for the fuel cell stack in time and stably through the cooperation of the air compressor and the throttle valve. The two outputs of the air supply system, air flow and pressure, are critical to the healthy and efficient operation of the fuel cell. However, as a typical coupling system, its two outputs (air flow and pressure) are simultaneously affected by the two inputs (air compressor speed and throttle opening). In general, air flow and pressure increase with increasing air compressor speed, but increasing throttle angle results in increased air flow and decreased pressure. In addition, the air supply system has the characteristics of nonlinearity, time variation, hysteresis and the like. Therefore, decoupling control of air flow and pressure is particularly difficult. In general, decoupling control of air supply systems is primarily challenged by: 1. the strong coupling between air flow and pressure, and the inherent nonlinearity, time-varying and hysteresis of the system, plagues the speed and accuracy of the decoupling control; 2. the control commands need to be smooth enough to enable the actuators (air compressor and throttle) to respond accurately to their control commands; 3. the computational load of the control scheme should be relatively light, facilitating implementation on a hardware platform.
The current main decoupling control method is to first perform model identification and then calculate a decoupling matrix, so as to convert the air supply system from a dual-input dual-output (TITO) system to two single-input single-output (SISO) systems. The above method inevitably requires model identification and decoupling matrix calculation, which not only results in a great deal of work, but also the performance of the controller is significantly affected by the model identification precision, and more importantly, the portability of the method is reduced due to different model parameters of different systems.
Disclosure of Invention
In order to solve the problems, the invention provides a decoupling control method of an air supply system of a proton exchange membrane fuel cell, which realizes stable, accurate and rapid decoupling control of air flow and pressure based on composite control of feedforward and Supercoiled Sliding Mode (SSM), does not involve a decoupling matrix, avoids the dilemma and a large amount of calculation that the existing decoupling method seriously depends on model identification, increases portability of a control algorithm, and has strong anti-interference capability.
The invention is realized by the following technical scheme:
a decoupling control method for an air supply system of a proton exchange membrane fuel cell comprises the following steps:
step one, collecting air flow and pressure data under different air compressor speeds and throttle opening degrees;
step two, carrying out linear interpolation and fitting on the acquired data, and establishing a feedforward lookup table:
(N f ,θ f ) T ＝[f 1 (W d ,P d ),f 2 (W d ,P d )] T (1)
step three, eliminating feedforward errors by using a feedback controller constructed by SSM, wherein the feedback controller is as follows:
wherein,
step four, performing self-adaptive optimization on parameters of a feedback controller by utilizing Extremum Searching (ES), wherein the self-adaptive optimization comprises the following steps:
wherein,for parameter->Is determined by the estimation of (a);
wherein,is->Is set to an initial value of (1); />Are respectively->Is the initial value of (2);
and fifthly, loading the optimized parameters into a feedback controller.
As a better technical scheme of the invention: the disturbance frequency omega i Update frequency with maximum less than cost functionAny two ofDisturbance frequency omega i The sum is not equal to the third disturbance frequency omega i 。
It is yet another object of the present invention to provide a decoupling control system for a proton exchange membrane fuel cell air supply system, comprising:
the acquisition module is used for acquiring air flow and pressure data of different air compressor rotating speeds and throttle opening degrees on the hardware platform;
the feedforward controller is used for carrying out linear interpolation and fitting on the acquired data and establishing a feedforward lookup table:
(N f ,θ f ) T ＝[f 1 (W d ,P d ),f 2 (W d ,P d )] T (1)
and the feedback controller is used for eliminating feedforward errors, and the feedback control vector is as follows:
wherein the method comprises the steps of
(s 1 ,s 2 ) T ＝(W-W d ,P-P d ) T (6)
Wherein phi is 1 ,φ 2 Is s 1 Is phi 4 ,φ 5 Is s 2 Is a function of (2).
The self-adaptive optimization module is used for carrying out self-adaptive optimization on the parameters of the feedback controller, and is realized by using the ES, and specifically comprises the following steps:
wherein,for parameter->Is determined by the estimation of (a);
wherein mu i In order to integrate the gain,is->Is set to an initial value of (1); />Are respectively->Is the initial value of (a).
It is still another object of the present invention to provide a computer readable storage medium having stored thereon a computer program which when executed by a processor implements the above-described proton exchange membrane fuel cell air supply system decoupling control method.
It is still another object of the present invention to provide an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the above-mentioned method for controlling decoupling of the proton exchange membrane fuel cell air supply system when executing the program.
The beneficial effects are as follows:
1. the invention can accurately realize the decoupling control of the air flow and the pressure of the air supply system without identifying the model of the air supply system and calculating a decoupling matrix;
2. the adjusting time of the air and the pressure is within 0.5 seconds;
3. the invention can learn corresponding parameters for different air supply systems, and has stronger portability.
Drawings
FIG. 1 is a block diagram of a control method according to the present invention, including two parts of feedforward and feedback, wherein (N f ,θ f ) T Is a feedforward control vector, (N) b ,θ b ) T Is a feedback control vector.
Fig. 2 is a diagram showing a feedforward control signal N for the rotational speed of the air compressor f With respect to the desired flow and pressure (W d ,P d ) T Is a feed forward table of (a).
FIG. 3 is a throttle angle feedforward control signal θ f With respect to the desired flow and pressure (W d ,P d ) T Is a feed forward table of (a).
FIG. 4 is a schematic diagram showing the structure of the ES-ASSM according to the present invention.
Fig. 5 is a schematic diagram of a locally gradient modulated perturbation signal.
Fig. 6 is an experimental environment for verifying the proposed control method.
FIG. 7 is an iterative process of tracking response and cost function during parameter optimization.
Fig. 8 is an iterative process of controlling vector parameters.
FIG. 9 is a graph of air flow and pressure response for the proposed method in case one, where (a) the flow response; (b) flow error; (c) a pressure response; (d) pressure error.
Fig. 10 is a control vector of the proposed method in case one, in which (a) the rotational speed control command (N) and the actual rotational speed (N act ) The method comprises the steps of carrying out a first treatment on the surface of the (b) Rotation speed feedback control signal (N) b ) The method comprises the steps of carrying out a first treatment on the surface of the (c) Angle control command (θ) and actual angle (θ) act ) The method comprises the steps of carrying out a first treatment on the surface of the (d) Angle feedback control signal (θ) b )。
FIG. 11 is the air flow and pressure response of the proposed method in case two, where (a) the flow response; (b) flow error; (c) a pressure response; (d) pressure error.
Fig. 12 is a control vector of the proposed method in case two, in which (a) the rotational speed control command and the actual rotational speed; (b) a rotational speed feedback control signal; (c) An angle control command and an actual angle, (d) an angle feedback control signal.
FIG. 13 is the air flow and pressure response of the DMDM in case one, where (a) the flow response; (b) flow error; (c) a pressure response; (d) pressure error.
FIG. 14 is the air flow and pressure response of the DMDM in case two, where (a) the flow response; (b) flow error; (c) a pressure response; (d) pressure error.
Detailed Description
For further explanation of technical content and constructional features of the present invention, an example is given below, and the detailed explanation is made with reference to the accompanying drawings. In addition, to demonstrate the effectiveness of the present invention, hardware-in-the-loop experiments were performed on a proton exchange membrane air supply system rack, with the result that the high performance of the control strategy was fully achieved. The scope of the invention is not limited to the following.
As shown in fig. 1, the present invention provides a composite control method based on feedforward and SSM, wherein the mutual interference between flow and pressure after feedforward is added is regarded as disturbance, and then the disturbance is processed by SSM, and the control method combines the advantages of the quick response of feedforward and the anti-disturbance capability of SSM, specifically: two feedforward lookup tables are established according to the data collected by the test bed. A feedback controller is then designed to eliminate feed forward errors using SSM. In addition, because the feedback control law is complex in form and has a plurality of parameters, the parameters are difficult to manually set, and the parameters are considered to be self-adaptively adjusted by using an optimization algorithm. And adopting ES to adaptively optimize parameters of SSM. The control performance is measured using a cost function, which is then reduced by a gradient descent method to obtain a better tracking response. Parameters in the SSM control law are optimized in an iterative process.
The control method provided by the invention consists of a feedforward control part and a feedback control part. The feedforward control has the advantages of quick response, stability, reliability and the like, and is widely applied to a system with time lag. The feedforward is thus considered for the time-lapse characteristics of the air supply system, and the static look-up table is used to construct the feedforward control taking into account the complex structure of the air supply system and the effect of its involved complex physical processes on mathematical modeling. Irrespective of the complex physical process, the feed-forward look-up table is directly constructed as a look-up table of control vectors with respect to reference signals:
(N f ,θ f ) T ＝[f 1 (W d ,P d ),f 2 (W d ,P d )] T (1)
wherein (W) d ,P d ) T Represents a reference vector, (N) f ,θ f ) T Representing a feedforward control vector. In order to create the lookup table, data of different air compressor speeds and throttle angles are collected. The air compressor speed was set from 30 to 90krpm, the step size was 10krpm, the throttle angle was set from 10 to 50 degrees, and the step size was 2.5 degrees. The collected data were linearly interpolated and fitted and the lookup tables for air compressor speed and throttle angle are shown in fig. 2 and 3. The air supply system is nonlinear, while the feed-forward table is constructed using a linear fit, which necessarily results in errors. Moreover, because of the state equation involving the ideal gas, the parameters of the air supply system model may vary with temperature and humidity, and it is difficult to obtain satisfactory control performance by means of feedforward alone. Thus, feedback control is required to eliminate the remaining tracking error. The strong coupling between air flow and pressure, as well as the nonlinearity, time-variability, and hysteresis of the air supply system, all affect error cancellation. Existing research is to eliminate errors by decoupling the air supply system into two SISO devices.
N b And theta b As flow and pressure feedback control signals, respectively, the coupling relationship is regarded as disturbance processed by sliding mode control. Meanwhile, the buffeting effect of the first-order sliding mode makes it difficult for the air compressor and the throttle valve to accurately respond to control instructions of the air compressor and the throttle valve, so that feedback control is considered to be performed by adopting the second-order sliding mode. The air flow (W) and pressure (P) will rise simultaneously with increasing air compressor speed (N) and, however, increasing throttle angle will result in an increase in W and a decrease in P. Under the feedforward action, (W, P) T And (N) b ,θ b ) T The relation between them is approximately
Wherein h is ij (W,P)>0 (i, j=1). Handle h 11 (W,P)θ b And h 21 (W,P)N b Considered as bounded disturbance, i.e. d 1 ＝h 12 (W,P)θ b ，d 2 ＝h 21 (W,P)N b Then (2) can be rewritten as
The sliding die surface is constructed as
(s 1 ,s 2 ) T ＝(W-W d ,P-P d ) T (4)
s 1 Sum s 2 Is a sliding die surface.
Note that(time derivative of flow) and N b Positive correlation, but->(time derivative of pressure) vs b And (5) negative correlation. Thus, the feedback control vector is constructed using SSM:
t represents the integral over time
Wherein the method comprises the steps of
And a multi-element optimization algorithm is needed to complete parameter setting of the feedback controller. As a typical model-free approach, ES is capable of multi-parameter optimization, introducing ES into a feedback controller as shown in fig. 4. To measure the control performance, a cost function (J) is constructed using the tracking error vector. In the m (m.gtoreq.1) th iteration period (t=10s), J has the following form:
wherein b= (β) 1 ,β 2 ,...,β 6 ) T ，(e w ,e p ) T ＝(W d -W,P d -P) T ，q 1 ＝1，q 2 =2 is the error weight matrix for flow and pressure, respectively. Priority is given to pressure stability in fuel cells for protection, thus letting q 1 <q 2 . That is, a small portion of the flow control accuracy is sacrificed to stabilize the pressure. For the system shown in fig. 4, there should be a suitable control parameter vector B such that J (B) is minimized, as controller parameters that are too large or too small would deteriorate control performance and lead to more accumulated errors. The following assumptions were made for ease of analysis: j (B) is a convex function with respect to B, inWith a minimum value. This assumption is to facilitate subsequent analysis. There may be multiple local minima for the optimization problem. However, the purpose of introducing ES is to set the parameters of the SSM control law to obtain a satisfactory effect, rather than to obtain an optimal parameter, under the premise of ensuring pressure stability to take precedence. For the expressed brief description, for the time domain signals u (t) and G(s), the following symbols are defined
u(t){G(s)}＝u(t)*L -1 [G(s)]
Where 'denotes the convolution operator,' L -1 (g) ' represents the inverse laplace transform. For the ith ES loop in fig. 4:
wherein the method comprises the steps ofRepresenting the optimal parameters->Estimate of->(0<h<ω i I=1, 2,.. 6,h denotes the cut-off frequency) is a high-pass filter, +.>Is an integrator with gain, mu i Determines the convergence rate of the parameter, ζ i And η is the intermediate transition letter of the algorithm and s is a special symbol in the laplace frequency domain. Sinusoidal perturbation (a) using input control system i sinω i t) extracting the local gradient of J (B), perturbation amplitude (a) i ) Should be relatively small. Disturbance frequency (omega) 1 -ω 6 ) It is particularly important for ES that it must first ensure a time-scale separation of the ES cycle and the cost function. Therefore, the maximum value of the disturbance frequency needs to be smaller than the update frequency of the cost function +.>And maintains a certain frequency interval. Furthermore, the sum of any two disturbance frequencies cannot be equal to the third disturbance frequency, otherwise stability at the extremum would be destroyed. The ES periodically updates the parameter vector (B) to reduce J (m, B) using a gradient descent method, thereby achieving more satisfactory control performance. The principle of gradient descent will be described below, in +.>The taylor expansion is performed on J (B), and second and above terms are ignored. ConsiderObtaining
Thus, the disturbance signal (a i sinω i t) is locally gradedThe modulation is shown in fig. 5. The ES loop 1 is first analyzed. Extracting partial derivative by coherent demodulation>H h (s) has zero Direct Current (DC) gain, thereby eliminating DC component
Then eta and sin omega 1 t multiplication, applicationObtaining
Due to the integratorWith infinite dc gain, the sinusoidal components in the filtered signal are ignored:
finishing (12) the available
Performing Laplace transform and Laplace inverse transform on (13) to generate
Wherein the method comprises the steps ofIs->Is set to be a constant value. Likewise, for ES loops 2 through 6
Wherein the method comprises the steps ofAre respectively->Is the initial value of (a). Due to mu i a i >0(i＝1,2,...,6)，/>Will move in the opposite direction to the gradient until the minimum point B is reached * 。
In summary, the control method provided by the invention optimizes the controller parameters by means of the gradient descent method, so as to obtain a better control effect.
The high-precision self-adaptive optimization control method provided by the invention is shown in figure 1. And collecting air flow and pressure data under different air compressor speeds and throttle openings on a hardware platform, performing linear interpolation and fitting on the collected data, establishing a feedforward lookup table, designing a feedback controller by means of a supercoiled sliding mode to eliminate feedforward errors, and introducing Extremum Searching (ES) to adaptively optimize feedback control parameters.
Example 1
In this example, the experimental environment is shown in fig. 6, in which an air buffer tank was used to simulate a cathode. The ECU (electronic control unit) sends control instructions to the compressor and the throttle valve, and the air flow, the air pressure, the actual rotation speed of the compressor and the actual angle of the throttle valve acquired by the sensor are transmitted back to the PC (upper computer). The parameters of the ES-ASSM are shown in Table 1, in which the disturbance frequency ω i Selected according to the principles described above. The initial value of the cost function is set to 15 (slightly greater than J (1)), and the initial value of the control parameter should enable the controller to have a certain control effect. The iteration period of the cost function is 10s, so two sinusoidal reference signals with a period of 10s are used for parameter optimization. The follow-up response of air flow and pressure and the evolution of the cost function J (m, B) are shown in fig. 7. The ES-ASSM optimizes parameters online to obtain a more favorable tracking response, and J (m, B) eventually converges to 5.348 over nine iterations. Furthermore, an iterative update procedure of the parameter vector is shown in FIG. 8, in whichAfter eight iterations, convergence to 0.02165, 0.05078, 1.00344, 0.09588, 0.02840, 1.00469 respectively.
TABLE 1
Loading the optimized parameters into a feedback controller, disabling the ES cycle to reduce the computational load, and then evaluating the performance of the control method provided by the invention. Consider the following conditions:
1) Case one: the reference trajectories for flow and pressure are chosen as a step signal and a sine signal, respectively, the results are shown in fig. 9 and 10.
2) And a second case: the reference trajectories for flow and pressure are chosen as sinusoidal and step signals, respectively, the results are shown in fig. 11 and 12.
From the viewpoints of flow and pressure response, the control method provided by the invention well realizes decoupling control:
1) The flow and pressure may track the respective reference trajectories independently, whether a stepped flow, sinusoidal pressure condition is shown in fig. 9 or a sinusoidal flow, stepped pressure condition is shown in fig. 11.
2) The pressure fluctuation is small at the time of the flow step as shown in fig. 9 (c), but the flow fluctuation is remarkable at the time of the pressure step as shown in fig. 11 (a). In addition, the effect of the pressure following the reference trajectory as shown in fig. 9 (c) and 11 (a) is significantly better than the flow rate when tracking the sinusoidal signal. The pressure error is weighted more than the flow error in designing the cost function.
3) The proposed scheme also performs well in terms of response speed and tracking accuracy. As shown in fig. 9 (a) and 11 (c). The step response of flow and pressure is completed within 0.5s when tracking a sinusoidal signal, the pressure error is limited to about 1kPa as shown in fig. 9 (d) and the flow error is limited to about 2g/s as shown in fig. 11 (b).
To further illustrate the superior performance of the control method of the present invention, the results of the comparison using the Diagonal Matrix Decoupling Method (DMDM) are shown in fig. 13 and 14. In case 1, the control method of the present invention has smaller flow overshoot as shown in fig. 9 (a) and 13 (a) and smaller pressure tracking error as shown in fig. 9 (d) and 13 (d) compared to DMDM. In case 2, the error of the flow rate of DMDM is larger as shown in fig. 11 (b) and 14 (b), while there is a steady-state error in the pressure as shown in fig. 14 (c).
Furthermore, quantitative analysis was also performed by means of Root Mean Square Error (RMSE):
wherein t is 0 And t f Representing the sample start and end times, respectively.
From the comparison of the two control methods of table 2, the control method provided by the present invention is superior to DMDM.
TABLE 2
The control method provided by the invention realizes decoupling of flow and pressure on the premise of ensuring pressure response priority, and combines the advantages of feedforward quick response and anti-disturbance of SSM to stably, accurately and quickly complete decoupling control of air flow and pressure; the dilemma that the existing decoupling method seriously depends on model identification is avoided, a large amount of calculation is avoided, a more excellent control effect is achieved, and portability of a control algorithm is improved.

Claims (5)

1. The decoupling control method of the proton exchange membrane fuel cell air supply system is characterized by comprising the following steps of:
step one, collecting air flow and pressure data under different air compressor speeds and throttle opening degrees;
step two, carrying out linear interpolation and fitting on the acquired data, and establishing a feedforward lookup table:
(N f ,θ f ) T ＝[f 1 (W d ,P d ),f 2 (W d ,P d )] T (1)
step three, eliminating feedforward errors by using a feedback controller constructed by SSM, wherein the feedback controller is as follows:
wherein,
step four, performing self-adaptive optimization on parameters of a feedback controller by utilizing Extremum Searching (ES), wherein the self-adaptive optimization comprises the following steps:
wherein,for parameter->Is determined by the estimation of (a);
wherein,is->Is set to an initial value of (1); />Are respectively->Is the initial value of (2);
and step five, loading the optimized parameters in the step four into a feedback controller.
2. The method for decoupling control of a pem fuel cell air supply system of claim 1 wherein said disturbance frequency ω i Update frequency with maximum less than cost functionAny two disturbance frequencies omega i The sum is not equal toThree disturbance frequencies omega i 。
3. A proton exchange membrane fuel cell air supply system decoupling control system, comprising:
the acquisition module is used for acquiring air flow and pressure data of different air compressor rotating speeds and throttle opening degrees on the hardware platform;
the feedforward controller is used for carrying out linear interpolation and fitting on the acquired data and establishing a feedforward lookup table:
(N f ,θ f ) T ＝[f 1 (W d ,P d ),f 2 (W d ,P d )] T (1)
and the feedback controller is used for eliminating feedforward errors, and the feedback control vector is as follows:
wherein the method comprises the steps of
(s 1 ,s 2 ) T ＝(W-W d ,P-P d ) T (6)
Wherein phi is 1 ,φ 2 Is s 1 Is phi 4 ,φ 5 Is s 2 Is a function of (2).
The self-adaptive optimization module is used for carrying out self-adaptive optimization on the parameters of the feedback controller, and is realized by using the ES, and specifically comprises the following steps:
wherein,for parameter->Is determined by the estimation of (a);
wherein mu i In order to integrate the gain,is->Is set to an initial value of (1); />Are respectively->Is the initial value of (a).
4. A computer-readable storage medium, having stored thereon a computer program which, when executed by a processor, implements the proton exchange membrane fuel cell air supply system decoupling control method as claimed in claim 1.
5. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor implements the proton exchange membrane fuel cell air supply system decoupling control method of claim 1 when executing the program.
CN202311088332.5A 2023-08-28 2023-08-28 Decoupling control method and control system for air supply system of proton exchange membrane fuel cell Pending CN117199459A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117518837A (en) * 2024-01-04 2024-02-06 中国科学院长春光学精密机械与物理研究所 Decoupling method based on parameterized model

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117518837A (en) * 2024-01-04 2024-02-06 中国科学院长春光学精密机械与物理研究所 Decoupling method based on parameterized model
CN117518837B (en) * 2024-01-04 2024-03-19 中国科学院长春光学精密机械与物理研究所 Decoupling method based on parameterized model

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