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

Abstract

The invention provides a decoupling control method and control system for a proton exchange membrane fuel cell air supply system, which collects air flow and pressure data at different air compressor speeds and throttle openings; and performs linear interpolation and fitting on the collected data. , establish a feedforward lookup table, eliminate the feedforward error with the help of the feedback controller constructed by the superhelical sliding model (SSM), use extreme value search (ES) to adaptively optimize the parameters of the feedback controller, and load the optimized parameters into the feedback In the controller, the present invention is based on the composite control of feedforward and SSM to achieve stable, accurate and rapid decoupling control of air flow and pressure. It does not involve a decoupling matrix and avoids the dilemma and difficulty of existing decoupling methods that rely heavily on model identification. A large amount of calculations also increases the portability of the control algorithm and has strong anti-interference ability.

Description

A decoupling control method and control of a proton exchange membrane fuel cell air supply system system

Technical field

The invention belongs to the field of fuel cell decoupling control, specifically relates to a proton exchange membrane fuel cell air supply system decoupling control method and control system, and more specifically relates to air flow and pressure decoupling control.

Background technique

Proton exchange membrane (PEM) fuel cells have been widely used in automobiles, manned aerospace, underwater submarines, distributed power generation and many other fields due to their advantages of high efficiency, high power density, low operating temperature and almost zero emissions. As an important part of the fuel cell, the air supply system provides sufficient fresh air to the fuel cell stack in a timely and stable manner through the cooperation of the air compressor and the throttle. Two outputs of the air supply system, air flow and pressure, are critical to healthy and efficient operation of the fuel cell. However, as a typical coupled system, its two outputs (air flow and pressure) are affected by two inputs (air compressor speed and throttle opening) at the same time. Under normal circumstances, air flow and pressure increase as the air compressor speed increases, but increasing the throttle angle will cause the air flow to increase and the pressure to decrease. In addition, the air supply system has the characteristics of nonlinearity, time variation and hysteresis. Therefore, decoupled control of air flow and pressure is particularly difficult. Generally speaking, the main challenges faced by the decoupled control of the air supply system are: 1. The strong coupling between air flow and pressure and the inherent nonlinearity, time variation and hysteresis of the system bring troubles to the speed and accuracy of the decoupled control. ; 2. The control commands need to be smooth enough so that the actuators (air compressor and throttle) can accurately respond to their control commands; 3. The calculation load of the control scheme should be relatively light and easy to implement on the hardware platform.

The current mainstream decoupling control method first performs model identification and then calculates the decoupling matrix, thereby converting 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 will not only cause a lot of work, but also the performance of the controller will be significantly affected by the accuracy of model identification. More importantly, the different model parameters of different systems reduce the efficiency of the method. portability.

Contents of the invention

In response to the above problems, the present invention provides a decoupling control method for a proton exchange membrane fuel cell air supply system. Based on the composite control of feedforward and superspiral sliding mode (SSM), the air flow and pressure can be solved stably, accurately and quickly. Coupled control does not involve the decoupling matrix, which avoids the dilemma of existing decoupling methods that rely heavily on model identification and a large amount of calculations. It also increases the portability of the control algorithm and has strong anti-interference ability.

The present invention is realized through the following technical solutions:

A decoupling control method for a proton exchange membrane fuel cell air supply system, including the following steps:

Step 1. Collect air flow and pressure data at different air compressor speeds and throttle openings;

Step 2: Perform linear interpolation and fitting on the collected data, and establish a feedforward lookup table:

(N _f ,θ _f ) ^T =[f ₁ (W _d ,P _d ),f ₂ (W _d ,P _d )] ^T (1)

Step 3. Use the feedback controller built with SSM to eliminate the feedforward error. The feedback controller is:

in,

Step 4: Use extreme value search (ES) to adaptively optimize the parameters of the feedback controller, specifically as follows:

in, for parameters/> estimate;

in, for/> Initial value;/> They are/> initial value;

Step 5: Load the optimized parameters into the feedback controller.

As a more optimal technical solution of the present invention: the maximum value of the disturbance frequency ω _i is less than the update frequency of the cost function The sum of any two disturbance frequencies ω _i is not equal to the third disturbance frequency ω _i .

Another object of the present invention is to provide a proton exchange membrane fuel cell air supply system decoupling control system, including:

The collection module is used to collect air flow and pressure data at different air compressor speeds and throttle openings on the hardware platform;

Feedforward controller is used to linearly interpolate and fit the collected data and establish a feedforward lookup table:

(N _f ,θ _f ) ^T =[f ₁ (W _d ,P _d ),f ₂ (W _d ,P _d )] ^T (1)

Feedback controller is used to eliminate feedforward error. The feedback control vector is:

in

(s ₁ ,s ₂ ) ^T = (WW _d ,PP _d ) ^T (6)

Among them, φ ₁ and φ ₂ are functions of s ₁ , and φ ₄ and φ ₅ are functions of s ₂ .

The adaptive optimization module is used to adaptively optimize the parameters of the feedback controller and is implemented using ES, specifically:

in, for parameters/> estimate;

Among them, μ _i is the integral gain, for/> Initial value;/> They are/> initial value.

Another object of the present invention is to provide a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the above-mentioned proton exchange membrane fuel cell air supply system decoupling control method is implemented.

Another object of the present invention is to provide an electronic device, including a memory, a processor and a computer program stored in the memory and executable on the processor. When the processor executes the program, the above-mentioned proton is realized. Decoupling control method of exchange membrane fuel cell air supply system.

The beneficial effects are as follows:

1. The present invention can accurately realize the decoupling control of air flow and pressure of the air supply system, without the need to identify the model of the air supply system and calculate the decoupling matrix;

2. The present invention adjusts air flow and pressure within 0.5 seconds;

3. The present invention can learn corresponding parameters for different air supply systems, and is more portable.

Description of the drawings

Figure 1 is a structural diagram of the control method of the present invention, which includes two parts: feedforward and feedback, where (N _f ,θ _f ) ^T is the feedforward control vector, and (N _b ,θ _b ) ^T is the feedback control vector.

Figure 2 is a feedforward table of the air compressor speed feedforward control signal N _f with respect to the desired flow rate and pressure (W _d , P _d ) ^T.

Figure 3 is a feedforward table of the throttle angle feedforward control signal θ _f with respect to the desired flow rate and pressure (W _d , P _d ) ^T.

Figure 4 is a schematic diagram of the specific structure of the ES-ASSM of the present invention.

Figure 5 is a schematic diagram of a local gradient modulated perturbation signal.

Figure 6 shows the experimental environment used to verify the proposed control method.

Figure 7 shows the iterative process of tracking the response and cost function during parameter optimization.

Figure 8 shows the iterative process of controlling vector parameters.

Figure 9 shows the air flow and pressure response of the proposed method in case 1, where (a) flow response; (b) flow error; (c) pressure response; (d) pressure error.

Figure 10 shows the control vector of the proposed method in case 1, where (a) speed control command (N) and actual speed (N _act ); (b) speed feedback control signal (N _b ); (c) angle control command (θ ) and the actual angle (θ _act ); (d) angle feedback control signal (θ _b ).

Figure 11 shows the air flow and pressure response of the proposed method in case 2, where (a) flow response; (b) flow error; (c) pressure response; (d) pressure error.

Figure 12 shows the control vector of the proposed method in case 2, where (a) speed control command and actual speed; (b) speed feedback control signal; (c) angle control command and actual angle, (d) angle feedback control signal.

Figure 13 shows the air flow and pressure response of DMDM in case 1, where (a) flow response; (b) flow error; (c) pressure response; (d) pressure error.

Figure 14 shows the air flow and pressure response of DMDM in case 2, where (a) flow response; (b) flow error; (c) pressure response; (d) pressure error.

Detailed ways

In order to further illustrate the technical content and structural features of the present invention, an example is given below, which will be described in detail with reference to the accompanying drawings. In addition, in order to demonstrate the effectiveness of the present invention, hardware-in-the-loop experiments were conducted on a proton exchange membrane air supply system bench, and the results fully demonstrated the high performance of the control strategy. The protection scope of the present invention is not limited to the following.

As shown in Figure 1, the present invention proposes a composite control method based on feedforward and SSM. After adding feedforward, the mutual interference between flow and pressure is regarded as a disturbance, and then processed by SSM. The control method combines The advantages of feedforward's fast response and SSM's anti-interference ability are specifically: two feedforward lookup tables are established based on the data collected on the test bench. Then a feedback controller is designed to use SSM to eliminate the feedforward error. In addition, due to the complex form of the feedback control law and many parameters, it is difficult to manually adjust the parameters. Therefore, the use of optimization algorithms to adaptively adjust the parameters is considered. ES was used to adaptively optimize the parameters of SSM. The control performance is measured using a cost function, which is subsequently reduced by gradient descent to obtain better tracking response. The parameters in the SSM control law are optimized during the iterative process.

The present invention proposes a control method consisting of feedforward control and feedback control. Feedforward control has the advantages of fast response, stability and reliability, and is widely used in systems with time delays. Therefore, feedforward is considered for the time-delay characteristics of the air supply system. Considering the complex structure of the air supply system and the impact of the complex physical processes involved on mathematical modeling, a static lookup table is used to construct feedforward control. Regardless of complex physical processes, the feedforward lookup table is directly constructed as a lookup table of the control vector with respect to the reference signal:

(N _f ,θ _f ) ^T =[f ₁ (W _d ,P _d ),f ₂ (W _d ,P _d )] ^T (1)

Among them, (W _d ,P _d ) ^T represents the reference vector, and (N _f ,θ _f ) ^T represents the feedforward control vector. To create the above lookup table, data were collected at different air compressor speeds and throttle angles. The air compressor speed is set from 30 krpm (thousand revolutions per minute) to 90 krpm in steps of 10 krpm, and the throttle angle is set from 10 degrees to 50 degrees in steps of 2.5 degrees. Linear interpolation and fitting are performed on the collected data, and the lookup tables of air compressor speed and throttle angle are shown in Figures 2 and 3. The gas supply system is nonlinear, and the feedforward table is constructed using a linear fit, which inevitably leads to errors. Moreover, since the state equation of an ideal gas is involved, the parameters of the air supply system model will change with changes in temperature and humidity, and it is difficult to obtain satisfactory control performance by relying only on feedforward. Therefore, feedback control is needed 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 elimination. Existing research is to eliminate errors by decoupling the air supply system into two SISO devices.

N _b and θ _b are used as flow and pressure feedback control signals respectively, and the coupling relationship is regarded as a disturbance and processed by sliding mode control. At the same time, the buffeting effect of the first-order sliding mode makes it difficult for the air compressor and throttle to accurately respond to their control instructions, so the second-order sliding mode is considered for feedback control. Air flow (W) and pressure (P) will increase simultaneously with the increase of air compressor speed (N) and, but increasing the throttle angle will cause W to increase and P to decrease. Under the action of feedforward, the relationship between (W,P) ^T and (N _b ,θ _b ) ^T is approximately

Among them, h _ij (W, P)>0 (i, j=1). Consider h ₁₁ (W,P)θ _b and h ₂₁ (W,P)N _b as bounded perturbations, that is, d ₁ =h ₁₂ (W,P)θ _b , d ₂ =h ₂₁ (W,P )N _b , then (2) can be rewritten as

The sliding mode surface is constructed as

(s ₁ ,s ₂ ) ^T = (WW _d ,PP _d ) ^T (4)

s ₁ and s ₂ are sliding mode surfaces.

noticed (time derivative of flow) is positively related to N _b , and/> (time derivative of pressure) is inversely related to θ _b . Therefore, SSM is used to construct the feedback control vector:

t represents the integral over time

in

A multivariate optimization algorithm is needed to complete parameter tuning of the feedback controller. As a typical model-free method, ES can perform multi-parameter optimization, and introducing ES into the feedback controller is shown in Figure 4. To measure the control performance, the cost function (J) is constructed using the tracking error vector. In the mth (m≥1) iteration cycle (T=10s), J has the following form:

Where B = (β ₁ , β ₂ ,..., β ₆ ) ^T , ( _ew , e _p ) ^T = (W _d -W, P _d -P) ^T , q ₁ =1, q ₂ =2 are the error weight matrices of flow rate and pressure respectively. In fuel cells, pressure stability needs to be prioritized for protection, so let q ₁ < q ₂ . In other words, a small part of the flow control accuracy is sacrificed to stabilize the pressure. For the system shown in Figure 4, there should be a suitable control parameter vector B such that J(B) reaches the minimum value, because controller parameters that are too large or too small will deteriorate the control performance and lead to more accumulated errors. For the convenience of analysis, the following assumptions are made: J(B) is a convex function about B, in has a minimum value. This assumption is made to facilitate subsequent analysis. Optimization problems may have multiple local minima. However, the purpose of introducing ES is to adjust the parameters of the SSM control law to obtain satisfactory results on the premise of ensuring pressure stability first, rather than to obtain optimal parameters. For a brief introduction to expression, 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)]

Among them, '*' represents the convolution operator, and 'L ^-1 (g)' represents the inverse Laplace transform. For the i-th ES loop in Figure 4:

in Represents the optimal parameters/> estimate,/> (0<h<ω _i ,i＝1,2,...,6, h represents the cutoff frequency) is a high-pass filter,/> is an integrator with gain, μ _i determines the convergence rate of parameters, ξ _i and eta are the intermediate transition letters of the algorithm, and s is a special symbol in the Laplace frequency domain. The local gradient of J(B) is extracted using the sinusoidal perturbation (a _i sinω _i t) input to the control system, and the perturbation amplitude (a _i ) should be relatively small. The perturbation frequency (ω ₁ -ω ₆ ) is particularly important for ES, which must first ensure that the time scales of the ES cycle and cost function are separated. Therefore, the maximum value of the disturbance frequency needs to be less than the update frequency of the cost function/> And maintain a certain frequency interval. In addition, the sum of any two disturbance frequencies cannot be equal to the third disturbance frequency, otherwise the stability at the extreme value will be destroyed. Using the gradient descent method, ES periodically updates the parameter vector (B) to reduce J(m,B), thereby achieving more satisfactory control performance. The following explains the principle of gradient descent, in/> Perform a Taylor expansion on J(B), ignoring second-order and above terms. consider get

Therefore, the perturbation signal (a _i sinω _i t) is transformed by the local gradient The modulation is shown in Figure 5. First, analyze ES loop 1. Extracting partial derivatives via coherent demodulation/> H _h (s) has zero direct current (DC) gain, thus eliminating the DC component

Then η is multiplied by sinω ₁ t, applying get

Since the integrator has infinite DC gain, so the sinusoidal component in the filtered signal is ignored:

Organize (12) available

Performing the Laplace transform and the inverse Laplace transform on (13) yields

in for/> initial value. Similarly, for ES loop 2 to loop 6

in They are/> initial value. Since μ _i a _i >0(i＝1,2,...,6),/> It will move in the opposite direction to the gradient until it reaches the minimum point B ^* .

To sum up, the control method proposed by the present invention uses the gradient descent method to optimize the controller parameters, thereby obtaining better control effects.

The high-precision adaptive optimization control method proposed by the present invention is shown in Figure 1. Collect air flow and pressure data under different air compressor speeds and throttle openings on the hardware platform, perform linear interpolation and fitting on the collected data, establish a feedforward lookup table, and design a feedback controller with the help of super-helical sliding mode. The feedforward error is eliminated and extreme value search (ES) is introduced to adaptively optimize the feedback control parameters.

Example 1

In this embodiment, the experimental environment is shown in Figure 6, where an air buffer tank is used to simulate the cathode. The ECU (Electronic Control Unit) issues control instructions to the compressor and throttle, and transmits the air flow, air pressure, actual compressor speed, and actual throttle angle collected by the sensor back to the PC (host computer). The parameters of ES-ASSM are shown in Table 1, where the disturbance frequency ω _i is selected according to the principles mentioned above. The initial value of the cost function is set to 15 (slightly larger than J(1)), and the initial value of the control parameters 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 tracking response of air flow and pressure and the evolution of cost function J(m,B) are shown in Figure 7. ES-ASSM optimizes parameters online to obtain a more favorable tracking response, and J(m,B) finally converges to 5.348 after nine iterations. In addition, the iterative update process of the parameter vector is shown in Figure 8, where After eight iterations, they converged to 0.02165, 0.05078, 1.00344, 0.09588, 0.02840, and 1.00469 respectively.

Table 1

The optimized parameters are loaded into the feedback controller, and the ES loop is disabled to reduce the computational load, and then the performance of the control method provided by the present invention is evaluated. Consider the following operating conditions:

1) Case 1: The reference trajectories of flow rate and pressure are selected as step signal and sinusoidal signal respectively. The results are shown in Figures 9 and 10.

2) Case 2: The reference trajectories of flow rate and pressure are selected as sinusoidal signal and step signal respectively. The results are shown in Figures 11 and 12.

From the perspective of flow and pressure response, the control method provided by the present invention realizes decoupling control well:

1) Flow and pressure can track their respective reference trajectories independently, whether it is step flow and sinusoidal pressure as shown in Figure 9, or sinusoidal flow and step pressure as shown in Figure 11.

2) When the flow rate jumps, the pressure fluctuation is very small as shown in Figure 9(c), but when the pressure step occurs, the flow rate fluctuation is obvious as shown in Figure 11(a). In addition, when tracking the sinusoidal signal, the effect of pressure following the reference trajectory as shown in Figure 9(c) and Figure 11(a) is significantly better than that of flow. When designing the cost function, the weight of the pressure error is greater than the weight of the flow error.

3) The proposed scheme also performs well in terms of response speed and tracking accuracy. As shown in Figure 9(a) and Figure 11(c). The step response of flow and pressure is completed within 0.5s. When tracking the sinusoidal signal, the pressure error is limited to approximately 1kPa as shown in Figure 9(d), and the flow error is limited to approximately 2g/s as shown in Figure 11(b). Within.

In order to further illustrate the superior performance of the control method of the present invention, the comparison results using the diagonal matrix decoupling method (DMDM) are shown in Figures 13 and 14. Compared with DMDM, in case 1, as shown in Figure 9(a) and Figure 13(a), the control method of the present invention has smaller flow overshoot, as shown in Figure 9(d) and Figure 13(d). Tracking error is also smaller. In case 2, the error in the flow rate of DMDM is larger as shown in Figure 11(b) and Figure 14(b), and at the same time, there is a steady-state error in the pressure as shown in Figure 14(c).

In addition, quantitative analysis is performed with the help of root mean square error (RMSE):

Where t ₀ and t _f represent the sampling start and end time respectively.

Judging from the comparative data of the two control methods in Table 2, the control method provided by the present invention is better than DMDM.

Table 2

The control method provided by the present invention realizes the decoupling of flow and pressure on the premise of ensuring the priority of pressure response. It combines the feedforward fast response and the anti-disturbance advantages of SSM to stably, accurately and quickly complete the solution of air flow and pressure. Coupling control; avoids the dilemma of existing decoupling methods that rely heavily on model identification, avoids a large amount of calculations, achieves better control effects, and increases the portability of the control algorithm.

Claims (5)

1. A decoupling control method for a proton exchange membrane fuel cell air supply system, characterized by comprising the following steps: Step 1. Collect air flow and pressure data at different air compressor speeds and throttle openings; Step 2: Perform linear interpolation and fitting on the collected data, and establish a feedforward lookup table: (N _f ,θ _f ) ^T =[f ₁ (W _d ,P _d ),f ₂ (W _d ,P _d )] ^T (1) Step 3. Use the feedback controller built with SSM to eliminate the feedforward error. The feedback controller is: in, Step 4: Use extreme value search (ES) to adaptively optimize the parameters of the feedback controller, specifically as follows: in, for parameters/> estimate; in, for/> Initial value;/> They are/> initial value; Step 5: Load the parameters optimized in Step 4 into the feedback controller. 2. The decoupling control method of the proton exchange membrane fuel cell air supply system according to claim 1, wherein the maximum value of the disturbance frequency ω _i is less than the update frequency of the cost function The sum of any two disturbance frequencies ω _i is not equal to the third disturbance frequency ω _i . 3. A proton exchange membrane fuel cell air supply system decoupling control system, characterized by including: The collection module is used to collect air flow and pressure data at different air compressor speeds and throttle openings on the hardware platform; Feedforward controller is used to linearly interpolate and fit the collected data and establish a feedforward lookup table: (N _f ,θ _f ) ^T =[f ₁ (W _d ,P _d ),f ₂ (W _d ,P _d )] ^T (1) Feedback controller is used to eliminate feedforward error. The feedback control vector is: in (s ₁ ,s ₂ ) ^T = (WW _d ,PP _d ) ^T (6) Among them, φ ₁ and φ ₂ are functions of s ₁ , and φ ₄ and φ ₅ are functions of s ₂ . The adaptive optimization module is used to adaptively optimize the parameters of the feedback controller and is implemented using ES, specifically: in, for parameters/> estimate; Among them, μ _i is the integral gain, for/> Initial value;/> They are/> initial value. 4. A computer-readable storage medium, characterized in that a computer program is stored thereon, and when the program is executed by a processor, the decoupling control method of a proton exchange membrane fuel cell air supply system as claimed in claim 1 is implemented. 5. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that when the processor executes the program, it implements claim 1 The decoupling control method of the proton exchange membrane fuel cell air supply system.