Air cooling PEMFC temperature control method based on preset performance PID

Abstract

The invention discloses an air cooling PEMFC temperature control method based on preset performance PID, and relates to the technical field of fuel cell thermal management. Determining a transfer function between current and temperature errors in the air-cooled PEMFC thermal management system according to physical characteristics of the air-cooled PEMFC thermal management system, calculating control parameters of a PID controller according to a preset time domain performance index and the transfer function between the current and temperature errors, and verifying approximate rationality of a dominant pole; and the control parameters are substituted into the air cooling PEMFC thermal management system, and whether the system meets preset performance indexes or not is verified. According to the method, the PID control parameters can be determined according to the preset time domain performance indexes, and therefore it can be guaranteed that the system accurately meets the time domain performance index requirements in the controller design stage.

Description

Technical Field

[0001] This application relates to the field of fuel cell thermal management technology, and in particular to a temperature control method for air-cooled PEMFCs based on preset performance PID. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs), as highly efficient and clean energy conversion devices, possess outstanding advantages such as zero emissions, low noise, and high energy density, making them highly favored in the field of renewable power generation. Air-cooled PEMFCs, which integrate the air supply system and thermal management system, have a more streamlined system structure compared to water-cooled PEMFCs, showing promising application prospects and advantages in areas such as small backup power supplies, portable power supplies, and drones. Operating temperature is a key factor affecting the stack's output performance; therefore, it is necessary to study appropriate temperature control strategies to maintain the efficient and stable operation of air-cooled PEMFC systems. PID control is currently the most widely used method in PEMFC temperature control, offering advantages such as simple structure, high robustness, and ease of engineering implementation. The control effect of a PID controller is entirely determined by its control parameters. K p , K i , K d Therefore, there is currently a lot of research on PID control parameter optimization, and commonly used optimization methods include heuristic algorithms, fuzzy control, neural networks, etc.

[0003] However, while the aforementioned intelligent optimization algorithms can improve the overall performance of PID control to varying degrees, this method has a fundamental limitation: it cannot guarantee the pre-set time-domain performance indicators (overshoot, settling time) of the system during the initial controller design phase. The optimization process is essentially a paradigm of "post-hoc correction" and "performance optimization." Therefore, in practical applications, engineers typically need to conduct extensive and tedious simulations and experiments, repeatedly trial and error, and adjust parameters to roughly meet the pre-set time-domain performance requirements. Summary of the Invention

[0004] Therefore, it is necessary to provide a temperature control method for air-cooled PEMFC based on preset performance PID to address the above-mentioned technical problems. This method can determine the PID control parameters by preset time-domain performance indicators, thereby ensuring that the system accurately meets the time-domain performance indicator requirements during the controller design stage.

[0005] The following technical solution is adopted in this specification: This manual provides a temperature control method for air-cooled PEMFCs based on preset performance PID, including: Based on the physical characteristics of the air-cooled PEMFC thermal management system, the transfer functions between the temperature error of the PID controller and the temperature control action PWM, the transfer function between the temperature control action PWM and the temperature, the transfer function between the current and the temperature, and the transfer function between the current and the temperature error in the air-cooled PEMFC thermal management system are determined. Substituting the specific expressions of the transfer function between temperature error and temperature control action PWM, the transfer function between temperature control action PWM and temperature, and the transfer function between current and temperature into the transfer function between current and temperature error, we obtain the specific expression of the transfer function between current and temperature error. The specific expression of the transfer function between current and temperature error is simplified into a second-order typical oscillation element, and the relationship between the transfer function and the second-order typical oscillation element is obtained. The expression of the second-order typical oscillation element in the relationship is then subjected to an inverse Laplace transform to obtain the calculation formula of the time-domain performance index of the air-cooled PEMFC thermal management system. Based on the preset time-domain performance index values, the calculation formula of the time-domain performance index is solved to obtain the damping ratio and undamped oscillation frequency of the second-order typical oscillation element. The control parameters of the PID controller are obtained by solving the relationship between the transfer function and the second-order typical oscillating element based on the damping ratio and the undamped oscillation frequency. The control parameters are input to the PID controller, which controls the temperature of the air-cooled PEMFC.

[0006] Optionally, based on the physical characteristics of the air-cooled PEMFC thermal management system, the transfer functions between the temperature error of the PID controller and the temperature control action PWM, the transfer function between the temperature control action PWM and temperature, the transfer function between current and temperature, and the transfer function between current and temperature error in the air-cooled PEMFC thermal management system are determined, including: Based on the physical characteristics of the air-cooled PEMFC thermal management system, the heat transfer process of the air-cooled PEMFC is abstracted into a system block diagram; the system block diagram is used to describe the signal transmission relationship between each link of the air-cooled PEMFC thermal management system. The signal transmission relationships in the system block diagram are analyzed to determine the transfer functions between the temperature error of the PID controller and the temperature control action PWM, the transfer function between the temperature control action PWM and the temperature, and the transfer function between the current and the temperature in the air-cooled PEMFC thermal management system. The system block diagram is simplified based on Mason's formula, and the transfer function between current and temperature error is determined.

[0007] Optionally, the method further includes: At the equilibrium operating point of the air-cooled PEMFC, multiple step perturbations are applied to the temperature control action PWM of the fuel cell stack while keeping the current constant, thus obtaining the specific expression of the transfer function between the temperature control action PWM and the temperature. ,in, For the Laplace operator; At the equilibrium operating point of the air-cooled PEMFC, multiple step perturbations are applied to the current of the air-cooled PEMFC while keeping the PWM constant, and the specific expression of the transfer function between current and temperature is identified. ; Obtain the time-domain expression of the PID controller: ,in, This is the proportionality coefficient. The integral coefficient is... The differential coefficients are... To control the amount of action, The temperature error between a given temperature value and the actual temperature value; By performing a Laplace transform on the time-domain expression of the PID controller, the specific expression of the transfer function between the temperature error and the temperature control action is obtained. ,in, for Laplace transform, for The Laplace transform of .

[0008] Optionally, the transfer function between current and temperature error is: ; in, For the Laplace transform of the current; The specific expression for the transfer function between current and temperature error is: .

[0009] Optionally, the specific expression of the transfer function between current and temperature error is simplified to a second-order typical oscillatory element, resulting in the relationship between the transfer function and the second-order typical oscillatory element, including: By approximating the dominant pole of the specific expression of the transfer function between current and temperature error, the reduced-order transfer function is obtained. The reduced transfer function is simplified into a second-order typical oscillatory element, and the relationship between the transfer function and the second-order typical oscillatory element is obtained. The reduced transfer function is: ; The relationship between the transfer function and a typical second-order oscillatory element is as follows: ; in, These are real numbers much greater than 1, used to configure poles. The damping ratio of a typical second-order oscillating element. The frequency of the undamped oscillation of a typical second-order oscillation element is given.

[0010] Optionally, by performing an inverse Laplace transform on the expression for the second-order typical oscillatory element in the relation, the calculation formula for the time-domain performance index of the air-cooled PEMFC thermal management system is obtained, including: Approximating the expression of a typical second-order oscillatory element using the dominant poles, we obtain the approximate expression for the typical second-order oscillatory element as follows: ; Based on the approximate expression of a typical second-order oscillating element, we obtain The expression is: ; right Taking the inverse Laplace transform of the expression, we obtain the expression for the temperature error e(t): ; in, Indicates the inverse Laplace transform. Indicates time; Based on temperature error Solving the expression yields the calculation formula for the time-domain performance index of the air-cooled PEMFC thermal management system.

[0011] Optionally, time-domain performance metrics include overshoot and settling time; based on temperature error Solving the expression yields the calculation formula for the time-domain performance index of the air-cooled PEMFC thermal management system, including: make first derivative The peak time of the response was obtained. t p : ; Peak response time t p Incorporating temperature error e ( t The expression for ) yields the peak error: ; Calculate the overshoot with steady-state temperature as the target temperature based on the error peak value. The calculation formula is: ; in, This is the steady-state temperature; Based on steady-state temperature and the preset error band Determine the adjustment time The calculation formula is: .

[0012] Optionally, based on preset time-domain performance index values, the calculation formula for the time-domain performance index is solved to obtain the damping ratio and undamped oscillation frequency of a typical second-order oscillation element, including: Set a damping ratio within the interval [0, 1]. e initial value e 0; Will e Substitute 0 and the preset overshoot into the overshoot value. The calculation formula yields the undamped oscillation frequency corresponding to... ; Will e 0 and Substitute adjustment time The calculation formula is obtained. ; Will With preset adjustment time If a comparison is made, Then determine and That is, the values ​​of the damping ratio and undamped oscillation frequency of a typical second-order oscillation element; otherwise, the bisection method is used to reset them. e 0 and recalculate until the condition is met. , will satisfy Time corresponding e 0 and The values ​​of damping ratio and undamped oscillation frequency for a typical second-order oscillation element are determined.

[0013] Optionally, the control parameters of the PID controller are obtained by solving the relationship between the transfer function and the second-order typical oscillating element based on the damping ratio and the undamped oscillation frequency, including: Balancing the coefficients in the denominator of the relationship between the transfer function and the typical second-order oscillatory element yields a system of three linear equations in three variables: ; Substituting the damping ratio and undamped oscillation frequency into a system of three linear equations, we obtain the control parameters of the PID controller. , and .

[0014] This manual provides a temperature control device for an air-cooled PEMFC based on a preset performance PID controller, including: The first determining module is used to determine, based on the physical characteristics of the air-cooled PEMFC thermal management system, the transfer function between the temperature error of the PID controller and the temperature control action PWM, the transfer function between the temperature control action PWM and the temperature, the transfer function between the current and the temperature, and the transfer function between the current and the temperature error in the air-cooled PEMFC thermal management system. The second determining module is used to substitute the specific expressions of the transfer function between temperature error and temperature control action PWM, the transfer function between temperature control action PWM and temperature, and the transfer function between current and temperature into the transfer function between current and temperature error to obtain the specific expression of the transfer function between current and temperature error. The simplification module is used to simplify the specific expression of the transfer function between current and temperature error into a typical second-order oscillatory element, and obtain the relationship between the transfer function and the typical second-order oscillatory element. The first solution module is used to perform an inverse Laplace transform on the expression of the second-order typical oscillation element in the relation to obtain the calculation formula of the time-domain performance index of the air-cooled PEMFC thermal management system. Based on the preset time-domain performance index values, the calculation formula of the time-domain performance index is solved to obtain the damping ratio and undamped oscillation frequency of the second-order typical oscillation element. The second solution module is used to solve the relationship between the transfer function and the second-order typical oscillating element based on the damping ratio and the undamped oscillation frequency, so as to obtain the control parameters of the PID controller. The control module is used to input control parameters to the PID controller, and the temperature of the air-cooled PEMFC is controlled by the PID controller with control parameters.

[0015] This specification provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described air-cooled PEMFC temperature control method based on a preset performance PID.

[0016] This specification provides a computer 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, it implements the above-described air-cooled PEMFC temperature control method based on a preset performance PID.

[0017] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: The air-cooled PEMFC temperature control method based on a preset performance PID controller provided in this specification first determines the transfer function between current and temperature error in the air-cooled PEMFC thermal management system based on its physical characteristics. Then, based on this transfer function and a second-order typical oscillating element, and using preset time-domain performance index values, the damping ratio and undamped oscillation frequency of the second-order typical oscillation element are determined. The control parameters of the PID controller are then obtained based on the damping ratio and undamped oscillation frequency. Compared to existing technologies that require repeated adjustments to the controller parameters through "post-hoc correction" to ensure the system performance indicators roughly meet preset values, this method determines the PID controller parameters using pre-set time-domain performance indicators, thus ensuring the system accurately meets performance requirements during the controller design phase. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0019] Figure 1 This document provides a schematic flowchart of a temperature control method for an air-cooled PEMFC based on a preset performance PID controller. Figure 2 This specification provides a block diagram of an air-cooled PEMFC thermal management system; Figure 3 This specification provides a waveform diagram for system identification of applied PWM disturbance signals; Figure 4 This specification provides a temperature response curve of a practical system and identification model to a PWM signal. Figure 5 This specification provides a waveform diagram for a system to identify an applied current disturbance signal; Figure 6 This specification provides a temperature response curve of a practical system and an identification model to a current signal. Figure 7 The zero-pole distribution diagram of the error transfer function of an air-cooled PEMFC thermal management system provided in this specification; Figure 8 This manual provides a diagram illustrating the effect of a preset performance PID controller on the actual system control. Figure 9 This document provides a preset performance PID design flowchart; Figure 10 This is a schematic diagram of a computer device for implementing a temperature control method for an air-cooled PEMFC based on a preset performance PID, as provided in this specification. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0021] This specification provides a temperature control method for air-cooled PEMFCs based on preset performance PID control. The method includes the following steps: Based on the physical characteristics of the air-cooled PEMFC thermal management system, a dynamic model is built using a Matlab / Simulink simulation platform; based on the established dynamic model, the system is abstracted into a system block diagram, and the transfer function in the block diagram is determined through system identification; based on the abstracted system block diagram, the transfer function between current disturbance and temperature error is calculated; preset performance indicators are set, and the PID parameter values ​​are calculated based on the current-temperature transfer function, and the approximate rationality of the dominant pole is verified; the determined PID parameters are substituted into the air-cooled PEMFC thermal management system to verify whether the system meets the preset performance indicators. Unlike currently widely used controllers that require multiple post-implementation corrections to roughly meet the preset performance indicators, the controller proposed in this invention can ensure that the system accurately meets the preset performance indicator requirements during the controller design stage, providing a solution for preset performance control of air-cooled PEMFCs.

[0022] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0023] Figure 1 This is a schematic diagram of a temperature control method for an air-cooled PEMFC based on a preset performance PID controller, as described in this specification. The method specifically includes the following steps: S101, Based on the physical characteristics of the air-cooled PEMFC thermal management system, determine the transfer functions between the temperature error of the PID controller and the temperature control action PWM, the transfer functions between the temperature control action PWM and temperature, the transfer functions between current and temperature, and the transfer functions between current and temperature error in the air-cooled PEMFC thermal management system.

[0024] Based on the physical characteristics of the air-cooled PEMFC thermal management system, the transfer functions between the temperature error and the temperature control action of the PID controller, the transfer function between the temperature control action and temperature, the transfer function between current and temperature, and the transfer function between current and temperature error in the air-cooled PEMFC thermal management system are determined, including the following steps: S201. Based on the physical characteristics of the air-cooled PEMFC thermal management system, the heat transfer process of the air-cooled PEMFC is abstracted into a system block diagram; the system block diagram is used to describe the signal transmission relationship between each link of the air-cooled PEMFC thermal management system.

[0025] Based on the physical characteristics of the air-cooled PEMFC thermal management system, a dynamic model of the system is built using the Matlab / Simulink simulation platform. Based on the dynamic model of the air-cooled PEMFC thermal management system, it is abstracted into a system block diagram.

[0026] The dynamic model of the air-cooled PEMFC thermal management system mainly consists of two parts: the PEMFC battery stack and the thermal analysis module. The PEMFC battery stack model is constructed using semi-empirical equations to reflect the relationship between operating parameters and the battery stack output voltage, and to calculate the output voltage. Semi-empirical equations are often used in PEMFC system-level simulation studies due to their fast calculation speed and high accuracy.

[0027] (1) (2) (3) (4) (5) (6) (7) (8) In the formula, Represents the output voltage. Represents Nernst voltage. Represents activation loss, Represents ohmic loss, This represents concentration loss. There are 9 coefficients, which can be calibrated through experimental data, among which The activation loss coefficient is... This is the no-load current. For external circuit resistance, The water content of the exchange membrane, This represents the limiting current density.

[0028] The thermal analysis module analyzes the heat generation, transfer, and dissipation of various components of the system, and establishes an energy conservation equation to reflect the dynamic temperature changes of the fuel cell stack, laying the foundation for subsequent temperature control strategy research. The thermal analysis module uses the energy conservation equation to calculate the temperature change rate of the PEMFC fuel cell stack. The main heat generation, transfer, and dissipation are described below:

[0029] (9) (10) (11) (12) (13) In the formula, Represents the total input energy of PEMFC. This represents the electrical energy output of PEMFC. This means that the cooling air carries away the heat. Represents heat loss through radiation and natural convection. For PEMFC heat capacity, The enthalpy of hydrogen combustion. The surface heat transfer coefficient, For ambient temperature, This represents the total area of ​​the cathode flow channel. This is the equivalent thermal resistance.

[0030] A system block diagram is a graphical model describing the signal transmission relationships between various components of a system, and it is a convenient method for describing complex systems. First, we analyze the signal transmission relationships between the various components of the system. In an air-cooled PEMFC thermal management system, the fuel cell stack temperature is mainly affected by two factors: current and the cooling fan PWM (duty cycle). The current change can be considered as an external disturbance, while the cooling fan PWM is calculated by the PID controller based on the system temperature error. Based on the above analysis, the system block diagram of the air-cooled PEMFC thermal management system is as follows: Figure 2 As shown.

[0031] S202, analyze the signal transmission relationship in the system block diagram, and determine the transfer function between the temperature error of the PID controller and the temperature control action PWM, the transfer function between the temperature control action PWM and the temperature, and the transfer function between the current and the temperature in the air-cooled PEMFC thermal management system.

[0032] Optionally, the transfer function between the temperature control action PWM and the temperature can be determined through system identification. and the transfer function between current and temperature System identification, based on statistical data of the inputs and outputs of the system under test, involves determining a system model from a defined set of system models, making it equivalent to the system under test. This invention selects the model set in transfer function form and performs identification using the system identification toolbox in Matlab. Since the air-cooled PEMFC is a complex nonlinear system, it needs to be locally linearized at its equilibrium operating point, and its transfer function is determined through system identification. and .

[0033] In one embodiment, at the equilibrium operating point of the air-cooled PEMFC, multiple step disturbances are applied to the temperature control action PWM of the fuel cell stack while keeping the current constant. The specific expression of the transfer function between the temperature control action PWM and the temperature is obtained as follows: (14) in, For the Laplace operator.

[0034] Specifically, regarding the transfer function between PWM and stack temperature At the equilibrium operating point, multiple step disturbances are first applied to the PWM, such as... Figure 3 As shown, keeping the current constant, the input data is recorded as PWM, and the output data is the fuel cell stack temperature. The data is processed using the Matlab system identification toolbox, and the transfer function model is selected. The identification result is as follows: The fitting accuracy (obtained from the normalized mean square error) was 92.06%. Figure 4 This demonstrates the relationship between the actual system and the identification model. Figure 3 The response curves of the perturbation show a good agreement between the two, verifying the accuracy of the identification model.

[0035] In one embodiment, at the equilibrium operating point of the air-cooled PEMFC, multiple step disturbances are applied to the current of the air-cooled PEMFC while keeping the PWM constant. The specific expression of the transfer function between current and temperature is then identified as follows: (15) The transfer function between current and stack temperature At the equilibrium operating point, multiple step disturbances are first applied to the current, such as... Figure 5 As shown, keeping the PWM constant, the input data is recorded as current, and the output data is the fuel cell stack temperature. The data is processed using the Matlab system identification toolbox, and the transfer function model is selected. The identification result is as follows: The fitting accuracy was 98.47%. Figure 6 This demonstrates the relationship between the actual system and the identification model. Figure 5 The response curves to the disturbances show a high degree of agreement, verifying the accuracy of the identification model.

[0036] In one embodiment, the time-domain expression of the PID controller is obtained: (16) in, This is the proportionality coefficient. The integral coefficient is... The differential coefficients are... To control the amount of action, Given the temperature error between the given temperature value and the actual temperature value, the time-domain expression of the PID controller is transformed using a Laplace transform to obtain the specific expression of the transfer function between the temperature error and the temperature control action: (17) in, for Laplace transform, for The Laplace transform of .

[0037] The PID controller is an error-based controller widely used in engineering practice due to its simple structure, high robustness, and ease of implementation. Regarding the transfer function of the PID controller... It can be obtained directly by performing a Laplace transform on the time-domain expression of the PID controller.

[0038] In the air-cooled PEMFC thermal management system This is the fan PWM signal. The temperature difference between the given and actual values ​​of the battery stack is represented by a setpoint of 60°C. Therefore, the transfer function can be obtained through a Laplace transform. .

[0039] S203. Based on Mason's formula, simplify the system block diagram and determine the transfer function between current and temperature error.

[0040] The transfer function between current and temperature error is: (18) in, This is the Laplace transform of the current.

[0041] S102, substitute the specific expressions of the transfer function between temperature error and temperature control action PWM, the transfer function between temperature control action PWM and temperature, and the transfer function between current and temperature into the transfer function between current and temperature error to obtain the specific expression of the transfer function between current and temperature error.

[0042] Substituting equations (14), (15), and (17) into equation (18), we obtain the specific expression for the transfer function between current and temperature error. The specific expression for the transfer function between current and temperature error is: (19) S103 simplifies the specific expression of the transfer function between current and temperature error into a typical second-order oscillating element, thus obtaining the relationship between the transfer function and the typical second-order oscillating element.

[0043] It can be seen that formula (19) is a fourth-order system, and it is difficult to directly calculate its time-domain performance index. It is necessary to reduce the system order by using the dominant pole approximation to design preset performance control.

[0044] In one embodiment, the specific expression of the transfer function between current and temperature error is simplified to a second-order typical oscillatory element to obtain the relationship between the transfer function and the second-order typical oscillatory element. This includes: approximating the specific expression of the transfer function between current and temperature error using the dominant pole to obtain the reduced-order transfer function; and simplifying the reduced-order transfer function to a second-order typical oscillatory element to obtain the relationship between the transfer function and the second-order typical oscillatory element.

[0045] The dominant pole approximation of formula (19) is applied to reduce the system order, facilitating the design of preset performance control. Note that the known zeros in the numerator of formula (19) are -119.266 and -0.03366, and the known pole in the denominator is -0.03191. The distance between the pole -0.03191 and the zero -0.03366 is much smaller than their respective distances from the imaginary axis, so they can be considered as dipoles and zero-pole cancellation can be performed. The zero -119.266 is too far from the imaginary axis, so its influence can be ignored. After the dominant pole approximation, the reduced transfer function of formula (19) is:

[0046] (20) The reduced transfer function (Equation (20)) is a third-order system, and it is still inconvenient to directly calculate its time-domain performance. Therefore, it is necessary to configure its poles to further simplify it into a second-order typical oscillatory element for analysis. The relationship between the transfer function and the second-order typical oscillatory element is as follows: (twenty one) in, These are real numbers much greater than 1, used to configure poles. The damping ratio of a typical second-order oscillating element. The frequency of the undamped oscillation of a typical second-order oscillation element is given.

[0047] S104. Perform an inverse Laplace transform on the expression for the second-order typical oscillation element in the relation to obtain the calculation formula for the time-domain performance index of the air-cooled PEMFC thermal management system. Based on the preset time-domain performance index values, solve the calculation formula for the time-domain performance index to obtain the damping ratio and undamped oscillation frequency of the second-order typical oscillation element.

[0048] In one embodiment, the expression for the second-order typical oscillatory element in the relation is subjected to an inverse Laplace transform to obtain the calculation formula for the time-domain performance index of the air-cooled PEMFC thermal management system, including the following steps: S301, by approximating the expression of a typical second-order oscillating element based on the dominant poles, we obtain the approximate expression of a typical second-order oscillating element as follows: (twenty two) because α It is much greater than 1 (it can be set freely, and this invention sets it to 70). Formula (21) is approximated again based on the dominant pole, and can finally be approximated as a typical second-order oscillation element analysis, namely formula (22).

[0049] S302, based on the approximate expression of a typical second-order oscillating element, yields... The expression is: (twenty three) It should be noted that in this embodiment, the given current disturbance changes from 24A to 26A (i.e., a 2A step disturbance). Therefore, =2 / , take the left side of formula (22) Multiplying to the right side, we get formula (23).

[0050] S303, for Performing an inverse Laplace transform on the expression yields the temperature error. e ( t The expression for ) is: (twenty four) in, Indicates the inverse Laplace transform. Indicates time.

[0051] S304, based on temperature error Solving the expression yields the calculation formula for the time-domain performance index of the air-cooled PEMFC thermal management system.

[0052] The key feature of the preset performance PID control proposed in this invention is that the PID parameters can be determined by pre-set time-domain performance indicators, thus ensuring that the system output accurately meets the time-domain performance requirements during the controller design phase. Therefore, the system's time-domain performance indicators are defined as: overshoot (σ=0.1%) and settling time (σ=0.1%). =3s), adjust the time corresponding to the error band (Δ=0.02%).

[0053] In one embodiment, based on temperature error Solving the expression yields the calculation formula for the time-domain performance index of the air-cooled PEMFC thermal management system, including the following steps: S401, order first derivative The peak time of the response was obtained. tp : (25) S402, the peak time of the response t p Incorporating temperature error e ( t The expression for ) is used to obtain the peak error.

[0054] Substituting formula (25) into formula (24), the peak error can be calculated: (25) S403, Calculate the overshoot with steady-state temperature as the target temperature based on the error peak value. The calculation formula is: (26) in, The target temperature.

[0055] Optionally, the system overshoot is set at a steady-state temperature of 60°C. The calculation formula is: (27) S404, based on steady-state temperature and the preset error band Determine the adjustment time The calculation formula is: (28) Specifically, adjusting the time ( The system enters the error band along the envelope of its response curve. The time is calculated, that is, by expanding formula (28), we get: (29) The adjustment time can be obtained from formula (29). The calculation formula is formula (28).

[0056] In one embodiment, based on a preset time-domain performance index value, the calculation formula for the time-domain performance index is solved to obtain the damping ratio and undamped oscillation frequency of a typical second-order oscillation element, including: setting a damping ratio in the interval [0, 1]. e initial value e 0; will e Substitute 0 and the preset overshoot into the overshoot value. The calculation formula yields the undamped oscillation frequency corresponding to... ;Will e 0 and Substitute adjustment time The calculation formula is obtained. ;Will With preset adjustment time If a comparison is made, Then determine e 0 and That is, the values ​​of the damping ratio and undamped oscillation frequency of a typical second-order oscillation element; otherwise, the bisection method is used to reset them. e 0 and recalculate until the condition is met. , will satisfy Time corresponding e 0 and The values ​​of damping ratio and undamped oscillation frequency for a typical second-order oscillation element are determined.

[0057] Specifically, the preset time-domain performance indicators =0.1% and Substituting =3s into equations (27) and (28) respectively, we can obtain a system of two linear nonlinear equations in two variables. and Let be the two unknowns in this system of equations. Since this system of equations is quite complex, an iterative method is used to obtain the results separately. and The numerical solution is obtained through the following steps:

[0058] (1) Assume a value in the interval [0, 1]. initial value e 0.

[0059] (2) Substitute into formula (25) to calculate the corresponding Value; and will e 0 and Substitute into formula (27) to find .

[0060] (3) To and If the comparison is performed over a period of 3 seconds, then... ,but and This is the numerical solution to the system of equations; otherwise, a new assumption is made using the bisection method. Repeat steps (2) to (3) until the convergence condition is met. Specifically, if Then let ; like Then let And let the new hypothesis .in, and Each is the current It can find the lower and upper limits of an interval.

[0061] S105, based on the damping ratio and the undamped oscillation frequency, solve the relationship between the transfer function and the typical second-order oscillation element to obtain the control parameters of the PID controller.

[0062] In one embodiment, the control parameters of the PID controller are obtained by solving the relationship between the transfer function and the second-order typical oscillating element based on the damping ratio and the undamped oscillation frequency. This includes balancing the coefficients of each term in the denominator of the relationship between the transfer function and the second-order typical oscillating element (Equation (21)) to obtain a system of three linear equations: (30) Substituting the damping ratio and undamped oscillation frequency into a system of three linear equations, we obtain the control parameters of the PID controller. , and .

[0063] Optionally, the solution can be obtained based on the above steps. , .because Given that, the solution is: and Then the coefficients of each term in the denominator of formula (21) can be balanced, which is specifically expressed as a system of three linear equations in three variables:

[0064] (31) Solving formula (30) yields the three parameters of the PID controller, and the calculation results are as follows: =186.259, =136.635, =-52.720.

[0065] S106 inputs control parameters to the PID controller, and the temperature of the air-cooled PEMFC is controlled by the PID controller with control parameters.

[0066] Compared with the prior art, the present invention has at least the following beneficial technical effects: 1. This invention provides a method for simplifying the structure of an air-cooled PEMFC thermal management system. As a complex nonlinear system, air-cooled PEMFCs are difficult to analyze directly to design controllers. To overcome their complexity and nonlinearity, this invention first abstracts the air-cooled PEMFC thermal management system into a system block diagram, and then determines the transfer function in the block diagram at the equilibrium point through system identification, thus condensing the system information and facilitating subsequent controller design.

[0067] 2. This invention provides a method for controlling the temperature of an air-cooled PEMFC using a preset performance PID controller. Generally, existing air-cooled PEMFC control methods require repeated adjustments to the controller parameters through "post-implementation correction" to ensure the system performance indicators roughly meet preset values. The preset performance PID controller proposed in this invention allows the PID parameters to be determined by pre-set performance indicators, thus ensuring the system accurately meets performance requirements during the controller design phase.

[0068] In one embodiment, the present invention also provides a temperature control method for an air-cooled PEMFC based on a preset performance PID, comprising the following steps: S1. Based on the physical characteristics of the air-cooled PEMFC thermal management system, a dynamic model of it is built using the Matlab / Simulink simulation platform.

[0069] S2, based on the dynamic model of the air-cooled PEMFC thermal management system established in S1, is abstracted into a system block diagram, and the transfer function in the system block diagram is determined through system identification.

[0070] S3, based on the system block diagram abstracted from S2, calculate the transfer function between current disturbance and temperature error.

[0071] S4: Set preset performance indicators, calculate PID parameter values ​​based on the transfer function obtained in S3, and verify the approximate rationality of the dominant pole.

[0072] Take the values ​​of the solved PID parameters , , Substitute back into formula (19) and plot its zero-pole distribution as follows: Figure 7 As shown, the transfer function can be observed. It contains 4 poles and 2 zeros.

[0073] According to the following dominant pole approximation criterion: Retain one or more poles closest to the imaginary axis as dominant poles; Closed-loop zeros and poles that are more than 5 times farther from the imaginary axis than the dominant poles are omitted; Dipoles that are not very close to the imaginary axis and are very close to each other are omitted (the distance of the zero and pole from the imaginary axis is more than 10 times their distance from each other).

[0074] from Figure 7 As can be seen from the figure, pole 1 and zero I are too far from the imaginary axis, and pole 2 and zero II can be regarded as dipoles. Therefore, it is reasonable to choose pole 3 and pole 4 as the dominant poles to simplify the system, thereby reducing the fourth-order system in formula (19) to the second-order system in formula (22) for controller design.

[0075] S5. Substitute the PID parameters determined in S4 into the air-cooled PEMFC thermal management system to verify whether the system meets the preset time-domain performance indicators.

[0076] Since the PID parameters are calculated by the air-cooled PEMFC thermal management system after local linearization at the equilibrium operating point and approximation of the dominant pole, its time-domain performance indicators may deviate from the preset values. The reasons for the deviation can be summarized as follows: 1. Local linearization of nonlinear systems 2. System identification error 3. Dominant Pole Approximation To verify the deviation between the actual system performance indicators and the preset values, the PID control parameters calculated in S4 were used. , , By controlling the air-cooled PEMFC thermal management system and applying corresponding current disturbances, its temperature control effect is as follows: Figure 8 As shown in Table 1, the time-domain performance indicators are recorded and compared with preset values. If the results are within the error operating range, the effectiveness of the method proposed in this invention is proven.

[0077] Table 1 Comparison of actual and preset values ​​of system performance indicators It can be seen that in the air-cooled PEMFC thermal management system using preset time-domain performance indicators for temperature control, the actual performance indicators are basically consistent with the preset performance indicators. This means that the system accurately meets the preset performance indicator requirements during the PID controller design stage, thus verifying the effectiveness of the method proposed in this invention. In summary, the preset performance PID design process proposed in this invention is as follows: Figure 9 As shown, a solution is proposed for the preset performance control of air-cooled PEMFC.

[0078] The execution subject of the methods provided in this specification can be a server, which can be a server set up on a business platform, or a device such as a desktop computer or laptop computer that can execute the solutions in this specification.

[0079] When applying the air-cooled PEMFC temperature control method based on preset performance PID provided in this manual, it is not necessary to... Figure 1 The steps shown are executed in sequence. The specific execution order of each step can be determined as needed, and this manual does not impose any restrictions on it.

[0080] The above describes one or more embodiments of the air-cooled PEMFC temperature control method based on a preset performance PID. Based on the same concept, this specification also provides a corresponding air-cooled PEMFC temperature control device based on a preset performance PID, which includes: The first determining module is used to determine, based on the physical characteristics of the air-cooled PEMFC thermal management system, the transfer function between the temperature error of the PID controller and the temperature control action PWM, the transfer function between the temperature control action PWM and the temperature, the transfer function between the current and the temperature, and the transfer function between the current and the temperature error in the air-cooled PEMFC thermal management system. The second determining module is used to substitute the specific expressions of the transfer function between temperature error and temperature control action PWM, the transfer function between temperature control action PWM and temperature, and the transfer function between current and temperature into the transfer function between current and temperature error to obtain the specific expression of the transfer function between current and temperature error. The simplification module is used to simplify the specific expression of the transfer function between current and temperature error into a typical second-order oscillatory element, and obtain the relationship between the transfer function and the typical second-order oscillatory element. The first solution module is used to perform an inverse Laplace transform on the expression of the second-order typical oscillation element in the relation to obtain the calculation formula of the time-domain performance index of the air-cooled PEMFC thermal management system. Based on the preset time-domain performance index values, the calculation formula of the time-domain performance index is solved to obtain the damping ratio and undamped oscillation frequency of the second-order typical oscillation element. The second solution module is used to solve the relationship between the transfer function and the second-order typical oscillating element based on the damping ratio and the undamped oscillation frequency, so as to obtain the control parameters of the PID controller. The control module is used to input control parameters to the PID controller, and the temperature of the air-cooled PEMFC is controlled by the PID controller with control parameters.

[0081] Specific limitations regarding the air-cooled PEMFC temperature control device based on preset performance PID can be found in the above description of the limitations of the air-cooled PEMFC temperature control method based on preset performance PID, and will not be repeated here. Each module in the aforementioned air-cooled PEMFC temperature control device based on preset performance PID can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0082] This specification also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 The provided method is an air-cooled PEMFC temperature control method based on preset performance PID.

[0083] This instruction manual also provides Figure 10 The schematic diagram of the computer device shown is as follows:Figure 10 At the hardware level, the computer device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then runs it to achieve the above-mentioned functions. Figure 1 The provided method is an air-cooled PEMFC temperature control method based on preset performance PID.

[0084] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0085] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A temperature control method for an air-cooled PEMFC based on a preset performance PID controller, characterized in that, include: Based on the physical characteristics of the air-cooled PEMFC thermal management system, the transfer functions between the temperature error of the PID controller and the temperature control action PWM, the transfer function between the temperature control action PWM and the temperature, the transfer function between the current and the temperature, and the transfer function between the current and the temperature error in the air-cooled PEMFC thermal management system are determined. Substituting the specific expressions of the transfer function between temperature error and temperature control action PWM, the transfer function between temperature control action PWM and temperature, and the transfer function between current and temperature into the transfer function between current and temperature error, we obtain the specific expression of the transfer function between current and temperature error. The specific expression of the transfer function between current and temperature error is simplified into a typical second-order oscillating element, and the relationship between the transfer function and the typical second-order oscillating element is obtained. By performing an inverse Laplace transform on the expression of the second-order typical oscillation element in the relation, the calculation formula of the time-domain performance index of the air-cooled PEMFC thermal management system is obtained. Based on the preset time-domain performance index values, the calculation formula of the time-domain performance index is solved to obtain the damping ratio and undamped oscillation frequency of the second-order typical oscillation element. The control parameters of the PID controller are obtained by solving the relationship between the transfer function and the second-order typical oscillating element based on the damping ratio and the undamped oscillation frequency. The control parameters are input to the PID controller, which controls the temperature of the air-cooled PEMFC.

2. The method according to claim 1, characterized in that, Based on the physical characteristics of the air-cooled PEMFC thermal management system, the transfer functions between the temperature error of the PID controller and the temperature control action PWM, the transfer function between the temperature control action PWM and temperature, the transfer function between current and temperature, and the transfer function between current and temperature error in the air-cooled PEMFC thermal management system are determined, including: Based on the physical characteristics of the air-cooled PEMFC thermal management system, the heat transfer process of the air-cooled PEMFC is abstracted into a system block diagram; the system block diagram is used to describe the signal transmission relationship between each link of the air-cooled PEMFC thermal management system. The signal transmission relationships in the system block diagram are analyzed to determine the transfer functions between the temperature error of the PID controller and the temperature control action PWM, the transfer function between the temperature control action PWM and the temperature, and the transfer function between the current and the temperature in the air-cooled PEMFC thermal management system. The system block diagram is simplified based on Mason's formula, and the transfer function between current and temperature error is determined.

3. The method according to claim 2, characterized in that, The method further includes: At the equilibrium operating point of the air-cooled PEMFC, multiple step perturbations are applied to the temperature control action PWM of the fuel cell stack while keeping the current constant, thus obtaining the specific expression of the transfer function between the temperature control action PWM and the temperature. ,in, For the Laplace operator; At the equilibrium operating point of the air-cooled PEMFC, multiple step perturbations are applied to the current of the air-cooled PEMFC while keeping the PWM constant, and the specific expression of the transfer function between current and temperature is identified. ; Obtain the time-domain expression of the PID controller: ,in, This is the proportionality coefficient. The integral coefficient is... These are the differential coefficients. To control the amount of action, The temperature error between a given temperature value and the actual temperature value; By performing a Laplace transform on the time-domain expression of the PID controller, the specific expression of the transfer function between the temperature error and the temperature control action is obtained. ,in, for Laplace transform, for The Laplace transform of .

4. The method according to claim 3, characterized in that, The transfer function between current and temperature error is: ； in, For the Laplace transform of the current; The specific expression for the transfer function between current and temperature error is: 。 5. The method according to claim 4, characterized in that, The specific expression of the transfer function between current and temperature error is simplified to a typical second-order oscillatory element, yielding the relationship between the transfer function and the typical second-order oscillatory element, including: By approximating the dominant pole of the specific expression of the transfer function between current and temperature error, the reduced-order transfer function is obtained. The reduced transfer function is simplified into a second-order typical oscillatory element, and the relationship between the transfer function and the second-order typical oscillatory element is obtained. The reduced transfer function is: ； The relationship between the transfer function and a typical second-order oscillatory element is as follows: ； in, These are real numbers much greater than 1, used to configure poles. The damping ratio of a typical second-order oscillating element. The frequency of the undamped oscillation of a typical second-order oscillation element is given.

6. The method according to claim 5, characterized in that, By performing an inverse Laplace transform on the expression for the second-order typical oscillatory element in the relation, the calculation formula for the time-domain performance index of the air-cooled PEMFC thermal management system is obtained, including: Approximating the expression of a typical second-order oscillatory element using the dominant poles, we obtain the approximate expression for the typical second-order oscillatory element as follows: ； Based on the approximate expression of a typical second-order oscillating element, we obtain The expression is: ； right Taking the inverse Laplace transform of the expression, we obtain the expression for the temperature error e(t): ； in, Indicates the inverse Laplace transform. Indicates time; Based on temperature error Solving the expression yields the calculation formula for the time-domain performance index of the air-cooled PEMFC thermal management system.

7. The method according to claim 6, characterized in that, Time-domain performance metrics include overshoot and settling time; based on temperature error Solving the expression yields the calculation formula for the time-domain performance index of the air-cooled PEMFC thermal management system, including: make first derivative The peak time of the response was obtained. t p : ； Peak response time t p Incorporating temperature error e ( t The expression for ) yields the peak error: ； Calculate the overshoot with steady-state temperature as the target temperature based on the error peak value. The calculation formula is: ； in, This is the steady-state temperature; Based on steady-state temperature and the preset error band Determine the adjustment time The calculation formula is: 。 8. The method according to claim 7, characterized in that, Based on preset time-domain performance index values, the calculation formulas for the time-domain performance indexes are solved to obtain the damping ratio and undamped oscillation frequency of a typical second-order oscillation element, including: Set a damping ratio within the interval [0, 1]. ε initial value ε 0; Will ε Substitute 0 and the preset overshoot into the overshoot value. The calculation formula yields the undamped oscillation frequency corresponding to... ; Will ε 0 and Substitute adjustment time The calculation formula is obtained. ; Will With preset adjustment time If a comparison is made, Then determine and That is, the values ​​of the damping ratio and undamped oscillation frequency of a typical second-order oscillation element; otherwise, the bisection method is used to reset them. ε 0 and recalculate until satisfied. , will satisfy Time corresponding ε 0 and The values ​​of damping ratio and undamped oscillation frequency for a typical second-order oscillation element are determined.

9. The method according to claim 7, characterized in that, The control parameters of the PID controller are obtained by solving the relationship between the transfer function and the typical second-order oscillating element based on the damping ratio and the undamped oscillation frequency, including: Balancing the coefficients in the denominator of the relationship between the transfer function and the typical second-order oscillatory element yields a system of three linear equations in three variables: ； Substituting the damping ratio and undamped oscillation frequency into a system of three linear equations, we obtain the control parameters of the PID controller. , and .

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