A method for temperature control of air-cooled PEMFC based on NSGAIII

Abstract

The application discloses a kind of air-cooled PEMFC temperature control method based on NSGAIII, it is related to fuel cell thermal management technical field, comprising the following steps: obtaining multiple adjustment parameters, overshoot, temperature identification error and temperature control error when RBF-PID controller controls thermal management system model;Establish single-objective optimization problem, solve single-objective optimization problem;Establish multi-objective optimization problem, solve multi-objective optimization problem by NSGAIII, obtain multiple optimal adjustment parameters;Multiple optimal adjustment parameters are input to RBF-PID controller, and the temperature of air-cooled PEMFC is controlled by RBF-PID controller with multiple optimal control parameters.The application can ensure that the obtained optimization result is in the Pareto frontier, realize the accurate control of the temperature of air-cooled PEMFC, while providing multiple optimal solutions for different design requirements, improve the solving efficiency.

Description

Technical Field

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

[0002] Proton exchange membrane fuel cells (PEMFCs) possess advantages such as low operating temperature, high power density, high energy conversion efficiency, and clean operation, making them considered the most promising clean energy conversion devices. Operating temperature is one of the most significant factors affecting the output performance of PEMFCs. Excessively high temperatures can cause membrane dehydration and even irreversible damage to the cell, while excessively low temperatures can reduce electrochemical reactions and even lead to flooding. Therefore, controlling the PEMFC at a suitable operating temperature is crucial for the efficient and stable operation of the PEMFC system.

[0003] Air-cooled PEMFCs are widely used in applications with low power requirements, such as drones and forklifts, due to their simple and compact structure. Currently, the most widely used method for temperature control in air-cooled PEMFCs is the classic PID (Proportional-Integral-Derivative) control. However, air-cooled PEMFC temperature control systems are highly nonlinear systems. Applying classic PID control can lead to problems such as low adjustment accuracy, slow settling time, and large overshoot. This is mainly due to the three parameters of the classic PID controller... , and Since the parameters are fixed and cannot be applied to the entire operating range of an air-cooled PEMFC temperature control system, researchers have developed many adaptive PID algorithms, such as the RBF-PID (Radial Basis Function-Proportional-Integral-Derivative) algorithm that combines neural networks.

[0004] When using the RBF-PID algorithm for temperature control, the controller parameters affect both the control and identification performance, requiring optimization of multiple objectives. Therefore, appropriate methods are needed to optimize these parameters to comprehensively improve the performance of the RBF-PID algorithm.

[0005] Currently, the Particle Swarm Optimization (PSO) algorithm is used to optimize the controller parameters of RBF-PID controllers. However, the PSO algorithm generally focuses on one-sided optimization, and its objective function is usually a single objective function. Even if it is constructed as the sum of multiple sub-objectives, it is still impossible to guarantee that the multiple sub-objectives are at the Pareto front. The controller parameters obtained are not optimal, and it is impossible to accurately control the temperature of air-cooled PEMFCs. At the same time, the single-objective optimization algorithm can only obtain one feasible solution per optimization. If the design requirements change, the weights of multiple sub-objectives need to be changed and optimization needs to be carried out again, resulting in low solution efficiency. Summary of the Invention

[0006] Based on the shortcomings of the existing technology, this invention provides a temperature control method for air-cooled PEMFCs based on NSGAIII, which solves the problems that the existing PSO algorithm cannot accurately control the temperature of air-cooled PEMFCs and has low solution efficiency.

[0007] The present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a temperature control method for an air-cooled PEMFC based on NSGAIII, comprising the following steps:

[0009] When the RBF-PID controller controls the thermal management system model of an air-cooled proton exchange membrane fuel cell (PEMFC), multiple adjustment parameters, temperature control error, overshoot, and temperature identification error are obtained. The temperature control error is integrated to obtain the first sub-objective; the overshoot is averaged to obtain the second sub-objective; and the temperature identification error is integrated to obtain the third sub-objective.

[0010] Using multiple adjustment parameters as decision variables, and minimizing the sum of the standardized first sub-objective, standardized second sub-objective, and standardized third sub-objective as the single optimization objective, a single-objective optimization problem is established. The single-objective optimization problem is solved to obtain the optimized adjustment parameters, the first optimization sub-objective, the second optimization sub-objective, and the third optimization sub-objective.

[0011] Using multiple optimization adjustment parameters as decision variables, a multi-optimization objective is constructed based on the first, second, and third optimization sub-objectives. A multi-objective optimization problem is established, and the multi-objective optimization problem is solved using NSGAIII to obtain multiple optimal adjustment parameters.

[0012] Multiple optimal adjustment parameters are input into the RBF-PID controller, which controls the temperature of the air-cooled PEMFC through multiple optimal control parameters.

[0013] Preferably, the acquisition of multiple adjustment parameters, temperature control error, overshoot, and temperature identification error when the RBF-PID controller controls the thermal management system model of the air-cooled proton exchange membrane fuel cell (PEMFC) specifically includes the following steps:

[0014] The control input of the thermal management system model at the previous time step, the actual temperature at the current time step, and the actual temperature at the previous time step are input into the RBF neural network.

[0015] A forward propagation is performed on the RBF neural network to obtain the temperature identification error; a performance index function of the RBF neural network is established based on the temperature identification error; the RBF neural network includes an input layer, a hidden layer, and an output layer;

[0016] Backpropagation of error is performed on the RBF neural network based on the performance index function to obtain the weights between each layer of the RBF neural network and the parameters of the hidden layer; during the backpropagation process, the first inertial weight, the second inertial weight, and the learning rate that control the weights between each layer of the RBF neural network and the parameters of the hidden layer are obtained.

[0017] Jacobian information of the thermal management system model is obtained through the RBF neural network after error backpropagation;

[0018] The temperature control error of the RBF-PID controller is obtained based on the given temperature and the actual temperature at the current moment; the performance index function of the RBF-PID controller is established based on the temperature control error;

[0019] Based on the performance index function, the proportional, integral, and derivative control parameters are adjusted online using Jacobi information; during the online adjustment, the adjustment rates of the proportional, integral, and derivative control parameters are obtained.

[0020] The proportional, integral, and derivative gains of the RBF-PID controller are controlled by adjusting the proportional, integral, and derivative control parameters online to obtain the control quantity at the current moment.

[0021] The temperature of the air-cooled PEMFC is controlled by the control quantity at the current moment.

[0022] Preferably, the backpropagation of error into the RBF neural network based on the performance index function specifically includes:

[0023] According to the gradient descent method, the algorithm for learning the weights from the hidden layer to the output layer is as follows:

[0024] ;

[0025] in,

[0026] ;

[0027] In the formula, As the first inertia weight, As the second inertial weight, for k Time of the first j The weights from the hidden layer to the output layer for k -1 moment j The weights from the hidden layer to the output layer for k -2 moments j The weights from the hidden layer to the output layer for k -3 o'clock j The weights from the hidden layer to the output layer For weight In the k The amount of change over time. For learning rate, This is the performance metric function for the RBF neural network.

[0028] Preferably, the online adjustment of the control parameters of the proportional, integral, and derivative functions using Jacobian information includes:

[0029] The gradient descent method is used to adjust the control parameters online.

[0030] ;

[0031] ;

[0032] ;

[0033] In the formula, for The proportional gain at time, for k Change in proportional gain at any given time For the performance index function of RBF-PID, The adjustment rate for the proportional gain. for k The change in integral gain at time step 1 for Integral gain at time step 1 The adjustment rate for the integral gain. for k The change in differential gain at time 1 for The differential gain at time step, This is the adjustment rate of the differential gain.

[0034] Preferably, the plurality of adjustment parameters include the learning rate, the first inertia weight, the second inertia weight, the adjustment rate of the proportional gain, the adjustment rate of the integral gain, and the adjustment rate of the derivative gain.

[0035] Preferably, the first sub-target, the second sub-target, and the third sub-target are as follows:

[0036] ;

[0037] ;

[0038] ;

[0039] In the formula, As the first sub-objective, t For time, Due to temperature control error, As the second sub-objective, n This represents the number of current step disturbances. This represents the temperature overshoot under each disturbance. As the third sub-objective, For the first in the continuous domain i Temperature identification error.

[0040] Preferably, the single optimization objective is to minimize the sum of the standardized first sub-objective, the standardized second sub-objective, and the standardized third sub-objective, wherein the standardized first sub-objective, the standardized second sub-objective, and the standardized third sub-objective are specifically as follows:

[0041] fit1 = ITAE / ITAE0;

[0042] fit2= / 0;

[0043] fit3 = IAIE / IAIE0;

[0044] In the formula, fit1 is the first standardized sub-objective, fit2 is the second standardized sub-objective, fit3 is the third standardized sub-objective, and ITAE0 = 10706.5951. 0=1.0358, IAIE0=0.87998.

[0045] Preferably, the single-objective optimization problem is solved using the PSO algorithm to obtain the first optimization sub-objective ITAE1 and the second optimization sub-objective. 1 and the third optimization sub-objective IAIE1.

[0046] Preferably, the multi-optimization objective is constructed based on the first optimization sub-objective, the second optimization sub-objective, and the third optimization sub-objective, and the specific multi-optimization objective is as follows:

[0047] fit4 = ITAE / ITAE1;

[0048] fit5= / 1;

[0049] fit6 = IAIE / IAIE1;

[0050] In the formula, fit4 is the fourth standardized sub-objective, fit5 is the fifth standardized sub-objective, and fit6 is the sixth standardized sub-objective.

[0051] Compared with the prior art, the above-mentioned at least one technical solution adopted by the present invention can achieve the following beneficial effects:

[0052] This invention first obtains multiple adjustment parameters, overshoot, temperature identification error, and temperature control error when the RBF-PID controller controls the thermal management system model. Multiple optimization objectives are then constructed using the overshoot, temperature identification error, and temperature control error. A single-objective optimization problem is then constructed and initially solved using the PSO algorithm. Finally, a multi-objective optimization problem is established and solved using the NSGAIII algorithm. The NSGAIII algorithm further optimizes the multi-objective problem based on the PSO optimization, improving the control and identification performance of the PSO-RBF-PID controller. This ensures that the obtained optimization results are at the Pareto front, achieving precise temperature control of the air-cooled PEMFC, while providing multiple optimal solutions for different design requirements, thus improving solution efficiency. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 This is a structural diagram of the PEMFC thermal management system for the air-cooled fuel cell of the present invention;

[0055] Figure 2 This is a schematic diagram of the NSGAIII-RBF-PID controller of the present invention;

[0056] Figure 3 This is an iterative curve diagram of PSO optimization according to the present invention;

[0057] Figure 4This is a flowchart of the controller program of the present invention;

[0058] Figure 5 This is a flowchart of the NSGAIII algorithm of the present invention;

[0059] Figure 6 To obtain the Pareto front solution for the NSGAIII algorithm of this invention;

[0060] Figure 7 This is a diagram of the current perturbation applied to the fuel cell in this invention;

[0061] Figure 8 This is a comparison chart of the temperature control effects of the present invention;

[0062] Figure 9 This is the RBF-PID temperature identification diagram of the present invention;

[0063] Figure 10 This is the temperature identification diagram of the PSO-RBF-PID of the present invention;

[0064] Figure 11 This is the temperature identification diagram of the NSGAIII-RBF-PID of the present invention;

[0065] Figure 12 This is a comparison chart of the temperature identification effects of the present invention;

[0066] Figure 13 This is a diagram showing the adaptive variation of the NSGAIII-RBF-PID control parameters of the present invention. Detailed Implementation

[0067] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] I. Explanatory and Illustrative Embodiments. To enable those skilled in the art to fully understand how the present invention is specifically implemented, this section provides an explanatory and illustrative description of the embodiments described in the claims.

[0069] This invention provides a method for temperature control of an air-cooled PEMFC based on the NSGAIII (Non-dominated Sorting Genetic Algorithm III) algorithm, which specifically includes the following steps:

[0070] S1: Based on the physical characteristics of the battery stack and auxiliary equipment in the air-cooled PEMFC system, a thermal management system model of the air-cooled PEMFC is built using the MATLAB / Simulink simulation platform.

[0071] This invention constructs a thermal management system model for an air-cooled PEMFC (Powered Internal Combustion Fuel Cell). Based on the physical characteristics of the battery stack and auxiliary equipment in the air-cooled PEMFC system, a thermal management system model for the air-cooled PEMFC is built using the MATLAB / Simulink simulation platform, which can reflect the dynamic changes in the battery stack temperature. Its specific structure is described in [reference needed]. Figure 1 As shown, it mainly includes a cooling fan model, a thermal management model, and a PEMFC battery stack model.

[0072] The PEMFC battery stack model uses a semi-empirical equation model to calculate the output voltage. Semi-empirical equation models are often used for simulation studies at the PEMFC system level due to their fast calculation speed and high accuracy. The specific PEMFC battery stack model is as follows:

[0073] (1);

[0074] In the formula, Represents the output voltage. Represents Nernst voltage. Represents activation loss, Represents ohmic loss, This represents concentration loss.

[0075] The specific formulas for each item are as follows:

[0076] (2);

[0077] (3);

[0078] (4);

[0079] (5);

[0080] (6);

[0081] (7);

[0082] (8);

[0083] In the formula, , , , , , , λ , band There are 9 coefficients, which can be calibrated through experimental data. For the reaction entropy, The number of electrons transferred in the reaction. It is Faraday's constant. Standard temperature The gas constant is For battery temperature, For hydrogen partial pressure, The partial pressure of oxygen. For water vapor partial pressure, Oxygen concentration, This is the operating current. For the total current, The area of ​​the reaction activation. For total internal resistance, For ohmic internal resistance, Resistivity This is the concentration loss coefficient. For the thickness of the exchange membrane, denoted as current density.

[0084] The thermal management model uses the energy conservation equation to calculate the temperature change rate of the PEMFC. The temperature change is related to the energy absorbed by the fuel cell, specifically the total energy released by the fuel cell minus the energy from electrical load output, coolant heat dissipation, and surface dissipation. The PEMFC temperature change rate is shown below:

[0085] (9);

[0086] 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. Represents the heat capacity of PEMFC. t For time.

[0087] The total input energy of a fuel cell is the total energy obtained from the combustion of hydrogen, while the amount of hydrogen consumed depends on the current and the number of cells. The calculation is as follows:

[0088] (10);

[0089] In the formula, This represents the amount of hydrogen consumed. F Represents Faraday's constant. The enthalpy of hydrogen combustion. This represents the number of individual cells.

[0090] The output electrical energy is the product of the battery stack voltage and current. The calculation is as follows:

[0091] (11);

[0092] In the formula, This represents the voltage of the battery stack.

[0093] Forced convection of air is defined as the heat carried away by the cooling air:

[0094] (12);

[0095] In the formula, The surface heat transfer coefficient, For ambient temperature, This represents the total area of ​​the cathode flow channel.

[0096] Natural convection and radiative heat transfer of air are defined as the surface heat dissipation of the battery stack:

[0097] (13);

[0098] In the formula, This is the equivalent thermal resistance.

[0099] S2: Design a temperature control strategy based on the air-cooled PEMFC thermal management model established in step S1 and use PID for temperature control.

[0100] The air-cooled PEMFC temperature control strategy is to adjust the fan... PWM By changing the airflow rate, the surface heat transfer coefficient of the cathode channel is altered, ultimately achieving precise control of the PEMFC battery stack temperature to a given value.

[0101] Assuming airflow velocity and duty cycle PWM If the relationship is linear, then the following expression can be obtained:

[0102] (14);

[0103] In the formula, V P represents air velocity. WM This represents the duty cycle, usually expressed as a percentage.

[0104] Since the convective heat transfer of air in the cathode channel is equivalent to the heat transfer in a laminar tube, the Zid-Tait formula is used to calculate the surface heat transfer coefficient:

[0105] (15);

[0106] In the formula, The Nucher number represents the cathode flow channel. Represents the Reynolds number, Representing Prandtl numbers, Represents feature size, Represents pipe diameter, Represents the dynamic viscosity of air. This represents the dynamic viscosity of the wall surface.

[0107] The qualitative temperature in equation (15) is the average fluid temperature, and the characteristic length is the pipe diameter. Its correlation formula has the following applicable range:

[0108] ;

[0109] .

[0110] With a PEMFC control temperature of 60℃ and a cathode air characterization temperature of 40℃, the following can be found from the air thermal property table:

[0111] ;

[0112] .

[0113] According to the Reynolds number calculation formula:

[0114] (16).

[0115] Appropriate PWM When the surface heat transfer coefficient is 100%, the corresponding Reynolds number is 752.97 < 2300, which satisfies the laminar flow condition. The Zid-Tait formula can be used to calculate the surface heat transfer coefficient.

[0116] PID controllers are the most widely used controllers in practical engineering, characterized by their simple structure, ease of implementation, and strong robustness. This invention first employs a PID controller to achieve temperature control in an air-cooled PEMFC. The PID controller will adjust the temperature control error accordingly. Calculate the control quantity using the following formula:

[0117] (17);

[0118] In the formula, To control the quantity, Due to temperature control error, , and These are proportional, integral, and derivative gains, respectively. By adjusting the parameters of the PID controller, the temperature of the PEMFC can be controlled to ensure that the battery stack temperature remains stable at a given value.

[0119] S3: The PID controller in S2 is optimized using an RBF neural network to obtain an RBF-PID temperature controller.

[0120] A Radial Basis Function (RBF) neural network is established to accurately identify the operating temperature of an air-cooled PEMFC, obtain the system's Jacobian information, and then pass this information to a self-tuning PID algorithm. The PID control parameters are adaptively updated using gradient descent. The RBF neural network consists of one input layer, one hidden layer, and one output layer.

[0121] The RBF neural network is configured with 3 nodes in the input layer, where the input data for the first input node is... Control of time The input data for the second input node is the actual temperature. The input data for the third input node is The actual temperature at that moment .

[0122] The hidden layer of the RBF neural network consists of 4 nodes, and its activation function is the Gaussian basis function. for:

[0123] (18);

[0124] In the formula, For the first j The center point of each basis function, and , n The number of input nodes, T For transpose, This is a freely selectable parameter that determines the width of the basis function around the center point. m This represents the number of hidden layer nodes. x This is the input to the RBF neural network.

[0125] The derivatives of the basis functions of the Gaussian function are:

[0126] (19);

[0127] (20);

[0128] In the formula, for k The input of the RBF neural network at time step, in this invention x ( k )=[ u ( k -1), y ( k ),y ( k -1)], for k Time of the first j The center points of the basis functions for k Time of the first j The nth basis function center point i Each component.

[0129] The output layer of the RBF neural network consists of one node, and its output is the temperature identified by the air-cooled PEMFC temperature control system. .

[0130] The output of the RBF neural network is:

[0131] (twenty one);

[0132] In the formula, for Time of the first j The weights from each hidden layer node to the output layer node.

[0133] The forward propagation process of the signal in an RBF neural network includes:

[0134] The output of the input layer nodes of the RBF neural network is:

[0135] (twenty two);

[0136] In the formula, and This is the input layer node.

[0137] The output of the hidden layer nodes in the RBF neural network is:

[0138] (twenty three).

[0139] The output of the output layer nodes of the RBF neural network is:

[0140] (twenty four);

[0141] The temperature identification error of the RBF neural network in the discrete domain is:

[0142] (25).

[0143] The performance metric function for the RBF neural network is:

[0144] (26).

[0145] The backpropagation process of the RBF neural network employs a delta learning algorithm to adjust the weights between each layer. Based on gradient descent, the learning algorithm for the weights from the hidden layer to the output layer is as follows:

[0146] (27);

[0147] In the formula, As the first inertia weight, As the second inertial weight, for k Time of the first j The weights from the hidden layer to the output layer for k -1 moment j The weights from the hidden layer to the output layer for k -2 moments j The weights from the hidden layer to the output layer for k -3 o'clock j The weights from the hidden layer to the output layer For weight In the k The amount of change over time.

[0148] From equations (25) and (26), we get:

[0149] (28).

[0150] Substituting equation (21) into the above equation, we get:

[0151] (29);

[0152] but The learning algorithm is as follows:

[0153] (30);

[0154] In the formula, This is the learning rate.

[0155] Similarly, the parameters of the hidden layer Hessick function and The learning algorithm is as follows:

[0156] (31);

[0157] (32).

[0158] From equations (21) and (28), we get:

[0159] (33).

[0160] Substituting equations (19) and (20) into equation (33), we get:

[0161] (34);

[0162] (35).

[0163] but and The learning algorithm is as follows:

[0164] (36);

[0165] (37).

[0166] In this invention, the RBF-PID controller adjusts based on RBF neural network identification. 、 and The performance index function of RBF-PID is defined as follows:

[0167] (38);

[0168] in, r ( k ( ) is a given temperature, y ( k (This refers to the actual temperature.) for k To address the temperature control error at any given time, the RBF-PID controller employs incremental PID, as shown below:

[0169] (39).

[0170] In order to reduce The self-tuning PID algorithm uses the gradient descent method to adjust the control parameters online.

[0171] (40);

[0172] (41);

[0173] (42);

[0174] in , and yes , and The adjustment rate.

[0175] Therefore, the control parameters of RBF-PID can be adjusted as follows:

[0176] (43);

[0177] (44);

[0178] (45).

[0179] From the above equations, it can be seen that the Jacobian information of the system needs to be calculated. However, this information cannot be obtained directly, but can be approximated as follows:

[0180] (46);

[0181] in, It is the output of RBF in equation (15). This can be obtained through an RBF neural network:

[0182] (47).

[0183] Therefore, accurate online identification ( Only by ensuring that the RBF neural network can provide accurate Jacobian information can this be guaranteed.

[0184] By using RBF neural network for accurate online temperature identification and adaptive adjustment of PID parameters, the temperature control effect of air-cooled PEMFC is improved, making it suitable for temperature control needs under different complex operating conditions.

[0185] S4: Use the PSO algorithm to perform single-objective optimization on the parameters of the RBF-PID controller in S3, and assign the optimized parameters to the RBF-PID.

[0186] Particle Swarm Optimization (PSO) is a swarm intelligence-based optimization algorithm that finds the optimal solution to a problem by simulating the movement and position adjustment of particles in a search space. Its basic principle is that in a multi-dimensional search space, the particle swarm iteratively updates the position and velocity of each particle to find the optimal solution. Each particle has a position and a velocity, and the particle's update is influenced by three factors: its own best position (the best position the particle has ever visited); the global best position (the best position among all particles in the swarm); and velocity adjustment (the particle's velocity is adjusted based on its historical experience and the behavior of other particles). The state of each particle consists of its position and velocity. The position represents the specific value of the solution, usually represented by a vector, and the velocity represents the particle's rate of change in the current dimension.

[0187] Specifically, the velocity update formula and position update formula of PSO are used to update the state of each particle.

[0188] First, the speed update formula:

[0189] (48);

[0190] in, particle a At any moment speed, It is a particle a At any moment t speed; It is the inertia coefficient, which controls the degree to which a particle's velocity is maintained; and It is the acceleration constant, the force that controls the particle's pull towards the individual and group optimal solutions; and It is a random number between [0,1]. It is the particle's optimal position; It is the best position globally. It is a particle a The position at time t.

[0191] Secondly, the position update formula:

[0192] (49);

[0193] in, It is the particle at time t +1 position, the updated position is the current position plus the speed.

[0194] The PSO algorithm consists of four main steps in its iterative process. First, it initializes the positions and velocities of a randomly generated swarm of particles. Then, it evaluates and calculates the fitness of each particle's current position. Subsequently, it updates each particle's own best position and global best position based on the fitness. Finally, before the termination condition is met, the swarm iterates according to the velocity and position update rules.

[0195] The PSO algorithm performs single-objective optimization of the parameters of the RBF-PID controller in S3 as follows: First, the particle swarm is initialized. In this invention, the particles represent the values ​​of six decision variables, and the six decision variables are the learning rate (…). ), first inertia weight ( ), second inertia weight ( ) and PID regulation ( , and The population size is set to 20, and the number of iterations is set to 100. Then, a single-objective fitness function is defined for optimization, consisting of three sub-objectives. The specific meanings of the three sub-objectives are as follows: Controlling the integral of time multiplied by absolute error (ITAE), i.e., the first sub-objective; controlling the average overshoot. The first is the second sub-objective. The second is the integral of absolute identification error (IAIE), which is the third sub-objective.

[0196] ;

[0197]

[0198] ;

[0199] In the formula, This represents temperature control error. This represents the temperature overshoot under each disturbance. This represents the temperature identification error in the continuous domain. The overshoot is obtained by calculating the ratio of the maximum instantaneous temperature deviation to the steady-state value under each current disturbance.

[0200] ITAE measures the controller's performance by integrating the absolute error of the air-cooled PEMFC temperature. A smaller ITAE indicates a smaller system error integral, resulting in better control performance. Average overshoot reflects the dynamic performance of the RBF-PID control process; a smaller overshoot indicates better dynamic performance. IAIE This measures the recognition performance of the RBF neural network; the smaller the value... IAIE This indicates that the more accurate the RBF neural network's identification, the better.

[0201] To avoid the influence of different orders of magnitude, the sub-objectives are standardized: fit1 = ITAE / ITAE0, fit2 = / 0, fit3 = IAIE / IAIE0, where ITAE0 = 10706.5951. 0 = 1.0358, IAIE0 = 0.87998, representing the results before optimization. The single-objective fitness function is fitness = fit1 + fit2 + fit3, where fit1 is the standardized first sub-objective, fit2 is the standardized second sub-objective, and fit3 is the standardized third sub-objective.

[0202] According to the update rules of the PSO algorithm, the position and velocity of particles are adjusted using inertia coefficients and acceleration constants. Each particle updates its velocity based on its own optimal position and the global optimal position, thereby searching towards a better combination of parameters, and continuously iterating and updating. Figure 3 The iterative curve of the PSO algorithm optimization is shown. After 100 iterations, the algorithm stops, and PSO converges in about 70 iterations. The global optimal position of the particle is the final optimization result. The optimized fitness function is fitness = 1.8995. The obtained PSO-RBF-PID can calculate three optimization sub-objectives: fit1 = 0.44071, fit2 = 0.67754, and fit3 = 0.78129.

[0203] S5: Use the NSGAⅢ algorithm to further optimize the parameters of the PSO-RBF-PID controller in S4 using multiple objectives, and assign the optimized parameters to the RBF-PID.

[0204] Appendix Figure 2 The present invention demonstrates the NSGAIII-RBF-PID controller structure proposed in this invention. First, a set of initial optimization parameters are obtained through PSO. Then, based on the PSO-RBF-PID obtained by NSGAIII in S4, further multi-objective optimization is performed to obtain the Pareto front solution. Finally, the optimized parameters are selected according to the design requirements and assigned to the RBF-PID controller.

[0205] The PSO algorithm outputs fit1=0.44071, fit2=0.67754, and fit3=0.78129. The goal of optimization is to reduce these three values.

[0206] This invention first uses PSO to optimize RBF-PID (6 decision variables) once, and then uses NSGAIII for two-stage optimization.

[0207] NSGAIII (Non-dominated sorting genetic algorithm III) is an evolutionary algorithm designed to solve multi-objective optimization problems, especially high-dimensional problems. Its operation is based on a genetic algorithm framework. By introducing the concept of reference points, it maintains a uniform distribution of solutions during the optimization process, thereby improving search efficiency and result diversity. NSGA-III achieves efficient solutions to multi-objective problems through population initialization, non-dominated sorting, reference point allocation, and selection operations.

[0208] The algorithm first randomly initializes a population. and the set of reference points in the target space The reference point represents the desired uniformly distributed solution in the target space, used to guide the diversity of the solution set. In each generation, the current population... Subpopulations are generated through selection, crossover, and mutation operations. The parent and offspring generations merge to form an intermediate population. = ∪ Subsequently Non-dominated sorting is performed, and the layers are divided into multiple frontier layers. , ,…,in This represents the Pareto front solution.

[0209] In order to build the next generation of population The algorithm selects solutions sequentially from the front layers until the population size reaches its upper limit. If a certain frontier layer If the addition of an individual would cause the population to exceed the limit, a reference point allocation mechanism is used to select the individuals to be retained. Specifically, each individual in the population is selected based on the Euclidean distance between its normalized target vector and the reference point. The allocation is performed using the following formula:

[0210] (35);

[0211] in It is an ideal point. It is the normalized distance from the target vector to the reference point. By selecting the individual closest to the reference point, the algorithm ensures a uniform distribution of solutions in the population, avoids excessive concentration of solutions on certain targets, and effectively improves the diversity of solutions.

[0212] NSGAIII is particularly well-suited for solving high-dimensional multi-objective optimization problems. It can avoid solution clustering when the objective dimension is high and provide rich and balanced Pareto front solutions, thereby meeting the diverse design needs in practical engineering.

[0213] Similar to PSO optimization, the decision variable for NSGAⅢ optimization is the learning rate ( ), first inertia weight ( ), second inertia weight ( ) and PID regulation ( , and The optimization objectives are: standardized fourth sub-objective fit4 (ITAE / ITAE1), and standardized fifth sub-objective fit5 (…). / 1) and the standardized sixth sub-target fit6 (IAIE / IAIE1), of which ITAE1, 1 and IAIE1 are the results obtained from running PSO-RBF-PID, which means that NSGAⅢ in S5 is a further optimization based on the results of PSO-RBF-PID in S4. The optimization results obtained in this way can reflect the advantages of multi-objective optimization algorithms over the currently popular single-objective optimization algorithms.

[0214] By effectively exploring and finding multiple Pareto front solutions in the solution space using the NSGAIII algorithm, the final NSGAIII-RBF-PID controller can ensure performance at the ITAE level. It reaches the Pareto frontier on the three objectives of IAIE, thus achieving better control and identification performance.

[0215] As attached Figure 4 As shown in the figure, this illustrates the application process of an RBF-PID control method based on the NSGAIII multi-objective optimization algorithm in the temperature control of an air-cooled PEMFC fuel cell. The core of the process is to first perform single-objective optimization on the parameters of the RBF-PID controller using the PSO algorithm to obtain a set of initial optimization parameters. The optimization objectives are ITAE (time multiplied by the integral of absolute error) and average overshoot (...). The sum of ITAE and IAIE (Integral of Identification Absolute Error). Then, the NSGAⅢ algorithm is used to further optimize PSO-RBF-PID using multiple objectives, selecting the same parameters as PSO, but with three optimization objectives: ITAE, ... And IAIE. Specifically, the PSO algorithm and NSGAIII algorithm apply the optimized parameters to the RBF-PID controller through fitness calculation, and continuously evaluate the fitness through feedback of control effect, search for better parameters, thus forming a closed-loop iterative optimization process.

[0216] In multi-objective optimization problems, the relationships between optimal solutions are usually non-dominated, and it is rare for one optimal solution to dominate all other feasible solutions. Therefore, the optimal solutions to an optimization problem are usually a set of solutions, often called the Pareto optimal solution set. This invention uses the NSGAIII algorithm to obtain the Pareto optimal solution set, and the specific process is shown in the attached figure. Figure 5 As shown.

[0217] During optimization, NSGAIII first sets the parameters, randomly initializes the population, and generates a uniformly distributed set of reference points in the target space to guide population diversity and compute the objective function. After selection, crossover, and mutation operations, the population generates offspring individuals. Parents and offspring are merged to form an intermediate population, which is then non-dominated and sorted into multiple front layers based on Pareto merit. The solutions in the Pareto front layers achieve a good balance in multi-objective optimization. To construct the next generation population, the algorithm selects individuals through a reference point allocation mechanism (based on reference point selection), calculates the distance between the normalized objective vector of each individual in the population and the reference points, and prioritizes the closest individuals to ensure a uniform distribution of solutions in the target space. This avoids excessive concentration of solutions on certain objectives and improves solution diversity and distribution quality.

[0218] The iterative optimization process of NSGAIII continues until the Pareto front solution set of the population stabilizes or the preset maximum number of iterations is reached. For example... Figure 6 As shown, the Pareto front output by NSGAIII provides multiple optimal solutions, from which different optimization schemes can be selected according to different design requirements. This invention selects the Pareto optimal solution where all three optimization objectives are less than 1. Since the optimization objectives have been standardized (fit1 = ITAE / ITAE1, fit2 = ...), ... / 1, fit3=IAIE / IAIE1), meaning that the corresponding NSGAⅢ-RBF-PID outperforms PSO-RBF-PID in all three targets.

[0219] S6: Compare the temperature control and identification effects of NSGAⅢ-RBF-PID and PSO-RBF-PID, and analyze the advantages of multi-objective optimization over single-objective optimization.

[0220] In S5, among all the Pareto front solutions obtained by NSGAIII, the optimal solution where each objective is less than the initial value was selected and substituted into the RBF-PID temperature controller. The operating performance was compared with that of the PSO-RBF-PID obtained in S4. The experimental results are shown in the specific implementation method. One major reason why NSGAIII-RBF-PID is superior to PSO-RBF-PID is that NSGAIII is a multi-objective optimization algorithm, which can guarantee that the obtained optimal solution is located at the Pareto front. PSO is a single-objective optimization algorithm, which, although taking the sum of three objectives as the fitness function, cannot guarantee that the three sub-objectives are located at the Pareto front.

[0221] Meanwhile, NSGAⅢ can obtain multiple Pareto front solutions in one run, providing a large number of optimization options for different design requirements, while PSO can only obtain one set of solutions in one run, with limited choices.

[0222] The six decision values ​​before optimization are: 0.25, 0.05, 0.01, 100000, 10, 10000.

[0223] The values ​​of the six decision variables after PSO optimization are: 0.410009415071648, 0.192497876357553, 0.0259715677144086, 199752.045841515, 61.8291225741132, and 79581.8319029502.

[0224] The values ​​of the six decision variables after NSGAⅢ optimization are: 0.4100100000000000, 209121868376257, 0.0259720000000000, 359228.714940697, 57.0156253742567, and 86551.7857141860.

[0225] As attached Figure 7 As shown, this experiment uses a step-type input current disturbance design to simulate the operation of an air-cooled PEMFC system under different operating conditions.

[0226] As attached Figure 8 As shown in the graph, the curves clearly demonstrate that the RBF-PID control performance is significantly better than that of the traditional PID control, thanks to its control parameters. , and Adaptive to changes in system state. After single-objective optimization using PSO, the temperature control performance of RBF-PID is improved. Based on PSO-RBF-PID, NSGAⅢ further optimizes the result, achieving faster settling time and smaller overshoot, thus achieving the best temperature control performance among the four.

[0227] As attached Figures 9-11 As shown, RBF-PID, PSO-RBF-PID, and NSGAIII-RBF-PID can all accurately identify the actual temperature, with maximum relative errors not exceeding 0.06%, 0.05%, and 0.05%, respectively, thus ensuring the accuracy of the system's Jacobian information.

[0228] As attached Figure 12As shown, the experiment compared the temperature identification performance of three controllers: RBF-PID, PSO-RBF-PID, and NSGAIII-RBF-PID. It can be seen that the NSGAIII-RBF-PID controller is more accurate in temperature identification, especially in the initial period after each current disturbance is applied. Its relative identification error is significantly smaller than that of the unoptimized RBF-PID controller and slightly smaller than that of the PSO-RBF-PID controller. It can be concluded that the NSGAIII-RBF-PID achieves the best temperature identification performance among the three and can provide more accurate system Jacobian information. This provides a self-calibrating PID algorithm.

[0229] Appendix Figure 13 The control parameters of NSGAⅢ-RBF-PID are shown. , and The changes in the parameters show that the PID control parameters achieve adaptive changes, especially during the initial period after each current disturbance is applied. This adaptive change in PID parameters allows the air-cooled PEMFC system to adapt to different operating conditions, thereby improving control performance.

[0230] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0231] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for temperature control of air-cooled PEMFC based on NSGAIII, characterized in that, The method comprises the following steps: obtain multiple adjustment parameters, temperature control errors, overshoots and temperature identification errors when an RBF-PID controller controls a thermal management system model of an air-cooled proton exchange membrane fuel cell (PEMFC); integrate the temperature control errors to obtain a first sub-target; average the overshoots to obtain a second sub-target; integrate the temperature identification errors to obtain a third sub-target; take the multiple adjustment parameters as decision variables, take minimization of a sum of the standardized first sub-target, the standardized second sub-target and the standardized third sub-target as a single optimization objective, establish a single-objective optimization problem, solve the single-objective optimization problem to obtain optimized adjustment parameters, a first optimized sub-target, a second optimized sub-target and a third optimized sub-target; take the multiple optimized adjustment parameters as decision variables, construct multiple optimization objectives based on the first optimized sub-target, the second optimized sub-target and the third optimized sub-target, establish a multi-objective optimization problem, and solve the multi-objective optimization problem by NSGAIII to obtain multiple optimal adjustment parameters; input the multiple optimal adjustment parameters into the RBF-PID controller, and control the temperature of the air-cooled PEMFC by the RBF-PID controller with the multiple optimal control parameters; The method for obtaining the multiple adjustment parameters, the temperature control errors, the overshoots and the temperature identification errors when the RBF-PID controller controls the thermal management system model of the air-cooled PEMFC comprises the following steps: input a control variable of the thermal management system model at a previous time, an actual temperature at a current time and the actual temperature at the previous time into an RBF neural network; perform forward propagation on the RBF neural network to obtain the temperature identification error; and establish a performance index function of the RBF neural network based on the temperature identification error; the RBF neural network comprises an input layer, a hidden layer and an output layer; perform error back propagation on the RBF neural network based on the performance index function to obtain weights between layers of the RBF neural network and parameters of the hidden layer; in the error back propagation process, first and second inertia weights and a learning rate for controlling the weights between the layers of the RBF neural network and the parameters of the hidden layer are obtained; obtain Jacobian information of the thermal management system model by the RBF neural network after the error back propagation; obtain a temperature control error of the RBF-PID controller based on a given temperature and the actual temperature at the current time; and establish a performance index function of the RBF-PID controller based on the temperature control error; based on the performance index function, adjust online control parameters of proportion, integration and differentiation by the Jacobian information; in the online adjustment, adjustment rates of the proportion, the integration and the differentiation for controlling the control parameters of the proportion, the integration and the differentiation are obtained; control the proportion, the integration and the differentiation gains of the RBF-PID controller by the control parameters of the proportion, the integration and the differentiation after the online adjustment to obtain a control variable at the current time; control the temperature of the air-cooled PEMFC by the control variable at the current time; The error back propagation on the RBF neural network based on the performance index function comprises: According to the gradient descent method, the learning algorithm of the weight from the hidden layer to the output layer is as follows: ； Wherein, ； In the formula, As the first inertia weight, As the second inertial weight, for k Time of the first j The weights from the hidden layer to the output layer for k -1 moment j The weights from the hidden layer to the output layer for k -2 moments j The weights from the hidden layer to the output layer for k -3 o'clock j The weights from the hidden layer to the output layer For weight In the k The amount of change over time. For learning rate, This is the performance metric function for the RBF neural network; The online adjustment of the control parameters of the proportion, integral and differential by the Jacobian information comprises: The control parameters are adjusted online by using the gradient descent method: ； ； ； In the formula, is the proportional gain at the moment, is k the proportional gain change amount at the moment, is the performance index function of the RBF-PID, is the adjustment rate of the proportional gain, is k the integral gain change amount at the moment, is the integral gain at the moment, is the adjustment rate of the integral gain, is k the differential gain change amount at the moment, is the differential gain at the moment, is the adjustment rate of the differential gain.

2. The NSGA III based temperature control method of air-cooled PEMFC of claim 1, wherein, The plurality of adjustment parameters comprise a learning rate, a first inertia weight, a second inertia weight, an adjustment rate of a proportional gain, an adjustment rate of an integral gain and an adjustment rate of a differential gain.

3. The NSGA III based temperature control method of air-cooled PEMFC of claim 1, wherein, The first sub-target, the second sub-target and the third sub-target are specifically as follows: ； ； ； wherein, is a first sub-target, t is time, is a temperature control error, is a second sub-target, n is a number of current step disturbances, is a temperature overshoot for each disturbance, is a third sub-target, is a first temperature identification error in a continuous domain, i is a second temperature identification error in a continuous domain.

4. The NSGA III based temperature control method of air-cooled PEMFC of claim 3, wherein, The sum of the normalized first sub-target, the normalized second sub-target and the normalized third sub-target is minimized as a single optimization target, wherein the normalized first sub-target, the normalized second sub-target and the normalized third sub-target are specifically as follows: fit1=ITAE / ITAE0; fit2= / 0; fit3=IAIE / IAIE0; In the formula, fit1 is the normalized first sub-target, fit2 is the normalized second sub-target, fit3 is the normalized third sub-target, ITAE0=10706.5951, 0=1.0358, IAIE0=0.87998.

5. The NSGA III based temperature control method of air-cooled PEMFC as claimed in claim 4, wherein, The single-target optimization problem is solved by the PSO algorithm to obtain a first optimization sub-target ITAE1, a second optimization sub-target 1 and a third optimization sub-target IAIE1.

6. The NSGA III based temperature control method of a air-cooled PEMFC of claim 5, wherein, The multi-optimization target is constructed based on the first optimization sub-target, the second optimization sub-target and the third optimization sub-target, and the multi-optimization target is specifically as follows: fit4=ITAE / ITAE1; fit5 = 1 1;​ fit6=IAIE / IAIE1; In the formula, fit4 is a normalized fourth sub-target, fit5 is a normalized fifth sub-target, and fit6 is a normalized sixth sub-target.

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