Design Method of Data-Driven Iterative Learning Controller for Fuel Cell Thermal Management System

Abstract

A design method of a data-driven iterative learning controller for a fuel cell thermal management system, belonging to the field of on-vehicle fuel cell engine control technology. The purpose of the present invention is to use a data-driven iterative learning control scheme to design a stack temperature decoupling controller, which can avoid modeling the complex thermal management system and is an easy-to-implement-in-engineering design method of a data-driven iterative learning controller for a fuel cell thermal management system. The steps of the present invention include: a fuel cell thermal management system model, an iterative-domain dynamic linearization data model, an iterative-domain extended state observer, and a model-free adaptive iterative learning controller. The control scheme proposed by the present invention can avoid modeling the complex thermal management system and is easy to implement in engineering. The simulation results show the effectiveness of the designed controller.

Description

Technical Field

[0001] The present invention belongs to the technical field of on-vehicle fuel cell engine control. Background Art

[0002] Global energy shortage and environmental pollution have made the traditional automotive energy forms unable to meet people's needs. Therefore, it is urgent to transform the automotive energy form. Due to the many advantages of proton exchange membrane fuel cell (PEMFC), such as pollution-free, high efficiency, long endurance, and hydrogen being a renewable energy source, it is considered the ultimate energy form for automobiles.

[0003] During the electrochemical reaction process of PEMFC, a part of heat energy will be released, which needs to be released from the fuel cell system, otherwise a temperature runaway phenomenon will occur. For a water-cooled PEMFC system, the temperature of the coolant is the most important control parameter, which will affect gas transfer, water balance, electrochemical reaction activity, and the output performance of the fuel cell. A higher stack temperature is beneficial to the catalyst activity, thus obtaining better output performance, but it will make it difficult to maintain the water balance. Therefore, an effective thermal management system is crucial for obtaining better output performance and extending the life of the fuel cell. The temperature of the stack can be maintained by controlling the outlet temperature and inlet temperature of the cooling water of the stack (generally controlled at a constant value).

[0004] Figure 1 is the structural block diagram of the thermal management system for PEMFC. The main purpose is to make the outlet temperature (T cl ) of the cooling water and the inlet temperature (T air ) of the cooling water track their expected values by controlling the cooling water flow rate (W st,out ) of the circulating water pump and the air flow rate (W st,in ) of the radiator, so as to achieve the purpose of controlling the stack temperature. Due to dynamic load changes and some uncertain information, T st,out and T st,in will deviate from the expected values. Therefore, the PEMFC thermal management system is a multi-input multi-output coupled nonlinear system. For the control of the thermal management system, there are mainly the following problems:

[0005] 1. The thermal management system of PEMFC is a complex system with multi-input multi-output, strong nonlinearity and strong coupling, and uncertain information such as internal and external disturbances, making it difficult to establish its accurate mechanism model. Therefore, model-based control schemes are difficult to apply.

[0006] 2. The two control outputs of the thermal management system of PEMFC, namely the outlet temperature of the stack cooling water and the inlet temperature of the cooling water, affect each other and have strong coupling, which will deteriorate the tracking performance of the system output and pose challenges to the controller design. Summary of the Invention

[0007] The object of the present invention is to design a stack temperature decoupling controller by using a data-driven iterative learning control scheme, which is a data-driven iterative learning controller design method for a fuel cell thermal management system that can avoid modeling a complex thermal management system and is easy to implement in engineering.

[0008] The steps of the present invention are as follows:

[0009] S1. Iterative domain dynamic linearization data model

[0010] The thermal management system of PEMFC is described as the following general nonlinear system:

[0011] Y(i,k + 1) = F(Y(i,k),…,Y(i,k - n y ),U(i,k),…,U(i,k - n u )) (1)

[0012] Wherein, is a time series, K is the iteration length; is the number of iterations, i max is the maximum number of drops; n y and n u represent unknown positive integers;

[0013] Y(i,k) = [y1(i,k),y2(i,k)] = [T st,out (i,k),T st,in (i,k)] is the output vector at the k-th moment in the i-th iteration,

[0014] y1(i,k) = T st,out (i,k) is the outlet temperature of the coolant of the stack, y2(i,k) = T st,in (i,k) is the inlet temperature of the coolant;

[0015] U(i,k) = [u1(i,k),u2(i,k)] = [W cl (i,k),W air (i,k)] is the input vector at the k-th moment in the i-th iteration,

[0016] u1(i,k) = W cl (i,k) is the coolant flow rate of the circulating water pump, u2(i,k) = W air (i,k) is the air flow rate of the radiator; F(·) represents a generalized nonlinear function;

[0017] The model (1) is transformed into the following iterative domain dynamic linearization data model:

[0018] ΔY(i,k + 1) = Φ(i,k)ΔU(i,k) (2)

[0019] where ΔY(i,k) = Y(i,k) - Y(i - 1,k), ΔU(i,k) = U(i,k) - U(i - 1,k); Φ(i,k) is the pseudo-Jacobian matrix, and its definition is as follows:

[0020]

[0021] where φ 11 , φ 12 , φ 21 and φ 22 are all elements in the pseudo-Jacobian matrix;

[0022] The pseudo-Jacobian matrix is estimated using the following estimation algorithm. Define the performance index function as:

[0023]

[0024] where μ is the penalty function. Let Then the following estimation algorithm is obtained:

[0025]

[0026] where,[[]] is the estimated value of Φ(i,k); μ is the step size factor;

[0027] Then the iterative domain dynamic linearization data model is converted into the following:

[0028]

[0029] S2. Iterative Domain Extended State Observer

[0030] The dynamic linearization data model (6) is converted into the following form:

[0031]

[0032] where, is a diagonal matrix, and are the estimated values of φ 11 (i,k) and φ 22 (i,k) respectively; D(i,k) = [d1(i,k), d2(i,k)] T is the coupling term vector, d1(i,k) is the coupling term of y1(i,k), and d2(i,k) is the coupling term of y2(i,k);

[0033] Then the decoupling model is as follows:

[0034]

[0035] The design of the iterative domain extended state observer is used to estimate and compensate the coupling term D(i,k), and the iterative domain extended state observer is designed as follows:

[0036]

[0037] where, is the estimated value of Y(i,k); is the estimated value of D(i,k), is the estimated value of d1(i,k), is the estimated value of d2(i,k); L1 and L2 are observer gains;

[0038] The decoupled dynamic linearized data model is:

[0039]

[0040] S3. Model-free adaptive iterative learning controller

[0041] The decoupled dynamic data model (9) is rewritten as:

[0042]

[0043] Consider the following control input criterion function:

[0044]

[0045] According to the optimization condition The control input is obtained as:

[0046]

[0047] where, j = 1, 2 is the expected value of the jth output, that is, is the expected value of the coolant outlet temperature T st,out of the fuel cell stack, is the expected value of the coolant inlet temperature T st,in of the fuel cell stack; λ is the weight factor; ρ is the step size factor.

[0048] The beneficial effects of the present invention are:

[0049] 1. Aiming at the problem of difficult to obtain accurate PEMFC thermal management system, the present invention proposes a pure data-driven iterative learning control scheme;

[0050] 2. Based on the dynamic linearization technology, the present invention establishes an iterative domain dynamic linearized data model only using the input and output data of the thermal management system, without using any model information of the thermal management system;

[0051] 3. In view of the strong coupling between the two outputs of the thermal management system, the present invention uses an iterative domain expansion state observer to decouple the outputs, further improving the control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a structural block diagram of a proton exchange membrane fuel cell thermal management system (structural block diagram of the thermal management system of PEMFC);

[0053] Figure 2 is a graph of the change in stack current, which is a series of random step curves, with the unit of A;

[0054] Figure 3 is a tracking curve of the stack coolant outlet temperature at the 70th iteration. The solid line is the desired stack coolant outlet temperature curve, and the dashed line is the actual system's stack coolant outlet temperature curve, with the unit of °C;

[0055] Figure 4 is a tracking curve of the stack coolant inlet temperature at the 70th iteration. The solid line is the desired stack coolant inlet temperature curve, and the dashed line is the actual system's stack coolant inlet temperature curve, with the unit of °C;

[0056] Figure 5 is the convergence performance of the stack coolant outlet temperature in the iterative domain;

[0057] Figure 6 is the convergence performance of the stack coolant inlet temperature in the iterative domain. DETAILED DESCRIPTION OF THE INVENTION

[0058] The present invention mainly focuses on the problem of stack temperature control in an on-vehicle fuel cell thermal management system, and uses a data-driven iterative learning control scheme to design a stack temperature decoupling controller. First, in view of the problem that it is difficult to establish an accurate mathematical model for the thermal management system, dynamic linearization technology is adopted in the iterative domain to obtain a dynamic linearization data model equivalent to the original system. This data model can be obtained only by using the input and output data of the system, without using any information of the system model, and belongs to a pure data-driven scheme. Then, based on this data model and using an iterative domain expansion state observer, the decoupling between the system outputs is realized. Finally, a model-free adaptive iterative learning controller is designed based on the decoupled data model to achieve precise control of the stack coolant outlet temperature and the stack coolant inlet temperature. The control scheme proposed by the present invention can avoid modeling a complex thermal management system and is easy to implement in engineering. The simulation results show the effectiveness of the designed controller. The present invention can well solve two problems existing in the prior art.

[0059] The present invention may structurally include the following parts: a fuel cell thermal management system model, an iterative domain dynamic linearization data model, an iterative domain extended state observer, and a model-free adaptive iterative learning controller.

[0060] The main function of the fuel cell thermal management system model is to simulate the real thermal management system, that is, to accurately describe the functions of the real fuel cell thermal management system to verify the effectiveness of the designed controller; the iterative domain dynamic linearization data model uses dynamic linearization technology to obtain a model equivalent to the original thermal management system, and this model is the basis for the subsequent design of the iterative domain extended state observer; the iterative domain extended state observer is used to achieve the decoupling between the outputs of the iterative domain dynamic linearization data model, and the decoupled iterative domain dynamic linearization data model is the basis for the subsequent design of the model-free adaptive iterative learning controller; the model-free adaptive iterative learning controller generates control signals for different operating conditions of the fuel cell - the cooling water flow rate of the circulation pump and the air flow rate of the radiator, and sends the control signals to the actuators of the fuel cell thermal management system - the circulation pump and the radiator, so that the cooling water outlet temperature and the cooling water inlet temperature of the fuel cell stack in the thermal management system track the expected values.

[0061] The implementation method of the present invention includes the following parts:

[0062] The design of the data-driven iterative learning controller for the fuel cell thermal management system described in the present invention is realized through a software system. The software system consists of Matlab / Simulink advanced simulation software. MATLAB / Simulink software is used to build the dynamic model of the fuel cell thermal management system and the controller, and provides a simulation experiment environment.

[0063] First, build a fuel cell thermal management system model in MATLAB / Simulink software. The cooling water outlet temperature and the cooling water inlet temperature of the fuel cell stack in the fuel cell thermal management system can be directly obtained from the built fuel cell thermal management system model.

[0064] Then, take the above-built fuel cell thermal management system model as the controlled object. Based on dynamic linearization technology, only use the input data (the cooling water flow rate of the circulation pump and the air flow rate of the radiator) and output data (the cooling water outlet temperature and the cooling water inlet temperature of the fuel cell stack) in the fuel cell thermal management system model to obtain the iterative domain dynamic linearization data model.

[0065] Based on the obtained iterative domain dynamic linearization data model above, use the iterative domain extended state observer to achieve the decoupling between system outputs.

[0066] Finally, a model-free adaptive iterative learning controller is designed based on the above decoupled dynamic linearization data model. Since there are two control signals in the present invention, two model-free adaptive iterative learning controllers are designed accordingly to generate these two control signals, namely the cooling water flow rate of the circulating water pump and the air flow rate of the radiator. The entire control system is built in the MATLAB / Simulink environment according to the working principle of the fuel cell thermal management system. The actual stack cooling water outlet temperature and the cooling water inlet temperature of the fuel cell thermal management system are directly obtained from the fuel cell thermal management system model, and compared with the desired stack cooling water outlet temperature and the cooling water inlet temperature (70 °C and 65 °C) to obtain the error amount. The control signals, i.e., the cooling water flow rate of the circulating water pump and the air flow rate of the radiator, are generated by the model-free adaptive iterative learning controller and sent to the actuators of the fuel cell thermal management system, namely the circulating water pump and the radiator, so that the cooling water outlet temperature and the cooling water inlet temperature of the stack in the thermal management system track the desired values.

[0067] The present invention will be described in detail below with reference to the accompanying drawings:

[0068] The measurable disturbance quantity in the present invention is I st , the load current, which is used to simulate the dynamic load change. The fuel cell thermal management system is built in Simulink and serves as the controlled object of the present invention. The control objective of the present invention is that the controller controls the coolant flow rate W cl of the circulating water pump and the air flow rate W air of the radiator according to the state of the fuel cell thermal management system, so that the T st,out of the stack in the fuel cell thermal management system, the cooling water outlet temperature and the T st,in , the cooling water inlet temperature track the desired values and

[0069] The present invention provides a set of devices based on the above operating principles and processes. The building and operation processes are as follows:

[0070] 1. Software selection

[0071] The simulation models of the controlled object and the controller of the control system are built through the software Matlab / Simulink. The software version is Matlab R2022a, and the solver is selected as ode3. The simulation step size is a fixed step size, and the step size is selected as 0.004 s.

[0072] 2. Iterative domain dynamic linearization data model

[0073] The thermal management system of PEMFC can be described as the following general nonlinear system:

[0074] Y(i,k + 1)=F(Y(i,k),…,Y(i,k - n y ),U(i,k),…,U(i,k - n u )) (1)

[0075] where is a time series; K is the iteration length; is the number of iterations; i max is the maximum number of drops; n y is an unknown positive integer; n u is an unknown positive integer; Y(i,k)=[y1(i,k),y2(i,k)]=[T st,out (i,k),T st,in (i,k)] is the output vector at time k in the i-th iteration; y1(i,k)=T st,out (i,k) is the outlet temperature of the cooling water of the stack; y2(i,k)=T st,in (i,k) is the inlet temperature of the cooling water; U(i,k)=[u1(i,k),u2(i,k)]=[W cl (i,k),W air (i,k)] is the input vector at time k in the i-th iteration; u1(i,k)=W cl (i,k) is the cooling water flow rate of the circulating pump; u2(i,k)=W air (i,k) is the air flow rate of the radiator; F(·) represents a general generalized nonlinear function.

[0076] For model (1), it can be transformed into the following iterative domain dynamic linearization data model:

[0077] ΔY(i,k + 1)=Φ(i,k)ΔU(i,k) (2)

[0078] where ΔY(i,k)=Y(i,k)-Y(i - 1,k); Y(i - 1,k) is the output vector at time k in the (i - 1)-th iteration ΔU(i,k)=U(i,k)-U(i - 1,k); U(i - 1,k) is the input vector at time k in the (i - 1)-th iteration; Φ(i,k) is the pseudo-Jacobian matrix, and its definition is as follows:

[0079]

[0080] where φ 11 , φ 12 , φ 21 and φ 22 are all elements in the pseudo-Jacobian matrix.

[0081] The pseudo-Jacobian matrix is estimated using the following estimation algorithm. Define the performance index function as:

[0082]

[0083] Among them, μ is the penalty function.

[0084] Let Then the following estimation algorithm can be obtained:

[0085]

[0086] Among them, is the estimated value of Φ(i,k); μ is the step factor.

[0087] Then the iterative domain dynamic linearization data model can be converted into the following:

[0088]

[0089] 2. Iterative Domain Extended State Observer

[0090] The dynamic linearization data model (6) can be converted into the following form:

[0091]

[0092] Among them, is a diagonal matrix; and are the estimated values of φ 11 (i,k) and φ 22 (i,k) respectively; D(i,k) = [d1(i,k), d2(i,k)] T is the coupling term vector; d1(i,k) is the coupling term of y1(i,k), and d2(i,k) is the coupling term of y2(i,k).

[0093] Then the decoupling model is as follows:

[0094]

[0095] Next, design an iterative domain extended state observer to estimate and compensate for the coupling term D(i,k). The iterative domain extended state observer is designed as follows:

[0096]

[0097] Among them, is the estimated value of Y(i,k); is the estimated value of D(i,k); is the estimated value of d1(i,k); is the estimated value of d2(i,k); L1 and L2 are the observer gains.

[0098] The further decoupled dynamic linearized data model is as follows:

[0099]

[0100] 3. Model-free Adaptive Iterative Learning Controller

[0101] Based on the decoupled dynamic linearized data model (9), a model-free adaptive iterative learning controller is designed in this part. The decoupled dynamic data model (9) can be rewritten as:

[0102]

[0103] Consider the following control input criterion function:

[0104]

[0105] According to the optimization condition The control input can be obtained as:

[0106]

[0107] where j = 1, 2 is the expected value of the j-th output; that is, is the expected value of the coolant temperature T st,out at the outlet of the fuel cell stack; is the expected value of the coolant temperature T st,in at the inlet of the fuel cell stack; λ is the weight factor; ρ is the step factor.

[0108] Experimental Verification and Analysis

[0109] To verify the effectiveness of the data-driven iterative learning control scheme proposed in the present invention for the stack temperature control of the proton exchange membrane fuel cell thermal management system, a series of random step conditions of the stack current are considered to simulate dynamic load changes, as Figure 2 shown. The time for each iteration is 480 s, and the simulation is carried out for 70 iterations in total. Figure 3 is the tracking curve of the coolant temperature at the outlet of the fuel cell stack at the 70th iteration, where the solid line is the expected value and the dashed line is the actual value. It can be seen that the coolant temperature at the outlet of the fuel cell stack can accurately track the expected value, and the maximum tracking error is 0.28 °C, meeting the actual engineering requirements. Figure 4 is the tracking curve of the coolant temperature at the inlet of the fuel cell stack at the 70th iteration, where the solid line is the expected value and the dashed line is the actual value. Similarly, the coolant temperature at the inlet of the fuel cell stack can track the expected value with high precision. Therefore, from Figure 3 and Figure 4From the tracking effect, the proposed data-driven iterative learning control scheme has good control performance. The mean absolute error (MAE) index is used to further measure the convergence performance of the designed iterative learning controller along the iteration axis. The mean absolute error index of the stack coolant outlet temperature is defined as MAE1, Figure 5 which is its convergence performance on the iteration axis. It can be seen that the stack coolant outlet temperature has a fast convergence speed in the iteration direction, and the MAE1 of the last iteration is 0.03 °C. The mean absolute error index of the stack coolant inlet temperature is defined as MAE2, Figure 6 which is its convergence performance on the iteration axis. It can be seen that the stack coolant inlet temperature also has a fast convergence speed on the iteration axis, and the MAE2 of the last iteration is 0.0048 °C. Therefore, Figure 5 and Figure 6 further verifies the effectiveness of the proposed data-driven iterative learning controller.

Claims

1. A design method of a data-driven iterative learning controller for a fuel cell thermal management system, characterized in that: The steps are as follows: S1. Iterative domain dynamic linearization data model The thermal management system of PEMFC is described as the following general nonlinear system: Y(i,k + 1)=F(Y(i,k),…,Y(i,k - n y ),U(i,k),…,U(i,k - n u )) (1) Among them, \(k\in\{0,1,\ldots,K\}\) is the time series, and \(K\) is the iteration length; \(i\in\{0,1,\ldots,i max}\) is the iteration number, \(i max \) is the maximum number of falling generations; \(n y \) and \(n u \) represent unknown positive integers; Y(i,k) = [y1(i,k), y2(i,k)] = [T st,out (i,k), T st,in (i,k)] is the output vector at the k-th moment in the i-th iteration, y1(i,k) = T st,out (i,k) is the coolant outlet temperature of the stack, y2(i,k) = T st, i n (i,k) is the coolant inlet temperature; U(i,k) = [u1(i,k), u2(i,k)] = [W cl (i,k), W air (i,k)] is the input vector at the k-th moment in the i-th iteration, u1(i,k) = W cl (i,k) is the cooling water flow rate of the circulating water pump, u2(i,k) = W air (i,k) is the air flow rate of the radiator; F(·) represents a generalized non - linear function; The model (1) is transformed into the following iterative domain dynamic linearization data model: ΔY(i,k + 1) = Φ(i,k)ΔU(i,k) (2) where ΔY(i,k) = Y(i,k) - Y(i - 1,k), ΔU(i,k) = U(i,k) - U(i - 1,k); Φ(i,k) is the pseudo-Jacobian matrix, and its definition is as follows: Among them, φ 11 , φ 12 , φ 21 and φ 22 are all elements in the pseudo-Jacobi matrix; The pseudo-Jacobian matrix is estimated by the following estimation algorithm, and the performance index function is defined as: where μ is the penalty function, and let Then the following estimation algorithm is obtained: Among them, is the estimated value of Φ(i,k); η is the step size factor; Then the iterative domain dynamic linearization data model is converted into the following: S2. Iterative domain extended state observer The dynamic linearization data model (6) is converted into the following form: Among them, is a diagonal matrix, and are the estimated values of φ 11 (i, k) and φ 22 (i, k) respectively; D(i, k) = [d1(i, k), d2(i, k)] T is the coupling term vector, d1(i, k) is the coupling term of y1(i, k), and d2(i, k) is the coupling term of y2(i, k); Then the decoupled model is as follows: Design an iterative domain extended state observer to realize the estimation and compensation of the coupling term D(i,k). The iterative domain extended state observer is designed as follows: wherein, is the estimated value of Y(i,k); is the estimated value of D(i,k), is the estimated value of d1(i,k), is the estimated value of d2(i,k); L1 and L2 are observer gains; The decoupled dynamic linearization data model is: S3. Model-free adaptive iterative learning controller The decoupled dynamic data model (10) is rewritten as: Consider the following control input criterion function: According to the optimization conditions The control input is obtained as follows: Among them, is the expected value of the j-th output, that is, is the expected value of the coolant outlet temperature T st,out of the fuel cell stack, is the expected value of the coolant inlet temperature T st,in of the fuel cell stack; λ is the weight factor; ρ is the step factor.

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