Data-driven discrete three-step decoupling control method for fuel cell air supply system

Abstract

The application discloses a data-driven discrete three-step decoupling control method for a fuel cell air supply system, and belongs to the field of vehicle fuel cell engine control.The application aims to generate control signals for the air compressor speed and the throttle opening degree based on a discrete three-step model-free adaptive controller for different working conditions of the fuel cell, so that the air mass flow and the cathode pressure in the air supply system are at the required expected values of the fuel cell air supply system data-driven discrete three-step decoupling control method.The application firstly adopts a dynamic linearization method to obtain a dynamic linearization model, without using any data of the system model, and then based on the data model, utilizes an extended state observer to decouple the system output.Finally, a model-free adaptive controller based on the discrete three-step method is developed based on the decoupled data model.The control scheme provided by the application can avoid modeling the air supply system and is easy to implement in engineering.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of vehicle fuel cell engine control. BACKGROUND

[0002] To reduce automobile exhaust emissions, proton exchange membrane fuel cell (PEMFC) is the best solution for automobile energy replacement. The air supply system of PEMFC has a great influence on its overall performance. The air flow through the cathode in the air supply system of PEMFC is usually represented by the oxygen excess ratio, which is defined as the ratio of the mass flow rate of oxygen entering the cathode of the fuel cell to the mass flow rate of oxygen reacting in the fuel cell. Generally, the air supply system of the fuel cell is composed of a compressor, an intercooler, a humidifier, a stack, a throttle valve and connecting pipelines. The power consumed by the compressor accounts for about 40% of the total power of the fuel cell. Figure 1 For the oxygen excess ratio and net power relationship curve of different stack currents, the higher the compressor power, the greater the air flow of the air supply system, resulting in a larger oxygen excess ratio, causing "oxygen saturation" phenomenon, thereby causing the net power of the fuel cell to decrease; when the compressor power is too low, the air flow of the air supply system is smaller, resulting in "oxygen starvation", the oxygen excess ratio becomes smaller, and in severe cases, it will damage the service life of the battery. Figure 2 For the optimal oxygen excess ratio and optimal net power fitting curve of the stack current, it can be seen that by controlling the air supply system of PEMFC, the oxygen excess ratio of the fuel cell can be stabilized at a reasonable value, thereby improving the net power of the fuel cell. Secondly, the output power level of the fuel cell is directly related to the cathode pressure. If the cathode pressure is not controlled within a reasonable range, the pressure difference on both sides of the proton exchange membrane will increase, which will damage the service life of the membrane. The control of the air supply system of PEMFC can be described as a coordinated control of the cathode flow and the cathode pressure.

[0003] For the control of the air supply system, the following problems exist:

[0004] 1. The air supply system of PEMFC is a complex system with multiple inputs and outputs, uncertain information such as internal and external disturbances, strong nonlinearity, and multiple variables coupled together, making it difficult to establish an accurate mechanism model. Therefore, the control scheme based on the mechanism model is difficult to apply.

[0005] 2. The two control outputs of the PEMFC air supply system, i.e. the air mass flow and the cathode pressure, interact with each other, which will worsen the tracking performance of the system output and bring problems to the controller design.

[0006] 3. The existing control algorithm of fuel cell, such as model predictive control, has high requirements for computing power, heavy computing burden for vehicle-mounted computer control module (ECU), low efficiency, and is difficult to be implemented in practical application. SUMMARY

[0007] The purpose of the present application is to use a model-free adaptive controller based on a discrete three-step method to generate control signals for the air compressor speed and the throttle opening degree under different working conditions of the fuel cell, so as to make the air mass flow in the air supply system and the cathode pressure of the fuel cell air supply system data-driven discrete three-step decoupling control method reach the required expected value.

[0008] The steps of the present application are:

[0009] S1, using the input data and output data of the fuel cell air supply system model, a dynamic linearization data model is obtained

[0010] S11, the air supply system of PEMFC is described as the following general nonlinear system:

[0011] (1)

[0012] wherein, is a time series; is the length; is an unknown positive integer; is an unknown positive integer; is the output vector at time t; is the air mass flow of the air supply system; is the cathode pressure; is the input vector at time t; is the air compressor speed; is the throttle opening degree; represents a general generalized nonlinear function;

[0013] S12, the model (1) is converted into a dynamic linearization data model:

[0014] (2)

[0015] wherein, is the next time of t, ; represents the output vector at time t; ; represents the input vector at time t; is a pseudo-Jacobian matrix, which is defined as follows:

[0016] (3)

[0017] in, These are all elements in a pseudo-Jacobi matrix;

[0018] S13. The pseudo-Jacobi matrix is ​​estimated using the following estimation algorithm, defining a performance index function. for:

[0019] (4)

[0020] in, For the penalty function;

[0021] S14, Order right Find the partial derivative. The following estimation algorithm is then obtained:

[0022] (5)

[0023] in, for The estimated value; Step size factor;

[0024] S15. The dynamically linearized data model is then transformed as follows:

[0025] (6);

[0026] S2. Use an extended state observer to decouple the system output and include the decoupled part in the extended state.

[0027] S21. The dynamically linearized data model (6) is transformed into the following form:

[0028] (7)

[0029] in, It is a diagonal matrix; They are The estimated value; This is the coupling term vector; yes Coupling terms, yes Coupling terms;

[0030] The decoupling model is as follows:

[0031] (8)

[0032] S22, design extended state observer to estimate and compensate the coupling term The extended state observer is designed as follows:

[0033] (9)

[0034] where, is the estimated value of ; is the estimated value of ; is the estimated value of ; is the estimated value of ; and are observer gains;

[0035] S23, further decouple the dynamic linearization data model as:

[0036] (10)

[0037] S3, design a model-free adaptive controller based on discrete three-step method

[0038] S31, decouple the dynamic data model (9) to rewrite as:

[0039] (11)

[0040] S32, next design a discrete three-step method controller:

[0041] S321, steady-state-like control

[0042] The system output at the next time of the system reaching steady state is equal to the system output at this time, and , substitute into formula 11 to solve the steady-state control input:

[0043] (12)

[0044] S322, feedforward tracking control

[0045] While satisfying the ability of the discrete system to reach steady state, the system output needs to track the given desired output , and , and substitute into formula 11 to solve the system feedforward tracking output as:

[0046] (13)

[0047] where, is the desired value of the jth output; that is, Desired value of air mass flow Desired value of cathode pressure

[0048] S323, discrete error feedback control

[0049] Adding feedback control based on error size selection:

[0050] (14)

[0051] Wherein, a and b are control coefficients.

[0052] The beneficial effects of the present application are:

[0053] 1. For the complex system with multiple input and output, strong nonlinearity, and uncertain information such as internal and external disturbance, a data-driven modeling method is proposed, and a dynamic linearization data model is generated only by using the input and output data of the air supply system;

[0054] 2. The present application is aimed at the coupling between the two outputs of the air supply system, and the extended state observer is used to realize the decoupling between the outputs, further improving the control performance;

[0055] 3. The model-free adaptive controller designed based on the discrete three-step method consists of three parts: discrete steady-state control, discrete feedforward control based on reference variable, and discrete error feedback control. The discrete steady-state control and the discrete feedforward control can quickly track the desired value, and the discrete error feedback control can improve the robustness of the system. The algorithm is efficient, fast in calculation, and has lower requirements for ECU computing power, which can better face engineering problems. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1 is a peroxide ratio and net power relationship curve diagram of different stack currents;

[0057] Figure 2 is an optimal peroxide ratio and optimal net power fitting curve diagram of stack current;

[0058] Figure 3 is a structure block diagram of proton exchange membrane fuel cell air supply system;

[0059] Figure 4 is a stack current change curve diagram, which is a series of random step curves, unit A;

[0060] Figure 5 is a cathode gas path tracking set value curve diagram; wherein the upper graph is an air supply system flow curve diagram; the lower graph is a cathode pressure curve;

[0061] ​​​Figure 6 is the cathode gas path tracking constant curve diagram after changing parameters; wherein the upper diagram is an air supply system flow curve diagram; the lower diagram is a cathode pressure curve diagram. DETAILED DESCRIPTION

[0062] The present application is directed to the difficulty of modeling and the control difficulty of strong coupling of the fuel cell air supply system, and proposes a data-driven decoupling control method based on the discrete three-step method. First, the fuel cell air supply system is a strong nonlinear coupled system, in addition, as the working condition changes, the internal parameters of the vehicle-mounted fuel cell also change, and the system itself has time-varying parameters, so a dynamic linearization method is used to obtain a dynamic linearization model, which only uses the input and output data of the controlled system, without using any data of the system model, and is a pure data-driven solution. Then, based on the data model, an extended state observer is used to decouple the system output. Finally, based on the decoupled data model, a model-free adaptive controller based on the discrete three-step method is developed to realize accurate control of the air compressor and the throttle. The control scheme proposed by the present application can avoid modeling the air supply system and is easy to implement in engineering. The present application can well solve the above three problems.

[0063] The present application can include the following parts in structure: a fuel cell air supply system model, a dynamic linearization data model, an extended state observer, and a model-free adaptive controller based on the discrete three-step method.

[0064] In order to test the effectiveness of the designed controller, a system model that can accurately describe the real fuel cell air supply system is built; the extended state observer is used to realize the decoupling between the outputs of the dynamic linearization data model, and the controller is designed based on the dynamic linearization data model; the model-free adaptive controller based on the discrete three-step method generates control signals for the air compressor speed and the throttle opening for different working conditions of the fuel cell, so that the air mass flow and the cathode pressure in the air supply system are at the required desired value.

[0065] The implementation method of the present application includes the following parts:

[0066] The design of the data-driven controller of the fuel cell air supply system of the present application is developed through a software system. The dynamic model and the controller of the fuel cell air supply system are established by using MATLAB / Simulink software, and a simulation experiment environment is provided.

[0067] First, the fuel cell air supply system model is built in MATLAB / Simulink software, and the speed of the air compressor, the opening of the throttle, the air mass flow and the cathode pressure in the fuel cell air supply system can be directly obtained from the built fuel cell air supply system model.

[0068] Then, the fuel cell air supply system model established above is taken as a control object. Based on dynamic linearization technology, only the input data (air compressor speed and throttle opening) and output data (air mass flow and cathode pressure) of the fuel cell air supply system model are used to obtain a dynamic linearization data model.

[0069] Based on the dynamic linearization data model derived above, an extended state observer is used to decouple the output of the system, and the decoupled part is listed in the extended state.

[0070] Finally, based on the decoupled dynamic linearization data model described above, a model-free adaptive controller based on the discrete three-step method is designed. Since there are two control signals in the present application, two model-free adaptive learning controllers based on the discrete three-step method are designed to generate the two control signals, i.e. the air compressor speed and the throttle opening. The entire control system is built in the MATLAB / Simulink environment according to the working principle of the fuel cell air supply system. The actual air mass flow and cathode pressure of the fuel cell air supply system are directly obtained from the system model, and compared with the expected air mass flow and cathode pressure to obtain the error amount. The air compressor speed and throttle opening are calculated by the model-free adaptive controller based on the discrete three-step method and sent to the actuators of the fuel cell air supply system, i.e. the air compressor and the throttle, so that the air mass flow and the cathode pressure can follow the desired values of the air supply system.

[0071] To explain the technical content, structural features, and implementation purposes of the present application in detail, the present application will be explained comprehensively in conjunction with the accompanying drawings:

[0072] Dynamic load changes are simulated by measurable disturbance quantities Load current in the present application. The fuel cell air supply system is built in Simulink as the controlled object of the present application. The control target of the present application is that the controller controls the air compressor speed and the throttle opening according to the state of the fuel cell air supply system, so that the air mass flow and the cathode pressure of the air supply system can track the desired values .

[0073] The present application provides a set of devices based on the above operating principle and operating process. The building and operating process are as follows:

[0074] 1. Software selection

[0075] The application builds a simulation model of the controlled object and the controller of the control system through software Matlab / Simulink, the software version is Matlab R2018b, and the solver is ode3. The simulation step is a fixed step, and the step length is 0.00001 s.

[0076] 2. Dynamic linearization data model

[0077] The air supply system of the PEMFC can be described as a general nonlinear system as follows:

[0078] (1)

[0079] wherein, is a time series; is a length; is an unknown positive integer; is an unknown positive integer; is an output vector at time t; is the air mass flow of the air supply system; is the cathode pressure; is an input vector at time t; is the air compressor speed; is the throttle opening degree; represents a general generalized nonlinear function.

[0080] For model (1), it can be converted into a dynamic linearization data model as follows:

[0081] (2)

[0082] wherein, is the next time of t, ; represents an output vector at time t. ; represents an input vector at time t; is a pseudo-Jacobian matrix, which is defined as follows:

[0083] (3)

[0084] wherein, are elements in the pseudo-Jacobian matrix.

[0085] The pseudo-Jacobian matrix is estimated by the following estimation algorithm, and the performance index function is defined as :

[0086] (4)

[0087] where, is a penalty function.

[0088] Let Take partial derivative of , then the following estimation algorithm can be obtained:

[0089] (5)

[0090] where, is the estimation value of ; is a step factor.

[0091] then the dynamic linearization data model can be converted to the following:

[0092] (6).

[0093] 2. Extended state observer

[0094] The dynamic linearization data model (6) can be converted to the following form:

[0095] (7)

[0096] where, is a diagonal matrix; are respectively the estimation values of ; is a coupling term vector; is the coupling term of ; is the coupling term of .

[0097] then the decoupling model is as follows:

[0098] (8).

[0099] The following designs an extended state observer to realize the estimation and compensation of the coupling term , and the extended state observer is designed as follows:

[0100] (9)

[0101] where, is the estimation value of ; is the estimation value of ; is the estimation value of ; is the estimation value of ; and is the observer gain.

[0102] The further decoupled dynamic linearized data model is:

[0103] (10).

[0104] 3. Discrete three-step method controller

[0105] This part designs a discrete three-step method controller based on the decoupled dynamic linearized data model (9). The decoupled dynamic data model (9) can be rewritten as:

[0106] (11).

[0107] Next, the discrete three-step method controller is designed:

[0108] First step: quasi-steady-state control

[0109] Assuming that the discrete system reaches a steady state, then the system output of the next time of the system reaching a steady state is equal to the system output at this time, and , into formula 11, the steady-state control input is solved:

[0110] (12).

[0111] Second step: feedforward tracking control

[0112] While meeting the ability of the discrete system to reach a steady state, the system output needs to track the given expected output , and , and into formula 11, the system feedforward tracking output is solved:

[0113] (13)

[0114] wherein, is the expected value of the jth output; that is, is the expected value of the air mass flow . is the expected value of the cathode pressure .

[0115] Third step: discrete error feedback control

[0116] Because of the disturbance signal, the first two steps cannot exhibit good robustness, so an error feedback control is added to ensure that the system can track the expected output as soon as the initial state, and also can continuously reduce the error to obtain good control effect, a feedback control based on the error size selection is added:

[0117] (14)

[0118] wherein are control coefficients, respectively.

[0119] Experimental verification and analysis

[0120] In order to verify the effectiveness of the discrete three-step model-free adaptive control scheme proposed in the present application for the air mass flow and cathode pressure control of the air supply system of the proton exchange membrane fuel cell, the stack current is considered to be a series of random step conditions, which are used to simulate dynamic load changes, as shown in the following table. Figure 5 It can be seen that the cathode pressure and air mass flow can be well tracked to the given desired parameters; the effectiveness of the discrete three-step model-free adaptive control can be verified from the experimental results. The data-driven controller has the advantage of good robustness and adaptability even if the controlled object parameters are changed or the controlled object is in different working conditions; therefore, in the case of simulating the limit working condition parameters, the relative humidity is 0.2, the oxygen content in the air is 0.11, and the fuel cell stack temperature is 0℃, the algorithm still performs well and can well track the given expected value, Figure 6 which further verifies the effectiveness of the data-driven learning controller proposed.

Claims

1. A data-driven discrete three-step decoupling control method for a fuel cell air supply system, characterized in that: The steps are as follows: S1. Using the input and output data of the fuel cell air supply system model, obtain a dynamic linearized data model. The air supply system of S11 and PEMFC is described as a general nonlinear system as follows: （1） in, It is a time series; For length; It is an unknown positive integer; It is an unknown positive integer; yes Output vector at time step; Air mass flow rate for the air supply system; Cathode pressure; yes The input vector at time step; This refers to the air compressor speed; Throttle opening; It represents a generalized nonlinear function; S12. Transform model (1) into a dynamically linearized data model: （2） in, yes The next moment, ; represent Output vector at time step; ; represent The input vector at time step; It is a pseudo-Jacobi matrix, defined as follows: （3） in, These are all elements in a pseudo-Jacobi matrix; S13. The pseudo-Jacobi matrix is ​​estimated using the following estimation algorithm, defining a performance index function. for: （4） in, For the penalty function; S14, Order right Find the partial derivative. The following estimation algorithm is then obtained: （5） in, for The estimated value; Step size factor; S15. The dynamically linearized data model is then transformed as follows: （6）； S2. Use an extended state observer to decouple the system output and include the decoupled part in the extended state. S21. The dynamically linearized data model (6) is transformed into the following form: （7） in, It is a diagonal matrix; They are The estimated value; This is the coupling term vector; yes Coupling terms, yes Coupling terms; The decoupling model is as follows: （8） S22. Design an extended state observer to implement the coupling terms. The estimation and compensation, and the extended state observer design are as follows: （9） in, yes The estimated value; yes The estimated value; yes The estimated value; yes The estimated value; and It is the observer gain; S23. A further decoupled dynamic linearized data model is as follows: （10） S3. Design a model-free adaptive controller based on the discrete three-step method. S31, Decoupling the dynamic data model (9) is rewritten as: （11） S32. Next, we will design a discrete three-step controller: S321, Quasi-steady-state control The system output at the next moment after reaching steady state is equal to the system output at this moment. Substituting into Equation 11, we obtain the steady-state control input: （12）； S322, Feedforward tracking control While ensuring that the discrete system is capable of reaching a steady state, the system output needs to track a given desired output. ,Other At the same time Substituting into Equation 11, we obtain the system feedforward tracking output as: （13） in, Let be the expected value of the j-th output; that is, air mass flow rate Expected value; Cathode pressure Expected value; S323, Discrete Error Feedback Control Add feedback control based on error magnitude: （14） in These are the control coefficients.

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