Fuel cell anode system adaptive model prediction control method fused with ESO

Abstract

The invention is suitable for the technical field of new energy, and provides a fuel cell anode system adaptive model prediction control method fused with ESO. The method comprises the following steps: firstly, establishing an anode system state space model and carrying out linearization and discretization processing; constructing MPC based on the discrete model, and solving a constrained optimization problem to obtain optimal control input; total disturbance of the system is estimated in real time through ESO and is fed forward and compensated to a control end; and designing a self-adaptive weight adjustment mechanism, and dynamically adjusting an MPC objective function weight matrix according to an output error, disturbance intensity and a working condition. The anti-interference capability and robustness of the system are enhanced, pressure and flow coordinated stable control is realized, the service life of the fuel cell is prolonged, and the method is suitable for complex dynamic working conditions.

Description

Technical Field

[0001] This invention belongs to the field of new energy technology, and in particular relates to an adaptive model predictive control method for a fuel cell anode system that integrates ESO. Background Technology

[0002] With increasing demands for energy conversion efficiency, intensified environmental pollution control, and rapid advancements in renewable energy utilization, proton exchange membrane fuel cells (PEMFCs) have garnered widespread attention in the energy and environmental sectors due to their high efficiency and cleanliness, and are rapidly being applied in the new energy vehicle industry. As a key subsystem within a fuel cell system, the performance of the anode hydrogen supply system not only affects hydrogen utilization but also directly relates to the dynamic response characteristics and long-term operational stability of the fuel cell stack. Among the various existing anode operating modes, the hydrogen recirculation mode can improve hydrogen utilization efficiency through tail gas recirculation while using intermittent purging to remove permeated impurities such as nitrogen. It exhibits excellent stability and durability, thus becoming the most widely used operating scheme currently.

[0003] However, in hydrogen recirculation mode, to prevent nitrogen permeating from the cathode from accumulating on the anode side, the system needs to periodically open the purge valve for venting. This purge operation inevitably leads to a momentary drop in recirculation flow, causing drastic fluctuations in anode channel pressure and flow. These fluctuations can result in a momentary drop in stack voltage and loss of control over the anode-cathode voltage difference, severely impacting stack operational safety and lifespan. Furthermore, the frequent changes in current load during actual fuel cell operation are also a significant disturbance factor causing dynamic fluctuations in anode pressure and flow. Summary of the Invention

[0004] The purpose of this invention is to provide an adaptive model predictive control method for fuel cell anode systems that integrates ESO, aiming to solve the technical problems existing in the prior art as identified in the background art.

[0005] This invention is implemented as follows: an adaptive model predictive control method for a fuel cell anode system incorporating ESO, comprising the following steps:

[0006] Step S1: Establish a state-space model of the fuel cell anode system, and linearize and discretize the state-space model to obtain discrete state-space equations;

[0007] Specifically, this includes: selecting system states: hydrogen partial pressure in the supply manifold, hydrogen partial pressure in the anode channel, hydrogen partial pressure in the return manifold, and angular velocity of the circulating pump; selecting control inputs: proportional valve opening and circulating pump input voltage; disturbance input $d$ is the change in purge valve opening and load current; system outputs: hydrogen partial pressure in the supply manifold and hydrogen flow rate at the anode channel inlet; establishing the system state-space equations; linearizing the state-space model by using Taylor expansion at the operating point to obtain continuous-time state-space equations; and then discretizing using the zero-order hold method to obtain discrete state-space equations.

[0008] Step S2: Based on the discrete state-space equations, construct a model predictive controller, and obtain the optimal control input for the fuel cell anode system by solving a constrained optimization problem;

[0009] Specifically, this includes: defining the prediction time domain and obtaining the prediction equation through recursion; establishing the objective function and setting constraints; transforming the nonlinear optimization problem into a constrained quadratic programming problem and solving it to obtain the optimal control input, which is then applied to the system.

[0010] Step S3: Construct an extended state observer to estimate the total disturbance of the fuel cell anode system in real time, and use the total disturbance as a feedforward compensation signal to compensate the control input of the model predictive controller;

[0011] Specifically, this includes: rewriting the system model as an integral cascade type; setting the disturbance terms of the system as new state variables and constructing an ESO model; tuning the observer gain through the observer bandwidth; obtaining an estimate of the total disturbance of the system through the ESO, and using it as a feedforward compensation signal to compensate the MPC control input to obtain the total control law.

[0012] Step S4: Design an adaptive weight adjustment mechanism to dynamically adjust the weight matrix in the objective function of the model predictive controller based on the output error, disturbance intensity, and operating conditions of the fuel cell anode system.

[0013] The system state is determined based on system error, QPHessian matrix condition number, and disturbance intensity; numerical stability is ensured through condition number optimization; and the weight matrix is ​​dynamically adjusted based on disturbance intensity and operating conditions.

[0014] The beneficial effects of this invention are:

[0015] This invention aims to improve the stability and control accuracy of fuel cell hydrogen systems under complex dynamic conditions by combining an Extended State Observer (ESO) with an adaptive weight adjustment mechanism. The ESO can estimate and compensate for disturbances and modeling errors in the system in real time, enhancing system robustness. Meanwhile, the adaptive weight adjustment mechanism dynamically adjusts the weight allocation in the Multi-Purpose Control (MPC) based on system errors, disturbance intensity, and changes in operating conditions, ensuring an adaptive balance between pressure and flow under different conditions. This improves the dynamic response performance of the system under complex conditions and extends the stack's lifespan. This method effectively solves the problems of multi-objective control imbalance, insufficient disturbance compensation, and inaccurate models in existing technologies, improving the overall operational stability and robustness of the system. Attached Figure Description

[0016] Figure 1 A framework diagram of an adaptive model predictive control method for a fuel cell anode system integrating ESO provided in an embodiment of the present invention;

[0017] Figure 2 A framework diagram of an adaptive model predictive control strategy for a fuel cell anode system integrating ESO provided in an embodiment of the present invention;

[0018] Figure 3 A framework diagram of the adaptive weight adjustment mechanism provided in the embodiments of the present invention;

[0019] Figure 4 This is a structural diagram of a fuel cell hydrogen system provided in an embodiment of the present invention;

[0020] Figure 5 A current load setting diagram provided for an embodiment of the present invention;

[0021] Figure 6 A comparison diagram of the anode pressure of three controllers provided in the embodiments of the present invention;

[0022] Figure 7 A comparison diagram of the anode inlet flow rates of three controllers provided in this embodiment of the invention;

[0023] Figure 8 A comparison diagram of the anode pressure of two controllers provided in an embodiment of the present invention;

[0024] Figure 9 A comparison diagram of the anode inlet flow of two controllers provided in an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0026] To address the pressure and flow fluctuations in fuel cell anode systems caused by purging operations and load changes, this invention employs a model predictive control (MPC) algorithm to achieve multi-objective collaborative control. This aims to effectively suppress fluctuations and maintain the anode-cathode pressure difference within a safe range, thereby preventing damage to the proton exchange membrane due to abnormal pressure differences. However, considering the model uncertainties, internal and external disturbances, and errors introduced by model linearization in the anode system model, these factors can reduce the control accuracy of MPC. To address this, this invention proposes a control strategy incorporating an extended state observer (ESO). The ESO is used to observe the aforementioned "total disturbance" experienced by the system in real time and feeds the observed values ​​forward to the control input calculated by MPC for active compensation. Furthermore, addressing the challenge of fixed weight matrices in traditional MPC, which struggle to accommodate different dynamic operating conditions, this invention proposes an adaptive weight adjustment mechanism. This mechanism dynamically adjusts the weight matrices Q and R online by tracking errors, disturbance intensity, and system operating states in real time, thereby improving the solution feasibility of the MPC algorithm and the dynamic control performance of the system under complex operating conditions.

[0027] like Figures 1 to 4 As shown, the technical solution of the present invention mainly consists of three parts: the design of the model prediction controller and the extended state observer, and the determination of the adaptive weight adjustment mechanism.

[0028] This embodiment provides an adaptive model predictive control method for a fuel cell anode system that integrates ESO, and the specific steps are as follows:

[0029] S1. Establish a state-space model of the fuel cell anode system, and linearize and discretize the state-space model to obtain discrete state-space equations;

[0030] Select system status To supply hydrogen partial pressure to the manifold ( ), Anode channel hydrogen partial pressure ( ), reflux manifold hydrogen partial pressure ( ) and the angular velocity of the circulating pump ( );

[0031] ;

[0032] Select control input For the proportional valve opening ( ) and the input voltage of the circulating pump ( ); Disturbance input For changes in the purge valve opening ( and load current ( );

[0033] ;

[0034] ;

[0035] The system output is the partial pressure of hydrogen supplied to the manifold ( ) and the hydrogen flow rate at the anode channel inlet ( According to the anode system modeling formula, the system output and system state are defined as follows:

[0036] ;

[0037] In the formula: ; For supply manifold flow coefficient.

[0038] Based on the above, the state-space model of the fuel cell anode system is established as follows:

[0039] ;

[0040] In the formula: The system state-space equations are shown below:

[0041] ;

[0042] In the formula: It is the gas constant; For temperature; , , These are the volumes of the supply manifold, the anode channel, and the return manifold, respectively. This refers to the molar mass of hydrogen gas. This refers to the output flow rate of the hydrogen tank. This is the flow rate calibration coefficient; This refers to the number of battery cells; It is Faraday's constant; The return manifold flow coefficient; The purging flow rate coefficient; Atmospheric pressure; It is the moment of inertia; This refers to the driving torque of the circulating pump motor. This refers to the resistance torque; For the mechanical efficiency of the motor; , , These are the motor parameters; Specific heat capacity; For circulating pump efficiency; Specific heat ratio.

[0043] Since this invention employs linear MPC, the state-space model needs to be linearized. This invention uses the Taylor expansion method to transform the nonlinear function... At work Perform linearization:

[0044] ;

[0045] After linearization, the continuous-time state-space equations are obtained:

[0046] ;

[0047] In the formula: , , , The matrix represents the weight matrix of the system.

[0048] To meet the design requirements of MPC, the linearized model is discretized. The discrete state-space equation obtained by the zero-order preservation method (ZOH) in this invention is as follows:

[0049] ;

[0050] .

[0051] in , , , These represent the discrete-time state transition matrix, the discrete-time control input matrix, the discrete-time disturbance input matrix, and the discrete-time constant bias term, respectively, where T is the sampling time.

[0052] S2. Based on the discrete state-space equations, a model predictive controller is constructed, and the optimal control input of the fuel cell anode system is obtained by solving the constrained optimization problem.

[0053] Define the prediction time domain Np and perform recursive processing to obtain the prediction equation as follows:

[0054] ;

[0055] In the formula: and This represents the predicted system state and output for the next Np steps at time k. and These represent the control input and disturbance quantity for the Np-step prediction in the time domain, respectively. , , as well as This is the weight matrix of the prediction equation. The matrix is ​​represented as follows:

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] ;

[0063] ;

[0064] in Indicates in The time predicted The system state at any given moment, and so on; Indicates in The time predicted The system output at each moment, and so on; Indicates in The time predicted The system input at any given time, and so on; Indicates in The time predicted The system disturbance at any given moment, and so on.

[0065] MPC control is used to track reference pressure and reference flow. To prevent excessive actuator adjustment from affecting system lifespan, it is necessary to minimize the change in the control signal. Therefore, the following objective function is defined:

[0066] ;

[0067] In the formula: and The weight matrix is ​​the objective function weight matrix; Output a reference matrix for the system.

[0068] The constraint section mainly focuses on limiting the magnitude of actuator changes:

[0069] ;

[0070] Through the above process, the nonlinear optimization problem of the fuel cell anode system is transformed into a constrained quadratic programming problem. Solving this problem yields the optimal control input, which is then applied to the system to complete the rolling optimization.

[0071] S3. Construct an extended state observer to estimate the total disturbance of the fuel cell anode system in real time, and use the total disturbance as a feedforward compensation signal to compensate the control input of the model predictive controller.

[0072] Set the anode inlet flow rate to The hydrogen partial pressure in the supply manifold is set to... Therefore, the system model is rewritten as follows:

[0073] ;

[0074] ;

[0075] In the formula: and This indicates the disturbance experienced by the system.

[0076] make , The system model is transformed into an integral cascade type:

[0077] ;

[0078] ;

[0079] By setting the disturbance terms experienced by the system as new state variables, the ESO model is obtained as follows:

[0080] ;

[0081] ;

[0082] In the formula: is the observer gain; z represents the estimated system state.

[0083] The observer gain can be set via the observer bandwidth. and controller bandwidth Perform the adjustment:

[0084] ;

[0085] ;

[0086] in , , These represent the first-order error injection gain, second-order error injection gain, and third-order error injection gain of the first ESO, respectively. , , These represent the first-order error injection gain, second-order error injection gain, and third-order error injection gain of the second ESO, respectively.

[0087] After obtaining the total disturbance to the system through ESO, it is compensated and applied to the control input calculated by MPC to obtain the total control law. and They are respectively:

[0088] ;

[0089] S4. Design an adaptive weight adjustment mechanism to dynamically adjust the weight matrix in the objective function of the model predictive controller based on the output error, disturbance intensity, and operating conditions of the fuel cell anode system.

[0090] An adaptive weight adjustment mechanism is established. By online correction of the Q and R weight matrices in model predictive control, the weight parameters can be automatically adjusted according to error changes, disturbance intensity, and system operating state. This ensures a dynamic balance between pressure and flow control performance under different operating conditions, improving the feasibility of optimization solutions and system stability. The specific adaptive weight adjustment mechanism is as follows: Figure 3 As shown.

[0091] The adaptive weight adjustment mechanism is mainly based on system error. The condition number of the QPHessian matrix and disturbance intensity To make a judgment, the definitions of the three are as follows:

[0092] ;

[0093] ;

[0094] ;

[0095] In the formula: It is a QPHessian matrix; This represents the predicted value of the system output;

[0096] Before adjusting the weights, numerical stability must be determined first to ensure that the optimization problem is solvable. This part mainly uses the condition number for judgment; if the condition number... If the problem fails to be solved, the condition number can be improved by adding diagonal terms:

[0097] ;

[0098] diagonal items Defined as:

[0099] ;

[0100] In the formula: It is the largest eigenvalue; This is a reference value for the condition number; This represents the maximum value of the condition number.

[0101] The weight matrices Q and R are adaptively adjusted according to the system operating conditions.

[0102] Define the initial weight matrix and update rate:

[0103] ;

[0104] ;

[0105] , The definition is as follows:

[0106] ;

[0107] ;

[0108] When the system is subjected to large disturbances, the R weight is increased to suppress abrupt changes and fluctuations in the system control signal; at the same time, the growth of the Q weight is limited to avoid conflict with input smoothness.

[0109] ;

[0110] ;

[0111] These are the weighting coefficients.

[0112] When the system is subjected to weak disturbances, the primary focus is on improving the system output tracking accuracy. In this case, the weighting of pressure and flow is determined by the operating conditions. During low load periods (less than 250A), pressure stability is prioritized; however, during high load periods, to meet the demands of the system's electrochemical reactions, ensuring a stable flow supply is paramount. Therefore, the weighting of flow is increased, while the weighting of pressure is decreased.

[0113] ;

[0114] In the formula: These are the error weighting coefficients; The definition is as follows:

[0115] ;

[0116] In the formula: express or The definition is as follows:

[0117] ;

[0118] In the formula: A scale for measuring the error in pressure and flow rate.

[0119] Through the above weight adjustment mechanism, the MPC objective function is adaptively adjusted based on the system's output error and disturbance intensity at the current moment. and Weight matrix, applying the adjusted , , Then, proceed to the next sampling time to achieve cyclic control.

[0120] Example 1:

[0121] like Figures 5 to 9 As shown, step-changing load currents were selected as external inputs, with values ​​of 54.1A, 225.9A, 200A, 298.8A, and 257.8A respectively. The range exceeding 250A was defined as a high-load condition and used as the basis for adaptive weight adjustment. Under these conditions, the ESO-AMPC method of this invention was compared and verified with fuzzy PI, Active Disturbance Rejection Reduction (ADRC), and traditional linear MPC to evaluate the performance differences of each strategy in terms of dynamic response and steady-state control accuracy. The results show that the proposed ESO-AMPC control strategy can limit pressure fluctuations to within 323 Pa and maintain flow fluctuations during the purging phase within 0.048 g / s. Compared with traditional linear MPC, ESO-AMPC reduces pressure fluctuation amplitude by approximately 176 Pa and flow overshoot by approximately 0.008 g / s. These results demonstrate that the control method proposed in this invention possesses excellent disturbance suppression and rapid response capabilities under complex dynamic conditions.

[0122] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0123] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

[0124] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An adaptive model predictive control method for a fuel cell anode system integrating ESO, characterized in that, The method includes: S1. Establish a state-space model of the fuel cell anode system, and perform linearization and discretization on the state-space model to obtain discrete state-space equations; S2. Based on the discrete state-space equations, a model predictive controller is constructed, and the optimal control input of the fuel cell anode system is obtained by solving the constrained optimization problem. S3. Construct an extended state observer to estimate the total disturbance of the fuel cell anode system in real time, and use the total disturbance as a feedforward compensation signal to compensate the control input of the model predictive controller. S4. Design an adaptive weight adjustment mechanism to dynamically adjust the weight matrix in the objective function of the model predictive controller based on the output error, disturbance intensity, and operating conditions of the fuel cell anode system.

2. The method according to claim 1, characterized in that, In step S1, the specific process of establishing the state-space model of the fuel cell anode system is as follows: Selecting the state of the fuel cell anode system To supply hydrogen partial pressure to the manifold Hydrogen partial pressure in the anode channel Hydrogen partial pressure in the reflux manifold and the angular velocity of the circulating pump , ; Select control input For proportional valve opening and the input voltage of the circulating pump , ; Select disturbance input For changes in purge valve opening and load current , ; Fuel cell anode system output To supply hydrogen partial pressure to the manifold Hydrogen flow rate at the anode channel inlet , ,in The system output matrix is ​​represented as follows: , To supply manifold flow coefficient; Establish the system state-space equations: ,in The first derivative of the system state with respect to time. The specific formula is: ； In the formula: , , , These represent the hydrogen partial pressure in the supply manifold, the hydrogen partial pressure in the anode channel, the hydrogen partial pressure in the return manifold, and the first derivative of the circulating pump angular velocity with respect to time, respectively. It is the gas constant; For temperature; , , These are the volumes of the supply manifold, the anode channel, and the return manifold, respectively. This refers to the molar mass of hydrogen gas. This refers to the output flow rate of the hydrogen tank. , , , This is the flow rate calibration coefficient; This refers to the number of battery cells; It is Faraday's constant; The return manifold flow coefficient; The purging flow rate coefficient; Atmospheric pressure; It is the moment of inertia; For the mechanical efficiency of the motor; , , These are the motor parameters; Specific heat capacity; For circulating pump efficiency; Specific heat ratio.

3. The method according to claim 1, characterized in that, In step S1, the linearization process uses the Taylor expansion method, and the specific formula is as follows: ,in For the working point; The discretization process uses the zero-order preservation method, and the resulting discrete state-space equations are: ,in , , , The matrix represents the weight matrix of the fuel cell anode system.

4. The method according to claim 1, characterized in that, In step S2, the specific process of constructing the model predictive controller is as follows: Define the prediction time domain And by performing recursive processing, the prediction equation is obtained: ； in, and Indicates in Predicting the future The status and output of the fuel cell anode system in step [step]. and Representing the prediction time domain The control input and disturbance amount of the step. , , as well as This is the weight matrix for the prediction equation; Define the objective function with the condition of minimizing the change in the control signal: ； in and The weight matrix is ​​the objective function. For the system's control input, Output a reference matrix for the fuel cell anode system; The constraint condition for the amplitude of the actuator change is: , ; in , These represent the proportional valve opening and the minimum input voltage of the circulating pump, respectively. , These represent the proportional valve opening and the maximum input voltage of the circulating pump, respectively.

5. The method according to claim 1, characterized in that, In step S3, the specific process of constructing the extended state observer is as follows: Set the anode inlet flow rate as The partial pressure of hydrogen supplied to the manifold is The fuel cell anode system model is rewritten as follows: ； ； in , This represents the first derivative of the system output with respect to time. , This represents the second derivative of the system output with respect to time. and This indicates the disturbance experienced by the system. , This refers to the input gain coefficient. make , The fuel cell anode system model is transformed into an integral series model: ； ； in , They are respectively and The first derivative with respect to time; The disturbance term experienced by the fuel cell anode system and Set as a new state variable and The ESO model is obtained as follows: ； ； in Each parameter represents the observer gain. , , They are respectively , , The estimated value, , , They represent , , The estimated value, State estimation The first derivative with respect to time.

6. The method according to claim 5, characterized in that, The observer gain Through observer bandwidth and controller bandwidth Adjustment.

7. The method according to claim 1, characterized in that, In step S4, based on system error The condition number of the QPHessian matrix and disturbance intensity Determine the adaptive weight adjustment mechanism: ； ； ； in Indicates that the system is in Reference value for time, It is a QPHessian matrix. Indicates that the system is in Time of the first The actual value of each output. express The predicted value of the output of the fuel cell anode system at any time. Indicates the system's first The normalized scale of each output.

8. The method according to claim 7, characterized in that, The specific process of dynamically adjusting the weight matrix is ​​as follows: Define the initial weight matrix and update rate: ； ； in , These represent the initial output weight matrix and the initial input weight matrix, respectively. , These represent the system outputs respectively. and The initial weights, , These represent control inputs respectively. and The initial weights, , express At any given time, output the weight matrix and input the weight matrix. , ,in , They represent respectively to and The scaling factor for the error weights, , They represent respectively to and Input the scaling factor for the weights; When the disturbance experienced by the fuel cell anode system exceeds the disturbance intensity threshold range... , ; When the disturbance experienced by the fuel cell anode system is below the disturbance intensity threshold range , ; in , They represent the first The error weight scaling factor of the output channel and the first Input weight scaling factor for the input channel. , These represent the adjustment gain of the output weights on the disturbance strength and the adjustment gain of the input weights on the disturbance strength, respectively. This indicates that the output weights are adjusted based on the error assignment. This is the error proportion coefficient. ,in For the first The normalized error amplitude of each output represents the pressure error amplitude. and flow error amplitude , ,in For the first The tracking error of each output. A scale for measuring the error in pressure and flow rate.

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