Research on Hydrogen-Fueled Turbojet Engine Control Method Based on Model-Based Design

Abstract

Due to the substantial disparities in physical attributes between hydrogen fuel and conventional fuels, the development of an efficient controller presents a formidable challenge. In this context, this paper delves into the utilization of a model-based design (MBD) methodology for the purpose of conceiving and enhancing control systems for hydrogen-fueled turbojet engines. The investigation commences by adopting an established physical model of a hydrogen-fueled turbojet engine and subsequently validates its performance through rigorous simulation exercises. Consequently, this research undertakes a systematic deconstruction of the design process into discrete sub-phases, thus facilitating a seamless progression from system requirement analysis to system verification. This approach engenders a concurrent design and optimization of the control system. The ultimate confirmation of the controller’s efficacy and reliability is achieved through exhaustive simulations and Hardware-In-the-Loop testing. The research findings not only serve to augment design efficiency and mitigate design expenditures, but also propose avenues for further performance ameliorations in the realm of hydrogen-fueled turbojet engines. The control system accuracy of MBD is compared with the experimental results, and under high hydrogen fuel flow conditions, the errors reach an extremely low level of 0.1%. This affords a novel design paradigm within the domain of aero-engine control.

1. Introduction

With the growing global demand for sustainable aviation, hydrogen-fueled turbojet engines are gaining attention in the aviation industry due to their low-carbon, efficient, and environmentally friendly characteristics [1]. This is mainly due to the fact that the main products of hydrogen fuel combustion are stream and trace amounts of nitrogen oxides (NOx), which have a significantly lower impact on the environment compared to conventional fuels [2,3]. In fact, through ground-based combustion engine experiments, researchers have found that carbon dioxide emissions can be reduced by as much as 51.1% when hydrogen fuel with a volume fraction of 75% is added to methane [4]. In the field of aero-engines, studies have also confirmed that if the hydrogen fraction is increased to 15%, the specific energy consumption (SEC) will be reduced by approximately 6.5% and the CO emissions will be reduced by approximately 33% [5], while the ambient exhaust emissions are reduced from 0.509 kg/s to 0.0045 kg/s [6]. These findings demonstrate the great potential of hydrogen fuel in the field of aero-engines.

However, the development of hydrogen-fueled aero-engines faces a number of challenges and the industry has not yet developed mature solutions, such as dealing with the high reactivity, high flame speed, low minimum ignition energy, and low stability of hydrogen [7], which require continuous testing and iteration to find solutions. These characteristics mean that hydrogen-fueled aero-engines face many uncertainties during the development process. During the implementation of a hydrogen-fueled turbojet engine, our research team experienced failures such as backfiring in the combustion chamber, excessive vibration of the engine due to unstable combustion, and engine overshoot due to inaccurate metering of the hydrogen fuel flow. These problems have required designers and engineers to continuously update and optimize the control system to better accommodate the uncertainties in the development of hydrogen-fueled aero-engines.

In today’s complex and dynamic research and development (R&D) environment, traditional document-based design methods face significant challenges. First and foremost, each change in requirements due to a technical fault of a hydrogen-fueled aero-engine triggers many document revisions and updates. This process adds complexity to the design and development, and is a significant drain on time and resources. Second, each update relies on manual coding, which further burdens the design effort and raises the risk of errors. Most seriously, a document-based design approach makes it difficult to effectively identify and resolve critical issues such as tempering at an early stage, which can lead to problems being revealed at a later stage of testing, allowing multiple hydrogen-fueled turbojet engines to fail during development. Such an outcome undoubtedly jeopardizes R&D efficiency and results. Therefore, there is an urgent need to explore a more efficient and flexible design strategy to adapt to the dynamic changes and uncertainties in the R&D process of hydrogen-fueled turbojet engines.

In the design and development chain of hydrogen aero-engines, model-based design (MBD) provides an effective solution to cope with emerging needs and challenges. First, the system-level perspective of MBD allows designers and engineers to have a comprehensive understanding of the entire engine system, which is essential for dealing with the high reactivity, high flame speed, low minimum ignition energy, and low stability characteristics of hydrogen fuel. Additionally, this global understanding allows designers and engineers to more precisely balance and coordinate between components to optimize the overall performance of the system. Second, MBD allows engineers to adjust and optimize parameters directly in the model to meet new requirements. For example, new environmental regulations may require further reductions in the emissions of hydrogen-fueled aero-engines, and designers and engineers can quickly respond to new challenges by adjusting the relevant parameters in the model and finding the best design solution to meet the new regulations through simulation testing. Finally, the automated code generation capabilities of the MBD approach significantly reduce the need for manual coding. When faced with a new requirement or challenge, engineers can achieve rapid design iterations by directly modifying the model and then generating new code. The flexibility and adaptability of this approach allows the design process to cope more effectively with dynamic changes and uncertainties in the design and development of hydrogen-fueled aero-engines.

There are several current studies on the application of MBD in control system design. In the aerospace field, Pasareanu et al. [8], of NASA and Vanderbilt University, proposed a model-based framework for flight software analysis and testing. The framework combined MATLAB/Simulink and UML 2.0 models, along with associated code generation tools, and a discussion on the application of the framework to NASA missions was presented. Miotto et al. [9], on the other hand, developed an embedded MATLAB/UML environment specifically for flight control software of model-based design. They first defined and designed the structure and program of the control software in UML and then automatically generated MATLAB code and C source code. Similarly, McAree et al. [10] described an MBD framework for the inspection of semi-autonomous control systems for UAVs. They used Simulink models for numerical coverage testing, high-fidelity simulation, off-board execution, and, ultimately, executable deployment. In the area of civil aircraft control system design, Xu et al. [11] presented the application of MBSE methodology to cabin pressurization control system design. They used Rhapsody and Simulink software as design and simulation tools. Finally, Tulpule et al. [12] illustrated the application of MBD and statistical methods in control system validation and verification from an engineering perspective.

In the field of aero-engines, Zhang [13] applied real-time simulation technology to engine control system design and emphasized that the MBD method is the key to performing forward design of the aero-engine control system. Li [14], on the other hand, investigated solutions applicable to aero-engine demand modeling from a macro-demand perspective. Although Guo [15] and others conducted a preliminary exploration on the application of MBD methodology, modeling language, and modeling tools in the forward design of aero-engines, their research mainly focuses on the functional modeling practice of aero-engine control design for the starting scenarios, and the discussion on the full process practice of MBD for aero-engines in full state appears to be somewhat insufficient.

Although the existing MBD-based research has achieved certain results in aircraft control and aero-engines in general, most of the research in the field of aero-engine control system design still focuses on modeling and simulation. There is a relative lack of research and in-depth exploration on the complete process of aero-engine control system design based on MBD, especially in the area of hydrogen-fueled aero-engine control system design, which is urgently needed to be carried out by researchers in related fields.

To address these challenges, this study proposes an MBD-based controller design method for hydrogen-fueled turbojet aero-engines. This study comprehensively explores the advantages of this scheme in terms of design, simulation testing, code generation, Hardware-In-the-Loop verification, and system testing, and evaluates its performance and reliability in a real-world environment. It is expected that this model-based design methodology can effectively solve the problems in the design of aero-engine control systems, such as low integration, poor interaction between the controller C-code and the simulation model, and complex iterative design, and provide a powerful reference for the research and design of hydrogen-fueled turbojet aero-engines to further promote the development of green aviation.

This paper is organized as follows: Section 1 briefly introduces the topic, Section 2 briefly describes the MDB methodology, Section 3 describes the hydrogen-fueled turbojet engine model and control methodology, Section 4 describes the simulation of the MBD-based control system design for the hydrogen-fueled turbojet engine, and Section 5 describes the conclusion of the paper.

2. Materials and Methods

2.1. MBD Methods

MBD is a project development method centered around model building. This method can avoid the tedious code writing and debugging process, greatly improve the project development efficiency, and shorten the development cycle. MBD steps usually include the following points, with the implementation process needing to be combined with the actual object to produce further trade-offs:

• System Requirements Analysis: First, the system to be designed to carry out a comprehensive requirements analysis, including the system’s functional requirements, performance indicators, working environment, and interaction with other systems, is determined.
• System Modeling: Based on the requirement analysis, a mathematical model of the system is established. According to the physical characteristics and behavior of the system, choose the appropriate modeling method, such as modeling based on physical principles, control system modeling, or statistical data modeling.
• Model Validation and Verification: The system model is verified and validated to ensure the accuracy and effectiveness of the model. Simulation tools are usually used for virtual testing and analysis to simulate the behavior of the system under different operating conditions, and to compare and verify the actual data.
• Control Algorithm Design: According to the control requirements and performance indexes of the system, appropriate control strategies and algorithms are selected and integrated into the system model. Evaluate the performance and stability of the control algorithm through simulation and analysis.
• System Optimization and Iteration: Optimize and iterate the system by using the model for simulation and analysis. By adjusting the model parameters, control algorithms, or system structure, the performance, response time, energy consumption, and other aspects of the system are improved. Continuously iterate and optimize the system model until it meets the design requirements.
• Automatic Code Generation: Use automatic code generation tools to convert the model into executable code.
• Hardware Realization and Testing: Deploy the generated code to the actual hardware platform and perform actual testing and verification of the system. By comparing it with the actual physical prototype, the accuracy and practicality of the model are evaluated and necessary adjustments and improvements are made.
• System Deployment and Maintenance: Once the system passes testing and validation, it can be deployed to the actual operating environment. At the same time, it is necessary to ensure the normal operation and maintenance of the system, monitor its performance, and repair and update it as needed.

2.2. Workflow for the Control System Design of Hydrogen-Fueled Turbojet Engines Based on MBD

In the design process of aero-engines, the entire process can be divided into three parts: the design phase, the model establishment phase, and the system verification phase. An object-oriented management method is used for task allocation in each sub-stage of the design process. Figure 1 [16] illustrates the workflow of the entire design process.

3. Hydrogen-Fueled Turbojet Aero-Engine Modeling and Control Strategy

3.1. Assumptions

• The flow is constant entropy.
• The flow is one-dimensional.
• The compression factor is constant.

3.2. Hydrogen-Fueled Turbojet Aero-Engine Modeling

This paper takes the hydrogen-fueled turbojet engine shown in Figure 2 as the research object and carries out the research on the MBD-based control method of the hydrogen-fueled turbojet engine based on its existing physical model (shown in Figure 3 Engine Model). Firstly, a turbojet engine model is constructed under a Simulink environment based on the component method, which mainly includes the start-up model, steady-state model, and accessory model. Secondly, based on the characteristics of the hydrogen-fueled engine, the emission prediction model, thermoacoustic combustion instabilities model, backfire model, and hydrogen leakage model are designed in this paper.

The commonly used emission prediction models include the direct method, P3-T3 method, flow rate method, etc. The disadvantage of the direct method is that the calculation process involves the combustion chamber design parameters and fuel atomization characteristics, which are difficult to model and calculate and the model is usually only applicable to a specific combustion chamber. The disadvantage of the P3-T3 method is that some combustion-related parameters (e.g., combustion chamber flame temperature to main combustion zone equivalent ratio, etc.) cannot be measured directly. The disadvantage of the flow rate method is that it cannot take into account the effect of actual operating conditions such as performance degradation on emissions, nor can it calculate the NOx content after water injection. Therefore, this paper adopts the NOx calculation method in GasTurb and establishes a NOx emissions prediction model to realize the empirical estimation of NOx emissions [17].

Thermoacoustic combustion instabilities is a self-excited oscillation phenomenon generated by the mutual coupling of the combustion process in the combustion chamber and the sound pressure fluctuations inside the system. It can cause serious effects on the structure and performance of the combustion chamber. Thermoacoustic combustion instabilities as well as NOx emissions are related to the staging ratio, and the pressure fluctuations caused by the thermoacoustic oscillations increase with an increase in the staging ratio, and the NOx emissions gradually increase with a decrease in the staging ratio, so there exists an interval in which the NOx emissions and thermoacoustic oscillations are in the appropriate interval, and from this, the regulation plan of the staging ratio can be obtained.

A higher concentration of hydrogen in the fuel leads to a high turbulent flame speed and the risk of boundary layer flashback, which is the upstream flame The flashback is a combustion instability phenomenon that propagates upstream from the combustion chamber into the premixing zone, which is one of the most basic and important phenomena in combustion and fundamentally determines the reliability of the combustion device [18]. Considering the influence of fuel components and other factors such as the pressure in the combustion chamber on the flashback, the dimensionless Peclet number model proposed by Putnam et al. is used [19]; this is based on the critical velocity gradient model, and the model is also more universal, which can better serve as a basis for judging whether the flashback occurs or not. Using the water injection control technique, the minimum ignition energy is increased by the dilution effect, which reduces the probability of backfire occurrence and its propagation. The control of backfires at ultra-low (near-zero) NOx emissions without affecting the performance of the hydrogen-fueled spark-ignition engine was achieved.

Hydrogen molecules are very small and easier to penetrate and diffuse than other common fuels or gases, resulting in sealing performance degradation or failure. Hydrogen leakage detection and the alarm system can monitor the hydrogen concentration in real-time, in the event of reaching the alarm threshold value of the external CAN communication alarm. This paper establishes a hydrogen leakage detection and alarm system; builds a one-, two-, or three-level alarm device, at different levels of alarm information; implements different control strategies; and realizes the monitoring of hydrogen leakage and safety protection control of hydrogen leakage.

3.3. Hydrogen-Fueled Turbojet Aero-Engine Control Strategy

The characteristics of hydrogen fuel, such as high calorific value and high combustion rate, lead to a faster parameter change process and stricter safety protection requirements for hydrogen-fueled turbojet engines, which will undoubtedly result in the control strategy of the engines facing greater challenges. In this section, we focus on various aspects, such as NOx emissions, thermoacoustic shock, backfire, and hydrogen leakage, during the implementation process (shown in Figure 3 EEC).

NOx control and thermoacoustic combustion instabilities control are two key indicators for the optimal control of a hydrogen-fueled turbojet engine. Since the pressure fluctuations of NOx and thermoacoustic combustion instabilities are closely related to the segment ratio, by establishing a thermoacoustic combustion instabilities model and adopting a model-based control method (e.g., model predictive control method), it is possible to realize the control of the segment ratio, so as to achieve the stabilization of the combustion chamber pressure and keep NOx emissions within the emission standards of the International Civil Aviation Organization (ICAO). In addition, this model-based control method eliminates the effects of time delays.

For backfire control, water injection control technology is used. By injecting water vapor into the combustion chamber for dilution, the minimum ignition energy can be increased, thereby reducing the probability of backfire occurrence and propagation. This enables backfire control while achieving ultra-low (near-zero) NOx emissions without negatively affecting the performance of spark ignition in hydrogen-fueled aero-engines.

For hydrogen leakage control, a different control strategy is used. When the hydrogen concentration reaches 0.4%, the system issues a first-level alarm to alert the operator and request a timely return to the factory for inspection. When the hydrogen concentration reaches 1%, the system will issue a secondary alarm, at which time the fuel cell system will be actively shut down and a reminder will be sent to check it immediately. When the hydrogen concentration reaches 2%, the system will issue a third-level alarm, the vehicle’s high-voltage safety system will carry out power-off protection, and a reminder will be sent for immediate inspection.

In the control of rotational speed for hydrogen-fueled turbojet engines, this research adopts the traditional Proportional–Integral (PI) control as well as the Min–Max framework. In contrast to the control strategy of standard turbojet engines, the main goal of this controller is to modulate rotational speed through the adjustment of the hydrogen flow rate, consequently controlling power output and turbine outlet temperature. The control of the turbine outlet temperature is of particular importance, as it indirectly reflects the quantity of emissions. Hence, in the design, the turbine outlet temperature is restricted within a certain range to mitigate the environmental impact [20].

In the design of the acceleration schedule for hydrogen-fueled turbojet engines, the differences between them and kerosene engines must be fully considered. Firstly, to ensure that hydrogen and kerosene produce equal amounts of heat when burned, the flow rate of injected hydrogen should be set at 0.36 times the flow rate of kerosene [21], based on the high calorific value of hydrogen. Secondly, the relationship between the hydrogen flow rate and rotational speed is determined as a function, to achieve precise control and ensure the stability and predictability of the rotational speed. Additionally, the speed control law should ensure that each speed segment corresponds to a specific metering valve opening, i.e., a specific hydrogen flow rate. To achieve smooth transitions between speed segments, interpolation is used to calculate the hydrogen flow rate between two speeds.

Additionally, due to the differences in characteristics between hydrogen and fuel oil, consideration must also be made for the matching of the compressor and turbine. With the high calorific value of hydrogen, even when maintaining the same temperature before the turbine (T4), the required hydrogen flow and combustion gas mass flow will decrease. However, because the combustion products of hydrogen are mainly water and small amounts of NOx, which have a relatively small molecular mass, there is an increase in the combustion gas volume flow. This means that upon conversion to hydrogen fuel, the engine cannot operate at the design point of a kerosene engine and requires a readjustment of the compressor and turbine match. The increase in combustion gas volume flow leads to an increase in turbine power under the condition of constant T4 and air flow. To achieve matching between the compressor and turbine, three strategies are proposed: first, by adjusting the variable guide vanes (VGV) of the compressor to influence its performance; second, by increasing the pressure ratio of the compressor to balance the increase in turbine power; and third, by designing a heat exchanger to change the cooling air flow, satisfying variable heat exchange requirements, while keeping the compressor flow and temperature before the turbine stable, thereby enhancing engine power. These strategies reveal significant differences between the design schemes of hydrogen-fueled turbojet engines and kerosene engines, providing a new theoretical basis for the design and optimization of hydrogen-fueled turbojet engines [22].

4. Discussion and Findings

4.1. Design and Simulation of MBD-Based Control System for Hydrogen-Fueled Turbojet Aero-Engines

In this paper, the MBD-based hydrogen-fueled turbojet engine control system design steps are divided into the following nine specific steps: Graphical Requirement, Closed-Loop, Virtual Testing and Verification, Rapid Prototyping, Hardware-In-the-Loop (HIL) Verification, System Verification, Graphical Programming, Simulation-Based Development, and Full-Process MBD. As shown in Figure 4, the horizontal coordinate is from simulation to productization and the vertical coordinate is from initial algorithm to the implementation of the system’s uppermost requirements.

4.2. Graphical Requirement

In the study of MBD-based control methods for hydrogen-fueled turbojet aero-engines, the process of graphical requirements is crucial for building an accurate system model. First, there is a need to clearly understand and define the system-level requirements, which usually stem from the overall design objectives of the vehicle, performance metrics, safety regulations, etc. Second, the requirements are decomposed and translated into specific control system design objectives, such as system stability, response time, and energy consumption efficiency. In order to specifically illustrate the application of graphical requirements in hydrogen engines, this paper takes the hydrogen engine starting control system design as an example. Based on the overall requirements of a hydrogen engine (shown in Figure 5), the overall requirements are decomposed into the specific system design objectives (shown in Figure 6) through in-depth analysis of the physical and chemical properties of hydrogen energy. The following is a detailed description of the requirements decomposition and a theoretical analysis of each specific requirement.

• Low-Temperature Starting Performance: Because liquid hydrogen is stored and supplied at very low temperatures, engines require a specially designed low-temperature starting system, including preheating equipment and special ignition procedures. This demand decomposition stems from the storage and supply mode of liquid hydrogen, as well as the physical state changes of liquid hydrogen in the low-temperature environment.
• Safety Needs: Due to the high flammability and explosiveness of hydrogen, safety during the starting process is critical. Therefore, there is a need to design systems that can detect and deal with starting abnormalities, fuel leaks, etc., in a timely manner, as well as take special measures to ensure safety during cold starts, such as preheating systems or special combustion programs.
• Combustion Efficiency: Due to the low energy density of hydrogen, it is necessary to improve combustion efficiency to obtain the same thrust. Therefore, combustion chamber design and airflow control become critical; they need to ensure adequate combustion of hydrogen and improve combustion efficiency by precisely controlling the mixing ratio of fuel and air. This breakdown of requirements is based on the physical properties and combustion characteristics of hydrogen.
• Rapid Response: The start-up response time of hydrogen-fueled aircraft engines is an important consideration due to the potentially complex storage and supply systems for liquid hydrogen. The ignition system, fuel supply system, and turbine start should all be able to respond as quickly as possible after receiving a start command. This breakdown of requirements takes into account the storage of liquid hydrogen, the complexity of the supply system, and the dynamic responsiveness of the engine.
• Prevent Combustion Chamber Backfire: The low ignition point of hydrogen means that under certain conditions, hydrogen is prone to flashback in the combustion chamber. Therefore, systems need to be designed to prevent combustion chamber flashback. This may involve several aspects, such as the design of the combustion chamber, the control of ignition time, and the mixing ratio of fuel and air.
• Combustion Stability: Due to the fact that the physical properties of hydrogen are different from those of kerosene, hydrogen-fueled aero-engines need to be able to ensure the stability of combustion and prevent excessive engine vibration due to unstable combustion. This may involve the design of the combustion chamber, the control of the fuel supply system, and the precise control of the mixing ratio of fuel and air and other aspects.
• Precise Hydrogen Fuel Flow Control: Due to the large volume difference between liquid and gaseous hydrogen, hydrogen-fueled aircraft engines need to be able to accurately measure and control the flow of hydrogen fuel to prevent engine overshoot. This may require the development of precise hydrogen fuel flow meters as well as high-performance fuel supply systems. This need breakdown is based on the volume variation of liquid and gaseous hydrogen and the importance of controlling the flow rate accurately.

Based on the requirements decomposition, this paper uses graphical modeling tools (e.g., System Modeling Language SysML or Unified Modeling Language UML) to create the requirements model of the system in order to visually understand and represent the system requirements. After the requirements model has been created and initially validated by MATLAB/Simulink, the requirements model will be converted into an executable model with the help of a model transformation tool, such as QVT or ATL. These models can be run directly in the simulation environment to check if the model behavior meets the predefined requirements. Finally, this paper tests the converted models using a testing tool such as ModelJUnit or Modelica Test to ensure that the models accurately reflect the system requirements.

Problems involving logic-related issues, such as aero-engine state transitions, aero-engine timing monitoring, and start timing scheduling, can be realized using Stateflow for logic-related issues. Figure 7 shows the schematic diagram of the Stateflow state machine model established in this paper based on the requirements document of the starting control system; in the state machine, you can clearly see the model running the current state, the system behavior, and the basis for switching to the next state.

First, the aero-engine carries out self-test and reset, zeroes all control signals, ensures that the speed and temperature are below the parking threshold, and completes the initialization. The nitrogen regulator valve is then opened for a nitrogen purge to remove oxygen. If the valve opening or differential pressure is insufficient, the initialization state will be entered. Subsequently, the starter motor begins to carry and operate at a predetermined power to establish a stable combustion airflow. On this basis, the hydrogen regulating valve is opened at regular intervals to start supplying hydrogen in preparation for ignition. After closing the nitrogen regulating valve, the ignition unit operates at a predetermined power. If the ignition is successful and the speed and temperature reach the required thresholds, the status is transferred to successful start.

During this process, if an emergency situation occurs, such as hydrogen leakage, over-temperature, backfire, explosion, or failure to ignite successfully after a timeout, an emergency state will be activated. During the emergency state, the nitrogen regulator valve is opened and other valves, ignition devices, and starter signals are zeroed to minimize the hydrogen–oxygen mixing ratio and prevent an explosion. Once the start is successful, success will be reported and the regulation laws above the slowdown will begin to be executed. This state machine provides a general framework for the proper sequence of the engine starting process and possible emergency handling.

4.3. Closed-Loop

System-level closed-loop simulation requires a full-system model that includes a hydrogen-fueled turbojet engine. The model needs to cover all the important components of the engine, such as the compressor, combustion chamber, turbine, etc., and be able to simulate the dynamic behavior of these components. In addition, environmental and operating parameters (e.g., air pressure, temperature, flight altitude and speed) need to be injected into the model to mimic the real flight environment during the simulation.

Next, the control strategy needs to be embedded in the full system model. The control strategy is derived based on the previous requirements analysis and control design and transformed into an executable model. This process must be implemented in such a way that the control strategy interacts correctly with the engine model and the environmental parameters.

Finally, the control strategy needs to be embedded in the full-system model and tested in closed-loop simulations, as shown in Figure 6. These simulation experiments should include baseline performance tests, operating condition change tests, fault injection tests, etc., in order to be able to cover all possible flight situations. During the simulation process, various important performance parameters (e.g., engine thrust, fuel consumption, temperature, pressure, etc.) are collected to evaluate and optimize the performance of the control strategy in different situations, and to verify whether the control strategy meets all system requirements. The test results are shown in Figure 8.

To assess the precision of the model, this study converted a conventional kerosene micro turbojet engine into a single-rotor hydrogen-fueled turbojet engine. After the conversion, a series of ground-run experiments were carried out. In these experiments, multiple steady-state points were chosen as benchmarks to compare the divergence between the model predictions and the actual experimental results. The detailed comparison results are displayed in

Table 1. Comparison Between Model Simulation Output and Actual Hydrogen-Fueled Turbojet Engine Output Error.

Hydrogen Fuel Flow Rate (%)	Model Predicted Rotation Speed (%)	Relative Rotation Speed (%)	Relative Error in Rotation Speed (%)	Model Exhaust Temperature (°C)	Actual Exhaust Temperature (°C)	Relative Error in Temperature
16.8	33.7	32	5.4	491.9	448	9.8
21.7	41.2	40	3.1	558.6	534	4.6
28.6	48.6	48	1.3	614.0	599	2.5
34.3	57.3	57	0.6	657.5	651	1.0
41.5	65.2	65	0.3	691.8	689	0.4
50.8	75.1	75	0.1	709.7	709	0.1

.

From the comparison in Table 1, it is evident that the relative errors between the model predictions and actual values of the rotational speed and exhaust temperature are marginal across all ranges of hydrogen fuel flow. Notably, under high hydrogen fuel flow conditions, these errors reach an extremely low level of 0.1%, demonstrating the high accuracy of the control system based on the MBD method under these operating conditions.

However, under low hydrogen fuel flow conditions, the model prediction errors are relatively larger. This issue mainly stems from the absence of accurate characteristic curves for the compressor and the turbine. The characteristic lines used in this research were derived through scaling at the design point; thus, when operating conditions deviate from the design point, the errors in the characteristic curves increase. This deviation is reflected in the prediction errors for rotational speed and exhaust temperature, especially under low hydrogen fuel flow conditions.

Based on the established accurate model, this study designed a control system for the hydrogen-fueled turbojet engine in Section 3.3. To evaluate the performance of the controller, a series of tests were conducted in a virtual environment, validating the controller’s performance across the entire operating range from idle to maximum thrust. The relevant simulation results are shown in Figure 9. As can be seen from Figure 9, the response time from idle acceleration to maximum thrust does not exceed 10 s, there is no overshoot during the acceleration process, and the steady-state error is zero, indicating that the controller can perform tracking control well. These results provide powerful verification for the performance of this control system.

4.4. Virtual Testing and Verification

The third phase in the development of a control system for a hydrogen-fueled aero-engine focuses on virtual testing and validation. The main task of this phase was to establish a clear correlation between the control system design and the specific requirements of the hydrogen-fueled aero-engine. By using the Simulink Requirements toolbox under the MATLAB platform, the specific requirements of the hydrogen-fueled aero-engine (e.g., anti-tempering, low NOx emissions, thermoacoustic oscillation instability control, hydrogen leakage protection, etc.) are mapped one-to-one with the design elements, resulting in a clear design-requirements traceability relationship. In this process, each design decision or control strategy for a hydrogen aero-engine, such as anti-tempering control, NOx emissions control, thermoacoustic combustion instability control, leak detection and response, etc., can be directly traced back to one or more specific requirements (shown in Figure 10).

With such traceability relationships, it is possible to validate the hydrogen-fueled turbojet engine control system with extensive virtual testing using the Simulink Test Manager toolbox. In the process, each requirement is checked individually to see if it is covered by the design and if it meets the predefined performance specifications, so that possible errors or omissions in the design can be detected and resolved at an early stage. This approach not only identifies and resolves issues during the design phase, but also ensures that the hydrogen-fueled turbojet aero-engine control system meets all performance requirements and safety regulations during actual flight. This in-depth model-driven design and verification approach provides solid support for the development of complex and demanding hydrogen-fueled turbojet aero-engine control systems.

4.5. Rapid Prototyping

The primary aim of rapid prototype testing is to affirm the real-time and control performance of the control algorithm within an authentic hydrogen-fueled turbojet aero-engine setting. This is to ensure that the system design aligns with specific requirements associated with a hydrogen-fueled turbojet aero-engine.

The HIL verification platform, based on Speedgoat, is depicted in Figure 11. It primarily consists of a performance real-time machine, a mobile real-time machine, and a host computer. The performance real-time machine executes the program of the hydrogen-fueled turbojet aero-engine, the mobile real-time machine executes the controller’s program, and the host computer issues real-time commands and monitors the hydrogen-fueled turbojet aero-engine in real-time. The performance real-time machine calculates the state and output of the hydrogen-fueled turbojet aero-engine system by capturing voltage signals through the AD module and converting the system’s state and output into voltage signals through the DA module. In addition, the mobile real-time machine calculates the input of the hydrogen-fueled turbojet aero-engine system by capturing voltage signals through the AD module and converting it into voltage signals through the DA module. The host computer’s primary function is to send control command signals to the controller and to read the monitoring signals of the hydrogen-fueled turbojet aero-engine, both of which are realized through UDP. The implementation flow chart is depicted in Figure 12.

The rapid prototype used in a hydrogen-fueled turbojet aero-engine differs from that of a traditional jet engine. It incorporates a hydrogen-fueled turbojet aero-engine model that can simulate certain physical characteristics of a hydrogen-fueled turbojet aero-engine, such as backfire problems. The corresponding control methods and monitoring signals will, therefore, differ. Specifically, hydrogen burns more quickly, necessitates higher safety limit protections, and the monitoring signals must include hydrogen fuel leakage signals.

The rapid prototyping process enables the observation and evaluation of the performance of the control algorithms under simulated real operating conditions. This evaluation encompasses not only the basic performance of the control system but also the response performance and safety performance under abnormal conditions, such as hydrogen leakage. This approach allows for the early identification and resolution of potential issues, such as algorithm limitations or mismatches between the hardware and the simulation environment.

4.6. HIL Verification

HIL technology is critical in the system-level verification of complex devices. The structure and test flow of HIL are shown in Figure 13 and Figure 14, respectively. Compared to rapid prototyping, the controller in HIL is a tangible hardware object rather than a real-time simulator, thus bringing it closer to real physical conditions.

• Analyze the Simulink block diagram model and compile the model description file.

The RTW code generation process starts with an analysis of the Simulink module diagram, which mainly includes calculating simulation parameters, analyzing recursive signal width and sampling time, determining the execution order of each module in the model, and calculating the size of the working vector. RTW reads and analyzes the model file (model.mdl) and compiles it to form the model’s intermediate description file (model.rtw), which is stored in binary code and is very similar in format to the Simulink model file. It describes the hierarchical structure of the Simulink model and all relevant information about the model.

2.

The target language compiler (TLC) generates code from the Simulink model.

The target language compiler converts the description file model.rtw into an interpretive language for the specified target. The target language compiler executes a program composed of several target language compiler files, which guides the generation of the required code from the model based on the model.rtw file.

3.

Generate a custom makefile file (model.mk).

The makefile is used to guide the compiler program to compile and link the source code, main program, or user-defined modules generated from the model. RTW generates model.mk based on the system template file (System Template Makefile) system.tmf. This system template file is specifically designed for the specified target environment. It allows users to specify the compiler, compilation options, and other configurations in the generation of executable files.

4.

Generate an executable program.

The final stage of code creation is generating an executable program. This stage is an optional part of the RTW code generation process. It depends on whether the RTW option is chosen to only generate code. If the option to only generate code is selected, then the first three stages are completed. Otherwise, the makefile generated in the previous process is compiled and linked into an executable program.

Under specific testing conditions, particularly when the actual hydrogen-fueled turbojet engine fails to meet the stipulated requirements, the simulator downloads the generated model code to form a real-time operating system based on tangible hardware for testing. This HIL verification provides an effective platform for verifying the feasibility of the newly designed hydrogen-fueled turbojet engine control system.

In the HIL verification phase, hydrogen-fueled aero-engines demonstrate a significant focus on the control of pipeline leakage and nitrogen oxides (NOx) emissions. This focus markedly contrasts with traditional kerosene aero-engines, a distinction that is attributed to the unique chemical properties of hydrogen as a fuel. To accommodate these characteristics, the system has incorporated pipeline monitoring devices and exhaust pollution monitoring devices. For future system optimizations, the inclusion of devices specifically designed to monitor backfire and thermoacoustic oscillation phenomena may be considered.

Considering the higher combustion reaction rate of hydrogen compared to traditional kerosene, it is essential for the controller to possess an advanced real-time response capability to effectively manage potential emergency situations. To facilitate this, the engine electronic controller (EEC) has been integrated into the HIL system, thereby enabling precise measurement and evaluation of the controller’s real-time performance. This integration imposes more stringent performance requirements on the controller compared to those used in conventional kerosene aviation engines. These highlighted differences underscore the unique challenges and considerations when dealing with hydrogen-fueled aero-engines during the HIL phase, as opposed to their kerosene-fueled counterparts.

In the early phases of a project, HIL verification can confirm that the design of a hydrogen-fueled turbojet engine meets specific requirements, including key metrics such as high-efficiency combustion and low emissions, and rapidly iterate and optimize the design and implementation methodology in a realistic real-time operating system. By collecting and analyzing test results from hydrogen-fueled turbojet engines, it becomes possible to scrutinize the operational performance of the control algorithms on tangible hardware, as well as assess the impact of potential hardware failures on system performance. This testing methodology aids in identifying potential system issues at an early stage, which significantly reduces the cost of subsequent testing and modifications, and is beneficial for developing and optimizing control systems for hydrogen-fueled turbojet engines.

Empirical validation conducted on the Hardware-In-the-Loop (HIL) verification platform elucidates the performance characteristics of the controller, with pertinent results graphically detailed in Figure 15 and Figure 16. Despite the presence of certain system noise, the HIL test results exhibit a conspicuous consistency with the preconducted virtual simulation results. This uniformity not only validates the accuracy of the simulation model, but also affirms its capability to effectively predict the response of the actual hardware system.

4.7. System Verification

According to the V-shaped development model, the unit test and integration test phases have been successfully completed, and the current research progresses to the system validation phase, i.e., the comparison and confirmation of top-level requirements. In this phase, the core task is to fully validate the hydrogen-fueled turbojet engine control system to ensure that it meets the predefined requirements and performance targets.

The validation work includes the performance examination of the hydrogen-fueled turbojet engine control system under various operating conditions, with particular attention to its operational performance in conventional and extreme environments. Considering the unique temperature and pressure sensitivity of hydrogen engines, the tests will be conducted in a specially designed test environment.

Key performance indicators such as system stability, response time, fuel efficiency, and performance under various fault conditions will be compared with the predetermined requirements to assess whether the system meets the predetermined performance targets. Special attention is paid to the fact that due to the characteristics of the hydrogen-fueled turbojet engine, the performance of the system under extreme conditions, such as high pressure, low temperature, and high rotational speed, will be scrutinized.

To ensure engine safety, a variety of possible failures are also included in the simulation, including interruption of hydrogen fuel supply, abnormal hydrogen pressure, control algorithm errors, sensor failures, etc. Under these fault conditions, the control system’s fault recognition and handling strategies, as well as its ability to return to normal conditions, will be rigorously verified.

Upon completion of the performance validation, the results of the actual system performance against the preset requirements will be analyzed in detail to confirm that all preset requirements have been met. If there are unmet requirements, the system design will be revisited and necessary adjustments will be made to the hydrogen fuel supply system, control algorithms, or sensors.

4.8. Productization

Productization is the ultimate goal of the research process, and key aspects include automated code generation at the algorithmic level and simulation-based development at the system level. At the algorithmic level, the automatic code generation transforms the product from the design stage directly into the executable stage, in a way that significantly improves the development efficiency and reduces the possibility of coding errors. This ability to rapidly iterate is especially important in the development of hydrogen-fueled aero-engines, where there are many challenges and where the industry has not yet developed mature solutions. When design problems are encountered, the model can be directly modified and the code immediately regenerated, and the consistency of the model with the code can be easily verified through equivalence testing.

At the system level, a simulation-based development strategy is critical. It allows the system to be validated and optimized in simulated real-world operating environments and failure scenarios. Especially when simulating the high reactivity and low-flashpoint characteristics of hydrogen fuels, it is possible to anticipate and solve possible problems in advance, reducing time, cost, and the risk of actual hardware testing.

Overall, the productization phase is a conversion process from theoretical research to practical operation. Automatic code generation and simulation-based development have made the process of realizing the MBD-based control method for hydrogen-fueled aero-turbine engines more efficient, providing a solid foundation for the advancement of aero-engine control technology, especially for the hydrogen-energy aero-engine.

5. Conclusions

This paper presents an in-depth study of MBD-based control methods for hydrogen-fueled turbojet engines. The study reveals the unique advantages of MBD in dealing with new problems arising from the design of control systems for hydrogen-fueled engines, which is of great engineering significance for the further development of future hydrogen-fueled turbojet engines. Specific conclusions are summarized below:

• This study validates the effectiveness of the MBD method in designing control systems for hydrogen-fueled turbojet engines. Across all ranges of hydrogen fuel flow, the error between the model prediction and the actual value is remarkably low, reaching only 0.1% under high flow conditions. Furthermore, the control system exhibits exceptional performance, no overshoot, quick response, absence of steady-state error, and effective tracking control, thereby further enhancing the overall performance of the hydrogen-fueled turbojet engine.
• The use of MBD-based control system design methods can significantly shorten the development cycle and reduce the complexity of the development process. The design and optimization of a hydrogen-fueled engine requires more complex considerations than a conventional kerosene engine, such as NOx emissions, thermoacoustic combustion instabilities, tempering anomalies, hydrogen fuel storage and transfer, etc. The MBD methodology provides a quick solution to these new and complex problems, as well as corrections and optimization strategies for these complex new problems, thereby reducing the cost of trial and error in the design of hydrogen-fueled engine control systems.

For future research, we will further deepen and refine our work in several areas:

• Model accuracy improvement: For the problem of large errors between the hydrogen-fueled aero-engine model and the real engine under small fuel flow rate, future research should be further deepened and the model should be improved through theoretical research and experimental validation to more accurately reflect the behavior of the hydrogen-fueled engine under different fuel flow rates.
• Empirical research and optimized application of MBD methods: Although MBD methods can potentially improve R&D efficiency and shorten iteration cycles, their specific effects need to be verified through a large number of actual comparisons. At the same time, the application of MBD methods in the design of hydrogen fuel aero-engines needs to be further optimized to improve research efficiency and shorten iteration cycles. This includes, but is not limited to, improving MBD application strategies, developing more effective tools and methods, and comprehensively assessing their performance under different circumstances.