Aero-engine fuel metering system high-order model reduction analysis method and application

Abstract

This invention discloses a method and application for reducing the order of a high-order model in an aero-engine fuel metering system, which reduces the complexity of system modeling and control design while maintaining dynamic accuracy. Based on the working principle and structural characteristics of the fuel metering system, this method constructs a nonlinear high-order dynamic model covering key components such as electro-hydraulic servo valves, fuel metering valves, and connecting chambers. Linearization is then performed at the steady-state point under typical operating conditions to obtain a high-order linear model in state-space form. Through frequency domain analysis, the dominant dynamic frequency band of the system is extracted, and model reduction is performed accordingly to construct a low-order simplified model, ensuring high fidelity of response characteristics within the target frequency band. This invention significantly reduces the complexity of fuel metering system modeling and control system design, improves control system design efficiency, and is applicable to aero-engine control system design, parameter tuning, and model predictive control, possessing significant engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine control technology, and relates to dynamic modeling and control of fuel metering systems. Specifically, it relates to a method for reducing the order of a high-order model of an aero-engine fuel metering system and its application. Background Technology

[0002] In control engineering, almost all control systems are high-order systems, that is, systems described by high-order differential equations. Due to the difficulty in solving high-order systems and the complexity of performance analysis, it is usually necessary to simplify high-order systems into low-order systems (first- or second-order systems) through order reduction methods to reduce system complexity while retaining their main dynamic characteristics. Then, the simplified first- or second-order systems are used to approximate the high-order system to analyze its performance. Through order reduction, the interpretability and computational efficiency of the model can be significantly improved, which helps to quickly carry out controller design, system simulation, and frequency domain analysis.

[0003] The fuel metering system of an aero-engine comprises numerous interconnected components. For example, the main fuel system of an aero-engine typically consists of electro-hydraulic servo valves, main fuel metering valves, differential pressure valves, constant pressure valves, locking valves, return valves, booster valves, gear fuel pumps, and LVDTs (Low-Level Drives). This fuel system is a typical high-order complex system. To obtain performance evaluation indicators for this fuel system, a linearized fuel system must be obtained through linearization methods. Due to the difficulty in analyzing and solving the system performance of high-order fuel systems, a method of reducing the order of the high-order model of the aero-engine fuel metering system is generally used to analyze its performance in order to facilitate the analysis and understanding of its time-domain and frequency-domain characteristics. However, existing order reduction methods (such as Chinese patents CN108919638B and CN117236104B) often lack specialized processing for the characteristics of aero-engine fuel metering systems, making it difficult to effectively reduce the system order while ensuring accuracy. Furthermore, there is a lack of systematic methods for evaluating the consistency between the reduced-order model and the original high-order model within a specific frequency range.

[0004] In summary, as a high-order complex system, the fuel metering system of aero-engines presents a pressing technical problem in the field of aero-engine fuel control: how to effectively reduce its order and ensure that the reduced model accurately reflects the dynamic characteristics of the original system within the bandwidth of the control system. Summary of the Invention

[0005] (I) Purpose of the Invention

[0006] To address the aforementioned deficiencies and shortcomings of existing technologies, this invention aims to provide a method and application for reducing the order of a high-order model of an aero-engine fuel metering system. By constructing a nonlinear high-order model of the fuel system and combining linearization techniques with the reduction analysis method, the complex high-order fuel system is simplified into a low-order linear model. Through frequency domain analysis and comparison, it is ensured that the simplified low-order model can accurately reflect the dynamic characteristics of the original high-order system within the bandwidth frequency range of the aero-engine control system, thereby significantly reducing the complexity of system analysis and control design and improving the design efficiency of the aero-engine fuel metering system.

[0007] (II) Technical Solution

[0008] To achieve the objective of this invention and solve its technical problems, the present invention adopts the following technical solution:

[0009] The first objective of this invention is to provide a method for reducing the order of a high-order model of an aero-engine fuel metering system. This method is used to model, linearize, and reduce the order of a high-order dynamic model of an aero-engine fuel metering system, thereby reducing the complexity of control design and preserving the dynamic characteristics of key frequency bands. The method, when implemented, includes at least the following steps:

[0010] SS1. Construct a nonlinear model of the fuel metering system:

[0011] Based on the working principle and design requirements of the fuel metering system, and combined with the system's internal actuation response, flow regulation and pressure coupling characteristics, a high-order nonlinear dynamic model is constructed to describe the nonlinear coupling relationship between the system's control input, state variables and output.

[0012] SS2. Linearization of the fuel metering system model:

[0013] Centered on the preset steady-state operating point, the constructed nonlinear high-order model is linearized using the Taylor series expansion method to generate a high-order linear model of the fuel metering system. The state matrix, input matrix, output matrix, and transfer matrix are determined by the partial derivatives of the model with respect to the state variables and control inputs, which are used to characterize the approximate linear response characteristics of the system under small disturbance conditions.

[0014] SS3. Frequency Domain Characteristic Analysis and Response Verification:

[0015] Frequency domain characteristic analysis is performed on the generated high-order linear model of the system to obtain the Bode plot frequency response curve of the system. Combined with the dominant dynamic frequency band of the control system (such as 1-30Hz), the amplitude and phase frequency characteristics of the high-order linear model in different frequency bands are analyzed to verify its dynamic accuracy in the target frequency band, and to provide a basis for the rationality evaluation of model reduction and control system design.

[0016] SS4. Model order reduction and structural simplification:

[0017] While ensuring that the dominant dynamic characteristics of the system remain unchanged, the linear high-order model is reduced in order based on the frequency domain analysis results to establish a simplified low-order model that can accurately reflect the dynamic behavior of the target frequency band. The simplified low-order model approximates the frequency response characteristics of the original high-order system with the minimum order, thereby reducing system complexity and improving the practicality and controllability of the model.

[0018] SS5. Simplified model validity verification:

[0019] The simplified model after order reduction was compared with the original high-order model under multiple operating conditions to confirm that its amplitude-frequency and phase-frequency characteristics in the dominant dynamic frequency band are highly consistent with those of the original high-order model. This ensures that the order reduction process did not introduce system distortion or performance degradation, and that it has engineering feasibility and promotion value.

[0020] The second objective of this invention is to provide an aircraft engine fuel metering system, the design of which is based on the aforementioned high-order model reduction analysis method for aircraft engine fuel metering systems.

[0021] (III) Technical Effects

[0022] Compared with the prior art, the high-order model reduction analysis method and application of the aero-engine fuel metering system of the present invention have the following beneficial and significant technical effects:

[0023] (1) This invention introduces a modeling mechanism based on the combination of nonlinear modeling and steady-state linearization to establish a high-order nonlinear system model covering the dynamic characteristics of key components such as electro-hydraulic servo valves and metering valves. On this basis, a first-order Taylor expansion method is used to obtain the high-order linear state space expression of the system, thereby enabling a comprehensive and accurate characterization of the dynamic response characteristics of the fuel metering system under small disturbance conditions, significantly improving the modeling accuracy and system observability in system frequency domain analysis and control system design.

[0024] (2) Based on the frequency domain characteristic analysis results, this invention employs a reduction-order method combining dominant mode preservation and response error control to construct a low-order model with a simple structure and highly faithful dynamic characteristics. The model's fidelity within the dominant dynamic frequency band is ensured through various verification methods, including frequency response curves and step response curves. This method can flexibly adapt to the dynamic characteristic requirements of different types of aero-engine fuel systems, significantly reducing the complexity and computational burden of control law design, and improving the model's adaptability and practicality in engineering controller parameter matching, simulation prediction, and control algorithm deployment. Attached Figure Description

[0025] The accompanying drawings, which form part of this specification, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. Hereinafter, embodiments of the invention will be described in detail with reference to the accompanying drawings, wherein:

[0026] Figure 1 The overall flowchart of the method for reducing the order of a high-order model of an aero-engine fuel metering system provided by the present invention is shown below.

[0027] Figure 2 This is a schematic diagram of the Amesim software modeling used in the embodiments of the present invention;

[0028] Figure 3 The graph shows the frequency response characteristics of different order models in this invention at typical operating points, displaying the amplitude and phase frequency response curves of the Amesim simulation model (19th order), the simplified Amesim model (6th order), the mathematically derived model (6th order), and the first-order reduced model in the frequency domain from 0.1Hz to 500Hz. Detailed Implementation

[0029] This invention aims to provide a method for order reduction analysis of high-order models of aero-engine fuel metering systems and its application. This method is used to model, linearize, and reduce the order of high-order dynamic models of aero-engine fuel metering systems, thereby reducing control design complexity while preserving dynamic characteristics in key frequency bands. This embodiment combines Amesim simulation and mathematical derivation techniques. By comparing the frequency domain characteristics of a 19th-order Amesim model, a 6th-order simplified model, and a 1st-order mathematical model, the effectiveness of the order reduction method is verified. The technical solution is described in detail below with reference to the accompanying drawings. The described embodiments are some, but not all, embodiments of this invention, and are exemplary, intended to explain the invention, and should not be construed as limiting the invention.

[0030] like Figure 1 As shown in the embodiment of the present invention, the method for reducing the order of a high-order model of an aero-engine fuel metering system mainly includes the following steps during implementation:

[0031] SS1. Construct a nonlinear model of the fuel metering system:

[0032] Based on the physical structure, working principle, and design requirements of the fuel metering system, and considering the system's internal actuation response, flow regulation, and pressure coupling characteristics, a high-order nonlinear dynamic model is established. This model considers multiple physical interactions, including actuators, electro-hydraulic servo systems, and fuel chamber flow coupling, to describe the nonlinear coupling relationships between the system's control inputs, state variables, and outputs. State equations can be used to describe this model. The system is represented by the general form y = g(x,u) for output equation. It is used to characterize the nonlinear dynamic relationship between the system control input u (mainly electro-hydraulic control signals, such as input current, voltage or command signals) and the state variables x (including internal state variables such as servo valve displacement, metering valve displacement, system chamber pressure, etc.) and the system output y (representing key physical quantities that can be measured or used for control feedback, such as main fuel flow rate Q, fuel pressure P, valve opening or displacement feedback S, etc.). f(·) and g(·) are both nonlinear mapping functions. The function f(·) describes the nonlinear dynamic relationship of the system's internal state changing with time, covering factors such as the coupling dynamic equations between various components of the system, actuator characteristics and chamber pressure response. The function g(·) is the nonlinear output mapping function of the system, used to associate the internal state with the output signal. Its structure can contain static mapping terms and dynamic coupling terms.

[0033] In constructing high-order nonlinear dynamic models, this embodiment of the invention combines two technical approaches: Amesim simulation and mathematical derivation. One approach is multiphysics simulation based on Amesim software (such as...). Figure 2 As shown, a complete system simulation model is constructed, including sub-modules such as electro-hydraulic servo valve, metering valve and multiple cavities, to obtain a high-order nonlinear model with 19 state variables; secondly, the relevant nonlinear state equations are derived through mathematical derivation modeling path.

[0034] Specifically, when constructing a high-order nonlinear dynamic model based on key components of the fuel metering system using mathematical derivation methods, the core metering system composed of the electro-hydraulic servo valve and the metering valve is considered. The system can select the servo valve input current I as the control variable and the metering valve spool displacement as the observed variable. The system state includes the servo valve, the metering valve spool displacement, and the pressure in each cavity. The coefficients in the state-space equations are determined by differentiating the fundamental equations governing the fuel system. Specifically, when establishing corresponding nonlinear differential equations for different components to characterize their dynamic behavior, the dynamic response of the electro-hydraulic servo valve is modeled using a second-order inertial oscillation element, and its displacement response relationship is expressed as follows: Where x1 is the valve core displacement, ω m Let ξ be the natural angular frequency of the servo valve. m I is the damping ratio of the servo valve, and I is the input current controlling the valve core displacement. m To account for the input current, this model can effectively describe the dynamic response characteristics of the electro-hydraulic servo valve under input disturbances; the motion differential equation of the metering valve is expressed as the algorithm formula. Where x2 is the valve core displacement of the fuel valve, m is the equivalent mass of the valve, and ∑F is the total force on the valve; the differential pressure equations for each chamber are expressed as follows: Where p is the chamber fuel pressure, β is the fuel bulk modulus, V is the effective volume of the chamber, and ∑Q is the total flow rate through the chamber.

[0035] SS2. Linearization of the fuel metering system model:

[0036] Centered on the preset steady-state operating point, the constructed nonlinear high-order model is linearized using the Taylor series expansion method to generate a high-order linear model of the fuel metering system. The state matrix, input matrix, output matrix, and transfer matrix are determined by the partial derivatives of the model with respect to the state variables and control inputs, which are used to characterize the approximate linear response characteristics of the system under small disturbance conditions.

[0037] In this embodiment of the invention, the preset steady-state operating point is the typical operating state point of the engine within a specific flight envelope (for example, centered on the 24th steady-state operating point, corresponding to the medium-to-high power cruise condition under stable voltage and current conditions). At this operating point, a first-order Taylor expansion is performed on the nonlinear high-order model, ignoring the higher-order nonlinear terms, to obtain the linearized state-space expression of the system. and Where: δx = x - x0 represents the small perturbation of the state variable, and x0 is the steady-state state vector; δu = u - u0 represents the control input perturbation, and u0 is the steady-state input vector; δy = y - y0 represents the output variable perturbation, and y0 is the steady-state output vector; A, B, C, and D represent the state, input, output, and transfer matrix, respectively.

[0038]

[0039] Where f is the nonlinear state equation and g is the nonlinear output equation, and the second-order and higher-order terms in the Taylor series expansion are ignored during the calculation. The parameters at the steady-state point are determined by dynamic sensitivity analysis to ensure the effectiveness of the linearized model under small perturbation conditions.

[0040] SS3. Frequency Domain Characteristic Analysis and Response Verification:

[0041] Frequency domain characteristic analysis is performed on the generated high-order linear model of the system to obtain the Bode plot frequency response curve of the system. Combined with the dominant dynamic frequency band of the control system (such as 1-30Hz), the amplitude and phase frequency characteristics of the high-order linear model in different frequency bands are analyzed to verify its dynamic accuracy in the target frequency band, and to provide a basis for the rationality evaluation of model reduction and control system design.

[0042] In this embodiment of the invention, the frequency domain analysis uses the Bode plot method to analyze the high-order linear model. The system frequency response curve is plotted in the logarithmic amplitude and phase frequency coordinate system to determine the dynamic characteristics of the system in the frequency range of 0.1-500Hz. The focus is on analyzing the frequency response characteristics of the system in the 1-30Hz frequency band, which covers the main operating bandwidth range and its extension range of the traditional engine fuel control system.

[0043] Specifically, this fuel case study uses the parameters of the 24th steady-state operating point for linearization. Therefore, it is necessary to define the parameters in the 6th-order state matrix derived from the 24th steady-state operating point. By performing frequency domain analysis on the 19th-order Amesim model, the 6th-order simplified Amesim model, the derived 6th-order mathematical model, and the 1st-order simplified mathematical model, and comparing the results, the following was obtained: Figure 3 The Bode plot shown is from Figure 3 It can be seen that:

[0044] Within the frequency range of 1 to 30 Hz, the frequency response curves of all models have a very high degree of overlap. This frequency band covers the bandwidth of the control system, indicating that the mathematical model derived during system design can accurately describe the dynamic behavior of the system, and the dynamic response of the fuel unit can be simplified to a first-order inertial element.

[0045] It should also be noted that differences between different models begin to emerge in the 30–500 Hz frequency band. Within this range, the first-order linearized system (mathematical model) still exhibits the characteristics of a first-order system, while the other three models show characteristics of a second-order system. This indicates that if a simple first-order or third-order model is required to accurately reflect the system characteristics in this frequency band, it may not be able to accurately describe the dynamic behavior of the system. Therefore, when designing control systems for high-frequency responses, more complex models are needed to more accurately reflect the actual characteristics of the system.

[0046] Frequency domain analysis of the fuel system shows that the frequency response curves of all models have a very high degree of overlap in the 1–30 Hz frequency range. This frequency band covers the bandwidth of the control system, indicating that the derived mathematical models can accurately describe the dynamic behavior of the system within this frequency range. In the 30–500 Hz frequency range, differences between different models begin to appear, and simple, low-order models may not be able to accurately describe the dynamic behavior of the system. Therefore, when designing control systems for high-frequency responses, more complex models are needed to more accurately reflect the actual characteristics of the system.

[0047] SS4. Model order reduction and structural simplification:

[0048] While ensuring that the dominant dynamic characteristics of the system remain unchanged, the linear high-order model is reduced in order based on the frequency domain analysis results to establish a simplified low-order model that can accurately reflect the dynamic behavior of the target frequency band. The simplified low-order model approximates the frequency response characteristics of the original high-order system with the minimum order, thereby reducing system complexity and improving the practicality and controllability of the model.

[0049] In this embodiment of the invention, for the basic control bandwidth (0–2 Hz), the simplified low-order model is constructed as a first-order system, whose transfer function is represented as G(s) = 1 / (Ts+1), where s is the Laplace operator and T is the system time constant, used to characterize the inertial delay characteristics of the system's response speed to disturbances or control commands. This time constant is determined by analyzing the amplitude and phase frequency characteristics of the original high-order system in the dominant dynamic frequency band, ensuring that the dynamic response of the simplified first-order system in this frequency band is highly consistent with the original high-order system. The time constant T is determined in one of two ways: Method 1: Based on the analysis of the frequency response curve of the high-order system's Bode plot, the amplitude and phase frequency characteristics in the dominant dynamic frequency band are extracted, and the T value is determined through curve fitting, so that the frequency response characteristics of the first-order system match the original high-order system to the greatest extent in the target frequency band; Method 2: An experimental method is used, by applying a known input signal to an actual fuel metering system and recording the output response, using system identification technology to analyze the input-output data relationship, calculating the time constant T value that most accurately characterizes the system's dynamic characteristics, and verifying its reliability and accuracy.

[0050] For high-frequency active control, when the first-order system cannot meet the accuracy requirements, a second-order or third-order reduced-order system can be selected. The second-order system is... Third order is K is the static gain parameter, representing the steady-state output level under unit amplitude input. T1, T2, and T3 are all time constants used to characterize the high-frequency resonant dynamics of the servo valve.

[0051] SS5. Simplified model validity verification:

[0052] The simplified model after order reduction was compared with the original high-order model under multiple operating conditions to confirm that its amplitude-frequency and phase-frequency characteristics in the dominant dynamic frequency band are highly consistent with those of the original high-order model. This ensures that the order reduction process did not introduce system distortion or performance degradation, and that it has engineering feasibility and promotion value.

[0053] SS6. Control System Design and Engineering Applications:

[0054] Based on the simplified low-order model after validity verification, we carry out control law modeling and parameter design for the fuel metering system. The resulting control law meets the requirements of response speed, stability and robustness while covering the dominant dynamic frequency band, ensuring the dynamic performance and precise control capability of the fuel system under typical operating conditions.

[0055] As a preferred option, the designed control law is optimized for the main fuel control loop bandwidth of 0-2Hz (approximately 10 rad / s). This bandwidth range includes the dominant dynamic characteristics of the engine. The control law design adopts a parameterization method based on a first-order simplified model, and its actual control effect on the original high-order system is verified through simulation to ensure that the control performance meets the requirements of steady-state accuracy and dynamic response.

[0056] The objectives of this invention have been fully and effectively achieved through the above embodiments. Those skilled in the art will understand that this invention includes, but is not limited to, the contents described in the accompanying drawings and the specific embodiments described above. Although the invention has been described with reference to what is currently considered the most practical and preferred embodiments, it should be understood that the invention is not limited to the disclosed embodiments, and any modifications that do not depart from the functional and structural principles of the invention will be included within the scope of the claims.

Claims

1. An aeroengine fuel metering system high order model reduction analysis method, characterized in that, It should include at least the following steps: SS1. Based on the working principle and design requirements of the fuel metering system, and combined with the system's internal actuation response, flow regulation and pressure coupling characteristics, a high-order nonlinear dynamic model is constructed to describe the nonlinear coupling relationship between the system's control input, state variables and output quantities. SS2. Using the preset steady-state operating point as the center, the constructed nonlinear high-order model is linearized by the Taylor series expansion method to generate a high-order linear model of the fuel metering system. Its state, input, output and transfer matrix are determined by the partial derivatives of the model with respect to the state variables and control inputs. SS3. Perform frequency domain characteristic analysis on the generated high-order linear model of the system, obtain the Bode plot frequency response curve of the system, and analyze the amplitude and phase frequency characteristics of the high-order linear model in different frequency bands in combination with the dominant dynamic frequency band of the control system to verify its dynamic accuracy in the target frequency band. The frequency domain characteristic analysis uses the Bode plot method to analyze the high-order linear model, plots the system frequency response curve in the logarithmic amplitude and phase frequency coordinate system, determines the dynamic characteristics of the system in the frequency range of 0.1-500Hz, and focuses on analyzing the frequency response characteristics of the system in the 1-30Hz frequency band. SS4. While ensuring the dominant dynamic characteristics of the system remain unchanged, the linear high-order model is reduced in order based on the frequency domain analysis results to establish a simplified low-order model that accurately reflects the dynamic behavior of the target frequency band. This simplified low-order model approximates the frequency response characteristics of the original high-order system with its minimum order, and is constructed as a first-order system with the transfer function expressed as follows: ,in s For the Laplace operator, T The system time constant is used to characterize the inertial delay characteristics of the system's response speed to disturbances or control commands, and is determined by analyzing the amplitude-frequency and phase-frequency characteristics of the original high-order system in the dominant dynamic frequency band. SS5. Compare the frequency response and dynamic behavior of the simplified model after order reduction under multiple operating conditions to confirm that its amplitude-frequency and phase-frequency characteristics in the dominant dynamic frequency band are highly consistent with the original high-order model, ensuring that the order reduction process does not introduce system distortion or performance degradation. SS6. Control System Design and Engineering Application: Based on the simplified low-order model after effectiveness verification, the control law modeling and parameter design of the fuel metering system are carried out to ensure that the obtained control law meets the requirements of response speed, stability and robustness while covering the dominant dynamic frequency band, thus ensuring the dynamic performance and precise control capability of the fuel system under typical operating conditions.

2. The aero-engine fuel metering system high-order model reduction analysis method of claim 1, wherein, In step SS1, the high-order nonlinear dynamic model is constructed based on key components of the fuel metering system. These key components include at least an electro-hydraulic servo valve, a main fuel metering valve, and their connecting chambers. Specifically, the dynamic response of the electro-hydraulic servo valve is modeled using a second-order inertial oscillation, and its displacement response relationship is expressed as follows: ,in x 1 represents the valve core displacement. ω m This is the natural angular frequency of the servo valve. ξ m For the damping ratio of the servo valve, I For input current, I m The reference input current; the differential equation of motion of the metering valve is expressed as the algorithm formula. ,in x 2 represents the valve core displacement of the fuel valve. m For the equivalent mass of the valve, ∑ F The sum of forces acting on the valve; the differential pressure equations for each connecting chamber are expressed as follows: ,in p The chamber fuel pressure, β The bulk modulus of fuel oil. V For the effective volume of the chamber, ∑ Q This represents the total flow rate through the cavity.

3. The aero-engine fuel metering system high-order model reduction analysis method according to claim 1 or 2, characterized in that, In step SS1, the higher-order nonlinear dynamic model is constructed in the form of state equations and output equations, wherein the state equations are: The output equation is Used to characterize system control input u With state variables x and system output y The nonlinear dynamic relationship between them f (·) g (·) are all nonlinear mapping functions.

4. The method for reducing the order of a high-order model of an aero-engine fuel metering system according to claim 3, characterized in that, In step SS2, the preset steady-state operating point is the typical operating state point of the engine within a specific flight envelope. At this operating point, a first-order Taylor expansion is performed on the nonlinear high-order model, ignoring higher-order nonlinear terms, to obtain the linearized state-space representation of the system. and ,in: δx = x - x 0 represents a small perturbation of the state variable. x 0 represents the steady-state vector; δu = u - u 0 indicates the amount of control input disturbance. u 0 represents the steady-state input vector; δy = y - y 0 indicates the perturbation amount of the output variable. y 0 represents the steady-state output vector; A, B, C, and D represent the state, input, output, and transfer matrix, respectively, where: in f It is a nonlinear state equation. g The output equation is nonlinear, and the second-order and higher-order terms in the Taylor series expansion are ignored during calculation to ensure the effectiveness of the linearized model under small perturbation conditions.

5. The aero-engine fuel metering system high-order model reduction analysis method of claim 1, wherein, In step SS4, the time constant T is determined by one of the following two ways: Method 1: Based on the analysis of the frequency response curves of the Bode plot of the high-order system, the amplitude and phase frequency characteristics within the dominant dynamic frequency band are extracted, and the results are determined through curve fitting. T The value is set such that the frequency response characteristics of the first-order system match those of the original higher-order system to the greatest extent possible within the target frequency band. Method 2 involves an experimental approach. By applying a known input signal to an actual fuel metering system and recording the output response, the relationship between the input and output data is analyzed using system identification technology. The time constant T value, which most accurately characterizes the dynamic characteristics of the system, is then calculated, and its reliability and accuracy are verified.

6. The method for reducing the order of a high-order model of an aero-engine fuel metering system according to claim 1, characterized in that, In step SS4, the order of the model after order reduction is flexibly selected for different types of aero-engine fuel metering systems. When a first-order system cannot meet the accuracy requirements, a second- or third-order system is selected. A second-order system is represented as... The third-order system is ,in K Here, represents the system's static gain parameter, indicating the steady-state output level under unit amplitude input. T 1 , T 2. T All three are time constants.

7. The method for order reduction analysis of a high-order model of an aero-engine fuel metering system according to claim 1, characterized in that, In step SS6, the designed control law is optimized for the main fuel control loop bandwidth of 0-2 Hz. This bandwidth range includes the dominant dynamic characteristics of the engine. The control law design adopts a parameterization method based on a first-order simplified model, and its actual control effect on the original high-order system is verified by simulation to ensure that the control performance meets the requirements of steady-state accuracy and dynamic response.

8. A fuel metering system for an aircraft engine, characterized in that, Its design is based on the high-order model reduction analysis method of the aero-engine fuel metering system described in any one of claims 1 to 7.

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