WO2021223461A1 - 一种变循环发动机机载实时模型的部件级无迭代构建方法 - Google Patents

一种变循环发动机机载实时模型的部件级无迭代构建方法 Download PDF

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WO2021223461A1
WO2021223461A1 PCT/CN2021/070665 CN2021070665W WO2021223461A1 WO 2021223461 A1 WO2021223461 A1 WO 2021223461A1 CN 2021070665 W CN2021070665 W CN 2021070665W WO 2021223461 A1 WO2021223461 A1 WO 2021223461A1
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model
component
variable
lpv
cycle engine
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French (fr)
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鲁峰
李志虎
黄金泉
周文祥
尉询楷
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南京航空航天大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F11/00—Error detection; Error correction; Monitoring
    • G06F11/30—Monitoring
    • G06F11/34—Recording or statistical evaluation of computer activity, e.g. of down time, of input/output operation ; Recording or statistical evaluation of user activity, e.g. usability assessment
    • G06F11/3447—Performance evaluation by modeling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

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  • the invention relates to the field of aeroengine modeling and simulation, in particular to a component-level non-iterative construction method of an airborne real-time model of a variable cycle engine.
  • variable-cycle engine Due to its adjustable geometric components, the variable-cycle engine can change the thermal cycle of the engine under different flight conditions to obtain the best flight performance.
  • the basic structure of the double-external culvert variable-cycle engine is shown in Figure 1. Typical working mode.
  • Single culvert mode close the mode selection valve, reduce the area of the front and rear adjustable area Bypass Injector (VABI), so that almost all the air flow through the front fan flows through the core drive fan and high pressure air Only a small part of the flow is allowed to pass through the external duct to cool the tail nozzle.
  • VABI adjustable area Bypass Injector
  • Double culvert mode open the mode selection valve, increase the area of the front and rear adjustable duct ejectors, increase the air flow of the front fan, and part of the air flow through the CDFS CDFS (Core Drive Fan Stage)
  • the CDFS duct flows into the main outer culvert, and the other part flows into the compressor.
  • the engine duct ratio is the largest, which can reduce the fuel consumption rate and is suitable for subsonic flight.
  • variable-cycle engine has a harsh working environment and is more complex than conventional engines. Its safety and reliability requirements are very high.
  • the design of aero engine control system, engine fault diagnosis, and resolution depend on the aero engine model. In airborne applications, not only the accuracy of the engine but also the real-time performance of the engine model must be considered.
  • Nonlinear Component Level Model (NCLM) and linearized state variable models.
  • NCLM Nonlinear Component Level Model
  • the non-linear component-level model is established based on the principle of engine aerodynamics and thermodynamics through analytical methods, with high accuracy and wide adaptability, but the real-time performance is not high enough.
  • the engine state variable model is based on the non-linear component-level model of the engine, linearized at a certain steady state point to establish a state variable model of the relationship between engine input and output, and a large number of state variable models constitute the engine LPV model.
  • the linear model has a small amount of calculation and good real-time performance, but there are secondary modeling errors.
  • the present invention combines the non-linear component-level general model of the variable-cycle engine with the traditional LPV modeling method, uses the various component models of the variable-cycle engine and the established LPV model about the speed and pressure ratio, and proposes an on-board real-time model of the variable-cycle engine There is no iterative construction method at the component level, which improves the real-time performance of the engine model with a small loss of accuracy.
  • the technical problem to be solved by the present invention is to provide a variable cycle engine model with higher real-time performance and accuracy in view of the defects of the background technology, and solve the real-time inadequacy of the original non-linear component-level model, and the linear model error is relatively low. Big problem.
  • Step A on the basis of the component-level model of the variable cycle engine, design the non-iterative solution algorithm of the nonlinear co-working equations in the form of LPV (Linear Parameter Varying), and establish the rotor acceleration equation matching with the LPV state transition equation Relationship, LPV output equations establish a component-level flow balance relationship, and solve to obtain state parameters such as engine speed and pressure ratio;
  • LPV Linear Parameter Varying
  • Step B) using the LPV non-iterative solution method to construct the relationship between the component parameters of the variable-cycle engine in the single-culvert mode and the double-culvert mode, introduce the output parameter inertia link in the single-culvert and double-culvert mode switching, and use the A8 variable in different modes.
  • the multi-cell method is used to establish an on-board real-time model without iteration at the component level of the variable-cycle engine.
  • step A As a further optimization scheme of the component-level non-iterative construction method of a variable cycle motive airborne real-time model of the present invention, the specific steps of step A) are as follows:
  • Step A1) obtain the state variable model matrix coefficients of the speed and pressure ratio in different states of the variable cycle engine, and compose the LPV model about the speed and pressure ratio;
  • Step A2) the state transition equation in the LPV model constructs the matching relationship of the engine rotation acceleration equation set, and the output parameter equation set constructs the balance relationship between the flow rate and the pressure ratio;
  • Step A3) the LPV model does not iteratively solve the common working equations of the engine with respect to the speed and pressure ratio.
  • step B) As a further optimization scheme of the component-level non-iterative construction method of a variable cycle motive airborne real-time model of the present invention, the specific steps of step B) are as follows:
  • Step B1) Combine the existing engine component model with the established LPV model to construct a component-level non-iterative model under single and double culvert modes;
  • Step B2 introducing an output parameter inertia link in the mode switching process to reduce the output error of the model when switching between single-culvert and double-culvert modes;
  • Step B3) Determine the corresponding LPV model form according to the working mode of the variable cycle engine, and use the A8 variable polycell method to schedule the LPV form system parameters to realize the non-iterative calculation of the airborne real-time model in different modes of the variable cycle engine.
  • the present invention adopts the above technical scheme and has the following technical effects:
  • the present invention proposes a component-level non-iterative construction method for the on-board real-time model of a variable-cycle engine.
  • Each component model is retained on the basis of a non-linear component-level general model, and the original non-linear component-level model is combined with the LPV modeling idea.
  • the process of iteratively solving the nonlinear co-working equation is replaced by the LPV model about the speed and the pressure ratio to avoid the iterative process.
  • the traditional nonlinear component-level model it has higher real-time performance, and has higher accuracy than the linearized state variable model, which is beneficial to practical engineering applications.
  • Figure 1 is a schematic diagram of a component-level non-iterative model
  • Figure 2 is a cross-section numbering diagram of a variable cycle engine
  • Figure 3 is the flight trajectory diagram of the engine within the envelope
  • Figure 4 is a graph showing the normalized fuel flow rate W f of the engine and the throat area A8 of the tail nozzle;
  • Figures 5-9 are engine output parameters NL, NH, T21, P21, T15, P15, T3, P3, T5, P5 non-linear component-level model and component-level non-iterative model simulation comparison diagram;
  • Figure 10 is the tracking error of engine output parameters
  • Figure 11 is a comparison of time-consuming simulation between a non-linear component-level model and a component-level non-iterative model.
  • the idea of the present invention is to improve and develop the existing aero-engine simulation model according to the advanced aero-engine's requirements for the real-time and accuracy of the airborne model, and establish the airborne real-time component-level non-iterative model of the state-variable cycle engine above the slow car.
  • the real-time performance of the engine model is significantly improved with a small loss of accuracy.
  • Fig. 1 is a schematic diagram of a component-level non-iterative real-time model of a variable-cycle engine.
  • the establishment of the simulation model includes the following steps:
  • Step A) based on the component-level model of the variable-cycle engine, design the non-iterative solution algorithm of the nonlinear co-working equations in the form of LPV, the LPV state transition equation establishes the matching relationship of the rotor acceleration equations, and the LPV output equations establish the component-level Flow balance relationship, solving to obtain state parameters such as engine speed and pressure ratio;
  • Step B) using the LPV non-iterative solution method to construct the relationship between the component parameters of the variable-cycle engine in the single-culvert mode and the double-culvert mode, introduce the output parameter inertia link in the single-culvert and double-culvert mode switching, and use the A8 variable in different modes.
  • the multi-cell method is used to establish an on-board real-time model without iteration at the component level of the variable-cycle engine.
  • step A The detailed steps of step A) are as follows:
  • Step A1) using the small disturbance method to obtain the state variable model matrix coefficients of the speed and pressure ratio in different states of the variable cycle engine, and compose the LPV model about the speed and pressure ratio;
  • W represents flow
  • P pressure
  • N power
  • n speed
  • ⁇ efficiency
  • J moment of inertia
  • t time
  • ⁇ the constant of the circumference.
  • the subscript a represents air
  • g gas (air and fuel mixture)
  • s static pressure
  • L low pressure rotor
  • H high pressure rotor
  • F fan
  • C Compressor
  • LT means low-pressure turbine
  • HT means high-pressure turbine
  • ex other power-consuming accessories 12, 23, 2, 114, 224, 4, 41, 43, 44, 7, 9, 16, 6 respectively indicate different engines
  • the position of the section is shown in Figure 2.
  • the steady state of the engine is a special case of dynamic, and the dynamic is more general.
  • equations (1) to (7) After introducing the input conditions of the component-level model, equations (1) to (7) can be written as follows:
  • u is the input of the component-level model
  • the subscript e represents the data of the steady-state point.
  • the superscript 1 represents the speed of the perturbed low-pressure rotor
  • the superscript 2 represents the speed of the high-pressure rotor
  • the engine's different throat cross-sectional area A8 and a large number of state variable models at different high-pressure speeds constitute an LPV model of speed and pressure ratio, which performs polynomial fitting on the matrix coefficients, and finally stores the polynomial coefficients.
  • p( ⁇ ) represents the polynomial about ⁇
  • ⁇ is the object to be fitted
  • ⁇ i represents the i-th power of ⁇
  • p i is the polynomial coefficient corresponding to ⁇ i.
  • Step A2) the state transition equation in the LPV model establishes the matching relationship of the engine rotation acceleration equation set, and the output parameter equation set establishes the balance relationship between the flow rate and the pressure ratio;
  • Step A2.1 the state transition equation in the LPV model matches the rotation acceleration equation in the common working equation to obtain the high and low pressure rotor speed;
  • Step A2.2 the output parameter equation in the LPV model establishes the balance relationship between the flow rate and the pressure in the common working equation, and obtains the pressure ratio of each rotating part.
  • Step A3) the LPV model does not iteratively solve the common working equations of the engine with respect to the speed and pressure ratio.
  • i, j represent the column and row of the element in the matrix.
  • the coefficient matrix A, B, C, D under the current high-pressure speed n H can be obtained, and the LPV model
  • the calculation of the speed and the pressure ratio of each component is as follows
  • interpolation is performed according to the current A8 to calculate the speed-pressure ratio under the current throat cross-sectional area A8.
  • step B The detailed steps of step B) are as follows:
  • Step B1) Combine the existing engine component model with the established LPV model, bring the solved speed and pressure ratio into the calculation of each component, and construct a component-level non-iterative model under single and double culvert modes.
  • Step B1.1 determine the current working mode of the variable cycle engine according to the input parameters
  • Step B1.2 load the corresponding LPV form model according to the current working mode of the variable cycle engine, and construct the component-level non-iterative model under the single and double culvert modes as shown in Figure 1.
  • Step B2 Introduce the output parameter inertia link in the mode switching process to reduce the output error of the model when switching between single-culvert and double-culvert modes.
  • the expression of the first-order inertial link is shown below;
  • T represents the time constant of the first-order inertial link.
  • Step B3) determine the corresponding LPV model form according to the variable cycle engine working mode, and use the A8 variable polycell method to schedule the LPV form system parameters to realize the non-iterative calculation of the airborne real-time model under different modes of the variable cycle engine, A8 variable polycell
  • the form is as follows.
  • Step B3.1 determine the change range of A8 of the variable-cycle engine in single-culvert and double-culvert modes
  • the subscript min represents the minimum value
  • max represents the maximum value
  • the superscript 1 represents single culvert
  • 2 represents double culvert.
  • Step B3.2 according to the determined variation range of A8, the interpolation points of A8 in different modes are selected to form the method of A8 variable polycell in single and double culvert mode.
  • the simulation environment is a 64-bit Windows 10 operating system, and the host is configured with Intel(R)Core(TM)i5 -5200u CPU@2.20GHz and RAM 8GB, the following digital simulations were performed under MATLAB R2016b software.
  • the variable model is the coefficient matrix A, B, C, D, and the corresponding elements of the coefficient matrix under different high-pressure speeds are fitted with a third degree polynomial to obtain the single culvert mode with different A8 and different high-pressure speeds.
  • A, B, C, D matrix Element polynomial fitting coefficient.
  • the measurement parameters of the variable cycle engine are selected as low-pressure rotor speed NL, high-pressure rotor speed NH, total temperature T21 and total pressure P21 after the fan, total temperature T15 and total pressure P15 of the outer culvert 15 section, and total temperature T3 and total pressure after the compressor Total pressure P3, total temperature T5 and total pressure P5 after the low pressure turbine.
  • the non-linear component-level model and component-level model are shown in Figure 11.
  • the comparison of the time-consuming simulation of the non-iterative model shows that it is more than twice the time-consuming of the component-level non-iterative model. Based on the above simulation results, this method achieves the goal of obtaining a higher real-time performance model with less accuracy loss.

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Abstract

一种变循环发动机机载实时模型的部件级无迭代构建方法，利用现有的变循环发动机非线性部件级动态通用模型，结合航空发动机LPV模型的建模思想，提出变循环发动机机载实时模型的部件级无迭代构建方法。原有的变循环发动机非线性部件级通用模型通过一组非线性共同工作方程将各个部件连接到一起，通过迭代求解非线性共同工作方程组获得各部件的特性参数，这种迭代求解非线性方程组的过程在模型运行过程的耗时很长，变循环发动机部件级无迭代的方法将这种迭代求解非线性方程组的过程用LPV模型代替，可以在精度损失较低的情况下显著降低变循环发动机模型耗时，提高变循环发动机模型的实时性。

Description

一种变循环发动机机载实时模型的部件级无迭代构建方法 技术领域
本发明涉及航空发动机建模与仿真领域，尤其涉及一种变循环发动机机载实时模型的部件级无迭代构建方法。
背景技术
变循环发动机因其具有可调几何部件，可以在不同飞行条件下改变发动机的热力循环，获得最佳的飞行性能，双外涵变循环发动机的基本结构如图1所示，其主要由两种典型的工作模式。
单涵模式：关闭模式选择活门，调小前、后可调涵道引射器(Variable Area Bypass Injector，VABI)的面积，使流经前段风扇的空气流量几乎全部流过核心驱动风扇和高压压气机，只允许一小部分流量经过外涵道冷却尾喷管，此时发动机单位推力最大，以满足飞机在起飞、爬升或超音速飞行时对推力的需求。
双涵模式：打开模式选择活门，调大前、后可调涵道引射器面积，前风扇空气流量增大，流经CDFS CDFS(Core Drive Fan Stage，核心驱动风扇级)的空气流量一部分从CDFS涵道流入主外涵，另一部分流入压气机，此时发动机涵道比最大，可以降低耗油率，以适用于亚音速飞行。
变循环发动机工作环境恶劣并且相比于常规发动机结构更为复杂，对其安全性以及可靠性要求都很高，航空发动机控制系统设计，发动机故障诊断，解析余度都依赖于航空发动机模型，在机载应用中不但要考虑发动机精度还要发动机模型的实时性能。
目前，变循环发动机的主流仿真模型有两种：非线性部件级模型(Nonlinear Component Level Model，NCLM)和线性化的状态变量模型。非线性部件级模型通过解析法根据发动机气动热力学原理建立，精度高，适应范围大，但实时性不够高。发动机状态变量模型是在发动机非线性部件级模型的基础上，在某一稳态点进行线性化，建立发动机输入和输出关系的状态变量模型，大量的状态变量模型构成发动机LPV模型。线性模型计算量较小、实时性好，但存在二次建模误差。本发明将变循环发动机非线性部件级通用模型与传统的LPV建模方法结合，利用变循环发动机各个部件模型以及建立的关于转速与压比的LPV模 型，提出一种变循环发动机机载实时模型的部件级无迭代构建方法，在精度损失较小的情况下提高发动机模型的实时性。
发明内容
本发明所要解决的技术问题是针对背景技术的缺陷，提供一种能够具有较高实时性能和精度的变循环发动机模型，解决原有的非线性部件级模型实时不性足，线化模型误差较大的问题。
本发明为解决上述技术问题采用以下技术方案：
步骤A)，在变循环发动机部件级模型的基础上，设计LPV(Linear Parameter Varying，线性变参数)形式的非线性共同工作方程组的无迭代求解算法，LPV状态转移方程建立转子加速度方程组匹配关系，LPV输出方程组建立部件级流量平衡关系，求解获得发动机的转速和压比等状态参数；
步骤B)，利用LPV无迭代求解方法，分别构造变循环发动机在单涵模式和双涵模式下部件参数关系，在单、双涵模式切换中引入输出参数惯性环节，在不同模式下采用A8变多胞的方法，从而建立变循环发动机部件级无迭代的机载实时模型。
作为本发明一种变循环动机机载实时模型的部件级无迭代构建方法的进一步的优化方案，步骤A)的具体步骤如下：
步骤A1)，求取变循环发动机不同状态下关于转速与压比的状态变量模型矩阵系数，并组成关于转速与压比的LPV模型；
步骤A2)，LPV模型中的状态转移方程构造发动机转加速度方程组匹配关系，输出参数方程组构建流量及压比的平衡关系；
步骤A3)，LPV模型无迭代求发动机关于转速及压比的共同工作方程解。
作为本发明一种变循环动机机载实时模型的部件级无迭代构建方法的进一步的优化方案，步骤B)的具体步骤如下：
步骤B1)，将现有的发动机部件模型与建立的LPV形式模型结合，构造单、双涵模式下的部件级无迭代模型；
步骤B2)，在模式切换过程引入输出参数惯性环节，减小模型在单涵和双涵模式切换时的输出误差；
步骤B3)，根据变循环发动机工作模式确定相应LPV模型形式，采用A8变多胞的方法调度LPV形式系统参数，实现变循环发动机不同模式下的机载实时模型的无迭代计算。
本发明采用以上技术方案与现有技术相比，具有以下技术效果：
本发明提出的一种变循环发动机机载实时模型的部件级无迭代构建方法，在非线性部件级通用模型基础上保留各部件模型，结合LPV建模思想，将原有的非线性部件级模型迭代求解非线性共同工作方程的过程用关于转速与压比的LPV模型替代，避免迭代过程。相比于传统的非线性部件级模型，具有更高的实时性能，相比于线性化的状态变量模型具有更高的精度，有利于实际的工程应用。
附图说明
图1是部件级无迭代模型原理图；
图2是变循环发动机截面编号图；
图3是发动机在包线内的飞行轨迹图；
图4是发动机归一化的燃油流量W f和尾喷管喉道面积A8变化图；
图5～图9是发动机输出参数NL,NH,T21,P21,T15,P15,T3,P3,T5,P5非线性部件级模型与部件级无迭代模型仿真对比图；
图10是发动机输出参数跟踪误差；
图11是非线性部件级模型与部件级无迭代模型仿真耗时对比。
具体实施方式
本发明的思路是针对先进航空发动机对于机载模型实时性以及精度的需求，对现有航空发动机仿真模型进行改进和开发，建立慢车以上状态变循环动机机载实时部件级无迭代模型，能在精度损失较小的情况下显著提高发动机模型的实时性能。
本发明的具体实施方式以某型双外涵变循环发动机部件级无迭代实时模型构建为例，图1是变循环发动机部件级无迭代模型实时模型原理图，该仿真模型的建立包括以下步骤：
步骤A)，在变循环发动机部件级模型的基础上，设计LPV形式的非线性共同工作方程组的无迭代求解算法，LPV状态转移方程建立转子加速度方程组匹配关系，LPV输出方程组建立部件级流量平衡关系，求解获得发动机的转速和压比等状态参数；
步骤B)，利用LPV无迭代求解方法，分别构造变循环发动机在单涵模式和双涵模式下部件参数关系，在单、双涵模式切换中引入输出参数惯性环节，在不同模式下采用A8变多胞的方法，从而建立变循环发动机部件级无迭代的机载实时模型。
其中步骤A)的详细步骤如下：
步骤A1)，采用小扰动法，求取变循环发动机不同状态下关于转速与压比的状态变量模型矩阵系数，并组成关于转速与压比的LPV模型；
变循环发动机部件级模型的共同工作方程
Figure PCTCN2021070665-appb-000001
e 2＝W g41/W g4-1                           (2)
e 3＝W g44/W g43-1                          (3)
e 4＝W g9/W g7-1                            (4)
e 5＝P s16/P s6-1                           (5)
Figure PCTCN2021070665-appb-000002
Figure PCTCN2021070665-appb-000003
其中e表示残差，W表示流量，P表示压力，N表示功率，n表示转速，η表示效率，J表示转动惯量，t表示时间，这里的π表示圆周率为常数。W，P，n，N,η，J中下标a表示空气，g表示燃气(空气与燃油混合气)，s表示静压，L表示低压转子，H表示高压转子，F表示风扇，C表示压气机，LT表示低压涡轮，HT表示高压涡轮，ex其它消耗功率的附件，12，23，2，114，224，4，41，43，44，7，9，16，6分别表示发动机不同的截面位置，如图2所示。当发动机进入稳态后转子转加速度dn L/dt和dn H/dt为零，即功率平衡，因此发动机稳态是动态的特殊情况，动态更通用。
引入部件级模型的输入条件后式(1)～式(7)可以写为如下形式：
Figure PCTCN2021070665-appb-000004
其中u为部件级模型的输入，n＝[n L,n H] T为转子转速，π＝[π 1,π 2,π 3,π 4,π 5] T分别为风扇，CDFS，压气机，高压涡轮和低压涡轮5个旋转部件的压比，e＝[e 1,e 2,e 3,e 4,e 5] T为 残差。
Figure PCTCN2021070665-appb-000005
由式(9)可得压比π的表达如下所示
π□g 1(u,n)             (10)
将式(10)带入式(9)可得
Figure PCTCN2021070665-appb-000006
则关于转速与压比的非线性表达如下所示
Figure PCTCN2021070665-appb-000007
线性化求取状态变量模型
Figure PCTCN2021070665-appb-000008
其中x＝Δn＝n-n e，y＝Δπ＝π-π e
Figure PCTCN2021070665-appb-000009
在平衡点处
Figure PCTCN2021070665-appb-000010
其中下标e表示稳态点的数据。
小扰动法求取系数矩阵
Figure PCTCN2021070665-appb-000011
其中
Figure PCTCN2021070665-appb-000012
分别表示两种不同扰动后非平衡态数据，上标1表示扰动低压转子转速，上标2表示高压转子转速。
Figure PCTCN2021070665-appb-000013
大量的状态变量模型组合成LPV模型
Figure PCTCN2021070665-appb-000014
发动机不同的喉道截面面积A8和不同的高压转速下的大量状态变量模型构成转速与压比的LPV模型，对矩阵系数进行多项式拟合，最终存储多项式系数。
在地面工作点，分别在不同的喉道面积下，建立LPV模型，再利用相似理论将该模型适用范围在包线内拓展，下标cor表示相似换算
Figure PCTCN2021070665-appb-000015
对矩阵中各元素对n H进行k阶多项式拟合
Figure PCTCN2021070665-appb-000016
其中p(θ)表示关于θ的多项式，θ为被拟合的对象，θ i表示θ的i次方，p i为θ i对应的多项式系数。
步骤A2)，LPV模型中的状态转移方程建立发动机转加速度方程组匹配关系，输出参数方程组建立流量及压比的平衡关系；
步骤A2.1)，LPV模型中的状态转移方程匹配共同工作方程中的转加速度方程，获得高低压转子转速；
Figure PCTCN2021070665-appb-000017
步骤A2.2)，LPV模型中的输出参数方程建立共同工作方程中的流量与压力的平衡关系,获得各旋转部件的压比。
Figure PCTCN2021070665-appb-000018
步骤A3)，LPV模型无迭代求发动机关于转速及压比的共同工作方程解。
加载存储的多项式系数，计算系数矩阵中的元素，进而得到各系数矩阵，通过转速与压比的LPV模型，进一步计算当前状态下的转速与压比；
Figure PCTCN2021070665-appb-000019
其中i,j表示该元素在矩阵中所处的列与行，由式(23)的各系数矩阵元素，可得当前高压转速n H下的系数矩阵A，B，C，D，通过LPV模型求解转速与各部件压比的计算如下
Figure PCTCN2021070665-appb-000020
Figure PCTCN2021070665-appb-000021
之后根据当前A8进行插值计算当前喉道截面面积A8下的转速压比。
Figure PCTCN2021070665-appb-000022
其中步骤B)的详细步骤如下：
步骤B1)，将现有的发动机部件模型与已经建立的LPV形式模型结合，将求解的转速及压比带入各部件的计算中，构造单、双涵模式下的部件级无迭代模型。
步骤B1.1)，根据输入参数确定当前变循环发动机的工作模式；
步骤B1.2)，根据当前变循环发动机的工作模式加载相应的LPV形式模型，构造单、双涵模式下的部件级无迭代模型如图1所示。
步骤B2)，在模式切换过程引入输出参数惯性环节，减小模型在单涵和双涵模式切换时 的输出误差，一阶惯性环节的表达式如下所示；
Figure PCTCN2021070665-appb-000023
其中T表示一阶惯性环节的时间常数。
步骤B3)，根据变循环发动机工作模式确定相应LPV模型形式，采用A8变多胞的方法调度LPV形式系统参数，实现变循环发动机不同模式下的机载实时模型的无迭代计算，A8变多胞的形式如下。
步骤B3.1)，确定变循环发动机在单涵和双涵模式下的A8的变化范围；
Figure PCTCN2021070665-appb-000024
其中下标min表示最小值，max表示最大值，上标1表示单涵，2表示双涵。
步骤B3.2)，根据已确定的A8的变化范围选取不同模式下A8的插值点，形成单双涵模式下A8变多胞的方法。
Figure PCTCN2021070665-appb-000025
为了验证本发明所设计的一种变循环发动机机载实时模型的部件级无迭代构建方法的有效性进行仿真，仿真环境为64位Windows 10操作系统，主机配置Intel(R)Core(TM)i5-5200u CPU@2.20GHz和RAM 8GB，在MATLAB R2016b软件下进行了如下数字仿真。
首先在单涵模式下，在地面点H＝0m，Ma＝0分别计算A8＝[1,1.05,1.10,1.15,1.20,1.25]情况下不同高压转速下变循环发动机关于转速与压比的状态变量模型即系数矩阵A、B、C、D，并对不同高压转速下系数矩阵的对应元素进行3次多项式拟合，获得单涵模式不同A8和不同高压转速下A、B、C、D矩阵元素多项式拟合系数。在双涵模式下，分别在H＝0m，Ma＝0，H＝5000m，Ma＝0.6和H＝8000m，Ma＝0.8三个工作点下分别计算A8＝[1.05,1.10,1.15,1.20,1.25,1.30]情况下不同高压转速下变循环发动机关于转速与压比的状态变量模型即系数矩阵A、B、C、D，并对不同高压转速下系数矩阵的对应元素进行3次多项式拟合，获得双涵模式不同A8和不同高压转速下A、B、C、D矩阵元素多项式拟合系数。
在地面点H＝0m，Ma＝0，加载双涵模式多项式拟合系数，以双涵模式起飞，在0～5000m相似换算至H＝0m，Ma＝0点，在5000m～8000m相似换算到H＝5000m，Ma＝0.6工作点,在 8000m以上相似换算到H＝8000m，Ma＝0.8工作点，飞行至H＝10000m，Ma＝1.2时进行模式切换，切换为单涵模式后加载单涵模式多项式拟合系数，之后飞回地面点，包线内的飞行轨迹如图3所示，归一化后的燃油流量W f与尾喷管喉道截面面积A8变化如图4所示，在这一飞行循环中进行数字仿真验证。
变循环发动机的测量参数选择为低压转子转速NL，高压转子转速NH，风扇后的总温T21和总压P21，外涵15截面的总温T15和总压P15，压气机后的总温T3和总压P3，低压涡轮后的总温T5和总压P5。
由图5～图9发动机输出参数部件级无迭代模型与非线性部件级模型的仿真对比图，从输出参数的仿真图可以看出，部件级无迭代模型在整个飞行过程中较好的跟踪了非线性部件级模型的输出，图10是各输出参数的跟踪误差，可以看出，各个测量参数的跟踪最大误差基本都在1％以内，仅在14min左右发动机进行模式切换以及17.5min由于处于多项式分段拟合分界点时会出现相对较大的误差，在其它情况下跟踪误差基本在0.5％以内，这说明部件级无迭代具有较高的精度，图11中非线性部件级模型与部件级无迭代模型仿真耗时对比可以看出是部件级无迭代模型耗时的2倍以上。综合以上仿真结果，该方法实现了在精度损失较小的情况下获得较高实时性能模型的目的。
以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下还可以做出若干改进，这些改进也应视为本发明的保护范围。

Claims (6)

  1. 变循环发动机机载实时模型的部件级无迭代构建方法，其特征在于，包括以下步骤：
    步骤A)，在变循环发动机部件级模型的基础上，设计LPV形式的非线性共同工作方程组的无迭代求解算法，LPV状态转移方程建立转子加速度方程组匹配关系，LPV输出方程组建立部件级流量平衡关系，求解获得发动机的转速和压比等状态参数；
    步骤B)，利用LPV无迭代求解方法，分别构造变循环发动机在单涵模式和双涵模式下部件参数关系，在单、双涵模式切换中引入输出参数惯性环节，在不同模式下采用A8变多胞的方法，从而建立变循环发动机部件级无迭代的机载实时模型。
  2. 如权利要求1所述的一种变循环动机机载实时模型的部件级无迭代构建方法，其特征在于，所述步骤A)的具体步骤如下：
    步骤A1)，求取变循环发动机不同状态下关于转速与压比的状态变量模型矩阵系数，并组成关于转速与压比的LPV模型；
    步骤A2)，LPV模型中的状态转移方程建立发动机转加速度方程组匹配关系，输出参数方程组建立流量及压力的平衡关系；
    步骤A3)，LPV模型无迭代求发动机关于转速及压比的共同工作方程解。
  3. 如权利要求1所述的一种变循环动机机载实时模型的部件级无迭代构建方法，其特征在于，所述步骤B)的具体步骤如下：
    步骤B1)，将现有的发动机部件模型与建立的LPV形式模型结合，构造单、双涵模式下的部件级无迭代模型；
    步骤B2)，在模式切换过程引入输出参数惯性环节，减小模型在单涵和双涵模式切换时的输出误差；
    步骤B3)，根据变循环发动机工作模式确定相应LPV模型形式，采用A8变多胞的方法调度LPV形式系统参数，实现变循环发动机不同模式下的机载实时模型的无迭代计算。
  4. 如权力要求2中所述的一种变循环动机机载实时模型的部件级无迭代构建方法，其特征在于，所述步骤A2)的具体步骤如下：
    步骤A2.1)，LPV模型中的状态转移方程匹配共同工作方程中的转加速度方程，获得高低压转子转速；
    步骤A2.2)，LPV模型中的输出参数方程建立共同工作方程中的流量与压力的平衡关系，获得各旋转部件的压比。
  5. 如权力要求3中所述的一种变循环动机机载实时模型的部件级无迭代构建方法，其特征在于，所述步骤B1)的具体步骤如下：
    步骤B1.1)，根据输入参数确定当前变循环发动机的工作模式；
    步骤B1.2)，根据当前变循环发动机的工作模式加载相应的LPV形式模型，构造单、双涵模式下的部件级无迭代模型。
  6. 如权力要求3中所述的一种变循环动机机载实时模型的部件级无迭代构建方法，其特征在于，所述步骤B3)的具体步骤如下：
    步骤B3.1)，确定变循环发动机在单涵和双涵模式下的A8的变化范围；
    步骤B3.2)，根据已确定的A8的变化范围选取不同模式下A8的插值点，形成单双涵模式下A8变多胞的方法。
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