A method for expanding the full - envelope accuracy of an airborne dynamic model of a turbofan engine

Abstract

The present invention discloses a method for expanding the full envelope accuracy of an airborne dynamic model of a turbofan engine. The method includes: establishing an LPV dynamic real-time model of the engine with respect to pressure ratio based on the data of the engine component-level model; designing an automatic scheduling logic for wide-range dynamic matrix coefficients within the envelope, and optimally selecting several envelope points at different total inlet temperatures T of the engine to establish a switched pressure ratio LPV dynamic real-time model, which forms a component-level airborne dynamic model with the pneumatic thermodynamics models of each component in the gas path; designing an expansion strategy for the switched pressure ratio LPV dynamic real-time model within the full envelope according to the output accuracy, so as to obtain the expansion of the full envelope accuracy of the turbofan engine airborne dynamic model. The present invention has a strong self-adjusting ability for the model error of the turbofan engine caused by similarity conversion error, and proposes an isothermal line self-adjustment scheme for the switching of the pressure ratio LPV dynamic real-time model, which can effectively improve the model accuracy of the turbofan engine within the full envelope range. t2 The present invention has a strong self-adjusting ability for the model error of the turbofan engine caused by similarity conversion error, and proposes an isothermal line self-adjustment scheme for the switching of the pressure ratio LPV dynamic real-time model, which can effectively improve the model accuracy of the turbofan engine within the full envelope range.

Description

Technical Field

[0001] The present invention relates to the field of aero-engine modeling and simulation, and particularly to the full-envelope accuracy extension of an airborne dynamic model of a turbofan engine. Background Art

[0002] Modern aero-engines are extremely complex non-linear aerothermodynamic systems, and a large amount of manpower and funds are required during the R & D process. The mathematical model of an aero-engine is the basis for the design and research of a control system, including three types of aero-engine mathematical models: component-level models, state-variable models, and LPV models.

[0003] Component-level models: They have high accuracy and can comprehensively reflect the working conditions of each section of the engine. However, due to the need for repeated flow iteration calculations during their calculation, their real-time performance is poor. When verifying the real-time simulation of a control algorithm, both high accuracy of the mathematical model and good real-time performance are required.

[0004] State-variable models: Models established by locally linearizing a non-linear component-level model, which are currently widely used in the design of engine variable controllers. The methods for establishing the state-variable model of an aero-engine include the partial derivative method, the fitting method, and the least square method.

[0005] LPV models: Since the state-variable model is a small-range linear model and it is difficult to meet the accuracy requirements of the engine in a large range, the LPV modeling method needs to be applied. The LPV model describes the dynamic characteristics of the system by using measurable external real-time parameters as scheduling parameters. The LPV controller is directly designed by using the linear robust control theory to ensure that the designed controller has robust stability. The LPV system has high potential value in both engineering applications and theoretical research. Therefore, in recent years, the LPV modeling technology has received great attention from the control academic community.

[0006] Due to the large state and envelope range of a turbofan engine, if working points are selected within the full envelope to establish an LPV model, then, in order to ensure the modeling accuracy, a sufficient number of working points need to be selected during linearization, which brings a huge workload. Another approach is to establish an LPV model at ground points and then use the similarity principle to process the models of other working points. However, since some engine parameters, such as thrust, do not satisfy the similarity conditions, this results in low modeling accuracy. Therefore, this method has poor generality. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide an airborne dynamic real-time model with high accuracy in view of the deficiencies of the background art, and expand it to the full envelope according to the principle of isotherms, and use this airborne dynamic model to improve the accuracy within the full envelope.

[0008] The present invention adopts the following technical solutions to solve the above technical problems:

[0009] Step A), using the small perturbation fitting method to solve and establish a wide - range LPV dynamic real - time model for the pressure ratio;

[0010] Step B), designing a wide - range dynamic matrix coefficient automatic scheduling logic within the envelope, optimizing the selection of envelope points at different total inlet temperatures T of the engine t2 to establish a switched pressure - ratio LPV dynamic real - time model; designing an extended strategy for the switched pressure - ratio LPV dynamic real - time model within the entire envelope according to the output accuracy, determining the switched LPV model, and forming a component - level airborne dynamic model with the pneumatic thermodynamics models of each component in the gas path, and developing a self - scheduling extended airborne dynamic model for the entire envelope.

[0011] As a further optimized solution for the research on the full - envelope accuracy extension of the airborne dynamic model of a turbofan engine in the present invention, the specific steps of Step A) are as follows:

[0012] Step A1), according to the engine similarity criterion, using the similar - normalized parameters to establish a state - variable model for the pressure ratio. The non - linear mathematical model of the turbofan engine is as follows:

[0013]

[0014] y = g(x, u, v)

[0015] In the formula, x is the state variable, u is the control variable, y is the output variable, and v is the vector of flight condition parameters including flight altitude, Mach number, and inlet temperature, etc. When the flight condition v is given, perform a Taylor series expansion on the non - linear model at a certain steady - state point (x0, u0, y0) of the engine, and ignore the influence of higher - order infinitesimals.

[0016]

[0017]

[0018] In the formula, the subscript 0 represents a certain steady - state point of the engine, Δx = x - x0, and Δu = u - u0.

[0019] Δy = y - y0 = g(x, u)-g(x0, u0), let the matrix The state - variable model of the engine at the steady - state point (x0, u0, y0) is:

[0020]

[0021] Δy = CΔx + DΔu

[0022] The parameter similarity normalization is as follows:

[0023]

[0024] $P_{A8} = A8 / A$ 8ds × 100%

[0025] In the formula, $P_N$ L 、$P_N$ H 、$P_W$ f 、$P_{A8}$ are the normalized high-pressure rotor speed, low-pressure rotor speed, main combustion chamber fuel supply, and tail nozzle throat area respectively. $T_2$ is the total inlet temperature of the engine. The subscript $d$ s represents the engine design point parameters. The engine state variable model expressed in similarity normalization parameters is as follows:

[0026]

[0027]

[0028] The state variables are the high and low pressure rotor speeds $N$ H and $N$ L , the control variables are the main combustion chamber fuel supply $W$ f and the tail nozzle throat area $A8$, and the output variables are the fan pressure ratio $\pi$ fan , the low-pressure compressor pressure ratio $\pi$ lcomp , the high-pressure compressor pressure ratio $\pi$ hcomp , the high-pressure turbine pressure ratio $\pi$ hturb and the low-pressure turbine pressure ratio $\pi$ lturb ; respectively represent matrices $A$, $B$, $C$, $D$. The initial solutions of the coefficient matrices $A$, $B$, $C$, $D$ at this operating point are obtained using the small perturbation method;

[0029] Step A2), at a certain altitude Mach number, establish an LPV model at different throat areas respectively. The LPV model of the engine is described as:

[0030]

[0031] In the formula, $x$ is the state, $y$ is the output, and the subscript $cor$ represents the parameters converted to the ground point by similarity conversion.

[0032] Obtain the model using the method of polytope interpolation:

[0033]

[0034] In the formula, $\gamma$ i is a weight coefficient. The closer the current $A8$ is to $A$ 8i the closer this value is to 1, and vice versa closer to 0;

[0035] To reduce the data storage space, a third-order polynomial fitting is performed on each element in the ABCD matrix with a quantity of k:

[0036]

[0037] Obtained through multiple trials using the fitting method Thereby establishing a wide-range LPV dynamic real-time model for the pressure ratio.

[0038] As a study on expanding the full-envelope accuracy of the airborne dynamic model of a turbofan engine, the specific steps of an optimization scheme for reducing errors in step B) are as follows:

[0039] Step B1), design a wide-range automatic scheduling logic for dynamic matrix coefficients within the envelope, establish a flight envelope division scheme based on isotherms, and according to the flight envelope division scheme, optimally select several t2 Envelope points at T to establish a switched pressure ratio LPV dynamic real-time model;

[0040] Step B2), for a certain flight point within the full envelope, design an automatic selection method for the LPV model at this flight point under isothermal conditions, determine a wide-range switched LPV model, and form a component-level airborne dynamic model with the pneumatic thermodynamics models of each component in the gas path, automatically obtaining a wide-range airborne dynamic real-time model for any flight point within the established isotherms of the full envelope;

[0041] Step B3), for the flight points within the envelope where the switched LPV model under isotherms has not been established, design an expansion strategy for the switched LPV dynamic real-time model within the full envelope based on the output accuracy. When the accuracy is low, calculate the wide-range dynamic matrix coefficients of the isotherm at this flight point, and construct a dynamic model in combination with the pneumatic thermodynamics models of each component in the gas path, thereby realizing the expansion of the airborne dynamic model under any isotherm within the full envelope.

[0042] Furthermore, the wide-range automatic scheduling logic for dynamic matrix coefficients designed in step B1) within the envelope is as follows: within the envelope, when T t2 differs from the T of the established switched LPV model t2 by no more than 20K, the switched LPV model with a smaller adjacent temperature difference can be used to achieve the automatic scheduling of wide-range dynamic matrix coefficients.

[0043] Furthermore, the specific steps in step B2) are as follows:

[0044] Step B2.1), use the pressure ratio LPV dynamic real-time model to record the five pressure ratios solved by the iterative convergence of the nonlinear model under different working conditions, and send these solutions back to the nonlinear model. Combine them with the pneumatic thermodynamics models of each component in the gas path to form a component-level airborne dynamic model, so that the nonlinear model can obtain the output parameters corresponding to the input without iteration;

[0045] Step B2.2), for a certain flight point within the full envelope, design an automatic selection method for the LPV model of this flight point under isothermal conditions: If T t2 is the same as the T of the established switched LPV model t2 , it is regarded as being on the same isothermal line, and directly call the switched LPV model of this isothermal line; when T t2 differs from the T of the established switched LPV model t2 by no more than 20K, the switched LPV model of the isothermal line with a smaller adjacent temperature difference can be used; input the flight conditions and fuel quantity of the verification point, automatically select the switched LPV model with a wide range of this isothermal line, and form a component-level airborne dynamic model with the pneumatic thermodynamic models of each component of the gas path. Obtain the key parameters P25, T25, Ps3, P5, T5 at the engine steady state at different operating points. If the error does not exceed 1%, a wide-range airborne dynamic real-time model for any flight point within the established isothermal line of the full envelope can be automatically obtained.

[0046] Furthermore, the specific steps for obtaining the output under any isothermal line within the envelope in step B3) are as follows:

[0047] Step B3.1), in order to improve the model output accuracy under any total inlet temperature T t2 within the full envelope, design an extended strategy for the switched LPV dynamic real-time model within the full envelope according to the output accuracy: When T t2 differs from the T of the established switched LPV model t2 by no more than 20K, the adjacent isothermal line can be directly used to switch the LPV model to automatically obtain the dynamic matrix coefficients in a wide range;

[0048] Step B3.2), in the extended strategy of the switched LPV dynamic real-time model within the full envelope, if the output error is higher than 1% and T t2 differs from the T of the established switched LPV model t2 by more than 10K, then calculate the dynamic matrix coefficients in a wide range of the isothermal line at this flight point, reselect the switched LPV model with a wide range of this isothermal line, and form a component-level airborne dynamic model with the pneumatic thermodynamic models of each component of the gas path, thereby realizing the extension of the airborne dynamic model under any isothermal line within the full envelope.

[0049] Compared with the existing solutions, the present invention adopts the above technical solutions and has the following technical effects:

[0050] (1) The airborne dynamic model used in the present invention is composed of the LPV dynamic real-time model regarding the pressure ratio and the pneumatic thermodynamic models of each component of the gas path. Compared with the conventional component-level model of a turbofan engine, it avoids the iteration of the component-level model, saves calculation time, and at the same time ensures the calculation accuracy of each section.

[0051] (2) The present invention uses isotherms to establish a dynamic real-time model of pressure ratio LPV for different inlet total temperatures and then generalizes it to the entire envelope. It has strong adaptability within the entire envelope. After changing working conditions such as altitude and Mach number, it still has high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Among them, (a) is the flowchart of the accuracy extension of the airborne dynamic model of the turbofan engine for the entire envelope, and (b) is the detailed description of the adjustment scheme for Fig. (a);

[0053] Figure 2 is the schematic diagram of the principle of the airborne dynamic model of the turbofan engine;

[0054] Figure 3 is the envelope division plan based on isotherms;

[0055] Figure 4 is the comparison of output parameters at H = 11 km, Ma = 0.8, T t2 = 244.38 K;

[0056] Figure 5 is the comparison of output parameters at H = 7.9 km, Ma = 0.4, T t2 = 244.38 K;

[0057] Figure 6 is the comparison of output parameters at H = 13 km, Ma = 1, T t2 = 244.38 K;

[0058] Figure 7 is the comparison of output parameters at H = 8.7 km, Ma = 1.17, T t2 = 295 K when using the LPV model with T t2 = 288.15 K;

[0059] Figure 8 is the comparison of output parameters at H = 8.7 km, Ma = 1.17, T t2 = 295 K when using the LPV model with T t2 = 314.14 K;

[0060] Figure 9 is the comparison of output parameters at H = 3.8 km, Ma = 0.94, T t2 = 310 K when using the LPV model with T t2 = 288.15 K;

[0061] Figure 10 is the comparison of output parameters at H = 3.8 km, Ma = 0.94, T t2 = 310 K when using the LPV model with T t2Output parameter comparison for the LPV model with = 314.14K;

[0062] Figure 11 is H = 1.16km, Ma = 1.16, T t2 when using T at = 270K t2 Output parameter comparison for the LPV model with = 244.38K;

[0063] Figure 12 is H = 1.16km, Ma = 1.16, T t2 when using T at = 270K t2 Output parameter comparison for the LPV model with = 314.14K;

[0064] Figure 13 is H = 1.16km, Ma = 1.16, T t2 when using T at = 270K t2 Output parameter comparison for the LPV model with = 270K. Specific implementation manner

[0065] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

[0066] The idea of the present invention is based on the data of the engine component - level model, establishing a pressure - ratio LPV dynamic real - time model of the engine, and carrying out research on the model output suitable for the full - envelope range; by deriving the similarity conversion criteria for key parameters, analyzing the reasons for the similarity conversion error between different operating points within the envelope range, and mastering the theory that the similarity conversion error can be reduced based on the isothermal - line similarity conversion; according to the derived isothermal - line similarity conversion error theory, several different Ts are optimally selected within the envelope range t2 to establish a switching LPV model, which forms a component - level airborne dynamic model with the pneumatic thermodynamics models of each component in the gas path, thereby avoiding the iteration of the component - level model; designing an expansion strategy for the switching LPV dynamic real - time model within the full - envelope range according to the output accuracy, ensuring the calculation accuracy of the parameters of each section, and realizing the expansion of the airborne dynamic model under any isothermal line within the full - envelope range.

[0067] The specific implementation manner of the present invention takes the construction of a component - level airborne dynamic model of a certain turbofan engine as an example, Figure 2 which is the schematic diagram of the turbofan engine airborne dynamic model. The full - envelope accuracy expansion of a turbofan engine airborne dynamic model described in the present invention specifically includes the following steps:

[0068] Step A), using the small - perturbation fitting method to solve and establish a wide - range LPV dynamic real - time model regarding the pressure ratio;

[0069] Step A1), according to the engine similarity criterion, a state variable model regarding the pressure ratio is established using similar normalized parameters. The nonlinear mathematical model of the turbofan engine is as follows:

[0070]

[0071] y = g(x, u, v)

[0072] where x is the state variable, u is the control variable, y is the output variable, and v is the vector of flight condition parameters including flight altitude, Mach number, and inlet temperature, etc. When the flight condition v is given, the nonlinear model is expanded by Taylor series at a certain steady-state point (x0, u0, y0) of the engine, and the influence of higher-order infinitesimals is ignored.

[0073]

[0074]

[0075] where the subscript 0 represents a certain steady-state point of the engine, Δx = x - x0, and Δu = u - u0.

[0076] Δy = y - y0 = g(x, u) - g(x0, u0). Let the matrix The state variable model of the engine at the steady-state point (x0, u0, y0) is:

[0077]

[0078] Δy = CΔx + DΔu

[0079] The parameter similarity normalization is as follows:

[0080]

[0081] PA8 = A8 / A 8ds ×100%

[0082] where PN L , PN H , PW f , PA8 are the normalized high-pressure rotor speed, low-pressure rotor speed, main combustion chamber fuel supply, and tail nozzle throat area respectively, T2 is the total inlet temperature of the engine, and the subscript d s represents the engine design point parameters. The engine state variable model expressed by similar normalized parameters is as follows:

[0083]

[0084]

[0085] The state variables are the high and low pressure rotor speeds N H and N L The control variable is the fuel supply W to the main combustion chamber f and the throat area A8 of the tail nozzle. The output variables are the fan pressure ratio π fan the low-pressure compressor pressure ratio π lcomp the high-pressure compressor pressure ratio π hcomp the high-pressure turbine pressure ratio π hturb and the low-pressure turbine pressure ratio π lturb ; They respectively represent matrices A, B, C, and D. The initial solutions of the coefficient matrices A, B, C, and D at this operating point are obtained using the small perturbation method;

[0086] Step A2), at a certain altitude Mach number, establish an LPV model at different throat areas respectively. The LPV model of the engine is described as:

[0087]

[0088] where x is the state, y is the output, and the subscript cor indicates similarity conversion to ground point parameters.

[0089] Obtain the model using the method of polytope interpolation:

[0090]

[0091] where γ i is a weight coefficient. The closer the current A8 is to A 8i the closer this value is to 1, and vice versa, closer to 0;

[0092] To reduce the data storage space, perform a third-order polynomial fitting on each element in the ABCD matrices with a quantity of k:

[0093]

[0094] Obtain through multiple trial selections using the fitting method Thus, establish a wide-range LPV dynamic real-time model for the pressure ratio.

[0095] Step B), design a wide-range dynamic matrix coefficient automatic scheduling logic within the envelope, optimize the selection of envelope points at different total inlet temperatures T t2 of the engine to establish a switched pressure ratio LPV dynamic real-time model; design an extended strategy for the switched pressure ratio LPV dynamic real-time model within the entire envelope based on the output accuracy, determine the switched LPV model, and form a component-level airborne dynamic model with the pneumatic thermodynamics models of each component of the gas path, and develop a self-scheduling extended airborne dynamic model for the entire envelope.

[0096] Step B1), design a wide-range automatic scheduling logic for dynamic matrix coefficients within the flight envelope, establish a flight envelope division scheme based on isotherms, and optimize the selection of several envelope points at T t2 to establish a switched pressure ratio LPV dynamic real-time model;

[0097] The wide-range automatic scheduling logic for dynamic matrix coefficients designed within the flight envelope in Step B1) is as follows: within the flight envelope, when T t2 differs from the T t2 of the established switched LPV model by no more than 20K, the switched LPV model with a smaller adjacent temperature difference can be used to achieve the automatic scheduling of wide-range dynamic matrix coefficients.

[0098] Step B2), for a certain flight point within the entire flight envelope, design an automatic selection method for the LPV model of this flight point under isothermal conditions, determine a wide-range switched LPV model, and form a component-level aircraft-borne dynamic model with the pneumo-thermodynamic models of each component in the gas path, automatically obtaining the wide-range aircraft-borne dynamic real-time model for any flight point within the established isotherms of the entire flight envelope;

[0099] Step B2.1), use the pressure ratio LPV dynamic real-time model to record the five pressure ratios solved by the iterative convergence of the non-linear model under different working conditions, and then send these solutions back to the non-linear model to form a component-level aircraft-borne dynamic model with the pneumo-thermodynamic models of each component in the gas path, enabling the non-linear model to obtain the output parameters corresponding to the input without iteration;

[0100] Step B2.2), for a certain flight point within the entire flight envelope, design an automatic selection method for the LPV model of this flight point under isothermal conditions: if T t2 is the same as the T t2 of the established switched LPV model, it is considered to be on the same isotherm, and the switched LPV model of this isotherm is directly called; when T t2 differs from the T t2 of the established switched LPV model by no more than 20K, the switched LPV model with a smaller adjacent temperature difference can be used; input the flight conditions and fuel quantity of the verification point, automatically select the wide-range switched LPV model of this isotherm, form a component-level aircraft-borne dynamic model with the pneumo-thermodynamic models of each component in the gas path, and obtain the key parameters P25, T25, Ps3, P5, T5 at the engine steady state at different working points. If the error does not exceed 1%, the wide-range aircraft-borne dynamic real-time model for any flight point within the established isotherms of the entire flight envelope can be automatically obtained.

[0101] Step B3), for the flight points within the envelope where the isothermal switching LPV model has not been established, design an extended strategy for the switching LPV dynamic real-time model within the entire envelope according to the output accuracy. When the accuracy is low, calculate the dynamic matrix coefficients within the isothermal width range at this flight point, and construct a dynamic model by combining the pneumatic thermodynamics models of each component in the gas path, thereby realizing the extension of the on-board dynamic model under any isothermal line within the entire envelope.

[0102] Step B3.1), in order to improve the model output accuracy under any total inlet temperature T t2 within the entire envelope, design an extended strategy for the switching LPV dynamic real-time model within the entire envelope according to the output accuracy: when the difference between T t2 and the T t2 for which the switching LPV model has been established does not exceed 20 K, the adjacent isothermal switching LPV model can be directly used to automatically obtain the dynamic matrix coefficients within a wide range.

[0103] Step B3.2), in the extended strategy for the switching LPV dynamic real-time model within the entire envelope, if the output error is higher than 1%, and the difference between T t2 and the T t2 for which the switching LPV model has been established is greater than 10 K, then calculate the dynamic matrix coefficients within the isothermal width range at this flight point, reselect the switching LPV model within this isothermal width range, and form a component-level on-board dynamic model with the pneumatic thermodynamics models of each component in the gas path, thereby realizing the extension of the on-board dynamic model under any isothermal line within the entire envelope.

[0104] In order to verify the effectiveness of the extended accuracy of the on-board dynamic model of the turbofan engine designed by the present invention, digital simulations of the model output within the envelope were carried out in the MATLAB environment.

[0105] First, select the LPV dynamic real-time model under the same isothermal line for verification. Select the LPV model established at the typical envelope point when H = 11 km and Ma = 0.8, and then select other envelope points (1. H = 7.9 km, Ma = 0.4; 2. H = 13 km, Ma = 1) at the temperature such as the total inlet temperature T t2 = 244.38 K. The output comparison between the on-board dynamic real-time model and the dynamic model is as shown in Figure 4 、 Figure 5 、 Figure 6 . The root mean square error is shown in Table 1. It can be seen from the table that the root mean square error along the isothermal line does not exceed 1%, and the result accuracy is relatively high. Therefore, when the total inlet temperature T t2 of the engine is the same, even if the flight conditions are different, the same LPV model can be selected, thereby realizing the self-adjustment scheme under the same isothermal line, automatically obtaining the on-board dynamic real-time model with a wide range at any flight point within the established isothermal line of the entire envelope, and being able to ensure the accuracy.

[0106] Table 1 Root Mean Square Error (10e-2) under the Same Isotherm

[0107]

[0108] Regarding the output accuracy problem of different envelope points of the LPV model without establishing an isotherm switching in the envelope of the turbofan engine, set T t2 Take every 25K as an isotherm, and the envelope division scheme is as Figure 3 shown. First, select the total inlet temperature T t2 = 288.15K and 314.14K isotherms respectively. Only select one envelope point on each isotherm to obtain the LPV model applicable to all operating points on the entire isotherm. Therefore, calculate the two selected envelope points respectively to obtain two switching LPV models, which form a component-level airborne dynamic model with the pneumatic thermodynamics models of each component in the gas path. In order to design the self-adjustment scheme of the switching LPV model in a wide envelope range, select T t2 = 295K, T t2 = 310K isotherms, and use the LPV models on both sides of them to compare the output errors. The outputs of the airborne dynamic real-time model and the dynamic model are as Figure 7 , Figure 8 , Figure 9 , Figure 10 shown, and the errors are shown in Table 2. It can be seen from the table that the root mean square error of the output parameters is greater when far from the isotherm than when close to the isotherm. Therefore, when using isotherms with a small temperature difference, the error is significantly reduced and is not greater than 1%.

[0109] Table 2 Root Mean Square Error (10e-2) of Using LPV Models with Different Isotherms

[0110]

[0111] In order to study the self-adjustment scheme of the LPV model when the temperature T t2 at the engine inlet is quite different from the temperature of the established switching LPV model, first establish the switching LPV model only with T t2 = 244.38K and 314.14K isotherms respectively, select the isotherm with T t2 = 270K. At this time, the temperature differences are all quite large, and at the same time, increase the rotational speed change rate. Still use the two established LPV models to compare the output errors. The outputs of the airborne dynamic real-time model and the dynamic model are as Figure 11 , Figure 12 shown, and the errors are shown in Table 3. It can be seen from the table that when the temperature difference is large, there are cases where the error is greater than 1%. In order to reduce the error, at this time, according to the self-adjustment scheme, automatically recalculate the dynamic matrix coefficients in the wide envelope range of the isotherm at this flight point, and establish T t2The LPV switching model at 270K, together with the pneumatic thermodynamic models of each component in the gas path, constitutes a component-level airborne dynamic model, thereby realizing the expansion of the airborne dynamic model under any isothermal line within the full envelope. The output is as Figure 11 shown, and the errors are shown in Table 3. It can be seen from the table that after re-establishing the LPV switching model, the errors are significantly reduced. Therefore, if the error exceeds one percent, the switching LPV model should be re-established.

[0112] Table 3T t2 Root mean square error (10e-2) at 270K

[0113]

[0114]

[0115] It should be noted that the above description is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes and substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. An all-envelope accuracy extension method for an airborne dynamic model of a turbofan engine, characterized in that It includes the following steps: Step A), using the small perturbation fitting method to solve and establish a wide - range LPV dynamic real - time model for the pressure ratio; Step B), design a wide-range dynamic matrix coefficient automatic scheduling logic within the envelope, and select envelope points under different total inlet temperatures T of the engine to establish a switched pressure ratio LPV dynamic real-time model; design an extended strategy for the switched pressure ratio LPV dynamic real-time model within the entire envelope based on the output accuracy, determine the switched LPV model, and form a component-level airborne dynamic model with the pneumatic thermodynamic models of each component in the gas path, and develop a self-scheduling extended airborne dynamic model for the entire envelope; t2 According to the output accuracy, design an extended strategy for the switched pressure ratio LPV dynamic real-time model within the entire envelope, determine the switched LPV model, and form a component-level airborne dynamic model with the pneumatic thermodynamic models of each component in the gas path, and develop a self-scheduling extended airborne dynamic model for the entire envelope; The specific steps of step B) are as follows: Step B1), design an automatic scheduling logic for dynamic matrix coefficients with a wide range within the flight envelope, establish a flight envelope division scheme based on isotherms, and select several envelope points at T t2 to establish a switched pressure ratio LPV dynamic real-time model; Step B2), for a certain flight point within the full envelope, design an automatic selection method for the LPV model of this flight point under isothermal conditions, determine a wide - range switching LPV model, and form a component - level airborne dynamic model with the aerodynamic and thermodynamic models of each component in the gas path, automatically obtaining a wide - range airborne dynamic real - time model for any flight point within the established isothermal line in the full envelope; Step B3), for the flight points within the envelope where the isothermal line switching LPV model is not established, design an extended strategy for the switching LPV dynamic real-time model within the full envelope according to the output accuracy. If the output error is higher than 1%, and T t2 differs from the T for which the switching LPV model has been established t2 by more than 10K, calculate the dynamic matrix coefficients for the isothermal line width range at this flight point, and construct a dynamic model in combination with the pneumatic thermodynamics models of each component of the gas path, thereby realizing the extension of the on-board dynamic model under any isothermal line within the full envelope.

2. A method for expanding the full - envelope accuracy of an airborne dynamic model of a turbofan engine as shown in claim 1, characterized in that, The specific steps of step A) are as follows: Step A1), according to the engine similarity criterion, establish a state - variable model for the pressure ratio using similar - normalized parameters; the nonlinear mathematical model of the turbofan engine is as follows: y = g(x, u, v) In the formula, x is the state variable, u is the control variable, y is the output variable, and v is the flight - condition parameter vector including flight altitude, Mach number, and inlet temperature; when the flight condition v is given, perform a Taylor series expansion on the nonlinear model at a certain steady - state point (x0, u0, y0) of the engine, and ignore the influence of higher - order infinitesimals; In the formula, the subscript 0 represents a certain steady - state point of the engine, Δx = x - x0, Δu = u - u0; Δy = y - y0 = g(x, u) - g(x0, u0). Let the matrix The state variable model of the engine at the steady state point (x0, u0, y0) is: Δy = CΔx + DΔu The parameter similarity normalization is as follows: Where, N H and N L are the rotational speeds of the high-pressure and low-pressure rotors respectively, W f is the fuel supply of the main combustion chamber, A8 is the throat area of the tail nozzle, PN H , PN L , PW f , PA8 are the normalized rotational speed of the high-pressure rotor, the rotational speed of the low-pressure rotor, the fuel supply of the main combustion chamber, and the throat area of the tail nozzle respectively, T2 is the total inlet temperature of the engine, and the subscript d s represents the engine design point parameters. The engine state variable model expressed by similar normalized parameters is as follows: The state variables are the normalized increments of the high and low pressure rotor speeds ΔPN L and ΔPN H The control variables are the normalized increments of the main combustion chamber fuel supply ΔPW f and the increment of the nozzle throat area ΔPA8, and the output variables are the increment of the fan pressure ratio Δπ fan , the increment of the low pressure compressor pressure ratio Δπ lcomp , the increment of the high pressure compressor pressure ratio Δπ hcomp , the increment of the high pressure turbine pressure ratio Δπ hturb and the increment of the low pressure turbine pressure ratio Δπ lturb ; Let A, B, C, and D represent matrices respectively. The initial solutions of the coefficient matrices A, B, C, and D at this operating point are obtained using the small perturbation method; Step A2), at a certain altitude and Mach number, establish an LPV model under different throat areas respectively, and describe the LPV model of the engine as: In the formula, x is the state, y is the output, and the subscript cor represents the parameters similar - converted to the ground - point parameters; Obtain the model by using the method of polytope interpolation: where γ i is a weight coefficient. The closer the current A8 is to A 8i the closer this value is to 1, and vice versa, closer to 0; To reduce the data storage space, perform a third - order polynomial fitting on each element in the ABCD matrix with the quantity of k; Obtained through multiple trials by the fitting method Thus, a wide-range LPV dynamic real-time model regarding the pressure ratio is established.

3. Research on the full - envelope accuracy extension of an airborne dynamic model of a turbofan engine as shown in claim 1, characterized in that, In step B1), the design of the wide-range dynamic matrix coefficient automatic scheduling logic within the envelope is as follows: within the envelope, when T t2 differs from the T of the established switched LPV model by no more than 20K, use the isothermal line with a small adjacent temperature difference to switch the LPV model to achieve the automatic scheduling of the wide-range dynamic matrix coefficient. t2 When the difference is no more than 20K, use the isothermal line with a small adjacent temperature difference to switch the LPV model to achieve the automatic scheduling of the wide-range dynamic matrix coefficient.

4. A study on the full - envelope accuracy expansion of an airborne dynamic model of a turbofan engine as shown in claim 1, characterized in that, The specific steps of step B2) are as follows: Step B2.1), use the pressure - ratio LPV dynamic real - time model to record the five pressure ratios solved by the iteration convergence of the nonlinear model under different working conditions, send these solutions back to the nonlinear model, and form a component - level airborne dynamic model with the aerodynamic and thermodynamic models of each component in the gas path, so that the output parameters of the nonlinear model corresponding to the corresponding input can be obtained without iteration; Step B2.2), for a certain flight point within the full envelope, design an automatic selection method for the LPV model of this flight point under isothermal conditions: If T t2 is the same as the T of the established switching LPV model t2 , it is considered to be on the same isothermal line, and directly call the switching LPV model of this isothermal line; when T t2 differs from the T of the established switching LPV model t2 by no more than 20K, use the isothermal line with a small adjacent temperature difference to switch the LPV model; input the flight conditions and fuel quantity of the verification point, automatically select the wide-range switching LPV model of this isothermal line, and form a component-level airborne dynamic model with the pneumodynamic and thermodynamic models of each component of the gas path. Obtain the key parameters P25, T25, Ps3, P5, and T5 at the engine steady state at different working points. If the error does not exceed 1%, automatically obtain the wide-range airborne dynamic real-time model for any flight point within the established isothermal lines of the full envelope.

5. A study on the full - envelope accuracy extension of an airborne dynamic model of a turbofan engine as shown in claim 1, characterized in that, The specific steps of step B3) are as follows: Step B3.1), in order to improve the model output accuracy at any total inlet temperature T within the full envelope t2 under, design a switching LPV dynamic real-time model expansion strategy within the full envelope according to the output accuracy: when T t2 differs from the T of the established switching LPV model by no more than 20 K t2 directly use the adjacent isothermal switching LPV model to automatically obtain the dynamic matrix coefficients in a wide range; Step B3.2), in the process of switching the LPV dynamic real-time model extension strategy within the full envelope, if the output error is higher than 1%, and T t2 differs from the T of the established switched LPV model t2 by more than 10K, then calculate the dynamic matrix coefficients for the isothermal line width range at this flight point, reselect the switched LPV model for this isothermal line width range, and form a component-level airborne dynamic model with the pneumatic thermodynamics models of each component of the gas path, thereby realizing the extension of the airborne dynamic model under any isothermal line within the full envelope.

Images