CN117195763A - Fixed wing aircraft element flight aerodynamic modeling method considering wind interference - Google Patents
Fixed wing aircraft element flight aerodynamic modeling method considering wind interference Download PDFInfo
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Abstract
The application discloses a fixed wing aircraft element flight pneumatic modeling method considering wind interference. The modeling flow comprises the following steps: step 1, acquiring discrete pneumatic data sets under different state conditions, and establishing a traditional pneumatic model of the fixed-wing aircraft; step 2, analyzing the approximation precision of aerodynamic force (moment) and determining the Taylor expansion order of each component; and step 3, calculating to obtain an aerodynamic common base function of the fixed-wing aircraft, and approximating aerodynamic force (moment) of the aircraft by taking the obtained common base function as a base to finally obtain the meta-flight aerodynamic model. The method can realize the online prediction of aerodynamic force and aerodynamic moment of the fixed-wing aircraft in flight under the condition of unknown wind conditions.
Description
Technical Field
The application relates to the technical field of aerodynamic modeling of aviation aircrafts, in particular to a method for aerodynamic modeling of a fixed wing aircraft element flight by considering wind interference.
Background
Wind in the environment severely affects the flight safety of the aircraft, and complex aerodynamics of the interaction between wind and aircraft can cause the aircraft to deviate from the course and even pose out of control. In order to realize accurate control of maneuvering flight of an aircraft and improve the safety and reliability of the aircraft in windy environment, it is necessary to accurately predict aerodynamic force (moment) of the aircraft in real time in the presence of wind interference.
The traditional fixed wing aircraft pneumatic modeling method aims at the motion of an aircraft under an airflow coordinate system, and introduces physical variables such as an attack angle, a sideslip angle and the like to describe the change rule of aerodynamic force (moment) of the aircraft. The method is widely applied, but is applied to on-line prediction of aerodynamic force (moment) requirements of the current aircraft to determine information such as attack angle, sideslip angle and the like in real time. When air disturbance exists, the attack angle and the sideslip angle are not easy to accurately measure on line, and although the wind speed can be determined by adopting a wind field motion filtering method, a speed vector triangle method and other methods, and then the information of the attack angle and the sideslip angle is solved, the traditional aerodynamic model is very sensitive to the attack angle error, and the aerodynamic force and the aerodynamic moment born by the aircraft are difficult to accurately predict through the traditional aerodynamic model, so that the traditional aerodynamic model is not beneficial to the online migration application in the flight of the aircraft.
Based on element learning methodology, students such as Connell and the like put forward a neuron flight (neuron-fly) method for a rotor craft aiming at online aerodynamic modeling under wind interference, and the idea is to build a general aerodynamic commonality basis function model of the rotor craft under different wind conditions, so that real-time aerodynamic modeling and migration application under unknown wind conditions are realized. The deep element learning of the architecture of the countermeasure network (Generative Adversative Nets, GAN) is specifically adopted to train the common basis function neural network model, so that the accurate prediction of aerodynamic force under strong wind interference is realized. Because the neuron flight aerodynamic model established based on the element learning methodology has better migration capability, the model is beneficial to realizing real-time aerodynamic modeling. The aerodynamic model of a fixed-wing aircraft is more complex than that of a rotary-wing aircraft, wherein not only aerodynamic force but also aerodynamic moment are required to be modeled, model input relates to more variables such as angular speed, rudder deflection angle and the like of the aircraft, and targeted research is required. Meanwhile, the 'neuron flight' is a black box modeling method based on a deep neural network, which lacks theoretical interpretation and is difficult to carry out theoretical analysis, and cannot answer how many common basis functions are selected to accurately approximate theoretical problems such as an original aerodynamic function, so that a large number of tests and verification are required to be carried out, and the engineering usability of the method is affected.
Disclosure of Invention
The application provides a fixed wing aircraft element flight pneumatic modeling method considering wind interference, which is based on a Taylor expansion multivariate function decomposition series theory, adopts a motion variable of an aircraft relative to a ground coordinate system to describe, and constructs a general fixed wing aircraft aerodynamic commonality basis function analysis model under different wind conditions by isolating the influence of the wind interference, thereby realizing the online prediction of aerodynamic force and aerodynamic moment of the aircraft in flight under the unknown wind conditions.
In order to achieve the above purpose, the present application provides the following technical solutions:
a fixed wing aircraft element flight aerodynamic modeling method considering wind interference comprises the following steps:
step 1, acquiring discrete pneumatic data sets under different state conditions, and establishing a traditional pneumatic model of the fixed-wing aircraft to obtain aerodynamic force and aerodynamic moment expressed under a machine body coordinate system as
Wherein F is x 、F y And F is equal to z The axial force, the transverse force and the normal force of the aircraft are respectively; m is M x 、M y And M is as follows z Respectively the rolling moment, the pitching moment and the yawing moment of the aircraft;v is the velocity amplitude of the aircraft, ρ is the air density, which is a function of the aircraft altitude h; s is the reference area of the aircraft, and b and c are the transverse reference length and the longitudinal reference length of the aircraft respectively;
C D 、C Y and C L The drag coefficient, side force coefficient and lift coefficient of the aircraft are respectively expressed as:
C l 、C m 、C n the roll moment coefficient, the pitch moment coefficient and the yaw moment coefficient of the aircraft are respectively expressed as:
the direction cosine array from the air flow coordinate system to the machine body coordinate system is expressed as:
alpha is the attack angle, beta is the sideslip angle, ma is the Mach number of the aircraft, C s l 、C s m 、C s n Representing static aerodynamic moment coefficient, C lp 、C mq 、C np As a dynamic derivative coefficient, delta e 、δ a And delta r Elevator, aileron and rudder, [ pqr ]] T The upper mark is the angular velocity vector of the airplane under the machine body coordinate system " T "transpose symbols for vectors;
step 2, based on the step (5), aiming at the wind speed vector under the machine body coordinate system by aerodynamic force and aerodynamic momentPerforming Taylor expansion, examining the approximation accuracy of aerodynamic force and aerodynamic moment, determining the expansion orders of aerodynamic force and aerodynamic moment components by comparing the approximation accuracy of finite-order Taylor expansion expressions to an original function under different orders, and further determining the total term number in each expansion expression;
step 3, calculating to obtain an aerodynamic common base function of the fixed-wing aircraft, approximating aerodynamic force and aerodynamic moment of the aircraft by taking the obtained common base function as a base, and finally obtaining a meta-flight aerodynamic model, wherein the meta-flight aerodynamic model is expressed as:
in the method, in the process of the application,is a nondimensionalized aerodynamic coefficient and aerodynamic moment coefficient; dynamic pressureMatrix Ω=diag ([ 1, b, c, b)])；a i ,(i＝F x ,F y ,F z ,M x ,M y ,M z ) Is only +.>A related coefficient function; ψ is a matrix of common basis functions related only to the aircraft motion variables x,comprises a height h and a ground speed vector +.>Euler attitude angle Θ= [ phi theta phi ]] T Angular velocity ω= [ pqr ]] T And rudder deflection angle delta= [ delta ] a δ e δ r ] T 。
Compared with the prior art, the application has the beneficial effects that:
1) The aerodynamic commonality basis function constructed in the meta-flight aerodynamic modeling is described by adopting the motion variable of the aircraft relative to the ground coordinate system, and the commonality basis function irrelevant to wind conditions and the coefficient function irrelevant to the aircraft motion can be obtained by separating the aircraft motion variable relative to the ground coordinate system from the air disturbance variable, so that good conditions are created for accurately identifying the influence of wind and predicting aerodynamic force on line.
2) The meta-flight aerodynamic modeling can effectively isolate the influence of an environmental wind disturbance variable in application, and can better predict aerodynamic force and aerodynamic moment of the fixed-wing aircraft under the condition of unknown wind conditions without obtaining the information of an attack angle and a sideslip angle by combining with an online estimated wind action coefficient function.
3) The application provides a general aerodynamic commonality basis function model in an analytic form, so that the meta-flight aerodynamic model has better migration capability and engineering applicability compared with the traditional aerodynamic model and the deep learning-based neuron flight aerodynamic model.
Drawings
FIG. 1 is a flow chart of a method for aerodynamic modeling of a fixed wing aircraft element flight taking wind interference into account, provided by an embodiment of the application;
FIG. 2 is an axial aerodynamic coefficient of an aircraft at different wind speedsA taylor expansion approximation result schematic diagram;
FIG. 3 shows the aerodynamic moment coefficients of pitch of an aircraft at different wind speedsA taylor expansion approximation result schematic diagram;
FIG. 4 is a schematic diagram of a discrete state case element flight aerodynamic model prediction result;
FIG. 5 is a schematic diagram of a continuous state bin aero-model prediction.
Detailed Description
The application is described in further detail below with reference to the attached drawings and to specific examples:
the fixed wing aircraft element flight aerodynamic modeling related coordinate system comprises an engine body coordinate system, an airflow coordinate system and a ground coordinate system. Aircraft body coordinate system S b Is fixedly connected with an airplane and has an origin o b Located at the aircraft centroid o b x b The axis being in plane of symmetry of the aircraft and pointing towards the nose o b y b The axis is perpendicular to the plane of symmetry of the aircraft and points to the right of the fuselage, o b z b The axis is directed downward of the fuselage in the plane of symmetry of the aircraft. Air flow coordinate system S a Is fixedly connected with the aircraftOrigin o a Located at the aircraft centroid o a x a The axis coincides with airspeed o a z a The axis being located in plane of symmetry of the aircraft and o a x a The axis being vertical and pointing under the fuselage, o a y a The axis being perpendicular to o a x a z a Plane, direction is determined by right hand rule. Ground coordinate system S g Is fixed on the ground, origin o g At a certain point on the ground o g x g The axis pointing in a certain direction in the horizontal plane o g z g The axis being perpendicular to the horizontal plane and pointing towards the centre of earth, o g y g The axis is determined by the right hand rule.
The implementation flow of the fixed wing aircraft element flight aerodynamic modeling is shown in fig. 1, and comprises the following 3 steps:
1) Traditional pneumatic modeling
The input of meta-flight aerodynamic modeling is still a discrete aerodynamic data set under different state conditions obtained by wind tunnel test, CFD numerical calculation and other means. When traditionally modeling discrete datasets, note that the partitioned attack angle, sideslip angle interval needs to encompass possible air disturbance scenarios. The aerodynamic and aerodynamic moment models of fixed-wing aircraft based on traditional modeling means can be generally expressed as
Wherein D, Y and L are respectively the drag, side force and lift force of the aircraft, M x 、M y And M is as follows z Respectively, the rolling moment, the pitching moment and the yawing moment of the aircraft, C D 、C Y And C L Respectively the drag coefficient, the side force coefficient and the lift coefficient of the aircraft, C l 、C m 、C n Respectively the roll moment coefficient, the pitch moment coefficient and the yaw moment coefficient of the aircraft,the dynamic pressure, V is the velocity amplitude of the aircraft, ρ is the air density, which is a function of the aircraft altitude h, S is the reference area, and b and c are the aircraft transverse reference length and longitudinal reference length, respectively.
In the application, the more commonly used method of modeling aerodynamic force under the air flow coordinate system is adopted in the step, and the aerodynamic force can be directly modeled under the machine body coordinate system in practice, so that the processing does not influence the implementation flow of the follow-up element flight aerodynamic modeling, and the difference is whether the conversion between the aerodynamic force expressed under the air flow coordinate system and the aerodynamic force expressed under the machine body coordinate system is carried out or not. The aerodynamic coefficient and the aerodynamic moment coefficient of the fixed wing aircraft are respectively
Wherein alpha is an attack angle, beta is a sideslip angle, ma is an aircraft Mach number, and C s l 、C s m 、C s n Representing static aerodynamic moment coefficient, C lp 、C mq 、C np As a dynamic derivative coefficient, delta e 、δ a And delta r Respectively, elevator deflection angle, aileron deflection angle and rudder deflection angle, [ pq r ]] T For the purpose of expressing the aircraft angular velocity vector under the machine body coordinates, the superscript "T" is the transposed symbol of the vector.
Based on the traditional pneumatic model given by the expression, the aerodynamic force and the aerodynamic moment expressed under the machine body coordinate system can be obtained as
Wherein F is x 、F y And F is equal to z The axial force, the transverse force and the normal force of the aircraft respectively,the direction cosine array from the air flow coordinate system to the machine system is
2) Unfolding accuracy analysis
In conventional aerodynamic modeling, variables such as velocity amplitude V, angle of attack α, sideslip angle β, mach number Ma are variables describing the motion of the aircraft relative to the airflow coordinate system. In the presence of wind, the motion speed of the aircraft relative to the ground coordinate system is assumed to be expressed in the body coordinate systemThe wind speed is expressed as +.>The speed of movement of the aircraft relative to the atmosphere is
At this time, the speed amplitude of the aircraft is
Mach number
Where c is the local speed of sound, which is a function of the aircraft altitude h. The attack angle alpha and sideslip angle beta of the aircraft are respectively
In the expansion accuracy analysis, the formula (5) is directed to the wind speed variable expressed in the machine body coordinate systemTaylor expansion is carried out, the approximation precision of aerodynamic force and aerodynamic moment is examined, the expansion orders of aerodynamic force and aerodynamic moment components are determined by comparing the approximation precision of finite-order Taylor expansion expressions of different orders to a primary function, and then the total term number in each expansion expression is determined by using ∈>Refer to axial force F x Transverse force F y Normal force F z Moment of roll M x Moment of pitch M y Yaw moment M z The total number of terms of the expanded expression.
3) Aerodynamic commonality basis function determination
The aerodynamic commonality basis function of the fixed-wing aircraft is obtained through calculation in the step. Representation of wind velocity vector in ground coordinate systemRepresentation in the body coordinate system +.>The following relationship exists:
wherein,a direction cosine array from a ground coordinate system to a machine body coordinate system is
Where φ is the roll attitude angle, θ is the pitch attitude angle, and ψ is the yaw attitude angle.
Obtaining a variable of wind speed expressed by the formula (5) in a ground coordinate system by using the relation (12)And carrying out the value of the derivative-by-derivative term of Taylor expansion. To reduce the calculation amount, the wind speed vector in the machine body coordinate system is basedThe aerodynamic force and aerodynamic moment expansion expression is analyzed to determine a main action item and a secondary action item which approximate the aerodynamic force and aerodynamic moment, the secondary action item can be ignored in modeling, and the aerodynamic force and aerodynamic moment expansion expression is directly set to zero. The common basis function of the aerodynamic (moment) components is calculated similarly to the axial force F x For example, for the 0 th order item, there is
For derivative terms of order 1 or even k, is
Wherein z is i Is thatIs the ith component of (c), P (t 1 ,t 2 ) As index variable t 1 ,t 2 Is a full permutation set of (c), i.e. P (t) 1 ,t 2 )＝{(t 1 ,t 2 ),(t 2 ,t 1 )}，P(t 1 ,t 2 ,...,t k ) As index variable t 1 ,t 2 ,...,t k Is a full permutation set of (a). />An expansion operator introduced for easy expression, which acts on index variable i according to a certain rule 1 ,i 2 ,...,i n To generate a vector. In vector generation, per i 1 ,i 2 ,...,i n Assuming that the index variable takes a range of 1 to m from the minimum value i j Starting with =1, (j=1, 2,., n), starting with i n Starting to increase, wherein the requirement in the increasing process meets the condition i 1 ≤i 2 ≤...≤i n Up to a maximum value i j =m, (j=1, 2,) n. If the order of appearance of the index variable in the brackets is consistent with the order in the subscript, the operator is expandedMiddle subscript i 1 i 2 ...i n May be omitted, i.e., abbreviated as S (). For index variable i according to extended operator definition 1 ,i 2 E {1, 2..m }, the following partial derivative calculation will generate dimension +.>Is a vector of (1):
the following product of variables will generate a vector:
the following index sets will be extended:
S(i 1 ,i 2 )＝[(1,1) (1,2)...(1,m) (2,2)...(2,m)...(m,m)] T
further, an index number function Λ (i 1 ,i 2 ,...,i n ) Which will be a certain index variable i 1 ,i 2 ,...,i n The value is mapped into
In the method, in the process of the application,represents taking l from n elements 1 The number of combinations of the individual elements, and so on, +.>Represents n- (l) 1 +l 2 +...+l k ) Counting the number of arranged elements, l 1 、l 2 … and l k Respectively indicate that the index sets are provided with l 1 、l 2 … and l k The index variable number with the same ordinal number and the corresponding different ordinal number is n- (l) 1 +l 2 +...+l k ). According to the index number function Λ (i 1 ,i 2 ,...,i n ) Definition (18) of
Λ(1,2,2)＝3
Λ(1,1,2,2)＝6
The function Λ can be defined as acting on the index set vector when it acts on each element in the index set vector, e.g
Λ([(1,1) (1,2) (1,3)])＝[1 2 2]
Matrix W j (j=2, 3,., k) is defined as
In the formula, (. Cndot.)! Representing a factorial operator.
In meta-flight aerodynamic modeling, in order to ensure that the values of the common basis functions are equivalent, scaling normalization processing can be performed according to the magnitude of the values. After determining the common base function, directly approximating aerodynamic force and aerodynamic moment of the aircraft by taking the obtained common base function as a base, and finally obtaining the meta-flight aerodynamic model as
In the method, in the process of the application,is a dimensionless aerodynamic (moment) coefficient, S is the aircraft reference area, note the dynamic pressure here +.>Unlike the dynamic pressure Q in conventional pneumatic modeling, the matrix Ω=diag ([ 1, b, c, b)])，a i ,(i＝F x ,F y ,F z ,M x ,M y ,M z ) Is only +.>The related coefficient function, ψ, is a matrix of common basis functions related only to the aircraft motion variable x, and for fixed wing aircraft, the state variables assumed to be the aircraft motion relative to the ground coordinate system and affecting aerodynamic and aerodynamic moments include altitude h, ground velocity vectorEuler attitude angle Θ= [ phi theta phi ]] T And angular velocity ω= [ pqr ]] T Further consider rudder deflection angle δ= [ δ ] a δ e δ r ] T The aircraft motion variable x is +.>The common basis function matrix ψ is in the form of
Wherein,is a common basis function vector, is
The dimensions of the different common basis function vectors, respectively, which are assigned the coefficient functions a, respectively i ,(i＝F x ,F y ,F z ,M x ,M y ,M z ) Is a dimension of (c).
In the meta-flight aerodynamic model, due to quantization errors caused by parameters such as function approximation errors, density and the like, problems of linear correlation of basic function values in specific motion (such as steady flight) of an aircraft and the like, an actual coefficient functionDoes not accurately characterize wind disturbancesVariable related information, which needs to be determined at the time of application, thereby realizing prediction of aerodynamic force (moment).
Example 1
And developing meta-flight aerodynamic modeling aiming at a certain fixed wing unmanned aerial vehicle and verifying.
1) Meta-flight aerodynamic modeling
Because traditional aerodynamic modeling is the prior art, meta-flight aerodynamic modeling research is directly performed based on a traditional aerodynamic model of a certain public fixed-wing aircraft. The smaller the ground speed of the aircraft, the greater the wind effect, and the speeds near the left boundary of the flight envelope are selected for analysis. Ground speed random generation of aircraftWind speed->From [ -10-10-10 under system] T Linear variation of m/s to [10 10 10 ]] T m/s. Figures 2 and 3 show the aerodynamic coefficients of the aircraft in axial direction at different wind speeds in the process, respectively>Coefficient of aerodynamic moment with pitch->The Taylor expansion approximation result of (2) is shown to have larger error in 1-order approximation, the 2-order approximation can better describe the overall change rule of aerodynamic coefficient and aerodynamic moment coefficient, the higher the expansion order is, the closer the result is to the true value, and the 6-order approximation result almost completely coincides with the true value. Further performing 1000 random sampling calculations, wherein the ground speed of the aircraft +.>Set to->v f 、w f Obeys [ -5,5]Average of m/s intervalEvenly distributed, the amplitude of the disturbance wind speed is +.>The direction is random throughout the three-dimensional space. Introducing an average error index E defined as
Wherein,and->The true and predicted values of the ith sample are represented, respectively, |·| represents the absolute value operator. Based on an average error of 1%, it can be seen that +.>Needs 4-step expansion->Requires 3-step expansion,>only 2 nd order, and +.>A 5 th order expansion is required to meet the 1% error requirement.
And analyzing the value of the expansion derivative function, and evaluating by adopting two indexes of mean and mean square error. For axial force coefficientAnalysis shows +.4 in the first 4 th expansion> The term impact is less; for normal force coefficient->In the first 3 rd order expansion->The term impact is less; for transverse force coefficient->In the first 3 rd order expansion->The term impact is less; for roll moment coefficient->In the first 3 rd order of expansionThe term impact is less; for pitch moment coefficient->In the first 2 nd order expansion->The term impact is less; for yaw moment coefficient->In 5 th order expansion-> The term impact is small. The approximation minor term value is taken to be zero, and an aerodynamic commonality basis function is calculated, so that the aircraft height h and ground speed can be obtained>The attitude Θ, the angular velocity omega and the rudder deflection angle delta are input aerodynamic and aerodynamic moment commonality basis functions of the fixed wing aircraft. For axial force, the common basis function of the axial force is 35; for normal force, transverse force and rolling moment, the common basis function is 20 items; for pitching moment, the common basis function is 10 items; for yaw moment, its common basis function is 56 terms. The common base functions are taken as bases in the flight, and the aerodynamic force (moment) received by the fixed-wing aircraft can be predicted by constructing a fixed-wing aircraft element flight aerodynamic model by combining the wind variable action coefficients determined by the identification means.
2) Meta-flight pneumatic model verification
And verifying the developed meta-flight aerodynamic model, and considering two situations.
a) Discrete state situation prediction
Aerodynamic and aerodynamic moment predictions for a randomly given aircraft state situation are considered. The speed of wind field in the environment is set to be 20m/s, and the direction vector is [ -10 ] under the ground coordinate system] T The altitude of the aircraft is h=900 m, the attitude angle is randomly given, and the representation of the speed of the aircraft relative to the ground in the body coordinate system is given as u f ＝80m/s，v f 、w f Obeys [ -5,5]The uniform random distribution of m/s interval, the representation of the ground speed of the aircraft under the ground coordinate system is determined by the calculation of attitude angle transformation, and the triaxial angular speeds of the aircraft all obey the interval [ -1,1]Uniform distribution of rad/s, elevator delta e Rudder delta r Aileron delta a Obeys [ -25,25]A uniform distribution of deg. Based on the least square method, aerodynamic force and aerodynamic moment measurement data of the first 500 states are taken as identification data to determine the wind action coefficient a i ,(i＝F x ,F y ,F z ,M x ,M y ,M z ) Then, the aerodynamic force and the aerodynamic moment of the last 1500 states are predicted, and the measured data have noise interference with a true value of 40%. Fig. 4 shows the predicted results of aerodynamic and aerodynamic moments of an aircraft, it can be seen that the predicted values based on the meta-flight aerodynamic model greatly reduce the measurement errors,the result is much closer to true.
b) Continuous state situation prediction
Aerodynamic and aerodynamic moment predictions that take into account the ideal forced pitch motion situation of the aircraft. The wind field speed in the environment is set to be 20m/s, and the direction is set to be [ -10 ] under the ground coordinate system] T The altitude of the aircraft is h=900 m, the pitching attitude angle changes in a regular way of θ=10sin (t) +2deg, the rolling angle and the yaw angle are 0deg, the corresponding triaxial angular velocity is determined through the attitude angle change, and the flying speed of the aircraft under the ground coordinate system is given as [3.04 80-2.09 ]]m/s, elevator control law is delta e = -10cos (t) deg, rudder deflection delta r =10 deg, aileron deflection delta a =0 deg, the data sampling time interval is Δt=0.05 s. Based on the least square method, aerodynamic force and aerodynamic moment measurement data of the first 10s are taken as identification data to determine the wind action coefficient a i ,(i＝F x ,F y ,F z ,M x ,M y ,M z ) Then, the aerodynamic force and aerodynamic moment data of the rear 40s are predicted, and the measured data have noise interference with a true value of 40 percent. The result of the prediction of aerodynamic force and aerodynamic moment is shown in fig. 5, and the result shows that the predicted value is well matched with the true value, and the effectiveness of the meta-flight aerodynamic model is illustrated.
The foregoing is merely exemplary of the present application, and specific technical solutions and/or features that are well known in the art have not been described in detail herein. It should be noted that, for those skilled in the art, several variations and modifications can be made without departing from the technical solution of the present application, and these should also be regarded as the protection scope of the present application, which does not affect the effect of the implementation of the present application and the practical applicability of the patent. The protection scope of the present application is subject to the content of the claims, and the description of the specific embodiments and the like in the specification can be used for explaining the content of the claims.
Claims (1)
1. The fixed wing aircraft element flight pneumatic modeling method considering wind interference is characterized by comprising the following steps of:
step 1, acquiring discrete pneumatic data sets under different state conditions, and establishing a traditional pneumatic model of the fixed-wing aircraft to obtain aerodynamic force and aerodynamic moment expressed under a machine body coordinate system as
Wherein F is x 、F y And F is equal to z The axial force, the transverse force and the normal force of the aircraft are respectively; m is M x 、M y And M is as follows z Respectively the rolling moment, the pitching moment and the yawing moment of the aircraft;v is the velocity amplitude of the aircraft, ρ is the air density, which is a function of the aircraft altitude h; s is the reference area of the aircraft, and b and c are the transverse reference length and the longitudinal reference length of the aircraft respectively;
C D 、C Y and C L Respectively, the drag coefficient, the side force coefficient and the lift coefficient of the aircraft, expressed as
C l 、C m 、C n The roll, pitch and yaw moment coefficients of the aircraft, respectively, are expressed as
The direction cosine array from the air flow coordinate system to the machine body coordinate system is expressed as
Alpha is the attack angle, beta is the sideslip angle, ma is the Mach number of the aircraft, C s l 、C s m 、C s n Representing static aerodynamic moment coefficient, C lp 、C mq 、C np As a dynamic derivative coefficient, delta e 、δ a And delta r Elevator, aileron and rudder, [ pqr ]] T For the aircraft angular velocity vector under the machine body coordinate system, the superscript "T" is the vector transposition symbol;
step 2, based on the step (5), aiming at the wind speed vector under the machine body coordinate system by aerodynamic force and aerodynamic momentPerforming Taylor expansion, examining the approximation accuracy of aerodynamic force and aerodynamic moment, determining the expansion orders of aerodynamic force and aerodynamic moment components by comparing the approximation accuracy of finite-order Taylor expansion expressions to an original function under different orders, and further determining the total term number in each expansion expression;
step 3, calculating to obtain an aerodynamic common base function of the fixed-wing aircraft, approximating aerodynamic force and aerodynamic moment of the aircraft by taking the obtained common base function as a base, and finally obtaining a meta-flight aerodynamic model expressed as
In the method, in the process of the application,is a nondimensionalized aerodynamic coefficient and aerodynamic moment coefficient; dynamic pressureMatrix Ω=diag ([ 1, b, c, b)])；a i ,(i＝F x ,F y ,F z ,M x ,M y ,M z ) Is only +.>A related coefficient function; ψ is a matrix of common basis functions related only to the aircraft motion variables x,comprises a height h and a ground speed vector +.>Euler attitude angle Θ= [ phi theta phi ]] T Angular velocity ω= [ pqr ]] T And rudder deflection angle delta= [ delta ] a δ e δ r ] T 。
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