CN117875090B - Fixed-wing unmanned aerial vehicle incremental element flight aerodynamic modeling method considering wind interference - Google Patents
Fixed-wing unmanned aerial vehicle incremental element flight aerodynamic modeling method considering wind interference Download PDFInfo
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Abstract
The invention discloses a fixed wing unmanned aerial vehicle increment element flight aerodynamic modeling method considering wind interference, which relates to the technical field of aerocraft aerodynamic modeling and has the technical scheme that: the aerodynamic force and the aerodynamic moment are decomposed into reference values which do not consider the influence of wind and increment values caused by the influence of the wind, the motion variables of the aircraft relative to a ground coordinate system are adopted to describe through a Taylor expansion multivariate function decomposition series theory, a common basis function analysis model of the aerodynamic force (moment) increment of the fixed-wing unmanned aerial vehicle which is universal under different wind conditions is built, and the online prediction of the aerodynamic force (moment) of the aircraft in flight under the unknown wind conditions is realized by combining the identification of the influence coefficient of the air disturbance. The method can well predict the aerodynamic force (moment) of the fixed wing unmanned aerial vehicle under the condition of unknown wind conditions, and lays a good foundation for accurate real-time aerodynamic modeling and online migration application; the aerodynamic commonality basis function model in an analytic form is provided, so that the incremental element flight aerodynamic model has better migration capability and engineering applicability.
Description
Technical Field
The invention relates to the technical field of aeronautical vehicle pneumatic modeling, in particular to a fixed-wing unmanned aerial vehicle incremental element flight pneumatic modeling method considering wind interference.
Background
Autonomous flight is a key technology of fixed-wing unmanned aerial vehicles. The unmanned aerial vehicle realizes the flight along the set route by sensing the state of the unmanned aerial vehicle in real time and implementing feedback control through the actuating mechanism, however, the wind in the environment seriously affects the flight safety of the fixed wing unmanned aerial vehicle, and the complex aerodynamics caused by wind can lead the fixed wing unmanned aerial vehicle to deviate from the route and even be out of control, which provides serious challenges for the safe flight of the fixed wing unmanned aerial vehicle. Due to the sensitivity of the current fixed wing unmanned aerial vehicle to environmental interference such as wind, the fixed wing unmanned aerial vehicle can usually carry out operation tasks under better weather conditions, and the application of the unmanned aerial vehicle is greatly limited. In order to improve the safety and reliability of the flying of the fixed-wing unmanned aerial vehicle in a windy environment, the aerodynamic force (moment) of the aircraft under the wind interference is necessary to be accurately predicted in real time, and a foundation is laid for the accurate flying control of the fixed-wing unmanned aerial vehicle.
The aerodynamic modeling of the fixed-wing unmanned aerial vehicle generally refers to the method of a traditional manned fixed-wing aircraft, and aims at the movement of the aircraft under an airflow coordinate system, and physical variables such as an attack angle, a sideslip angle and the like are introduced to describe the change rule of aerodynamic force and aerodynamic moment of the unmanned aerial vehicle. The method is widely applied to stability characteristic analysis, performance evaluation, control law design and the like. If the model is applied to the prediction of aerodynamic force and aerodynamic moment received by the current unmanned aerial vehicle on line, information such as an attack angle and a sideslip angle of the unmanned aerial vehicle is required to be determined in real time, but the attack angle sensor is high in price, so that the model is unfavorable for the wide application of the unmanned aerial vehicle. Meanwhile, when air disturbance exists, the attack angle and the sideslip angle are not easy to accurately measure on line, and the traditional pneumatic model is very sensitive to attack angle errors, so that aerodynamic force and aerodynamic moment received by an aircraft are difficult to accurately predict through the traditional pneumatic model, and the traditional pneumatic model is not beneficial to the on-line migration application in the flying of the fixed wing unmanned plane.
Scholars have conducted extensive researches on aerodynamic characteristics of a fixed-wing unmanned aerial vehicle under the condition of wind interference, but the researches mainly analyze the influence of wind on the aerodynamic characteristics of the unmanned aerial vehicle, and the researches on online real-time aerodynamic modeling considering wind interference are few. Aiming at online aerodynamic modeling under wind interference, connell and other scholars propose a neuron flight method for a rotor craft, and the method is based on a meta-learning methodology, and adopts deep meta-learning for generating an antagonism network (GENERATIVE ADVERSATIVE NETS, GAN) architecture to establish a general aerodynamic commonality basis function neural network model of the rotor craft under different wind conditions, so that real-time aerodynamic modeling and migration application under unknown wind conditions are 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 the fixed-wing unmanned aerial vehicle is more complex than that of the rotary wing aircraft, wherein not only aerodynamic force but also aerodynamic moment are needed to be modeled, and model input relates to more variables such as angular velocity, rudder deflection angle and the like of the aircraft, so that research is needed to be conducted pertinently. Particularly, the 'neuron flight' is a black box modeling method based on a deep neural network, which lacks theoretical explanation and is difficult to carry out theoretical analysis, and a great amount of training, testing and verification are required to obtain a group of proper common basis function neural network models, so that the engineering usability of the method is affected.
Disclosure of Invention
The invention aims to solve the problems, and provides a fixed-wing unmanned aerial vehicle increment flight aerodynamic modeling method considering wind interference, which is characterized in that aerodynamic force and aerodynamic moment are decomposed into a reference value which does not consider the wind influence and an increment value caused by the wind interference, a motion variable of an aircraft relative to a ground coordinate system is adopted to describe through a taylor expansion multiple function decomposition series theory, a common basis function analysis model of the fixed-wing unmanned aerial vehicle aerodynamic force (moment) increment under different wind conditions is constructed, and the identification of the wind interference action coefficient is combined, so that the online prediction of the aerodynamic force and the aerodynamic moment of the aircraft in flight under the unknown wind conditions is realized.
The technical aim of the invention is realized by the following technical scheme: a fixed-wing unmanned aerial vehicle incremental element flight aerodynamic modeling method considering wind interference comprises the following steps:
S1: obtaining aerodynamic force and aerodynamic moment expressed under an unmanned aerial vehicle body coordinate system, wherein the aerodynamic force and aerodynamic moment are expressed as follows:
（1）
In the method, in the process of the invention, 、And (3) withThe axial force, the transverse force and the normal force of the aircraft are respectively;、 And (3) with Respectively the rolling moment, the pitching moment and the yawing moment of the aircraft;
Is a dynamic pressure, which is a dynamic pressure, For the magnitude of the velocity of the aircraft,Is the air density, which is the altitude of the aircraftIs a function of (2); For a reference area of the aircraft, 、Respectively a transverse reference length and a longitudinal reference length of the aircraft;
And (3) with The drag coefficient, side force coefficient and lift coefficient of the aircraft are respectively expressed as:
（2）
the roll moment coefficient, the pitch moment coefficient and the yaw moment coefficient of the aircraft are respectively expressed as:
（3）
The direction cosine array from the air flow coordinate system to the machine body coordinate system is expressed as:
（4）
In the method, in the process of the invention, In order to be the angle of attack,As the slip angle of the slide-in plate,For the mach number of the aircraft,Representing the coefficient of static aerodynamic moment,、、As a coefficient of the dynamic derivative,、And (3) withRespectively an elevator, an aileron and a rudder,The upper mark is the angular velocity vector of the airplane under the machine body coordinate system ""Transpose symbols for vectors;
S2: the aerodynamic forces and moments are decomposed into reference amounts and increments, expressed as:
（5）
In the method, in the process of the invention, Is the aerodynamic force and aerodynamic moment reference quantity corresponding to the motion state of the fixed-wing unmanned aerial vehicle relative to the ground under the windless condition,Is the aerodynamic force and aerodynamic moment increment caused by wind;
S3: increment is increased For the variable of wind speed expressed under the machine body coordinate systemPerforming Taylor expansion, determining expansion orders of aerodynamic force increment and aerodynamic moment increment components, and further determining the total number of terms in an expansion approximate expression;
S4: calculating a common basis function of aerodynamic force increment and aerodynamic moment increment, approximating the aerodynamic force increment and the aerodynamic moment increment as a basis, and combining aerodynamic force and aerodynamic moment reference quantity to obtain an increment element flight aerodynamic model of the fixed-wing unmanned aerial vehicle:
（19）
In the method, in the process of the invention, 、、Is a dimensionless incremental aerodynamic (moment) coefficient; dynamic pressure; Matrix array；Is only related to the wind speed variable expressed in the ground coordinate systemA related coefficient function; is a variable corresponding to the movement of the aircraft only A matrix of related common basis functions,Comprising a height ofGround speed vector expressed in ground coordinatesEuler attitude angleAngular velocity ofAnd rudder deflection angle。
The invention is further provided with: the reference quantity in S2The calculation of (1) comprises the following steps:
S21: ground speed vector representing aircraft in ground coordinate system Conversion to ground speed vectors expressed under the body；
（11）
In the attitude angle of an aircraftGround coordinate systemTo the machine body coordinate systemDirection cosine array of (2)The method comprises the following steps:
（12）
In the method, in the process of the invention, In order to roll the attitude angle,In order to be the pitch attitude angle,Is the yaw attitude angle
S22: calculating the movement speed of the aircraft relative to the atmosphere:
（6）
In the formula, the wind speed is expressed as in the coordinate system of the aircraft body ；
The speed amplitude of an aircraft is expressed as:
（7）
Mach number is:
（8）
Wherein, For the local speed of sound,Is the altitude of the aircraftIs a function of (2);
Angle of attack of aircraft Sideslip angleThe method comprises the following steps of:
（9）
（10）
s23: wind speed control Obtaining the speed amplitude of the aircraft at the momentMach numberAngle of attackAngle of sideslipBased on the traditional pneumatic model, the reference quantity is calculated。
The invention is further provided with: the S4 incremental element flight aerodynamic model has a common basis function matrixThe form of (2) is:
（20）
Wherein, Is a common basis function vector, expressed as:
（21）
（22）
（23）
（24）
（25）
（26）
、、、、、 the dimensions of the different common basis function vectors are respectively specified, and the coefficient functions are respectively specified Is a dimension of (c).
The invention is further provided with: the calculation of the common basis function vector comprises the following steps:
s41: the first component in the basis function vector is set to ; Remaining componentsBy aerodynamic (moment) incrementFor variable of wind speed expressed in ground coordinate systemIs obtained by sequentially arranging derivative items of the formula (I);
S42: calculating a common basis function vector Other common basis function vectorsThe calculation mode is the same as；
Introducing an expansion operatorActing on index variablesTo generate a vector: in vector generation, the following is pressedIs assumed to have a value ranging from 1 to 1From the minimum valueStarting fromStarting to increase, and meeting the conditions in the increasing processUp to a maximum value; If the order of appearance of the index variable in the brackets is consistent with the order in the subscript, the operator is expandedMiddle subscriptCan be omitted, i.e. abbreviated as; For index variables according to extended operator definitionGenerating dimension by partial derivative calculationIs calculated as:
（15）
Variable product generation vector:
（16）
The index set is expanded as follows:
s43: calculating axial force delta For the variable of wind speed expressed under the machine body coordinate systemAt the position ofLevel 1 or evenThe value of the derivative term, letDetermining a vector:
，，…，；
S44: defining index number functions To change index variableThe value mapping is as follows:
（17）
In the method, in the process of the invention, Representative ofFetching from individual elementsThe number of combinations of the individual elements,Representative ofThe number of permutations of the individual elements is calculated,、… AndRespectively indicate that the index sets have、… AndThe number of index variables with the same ordinal number and different corresponding values is；
S45: function ofThe expansion is defined as acting on the index set vector, and the matrix is calculated：
（18）
In the method, in the process of the invention,Representing a factorial operator;
S46: calculating axial force delta For variable of wind speed expressed in ground coordinate system1 St order of (2) or evenThe order derivative term is calculated by the following formula:
（14）
Wherein, Is thatIs the first of (2)The number of components of the composition,，，…，，As index variableIs provided with a full-permutation set of (a),As index variableIs a full permutation set of (a); the direction cosine array is from the ground coordinate system to the machine body coordinate system;
s47: will be ，，…，Normalization processing is carried out to obtain a common basis functionThe term by term of the vector.
In summary, the invention has the following beneficial effects:
1) The aerodynamic force (moment) of the fixed-wing unmanned aerial vehicle is decomposed into an aerodynamic force (moment) reference quantity under the windless condition and an aerodynamic force (moment) increment caused by wind by the aerodynamic force (moment) modeling, and the aerodynamic force (moment) increment is taken as an estimated quantity to correct the aerodynamic force (moment) of the fixed-wing unmanned aerial vehicle, so that a good foundation is laid for accurate real-time aerodynamic modeling and online migration application.
2) The aerodynamic commonality basis function constructed in the incremental element flight aerodynamic modeling is described by adopting a motion variable of an aircraft relative to a ground coordinate system, and by separating the aircraft motion variable and the air disturbance variable relative to the ground coordinate system, a commonality basis function irrelevant to wind conditions and a coefficient function irrelevant to the aircraft motion can be obtained, and the aerodynamic force (moment) of the fixed-wing unmanned aerial vehicle under the unknown wind conditions can be predicted better without obtaining the attack angle and sideslip angle information by combining the wind action coefficient function estimated on line.
3) The invention provides a general aerodynamic commonality basis function model in an analytic form, so that the incremental element flight aerodynamic model has better migration capability and engineering applicability compared with the traditional aerodynamic model and the neuron flight aerodynamic model based on deep learning.
Drawings
FIG. 1 is a flow chart of an implementation of a modeling method in an embodiment of the invention;
FIG. 2 is a schematic diagram of the approximation result of the fixed wing unmanned aerial vehicle incremental axial aerodynamic coefficient at different wind speeds in an embodiment of the present invention;
FIG. 3 is a schematic diagram of an approximation result of an increment normal aerodynamic coefficient of a fixed-wing unmanned aerial vehicle at different wind speeds in an embodiment of the invention;
FIG. 4 is a schematic diagram of the approximation result of the fixed wing unmanned aerial vehicle incremental transverse aerodynamic coefficient at different wind speeds in an embodiment of the present invention;
FIG. 5 is a schematic diagram of an approximation result of an incremental roll aerodynamic moment coefficient of a fixed wing unmanned aerial vehicle at different wind speeds in an embodiment of the present invention;
FIG. 6 is a schematic diagram of an approximation result of an incremental pitch aerodynamic moment coefficient of a fixed wing unmanned aerial vehicle at different wind speeds in an embodiment of the present invention;
FIG. 7 is a schematic diagram of an approximation result of an incremental yaw aerodynamic moment coefficient of a fixed wing unmanned aerial vehicle at different wind speeds in an embodiment of the present invention;
FIG. 8 is a schematic diagram of an axial aerodynamic force prediction result based on an incremental meta-flight aerodynamic model for a constant wind situation in an embodiment of the present invention;
FIG. 9 is a schematic diagram of a normal aerodynamic force prediction result based on an incremental meta-flight aerodynamic model for a constant wind situation in an embodiment of the present invention;
FIG. 10 is a schematic diagram of a transverse aerodynamic force prediction result based on an incremental meta-flight aerodynamic model for a constant wind situation in an embodiment of the present invention;
FIG. 11 is a schematic diagram of a roll aerodynamic moment prediction result based on an incremental element flight aerodynamic model for a constant wind situation in an embodiment of the invention;
FIG. 12 is a schematic diagram of a pitch aerodynamic moment prediction result based on an incremental element flight aerodynamic model for a constant wind situation in an embodiment of the invention;
FIG. 13 is a schematic diagram of a yaw aerodynamic moment prediction result based on an incremental element flight aerodynamic model for a constant wind situation in an embodiment of the invention;
FIG. 14 is a schematic diagram of an axial aerodynamic force prediction result of a time-varying wind scenario based on an incremental element flight aerodynamic model in an embodiment of the present invention;
FIG. 15 is a schematic diagram of a normal aerodynamic force prediction result of a time-varying wind situation based on an incremental element flight aerodynamic model in an embodiment of the present invention;
FIG. 16 is a schematic diagram of a transverse aerodynamic force prediction result of a time-varying wind scenario based on an incremental element flight aerodynamic model in an embodiment of the present invention;
FIG. 17 is a schematic diagram of a roll aerodynamic moment prediction result of a time-varying wind scenario based on an incremental element flight aerodynamic model in an embodiment of the present invention;
FIG. 18 is a diagram of a pitch aerodynamic moment prediction result of a time-varying wind regime based on an incremental-element flight aerodynamic model in an embodiment of the present invention;
FIG. 19 is a graph showing the predicted yaw aerodynamic moment of a time-varying wind scenario based on an incremental-element flight aerodynamic model in an embodiment of the invention.
Detailed Description
In order that those skilled in the art will better understand the present invention, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings, wherein it is to be understood that the illustrated embodiments are merely exemplary of some, but not all, of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other. The present invention will be described in detail with reference to examples.
Examples:
The fixed wing unmanned aerial vehicle incremental element flight aerodynamic modeling related coordinate system comprises a machine body coordinate system, an airflow coordinate system and a ground coordinate system. Machine body coordinate system Fixedly connected with the unmanned aerial vehicle and provided with an originIs positioned at the mass center of the unmanned aerial vehicle,The axis is in the plane of symmetry of the unmanned aerial vehicle and is directed towards the nose,The axis is perpendicular to the plane of symmetry of the unmanned aerial vehicle and points to the right of the fuselage,The axis points below the fuselage in the plane of symmetry of the unmanned aerial vehicle. Air flow coordinate systemFixedly connected with the unmanned aerial vehicle and provided with an originIs positioned at the mass center of the unmanned aerial vehicle,The axis coincides with the space velocity and,The axis is positioned in the plane of symmetry of the unmanned planeThe axis is vertical and directed below the fuselage,The axis being perpendicular toPlane, direction is determined by right hand rule. Ground coordinate systemIs fixed on the ground and has an originIs positioned at a certain point on the ground,The axis is directed in a certain direction in the horizontal plane,The axis is perpendicular to the horizontal plane and directed towards the earth's center,The axis is determined by the right hand rule.
As shown in FIG. 1, the fixed wing unmanned aerial vehicle incremental element flight aerodynamic modeling method considering wind interference comprises the following steps:
s1: acquiring discrete pneumatic data sets under different state conditions, and establishing a traditional pneumatic model of the fixed-wing unmanned aerial vehicle to obtain aerodynamic force and aerodynamic moment expressed under an unmanned aerial vehicle body coordinate system as
（1）
In the method, in the process of the invention,、And (3) withThe axial force, the transverse force and the normal force of the aircraft are respectively;、 And (3) with Respectively the rolling moment, the pitching moment and the yawing moment of the aircraft; Is a dynamic pressure, which is a dynamic pressure, For the magnitude of the velocity of the aircraft,Is the air density, which is the altitude of the aircraftIs a function of (2); For a reference area of the aircraft, 、Respectively a transverse reference length and a longitudinal reference length of the aircraft;
And (3) with The drag coefficient, side force coefficient and lift coefficient of the aircraft are respectively expressed as:
（2）
the roll moment coefficient, the pitch moment coefficient and the yaw moment coefficient of the aircraft are respectively expressed as:
（3）
The direction cosine array from the air flow coordinate system to the machine body coordinate system is expressed as:
（4）
In order to be the angle of attack, As the slip angle of the slide-in plate,For the mach number of the aircraft,Representing the coefficient of static aerodynamic moment,、、As a coefficient of the dynamic derivative,、And (3) withRespectively an elevator, an aileron and a rudder,The upper mark is the angular velocity vector of the airplane under the machine body coordinate system ""Transpose symbols for vectors;
S2: considering the influence of wind in flying a fixed-wing unmanned aerial vehicle, decomposing aerodynamic force (moment) represented by formula (1) into aerodynamic force (moment) reference quantity under windless condition and aerodynamic force (moment) increment caused by wind as
（5）
In the method, in the process of the invention,Is the aerodynamic force (moment) reference quantity corresponding to the motion state of the fixed-wing unmanned aerial vehicle relative to the ground under the windless condition,Is the aerodynamic (moment) increment due to wind.
In conventional pneumatic modeling, velocity amplitudeAngle of attackSideslip angleMach numberEqual variables are all variables that describe the movement of the aircraft relative to the airflow coordinate system. The motion speed of the aircraft relative to the ground coordinate system is assumed to be expressed as under the machine body coordinate systemThe wind speed is expressed as under the coordinate system of the aircraft bodyThe movement speed of the aircraft relative to the atmosphere is
（6）
At this time, the speed amplitude of the aircraft is
（7）
Mach number
（8）
Wherein,For the local speed of sound,Is the altitude of the aircraftIs a function of (2);
Angle of attack of aircraft Sideslip angleThe method comprises the following steps of:
（9）
（10）
furthermore, according to the attitude angle of the aircraft The ground speed vector of the aircraft expressed under the ground coordinate system can be calculatedGround speed vector expressed in machine body coordinate systemIs the relation of:
（11）
Ground coordinate system To the machine body coordinate systemDirection cosine array of (2)Is that
（12）
In the method, in the process of the invention,In order to roll the attitude angle,In order to be the pitch attitude angle,Is the yaw attitude angle.
Using equation (11), the ground velocity vector of the aircraft in the ground coordinate system can be expressedConversion to ground speed vectors expressed under the bodyBased on the traditional pneumatic model, let wind speedBy using the relation given by the formulas (7) to (10), the height of the fixed wing unmanned plane is combinedInformation to obtain the speed amplitude of the aircraftMach numberAngle of attackAngle of sideslipFurther utilizing angular velocityAnd rudder deflection angleInformation, through the formula (1) to formula (3), the aerodynamic force (moment) reference quantity is calculated and obtained。
S3, based on the formula (5), using the relational formulas (7) to (10), increasing the aerodynamic force (moment)For the variable of wind speed expressed under the machine body coordinate systemPerforming Taylor expansion, examining the approximation accuracy of aerodynamic force increment and aerodynamic moment increment, and determining the expansion order of each aerodynamic force increment and aerodynamic moment increment component by comparing the approximation accuracy of finite-order Taylor expansion expressions on aerodynamic force (moment) increment under different orders, thereby determining the total number of terms in the expansion approximation expression;
s4: and calculating to obtain an aerodynamic commonality basis function of the aerodynamic force (moment) increment of the fixed-wing unmanned aerial vehicle:
to enhance the robustness of the incremental meta-analysis aerodynamic model, the first component in the basis function vector is set to The remaining componentsFrom the determined expansion order of S3, the increment of aerodynamic force (moment)For variable of wind speed expressed in ground coordinate systemIs obtained by sequentially arranging the derivative terms of (a).
In order to calculate and obtain aerodynamic commonality basis functions of aerodynamic force (moment) increment of fixed-wing unmanned aerial vehicle, the patent provides the following calculation method, and firstly, the representation of wind speed vector under a ground coordinate system is providedRepresentation in a body coordinate systemIs the relation of:
（13）
Wherein, Is a directional cosine array from the ground coordinate system to the machine body coordinate system. Using relation (13), in S3, the aerodynamic (moment) increment is obtained for the wind speed variable expressed in the body coordinate systemFurther determining on the basis of the derivative-by-derivative term of (c). Common basis function calculations for components of aerodynamic (moment) increment are similar to each other, in terms of axial force incrementFor example, 1 st order or evenThe derivative term can be calculated as
（14）
Wherein,Is thatIs the first of (2)The number of components of the composition,As index variableIs a full permutation set of (a), i.e，Is a fully arranged set of index variables.An expansion operator for easy expression, which acts on index variable according to a certain ruleTo generate a vector. In vector generation, the following is pressedIs assumed to have a value ranging from 1 to 1From the minimum valueStarting fromStarting to increase, and meeting the conditions in the increasing processUp to a maximum value. If the order of appearance of the index variable in the brackets is consistent with the order in the subscript, the operator is expandedMiddle subscriptCan be omitted, i.e. abbreviated as。
For index variables according to extended operator definitionThe following partial derivative calculation will generate dimension asIs a vector of (1):
（15）
the following product of variables will generate a vector:
（16）
The following index sets will be extended:
The left derivative terms in formula (15) are defined as ，，…，Right end、、The term definitions are similar. Further, an index number function is definedWhich will be a certain index variableThe value is mapped into
（17）
In the method, in the process of the invention,Representative ofFetching from individual elementsThe number of combinations of the individual elements,Representative ofThe number of permutations of the individual elements is calculated,、… AndRespectively indicate that the index sets have、… AndThe number of index variables with the same ordinal number and different corresponding values is. According to the index number functionDefinition (17) has
Function ofExpandable definition is applied to the index set vector when it is applied to each element in the index set vector, e.g
Matrix arrayIs defined as
（18）
In the method, in the process of the invention,Representing a factorial operator. Obtaining，，，…，Normalization processing is carried out to obtain a common basis functionThe term by term of the vector.
Approximating aerodynamic force increment and aerodynamic moment increment of the unmanned aerial vehicle by taking the obtained common basis function as a basis, and combining aerodynamic force (moment) reference quantityFinally, the fixed wing unmanned aerial vehicle increment element flight aerodynamic model is obtained
（19）
In the method, in the process of the invention,、、Is a dimensionless incremental aerodynamic (moment) coefficient; dynamic pressure; Matrix array；Is only related to the wind speed variable expressed in the ground coordinate systemA related coefficient function; is a variable corresponding to the movement of the aircraft only A matrix of related common basis functions,Comprising a height ofGround speed vector expressed in ground coordinatesEuler attitude angleAngular velocity ofAnd rudder deflection angle。
Commonality basis function matrix in incremental element flight aerodynamic modelIs in the form of
（20）
Wherein,Is a common basis function vector, is
（21）
（22）
（23）
（24）
（25）
（26）
、、、、、The dimensions of the different common basis function vectors, respectively, which are also respectively assigned coefficient functionsIs a dimension of (c).
In the fixed-wing unmanned plane incremental element flight aerodynamic model, due to quantization errors caused by parameters such as function approximation errors, density and the like, and problems of linear correlation of basic function values in specific motions (such as steady flight) of an aircraft, and the like, an actual coefficient functionThe related items in (1) do not accurately represent the wind disturbance variable related information, and the related items need to be determined when in application, and are further combined with aerodynamic force (moment) reference quantity, so that the prediction of the aerodynamic force (moment) of the fixed-wing unmanned aerial vehicle is realized.
And performing incremental element flight aerodynamic modeling and verification aiming at a certain fixed wing aircraft.
1) Incremental meta-flight aerodynamic modeling
Because the traditional pneumatic modeling is the prior art, the incremental element flight pneumatic modeling research is directly carried out based on the traditional pneumatic 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. The ground speed of the aircraft isM/s, and calculating aerodynamic force (moment) reference quantity based on the speed and other state information such as the attitude of the aircraft. Further analysis of aerodynamic (moment) increment, taking into account wind speedFrom under the systemLinear change of m/s toM/s. Fig. 2 and fig. 3 respectively show taylor expansion approximation results of the incremental aerodynamic coefficient and the incremental aerodynamic moment coefficient of the aircraft at different wind speeds in the process, and it can be seen from the graph that the 1-order approximation has larger error, the 2-order approximation can better describe the overall change rule of the incremental aerodynamic (moment) coefficient, and the higher the expansion order is, the closer the result is to a true value.
Further developing 1000 random sampling calculations, wherein the ground speed of the aircraftIs arranged as=50m/s，、Compliance withThe m/s interval is uniformly distributed, and the amplitude of the interference wind speed is=12 M/s, the direction is random throughout the three-dimensional space. Introducing an average error indexDefined as
Wherein,And (3) withRespectively represent the firstThe true value and the predicted value of each sample,Representing an absolute value operator. The aerodynamic (moment) coefficient is increased by taking the average aerodynamic (moment) error of 1% as a standardA 4-order deployment is required and,、、A 3-order deployment is required and,Only the 2 nd order is neededA5 th order expansion is required to meet the 1% error requirement. After determining the unfolding order, further calculating aerodynamic commonality basis functions of aerodynamic (moment) increment, and obtaining the altitude of the aircraftGround speedPosture and attitudeAngular velocity ofRudder deflection angleIs an input fixed-wing unmanned aerial vehicle aerodynamic force (moment) increment commonality basis function. In the incremental element flight aerodynamic model of the fixed wing aircraft, 35 common basis functions of axial force increment are added; the common basis functions of the normal force increment, the transverse force increment and the rolling moment increment are respectively 20 items; the common basis function of the pitching moment increment is 10 items; the common basis function of yaw moment increment is 56 terms. And taking the common base functions as bases in the flight, determining the action coefficient of wind variables by utilizing an identification means, constructing an incremental element flight aerodynamic model of the fixed-wing unmanned aerial vehicle by combining the aerodynamic force (moment) reference quantity, and predicting the aerodynamic force (moment) received by the fixed-wing unmanned aerial vehicle.
2) Incremental meta-flight pneumatic model verification
And verifying the developed incremental element flight aerodynamic model, and considering two situations of normal wind and time-varying wind for examination.
Aerodynamic and aerodynamic moment predictions for an ideal forced pitching motion of a fixed-wing aircraft are considered for a constant wind situation. The wind field speed in the environment is set to be 20m/s, and the direction is set to be in a ground coordinate systemThe aircraft has the height ofPitch attitude angle =900 mRegular variation of deg, roll angle and yaw angle of 0deg, corresponding triaxial angular velocity is determined by attitude angle variation, and flying speed of the aircraft under the geodetic coordinate system is given asM/s, elevator control law isDeg, rudder deflection of=10 Deg, aileron deflection as=0 Deg, data sampling time interval isAerodynamic and aerodynamic moment data are measured data in which there is a true 40% level of noise disturbance. Based on Kalman filtering method, wind action coefficients are identified onlineAnd determining an incremental element flight aerodynamic model, and further predicting aerodynamic force (moment). Fig. 8 and fig. 13 respectively show the prediction results of aerodynamic force and aerodynamic moment of the fixed wing unmanned aerial vehicle, and only the measurement data of aerodynamic force (moment) containing noise for the first 25 seconds are shown in the figures for comparison effect, and the calculation result shows that the incremental element flight aerodynamic modeling method provided by the invention has good matching of the Kalman filtering prediction value and the true value, and effectively eliminates the interference of noise.
Further consider aerodynamic and aerodynamic moment predictions of an ideal forced pitch motion of a time-varying wind situation aircraft. The wind field speed changing in the environment is set as in the ground coordinate systemThe aircraft motion and corresponding conditions are the same as in a normal wind situation. Still, the incremental meta-flight aerodynamic model is determined on-line based on a Kalman filtering method to predict aerodynamic force and aerodynamic moment data. Fig. 14 and fig. 19 respectively show the prediction results of aerodynamic force and aerodynamic moment of the fixed-wing unmanned aerial vehicle, and for comparison effect, the figure also only shows the noisy aerodynamic force (moment) measurement data of the first 25 seconds, and the calculation result shows that even for the time-varying wind situation, based on the incremental element flight aerodynamic model provided by the invention, the Kalman filtering prediction value and the true value are better matched, and the effectiveness of the established fixed-wing unmanned aerial vehicle incremental element flight aerodynamic model is illustrated.
The present embodiment is only for explanation of the present invention and is not to be construed as limiting the present invention, and modifications to the present embodiment, which may not creatively contribute to the present invention as required by those skilled in the art after reading the present specification, are all protected by patent laws within the scope of claims of the present invention.
Claims (4)
1. A fixed-wing unmanned aerial vehicle increment element flight aerodynamic modeling method considering wind interference is characterized in that: the method comprises the following steps:
S1: obtaining aerodynamic force and aerodynamic moment expressed under an unmanned aerial vehicle body coordinate system, wherein the aerodynamic force and aerodynamic moment are expressed as follows:
（1）
In the method, in the process of the invention, 、And (3) withThe axial force, the transverse force and the normal force of the aircraft are respectively;、 And (3) with Respectively the rolling moment, the pitching moment and the yawing moment of the aircraft;
Is a dynamic pressure, which is a dynamic pressure, For the magnitude of the velocity of the aircraft,Is the air density, which is the altitude of the aircraftIs a function of (2); For a reference area of the aircraft, 、Respectively a transverse reference length and a longitudinal reference length of the aircraft;
And (3) with The drag coefficient, side force coefficient and lift coefficient of the aircraft are respectively expressed as:
（2）
the roll moment coefficient, the pitch moment coefficient and the yaw moment coefficient of the aircraft are respectively expressed as:
（3）
The direction cosine array from the air flow coordinate system to the machine body coordinate system is expressed as:
（4）
In the method, in the process of the invention, In order to be the angle of attack,As the slip angle of the slide-in plate,For the mach number of the aircraft,Representing the coefficient of static aerodynamic moment,、、As a coefficient of the dynamic derivative,、And (3) withRespectively an elevator, an aileron and a rudder,The upper mark is the angular velocity vector of the airplane under the machine body coordinate system ""Transpose symbols for vectors;
S2: the aerodynamic forces and moments are decomposed into reference amounts and increments, expressed as:
（5）
In the method, in the process of the invention, Is the aerodynamic force and aerodynamic moment reference quantity corresponding to the motion state of the fixed-wing unmanned aerial vehicle relative to the ground under the windless condition,Is the aerodynamic force and aerodynamic moment increment caused by wind;
S3: increment is increased For the variable of wind speed expressed under the machine body coordinate systemPerforming Taylor expansion, determining expansion orders of aerodynamic force increment and aerodynamic moment increment components, and further determining the total number of terms in an expansion approximate expression;
S4: calculating a common basis function of aerodynamic force increment and aerodynamic moment increment, approximating the aerodynamic force increment and the aerodynamic moment increment as a basis, and combining aerodynamic force and aerodynamic moment reference quantity to obtain an increment element flight aerodynamic model of the fixed-wing unmanned aerial vehicle:
（19）
In the method, in the process of the invention, 、、Is a dimensionless incremental aerodynamic (moment) coefficient; dynamic pressure; Matrix array；Is only related to the wind speed variable expressed in the ground coordinate systemA related coefficient function; is a variable corresponding to the movement of the aircraft only A matrix of related common basis functions,Comprising a height ofGround speed vector expressed in ground coordinatesEuler attitude angleAngular velocity ofAnd rudder deflection angle。
2. The fixed-wing unmanned aerial vehicle incremental element flight aerodynamic modeling method considering wind interference according to claim 1, wherein the method is characterized by comprising the following steps: the reference quantity in S2The calculation of (1) comprises the following steps:
S21: ground speed vector representing aircraft in ground coordinate system Conversion to ground speed vectors expressed under the body；
（11）
In the attitude angle of an aircraftGround coordinate systemTo the machine body coordinate systemDirection cosine array of (2)The method comprises the following steps:
（12）
In the method, in the process of the invention, In order to roll the attitude angle,In order to be the pitch attitude angle,Is the yaw attitude angle
S22: calculating the movement speed of the aircraft relative to the atmosphere:
（6）
In the formula, the wind speed is expressed as in the coordinate system of the aircraft body ；
The speed amplitude of an aircraft is expressed as:
（7）
Mach number is:
（8）
Wherein, For the local speed of sound,Is the altitude of the aircraftIs a function of (2);
Angle of attack of aircraft Sideslip angleThe method comprises the following steps of:
（9）
（10）
s23: wind speed control Obtaining the speed amplitude of the aircraft at the momentMach numberAngle of attackAngle of sideslipBased on the traditional pneumatic model, calculating aerodynamic force (moment) reference quantity。
3. The fixed-wing unmanned aerial vehicle incremental element flight aerodynamic modeling method considering wind interference according to claim 1, wherein the method is characterized by comprising the following steps: the S4 incremental element flight aerodynamic model has a common basis function matrixThe form of (2) is:
（20）
Wherein, Is a common basis function vector, expressed as:
（21）
（22）
（23）
（24）
（25）
（26）
、、、、、 The dimensions of the vectors of the different aerodynamic (moment) commonality basis functions, respectively, which at the same time respectively specify coefficient functions Is a dimension of (c).
4. The fixed-wing unmanned aerial vehicle incremental element flight aerodynamic modeling method considering wind interference according to claim 3, wherein the method is characterized by comprising the following steps: the calculation of the common basis function vector comprises the following steps:
s41: the first component in the basis function vector is set to ; Remaining componentsBy aerodynamic (moment) incrementFor variable of wind speed expressed in ground coordinate systemIs obtained by sequentially arranging derivative items of the formula (I);
S42: calculating a common basis function vector Other common basis function vectorsThe calculation mode is the same as；
Introducing an expansion operatorActing on index variablesTo generate a vector: in vector generation, the following is pressedIs assumed to have a value ranging from 1 to 1From the minimum valueStarting fromStarting to increase, and meeting the conditions in the increasing processUp to a maximum value; If the order of appearance of the index variable in the brackets is consistent with the order in the subscript, the operator is expandedMiddle subscriptCan be omitted, i.e. abbreviated as; For index variables according to extended operator definitionGenerating dimension by partial derivative calculationIs calculated as:
（15）
Variable product generation vector:
（16）
The index set is expanded as follows:
；
s43: calculating axial force delta For the variable of wind speed expressed under the machine body coordinate systemAt the position ofLevel 1 or evenThe value of the derivative term, letDetermining a vector:
，，…，；
S44: defining index number functions To change index variableThe value mapping is as follows:
（17）
In the method, in the process of the invention, Representative ofFetching from individual elementsThe number of combinations of the individual elements,Representative ofThe number of permutations of the individual elements is calculated,、… AndRespectively indicate that the index sets have、… AndThe number of index variables with the same ordinal number and different corresponding values is；
S45: function ofThe expansion is defined as acting on the index set vector, and the matrix is calculated：
（18）
In the method, in the process of the invention,Representing a factorial operator;
S46: calculating axial force delta For variable of wind speed expressed in ground coordinate system1 St order of (2) or evenThe order derivative term is calculated by the following formula:
（14）
Wherein, Is thatIs the first of (2)The number of components of the composition,，，…，，As index variableIs provided with a full-permutation set of (a),As index variableIs a full permutation set of (a); the direction cosine array is from the ground coordinate system to the machine body coordinate system;
s47: will be ，，…，Normalization processing is carried out to obtain a common basis functionThe term by term of the vector.
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