CN110348080A - Fighter plane HAOA characteristics analysis method based on Bifurcation Analysis - Google Patents

Fighter plane HAOA characteristics analysis method based on Bifurcation Analysis Download PDF

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CN110348080A
CN110348080A CN201910558970.6A CN201910558970A CN110348080A CN 110348080 A CN110348080 A CN 110348080A CN 201910558970 A CN201910558970 A CN 201910558970A CN 110348080 A CN110348080 A CN 110348080A
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branch
angle
point
fighter plane
attack
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季雨璇
甄子洋
王志刚
王业光
王家兴
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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Abstract

The fighter plane HAOA characteristics analysis method based on Bifurcation Analysis that the invention discloses a kind of, comprising the following steps: it is step 1, theoretical based on Bifurcation Analysis when fighter plane is in high-incidence condition, calculate the stable equilibrium point and branch point of fighter plane；Step 2, for different branch's vertex types, branch's vertex type is divided by the characteristic value of the mathematical model of air-combat maneuver mechanical system Jacobian matrix at branch point；Step 3, pass through continuation algorithm, the balanced surface and branch face for calculating the fighter plane angle of attack, yaw angle, rolling angular speed, pitch rate and yawrate change with control rudder face drift angle and the process of variation judges equalization point distributing area according to the stability of acquired balanced surface and branch face.The safe range flown under fighter plane High Angle of Attack can be predicted in the present invention, analyzes the state of development and Crack cause of deep stall, tailspin, has good reference meaning to practical implementation.

Description

Fighter plane HAOA characteristics analysis method based on Bifurcation Analysis
Technical field
The present invention relates to the fighter plane HAOA characteristics analysis methods based on Bifurcation Analysis, belong to aviation specificity analysis technology Field.
Background technique
Fighter plane is the military aircraft for eliminating enemy plane He other aircraft-type configuration aerial attackers in the sky, is that military aerial is made The main machine of war, over the ground and to all occupying not replaceable status in air battle bucket.Empty field power, global section are made to obtain The more new development of the machine that largely goes into battle of skill, military power, wherein super maneuver ability is considered as the following high-performance fighter aircraft Indispensable important symbol feature receives the unprecedented great attention of every country and area.
High maneuverability requirement in the static unstability design and air battle of modern combat aircraft, when fighter plane realizes some systems enemies When the maneuver of strike, High Angle of Attack state will certainly be entered, aerodynamic characteristic and flight characteristics will great changes will take place, wing and Fuselage can generate air-flow separation, lead to the complex characteristics such as nonlinear unsteady, hesitation, aerodynamic force asymmetry occur.At this point, Change dramatically occurs for the stability and control of aircraft, and aerodynamic characteristic is very sensitive to attitudes vibration, and it is many special easily to occur Flying, such as inertia coupling, Wing-Rock, deep stall even tailspin.So that being easier to enter dangerous shape in Campaign Process State.If boundary can be predicted in advance, driver can avoid enter into or help to change precarious position.Due to nonlinear system compared with For complexity, time response is difficult to obtain, and is difficult to acquire the general solution of Nonlinear differential eguations, conventional sky by the method for parsing Aerodynamics analysis method can not accurately analyze the aircraft aerodynamic characteristic under High Angle of Attack state, need through numerical value calculating side Method solves the needs that can satisfy analysis and research and the solution with certain physical significance.
The angle of attack refers to aircraft flight directional velocity in the projection on ground and the angle of wing chord.Flying angle is when lesser It waits lift and is greater than resistance, and be more than that then lift is less than resistance to certain angle, then lose lift more than the critical angle of attack.Lift is less than Resistance is known as " high-incidence condition " to the angle of attack for losing this stage of lift.High-angle-of-attack flight angle has according to airplane design Institute is different, can not provide specific value, but High Angle of Attack of the general aircraft flight angle of attack only in or so several years, the present invention refers to 50 ° or more.
To sum up, lack effective analysis method for fighter plane characteristic under High Angle of Attack in the prior art, it can not Accurate Prediction Safe range that fighter plane flies under High Angle of Attack and possibly into precarious position, can not the stall of Accurate Analysis depth, tailspin etc. The Crack cause and development mode of precarious position.
Summary of the invention
The fighter plane HAOA characteristics analysis method based on Bifurcation Analysis that the object of the present invention is to provide a kind of, for fight When machine carries out super maneuver movement and enters High Angle of Attack state, the safe range flown under High Angle of Attack to fighter plane is realized and may be into The Accurate Prediction of the precarious position entered, and the Crack causes of the precarious positions such as the stall of Accurate Analysis depth, tailspin and develop mode Effect.
To achieve the above object, the technical solution adopted by the present invention are as follows:
A kind of fighter plane HAOA characteristics analysis method based on Bifurcation Analysis, comprising the following steps:
Step 1, theoretical based on Bifurcation Analysis when fighter plane is in high-incidence condition, calculate the stabilization of fighter plane Equalization point and branch point；
Step 2, for different branch's vertex types, through the mathematical model of air-combat maneuver mechanical system refined gram at branch point Branch's vertex type is divided than the characteristic value of matrix；
Step 3, by continuation algorithm, the fighter plane angle of attack, yaw angle, rolling angular speed, pitch rate and yaw are calculated The process that the balanced surface of angular speed and branch face change with the change of control rudder face drift angle, according to acquired balanced surface and branch face Stability, judge equalization point distributing area.
The specific steps of the step 1 are as follows:
The mathematical model for describing air-combat maneuver mechanical system is Nonlinear System of Equations, is indicated are as follows:
Wherein, X=[α, β, p, q, r]TFor quantity of state,Indicate the first differential of X, U=[δe,δa,δr]TBecome for control Amount, α, β, p, q, r are respectively the angle of attack, yaw angle, rolling angular speed, pitch rate and yawrate, δe、δa、δrRespectively Go up and down angle of rudder reflection, aileron drift angle and rudder；
The equilibrium equation expression formula of air-combat maneuver mechanical system mathematical model are as follows:
F (X, U)=0
When the control amount U in system is gradually changed, then the variation of matter can occur for the equilibrium state of system and its stability, when U=U0When, the equilibrium state of system is X=X at this time0, wherein U0Refer to initial control amount, X0Refer to the equilibrium-like under initial control amount State；
By seeking partial derivative to equilibrium equation, know equilibrium state X to the dependence of control amount U,
The expression formula of partial derivative is sought equilibrium equation are as follows:
If in equalization point (X0,U0) at have FX(X0,U0) ≠ 0, then obtain Known by implicit function theo- rem, existence anduniquess function:
WhereinThen obtain the stable equilibrium point of fighter plane；
If in equalization point (X0,U0) at FX(X0,U0)=0, then obtain (X0,U0) be fighter plane branch point.
The specific steps of the step 2 are as follows:
The Jacobian matrix of the mathematical model of air-combat maneuver mechanical system are as follows:
WhereinThe first differential of respectively α, β, p, q, r, The characteristic value of Jacobian matrix is related with U at branch point.According to the characteristic value of Jacobian matrix, branch point is divided into three kinds of feelings Shape is respectively as follows:
Trouble shape fork: a factual investigation passes through origin to positive real axis from the negative real axis of complex plane；
Hough (hopf) fork: Conjugate complex roots pass through the imaginary axis to right-half plane from the left demifacet of complex plane；
Saddle: factual investigation tends to the imaginary axis along real axis or so.
The step 3 the following steps are included:
Step 31, for going up and down angle of rudder reflection, only variation controls a variable δ in variable Ue, δeConstant interval isOther control variable δa、δrIt need to immobilize, take initial value (X first0,U0), makeBy hidden letter Number theorem, knows that non trivial solution is
Step 32, variable δ will be controlledeDiscretization is carried out in constant interval, is obtainedThen each discrete point The solution at place is respectivelyWith X0For initial value, solved by Newton iteration theorem operation, expression formula Are as follows:
Df(X0(k))(X0(k+1)-X0(k))+F(X0(k))=0
Obtain next equilibrium state:
X0(k+1)=X0(k)-[Df(X0(k))]-1F(X0(k))
Wherein,K=1,2 ... be the number of iterations, X1=X0(k+1)For new equilibrium state；
Step 33, judge new equalization point (X1,U1) at steadiness, such as FX(X0,U0)=0 item calculates at new branch point Jacobian matrix characteristic value, and branch's vertex type is judged according to characteristic value；
Step 34, with (X1,U1) it is new equalization point, above step is repeated until (Xn,Un), then by these equalization points and Branch point forms control variable δeUnder balanced surface and branch face；
Step 35, using method same as above-mentioned steps 31-34, the angle of attack, yaw angle, rolling angular speed, pitching are calculated Angular speed and yawrate respectively with aileron drift angle δaWith rudder δrBalanced surface and branch face.
The utility model has the advantages that the present invention analyzes fighter plane HAOA characteristics using Bifurcation Analysis method, it is by continuously calculating The fighter plane balanced surface of system and branch face under High Angle of Attack state is calculated in method, judges rough equalization point distributing area That is stability range.It takes the balanced surface under different variable elements to be analyzed, obtains state of the system after variable element variation Response process.When entering High Angle of Attack state for fighter plane progress super maneuver movement, realization flies under High Angle of Attack to fighter plane Safe range and possibly into precarious position Accurate Prediction, and the shape of the precarious positions such as the stall of Accurate Analysis depth, tailspin At the effect of reason and development mode.
Detailed description of the invention
Fig. 1 is in the embodiment of the present invention using elevator as the angle of attack Bifurcation Analysis figure of variable element；
Fig. 2 is in the embodiment of the present invention using aileron as the angle of attack Bifurcation Analysis figure of variable element；
Fig. 3 is in the embodiment of the present invention using aileron as the yawrate Bifurcation Analysis figure of variable element.
Specific embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the accompanying drawings.Below by The embodiment being described with reference to the drawings is exemplary, and for explaining only the invention, and is not construed as limiting the claims.
By taking certain type fighter plane as an example, it is an object of the present invention to carry out super maneuver movement for fighter plane to enter High Angle of Attack state When, realize the safe range flown under High Angle of Attack to fighter plane and possibly into precarious position Accurate Prediction, and it is accurate It analyzes the Crack causes of precarious positions such as deep stall, tailspin and develops the effect of mode.
Fighter plane HAOA characteristics analysis method based on Bifurcation Analysis of the invention the following steps are included:
Step 1, theoretical based on Bifurcation Analysis when fighter plane is in high-incidence condition, calculate the stabilization of fighter plane Equalization point and branch point；Specific steps are as follows:
The mathematical model for describing air-combat maneuver mechanical system is Nonlinear System of Equations, is indicated are as follows:
Wherein, X=[α, β, p, q, r]TFor quantity of state,Indicate the first differential of X, U=[δe,δa,δr]TBecome for control Amount, α, β, p, q, r are respectively the angle of attack, yaw angle, rolling angular speed, pitch rate and yawrate, δe、δa、δrRespectively Go up and down angle of rudder reflection, aileron drift angle and rudder；
The equilibrium equation expression formula of air-combat maneuver mechanical system mathematical model are as follows:
F (X, U)=0
When the control amount U in system is gradually changed, then the variation of matter can occur for the equilibrium state of system and its stability, when U=U0When, the equilibrium state of system is X=X at this time0, wherein U0Refer to initial control amount, X0Refer to the equilibrium-like under initial control amount State；
By seeking partial derivative to equilibrium equation, know equilibrium state X to the dependence of control amount U,
The expression formula of partial derivative is sought equilibrium equation are as follows:
If in equalization point (X0,U0) at have FX(X0,U0) ≠ 0, then obtain Known by implicit function theo- rem, existence anduniquess function:
WhereinThen obtain the stable equilibrium point of fighter plane；
If in equalization point (X0,U0) at FX(X0,U0)=0, then obtain (X0,U0) be fighter plane branch point.
Step 2, for different branch's vertex types, through the mathematical model of air-combat maneuver mechanical system refined gram at branch point Branch's vertex type is divided than the characteristic value of matrix；Specific steps are as follows:
The Jacobian matrix of the mathematical model of air-combat maneuver mechanical system are as follows:
WhereinThe first differential of respectively α, β, p, q, r, The characteristic value of Jacobian matrix is related with U at branch point, and according to the characteristic value of Jacobian matrix, branch point is divided into three kinds of feelings Shape is respectively as follows:
Trouble shape fork: a factual investigation passes through origin to positive real axis from the negative real axis of complex plane；
Hough (hopf) fork: Conjugate complex roots pass through the imaginary axis to right-half plane from the left demifacet of complex plane；
Saddle: factual investigation tends to the imaginary axis along real axis or so.
Step 3, by continuation algorithm, the fighter plane angle of attack, yaw angle, rolling angular speed, pitch rate and yaw are calculated The process that the balanced surface of angular speed and branch face change with the change of control rudder face drift angle, according to acquired balanced surface and branch face Stability, judge equalization point distributing area；Wherein, balanced surface and branch face are the fighter planes using some rudder face as independent variable The angle of attack, yaw angle, three angular speeds (five states) be dependent variable, the balanced surface sought by continuation algorithm and branch Face, this step are sought under three rudder faces respectively by continuation algorithm, (the 15) balanced surface of five state variables and branch Face；
Steps are as follows for continuation algorithm calculating:
Step 31, for going up and down angle of rudder reflection, only variation controls a variable δ in variable Ue, δeConstant interval isOther control variable δa、δrIt need to immobilize, take initial value (X first0,U0), makeBy hidden letter Number theorem, knows that non trivial solution is
Step 32, variable δ will be controlledeDiscretization is carried out in constant interval, is obtainedThen each discrete point The solution at place is respectivelyWith X0For initial value, solved by Newton iteration theorem operation, expression formula Are as follows:
Df(X0(k))(X0(k+1)-X0(k))+F(X0(k))=0
Obtain next equilibrium state:
X0(k+1)=X0(k)-[Df(X0(k))]-1F(X0(k))
Wherein,K=1,2 ... be the number of iterations, X1=X0(k+1)For new equilibrium state；
Step 33, judge new equalization point (X1,U1) at steadiness, such as FX(X0,U0)=0 item calculates at new branch point Jacobian matrix characteristic value, and branch's vertex type is judged according to characteristic value；
Step 34, with (X1,U1) it is new equalization point, above step is repeated until (Xn,Un), then by these equalization points and Branch point forms control variable δeUnder balanced surface and branch face；
Step 35, using method same as above-mentioned steps 31-34, the angle of attack, yaw angle, rolling angular speed, pitching are calculated Angular speed and yawrate respectively with aileron drift angle δaWith rudder δrBalanced surface and branch face.
Embodiment 1
To go up and down angle of rudder reflection as variable element, take aileron and rudder neutral, i.e. δa=δr=0 °, height H=914m, speed Spend V=61m/s.Bifurcation Analysis result is as shown in Figure 1, indicate that fighter plane obtains the branch point of the angle of attack by variable element of elevator Analysis figure.
Find out from above-mentioned Bifurcation Analysis result figure, there is a stable branch in whens angle of attack α > 60 °.When lifting angle of rudder reflection is negative When big, aircraft only has Bifurcation of The Equilibrium in daying angular zone, and elevator deflection, there is no too big changes for the branch location and characteristic Change, so the branch is likely to be a Tiao Shen stall branch.Since center of gravity moves back at this time, aircraft has static unstability, small Angle of attack regional stability point is less.
Embodiment 2
Selection aileron is variable element, and taking lifting angle of rudder reflection is δe=-18 °, direction degree drift angle is δr=-5 °, height H= 3000m, speed V=65m/s.Bifurcation Analysis result is as shown in Figures 2 and 3, respectively indicates fighter plane using aileron as variable element Obtain the Bifurcation Analysis figure and yawrate Bifurcation Analysis figure of the angle of attack.
In Fig. 1-3, the stable branch of the branching representation of solid line, the unstable branch of dotted line branching representation (puts down in the branch Jacobian matrix characteristic value is not entirely in the left demifacet of complex plane at weighing apparatus point), real point ' ● ' indicates saddle-node bifurcation point, five-pointed star ' ★ ' table Show Hough bifurcation point.
Find out from above-mentioned Bifurcation Analysis result figure, under High Angle of Attack state, -10 ° of aileron < δaHave at < 13 ° one it is stable Branch, but equalization point yawrate is not zero in the branch, so the branch is likely to be a stable horizontal tail rotation branch.? When the angle of attack is 13 °, when yawrate is respectively 40 °/s and 80a/s, there are two Hough branch points, it is possible that the period shakes Swing tailspin.
The time response that Bifurcation Analysis method of the invention does not depend on nonlinear system seeks analytic solutions, and passes through continuation algorithm, Calculate Kind of Nonlinear Dynamical System balanced surface and branch face with variable element change procedure, to the power of nonlinear system Learn the numerical solution that characteristic carries out global analysis.Thus it has certain generality, and carries out super maneuver for fighter plane When movement enters High Angle of Attack state, realize to the safe range of fighter flight and possibly into precarious position it is accurate pre- It surveys, can apply in linear and nonlinear system, applicability is relatively broad.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered It is considered as protection scope of the present invention.

Claims (4)

1. a kind of fighter plane HAOA characteristics analysis method based on Bifurcation Analysis, it is characterised in that: the following steps are included:
Step 1, theoretical based on Bifurcation Analysis when fighter plane is in high-incidence condition, calculate the stable equilibrium of fighter plane Point and branch point；
Step 2, for different branch's vertex types, by the mathematical model of air-combat maneuver mechanical system at branch point Jacobi square The characteristic value of battle array divides branch's vertex type；
Step 3, by continuation algorithm, the fighter plane angle of attack, yaw angle, rolling angular speed, pitch rate and yaw angle speed are calculated The balanced surface of rate and branch face change with control rudder face drift angle and the process that changes, according to the steady of acquired balanced surface and branch face It is qualitative, judge equalization point distributing area.
2. the fighter plane HAOA characteristics analysis method according to claim 1 based on Bifurcation Analysis, it is characterised in that: institute State the specific steps of step 1 are as follows:
The mathematical model for describing air-combat maneuver mechanical system is Nonlinear System of Equations, is indicated are as follows:
Wherein, X=[α, β, p, q, r]TFor quantity of state,Indicate the first differential of X, U=[δe,δa,δr]TFor control variable, α, β, p, q, r are respectively the angle of attack, yaw angle, rolling angular speed, pitch rate and yawrate, δe、δa、δrRespectively go up and down Angle of rudder reflection, aileron drift angle and rudder；
The equilibrium equation expression formula of air-combat maneuver mechanical system mathematical model are as follows:
F (X, U)=0
When the control amount U in system is gradually changed, then the variation of matter can occur for the equilibrium state of system and its stability, work as U=U0 When, the equilibrium state of system is X=X at this time0, wherein U0Refer to initial control amount, X0Refer to the equilibrium state under initial control amount；
By seeking partial derivative to equilibrium equation, know equilibrium state X to the dependence of control amount U,
The expression formula of partial derivative is sought equilibrium equation are as follows:
If in equalization point (X0,U0) at have FX(X0,U0) ≠ 0, then obtainBy hidden Function existential theorem knows, existence anduniquess function:
WhereinThen obtain the stable equilibrium point of fighter plane；
If in equalization point (X0,U0) at FX(X0,U0)=0, then obtain (X0,U0) be fighter plane branch point.
3. the fighter plane HAOA characteristics analysis method according to claim 1 based on Bifurcation Analysis, it is characterised in that: institute State the specific steps of step 2 are as follows:
The Jacobian matrix of the mathematical model of air-combat maneuver mechanical system are as follows:
Wherein The first differential of respectively α, β, p, q, r, branch The characteristic value of Jacobian matrix is related with U at point；According to the characteristic value of Jacobian matrix, branch point is divided into three kinds of situations, It is respectively as follows:
Trouble shape fork: a factual investigation passes through origin to positive real axis from the negative real axis of complex plane；
Hough (hopf) fork: Conjugate complex roots pass through the imaginary axis to right-half plane from the left demifacet of complex plane；
Saddle: factual investigation tends to the imaginary axis along real axis or so.
4. the fighter plane HAOA characteristics analysis method according to claim 1 based on Bifurcation Analysis, it is characterised in that: institute State step 3 the following steps are included:
Step 31, for going up and down angle of rudder reflection, only variation controls a variable δ in variable Ue, δeConstant interval isIts It controls variable δa、δrIt need to immobilize, take initial value (X first0,U0), makeBy implicit function theorem, know Non trivial solution is
Step 32, variable δ will be controlledeDiscretization is carried out in constant interval, is obtainedThe then solution at each discrete point RespectivelyWith X0For initial value, solved by Newton iteration theorem operation, expression formula are as follows:
Df(X0(k))(X0(k+1)-X0(k))+F(X0(k))=0
Obtain next equilibrium state:
X0(k+1)=X0(k)-[Df(X0(k))]-1F(X0(k))
Wherein,For the number of iterations, X1=X0(k+1)For new equilibrium state；
Step 33, judge new equalization point (X1,U1) at steadiness, such as FX(X0,U0)=0 item calculates refined at new branch point Gram than matrix characteristic value, and branch's vertex type is judged according to characteristic value；
Step 34, with (X1,U1) it is new equalization point, above step is repeated until (Xn,Un), then by these equalization points and branch point Form control variable δeUnder balanced surface and branch face；
Step 35, using method same as above-mentioned steps 31-34, the angle of attack, yaw angle, rolling angular speed, pitch angle speed are calculated Rate and yawrate respectively with aileron drift angle δaWith rudder δrBalanced surface and branch face.
CN201910558970.6A 2019-06-26 2019-06-26 Fighter plane HAOA characteristics analysis method based on Bifurcation Analysis Pending CN110348080A (en)

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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107525647A (en) * 2017-07-26 2017-12-29 北京航空航天大学 A kind of dynamical bifurcation generating means of aerodynamic stalling

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107525647A (en) * 2017-07-26 2017-12-29 北京航空航天大学 A kind of dynamical bifurcation generating means of aerodynamic stalling

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
李晓刚: "歼击机大迎角尾旋特性分析和改出研究", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 *

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Application publication date: 20191018