CN116880527B - Control method and system for maximum jump glide flight range of hypersonic aircraft - Google Patents
Control method and system for maximum jump glide flight range of hypersonic aircraft Download PDFInfo
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Abstract
The invention discloses a control method and a system for maximum jump glide flight range of a hypersonic aircraft, comprising the following steps: step 1, establishing a three-degree-of-freedom flight mechanics model of a hypersonic aircraft jump trajectory; step 2, improving a range maximum jump gliding type flight trajectory calculation method, and optimizing six conjugate variable initial values into four conjugate variable initial values; step 3, comparing and analyzing through five different jump trajectory control methods to obtain a range maximum control mode of the maximum lift-drag ratio flight; performing range maximum optimization on the full trajectory by adopting a range maximum jump gliding type flight trajectory calculation method, and optimizing to obtain maximum lift-drag ratio gliding flight which is an optimal control mode for realizing the maximum jump gliding type flight trajectory; and 4, determining the boundary condition of the maximum lift-drag ratio gliding flight, and proving that the maximum lift-drag ratio gliding flight is the optimal control mode with the maximum range by using a theoretical analysis method. The maximum lift-drag ratio gliding flight obtained by the invention is an optimal control mode for realizing the maximum flight range of the jump slip trajectory.
Description
Technical Field
The invention relates to the field of aircraft control, in particular to a control method and a system for maximum jump gliding flight range of a hypersonic aircraft.
Background
The calculation of the maximum range trajectory of the jump gliding flight has the significance on mathematics and theoretical researches firstly, and has important guiding significance on the design of the maneuvering trajectory and the most energy-saving design of the hypersonic aircraft secondly.
From the prior art, the range method for jumping and gliding flight of an aircraft is increased currently: there are methods of increasing range by reducing drag flight; there are also ways to increase range in a lift-increasing flight; also increasing range in a lift-drag ratio flight mode; there are flying in a jumping manner and also flying in a gliding manner. None of the above methods maximize the range of the aircraft for jumping and gliding flights.
What control strategy would then be such that the range of the jump glide trajectory is furthest? There is an urgent need to study a control method for maximizing the range of hypersonic aircraft during jumping and gliding type flight.
Disclosure of Invention
The invention aims to solve the technical problem that a control method for maximizing the range of a hypersonic aircraft in the jumping and gliding type flight process is lacking in the prior art.
The invention aims to provide a control method and a system for maximizing the flight range of a hypersonic aircraft in a jumping and gliding mode, namely a control method for maximizing the flight range of the hypersonic aircraft in the jumping and gliding mode; according to the invention, through the comparison research of various control modes and the optimization of trajectory, the optimal control mode with the maximum lift-drag ratio and the maximum flight range is obtained; and the conclusion is verified by a sensitivity method. The boundary condition of maximum lift-drag ratio gliding flight is then presented and proved by a method of ballistic simulation and theoretical analysis.
The invention is realized by the following technical scheme:
in a first aspect, the present invention provides a control method for maximum flight range of a hypersonic aircraft jump glide, the method comprising:
step 1, establishing a three-degree-of-freedom flight mechanics model of a hypersonic aircraft jump trajectory;
step 2, according to a three-degree-of-freedom flight mechanics model, improving a range maximum jump gliding type flight trajectory calculation method, and optimizing six conjugate variable initial values into four conjugate variable initial values;
step 3, obtaining a range maximum control mode of the maximum lift-drag ratio flight through the comparative analysis of a plurality of different jump trajectory control methods; on the basis of a range maximum control mode based on maximum lift-drag ratio flight, adopting a range maximum jump gliding type flight trajectory calculation method to carry out range maximum optimization on a full trajectory, and optimizing to obtain the maximum lift-drag ratio gliding type flight which is an optimal control mode for realizing the maximum jump gliding type flight range;
and 4, determining the boundary condition of the maximum lift-drag ratio gliding flight, and proving that the maximum lift-drag ratio gliding flight is the optimal control mode with the maximum range by using a theoretical analysis method.
Further, the three-degree-of-freedom flight mechanics model is a three-degree-of-freedom space maneuver trajectory state equation under a half-speed coordinate system obtained under the assumption condition; the assumed conditions include, among others, the effects of earth rotation and flatness, zero engine thrust, and zero sideslip angle throughout the maneuver.
Further, optimizing the six initial conjugate variable values to four initial conjugate variable values includes:
will satisfy r (t) f )＝R e +h f Terminating constraints to stop integration to automatically determine time of flight t f The other five variables are obtained by directly optimizing with the range as an optimization target instead of taking the other five variables as terminal constraint conditions without being required; wherein r (t) f ) Is the terminal value of the geocentric sagittal diameter, R e Is the radius of the earth, h f Is a terminal value of the flying height;
one conjugate variable (lambda is assumed to be the initial value of six conjugate variables 10 ) The initial value is set to 1;
by usingThe other conjugate variable (assumed to be lambda 20 ) An initial value; wherein H (t) 0 ) Is Hamiltonian initial value, lambda i0 As the initial value of the conjugate function, f i0 Is the initial value of the right function;
thus, only four conjugate variable initial values are required to be solved, and the optimization of six conjugate variable initial values into four conjugate variable initial values is realized.
Further, a number of different skip trajectory control methods include maximum control of flight at lift-drag ratio, control of flight at a fixed angle of attack, maximum control of flight at lift, horizontal flight, and minimum control of flight at drag.
Further, the boundary conditions of the maximum lift-drag ratio glide flight determined in the step 4 are:
wherein h is the flying height, R e The earth radius, m is the aircraft mass; g is gravity acceleration; v is the flight speed; ρ is the atmospheric density, S M For reference area, C L Is the lift coefficient.
Further, the method further comprises:
a sensitivity method is adopted to prove whether the maximum lift-drag ratio gliding flight is a control mode with the maximum jump-gliding flight range;
the sensitivity method is to carry out trajectory simulation on the sensitivity parameters by giving control variables and selecting the sensitivity parameters, and compare the range; sensitivity parameters included + -0.2 degrees, + -0.4 degrees, + -0.6 degrees program attack angle.
In a second aspect, the invention further provides a control system for the maximum jump and glide flight range of the hypersonic aircraft, wherein the control system uses the control method for the maximum jump and glide flight range of the hypersonic aircraft; the system comprises:
the mechanical model building unit is used for building a three-degree-of-freedom flight mechanical model of the hypersonic aircraft jump trajectory;
the conjugate variable optimizing unit is used for improving a range maximum jump gliding type flight trajectory calculation method according to the three-degree-of-freedom flight mechanics model and optimizing six conjugate variable initial values into four conjugate variable initial values;
the maximum lift-drag ratio flight unit is used for obtaining a range maximum control mode of the maximum lift-drag ratio flight through the comparative analysis of five different jump-slip trajectory control methods;
the maximum lift-drag ratio gliding flight unit adopts a range maximum jump gliding type flight trajectory calculation method to carry out range maximum optimization on a full trajectory on the basis of a range maximum control mode based on the maximum lift-drag ratio flight, and the maximum lift-drag ratio gliding flight obtained through optimization is an optimal control mode for realizing the maximum jump gliding type flight range;
and the boundary condition determining and analyzing unit is used for determining the boundary condition of the maximum lift-drag ratio gliding flight and proving that the maximum lift-drag ratio gliding flight is the optimal control mode with the largest range by using a theoretical analysis method.
Further, optimizing the six initial values of the conjugate variables to four initial values of the conjugate variables in the conjugate variable optimizing unit includes:
will satisfy r (t) f )＝R e +h f Terminating constraints to stop integration to automatically determine time of flight t f The other five variables are obtained by directly optimizing with the range as an optimization target instead of taking the other five variables as terminal constraint conditions without being required; wherein r (t) f ) Is the earth centerVector terminal value, R e Is the radius of the earth, h f Is a terminal value of the flying height;
one conjugate variable (lambda is assumed to be the initial value of six conjugate variables 10 ) The initial value is set to 1;
by usingThe other conjugate variable (assumed to be lambda 20 ) An initial value; wherein H (t) 0 ) Is Hamiltonian initial value, lambda i0 As the initial value of the conjugate function, f i0 Is the initial value of the right function;
thus, only four conjugate variable initial values are required to be solved, and the optimization of six conjugate variable initial values into four conjugate variable initial values is realized.
Further, the boundary conditions of the maximum lift-drag ratio glide flight are:
wherein h is the flying height, R e The earth radius, m is the aircraft mass; g is gravity acceleration; v is the flight speed; ρ is the atmospheric density, S M For reference area, C L Is the lift coefficient.
In a third aspect, the present invention further provides a computer readable storage medium, where a computer program is stored, where the computer program when executed by a processor implements the control method for maximum jump glide flight range of a hypersonic aircraft as described above.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention provides a control method and a system for maximizing the jump gliding flight range of a hypersonic aircraft, namely a control method for maximizing the flight range of the hypersonic aircraft in the jump gliding flight process; according to the invention, through the comparison research of various control modes and the optimization of trajectory, the optimal control mode with the maximum lift-drag ratio and the maximum flight range is obtained; and the conclusion is verified by a sensitivity method. The boundary condition of maximum lift-drag ratio gliding flight is then presented and proved by a method of ballistic simulation and theoretical analysis.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention. In the drawings:
FIG. 1 is a flow chart of a control method for maximum flight range of a hypersonic aircraft in jump glide of the present invention;
FIG. 2 is a graph showing the comparison of unpowered skip trajectory in a single control mode of the present invention;
FIG. 3 is a graph of the maximum range jump glide type flight trajectory parameters of the present invention;
FIG. 4 is a sensitivity analysis (global plot) of the maximum range jump trajectory of the present invention;
FIG. 5 is a sensitivity analysis (end-of-range enlargement) of the maximum range jump trajectory of the present invention;
FIG. 6 is a graph of velocity altitude for a glide boundary condition according to the present invention;
FIG. 7 is a schematic diagram of an optimized trajectory of the present invention with glide boundary conditions as the starting flight condition;
FIG. 8 is a graph of the altitude contrast of velocity in the glide boundary conditions and optimized trajectory of the present invention;
fig. 9 is a block diagram of a control system with maximum flight range for jumping and gliding of the hypersonic vehicle.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present invention and the descriptions thereof are for illustrating the present invention only and are not to be construed as limiting the present invention.
The control method for maximizing the range of the hypersonic aircraft in the jumping and gliding flight process is lacked in the prior art. Therefore, the invention designs a control method and a system for maximizing the flight range of the hypersonic aircraft in jumping and gliding, namely provides a control method for maximizing the flight range of the hypersonic aircraft in jumping and gliding flight; according to the invention, through the comparison research of various control modes and the optimization of trajectory, the optimal control mode with the maximum lift-drag ratio and the maximum flight range is obtained; and the conclusion is verified by a sensitivity method. The boundary condition of maximum lift-drag ratio gliding flight is then presented and proved by a method of ballistic simulation and theoretical analysis.
Example 1
As shown in fig. 1, the control method for the maximum jump glide flight range of the hypersonic aircraft comprises the following steps:
step one, establishing a three-degree-of-freedom flight mechanics model of a hypersonic aircraft jump trajectory;
hypersonic speed jump flight time is long, flight distance is long, and therefore the influence of the rotation and the flat rate of the earth is not negligible; because the aircraft is in unpowered jumping and gliding maneuver, the thrust of the engine is zero; in addition, in order to facilitate the study of the problems, only the jumping and gliding maneuver of the aircraft in the longitudinal plane is considered, namely, the sideslip angle is zero in the whole maneuver flying process. Under the assumption condition, a three-degree-of-freedom space maneuvering trajectory state equation under a half-speed coordinate system can be obtained, and is as follows:
wherein: v, θ T 、σ T Phi, lambda and r are respectively the flying speed, the speed dip angle, the track yaw angle, the geocentric latitude, the longitude and the geocentric sagittal diameter; c (C) D 、C L The drag coefficient and the lift coefficient of the aircraft are respectively; m, S, q are the mass, reference area and dynamic pressure of the aircraft respectively; f. m, J, a e And omega e The gravity constant, the earth mass, the harmonic coefficient, the average radius of the earth equator and the earth rotation angular velocity are respectively.
And (3) making: state vector x= (v, θ) T ,σ T ,φ,λ,r) T The method comprises the steps of carrying out a first treatment on the surface of the Right function vector f= (f) 1 ,f 2 ,f 3 ,f 4 ,f 5 ,f 6 ) T The method comprises the steps of carrying out a first treatment on the surface of the Conjugate vector λ= (λ) 1 ,λ 2 ,λ 3 ,λ 4 ,λ 5 ,λ 6 ) T The method comprises the steps of carrying out a first treatment on the surface of the The equation of state can be abbreviated as
Hamiltonian:
H＝λ 1 f 1 +λ 2 f 2 +λ 3 f 3 +λ 4 f 4 +λ 5 f 5 +λ 6 f 6 (2)
then the conjugate equation isThe unfolding can be obtained:
wherein,is the partial derivative of the right function of state equation (1).
The optimal control variable u=α (α is the angle of attack) should maximize the hamilton function H, the term relating to the control variable being written as H 1 (alpha), irrelevant write H 2 Then:
the fit forms of the drag coefficient and the lift coefficient are respectively as follows:
C D ＝C D0 +C D1 α+C D2 α 2 (5)
C L ＝C L0 +C L1 α (6)
substituting the aerodynamic parameters into formula (4) and retaining only the terms related to the optimal control variable u=α, the result is obtained by finishing:
according to the maximum principle, the control variable α should satisfy the following equation:
the method can be simplified to obtain:
step two, according to a three-degree-of-freedom flight mechanics model, improving a range maximum jump gliding type flight trajectory calculation method, and optimizing six conjugate variable initial values into four conjugate variable initial values; thus, the convergence of the optimization algorithm is greatly improved.
For the maximum range jump glide trajectory, one of the state variables time of flight t f Is not required, i.e. is free, state variable terminal constraint divides requirement r (t f )＝r f Other five state variables v f ，θ Tf ，σ Tf ，φ f ，λ f All have no requirement, only the height h f ＝10km(h f ＝r(t f )-R e R is the sagittal diameter of the earth, R e The earth radius, h is the altitude) range, lmax. Wherein the terminal flight time t f Terminal flight speed v of the other five state variables f Terminal speed inclination angle theta Tf Terminal track yaw angle sigma Tf Terminal latitude phi f Terminal longitude lambda f Six conjugate variables.
And range is a function of the longitude and latitude of the terminal, expressed as follows:
L(φ f ,λ f )＝R e arcos[sinφ f sinφ 0 +cosφ f cosφ 0 cos(λ f -λ 0 )] (10)
if the conventional maximum principle is adopted, the cross-sectional condition of the optimal trajectory is determined by the following formula:
wherein: ψ= (r (t) f )-r f )＝0；v＝v 1 。
Then
Wherein,is a function of the longitude and latitude of the terminal. v 1 Is a certain uncertainty constant.
Thus, it is quite difficult to simultaneously satisfy six terminal conditions with extremely high sensitivity to the initial values of the conjugate variables, and in some cases, the terminal conditions cannot be satisfied at the same time, but this cannot indicate that there is no optimal control solution, and in a physical sense, the maximum range trajectory is the only one given the initial conditions. It is therefore necessary to change the optimization strategy.
Considering the terminal constraint conditions as follows: r (t) f )＝R e +h f The remaining five state variables v f ，θ Tf ，σ Tf ，φ f ，λ f There is no requirement, so the invention can consider: satisfy r (t) f )＝R e +h f Terminating constraints to stop integration to automatically determine t f The other five variables are not required to be used as terminal constraint conditions, and are directly used as optimization targets by taking the range, so that the range maximum optimization control problem is converted into: because the conjugate equation is a linear differential equation set, the initial value of a certain conjugate variable can be 1, and thenThe other conjugate variable initial value can be obtained, so that only four conjugate initial value variables are needed to be solved, when r (t f )＝R e +h f In this case, the range of the skid trajectory is maximized. Thereby greatly simplifying the optimization control problem.
Step three, obtaining a range maximum control mode of the maximum lift-drag ratio flight through the comparative analysis of five different jump trajectory control methods; on the basis of a range maximum control mode based on maximum lift-drag ratio flight, adopting a range maximum jump gliding type flight trajectory calculation method to carry out range maximum optimization on a full trajectory, and optimizing to obtain the maximum lift-drag ratio gliding type flight which is an optimal control mode for realizing the maximum jump gliding type flight range; the method comprises the steps of firstly determining the range maximum control mode of the maximum lift-drag ratio flight, and then determining the range maximum control mode of the maximum lift-drag ratio gliding flight.
Specifically, in the case where the initial conditions are the same: shutdown point height: h is a k =150,000m, shutdown point speed: v k =6,100 m/s, shutdown point speed dip: θ k Comparative analysis was performed on the unpowered skip trajectory when using several different control modes (all the full trajectory is using this single control mode): a) Maximum control flight (LDmax) at lift-drag ratio; b) Controlling the flight at a fixed angle of attack (currently 0 degree angle of attack) (alpha 0); c) Controlling the flight (Clmax) with the lift force maximum; d) Horizontal flight (pingfei); e) Flight (Cdmin) is controlled with minimal drag. As the simulation result is shown in fig. 2, it can be seen from fig. 2 that the maximum lift-drag ratio has the maximum flight range, because when flying at the maximum lift-drag ratio, the lift force is large enough, and the flying height of the flying vehicle is high, so that the flying vehicle can be easily lifted up to climb jump, and compared with other control modes, the flying vehicle has longer flight time outside the atmosphere with smaller atmosphere density or in the rarefaction atmosphere, and has less energy consumption; on the other hand, the minimum drag of the maximum lift-drag ratio flight means that the energy loss is small under the condition of providing the same lift, and therefore, the range of the flight with the maximum lift-drag ratio is maximum compared with other control modes.
Based on the maximum lift-drag ratio flight control mode, the full trajectory is subjected to range maximum optimization, and the full trajectory is obtained after optimization, as shown in fig. 3, from the optimization result, the jump gliding type maximum range flight trajectory consists of two sections, wherein the former section is the jump trajectory, and the latter section is the gliding trajectory. The optimal program attack angle (alpha) in the jump trajectory oscillates up and down with the maximum lift-drag ratio corresponding to the attack angle (2.25 degrees), the velocity dip angle (thita) oscillates up and down with zero degrees as the axis, and the jump height (H) fluctuates greatly. At the end of the jump, the optimum path angle of attack converges substantially to the angle of attack corresponding to the maximum lift-drag ratio, the velocity dip converges to zero, and the amplitude of the jump height also tends to zero. The optimum program attack angle of the following glide segment is basically equal to the attack angle corresponding to the maximum lift-drag ratio, the speed dip angle is nearly zero, and the flying height slowly descends.
From the analysis, it is clear that the maximum lift-drag ratio glide flight is the optimal control method for realizing the maximum flight trajectory range. In the initial stage of the flight of the skip-sliding across the atmosphere, the flight is carried out at a program attack angle with larger amplitude, and a plurality of jumps occur, so that the purpose of gradually adjusting the flight state to zero speed inclination angle is that the speed is matched with the height, and the aircraft does not have larger jumps when flying at the maximum lift-drag ratio, namely the maximum lift-drag ratio gliding flight is realized, thereby achieving the purpose of the maximum range.
Step four, a sensitivity method is adopted to prove whether the maximum lift-drag ratio gliding flight is a control mode with the maximum jumping-gliding flight range;
the comparison research and the trajectory optimization of various control modes are conducted to obtain the conclusion that the maximum lift-drag ratio gliding flight is the optimal control mode with the maximum range, and a sensitivity method is used for verifying whether the control mode is the control mode with the maximum jump-gliding flight range. The sensitivity parameters are selected as follows: program attack angles of +/-0.2 degrees, +/-0.4 degrees and +/-0.6 degrees are subjected to ballistic simulation, the range is compared, and the stability of the maximum value is observed.
The simulation results show that as shown in the figure 4, the change of the trajectory along with the sensitivity parameter is obvious, the trajectory with the sensitivity parameter has oscillation with a certain amplitude near the maximum range trajectory, and when the sensitivity parameter is positive (i.e. the attack angle of the program is increased), the larger the sensitivity parameter is, the larger the peak value at the wave crest is, and the smaller the peak value at the wave trough is; when the sensitivity parameter is negative (i.e., the procedure attack angle is reduced), the larger the sensitivity parameter (referring to absolute value), the smaller its peak at the ballistic peak and the larger its peak at the trough. It can be seen that the ballistic parameter is continuously changing as the sensitivity parameter changes with the optimum program angle of attack, so the optimum value is stable.
It is also known from the enlarged ballistic end-stage diagram of fig. 5 that whether the optimum program angle of attack is increased or decreased by a certain angle, the range is reduced. It follows that maximum lift-drag ratio glide flight is indeed the best control mode for the maximum range, which corresponds to an optimal program attack angle that not only maximizes the range of the trajectory, but also stabilizes the optimal value.
And fifthly, determining boundary conditions of maximum lift-drag ratio gliding flight, and proving that the maximum lift-drag ratio gliding flight is the optimal control mode with the maximum range by using a theoretical analysis method.
This is because, in order to achieve maximum lift/drag ratio glide flight, the initial value of the flight trajectory must satisfy a condition called the maximum lift/drag ratio glide flight boundary condition, and if the initial value of the flight trajectory does not satisfy the condition, the maximum lift/drag ratio flight cannot be performed simultaneously. Jump occurs when the maximum lift-drag ratio is flown, and glide flight cannot be realized at the same time. And determining a maximum lift-drag ratio gliding flight boundary condition of the flight height H=30 km-60 km through an optimization algorithm, and proving that the maximum lift-drag ratio flight can be realized when the boundary condition is met.
As mentioned above, the several jumps of the optimal trajectory front stage are to match the velocity with the altitude when the flight state is gradually adjusted to zero velocity inclination, and then the maximum lift-drag ratio gliding flight is only entered when the velocity and altitude are matched when the velocity inclination is determined to be zero, that is, the determination of the maximum lift-drag ratio gliding flight boundary condition is determined. As can be seen from fig. 3, the maximum lift-drag ratio is in gliding flight, and the velocity tilt angle (thita) oscillates slightly about a value slightly smaller than zero. Thus predictingThe initial boundary conditions for maximum lift-drag ratio glide flight are: (1) velocity dip angle: θ=0; (2) when flying at maximum lift-to-drag ratio:
the accuracy of the initial boundary condition prediction for the gliding flight is analyzed and verified by taking a certain aircraft as an example. The mass of the aircraft is m=1000 kg, reference area: s is S ref ＝0.74m 2 The aerodynamic parameters are approximately fitted to: c (C) D ＝0.109+0.0115α+0.0006α 2 ；C L ＝0.3605+0.0483α。
Initial boundary conditions for gliding flight by maximum lift-to-drag ratio: θ=0 andthe one-to-one correspondence of altitude and speed at the aircraft glide boundary can be back calculated. The correspondence between the altitude and the speed of the altitude h=30 km to 60km is obtained by solving, as shown in fig. 6.
The following glide boundary conditions at 60km height: h=60 km, θ=0, v= 6909.5m/s as the initial flight state, and trajectory optimization is performed based on the maximum range, and the trajectory shown in fig. 7 is obtained after the optimization. As can be seen from the curves of the height (H), the optimal procedure attack angle (alpha) and the velocity dip angle (thita) in the figure, the jump amplitude of the trajectory is very small in the whole flight process, the optimal procedure attack angle is slightly oscillated near the attack angle (2.25 degrees) corresponding to the maximum lift-drag ratio, the amplitude in most of the flight time is within 0.1 degrees, the velocity dip angle change rate is very small, and the value of the velocity dip angle change rate is basically very close to the negative value of zero. It follows that when the above proposed glide flight boundary condition is set as the initial flight state, the range maximum flight trajectory thereof is the maximum lift-drag ratio glide flight trajectory.
The reason for the slight jump in height is: the slight jump of the forefront section occurs because the initial speed is very high, the speed dip angle is theta=0, andthus in a small sizeThe flight trajectory during the period of time is approximately a straight line tangential to the earth, but since the earth is an ellipsoid and not a plane, the situation occurs in which the altitude increases as shown; the small jump behind is due to the speed drop caused by the influence of the resistance and the aforementioned earth is an ellipsoid, so that +.>The speed inclination angle theta is slightly changed when the speed inclination angle theta is not completely equal to zero, and the attack angle of the optimal program is correspondingly adjusted at the moment, so that the attack angle is not completely equal to the attack angle corresponding to the maximum lift-drag ratio. The jump amplitude is smaller and smaller, the optimal program attack angle is closer and closer to the maximum lift-drag ratio corresponding attack angle, the speed dip angle change rate is smaller and smaller, and the flight trajectory is infinitely close to the maximum lift-drag ratio glide trajectory.
Comparing the velocity height parameter of the optimized trajectory with the velocity height relationship on the glide boundary condition, it can be seen from fig. 8 that the velocity heights of the glide trajectory and the glide boundary are almost coincident, so that, on the one hand, the glide boundary condition at 60km height is demonstrated: h=60 km, θ=0, v= 6909.5m/s as the starting flight state, the trajectory with the largest range is the maximum lift-drag ratio glide trajectory, because any of the flight states in the trajectory is in the glide flight state; on the other hand, it was also confirmed that the maximum range trajectory using the glide boundary condition as the initial state was the maximum lift-drag ratio glide trajectory, because any of the flight states obtained after the optimization satisfies the glide boundary condition, and it is known from the glide trajectory optimization that if any of the glide trajectories is the initial state, the trajectory of the subsequent stage is the maximum range glide trajectory, and therefore, the maximum range trajectory satisfying the glide boundary condition at the 60km height is the maximum lift-drag ratio glide trajectory satisfying the previously obtained glide boundary condition of h=30 km to 60 km.
The maximum lift-drag ratio gliding flight has been proved to be the best control mode with the maximum range by the sensitivity method, and is proved by the theoretical analysis method. This can be demonstrated in two ways, on the one hand, the furthest flight range in maximum lift-drag ratio control mode when the glide boundary condition is met; on the other hand, it has been demonstrated that the range of the aircraft in the flat flight state is furthest maintained when the aircraft is flown in the maximum lift-to-drag control mode.
(1) When the glide boundary condition is satisfied, whether the flight range is furthest in the maximum lift-drag ratio control mode
For ease of presentation and demonstration, the following assumptions are made: irrespective of earth rotation; the earth is a sphere, i.e. the gravitational field is a centered ground field inversely proportional to the square of the centroid distance; the longitudinal axis of the aircraft is considered to be always in the plane of incidence determined by the velocity vector of the reentry point and the geocentric vector, i.e. the sideslip angle is zero. The reentry ballistic equation can be obtained as follows:
wherein: v, θ, r and L are respectively the flying speed, the speed dip angle, the geocentric sagittal diameter and the range; x, Y is the drag and lift of the aircraft, respectively; g. r is R e Gravity acceleration and earth radius, respectively.
By gliding flight boundary conditions: θ=0 andthe above equation set may be formed as:
and: resistance forceLift force->(wherein ρ is the atmospheric density, v is the flying speed, S M For reference area, C D As drag coefficient, C L Lift coefficient), lift-drag ratio ∈>Then:
also, since r is a constant, the magnitude of the range L is related only to the magnitude of the velocity and the time of flight, anConstant less than zero, the range is maximally equivalent to:
that is, when the glide boundary condition is satisfied, the flight control mode with the largest range is the maximum lift-drag ratio flight. The glide boundary conditions (i.e. height versus speed) at this time are:
wherein: y is lift:m is the aircraft mass; g is gravity acceleration; v is the flight speed; r is the sagittal diameter of the earth: r=r e +h(R e The earth radius, h is the flying height).
The preparation method comprises the following steps of:
equation (18) is the relation between altitude and speed when the glide boundary condition is satisfied, that is, the maximum lift-drag ratio glide boundary condition.
The boundary condition is a digital solution, then a theoretical interpretation method is adopted to deduce an analytical solution of the maximum lift-drag ratio gliding flight boundary condition, and the analytical method is used to prove that the maximum lift-drag ratio gliding flight is the optimal control mode with the largest range.
(2) When flying with maximum lift-drag ratio, the energy is most saved and the range is maximum when flying at level
If the aircraft makes a small swing of periodic motion around the maximum lift-drag ratio trim fly height, it may be assumed that the aircraft is centered on height h, with A as amplitude, 2pi L P For periodic sinusoidal motion, there are: h=h+asin (L/L P )
Consider l=0 to 2pi L P Work done by internal resistance, flat missile passage:
sinusoidal trajectory:
then:
wherein: ρ=ρ 0 e -βh Is an atmospheric density estimation formula ρ 0 =1.225 is sea level atmospheric density and β=1/7110 is an empirical estimate.
And (3) making: l' =l/Lp, then there is:
and (3) segment integration to obtain:
and (3) the following steps: l (L) * =l' -pi, with:
then:
and there are: e, e -βAsin(l) +e βAsin(l) Constant > 2 holds true, if and only if a=0, i.e. fly flat, "=", then:namely: w (W) Ping Fei ≤W Sinusoidal shape 。
Therefore, when the fly is controlled by the maximum lift-drag ratio, the energy is saved most (the resistance acting is minimum) and the range is maximum when the fly is kept in the flat fly state.
In conclusion, the optimal control mode with the maximum jump-glide flight range is the maximum lift-drag ratio glide flight, which is obtained through comparison research of various flight control modes and optimal design of trajectory, and is verified through sensitivity analysis. And then, boundary conditions of maximum lift-drag ratio gliding flight are proposed, and two methods of ballistic simulation and theoretical analysis are used for proving.
Example 2
As shown in fig. 9, the difference between the present embodiment and embodiment 1 is that the present embodiment provides a control system for the maximum jump glide flight range of the hypersonic vehicle, which uses the control method for the maximum jump glide flight range of the hypersonic vehicle of embodiment 1; the system comprises:
the mechanical model building unit is used for building a three-degree-of-freedom flight mechanical model of the hypersonic aircraft jump trajectory;
the conjugate variable optimizing unit is used for improving a range maximum jump gliding type flight trajectory calculation method according to the three-degree-of-freedom flight mechanics model and optimizing six conjugate variable initial values into four conjugate variable initial values;
the maximum lift-drag ratio flight unit is used for obtaining a range maximum control mode of the maximum lift-drag ratio flight through the comparative analysis of five different jump-slip trajectory control methods;
the maximum lift-drag ratio gliding flight unit adopts a range maximum jump gliding type flight trajectory calculation method to carry out range maximum optimization on a full trajectory on the basis of a range maximum control mode based on the maximum lift-drag ratio flight, and the maximum lift-drag ratio gliding flight obtained through optimization is an optimal control mode for realizing the maximum jump gliding type flight range;
and the boundary condition determining and analyzing unit is used for determining the boundary condition of the maximum lift-drag ratio gliding flight and proving that the maximum lift-drag ratio gliding flight is the optimal control mode with the largest range by using a theoretical analysis method.
As a further implementation, optimizing six conjugate variable initial values to four conjugate variable initial values in the conjugate variable optimizing unit includes:
will satisfy r (t) f )＝R e +h f Terminating constraints to stop integration to automatically determine time of flight t f The other five variables are obtained by directly optimizing with the range as an optimization target instead of taking the other five variables as terminal constraint conditions without being required; wherein r (t) f ) Is the terminal value of the geocentric sagittal diameter, R e Is the radius of the earth, h f Is a terminal value of the flying height;
one conjugate variable (lambda is assumed to be the initial value of six conjugate variables 10 ) The initial value is set to 1;
by usingThe other conjugate variable (assumed to be lambda 20 ) An initial value; wherein H (t) 0 ) Is Hamiltonian initial value, lambda i0 As the initial value of the conjugate function, f i0 Is the initial value of the right function;
thus, only four conjugate variable initial values are required to be solved, and the optimization of six conjugate variable initial values into four conjugate variable initial values is realized.
As a further implementation, the boundary conditions for maximum lift-drag ratio glide flight are:
wherein h is the flying height, R e The earth radius, m is the aircraft mass; g is gravity acceleration; v is the flight speed; ρ is the atmospheric density, S M For reference area, C L Is the lift coefficient.
The execution process of each unit is performed according to the flow steps of the control method with the maximum jump glide flight range of the hypersonic aircraft in embodiment 1, and the details of this embodiment are not repeated.
Meanwhile, the invention also provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and when the computer program is executed by a processor, the control method for the maximum jump glide flight range of the hypersonic aircraft in the embodiment 1 is realized.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (7)
1. A control method for maximum jump glide flight range of a hypersonic aircraft, the method comprising:
step 1, establishing a three-degree-of-freedom flight mechanics model of a hypersonic aircraft jump trajectory;
step 2, according to the three-degree-of-freedom flight mechanics model, improving a range maximum jump gliding type flight trajectory calculation method, and optimizing six conjugate variable initial values into four conjugate variable initial values;
step 3, obtaining a range maximum control mode of the maximum lift-drag ratio flight through the comparative analysis of a plurality of different jump trajectory control methods; on the basis of a range maximum control mode based on the maximum lift-drag ratio flight, adopting a range maximum jump gliding type flight trajectory calculation method to carry out range maximum optimization on a full trajectory, and optimizing to obtain the maximum lift-drag ratio gliding type flight, wherein the optimal control mode for realizing the maximum jump gliding type flight range is adopted;
step 4, determining boundary conditions of the maximum lift-drag ratio gliding flight, and proving that the maximum lift-drag ratio gliding flight is the optimal control mode with the largest range by using a theoretical analysis method;
the six conjugate variables include the terminal flight time t f Terminal flying speed v f Terminal speed tilt angle theta Tf Yaw angle sigma of terminal track Tf Terminal latitude phi f And terminal longitude lambda f ；
The optimizing the six initial values of the conjugate variables into four initial values of the conjugate variables comprises the following steps:
will satisfy r (t) f )＝R e +h f Terminating constraints to stop integration to automatically determine time of flight t f And directly optimizing by taking the range as an optimization target; wherein r (t) f ) Is the terminal value of the geocentric sagittal diameter, R e Is the radius of the earth, h f Is a terminal value of the flying height;
setting one conjugate variable initial value of six conjugate variable initial values to be 1;
by usingObtaining another conjugate variable initial value; wherein H (t) 0 ) Is Hamiltonian initial value, lambda i0 As the initial value of the conjugate function, f i0 Is the initial value of the right function;
only four conjugate variable initial values are needed to be solved, and the optimization of six conjugate variable initial values into four conjugate variable initial values is realized;
the various different jump trajectory control methods comprise maximum control flight with lift-drag ratio, control flight with fixed attack angle, maximum control flight with lift, horizontal flight and minimum control flight with resistance;
the maximum lift-drag ratio gliding flight is proved to be the optimal control mode with the largest range by a theoretical analysis method, and the maximum lift-drag ratio gliding flight range is proved to be furthest in the maximum lift-drag ratio control mode when the gliding boundary condition is met; the aircraft keeps the furthest range in a flat flight state when the aircraft flies in a maximum lift-drag ratio control mode;
the method directly uses the range as an optimization target to perform optimization, and comprises the following steps: the range is directly used as an optimization target, so that the problem of maximum optimal control of the range is converted into: because the conjugate equation is a linear differential equation set, the initial value of a certain conjugate variable can be 1, and thenThe other conjugate variable initial value can be obtained, so that only four conjugate initial value variables are needed to be solved, when r (t f )＝R e +h f When the method is used, the range of the jump slip trajectory is maximized; thereby simplifying the optimization control problem.
2. The control method for the maximum jump glide flight range of the hypersonic vehicle according to claim 1 wherein the three-degree-of-freedom flight mechanics model is a three-degree-of-freedom space maneuver trajectory state equation under a half-speed coordinate system obtained under a hypothetical condition; wherein the hypothetical conditions include the effects of earth rotation and ellipticity, zero engine thrust, and zero sideslip angle throughout the maneuver.
3. The method for controlling the maximum flying range of a hypersonic aircraft in jumping and gliding according to claim 1, wherein the boundary conditions of the maximum lift-drag ratio and gliding determined in the step 4 are:
wherein h is the flying height, R e The earth radius, m is the aircraft mass; g is gravity acceleration; v is the flight speed; ρ is the atmospheric density, S M For reference area, C L Is the lift coefficient.
4. The method for controlling the maximum flying range of a hypersonic vehicle in jumping glide as set forth in claim 1, further comprising:
a sensitivity method is adopted to prove whether the maximum lift-drag ratio gliding flight is a control mode with the maximum jump-gliding flight range;
the sensitivity method is to carry out ballistic simulation on the sensitivity parameters by giving control variables and selecting the sensitivity parameters, and compare the range; the sensitivity parameters include + -0.2 degrees, + -0.4 degrees, + -0.6 degrees program attack angle.
5. A hypersonic aircraft jump glide flight range maximization control system, characterized in that the system uses a hypersonic aircraft jump glide flight range maximization control method according to any one of claims 1 to 4; the system comprises:
the mechanical model building unit is used for building a three-degree-of-freedom flight mechanical model of the hypersonic aircraft jump trajectory;
the conjugate variable optimizing unit is used for improving a range maximum jump gliding type flight trajectory calculation method according to the three-degree-of-freedom flight mechanics model, and optimizing six conjugate variable initial values into four conjugate variable initial values;
the maximum lift-drag ratio flight unit is used for obtaining a range maximum control mode of the maximum lift-drag ratio flight through the comparative analysis of five different jump-slip trajectory control methods;
the maximum lift-drag ratio gliding flight unit adopts a range maximum jump gliding type flight trajectory calculation method to carry out range maximum optimization on a full trajectory on the basis of a range maximum control mode based on the maximum lift-drag ratio flight, and the maximum lift-drag ratio gliding flight is an optimal control mode for realizing the maximum jump gliding type flight range after optimization;
the boundary condition determining and analyzing unit is used for determining the boundary condition of the maximum lift-drag ratio gliding flight and proving that the maximum lift-drag ratio gliding flight is the optimal control mode with the maximum range by using a theoretical analysis method;
the six conjugate variables include the terminal flight time t f Terminal flying speed v f Terminal speed tilt angle theta Tf Yaw angle sigma of terminal track Tf Terminal latitude phi f And terminal longitude lambda f ；
The conjugate variable optimizing unit optimizes six conjugate variable initial values to four conjugate variable initial values, and comprises:
will satisfy r (t) f )＝R e +h f Terminating constraints to stop integration to automatically determine time of flight t f And directly optimizing by taking the range as an optimization target; wherein r (t) f ) Is the terminal value of the geocentric sagittal diameter, R e Is the radius of the earth, h f Is a terminal value of the flying height;
setting one conjugate variable initial value of six conjugate variable initial values to be 1;
by usingObtaining another conjugate variable initial value; wherein H (t) 0 ) Is Hamiltonian initial value, lambda i0 As the initial value of the conjugate function, f i0 Is the initial value of the right function;
only four conjugate variable initial values are needed to be solved, and the optimization of six conjugate variable initial values into four conjugate variable initial values is realized;
the various different jump trajectory control methods comprise maximum control flight with lift-drag ratio, control flight with fixed attack angle, maximum control flight with lift, horizontal flight and minimum control flight with resistance;
the maximum lift-drag ratio gliding flight is proved to be the optimal control mode with the largest range by a theoretical analysis method, and the maximum lift-drag ratio gliding flight range is proved to be furthest in the maximum lift-drag ratio control mode when the gliding boundary condition is met; the aircraft keeps the furthest range in a flat flight state when the aircraft flies in a maximum lift-drag ratio control mode;
the method directly uses the range as an optimization target to perform optimization, and comprises the following steps: the range is directly used as an optimization target, so that the problem of maximum optimal control of the range is converted into: because the conjugate equation is a linear differential equation set, the initial value of a certain conjugate variable can be 1, and thenThe other conjugate variable initial value can be obtained, so that only four conjugate initial value variables are needed to be solved, when r (t f )＝R e +h f When the method is used, the range of the jump slip trajectory is maximized; thereby simplifying the optimization control problem.
6. The hypersonic aircraft skip-glide flight range maximization control system of claim 5 wherein the maximum lift-drag ratio glide boundary conditions are:
wherein h is the flying height, R e The earth radius, m is the aircraft mass; g is gravity acceleration; v is the flight speed; ρ is the atmospheric density, S M For reference area, C L Is the lift coefficient.
7. A computer-readable storage medium storing a computer program, characterized in that the computer program, when executed by a processor, implements a control method of maximum jump glide flight range of a hypersonic aircraft according to any one of claims 1 to 4.
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104176268A (en) * | 2014-08-06 | 2014-12-03 | 北京航空航天大学 | Method for controlling glide flying ballistic curve damping |
| CN104392047A (en) * | 2014-11-25 | 2015-03-04 | 北京航空航天大学 | Quick trajectory programming method based on smooth glide trajectory analytic solution |
| US9639085B1 (en) * | 2015-08-05 | 2017-05-02 | The United States Of America As Represented By The Secretary Of The Air Force | Phugoid peaks trajectory for hypersonic glide vehicles |
| CN106873615A (en) * | 2015-12-11 | 2017-06-20 | 中国航空工业第六八研究所 | Emergent landing speed instruction set design method of giving an encore |
| CN109459929A (en) * | 2018-12-04 | 2019-03-12 | 北京理工大学 | The parsing Homotopy Method that martian atmosphere approach section longitudinal direction accessoble region generates |
| EP3506041A1 (en) * | 2017-12-29 | 2019-07-03 | Deutsches Zentrum für Luft- und Raumfahrt e.V. | Method, apparatus and spacecraft for constrained atmospheric entry |
| CN110147521A (en) * | 2019-04-25 | 2019-08-20 | 北京航空航天大学 | A kind of hypersonic aircraft jump glide trajectories Analytical Solution method |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7028631B2 (en) * | 2003-11-24 | 2006-04-18 | The Boeing Company | Gliding submersible transport system |
| US20220107160A1 (en) * | 2020-10-02 | 2022-04-07 | United States Of America, As Represented By The Secretary Of The Navy | Glide Trajectory Optimization for Aerospace Vehicles |
-
2023
- 2023-07-20 CN CN202310895939.8A patent/CN116880527B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104176268A (en) * | 2014-08-06 | 2014-12-03 | 北京航空航天大学 | Method for controlling glide flying ballistic curve damping |
| CN104392047A (en) * | 2014-11-25 | 2015-03-04 | 北京航空航天大学 | Quick trajectory programming method based on smooth glide trajectory analytic solution |
| US9639085B1 (en) * | 2015-08-05 | 2017-05-02 | The United States Of America As Represented By The Secretary Of The Air Force | Phugoid peaks trajectory for hypersonic glide vehicles |
| CN106873615A (en) * | 2015-12-11 | 2017-06-20 | 中国航空工业第六八研究所 | Emergent landing speed instruction set design method of giving an encore |
| EP3506041A1 (en) * | 2017-12-29 | 2019-07-03 | Deutsches Zentrum für Luft- und Raumfahrt e.V. | Method, apparatus and spacecraft for constrained atmospheric entry |
| CN109459929A (en) * | 2018-12-04 | 2019-03-12 | 北京理工大学 | The parsing Homotopy Method that martian atmosphere approach section longitudinal direction accessoble region generates |
| CN110147521A (en) * | 2019-04-25 | 2019-08-20 | 北京航空航天大学 | A kind of hypersonic aircraft jump glide trajectories Analytical Solution method |
Non-Patent Citations (3)
| Title |
|---|
| a multiobjective evolutionary algorithm based on decomposition;XIE Yu，PAN Liang;IEEE Transactions on Evolutionary Computation;712-731 * |
| 新型远程制导炸弹攻击区影响因素研究;庞威;谢晓方;郑力会;孙涛;孙海文;孙明军;;兵器装备工程学报(第02期);全文 * |
| 滑翔飞行器多目标弹道优化的进化-配点混合求解策略;丰志伟;江增荣;张青斌;葛健全;黄浩;;国防科技大学学报(第01期);全文 * |
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