CN105550402A - Attack angle or inclination angle frequency conversion based design method for hypersonic steady maneuver gliding trajectory - Google Patents

Abstract

The invention discloses an attack angle or inclination angle frequency conversion based design method for a hypersonic steady maneuver gliding trajectory. The method comprises the eight steps of 1, performing constraint modeling of a hypersonic aircraft reentry process; 2, establishing an attack angle corridor of steady gliding; 3, establishing an inclination angle corridor of steady gliding; 4, designing a reference attack angle curve of steady maneuver gliding; 5, designing a reference inclination angle curve of steady maneuver gliding; 6, calculating an initial gliding height and a trajectory inclination angle; 7, making a damp differential feedback control scheme; and 8, generating the steady maneuver gliding trajectory. The invention proposes a concept of steady maneuver gliding, which is a new reentry flight mode, can combine the advantages of convenient tracking guidance of balanced gliding and good defense penetration capability of jump gliding, and lowers the difficulty in trajectory planning.

Description

A kind of superb steady motor-driven glide trajectories method for designing based on the angle of attack or angle of heel frequency conversion

Technical field

The invention provides a kind of superb steady motor-driven glide trajectories method for designing based on the angle of attack or angle of heel frequency conversion, belong to spationautics, weapon technologies field.

Background technology

Hypersonic aircraft generally refer to flying speed more than 5 times of velocities of sound aircraft, guided missile, shell and so on have the wing or wingless vehicle, it has the advantage that flying height is high, speed is fast, lateral maneuverability is good, has become a Main way of 21 century Global Aerospace career development.Glide trajectories planning effectively can excavate the task potential of hypersonic aircraft, and ensure the safety of flight course, be a gordian technique wherein simultaneously.

Hypersonic aircraft glide trajectories is divided into equilibrium glide and jump glide two kinds of offline mode usually, wherein equilibrium glide have that height change is mild, the advantage such as heat flow density and dynamic pressure peak value is little, the angle of attack and angle of heel line smoothing, be convenient to reenter homing guidance; Jumping glides then has the advantage that flying distance is far away, penetration ability is strong.Steady glide is a kind of offline mode of new proposition on the basis of the above, for the given reference angle of attack can led continuously and angle of heel curve, all there is corresponding steadily glide trajectories.Therefore, by the reference angle of attack and the angle of heel curve of design variation, obtain the steady motor-driven glide trajectories taken into account equilibrium glide and jump both glides advantage.

Summary of the invention

The object of this invention is to provide a kind of superb steady motor-driven glide trajectories method for designing based on the angle of attack or angle of heel frequency conversion, it utilizes equilibrium glide condition will reenter process constraints and transforms into angle of attack corridor (angle of heel corridor), and gives a kind of design proposal of the corridor internal reference angle of attack (angle of heel); Give elemental height and the trajectory tilt angle of this reference angle of attack and the corresponding steady motor-driven glide trajectories of angle of heel on this basis; And adopt and determine damping Derivative Feedback and eliminate the state deviation that may exist; Finally utilize trajectory integration can obtain corresponding steady motor-driven glide trajectories.

The present invention is a kind of superb steady motor-driven glide trajectories method for designing based on the angle of attack or angle of heel frequency conversion, comprises following step:

Step 1: hypersonic aircraft reenters process constraints modeling

Hypersonic aircraft reenters in process to be needed to consider the process constraints such as maximum heat current density, max-Q and maximum overload, and the angle of attack and angle of heel also have boundary constraint simultaneously, specific as follows:

$\begin{array}{cc}\stackrel{\·}{Q}=k\sqrt{\mathrm{\ρ}}{V}^3\≤{\stackrel{\·}{Q}}_{max}& q=\frac{1}{2}{\mathrm{\ρV}}^2\≤q_{max}\end{array}$

$\begin{array}{ccc}n=\sqrt{L^2+D^2}\≤n_{max}& {\mathrm{\α}}_{\min }\≤\mathrm{\α}\≤{\mathrm{\α}}_{max}& {\mathrm{\σ}}_{\min }\≤\left|\mathrm{\σ}\right|\≤{\mathrm{\σ}}_{max}\end{array}$

In formula, for heat flow density; for maximum heat current density; ρ is atmospheric density; V is speed; K is the heat flow density constant of aircraft.Q is dynamic pressure; N is overload; q _maxand n _maxbe respectively max-Q and maximum overload.α is the angle of attack; σ is angle of heel; α _min, α _maxbe respectively the minimum angle of attack, the maximum angle of attack; σ _minand σ _maxbe respectively minimum angle of heel and maximum angle of heel.L and D is respectively normalized lift and resistance.

Step 2: the steadily foundation in glide angle of attack corridor

If the reference angle of heel absolute value of glide section is as follows:

|σ _ref|＝f _σ(V)

In above formula, σ _reffor reference angle of heel, f _σ(V) be velocity correlation function.The angle of attack lower bound utilizing equilibrium glide condition can obtain maximum heat current density, max-Q and maximum overload corresponding is respectively α _q, α _qand α _n, then the lower bound in angle of attack corridor is,

α _low＝max(α _Q,α _q,α _n,α _min)

In above formula, α _lowfor the lower bound in angle of attack corridor.The upper bound in angle of attack corridor is then α _up=α _max.

Step 3: the steadily foundation in glide angle of heel corridor

If the angle of attack curve of glide section is as follows,

α _ref＝f _α(V)

In above formula, α _reffor the reference angle of attack, f _α(V) be velocity correlation function.The upper bound utilizing equilibrium glide condition can obtain angle of heel absolute value corresponding to maximum heat current density, max-Q and maximum overload is respectively | σ _q|, | σ _q| with | σ _n|, then the upper bound in angle of heel corridor is,

σ _up＝min(|σ _Q|,|σ _q|,|σ _n|,σ _max)

In above formula, σ _upfor the upper bound in angle of heel corridor.The lower bound in angle of heel corridor is then σ _low=σ _min.

Step 4: steady motor-driven glide is with reference to angle of attack Curve Design

The present invention adopts polynomial function and trigonometric function composite design with reference to angle of attack curve, as follows:

${\mathrm{\α}}_{ref}=f_{\mathrm{\α}1}\left(V\right)+C_{a1}\sin (\frac{C_{a2}\mathrm{\π}(V-V_f)}{C_{a3}}+C_{a4})$

In formula, α _reffor reference angle of attack curve; f _{α 1}(V) being take speed as the polynomial function of independent variable, which determines the average with reference to the angle of attack; C _a1for controlling the constant of angle of attack amplitude, usually determine its size by angle of attack corridor; C _a2for controlling the constant of angle of attack oscillation frequency, it is the major parameter adjusting steady motor-driven gliding flight mode; C _a3for velocity constant, C _a3=V ₀-V _f, wherein V ₀and V _fbe respectively initial velocity and the terminal velocity of glide trajectories; C _a4for phase place adjustment constant.

Step 5: the reference angle of heel Curve Design of steady motor-driven glide

Similar with step 4, adopt polynomial function and trigonometric function composite design with reference to angle of heel curve, as follows:

${\mathrm{\σ}}_{ref}=f_{\mathrm{\σ}1}\left(V\right)+C_{s1}sin(\frac{C_{s2}\mathrm{\π}(V-V_f)}{C_{s3}}+C_{s4})$

In formula, σ _reffor reference angle of heel curve; f _{σ 1}(V) being take speed as the polynomial function of independent variable, which determines the average with reference to angle of heel, and then have impact on the range of planning trajectory; C _s1for controlling the constant of angle of heel amplitude, usually determine its size by angle of heel corridor; C _s2for controlling the constant of angle of heel oscillation frequency, it is the major parameter adjusting steady motor-driven gliding flight mode; C _s3for velocity constant, C _s3=V ₀-V _f, wherein V ₀and V _fbe respectively initial velocity and the terminal velocity of glide trajectories; C _s4for phase place adjustment constant.

Step 6: initial gliding height and trajectory tilt angle solve

The reference angle of attack determined according to step 2 and step 4 (or step 3 and step 5) and angle of heel, solve elemental height and the trajectory tilt angle of steady motor-driven glide trajectories, specific as follows:

$h_{sg}=-\frac{1}{\mathrm{\β}}ln\left(\frac{g-V^2/r-a_{sg}}{k_c{V}^2{C}_{L1}^{*}}\right)$

${\mathrm{\γ}}_{sg}=-\frac{(f_a+f_V)(g+a_{sg}-V^2/r)}{K_1^{*}\mathrm{\β}V+K_1^{*}g(f_a+f_V)}---\left(1\right)$

In above formula, h _sg, γ _sgand a _sgbe respectively steady gliding height, trajectory tilt angle and longitudinal acceleration; k _cfor the coupling constant of aircraft, k _c=ρ ₀s/ (2m); with be respectively with reference to the angle of attack and lift coefficient longitudinal component corresponding to angle of heel and lift-drag ratio longitudinal component; f _aand f _vbe velocity correlation function; a _sgfor longitudinal acceleration of steadily gliding.

Step 7: determine damping Derivative Feedback control program

Determine damping Derivative Feedback to control to make glide trajectories rapidly converge to steady glide state, specific as follows:

$k_2=2{\mathrm{\ζ}}_c\sqrt{(g-V^2/r)\mathrm{\β}}-(g-V^2/r)/\left({\mathrm{VK}}_1^{*}\right)$

$C_{L1}^{\left(real\right)}=C_{L1}^{*}-\frac{2{\mathrm{mk}}_2{C}_{L1}^{*}}{{\mathrm{\ρVScos\σ}}^{*}}(\mathrm{\γ}-{\mathrm{\γ}}_{sg})$

In above formula, ζ _cfor given damping, usually get ζ _c=0.707; ρ, g, V, r, γ are respectively the current atmospheric density of aircraft, acceleration of gravity, speed, the earth's core distance and trajectory tilt angle; for the lift coefficient longitudinal component of reality; γ _sgfor reference trajectory inclination angle, obtained by formula (1); σ ^*for reference angle of heel; for by with reference to lift coefficient longitudinal component; k ₂for Derivative Feedback coefficient.

Step 8: the generation of steady motor-driven glide trajectories

The elemental height obtained with step 6 and trajectory tilt angle are for initial value for integral, and the actual lift coefficient longitudinal component obtained with step 7, for control variable, carries out trajectory integration; Steady motor-driven glide trajectories can be obtained.

The invention has the advantages that:

Propose the concept of steady motor-driven glide, it is a kind of new ablated configuration pattern, can take into account equilibrium glide and be convenient to homing guidance and the strong advantage of jump glide penetration ability.

When carrying out steady motor-driven glide trajectories design, angle of attack corridor or angle of heel corridor can be adopted to carry out processing procedure constraint, reduce the difficulty of trajectory planning.

Propose a kind of steady motor-driven glide reference angle of attack and the angle of heel design proposal that meet the requirement of process constraints.On this basis, utilize steady glide trajectories dynamic perfromance, required steady motor-driven glide trajectories can be obtained by trajectory integration.

Accompanying drawing explanation

Fig. 1 is steady motor-driven glide trajectories planning process schematic diagram.

Fig. 2 is steady glide angle of attack corridor schematic diagram when being 0deg with reference to angle of heel.

Fig. 3 is different from the steady glide angle of attack corridor schematic diagram under angle of heel.

Fig. 4 is steady glide angle of heel corridor schematic diagram when being 15deg with reference to the angle of attack.

Fig. 5 is different from the steady glide angle of heel corridor schematic diagram under the angle of attack.

Fig. 6 is that steady motor-driven glide is with reference to angle of attack curve synoptic diagram.

Fig. 7 is that steady motor-driven glide is with reference to angle of heel curve synoptic diagram.

Fig. 8 is the steady motor-driven glide Longitudinal Trajectory schematic diagram that change angle of attack curve obtains.

Fig. 9 is the rate curve schematic diagram that change angle of attack curve obtains.

Figure 10 is the horizontal trajectory schematic diagram that change angle of attack curve obtains.

Figure 11 is the normal acceleration schematic diagram that change angle of attack curve obtains.

Figure 12 is the steady motor-driven glide Longitudinal Trajectory schematic diagram that change angle of heel curve obtains.

Figure 13 is the rate curve schematic diagram that change angle of heel curve obtains.

Figure 14 is the horizontal trajectory schematic diagram that change angle of heel curve obtains.

Figure 15 is the normal acceleration schematic diagram that change angle of heel curve obtains.

In figure, symbol description is as follows:

σ _ref: be reference angle of heel; α _reffor the reference angle of attack.

Specific embodiments

See Fig. 1-Figure 15, below in conjunction with accompanying drawing and case study on implementation, the present invention is described in further detail.

The present invention proposes a kind of reentry trajectory offline mode of steady motor-driven glide; And give corresponding trajectory planning method.First utilize equilibrium glide condition will reenter process constraints and transform into corresponding angle of attack corridor (or angle of heel corridor); Then the design reference angle of attack (or angle of heel) curve in corridor; Finally utilize the steady motor-driven glide trajectories needed for the acquisition of steady glide trajectories dynamic perfromance integration.

A kind of superb steady motor-driven glide trajectories method for designing based on the angle of attack or angle of heel frequency conversion of the present invention, it comprises the following steps: step 1: hypersonic aircraft reenters process constraints modeling

Hypersonic aircraft reenters in process to be needed to consider the process constraints such as maximum heat current density, max-Q and maximum overload, and the angle of attack and angle of heel also have boundary constraint simultaneously, specific as follows:

$\stackrel{\·}{Q}=k\sqrt{\mathrm{\ρ}}{V}^3\≤{\stackrel{\·}{Q}}_{max}---\left(2\right)$

$q=\frac{1}{2}{\mathrm{\ρV}}^2\≤q_{max}---\left(3\right)$

$n=\sqrt{L^2+D^2}\≤n_{max}---\left(4\right)$

α _min≤α≤α _max(5)

σ _min≤|σ|≤σ _max(6)

In formula, for heat flow density; for maximum heat current density; ρ is atmospheric density; V is speed; K is the heat flow density constant of aircraft.Q is dynamic pressure; N is overload; q _maxand n _maxbe respectively max-Q and maximum overload.α is the angle of attack; σ is angle of heel; α _min, α _maxbe respectively the minimum angle of attack, the maximum angle of attack; σ _minand σ _maxbe respectively minimum angle of heel and maximum angle of heel.L and D is respectively normalized lift and resistance, specific as follows:

$\begin{array}{cc}L=\frac{{\mathrm{\ρV}}^2{\mathrm{SC}}_L}{2{\mathrm{mg}}_0}& D=\frac{{\mathrm{\ρV}}^2{\mathrm{SC}}_D}{2{\mathrm{mg}}_0}\end{array}$

In formula, S is the pneumatic area of reference of aircraft, and m is the quality of aircraft; g ₀for sea level acceleration of gravity, c _land C _dbe respectively lift coefficient and resistance coefficient.

If meet steady glide condition in hypersonic glide section flight course, then longitudinal stress is as follows,

$\frac{{\mathrm{\ρV}}^2{\mathrm{SC}}_{L}cos\mathrm{\σ}}{2m}+(\frac{V^2}{r}-g)cos\mathrm{\γ}-a_{\mathrm{\ϵ}}=0$

In above formula, g is acceleration of gravity, g=μ/r ², μ is Gravitational coefficient of the Earth, and r is the earth's core distance of aircraft; a _εfor the grade rate acceleration that steadily glides, relevant with reference to the angle of attack, be an a small amount of; γ is trajectory tilt angle.When carrying out reentry corridor and analyzing, usually a can be ignored _εimpact, and suppose cos γ ≈ 1, then can obtain equilibrium glide condition as follows:

$\frac{{\mathrm{\ρV}}^2{\mathrm{SC}}_{L}cos\mathrm{\σ}}{2m}+(\frac{V^2}{r}-g)=0---\left(7\right)$

When carrying out glide trajectories planning, if specify with reference to angle of heel curve, then equilibrium glide condition can be utilized formula (2) to the process constraints that formula (6) provides to be converted into the constraint of angle of attack corridor; Otherwise, if specify with reference to angle of attack curve, then equilibrium glide condition can be utilized formula (2) to the process constraints that formula (6) provides to be converted into the constraint of angle of heel corridor.

Step 2: the steadily foundation in glide angle of attack corridor

If the reference angle of heel absolute value of glide section is as follows:

|σ _ref|＝f _σ(V)

In above formula, σ _reffor reference angle of heel, f _σ(V) be velocity correlation function.The lift coefficient lower bound then utilizing formula (7) can try to achieve maximum heat current density, max-Q and maximum overload corresponding is respectively,

$C_{LQ}=\frac{2m(g_Q-V^2/r_Q)}{S{\mathrm{cos\σ}}_{ref}}{\left(\frac{{\mathrm{kV}}^2}{{\stackrel{\·}{Q}}_{\max }}\right)}^2$

$C_{Lq}=\frac{m(g_q-V^2/r_q)}{q_{max}S{\mathrm{cos\σ}}_{ref}}$

$\frac{C_{Ln}}{\sqrt{C_{Ln}^2+C_{Dn}^2}}=\frac{(g_n-V^2/r_n)}{n_{max}{g}_0{\mathrm{cos\σ}}_{ref}}$

In above formula, C _lQand C _lqbe respectively maximum heat current density and lift coefficient corresponding to max-Q; C _lnand C _dnbe respectively the resistance coefficient that maximum overload is corresponding; K is the constant relevant to reentry vehicle heat flow density.Above-mentioned four is relevant to present speed and the angle of attack, adopts secant method can go out angle of attack lower bound α corresponding to maximum heat current density by rapid solving _q, angle of attack lower bound α corresponding to max-Q _qthe angle of attack lower bound α corresponding with maximum overload _n.G _q, g _qand g _nbe respectively the acceleration of gravity that maximum heat current density, max-Q and maximum overload are corresponding; r _q, r _qand r _nbe respectively the earth's core distance that maximum heat current density, max-Q and maximum overload are corresponding, as follows:

$r_Q=R_0-\frac{1}{\mathrm{\β}}ln\[\frac{1}{{\mathrm{\ρ}}_0}{\left(\frac{{\stackrel{\·}{Q}}_{max}}{{\mathrm{kV}}^3}\right)}^2\]$

$r_q=R_0-\frac{1}{\mathrm{\β}}ln\left(\frac{2q_{max}}{p_0{V}^2}\right)$

$r_n=R_0-\frac{1}{\mathrm{\β}}ln\left(\frac{2n_{max}{\mathrm{mg}}_0}{{\mathrm{\ρ}}_0{V}^{2}S\sqrt{C_{L_n}^2+C_{D_n}^2}}\right)---\left(8\right)$

In above formula, R ₀for earth radius; ρ ₀for sea-level atmosphere density; β is exponential atmosphere model constants, usually gets β=1/7200m ^-1.Solving r _ntime, first can suppose r _n≈ R ₀, then solve formula (12) estimation value, finally utilize formula (8) obtain r _nsolution.Finally, the lower bound that can obtain angle of attack corridor is,

α _low＝max(α _Q,α _q,α _n,α _min)

In above formula, α _lowfor the lower bound in angle of attack corridor.The upper bound in angle of attack corridor is then α _up=α _max.

Step 3: the steadily foundation in glide angle of heel corridor

If the angle of attack curve of glide section is as follows,

α _ref＝f _α(V)(9)

In above formula, α _reffor the reference angle of attack, f _α(V) be velocity correlation function.The angle of heel upper bound utilizing formula (7) can try to achieve maximum heat current density, max-Q and maximum overload corresponding is respectively,

$\left|{\mathrm{\σ}}_Q\right|=arccos\[\frac{2m(g_Q-V^2/r_Q)}{{\mathrm{SC}}_L^{*}}{\left(\frac{{\mathrm{kV}}^2}{{\stackrel{\·}{Q}}_{\max }}\right)}^2\]$

$\left|{\mathrm{\σ}}_q\right|=arccos\[\frac{m(g_q-V^2/r_q)}{q_{max}{\mathrm{SC}}_L^{*}}\]$

$\left|{\mathrm{\σ}}_n\right|=arccos\[\frac{(g_n-V^2/r_n)\sqrt{1+{(C_D^{*}/C_L^{*})}^2}}{n_{max}{g}_0}\]$

In above formula, with be respectively with reference to lift coefficient corresponding to the angle of attack and resistance coefficient; | σ _q|, | σ _q| with | σ _n| be respectively the coboundary of angle of heel absolute value corresponding to maximum heat current density, max-Q and maximum overload.The upper bound that finally can obtain angle of heel corridor is,

σ _up＝min(|σ _Q|,|σ _q|,|σ _n|,σ _max)

In above formula, σ _upfor the upper bound in angle of heel corridor.The lower bound in angle of heel corridor is then σ _low=σ _min.

Step 4: steady motor-driven glide is with reference to angle of attack Curve Design

Utilizing after step 2 obtains the reentry corridor of the steady glide angle of attack, also need design the reference angle of attack curve can led continuously needed for motor-driven glide in reentry corridor, finally could determine steady motor-driven glide trajectories.The present invention adopts polynomial function and trigonometric function composite design with reference to angle of attack curve, as follows:

${\mathrm{\α}}_{ref}=f_{\mathrm{\α}1}\left(V\right)+C_{a1}sin(\frac{C_{a2}\mathrm{\π}(V-V_f)}{C_{a3}}+C_{a4})$

In formula, α _reffor reference angle of attack curve; f _{α 1}(V) being take speed as the polynomial function of independent variable, which determines the average with reference to the angle of attack; C _a1for controlling the constant of angle of attack amplitude, usually determine its size by angle of attack corridor; C _a2for controlling the constant of angle of attack oscillation frequency, it is the major parameter adjusting steady motor-driven gliding flight mode; C _a3for velocity constant, C _a3=V ₀-V _f, wherein V ₀and V _fbe respectively initial velocity and the terminal velocity of glide trajectories; C _a4for phase place adjustment constant.

Step 5: the reference angle of heel Curve Design of steady motor-driven glide

Similar with step 4, determine in step 3 on the basis of steady glide angle of heel reentry corridor, adopt polynomial function and trigonometric function composite design with reference to angle of heel curve, as follows:

${\mathrm{\σ}}_{ref}=f_{\mathrm{\σ}1}\left(V\right)+C_{s1}sin(\frac{C_{s2}\mathrm{\π}(V-V_f)}{C_{s3}}+C_{s4})$

In formula, σ _reffor reference angle of heel curve; f _{σ 1}(V) being take speed as the polynomial function of independent variable, which determines the average with reference to angle of heel, and then have impact on the range of planning trajectory; C _s1for controlling the constant of angle of heel amplitude, usually determine its size by angle of heel corridor; C _s2for controlling the constant of angle of heel oscillation frequency, it is the major parameter adjusting steady motor-driven gliding flight mode; C _s3for velocity constant, C _s3=V ₀-V _f, wherein V ₀and V _fbe respectively initial velocity and the terminal velocity of glide trajectories; C _s4for phase place adjustment constant.

Step 6: initial gliding height and trajectory tilt angle solve

The reference angle of attack determined according to step 2 and step 4 (or step 3 and step 5) and angle of heel, solve elemental height and the trajectory tilt angle of steady motor-driven glide trajectories, specific as follows:

$h_{sg}=-\frac{1}{\mathrm{\β}}ln\left(\frac{g-V^2/r-a_{sg}}{k_c{V}^2{C}_{L1}^{*}}\right)---\left(10\right)$

${\mathrm{\γ}}_{sg}=-\frac{(f_a+f_V)(g+a_{sg}-V^2/r)}{K_1^{*}\mathrm{\β}V+K_1^{*}g(f_a+f_V)}---\left(11\right)$

In above formula, h _sg, γ _sgand a _sgbe respectively steady gliding height, trajectory tilt angle and longitudinal acceleration; k _cfor the coupling constant of aircraft, k _c=ρ ₀s/ (2m); with be respectively with reference to the angle of attack and lift coefficient longitudinal component corresponding to angle of heel and lift-drag ratio longitudinal component, expression formula is as follows,

$\begin{array}{cc}{C}_{L1}^{*}=C_L^{*}{\mathrm{cos\σ}}_{ref}& K_1^{*}=C_L^{*}{\mathrm{cos\σ}}_{ref}/C_D^{*}\end{array}$

F _aand f _vbe velocity correlation function, expression formula is as follows respectively,

$f_a=(\∂C_{L1}^{*}/\∂V)/C_{L1}^{*}$

$f_V=2(g-a_{sg})/(gV-a_{sg}V-V^3/r)$

A _sgcan following formula estimation be adopted:

$a_{sg}=\frac{\left(gr-V^2\right)}{{\left(K_1^{*}\right)}^2\mathrm{\β}r}\[-\frac{{\mathrm{gf}}_{a}V+4g+V^3{f}_a/r}{V^3}+\left(g-\frac{V^2}{r}\right)\frac{\∂f_a}{\∂V}-\left(\frac{{\mathrm{gf}}_a-V^2{f}_a/r+2g/V}{K_1^{*}}\right)\frac{\∂K_1^{*}}{\∂V}\]$

In formula, with be respectively f _awith to the first-order partial derivative of speed.Speed V in formula (10) and (11) is taken as the initial velocity V of steady motor-driven glide trajectories ₀, corresponding elemental height and trajectory tilt angle can be obtained.

Step 7: determine damping Derivative Feedback control program

Determine damping Derivative Feedback to control to make glide trajectories rapidly converge to steady glide state, specific as follows:

$k_2=2{\mathrm{\ζ}}_c\sqrt{(g-V^2/r)\mathrm{\β}}-(g-V^2/r)/\left({\mathrm{VK}}_1^{*}\right)---\left(12\right)$

$C_{L1}^{\left(real\right)}=C_{L1}^{*}-\frac{2{\mathrm{mk}}_2{C}_{L1}^{*}}{{\mathrm{\ρVScos\σ}}^{*}}(\mathrm{\γ}-{\mathrm{\γ}}_{sg})---\left(13\right)$

In above formula, ζ _cfor given damping, usually get ζ _c=0.707; ρ, g, V, r are respectively the current atmospheric density of aircraft, acceleration of gravity, speed and the earth's core distance; for the lift coefficient longitudinal component of reality; γ _sgfor reference trajectory inclination angle, obtained by formula (11); σ ^*for reference angle of heel; for reference lift coefficient longitudinal component; k ₂for Derivative Feedback coefficient.

Step 8: the generation of steady motor-driven glide trajectories

The elemental height obtained with step 6 and trajectory tilt angle are for initial value for integral, and the actual lift coefficient longitudinal component obtained with step 7, for control variable, carries out trajectory integration; Steady motor-driven glide trajectories can be obtained.

Case study on implementation

Resolve the precision of derivation algorithm to check, select CAV to be the dummy vehicle of simulation calculation, in emulation, optimum configurations is as form 1.If get with reference to angle of heel | σ _ref|=0deg, then angle of attack corridor is as shown in Figure 2.Can find out, the upper bound in angle of attack corridor is determined by the maximum angle of attack, and the lower bound in angle of attack corridor then determines primarily of the constraint of maximum heat current density and max-Q constraint.Fig. 3 then gives the different angle of attack corridor corresponding with reference to angle of heel, can find out, larger with reference to angle of heel, then the lower bound in angle of attack corridor is higher.If get with reference to angle of attack _ref=15deg, then angle of heel corridor as shown in Figure 4.Can find out, the lower bound in angle of heel corridor is determined by minimum angle of heel, and the upper bound of angle of heel is then determined by the constraint of maximum heat current density, maximum angle of heel and max-Q.Fig. 5 then gives the different angle of heel corridor corresponding with reference to the angle of attack, can find out that the upper bound with reference to the angle of attack larger then angle of heel corridor is higher.Form 2 gives the reference angle of attack needed for steady motor-driven glide and with reference to angle of heel, and their positions in reentry corridor as shown in Figure 6 and Figure 7.

Form 1CAV process constraints restriction value

Form 2 is with reference to angle of attack curve with reference to angle of heel

Numbering	With reference to the angle of attack (deg)	With reference to angle of heel (deg)
			Example 1	17-0.0004V+4sin[0.0004π(V-2000)]	45
Example 2	17-0.0004V+4sin[0.0006π(V-2000)]	45
			Example 3	17-0.0004V+4sin[0.0008π(V-2000)]	45
Example 4	17-0.0004V+4sin[0.001π(V-2000)]	45

Example 5	15	45+15sin[0.0004π(V-2000)]
			Example 6	15	45+15sin[0.0006π(V-2000)]
Example 7	15	45+15sin[0.0008π(V-2000)]
			Example 8	15	45+15sin[0.001π(V-2000)]

Fig. 8 to Figure 11 corresponding to different angle of attack variation frequency gives at steady motor-driven glide trajectories; And Figure 12 to Figure 15 corresponding to different angle of heel change frequency gives at steady motor-driven glide trajectories.From Fig. 8 and Figure 12 relatively, both all can live to obtain the steady glide Longitudinal Trajectory of height relief change, but the result obtained by change angle of attack curve is more level and smooth; Contrasted from Fig. 9 and Figure 13, the impact of change angle of attack curve on speed is less; Contrasted from Figure 10 and Figure 14, change angle of attack curve is also less on the impact of horizontal trajectory; Contrasted from Figure 11 and Figure 15, the method phase acceleration that change angle of attack Curves needs is also less.To sum up can obtain, when carrying out steady motor-driven glide trajectories planning, by planning that in the angle of attack corridor change angle of attack can led continuously is the best mode designing steady motor-driven glide.

Claims (1)

1., based on a superb steady motor-driven glide trajectories method for designing for the angle of attack or angle of heel frequency conversion, it is characterized in that: it comprises following steps:

Step 1: hypersonic aircraft reenters process constraints modeling

Hypersonic aircraft reenters in process will consider maximum heat current density, max-Q and maximum overload process constraints, and the angle of attack and angle of heel also have boundary constraint simultaneously, specific as follows:

$\begin{array}{cc}\stackrel{\·}{Q}=k\sqrt{\mathrm{\ρ}}{V}^3\≤{\stackrel{\·}{Q}}_{max}& q=\frac{1}{2}{\mathrm{\ρV}}^2\≤q_{max}\end{array}$

$\begin{array}{ccc}n=\sqrt{L^2+D^2}\≤n_{max}& {\mathrm{\α}}_{\min }\≤\mathrm{\α}\≤{\mathrm{\α}}_{max}& {\mathrm{\σ}}_{\min }\≤\left|\mathrm{\σ}\right|\≤{\mathrm{\σ}}_{max}\end{array}$

In formula, for heat flow density; for maximum heat current density; ρ is atmospheric density; V is speed; K is the heat flow density constant of aircraft; Q is dynamic pressure; N is overload; q _maxand n _maxbe respectively max-Q and maximum overload; α is the angle of attack; σ is angle of heel; α _min, α _maxbe respectively the minimum angle of attack, the maximum angle of attack; σ _minand σ _maxbe respectively minimum angle of heel and maximum angle of heel; L and D is respectively normalized lift and resistance;

Step 2: the steadily foundation in glide angle of attack corridor

If the reference angle of heel absolute value of glide section is as follows:

|σ _ref|＝f _σ(V)

In above formula, σ _reffor reference angle of heel, f _σ(V) be velocity correlation function, the angle of attack lower bound utilizing equilibrium glide condition to obtain maximum heat current density, max-Q and maximum overload corresponding is respectively α _q, α _qand α _n, then the lower bound in angle of attack corridor is,

α _low＝max(α _Q,α _q,α _n,α _min)

In above formula, α _lowfor the lower bound in angle of attack corridor, the upper bound in angle of attack corridor is then α _up=α _max;

Step 3: the steadily foundation in glide angle of heel corridor

If the angle of attack curve of glide section is as follows,

α _ref＝f _α(V)

In above formula, α _reffor the reference angle of attack, f _α(V) be velocity correlation function, the upper bound utilizing equilibrium glide condition to obtain angle of heel absolute value corresponding to maximum heat current density, max-Q and maximum overload is respectively | σ _q|, | σ _q| with | σ _n|, then the upper bound in angle of heel corridor is,

σ _up＝min(|σ _Q|,|σ _q|,|σ _n|,σ _max)

In above formula, σ _upfor the upper bound in angle of heel corridor, the lower bound in angle of heel corridor is then σ _low=σ _min;

Step 4: steady motor-driven glide is with reference to angle of attack Curve Design

Adopt polynomial function and trigonometric function composite design with reference to angle of attack curve, as follows:

${\mathrm{\α}}_{ref}=f_{\mathrm{\α}1}\left(V\right)+C_{a1}sin(\frac{C_{a2}\mathrm{\π}(V-V_f)}{C_{a3}}+C_{a4})$

In formula, α _reffor reference angle of attack curve; f _{α 1}(V) being take speed as the polynomial function of independent variable, which determines the average with reference to the angle of attack; C _a1for controlling the constant of angle of attack amplitude, usually determine its size by angle of attack corridor; C _a2for controlling the constant of angle of attack oscillation frequency, it is the major parameter adjusting steady motor-driven gliding flight mode; C _a3for velocity constant, C _a3=V ₀-V _f, wherein V ₀and V _fbe respectively initial velocity and the terminal velocity of glide trajectories; C _a4for phase place adjustment constant;

Step 5: the reference angle of heel Curve Design of steady motor-driven glide

Similar with step 4, adopt polynomial function and trigonometric function composite design with reference to angle of heel curve, as follows:

${\mathrm{\σ}}_{ref}=f_{\mathrm{\σ}1}\left(V\right)+C_{s1}sin(\frac{C_{s2}\mathrm{\π}(V-V_f)}{C_{s3}}+C_{s4})$

In formula, σ _reffor reference angle of heel curve; f _{σ 1}(V) being take speed as the polynomial function of independent variable, which determines the average with reference to angle of heel, and then have impact on the range of planning trajectory; C _s1for controlling the constant of angle of heel amplitude, usually determine its size by angle of heel corridor; C _s2for controlling the constant of angle of heel oscillation frequency, it is the major parameter adjusting steady motor-driven gliding flight mode; C _s3for velocity constant, C _s3=V ₀-V _f, wherein V ₀and V _fbe respectively initial velocity and the terminal velocity of glide trajectories; C _s4for phase place adjustment constant;

Step 6: initial gliding height and trajectory tilt angle solve

The reference angle of attack determined according to step 2 and step 4 or step 3 and step 5 and angle of heel, solve elemental height and the trajectory tilt angle of steady motor-driven glide trajectories, specific as follows:

$h_{sg}=-\frac{1}{\mathrm{\β}}ln\left(\frac{g-V^2/r-a_{sg}}{k_c{V}^2{C}_{L1}^{*}}\right)$

${\mathrm{\γ}}_{sg}=-\frac{(f_a+f_V)(g+a_{sg}-V^2/r)}{K_1^{*}\mathrm{\β}V+K_1^{*}g(f_a+f_V)}---\left(1\right)$

In above formula, h _sg, γ _sgand a _sgbe respectively steady gliding height, trajectory tilt angle and longitudinal acceleration; k _cfor the coupling constant of aircraft, k _c=ρ ₀s/ (2m); with be respectively with reference to the angle of attack and lift coefficient longitudinal component corresponding to angle of heel and lift-drag ratio longitudinal component; f _aand f _vbe velocity correlation function; a _sgfor longitudinal acceleration of steadily gliding;

Step 7: determine damping Derivative Feedback control program

Determine damping Derivative Feedback to control to make glide trajectories rapidly converge to steady glide state, specific as follows:

$k_2=2{\mathrm{\ζ}}_c\sqrt{(g-V^2/r)\mathrm{\β}}-(g-V^2/r)/\left({\mathrm{VK}}_1^{*}\right)$

$C_{L1}^{\left(real\right)}=C_{L1}^{*}-\frac{2{\mathrm{mk}}_2{C}_{L1}^{*}}{\mathrm{\ρ}VS{\mathrm{cos\σ}}^{*}}(\mathrm{\γ}-{\mathrm{\γ}}_{sg})$

In above formula, ζ _cfor given damping, usually get ζ _c=0.707; ρ, g, V, r, γ are respectively the current atmospheric density of aircraft, acceleration of gravity, speed, the earth's core distance and trajectory tilt angle; for the lift coefficient longitudinal component of reality; γ _sgfor reference trajectory inclination angle, obtained by formula (1); σ ^*for reference angle of heel; for by with reference to lift coefficient longitudinal component; k ₂for Derivative Feedback coefficient;

Step 8: the generation of steady motor-driven glide trajectories

The elemental height obtained with step 6 and trajectory tilt angle are for initial value for integral, and the actual lift coefficient longitudinal component obtained with step 7, for control variable, carries out trajectory integration; Namely steady motor-driven glide trajectories is obtained.