CN100576124C - A kind of longitudinal control method for high altitude lifting of aerospaceplane - Google Patents

Abstract

The invention discloses a kind of longitudinal control method for high altitude lifting of aerospaceplane, step is: (1) is according to the pneumatic characteristics computing velocity of controlled device kinetics equation and high-altitude upcurve; (2) calculate the aircraft pursuit course of the angle of climb along the speed upcurve; (3) according to the aircraft pursuit course of the aircraft pursuit course of the angle of climb design angle of attack; (4) design angle of pitch speed aircraft pursuit course; (5) the design angle of attack and angle of pitch speed tracking Control rule.Control method of the present invention has been established theoretical foundation for aircraft pursuit course design, has not only realized coordinating the target of control, and has satisfied the angle of pitch and overload restriction, has overcome the accent ginseng problem in the existing aircraft control, has reduced the complicacy of design.

Description

A kind of longitudinal control method for high altitude lifting of aerospaceplane

Technical field

The invention belongs to Aero-Space control field, the vertical control method when relating to a kind of sky and space plane and climbing in the high-altitude.

Background technology

The notion of sky and space plane proposed in early 1980s.Increase along with space operation, Development of Manned Spaceflight particularly, the great number launching costs of disposable use rocket, airship and space shuttle becomes " bottleneck " of carrying out space operation on a large scale day by day, press for a kind of aircraft that can travel to and fro between economy between the world, safety as the conventional airplane landing again, Here it is sky and space plane.It can finish the civil aviation space mission, can carry out multiple military aviation space mission again, to be one of crucial weaponry of controlling 21 century space, contention system Megrez, be a kind of tool manned space flight weapons with broad prospects for development, will bring major transformation for future war.

Sky and space plane is carried to certain altitude by carrier aircraft and throws in, after the input, and rocket motor ignition, the rapid pull-up of sky and space plane is climbed rapidly, and after fuel consume was intact, engine shutdown entered unpowered ramp-up period, reaches predetermined altitude and track.When climbing flight in the endoatmosphere, because huge motor power, sky and space plane climbs in the process of climbing rapidly, flying speed and highly sharply variation, from the subsonic speed to the hypersonic speed, make the aerodynamic characteristic of sky and space plane produce sharply variation, the lift efficiency of sky and space plane, focus and control surface efficient all can produce rapid variation.In order to reach predetermined height, sky and space plane need carry a large amount of fuel, and these fuel consume in the process of climbing fast.Therefore can cause the weight of sky and space plane in the process of climbing, the sharply and significantly variation of the center of gravity and the moments of inertia.These change can be to the operation stabilization characteristic and the dynamic response characteristic generation influence greatly of sky and space plane.

For the CONTROL LAW DESIGN problem of the high-altitude section of climbing sky and space plane,, mainly face following difficulty as can be seen in the section of the climbing design: (1) height and speed coordination control problem by every data are carried out labor.Because huge motor power, sky and space plane speed rises very fast.The section of climbing controlled target is: flying height surpasses the altitude range that pre-establishes, and flying speed then should be less than the Mach Number Never To Be Exceeded requirement of housing construction restriction.Therefore how to realize that the control of height and speed coordination is a difficult point of design.(2) the uncontrollable problem of long period.In the scope at a high speed of high-altitude, because atmospheric density sharply reduces, cause the speed variable is to increase fast always, and the angle of climb is difficult to control.Promptly in this scope, the problem that the outer shroud long period can not be controlled.(3) how at short period variable, design suitable controlled target, as the angle of attack and angle of pitch speed aircraft pursuit course,, also be one of problem that faces to realize the control of the section of climbing.

From top analysis as can be seen, the sky and space plane high-altitude section of climbing is different with the conventional airplane control model, but the document of publishing does not still have corresponding control methods.Therefore, be necessary to seek a kind of new method and finish the control of climbing of sky and space plane high-altitude, solve above-mentioned three difficult points, promptly design the angle of attack and angle of pitch speed aircraft pursuit course and be suitable for the control method that engineering is used, coordination control with realization speed and height, and satisfy the angle of pitch and overload restriction, overcome the accent ginseng problem in the aircraft control, thereby reduce the complexity of design.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provide a kind of tunable controlled good, the longitudinal control method for high altitude lifting of aerospaceplane that satisfies the angle of pitch and overload restriction, can carry out six degree of freedom control.

Technical solution of the present invention is: a kind of longitudinal control method for high altitude lifting of aerospaceplane, and step is as follows:

(1) according to the pneumatic characteristics of sky and space plane kinetics equation and high-altitude, determines sky and space plane high-altitude climbing speed upcurve;

(2) the speed upcurve that obtains according to step (1) obtains the aircraft pursuit course of angle of climb γ;

(3) aircraft pursuit course of the angle of climb γ that obtains according to step (2) is determined the aircraft pursuit course of angle of attack;

(4) determine the aircraft pursuit course of angle of pitch speed q;

(5), determine the tracking Control rule of angle of attack and angle of pitch speed q according to the result of step (3) and (4).

The sky and space plane high-altitude climbing speed upcurve equation that obtains in the described step (1) is:

$\stackrel{\&CenterDot;}{V}=\frac{P}{m}-\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}\sin \mathrm{\&gamma;}$

Wherein, V is the climbing speed of sky and space plane, the thrust that P is subjected to for empty day extension set, and m is the quality of sky and space plane, and μ is the terrestrial gravitation constant, and r is the distance of sky and space plane apart from the earth's core, and γ is the angle of climb of sky and space plane.

The aircraft pursuit course equation of the angle of climb γ that obtains in the described step (2) is:

$\mathrm{\&gamma;}=\arcsin (\frac{P}{m}/(\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}+\mathrm{Va}\&times;{10}^{-4}))$

Wherein, γ is the angle of climb of sky and space plane, the thrust that P is subjected to for empty day extension set, and m is the quality of sky and space plane, and μ is the terrestrial gravitation constant, and r is the distance of sky and space plane apart from the earth's core, and V is the climbing speed of sky and space plane, a is the velocity of sound.

The aircraft pursuit course equation of the angle of attack that obtains in the described step (3) is:

$\mathrm{\&alpha;}=-\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}$

Wherein, α is the angle of attack, and γ is the angle of climb of sky and space plane.

The aircraft pursuit course equation of angle of pitch speed q is in the described step (4):

q＝0。

The tracking Control of angle of attack and angle of pitch speed q rule adopts the overall coefficient self-adaptation control method based on characteristic model to obtain in the described step (5), and step is:

The characteristic model of setting up angle of attack and angle of pitch speed q at first respectively is as follows:

α(k+2)＝f ₁₁(k)α(k+1)+f ₁₂(k)α(k)+g ₁(k)u(k)

q(k+2)＝f ₂₁(k)q(k+1)+f ₂₂(k)q(k)+g ₂(k)u(k)

In the formula, f _I1(k) ∈ [1.4331,1.9974], i=1,2; f _I2(k) ∈ [0.9999 ,-0.5134], i=1,2;

Determine g then _i(k), i=1,2 scope, the use least square method is determined 6 parameters in the formula,

I, j=1,2 and

I=1,2;

At last, utilization obtains

I, j=1,2 and I=1,2 design overall coefficient adaptive control laws u _j=u _Gj+ u _Ij+ u _Dj, j=1,2,

In the formula, $u_{\mathrm{gj}}\left(k\right)=\frac{l_1{\hat{f}}_{j1}\left(k\right)e_j\left(k\right)+l_2{\hat{f}}_{j2}\left(k\right)e_j(k-1)}{{\hat{g}}_j\left(k\right)},j=\mathrm{1,2}$

u _ij(k)＝u _ij(k-1)-k _ije _j(k)，j＝1，2

u _dj(k)＝-k _dj(e _j(k)-e _j(k-1))，j＝1，2

l ₁＝0.382，l ₂＝0.618

e ₁(k)=α (k)-α _r(k), α (k) is a state variable, α _r(k) expression angle of attack aircraft pursuit course;

e ₂(k)=q (k)-q _r(k), q (k) is a state variable, q _r(k) expression rate of pitch aircraft pursuit course;

$k_{\mathrm{ij}}=\left\{\begin{array}{c}{k}_{i1j},e_j\left(k\right){\stackrel{\&CenterDot;}{e}}_j\left(k\right)>0,\\ k_{i2j},e_j\left(k\right){\stackrel{\&CenterDot;}{e}}_j\left(k\right)\&le;0,\end{array}\right.,k_{i1j}>k_{i2j}>0,j=\mathrm{1,2}$

$k_{\mathrm{dj}}=c_{\mathrm{dj}}\sqrt{\underset{r=0}{\overset{l_{\mathrm{dj}}}{\mathrm{\&Sigma;}}}\left|e_j\left(k\right)\right|}>0,j=\mathrm{1,2}$

k _Ijl, j, l=1,2, c _Dj, l _Dj, j=1,2 for needing tuning parameter.

The present invention's advantage compared with prior art is:

(1) control method of the present invention comprises aircraft pursuit course design and tracking and controlling method design two parts, the kinetic character and the high-altitude aerodynamic characteristic of controlled device itself have been taken into full account, not only realized coordinating the target of control, and satisfy the angle of pitch and overload restriction, for the further six degree of freedom high-altitude controlling Design of climbing provides thinking;

(2) the inventive method is by anatomizing every data of high-altitude controlled device kinetics equation, and the clear and definite uncontrollable problem in aircraft long-period variable high-altitude has disclosed the essence of high-altitude vehicle flight.Obtained the speed upcurve according to the controlled device own characteristic, coordinated control for sky and space plane and lay a good foundation;

(3) the inventive method has provided angle of climb computing formula, for aircraft pursuit course design has been established theoretical foundation according to sky and space plane high-altitude controlled device dynamics and coordination control features;

(4) the inventive method has provided angle of attack computing formula based on the essential characteristic of sky and space plane kinetics equation and aircraft control, for the design of angle of attack aircraft pursuit course provides theoretical foundation;

(5) the inventive method is controlled essential requirement according to aircraft, has clearly provided angle of pitch speed aircraft pursuit course, for ring control in the sky and space plane of high-altitude is laid a good foundation;

(6) the present invention designs the overall coefficient self-adaptation control method of employing based on characteristic model, overcome the deficiency of existing adaptation theory in application, has stronger robustness and to the adaptability of initial parameter, being suitable for engineering uses, overcome the accent ginseng problem in the existing aircraft control, reduced the complicacy of design.

Description of drawings

Fig. 1 is the FB(flow block) of the inventive method;

Fig. 2 is the Changing Pattern figure of the embodiment of the invention hollow sky center of gravity of airplane;

Fig. 3 is the Changing Pattern figure of embodiment of the invention hollow sky Aircraft Quality;

Fig. 4 is the Changing Pattern figure of the sky and space plane moments of inertia in the embodiment of the invention;

Fig. 5 is according to the designed rate curve of the inventive method and the comparison synoptic diagram of straight line upcurve in the embodiment of the invention;

Fig. 6 is according to the resulting angle of climb γ aircraft pursuit course of the inventive method in the embodiment of the invention;

Fig. 7 is according to the resulting angle of attack aircraft pursuit course of the inventive method in the embodiment of the invention;

The tracking results that Fig. 8 obtains for the angle of attack aircraft pursuit course that adopts Fig. 7;

Fig. 9 is the tracking results of angle of pitch speed q in the embodiment of the invention;

Figure 10 is the height simulation result in the embodiment of the invention;

Figure 11 is the Mach number simulation result in the embodiment of the invention;

Figure 12 is the angle of pitch simulation result in the embodiment of the invention;

Figure 13 is the angle of climb simulation result in the embodiment of the invention;

Figure 14 is the control input simulation result in the embodiment of the invention;

Figure 15 is the overload simulation result in the embodiment of the invention;

Figure 16 is the angle of attack tracking results in the embodiment of the invention;

Figure 17 is the rate of pitch tracking results in the embodiment of the invention.

Embodiment

As shown in Figure 1, be the FB(flow block) of the inventive method, step is: (1) determines sky and space plane high-altitude climbing speed upcurve according to the pneumatic characteristics of sky and space plane kinetics equation and high-altitude; (2), calculate the aircraft pursuit course of angle of climb γ according to the speed upcurve; (3) determine the aircraft pursuit course of angle of attack according to the aircraft pursuit course of angle of climb γ; (4) aircraft pursuit course of design angle of pitch speed q; (5) according to the result of step (3) and (4), the tracking Control of design angle of attack and angle of pitch speed q is restrained.

Among the present invention, the velocity correlation kinetics equation adopts $\stackrel{\&CenterDot;}{V}=-\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}\sin \mathrm{\&gamma;}+\frac{P\cos \mathrm{\&alpha;}}{m}-\frac{D}{m},$ V wherein, P, r, m, γ, μ, α, D represent the speed, thrust of sky and space plane respectively, apart from geocentric distance, quality, the angle of climb, terrestrial gravitation constant, the angle of attack and external drag.Because altitude air density is very little, causes

The 3rd very little, can ignore, and cos α is about 1, therefore

Can be reduced to: $\stackrel{\&CenterDot;}{V}=\frac{P}{m}-\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}\sin \mathrm{\&gamma;}.$

Comprehensive above-mentioned derivation can obtain high-altitude speed upcurve computing formula and is: $\stackrel{\&CenterDot;}{V}=\frac{P}{m}-\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}\sin \mathrm{\&gamma;},$ Wherein γ is according to the working point angle calculation.

Consider the rate of change of the rate of change of velocity of sound a much smaller than speed, by $M=\frac{V}{a},$ Wherein M represents Mach number, can get $\stackrel{\&CenterDot;}{M}=\frac{\stackrel{\&CenterDot;}{V}}{a},$ Controlled target requires Mach number and highly has the approximately uniform rate of rise because sky and space plane climbs, and therefore has $\stackrel{\&CenterDot;}{M}=\stackrel{\&CenterDot;}{h}\&times;{10}^{-4},$ Can get by above two formulas $\stackrel{\&CenterDot;}{h}=\frac{\stackrel{\&CenterDot;}{V}\&times;{10}^4}{a}.$ Again according to kinetics equation $\stackrel{\&CenterDot;}{h}=V\sin \mathrm{\&gamma;},$ Can obtain $\stackrel{\&CenterDot;}{V}=\mathrm{Va}\sin \mathrm{\&gamma;}\&times;{10}^{-4},$ Consider above-mentioned sky and space plane high-altitude climbing speed upcurve equation $\stackrel{\&CenterDot;}{V}=\frac{P}{m}-\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}\sin \mathrm{\&gamma;},$ Can obtain $\frac{P}{m}=(\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}+\mathrm{Va}\&times;{10}^{-4})\sin \mathrm{\&gamma;}.$

Comprehensive above-mentioned derivation can obtain γ angle computing formula and is: $\mathrm{\&gamma;}=\arcsin (\frac{P}{m}/(\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}+\mathrm{Va}\&times;{10}^{-4})).$

According to the characteristics of aircraft control, design angle of pitch speed aircraft pursuit course q=0.And then by kinetics equation $\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}=q-\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}$ And the aircraft pursuit course of above-mentioned γ can obtain the aircraft pursuit course of angle of attack.

Among the present invention, the tracking Control of angle of attack and angle of pitch speed q rule adopts the overall coefficient self-adaptation control method based on characteristic model to obtain, and the characteristic model of setting up the angle of attack and rate of pitch at first respectively is as follows:

α(k+2)＝f ₁₁(k)α(k+1)+f ₁₂(k)α(k)+g ₁(k)u(k)

q(k+2)＝f ₂₁(k)q(k+1)+f ₂₂(k)q(k)+g ₂(k)u(k)

F wherein _I1(k) ∈ [1.4331,1.9974], i=1,2; f _I2(k) ∈ [0.9999 ,-0.5134], i=1,2; Suitably choose g _i(k), i=1,2 scope is used above-mentioned 6 parameters of least square method identification, and identification result is designated as respectively

I, j=1,2 and

I=1,2; Utilize above-mentioned parameter design overall coefficient adaptive control laws

u _j＝u _gj+u _ij+u _dj，j＝1，2

Wherein,

$u_{\mathrm{gj}}\left(k\right)=-\frac{l_1{\hat{f}}_{j1}\left(k\right)e_j\left(k\right)+l_2{\hat{f}}_{j2}\left(k\right)e_j(k-1)}{{\hat{g}}_j\left(k\right)},j=\mathrm{1,2}$

u _ij(k)＝u _ij(k-1)-k _ije _j(k)，j＝1，2

u _dj(k)＝-k _dj(e _j(k)-e _j(k-1))，j＝1，2

l ₁＝0.382，l ₂＝0.618

e ₁(k)=α (k)-α _r(k), α _r(k) expression angle of attack aircraft pursuit course;

e ₂(k)=q (k)-q _r(k), q _r(k) expression rate of pitch aircraft pursuit course;

$k_{\mathrm{ij}}=\left\{\begin{array}{c}{k}_{i1j},e_j\left(k\right){\stackrel{\&CenterDot;}{e}}_j\left(k\right)>0,\\ k_{i2j},e_j\left(k\right){\stackrel{\&CenterDot;}{e}}_j\left(k\right)\&le;0,\end{array}\right.,k_{i1j}>k_{i2j}>0,j=\mathrm{1,2}$

$k_{\mathrm{dj}}=c_{\mathrm{dj}}\sqrt{\underset{r=0}{\overset{l_{\mathrm{dj}}}{\mathrm{\&Sigma;}}}\left|e_j\left(k\right)\right|}>0,j=\mathrm{1,2}$

k _Ijl, j, l=1,2, c _Dj, l _Dj, j=1,2, be the need tuning parameter.(derivation can be referring to Wu Hongxin in detail, overall coefficient Adaptive Control Theory and method thereof, Beijing: National Defense Industry Press, 1990)

Embodiment

Vertically climb with the high-altitude of spacecraft X-34 below and be controlled to be example detailed description the inventive method.

Empty day aircraft X-34 is carried to height 7 kilometers (0.7M) by carrier aircraft and throws in; after aircraft is thrown in; rocket motor ignition, the rapid pull-up of aircraft is climbed rapidly; to 72 kilometers (7.2M); after fuel consume was intact, engine shutdown entered unpowered ramp-up period; reach predetermined altitude and track, carry out unpowered decline at last.Here consider the CONTROL LAW DESIGN problem of the high-altitude section of climbing 25 kilometers (2.5M) to 72 kilometers (7.2M).For above-mentioned kinetics equation $\stackrel{\&CenterDot;}{V}=-\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}\sin \mathrm{\&gamma;}+\frac{P\cos \mathrm{\&alpha;}}{m}-\frac{D}{m}$ In every aerodynamic parameter CLB, CDB, CMB, CLDE, CDDE, CMDE, CMQ, adopt the aerodynamic data (providing two pieces of document 1.Aerodynamic Characteristics and Development of theAerodynamic Database of the X-34 Reusable Launch Vehicle.2.Aerodynamic Characteristics herein, Database Development and Flight Simulation of the X-34 Vehicle.) in the relevant references.In the process of climbing, because huge motor power, aircraft center of gravity, quality and the moments of inertia be acute variation in time, and its rule is shown in Fig. 2～4.Sky and space plane control rudder face is elevating rudder and wing flap.

The task object of striding the atmospheric envelope section of climbing is after rising of experience power and unpowered rising, the factor regulation (necessity of the control of embodiment coordination here because of thermally protective materials, if aircraft flies with big speed at lower height, then pneumatic heat is higher, if at higher height, then aerodynamic effect is poor), flying height should be able to surpass the altitude range that pre-establishes, and flying speed then should be less than the Mach Number Never To Be Exceeded requirement of housing construction restriction.In addition, require 72 kilometers (7.2M) of sky and space plane arrival in the time of 200 seconds, and satisfy the overload requirement.

Under circle rotation earth situation, the vertical kinetics equation of aircraft is:

$\left\{\begin{array}{c}\stackrel{\&CenterDot;}{V}=-\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}\sin \mathrm{\&gamma;}+\frac{(P\cos \mathrm{\&alpha;}-D)}{m}+{\mathrm{\&omega;}}_E^{2}r\sin \mathrm{\&gamma;}---\left(1\right)\\ V\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}=-(\frac{\mathrm{\&mu;}}{r^2}-\frac{V^2}{r})\cos \mathrm{\&gamma;}+\frac{(P+\sin \mathrm{\&alpha;}+L)}{m}+2{\mathrm{\&omega;}}_{E}V+{\mathrm{\&omega;}}_E^{2}r\cos \mathrm{\&gamma;}---\left(2\right)\\ \stackrel{\&CenterDot;}{h}=V\sin \mathrm{\&gamma;}---\left(3\right)\\ \stackrel{\&CenterDot;}{q}=\frac{M_y}{I_y}\\ \stackrel{\&CenterDot;}{\mathrm{\&alpha;}}=q-\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}\end{array}\right.$

r＝h+R _E

$L=\frac{1}{2}\mathrm{\&rho;}{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">V</figure-callout>}}^2{\mathrm{SC}}_L$

$D=\frac{1}{2}\mathrm{\&rho;}{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">V</figure-callout>}}^2{\mathrm{SC}}_D$

$M_y=\frac{1}{2}\mathrm{\&rho;}{V}^{2}S\stackrel{\&OverBar;}{c}$

C _L＝CLB+CLDE

C _D＝CDB+CDDE

C _Z＝-C _Lcosα-C _Dsinα

$C_M=\mathrm{CMB}+\mathrm{CMDE}+\frac{\stackrel{\&OverBar;}{c}q}{2V}\mathrm{CMQ}-\frac{C_Z(\mathrm{XCG}-\mathrm{CGREF})}{\stackrel{\&OverBar;}{c}}$

The physical significance of above-mentioned each variable is:

V: flight path speed (aircraft barycenter speed relative to the earth)

H: aircraft height

γ: the angle of climb

M: vehicle mass

I _y: around the pitch axis moment of inertia

P: thrust

Q: angle of pitch speed

α: the angle of attack

μ: terrestrial gravitation constant (3.986005 * 10 ¹⁴m ³/ s ²)

ω _E: earth angular velocity of rotation (7.292116 * 10 ^-5Rad/s)

R _E: earth radius, 6371386m

M: Mach number

L, D, M _yRepresent aerodynamic lift, aerodynamic drag and pitching moment respectively

ρ: atmospheric density

S: aircraft area of reference (33.2m ²)

C: aircraft is with reference to chord length (4.43m)

C _L, C _D, C _MRepresent lift, resistance and pitching moment coefficient respectively

C _Z: the aerodynamic coefficient that body coordinate system Z direction is total

CLB, CDB, CMB represent lift coefficient, resistance coefficient and pitching moment coefficient fundamental quantity respectively

CLDE, CDDE, CMDE represent aerodynamic lift, resistance and the pitching moment coefficient that elevating rudder produce respectively

CMQ: pitch-damping ratio

XCG: centre of gravity place

CGREF: with reference to center of gravity (10.668m)

Qs: dynamic pressure

By the every data mu/r in the analytic dynamics equation (1) ², P/m and qs/m as can be seen, speed is uncontrollable when the high-altitude, in order to arrive set speed and height according to design time, must according to the aircraft own characteristic from after design forward, designed speed upcurve is as shown in Figure 5.The line that circle is formed among Fig. 5 is designed speed upcurve.

By kinetics equation (3) as can be known, if speed reaches controlled target as requested, by the suitable γ angle of design, can realize the design of height so.Therefore the key that realizes the control of height and speed coordination is the control problem at γ angle.Below by analytic dynamics equation and every data thereof, obtained the aircraft pursuit course at γ angle along above-mentioned speed upcurve, computing formula is as follows:

In the section of climbing more than 40 kilometers:

$\frac{P}{m}=(\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}+\mathrm{Va}\&times;{10}^{-4})\sin \mathrm{\&gamma;}---\left(4\right)$

The section of climbing at 25 to 40 kilometers:

$\frac{P}{m}-1=(\frac{\mathrm{\&mu;}}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C2008102251740018H3.png,C2008102251740021H1.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}+\mathrm{Va}\&times;{10}^{-4})\sin \mathrm{\&gamma;}---\left(5\right)$

Utilize above-mentioned formula (4) and (5), designed γ aircraft pursuit course as shown in Figure 6.

Because when the high-altitude, atmospheric density sharply descends.Every data by analytic dynamics equation (3) γ as can be known are uncontrollable, when 166-200s,

Be about for-0.12 degree/second.But required γ in rising trend later in 166 seconds in Fig. 6, this can't realize in practice, must revise above-mentioned curve according to the characteristics of controlled device.Simulation result shows, carries out controlling Design according to the gamma curve of revising, and can reach final controlled target.

By above-mentioned analysis as can be known, when the high speed of high-altitude, the aircraft long-period variable is uncontrollable, its control problem need be converted into the control problem of short period variable angle of attack and angle of pitch speed q.Here we are according to the aircraft pursuit course of following Rule Design α and q.By the working point data are analyzed, the restriction angle of attack is at 5～10 degree, according to formula

$\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}=-\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}---\left(6\right)$

Carry out the aircraft pursuit course design of α with actual γ aircraft pursuit course.

According to the characteristics of aircraft control, design angle of pitch speed aircraft pursuit course q=0.And then by kinetics equation $\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}=q-\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}$ And the aircraft pursuit course of above-mentioned γ can obtain the aircraft pursuit course of angle of attack, as shown in Figure 7.From the above analysis, stride the weight of aerial vehicle and aerodynamic parameter etc. huge variation takes place in the process of climbing.Here adopt overall coefficient adaptive control laws, reduced the complexity of design of Controller based on characteristic model.

The selection sampling period is 50ms, and the characteristic model of setting up the angle of attack and rate of pitch at first respectively is as follows:

α(k+2)＝f ₁₁(k)α(k+1)+f ₁₂(k)α(k)+g ₁(k)u(k)

q(k+2)＝f ₂₁(k)q(k+1)+f ₂₂(k)q(k)+g ₂(k)u(k)

F wherein _I1(k) ∈ [1.4331,1.9974], i=1,2; f _I2(k) ∈ [0.9999 ,-0.5134], i=1,2; Suitably choose g _i(k) ∈ [0.003,0.3], i=1,2, use above-mentioned 6 parameters of least square method identification, identification result is designated as respectively

I, j=1,2 and

I=1,2, and it is limited in the above-mentioned scope.Utilize above-mentioned parameter design overall coefficient adaptive control laws

u _j＝u _gj+u _ij+u _dj，j＝1，2 (7)

Wherein,

$u_{\mathrm{gj}}\left(k\right)=-\frac{l_1{\hat{f}}_{j1}\left(k\right)e_j\left(k\right)+l_2{\hat{f}}_{j2}\left(k\right)e_j(k-1)}{{\hat{g}}_j\left(k\right)},j=\mathrm{1,2}$

u _ij(k)＝u _ij(k-1)-k _ije _j(k)，j＝1，2

u _dj(k)＝-k _dj(e _j(k)-e _j(k-1))，j＝1，2

l ₁＝0.382，l ₂＝0.618

e ₁(k)=α (k)-α _r(k), α _r(k) expression angle of attack aircraft pursuit course;

e ₂(k)=q (k)-q _r(k), q _r(k) expression rate of pitch aircraft pursuit course;

$k_{\mathrm{ij}}=\left\{\begin{array}{c}{k}_{i1j},e_j\left(k\right){\stackrel{\&CenterDot;}{e}}_j\left(k\right)>0,\\ k_{i2j},e_j\left(k\right){\stackrel{\&CenterDot;}{e}}_j\left(k\right)\&le;0,\end{array}\right.,k_{i1j}>k_{i2j}>0,j=\mathrm{1,2}$

$k_{\mathrm{dj}}=c_{\mathrm{dj}}\sqrt{\underset{r=0}{\overset{l_{\mathrm{dj}}}{\mathrm{\&Sigma;}}}\left|e_j\left(k\right)\right|}>0,j=\mathrm{1,2}$

k _Ijl, j, l=1,2, c _Dj, l _Dj, j=1,2, be the need tuning parameter.

The control rudder face that need design here is elevating rudder deviation and wing flap.By the pitching aerodynamic parameter is investigated, when wing flap is-15 ° as can be known, can provide maximum pitching moment, and occur the reversal phenomenon during less than-15 °.Therefore here at first fixedly wing flap be-15 °, so that pitching moment to be provided.Only designing adaptive control input elevating rudder deviation is u ₁+ u ₂, u ₁, u ₂See (7) formula.

At initial parameter engine operation initial time is ENGWT=110 second, the h=25 km, and M=2.5 Mach, α=5 °, γ=28 °, in the time of DE=-12 °, simulation result is shown in Fig. 8-15, and Fig. 8 and Fig. 9 are the tracking results of angle of attack and angle of pitch speed q; Figure 10-15 is respectively height simulation result, Mach number, the angle of pitch, the angle of climb, control input and overload simulation result.From simulation result as seen, above-mentioned design has not only realized the coordination control of height and speed, and satisfies the requirement for restriction of the angle of pitch and overload etc., and has reduced the complexity of design.

Investigate the robustness to initial parameter of above-mentioned control law below by emulation.Above-mentioned simulation result initial parameter is respectively engine operation initial time ENGWT, height initial value h, and Mach number initial value M, angle of attack initial value α, angle of climb initial value γ, elevating rudder deviation initial value DE, carried out emulation below under following several situations that above-mentioned initial value changes:

1, ENGWT=110 second, M=2.5 Mach, α=5 °, γ=28 °, DE=-12 °, height initial value h is in 23～25.3 kilometer range;

2, ENGWT=110 second, the h=25 km, α=5 °, γ=28 °, DE=-12 °, Mach number initial value M is in 2～2.9 range of Mach numbers;

3, ENGWT=110 second, the h=25 km, M=2.5, α=5 °, DE=-12 °, angle of climb initial value γ is in 20 °～29 ° scopes;

4, ENGWT=110 second, the h=25 km, M=2.5, α=5 °, γ=28 °, elevating rudder deviation D E initial value is in-9 °～-14 ° scopes;

5, ENGWT=110 second, the h=25 km, M=2.5, γ=28 °, DE=-10 °, angle of attack initial value α is in 4.8 °～5.2 ° scopes;

6, h=25 km, M=2.5, α=5 °, γ=28 °, DE=-10 °, engine operation initial time ENGWT is in 109.1 seconds～110.4 seconds scopes.

Simulation result shows under above-mentioned initial condition, for the angle of attack and rate of pitch good tracking effect is arranged all.Because when the time was 90 seconds, great changes had taken place from 240,000 Niu Bianwei 0 in thrust.Prolong simulation time, simulation result is respectively the tracking results of angle of attack and angle of pitch speed q shown in Figure 16 and 17.As seen control law is working properly after 90 seconds.

The content that is not described in detail in the instructions of the present invention belongs to those skilled in the art's known technology.

Claims (1)

1, a kind of longitudinal control method for high altitude lifting of aerospaceplane is characterized in that step is as follows:

(1) according to the pneumatic characteristics of sky and space plane kinetics equation and high-altitude, determines sky and space plane high-altitude climbing speed upcurve; Described step sky and space plane high-altitude climbing speed upcurve equation is:

$\stackrel{\&CenterDot;}{V}=\frac{P}{M}-\frac{\mathrm{\&mu;}}{r^2}\sin \mathrm{\&gamma;},$

Wherein, V is the climbing speed of sky and space plane, and P is the thrust that sky and space plane is subjected to, and m is the quality of sky and space plane, and μ is the terrestrial gravitation constant, and r is the distance of sky and space plane apart from the earth's core, and γ is the angle of climb of sky and space plane;

(2) the speed upcurve that obtains according to step (1) obtains the aircraft pursuit course of angle of climb γ; The aircraft pursuit course equation of described angle of climb γ is:

$\mathrm{\&gamma;}=\arcsin (\frac{P}{M}/(\frac{\mathrm{\&mu;}}{r^2}+\mathrm{Va}\&times;{10}^{-4})),$

Wherein, a is the velocity of sound;

(3) aircraft pursuit course of the angle of climb γ that obtains according to step (2) is determined the aircraft pursuit course of angle of attack; The aircraft pursuit course equation of described angle of attack is:

$\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}=-\stackrel{\&CenterDot;}{\mathrm{\&gamma;}};$

(4) determine the aircraft pursuit course of angle of pitch speed q; The aircraft pursuit course equation of described angle of pitch speed q is: q=0;

(5), determine the tracking Control rule of angle of attack and angle of pitch speed q according to the result of step (3) and (4); The tracking Control rule of described angle of attack and angle of pitch speed q adopts the overall coefficient self-adaptation control method based on characteristic model to obtain, and step is:

The characteristic model of setting up angle of attack and angle of pitch speed q at first respectively is as follows:

α(k+2)＝f ₁₁(k)α(k+1)+f ₁₂(k)α(k)+g ₁(k)u(k)

q(k+2)＝f ₂₁(k)q(k+1)+f ₂₂(k)q(k)+g ₂(k)u(k)

In the formula, f _I1(k) ∈ [1.4331,1.9974], i=1,2; f _I2(k) ∈ [0.9999 ,-0.5134], i=1,2;

Determine g then _i(k), i=1,2 scope, the use least square method is determined 6 parameters in the formula,

I, j=1,2 and

I=1,2;

At last, utilization obtains

I, j=1,2 and

I=1,2 design overall coefficient adaptive control laws u _j=u _Gj+ u _Ij+ u _Dj, j=1,2,

In the formula, $u_{\mathrm{gj}}\left(k\right)=-\frac{l_1{\hat{f}}_{j1}\left(k\right)e_j\left(k\right)+l_2{\hat{f}}_{j2}\left(k\right)e_j(k-1)}{{\hat{g}}_j\left(k\right)};$ j＝1，2

u _ij(k)＝u _ij(k-1)-k _ije _j(k)，j＝1，2

u _dj(k)＝-k _dj(e _j(k)-e _j(k-1))，j＝1，2

l ₁＝0.382，l ₂＝0.618

e ₁(k)=α (k)-α _r(k), α (k) is a state variable, α _r(k) expression angle of attack aircraft pursuit course;

e ₂(k)=q (k)-q _r(k), q (k) is a state variable, q _r(k) expression angle of pitch speed aircraft pursuit course;

$k_{\mathrm{ij}}=\left\{\begin{array}{c}{k}_{i1j},e_j\left(k\right){\stackrel{\&CenterDot;}{e}}_j\left(k\right)>0,\\ k_{i2j},e_j\left(k\right){\stackrel{\&CenterDot;}{e}}_j\left(k\right)\&le;0,\end{array}\right.k_{i1j}>k_{i2j}>0,$ j＝1，2

$k_{\mathrm{dj}}=c_{\mathrm{dj}}\sqrt{\underset{r=0}{\overset{l_{\mathrm{dj}}}{\mathrm{\&Sigma;}}}\left|e_j\left(k\right)\right|}>0,$ j＝1，2

k _Ilj, j, l=1,2, c _Dj, l _Dj, j=1,2 for needing tuning parameter.

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