CN104567917B - Based on the variable step reentry vehicle position and speed Forecasting Methodology of dynamics - Google Patents

Based on the variable step reentry vehicle position and speed Forecasting Methodology of dynamics Download PDF

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CN104567917B
CN104567917B CN201410790941.XA CN201410790941A CN104567917B CN 104567917 B CN104567917 B CN 104567917B CN 201410790941 A CN201410790941 A CN 201410790941A CN 104567917 B CN104567917 B CN 104567917B
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reentry vehicle
speed
reentry
kinetics equation
vehicle
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CN104567917A (en
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胡军
杨鸣
张钊
董文强
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Beijing Institute of Control Engineering
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20Instruments for performing navigational calculations

Abstract

Based on the variable step reentry vehicle position and speed Forecasting Methodology of dynamics, step is: (1) utilizes navigational system, obtains the initial position speed of reentry vehicle; (2) the flying height H of current reentry vehicle is judged, if H & is gt; H th1, then go to step (3), if H th2aMP.AMp.Amp lt; H≤H th1, then go to step (4), if H≤H th2, then stop predicting and terminating; Wherein, H th1and H th2for height threshold; (3) with t bfor material calculation, utilize the first barycenter kinetics equation, a step reentry vehicle of extrapolating returns step (2) after the real time position and speed in space; (4) with t sfor material calculation, utilize the second barycenter kinetics equation, a step reentry vehicle of extrapolating returns step (2) after the real time position and speed in space.The inventive method overlaps different kinetics equations by two, carries out outside forecast respectively, and two cover kinetics equation step-lengths take different value, improve the speed of reentry vehicle position and speed prediction while ensureing precision.

Description

Based on the variable step reentry vehicle position and speed Forecasting Methodology of dynamics
Technical field
The invention belongs to reentry vehicle control field, relate to the Forecasting Methodology of a kind of reentry vehicle position and speed.
Background technology
Lunar exploration returns exerciser and adopts great-jump-forward reentry mode, and voyage demand span scope is within 4000-8000km scope, and trajectory often exists and significantly rises to process.Owing to reentering the difference of energy level, ballistic characteristics and the Perturbation Effect degree of first reentry stage and secondary reentry stage (or the descending flight stage after energy damping to the first cosmic velocity) have larger difference, therefore the method for guidance of usage forecastings-correction is needed in the high-energy ablated configuration stage, ensure to reenter by returner energy damping in suitable scope for the first time, provide good reenter original state for secondary reenters.
Because the computing power of device borne computer is more weak, and need to complete prediction as early as possible at reentry stage and resolve, thus ensure that within the shorter cycle, treat pursuit path upgrades, ensure guidance closed-loop characteristic.For realizing this target, the prediction and calculation time is subject to strict restriction.
In current reentry vehicle position in-orbit and speed predicting method, or adopt unified kinetics equation, or adopt single step-length to predict, in order to keep the precision predicted, calculated amount is larger.Because reentry vehicle computer computation ability is limited, this Forecasting Methodology is difficult to meet the requirement to predetermined speed.
Summary of the invention
The technical matters that the present invention solves is: overcome the deficiencies in the prior art, provide a kind of variable step reentry vehicle position and speed Forecasting Methodology based on dynamics, aerodynamic force suffered by the outer reentry vehicle of air is limited, ignoring affects limited characteristic afterwards on precision of prediction, after flying height is higher than certain threshold value, adopt first set kinetics equation, aerodynamic force is not calculated in kinetics equation, after flying height is lower than threshold value, adopt the second cover kinetics equation, calculate aerodynamic force, two cover kinetics equation step-lengths take different value, the speed of reentry vehicle position and speed prediction is improve while ensureing precision.
Technical solution of the present invention is: based on the variable step reentry vehicle position and speed Forecasting Methodology of dynamics, comprise the steps:
(1) utilize satellite navigation system, the position of acquisition reentry vehicle and speed, as initial position speed, are designated as X (0)=[x 0, y 0, z 0, v x0, v y0, v z0, γ v0] t, wherein (x 0, y 0, z 0) for reentry vehicle is at the initial position in space, (v x0, v y0, v z0) for reentry vehicle is at the initial velocity in space, γ v0for angle of heel;
(2) the flying height H of current reentry vehicle is judged, if H>H th1, then go to step (3), if H th2<H≤H th1, then go to step (4), if H≤H th2, then stop outside forecast and terminate; Wherein, H th1be the first height threshold, H th1span be 80 ~ 100Km, H th2be the second height threshold, H th2span be 10 ~ 20km;
(3) with t bfor material calculation, utilize the first barycenter kinetics equation, a step reentry vehicle of extrapolating returns step (2) after the real time position and speed in space; Described t bspan be 1s to 100s, the first described barycenter kinetics equation is:
G k=f(X k)
V k+1=V k+G kt B
X k+1=X k+V kt B
Wherein X={x, y, z} represent the predicted position of reentry vehicle, V={v x, v y, v zrepresent predetermined speed of reentry vehicle, G={g x, g y, g zrepresenting the acceleration of gravity of reentry vehicle present position, f (X) is reentry vehicle position and the funtcional relationship of acceleration of gravity, the value before footmark k and k+1 represents extrapolation one step respectively and after a step of extrapolating, and the initial value of k is 0;
(4) with t sfor material calculation, utilize the second barycenter kinetics equation, a step reentry vehicle of extrapolating returns step (2) after the real time position and speed in space; Described t sspan be 0.1s to 2s, the second described barycenter kinetics equation is:
γ k=Γ(t k)
G k=f(X k)
F k=l(X k,V kk)
V k+1=V k+G kt S+F kt S
X k+1=X k+V kt S
Wherein F represents the Pneumatic acceleration degree of reentry vehicle present position, Γ (t k) be reentry vehicle angle of heel and the funtcional relationship of time, l (X k, V k, γ k) funtcional relationship of Pneumatic acceleration degree suffered by reentry vehicle position, speed and angle of heel and reentry vehicle.
The first described height threshold H th1value is 90km.The second described height threshold H th2value is 10km.
The present invention's advantage is compared with prior art: the inventive method according to reentry vehicle after flying height is higher than certain threshold value, air is thin, the feature that density is less, height higher than during this threshold value to not calculating the position and speed change that aerodynamic force suffered by reentry vehicle causes when reentry vehicle position and prediction of speed, when height is lower than this threshold value, calculate the acceleration that aerodynamic force causes again, and according to height higher than threshold value with highly lower than the different relations of kinetics equation computational accuracy during threshold value from material calculation, higher than adopting large step-length during threshold value, height is lower than adopting little step-length during threshold value, make height simple higher than kinetics equation during threshold value, and adopt larger step-length still can ensure certain precision, and position and prediction of speed computing velocity are fast, are applicable to device borne computer and use, when identical computational accuracy, improve computing velocity.
Accompanying drawing explanation
Fig. 1 is the FB(flow block) of the inventive method.
Embodiment
In order to realize computing velocity faster, need to analyze the dynamic (dynamical) characteristic of prediction.In reentry vehicle flight course, barycenter dynamics mainly considers the impact of suffered external force, when flying height is lower, due to the impact of atmospheric density effect, makes Aerodynamic force action strongly, needs to consider especially; And when highly higher, along with the reduction of atmospheric density, the impact also index decreased of aerodynamic force, until can ignore compared with gravity.In fact, the interface of this conversion is a process gradually, and after not reaching a certain height, the effect of aerodynamic force just suddenly disappears.But consider from mathematical angle, the division at this interface adopts the means switched the most easily to realize.
For the prediction and calculation outside air, adopt large step-length can realize good precision, reason is, the change of gravity field along with the change of position relatively little, in the region that one, space is larger, gravity field is evenly constant substantially.Prediction in air is then different with it, the size of aerodynamic force and the speed of aircraft, highly all has strong correlativity, and change acutely, large step-length now just should not be adopted to resolve, and must reduce material calculation.
Below for the position of a class half trajectory great-jump-forward returner and prediction of speed, the step of the inventive method is described, as shown in Figure 1:
(1) utilize navigational system, the position of acquisition reentry vehicle and speed, as initial position speed, are designated as X (0)=[x 0, y 0, z 0, v x0, v y0, v z0, γ v0] t, wherein (x 0, y 0, z 0) for reentry vehicle is at the initial position in space, (v x0, v y0, v z0) for reentry vehicle is at the initial velocity in space, γ v0for angle of heel, due to H>H th1time, ignore atmospheric action, γ v0at H≤H th1in time, uses, at H>H th1time, γ v0reentry vehicle position and speed is not affected;
(2) the flying height H of current reentry vehicle is judged, if H>H th1, then go to step (3), if H th2<H≤H th1, then go to step (4), if H≤H th2, then stop outside forecast and terminate; Wherein H th1be the first height threshold, H th1span be 80 ~ 100Km, H th2be the second height threshold, H th2span be 10 ~ 20km;
H th1span and atmospheric density affect relevant by solar activity, geomagnetic activity etc., can H be selected when the atmospheric density of space environment forecast is lower th1near 80Km, when the atmospheric density of space environment forecast is higher, select H th1near 100Km, generally 90Km can be selected.H th2selection relevant with the target of forecast to the aerodynamic characteristic of reentry vehicle, select 10Km as the threshold value terminating prediction according to the requirement of parachute-opening here.
(3) with t bfor material calculation, utilize the first barycenter kinetics equation, a step reentry vehicle of extrapolating returns step (2) after the real time position and speed in space; Described t bspan 1s ~ 100s, concrete value is relevant to required precision of prediction, here because mission requirements precision of prediction is high, preferred 1s.The first described barycenter kinetics equation is:
g r = - GM r 2 - &mu; r 4 ( 1 - 5 y 2 r 2 )
g w = - 2 &mu;y r 5
g x = x r g r
g y = y r g r
g z = z r g r + g w
V k+1=V k+G kt B
X k+1=X k+V kt B
Wherein X={x, y, z} represent the predicted position of reentry vehicle, V={v x, v y, v zrepresent predetermined speed of reentry vehicle, G={g x, g y, g zrepresent the acceleration of gravity of reentry vehicle present position; GM=3.986005e14; μ=2.633280000000000e25, footmark k+1 and k is for distinguishing the response before and after prediction, and the initial value of k is 0, the initial position of the reentry vehicle also namely obtained by satellite navigation system and initial velocity value.
T bspan 1s ~ 100s, concrete numerical value is studied by numerical evaluation, selects different step size computation according to self mission requirements, therefrom chooses suitable step-length.
Be presented above a kind of G k=f (X k) embody form, certainly, also can adopt other forms, as Chen Kejun, Liu Luhua, Meng Yunhe write, long-range rocket flight dynamics and guidance, in National Defense Industry Press one book 2.2.2 joint described in form.
(4) with t sfor material calculation, utilize the second barycenter kinetics equation, a step reentry vehicle of extrapolating returns step (2) after the real time position and speed in space; Described t svalue 0.1 ~ 2s, be preferably 0.4s.The second described barycenter kinetics equation is:
γ k=Γ(t k)
G k=f(X k)
F k=l(X k,V kk)
V k+1=V k+G kt s+F kt s
X k+1=X k+V kt s
Wherein F={f x, f y, f zrepresent the Pneumatic acceleration degree of reentry vehicle present position; Γ (t k) be the time dependent function of angle of heel, this function is relevant to embody rule task, can be taken as constant function or piecewise constant function.L (X k, V k, γ k) be the method calculating suffered Pneumatic acceleration degree according to reentry vehicle position and speed.Here the method for computation of table lookup is adopted, calculated off-line goes out reentry vehicle at height h in advance, Pneumatic acceleration degree suffered under velocity magnitude V and angle of heel γ (specifically can be write with reference to Chen Kejun, Liu Luhua, Meng Yunhe, long-range rocket flight dynamics and guidance, 2.3 joints in National Defense Industry Press one book) and be loaded on reentry vehicle, first according to position X in forecasting process k, speed V kcalculate the height h of reentry vehicle kand velocity magnitude || V k||
h k = x k 2 + y k 2 + z k 2 - R e
| | V k | | = x x 2 + v y 2 + v z 2
Wherein R efor earth radius, according to h k, || V k|| and γ kcomputation of table lookup can go out { f x, f y, f z.
T svalue 0.1 ~ 2s, concrete numerical value is studied by numerical evaluation, selects different step size computation according to self mission requirements, therefrom chooses suitable step-length, here according to the requirement of certain aircraft computing power and impact accuracy, selects 0.4s as step-length.
The content be not described in detail in instructions of the present invention belongs to the known technology of those skilled in the art.

Claims (3)

1., based on the variable step reentry vehicle position and speed Forecasting Methodology of dynamics, it is characterized in that comprising the steps:
(1) utilize satellite navigation system, the position of acquisition reentry vehicle and speed, as initial position speed, are designated as X (0)=[x 0, y 0, z 0, v x0, v y0, v z0, γ v0] t, wherein (x 0, y 0, z 0) for reentry vehicle is at the initial position in space, (v x0, v y0, v z0) for reentry vehicle is at the initial velocity in space, γ v0for angle of heel;
(2) the flying height H of current reentry vehicle is judged, if H>H th1, then go to step (3), if H th2<H≤H th1, then go to step (4), if H≤H th2, then stop outside forecast and terminate; Wherein, H th1be the first height threshold, H th1span be 80 ~ 100Km, H th2be the second height threshold, H th2span be 10 ~ 20km;
(3) with t bfor material calculation, utilize the first barycenter kinetics equation, a step reentry vehicle of extrapolating returns step (2) after the real time position and speed in space; Described t bspan be 1s to 100s, the first described barycenter kinetics equation is:
G k=f(X k)
V k+1=V k+G kt B
X k+1=X k+V kt B
Wherein X={x, y, z} represent the predicted position of reentry vehicle, V={v x, v y, v zrepresent predetermined speed of reentry vehicle, G={g x, g y, g zrepresenting the acceleration of gravity of reentry vehicle present position, f (X) is reentry vehicle position and the funtcional relationship of acceleration of gravity, the value before footmark k and k+1 represents extrapolation one step respectively and after a step of extrapolating, and the initial value of k is 0;
(4) with t sfor material calculation, utilize the second barycenter kinetics equation, a step reentry vehicle of extrapolating returns step (2) after the real time position and speed in space; Described t sspan be 0.1s to 2s, the second described barycenter kinetics equation is:
γ k=Γ(t k)
G k=f(X k)
F k=l(X k,V kk)
V k+1=V k+G kt S+F kt S
X k+1=X k+V kt S
Wherein F represents the Pneumatic acceleration degree of reentry vehicle present position, Γ (t k) be reentry vehicle angle of heel and the funtcional relationship of time, l (X k, V k, γ k) funtcional relationship of Pneumatic acceleration degree suffered by reentry vehicle position, speed and angle of heel and reentry vehicle, adopt the method for computation of table lookup, calculated off-line goes out reentry vehicle at height h in advance, Pneumatic acceleration degree suffered under velocity magnitude V and angle of heel γ is also loaded on reentry vehicle, first according to position X in forecasting process k, speed V kcalculate the height h of reentry vehicle kand velocity magnitude || V k||
h k = x k 2 + y k 2 + z k 2 - R e
| | V k | | = v x 2 + v y 2 + v z 2
Wherein R efor earth radius, according to h k, || V k|| and γ kcomputation of table lookup can go out { f x, f y, f z.
2. the variable step reentry vehicle position and speed Forecasting Methodology based on dynamics according to claim 1, is characterized in that: the first described height threshold H th1value is 90km.
3. the variable step reentry vehicle position and speed Forecasting Methodology based on dynamics according to claim 1 and 2, is characterized in that: the second described height threshold H th2value is 10km.
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