CN104925271B - The defining method reentering standard trajectory instruction of lift formula aircraft - Google Patents

Abstract

The invention discloses the defining method reentering standard trajectory instruction of lift formula aircraft, comprising: reenter according to what determine the mapping relations that standard trajectory determines height-speed, drag acceleration-speed; Utilize Mathematical Fitting instrument, determine the mapping expression formula of the analytical form of height-speed, drag acceleration-speed, thus determine drag acceleration instruction and height instruction; Utilize Mathematical Fitting to determine the match value of the undetermined coefficient in described mapping expression formula, the drag acceleration instruction, the highly matching of instruction and speed that obtain determining map expression formula; Map expression formula according to the drag acceleration instruction determined, height instruction and the matching of speed, determine to reenter the drag acceleration derivative of standard trajectory, second derivative and local trajectory tilt angle instruction.The present invention can generate the path instructions needed for homing guidance in real time, reduces to generate complexity in line, reduces the susceptibility to tracing control rule parameter designing.

Description

The defining method reentering standard trajectory instruction of lift formula aircraft

Technical field

The present invention relates to lift formula vehicle technology, particularly refer to a kind of defining method reentering standard trajectory instruction of lift formula aircraft.

Background technology

For the lift formula glide vehicle with high lift-drag ratio characteristic, generally adopt based on standard trajectory homing guidance scheme in prior art, standard trajectory section can choose drag acceleration-velocity profi1e form, needs to calculate in real time drag acceleration instruction, drag acceleration instruction to the first derivative of time, drag acceleration instruction to parameters such as the second derivatives of time in tracing process.Calculate in real time drag acceleration instruction, drag acceleration instruction to the first derivative of time, the isoparametric process of the second derivative of drag acceleration instruction to the time in often adopt the mode of difference derivation.But, adopt and may there is instruction sudden change during difference derivation or the non-problem such as to lead occurs, parameter designing difficulty when causing homing guidance, and the problem of the angle of heel instruction shake produced.

Therefore, exist in prior art to based on the path instructions that can produce in the homing guidance scheme of canonical profile needed for tracking and path instructions derivative term thus avoid the needs of homing guidance parameter designing difficulty.

Summary of the invention

The present invention be a kind of be applicable to lift formula aircraft reenter standard trajectory command calculations method, be mainly used in canonical profile homing guidance scheme, for generation of the path instructions needed for following the tracks of and the derivative term of path instructions, by institute of the present invention extracting method, the path instructions needed for homing guidance can be generated in real time, reduce to generate complexity in line, reduce the susceptibility to tracing control rule parameter designing.

For solving the technical matters existed in prior art, embodiments of the invention provide a kind of defining method reentering standard trajectory instruction of lift formula aircraft, comprising: according to the mapping relations reentering standard trajectory to determine height-speed, drag acceleration-speed determined; Utilize Mathematical Fitting instrument, determined the mapping expression formula of the analytical form of height-speed, drag acceleration-speed by Mathematical Fitting, and determine drag acceleration instruction D according to determined mapping expression formula _cxwith height instruction H _cx,

D _cx=b ₁v _e+ b ₂v _e ²+ b ₃v _e ³+ b ₄v _e ⁴+ b ₅formula (1)

H _cx=c ₁v _e+ c ₂v _e ²+ c ₃v _e ³+ c ₄v _e ⁴+ c ₅formula (2)

Wherein, D _cxfor drag acceleration instruction, H _cxfor height instruction, V _e=V _d/ V _c, V _dfor aircraft ground speed, V _cfor normaliztion constant, its value is first cosmic velocity 7910m/s, b ₁, b ₂, b ₃, b ₄, b ₅, c ₁, c ₂, c ₃, c ₄, c ₅for undetermined coefficient;

Utilize Mathematical Fitting to determine the match value of the undetermined coefficient in the mapping expression formula of the analytical form of height-speed, drag acceleration-speed, obtain the drag acceleration instruction D determined _cx, height instruction H _cxexpression formula is mapped with the matching of speed;

According to the drag acceleration instruction D determined _cx, height instruction H _cxmap expression formula with the matching of speed, determine the drag acceleration derivative reentering standard trajectory second derivative with local trajectory tilt angle instruction Θ _cx.

Wherein, utilize Mathematical Fitting to determine the match value of the undetermined coefficient in the mapping expression formula of the analytical form of height-speed, drag acceleration-speed to comprise:

The one group of standard trajectory Parameter Mapping table obtained in advance is substituted into formula (1) and (2), and utilizes Mathematical Fitting instrument, under given accuracy, solve described undetermined coefficient b ₁, b ₂, b ₃, b ₄, b ₅, c ₁, c ₂, c ₃, c ₄, c ₅distinguish corresponding match value

The match value determined is substituted into respectively formula (1) and (2) replace undetermined coefficient b ₁, b ₂, b ₃, b ₄, b ₅, c ₁, c ₂, c ₃, c ₄, c ₅, obtain the drag acceleration instruction D determined _cx, height instruction H _cxexpression formula is mapped with the matching of speed.

Wherein, according to the drag acceleration instruction D determined _cx, height instruction H _cxmap expression formula with the matching of speed, determine the drag acceleration derivative reentering standard trajectory second derivative with local trajectory tilt angle instruction Θ _cxstep comprise:

Based on formula (1), determine drag acceleration derivative respectively and second derivative and local trajectory tilt angle instruction Θ _cx.

$\begin{array}{c}{\stackrel{\·}{D}}_{cx}=\frac{{\mathrm{dD}}_{cx}}{{\mathrm{dV}}_e}\frac{{\mathrm{dV}}_e}{dt}\left(\frac{{\stackrel{\‾}{b}}_1+2{\stackrel{\‾}{b}}_2\·V_e+3{\stackrel{\‾}{b}}_3\·V_e^2+4{\stackrel{\‾}{b}}_4\·V_e^3}{V_c}\right)\frac{{\mathrm{dV}}_d}{dt}\\ \≈\left(\frac{{\stackrel{\‾}{b}}_1+2{\stackrel{\‾}{b}}_2\·V_e+3{\stackrel{\‾}{b}}_3\·V_e^2+4{\stackrel{\‾}{b}}_4\·V_e^3}{V_c}\right)(-D_{cx})\end{array}$ Formula (3)

${\stackrel{\·\·}{D}}_{cx}=\frac{d{\stackrel{\·}{D}}_{cx}}{dt}\≈\left(2{\stackrel{\‾}{b}}_2+6{\stackrel{\‾}{b}}_3\·V_e+12{\stackrel{\‾}{b}}_4\·V_e^2\right){\left(\frac{-D_{cx}}{V_c}\right)}^2+\left({\stackrel{\‾}{b}}_1+2{\stackrel{\‾}{b}}_2\·V_e+3{\stackrel{\‾}{b}}_3\·V_e^2+4{\stackrel{\‾}{b}}_4\·V_e^3\right)\left(\frac{-{\stackrel{\·}{D}}_{cx}}{V_c}\right)$ Formula (4)

Based on formula (2) and following formula (5), determine local trajectory tilt angle instruction Θ _cx

$\begin{array}{c}{\mathrm{\Θ}}_{cx}\≈a\sin \left(\frac{{\mathrm{dH}}_{cx}}{dt}/V_d\right)\≈\frac{{\mathrm{dH}}_{cx}}{{\mathrm{dV}}_e}\frac{{\mathrm{dV}}_e}{dt}\frac{1}{V_d}\\ =\left({\stackrel{\‾}{c}}_1+2{\stackrel{\‾}{c}}_2\·V_e+3{\stackrel{\‾}{c}}_3\·V_e^2+4{\stackrel{\‾}{c}}_4\·V_e^3\right)\left(\frac{-D_{cx}}{V_c{V}_d}\right)\end{array}$ Formula (5)

Wherein, based on equilibrium glide principle, lift formula aircraft is dV when endoatmosphere gliding flight _d/ dt ≈-D _cx, ${\mathrm{\Θ}}_{cx}\≈asin\left({\stackrel{\·}{H}}_{cx}/V_d\right)\≈{\stackrel{\·}{H}}_{cx}/V_d.$

The beneficial effect of technique scheme of the present invention is as follows:

In such scheme, reenter for lift formula aircraft and reenter stereotyped command Generating Problems in glide process, first determine by Mathematical Fitting the drag acceleration-speed reentering standard trajectory, highly-speed mapping relations, and then based on equilibrium glide principle, by simplifying speed, the relation of inclination angle and drag acceleration, direct employing analytical form obtains drag acceleration derivative, the calculation expression of second derivative and local trajectory tilt angle instruction, avoid the repeatedly above-mentioned derivative term of segmentation high order fitting, effectively reduce computation complexity, improve the commonality of design, can be directly used in the Celestial Guidance Scheme design in gliding flight process.

Accompanying drawing explanation

Fig. 1 is the diagram of circuit reentering the defining method of standard trajectory instruction of the lift formula aircraft of the embodiment of the present invention.

Detailed description of the invention

For making the technical problem to be solved in the present invention, technical scheme and advantage clearly, be described in detail below in conjunction with the accompanying drawings and the specific embodiments.

For reentering stereotyped command Generating Problems in lift formula aircraft gliding flight process, the invention provides the defining method of the reentry trajectory instruction being applicable to lift formula aircraft, avoid repeatedly segmentation high order fitting path instructions derivative term, effective reduction computation complexity, improve design commonality, for the guidance system design in gliding flight process provides instruction.

As shown in Figure 1, the defining method reentering standard trajectory instruction according to lift formula aircraft of the present invention is shown.In step 100, that determines lift formula aircraft reenters standard trajectory, and determines the mapping relations of height-speed, drag acceleration-speed according to the standard trajectory determined.Particularly, according to the process reentered of lift formula aircraft and end conswtraint condition and air vehicle overall parameter, aerodynamic characteristic, calculate standard trajectory, and determine height-speed, drag acceleration-speed mapping relations according to the standard trajectory calculated.According to embodiments of the invention, in the glide section flight course of lift formula aircraft, the process constraints such as strict hot-fluid, overload, dynamic pressure need be met, and the restriction of the constraint condition such as terminal velocity, terminal height, voyage, and based on equilibrium glide principle, adopt various ways generate fast one meet process constraints and end conswtraint reenter standard trajectory, thus obtain height-velocity profi1e and drag acceleration-velocity profi1e standard trajectory.The method of designing reentering standard trajectory of lift formula aircraft belongs to prior art, does not describe in detail at this.

In step 102, utilize Mathematical Fitting instrument, determined the mapping expression formula of the analytical form of height-speed, drag acceleration-speed by Mathematical Fitting, and determine drag acceleration instruction D according to determined mapping expression formula _cxwith height instruction H _cx.In embodiments of the invention, utilize Mathematical Fitting instrument, height-speed, drag acceleration-speed mapping relations are analyzed, suitable mapping relations expression formula can be found out, as:

D _cx=b ₁v _e+ b ₂v _e ²+ b ₃v _e ³+ b ₄v _e ⁴+ b ₅formula (1)

H _cx=c ₁v _e+ c ₂v _e ²+ c ₃v _e ³+ c ₄v _e ⁴+ c ₅formula (2)

Wherein, D _cxfor drag acceleration instruction, H _cxfor height instruction, V _e=V _d/ V _c, V _dfor aircraft ground speed, V _cfor normaliztion constant, preferably can be taken as first cosmic velocity 7910m/s, b ₁, b ₂, b ₃, b ₄, b ₅, c ₁, c ₂, c ₃, c ₄, c ₅for undetermined coefficient.In the present invention, these undetermined coefficients are real number.

Step 104, utilizes Mathematical Fitting to determine the match value of the undetermined coefficient in the mapping expression formula of the analytical form of height-speed, drag acceleration-speed.According to embodiments of the invention, based on the standard trajectory Parameter Mapping table obtained in advance, one group of concrete trajectory parameters is substituted into above-mentioned formula (1) and (2), and utilizes Mathematical Fitting instrument, above-mentioned undetermined coefficient b can be solved under given precision ₁, b ₂, b ₃, b ₄, b ₅, c ₁, c ₂, c ₃, c ₄, c ₅distinguish corresponding match value the match value determined is substituted into respectively formula (1) and (2) replace undetermined coefficient b ₁, b ₂, b ₃, b ₄, b ₅, c ₁, c ₂, c ₃, c ₄, c ₅, obtain the drag acceleration instruction D determined _cx, height instruction H _cxexpression formula is mapped with the matching of speed.Wherein, given precision is that those skilled in the art are predetermined.To those skilled in the art, utilize Mathematical Fitting instrument to be known to solve the concrete numerical value of undetermined coefficient, do not repeat them here.Equally, the acquisition of standard trajectory Parameter Mapping table is as known in the art, omits detailed description at this.

In step 106, according to the drag acceleration instruction D determined _cx, height instruction H _cxmap expression formula with the matching of speed, determine the drag acceleration derivative reentering standard trajectory second derivative with local trajectory tilt angle instruction Θ _cx.

According to embodiments of the invention, in the Celestial Guidance Scheme in gliding flight process, what needs were used reenters standard trajectory instruction except drag acceleration instruction, height instruction, also needs to use drag acceleration derivative, second derivative and local trajectory tilt angle instruction.Drag acceleration-speed that above-mentioned order parameter all can obtain according to step 102 matching, highly-speed mapping relations are determined.Particularly, according to formula (3), (4) and (5), can determine drag acceleration derivative respectively second derivative and local trajectory tilt angle instruction Θ _cx.

$\begin{array}{c}{\stackrel{\·}{D}}_{cx}=\frac{{\mathrm{dD}}_{cx}}{{\mathrm{dV}}_e}\frac{{\mathrm{dV}}_e}{dt}\left(\frac{{\stackrel{\‾}{b}}_1+2{\stackrel{\‾}{b}}_2\·V_e+3{\stackrel{\‾}{b}}_3\·V_e^2+4{\stackrel{\‾}{b}}_4\·V_e^3}{V_c}\right)\frac{{\mathrm{dV}}_d}{dt}\\ \≈\left(\frac{{\stackrel{\‾}{b}}_1+2{\stackrel{\‾}{b}}_2\·V_e+3{\stackrel{\‾}{b}}_3\·V_e^2+4{\stackrel{\‾}{b}}_4\·V_e^3}{V_c}\right)(-D_{cx})\end{array}$ Formula (3)

${\stackrel{\·\·}{D}}_{cx}=\frac{d{\stackrel{\·}{D}}_{cx}}{dt}\≈\left(2{\stackrel{\‾}{b}}_2+6{\stackrel{\‾}{b}}_3\·V_e+12{\stackrel{\‾}{b}}_4\·V_e^2\right){\left(\frac{-D_{cx}}{V_c}\right)}^2+\left({\stackrel{\‾}{b}}_1+2{\stackrel{\‾}{b}}_2\·V_e+3{\stackrel{\‾}{b}}_3\·V_e^2+4{\stackrel{\‾}{b}}_4\·V_e^3\right)\left(\frac{-{\stackrel{\·}{D}}_{cx}}{V_c}\right)$ Formula (4)

$\begin{array}{c}{\mathrm{\Θ}}_{cx}\≈a\sin \left(\frac{{\mathrm{dH}}_{cx}}{dt}/V_d\right)\≈\frac{{\mathrm{dH}}_{cx}}{{\mathrm{dV}}_e}\frac{{\mathrm{dV}}_e}{dt}\frac{1}{V_d}\\ =\left({\stackrel{\‾}{c}}_1+2{\stackrel{\‾}{c}}_2\·V_e+3{\stackrel{\‾}{c}}_3\·V_e^2+4{\stackrel{\‾}{c}}_4\·V_e^3\right)\left(\frac{-D_{cx}}{V_c{V}_d}\right)\end{array}$ Formula (5)

Wherein, based on equilibrium glide principle, can be similar to and think that lift formula aircraft has when endoatmosphere gliding flight: dV _d/ dt ≈-D _cx, and then can derive and draw drag acceleration derivative in standard trajectory second derivative and local trajectory tilt angle instruction Θ _cxexpression formula.

In the present invention, reenter for lift formula aircraft and reenter stereotyped command Generating Problems in glide process, first determine by Mathematical Fitting the drag acceleration-speed reentering standard trajectory, highly-speed mapping relations, and then based on equilibrium glide principle, by simplifying speed, the relation of inclination angle and drag acceleration, direct employing analytical form obtains drag acceleration derivative, the calculation expression of second derivative and local trajectory tilt angle instruction, avoid the repeatedly above-mentioned derivative term of segmentation high order fitting, effectively reduce computation complexity, improve the commonality of design, can be directly used in the Celestial Guidance Scheme design in gliding flight process.

Method of the present invention can utilize computer technology to realize.Such as, each step of method of the present invention can be decomposed into different functional modules or subsystem and be realized by computer software technology.Certainly, each step of method of the present invention also can be realized by hardware such as firmware, dsp chip, IC chip etc.In the present invention, terms such as " modules ", " subsystem " of use is intended to comprise the entity relevant to computing machine, such as but not limited to hardware, firmware, combination thereof, software or executory software.Such as, module can be, but be not limited in: the thread of the process that treater runs, treater, object, executable program, execution, program and/or computing machine.For example, application program computing equipment run and this computing equipment can be modules.One or more module can be positioned at an executory process and/or thread.

The above is the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite not departing from principle of the present invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (2)

1. the defining method reentering standard trajectory instruction of lift formula aircraft, comprising:

According to the mapping relations reentering standard trajectory to determine height-speed, drag acceleration-speed determined;

Utilize Mathematical Fitting instrument, determined the mapping expression formula of the analytical form of height-speed, drag acceleration-speed by Mathematical Fitting, and determine drag acceleration instruction D according to determined mapping expression formula _cxwith height instruction H _cx,

D _cx=b ₁v _e+ b ₂v _e ²+ b ₃v _e ³+ b ₄v _e ⁴+ b ₅formula (1)

H _cx=c ₁v _e+ c ₂v _e ²+ c ₃v _e ³+ c ₄v _e ⁴+ c ₅formula (2)

Wherein, D _cxfor drag acceleration instruction, H _cxfor height instruction, V _e=V _d/ V _c, V _dfor aircraft ground speed speed, V _cfor normaliztion constant, its value is first cosmic velocity 7910m/s, b ₁, b ₂, b ₃, b ₄, b ₅, c ₁, c ₂, c ₃, c ₄, c ₅for undetermined coefficient;

Utilize Mathematical Fitting to determine the match value of the undetermined coefficient in the mapping expression formula of the analytical form of height-speed, drag acceleration-speed, obtain the drag acceleration instruction D determined _cx, height instruction H _cxmap expression formula with the matching of speed, comprising:

The one group of standard trajectory Parameter Mapping table obtained in advance is substituted into formula (1) and (2), and utilizes Mathematical Fitting instrument, under given accuracy, solve described undetermined coefficient b ₁, b ₂, b ₃, b ₄, b ₅, c ₁, c ₂, c ₃, c ₄, c ₅distinguish corresponding match value

The match value determined is substituted into respectively formula (1) and (2) replace undetermined coefficient b ₁, b ₂, b ₃, b ₄, b ₅, c ₁, c ₂, c ₃, c ₄, c ₅, obtain the drag acceleration instruction D determined _cx, height instruction H _cxexpression formula is mapped with the matching of speed;

According to the drag acceleration instruction D determined _cx, height instruction H _cxmap expression formula with the matching of speed, determine the drag acceleration derivative reentering standard trajectory second derivative with local trajectory tilt angle instruction Θ _cx.

2. the defining method reentering standard trajectory instruction of lift formula aircraft according to claim 1, wherein, according to the drag acceleration instruction D determined _cx, height instruction H _cxmap expression formula with the matching of speed, determine the drag acceleration derivative reentering standard trajectory second derivative with local trajectory tilt angle instruction Θ _cxstep comprise:

Based on formula (1), determine drag acceleration derivative respectively and second derivative and local trajectory tilt angle instruction Θ _cx;

$\begin{array}{c}{\stackrel{\·}{D}}_{cx}=\frac{{\mathrm{dD}}_{cx}}{{\mathrm{dV}}_e}\frac{{\mathrm{dV}}_e}{dt}=\left(\frac{{\stackrel{\‾}{b}}_1+2{\stackrel{\‾}{b}}_2\·V_e+3{\stackrel{\‾}{b}}_3\·V_e^2+4{\stackrel{\‾}{b}}_4\·V_e^3}{V_c}\right)\frac{{\mathrm{dV}}_d}{dt}\\ \≈\left(\frac{{\stackrel{\‾}{b}}_1+2{\stackrel{\‾}{b}}_2\·V_e+3{\stackrel{\‾}{b}}_3\·V_e^2+4{\stackrel{\‾}{b}}_4\·V_e^3}{V_c}\right)(-D_{cx})\end{array}$ Formula (3)

${\stackrel{\·\·}{D}}_{cx}=\frac{d{\stackrel{\·}{D}}_{cx}}{dt}\≈(2{\stackrel{\‾}{b}}_2+6{\stackrel{\‾}{b}}_3\·V_e+12{\stackrel{\‾}{b}}_4\·V_e^2){\left(\frac{-D_{cx}}{V_c}\right)}^2+({\stackrel{\‾}{b}}_1+2{\stackrel{\‾}{b}}_2\·V_e+3{\stackrel{\‾}{b}}_3\·V_e^2+4{\stackrel{\‾}{b}}_4\·V_e^3)\left(\frac{-{\stackrel{\·}{D}}_{cx}}{V_c}\right)$ Formula (4)

Based on formula (2) and following formula (5), determine local trajectory tilt angle instruction Θ _cx

$\begin{array}{c}{\mathrm{\Θ}}_{cx}\≈a\sin (\frac{{\mathrm{dH}}_{cx}}{dt}/V_d)\≈\frac{{\mathrm{dH}}_{cx}}{{\mathrm{dV}}_e}\frac{{\mathrm{dV}}_e}{dt}\frac{1}{V_d}\\ =({\stackrel{\‾}{c}}_1+2{\stackrel{\‾}{c}}_2\·V_e+3{\stackrel{\‾}{c}}_3\·V_e^2+4{\stackrel{\‾}{c}}_4\·V_e^3)\left(\frac{-D_{cx}}{V_c{V}_d}\right)\end{array}$ Formula (5)

Wherein, based on equilibrium glide principle, lift formula aircraft is dV when endoatmosphere gliding flight _d/ dt ≈-D _cx, ${\mathrm{\Θ}}_{cx}\≈asin({\stackrel{\·}{H}}_{cx}/V_d)\≈{\stackrel{\·}{H}}_{cx}/V_d.$