CN114740884A - A dual-pulse mid-range guidance method and device for short-range interception - Google Patents

Abstract

The invention provides a double-pulse guidance method and a double-pulse guidance device for short-range interception, wherein the method comprises the following steps: establishing a kinetic equation of the interception missile and the target missile in the gliding section, and constructing a differential equation of the relative movement speed of the missile and the target missile in a sight line coordinate system based on the kinetic equation and a coordinate transformation matrix; establishing a dynamic equation of a boosting section, and predicting a terminal position vector and a speed vector of the boosting section; according to the terminal position vector and the speed vector of the boosting section ending moment, based on the strategy of the zero control interception triangle, obtaining a shutdown point parameter meeting the requirement of the zero control interception triangle at the sliding section; deducing the optimal ignition time of the second pulse of the interception bomb based on the performance index function of the ignition time of the second pulse of the interception bomb according to the shutdown point parameter, the position vector analytic expression and the boundary condition; and acquiring a double-pulse optimal guidance instruction based on the predicted values and the expected values of the speed inclination angle and the speed deflection angle at the shutdown time of the interceptor projectile and the second-pulse optimal ignition time of the interceptor projectile. The interception performance can be improved.

Description

A dual-pulse mid-range guidance method and device for short-range interception

technical field

The present invention relates to the technical field of guidance control, in particular, to a dual-pulse mid-range guidance method and device for short-range interception.

Background technique

With the continuous development of missile technology, the range of missiles and the power of warheads are constantly increasing, and the threat is also increasing. In order to reduce the damage effect of enemy missiles, it is an effective method to use anti-missile interception technology to intercept enemy missiles. In the process of anti-missile interception, in order to completely destroy the target missile, it is necessary to achieve direct collision between the interceptor missile launched by oneself and the target missile, but due to the extremely high relative speed of the two sides, guidance control with high control accuracy is required. System and better performance interceptor guidance law.

In order to intercept enemy long-range or even intercontinental ballistic missiles in the mid-flight outside the atmosphere, the guidance and control system needs to precisely control the speed and direction of the interceptor. However, the current interceptor generally uses solid rocket motors, which cannot adjust the thrust and working time, which limits the interception ability of the interceptor. In order to improve the interception capability of the interceptor, the dual-pulse solid rocket motor has become the forefront of interceptor power research. Using the dual-pulse solid rocket motor, the interval between the two working pulses can be flexibly adjusted to meet the needs of more work scenarios. Therefore, It is necessary to design a new guidance law according to the characteristics of the dual-pulse solid rocket motor to improve and realize its interception capability.

SUMMARY OF THE INVENTION

In view of this, the purpose of the present invention is to provide a dual-pulse mid-range guidance method and device for short-range interception, so as to improve the interception performance of the interceptor.

In a first aspect, an embodiment of the present invention provides a dual-pulse mid-range guidance method for short-range interception, including:

Establish the dynamic equations of the interceptor and target missiles in the local ground coordinate system in the gliding section, and build the differential equation of the relative motion velocity of the missile in the line of sight coordinate system based on the dynamic equation and the coordinate transformation matrix between the line of sight coordinate system and the local ground coordinate system ;

Establish the dynamic equation of the booster segment, and predict the end position vector and velocity vector of the booster segment;

According to the terminal position vector and velocity vector at the end of the booster segment of the interceptor missile, and based on the strategy of the zero-control interception triangle, the shutdown point parameters that satisfy the zero-control interception triangle in the gliding segment are obtained, and the shutdown point parameters include the interceptor missile speed inclination angle and speed declination;

According to the parameters of the shutdown point, the analytical formula of the position vector and the boundary conditions, and based on the preset performance index function of the ignition time of the second pulse of the interceptor, the optimal ignition time of the second pulse of the interceptor is deduced;

Based on the predicted value and expected value of the velocity inclination angle and velocity declination angle at the time of shutdown of the interceptor missile and the optimal ignition time of the interceptor's second pulse, the optimal guidance command of the dual-pulse is obtained.

In conjunction with the first aspect, an embodiment of the present invention provides the first possible implementation of the first aspect, wherein the establishment of the dynamic equations of the interceptor missile and the target missile in the gliding segment under the local ground coordinate system includes:

According to the geocentric distance of the origin of the local ground coordinate system of the taxiing segment, and the position vector of the interceptor and the target missile under the local ground coordinate system, the geocentric distance vectors of the interceptor and the target missile are obtained respectively;

Determine the gravitational acceleration vector of the interceptor and target missile respectively in the local ground coordinate system based on the distance vector and the gravitational constant;

Based on the gravitational acceleration vector, the dynamic equations of the interceptor and the target missile in the local ground coordinate system are obtained.

With reference to the first possible implementation manner of the first aspect, the embodiment of the present invention provides the second possible implementation manner of the first aspect, wherein the coordinate based on the dynamic equation and the line-of-sight coordinate system and the local ground coordinate system The transformation matrix is used to construct the differential equation of the relative motion velocity of the projectile under the line of sight coordinate system, including:

Based on the component of the position vector in the dynamic equation and the relative position of the target missile between the interceptor and the target missile, obtain the expressions of the line-of-sight elevation angle and the line-of-sight declination angle of the line-of-sight coordinate system;

According to the expressions of the line of sight elevation angle and the line of sight declination angle, construct the coordinate transformation matrix of the line of sight coordinate system and the local ground coordinate system;

Based on the coordinate transformation matrix, the velocity vector of the interceptor in the dynamic equation and the velocity vector of the target missile in the dynamic equation, the velocity component equations of the interceptor and the target missile in the line-of-sight coordinate system are obtained respectively;

According to the expressions of line-of-sight elevation angle and line-of-sight declination angle, the relative position between interceptor and target missile, and their respective velocity component equations, construct the relative motion velocity equation of the missile and target in the line-of-sight coordinate system;

Differential operation is performed on the relative motion velocity equation of the projectile, and the differential equation of the relative movement speed of the projectile under the line of sight coordinate system is constructed.

In conjunction with the first aspect, the embodiment of the present invention provides a third possible implementation manner of the first aspect, wherein the establishing the dynamic equation of the booster segment and predicting the end position vector and velocity vector of the booster segment include:

Based on the angular momentum of the interceptor in the geocentric inertial coordinate system, the orbital inclination of the orbital plane and the right ascension of the ascending node are obtained;

In the orbital plane, based on the differential equation of the relative motion velocity of the projectile, the operating parameters of the interceptor and the speed of the interceptor, the dynamic model of the booster section is established;

Based on the dynamic model of the booster segment, the terminal position vector and velocity vector at the end of the booster segment of the interceptor are determined.

With reference to the third possible implementation manner of the first aspect, the embodiment of the present invention provides the fourth possible implementation manner of the first aspect, wherein the end of the booster segment of the interceptor is determined based on the dynamic model of the booster segment The end position vector and velocity vector of the moment, including:

Simplify the derivative of the speed of the interceptor in the booster segment in the booster segment dynamics model to obtain the simplified derivative of the speed;

Integrate the simplified derivative of the velocity to obtain the velocity at the end of the booster segment of the interceptor.

With reference to the fourth possible implementation manner of the first aspect, the embodiment of the present invention provides the fifth possible implementation manner of the first aspect, wherein the simplified derivative of the velocity vector is integrated to obtain the end of the booster segment of the interceptor missile Velocity vector at time, including:

Construct an intermediate variable representing the end time of the booster segment, and obtain the derivative of the intermediate variable according to the interceptor ballistic inclination equation in the booster segment dynamics model;

Integrate the derivative of the intermediate variable to obtain the integral term of the boost velocity and the ballistic inclination at the end of the boost segment;

Based on the obtained value of the integral term of boost speed and the ballistic inclination angle at the end of the boost segment, the velocity vector at the end of the boost segment of the interceptor is obtained.

In conjunction with the first aspect, the embodiment of the present invention provides a sixth possible implementation manner of the first aspect, wherein the establishing the dynamic equation of the booster segment and predicting the end position vector and velocity vector of the booster segment include:

Fitting the interceptor ballistic inclination based on the derivative equation of the interceptor ballistic inclination in the dynamic model of the booster segment;

Based on the fitted interceptor ballistic inclination, obtain the end position equation of the interceptor's booster segment and the included angle equation between the end position vector and the line connecting the center of the earth to the ascending node;

Determine the booster segment of the interceptor missile based on the orbit inclination, the right ascension of the ascending node, the end speed of the booster segment of the interceptor, the ballistic inclination at the end of the booster segment, the end position equation, and the included angle equation between the end position vector and the line connecting the center of the earth to the ascending node. End point position vector and velocity vector at the end time.

In a second aspect, an embodiment of the present invention also provides a dual-pulse mid-range guidance law device for short-range interception, including:

The differential equation building module is used to establish the dynamic equation of the interceptor missile and the target missile in the taxiing section in the local ground coordinate system. Based on the dynamic equation and the coordinate transformation matrix between the line of sight coordinate system and the local ground coordinate system, construct the line of sight coordinate system. Differential equation of relative velocity of projectile;

The prediction module is used to establish the dynamic equation of the booster segment and predict the end position vector and velocity vector of the booster segment;

The shutdown point parameter acquisition module is used to obtain shutdown point parameters that satisfy the zero-control interception triangle in the taxi segment according to the terminal position vector and velocity vector at the end of the booster segment of the interceptor, and based on the strategy of the zero-control interception triangle, the shutdown Point parameters include interceptor velocity inclination and velocity declination;

The derivation module is used for deriving the optimal ignition time of the second pulse of the interceptor missile based on the preset performance index function of the ignition time of the second pulse of the interceptor missile according to the shutdown point parameters, the analytical expression of the position vector and the boundary conditions;

The optimal command acquisition module is used to obtain the dual-pulse optimal guidance command based on the predicted value and expected value of the velocity inclination angle and the velocity declination angle at the time of shutdown of the interceptor missile and the optimal ignition time of the interceptor's second pulse.

In a third aspect, an embodiment of the present application provides a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, when the processor executes the computer program Implement the steps of the above method.

In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the foregoing method when the computer program is run by a processor.

The dual-pulse mid-range guidance method and device for short-range interception provided by the embodiments of the present invention, by establishing the dynamic equations of the interceptor missile and the target missile in the sliding section in the local ground coordinate system, based on the dynamic equation and the line-of-sight coordinate system and the The coordinate transformation matrix of the local ground coordinate system is used to construct the differential equation of the relative motion velocity of the missile under the line-of-sight coordinate system; the dynamic equation of the booster segment is established to predict the end position vector and velocity vector of the booster segment; according to the end time of the booster segment of the interceptor Based on the zero-control interception triangle strategy, the shutdown point parameters that satisfy the zero-control interception triangle in the taxiing segment are obtained, and the shutdown point parameters include the interceptor’s velocity inclination and velocity declination; according to the shutdown point parameters , position vector analytical formula and boundary conditions, based on the preset performance index function of the ignition time of the interceptor's second pulse, the optimal ignition time of the interceptor's second pulse is derived; based on the prediction of the velocity inclination and velocity declination at the time of the interceptor's shutdown value and expected value and the optimal ignition time of the second pulse of the interceptor, and obtain the optimal guidance command of the dual pulse. In this way, by analyzing the position and speed of the end point of the booster stage, the position and speed of the engine shutdown time of the booster stage can be obtained, and the optimal dual-pulse guidance command can be deduced according to the optimal control theory, which can satisfy the optimality of the guidance command. Improve the interception capability and reliability of interceptors.

In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below, and are described in detail as follows in conjunction with the accompanying drawings.

Description of drawings

In order to illustrate the technical solutions of the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings used in the embodiments. It should be understood that the following drawings only show some embodiments of the present invention, and therefore do not It should be regarded as a limitation of the scope, and for those of ordinary skill in the art, other related drawings can also be obtained according to these drawings without any creative effort.

1 shows a schematic flowchart of a dual-pulse mid-range guidance method for short-range interception provided by an embodiment of the present invention;

2 is a schematic diagram of the relationship between the line-of-sight coordinate system and the local ground coordinate system according to an embodiment of the present invention;

FIG. 3 shows a schematic diagram of the operation parameters of the interceptor provided by an embodiment of the present invention;

4 shows a schematic diagram of a three-dimensional interception in a local ground coordinate system provided by an embodiment of the present invention;

FIG. 5 shows a schematic structural diagram of a dual-pulse mid-range guidance law device for short-range interception provided by an embodiment of the present invention;

FIG. 6 is a schematic structural diagram of a computer device 600 according to an embodiment of the present application.

Detailed ways

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only These are some embodiments of the present invention, but not all embodiments. The components of the embodiments of the invention generally described and illustrated in the drawings herein may be arranged and designed in a variety of different configurations. Thus, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present invention.

Embodiments of the present invention provide a dual-pulse mid-range guidance method and device for short-range interception, which will be described below through embodiments.

FIG. 1 shows a schematic flowchart of a dual-pulse mid-range guidance method for short-range interception provided by an embodiment of the present invention. As shown in Figure 1, the method is a short-range interception dual-pulse mid-range guidance method based on gravity difference fitting, including:

Step 101, establish the dynamic equation of the interceptor and target missile in the taxiing section in the local ground coordinate system, and construct the relative motion of the missile in the line of sight coordinate system based on the dynamic equation and the coordinate transformation matrix between the line of sight coordinate system and the local ground coordinate system Velocity differential equation;

In the embodiment of the present invention, as an optional embodiment, the dynamic equations of the interceptor missile and the target missile in the sliding section under the local ground coordinate system are established, including:

A11, according to the geocentric distance of the origin of the local ground coordinate system of the taxiing segment, and the position vector of the interceptor and the target missile under the local ground coordinate system, respectively obtain the geocentric distance vector of the interceptor and the target missile;

A12, determine the gravitational acceleration vector of the interceptor and the target missile in the local ground coordinate system based on the ground-to-center distance vector and the gravitational constant;

A13, based on the gravitational acceleration vector, obtain the dynamic equations of the interceptor and the target missile respectively in the local ground coordinate system.

In the embodiment of the present invention, in the sliding section, it is only necessary to consider the influence of gravitational acceleration. In this way, the dynamic equation of the interceptor-target missile in the local ground coordinate system can be described as:

In the formula,

r _Md and r _Td are the position vectors of the interceptor and target missile in the local ground coordinate system, respectively;

和

分别为拦截弹和目标导弹的位置矢量的导数(微分)；

and

are the derivative (differential) of the position vector of the interceptor and the target missile, respectively;

V _Md and V _Td are the velocity vectors of the interceptor and target missile in the local ground coordinate system, respectively;

和

分别为拦截弹和目标导弹的速度矢量的导数；

and

are the derivatives of the velocity vectors of the interceptor and target missiles, respectively;

g _Md and g _Td are the gravitational acceleration vectors of the interceptor and target missile in the local ground coordinate system, respectively. Its expression is:

In the formula,

μ is the gravitational constant;

和

分别为拦截弹和目标导弹的地心距矢量。其表达式为：

and

are the geocentric distance vectors of the interceptor and target missiles, respectively. Its expression is:

where:

r _M0 is the geocentric distance of the origin O _d of the local ground coordinate system.

In the embodiment of the present invention, as an optional embodiment, based on the dynamic equation and the coordinate transformation matrix between the line of sight coordinate system and the local ground coordinate system, a differential equation of the relative motion velocity of the projectile under the line of sight coordinate system is constructed, including:

A21, based on the component of the position vector in the dynamic equation and the relative position of the target missile between the interceptor and the target missile, obtain the expression of the line of sight elevation angle and the line of sight declination angle of the line of sight coordinate system;

A22, construct the coordinate transformation matrix of the line of sight coordinate system and the local ground coordinate system according to the expressions of the line of sight elevation angle and the line of sight declination angle;

A23, based on the coordinate transformation matrix, the velocity vector of the interceptor in the dynamic equation and the velocity vector of the target missile in the dynamic equation, obtain the velocity component equations of the interceptor and the target missile in the line-of-sight coordinate system respectively;

A24, according to the expressions of the line of sight elevation angle and the line of sight declination angle, the relative position between the interceptor and the target missile, and the respective velocity component equations, construct the relative motion velocity equation of the projectile under the line of sight coordinate system;

A25, carry out differential operation on the relative motion velocity equation of the projectile, and construct the differential equation of the relative movement speed of the projectile under the line of sight coordinate system.

FIG. 2 is a schematic diagram of the relationship between the line-of-sight coordinate system and the local ground coordinate system according to an embodiment of the present invention. As shown in FIG. 2, in the embodiment of the present invention, the line of sight coordinate system _OL - _xLyLzL is defined, the coordinate origin _OL is set to coincide with the current position of the _interceptor , the _xL axis points to the line of sight direction, and the _{yL axis} is vertical In the plane perpendicular to the x _L axis, the z _L axis, the x _L axis and the y _L axis constitute a right-handed coordinate system. Among them, q and λ are the line-of-sight elevation angle and line-of-sight declination angle, respectively, and the expression for the relative position of the projectile and the target is:

λ=sin ^-1 [(r _Tyd -r _Myd )/r]

q=tan ^-1 [(r _Tzd -r _Mzd )/(r _Txd -r _Mxd )] (4)

where:

r _Mxd , r Myd and r _Mzd are the _components of the interceptor's position vector in the local ground coordinate system, respectively;

r _Txd , r _Tyd and r _Tzd are the components of the position vector of the target missile in the local ground coordinate system, respectively;

r is the relative distance between the interceptor and the target missile.

In the embodiment of the present invention, according to the relative positional relationship between the two coordinate systems, the coordinate transformation matrix L _Ld from the local ground coordinate system to the line-of-sight coordinate system is:

Using the coordinate transformation matrix, the velocity component equations of the interceptor and the target missile under the line-of-sight coordinate system can be obtained, namely, the components of the interceptor's velocity vector V _MxL , V _MyL , V _MzL and the target missile's velocity vector in the line-of-sight coordinate system. The components V _TxL , V _TyL , and V _TzL are respectively:

In the embodiment of the present invention, in the line-of-sight coordinate system, the relative motion equation of the projectile can be expressed as:

In the formula, V _r , V _λ , and V _q are the components of the relative velocity vector of the projectile under the line-of-sight coordinate system, respectively.

Then the relative motion velocity equation of the projectile under the line of sight coordinate system can be expressed as:

Taking the time derivative of the above formula, we can get:

Substitute equations (8) and (1) into equations (10)-(12), and through a series of algebraic operations, the differential equation of the relative motion velocity of the projectile in the gliding phase can be obtained, that is, the differential of V _r , V _λ and V _q The equations are:

where:

In the formula,

Δg _r , Δg _λ , Δg _q are the three projection components of the projectile gravitational acceleration vector difference in the line-of-sight coordinate system;

g _Mx , g _My and g _Mz are the projection components of the gravitational acceleration vector g _Md of the interceptor under the local ground coordinate system, respectively;

g _Tx , g _Ty and g _Tz are the projected components of the gravitational acceleration vector g _Td on the local ground coordinate system, respectively, which the target missile is subjected to.

Step 102, establishing the dynamic equation of the booster segment, and predicting the end position vector and velocity vector of the booster segment;

In the embodiment of the present invention, as an optional embodiment, the dynamic equation of the booster segment is established, and the end position vector and velocity vector of the booster segment are predicted, including:

B11, based on the angular momentum of the interceptor in the geocentric inertial coordinate system, obtain the orbital inclination of the orbital plane and the right ascension of the ascending node;

B12, in the orbital plane, based on the interceptor thrust, initial mass, mass flow and operating parameters, establish a dynamic model of the booster segment;

B13, based on the dynamic model of the booster segment, determine the end position vector and velocity vector at the end of the booster segment of the interceptor.

In the embodiment of the present invention, since the double-pulse engine of the interceptor is generally used in the third or second stage, at this time, the interceptor is located at a high altitude and has a low air density, so the influence of aerodynamic force can be ignored.

In the embodiment of the present invention, it is assumed that the interceptor is in a standard control state, that is, the thrust direction is the same as the current velocity vector direction. At this time, the orbital plane of the interceptor will not change. The orbital plane can be defined using the orbital inclination and the ascending node right ascension:

i _M = cos ^-1 (H _Mz0 /H _M0 ) (15)

Ω _M = tan ^-1 (-H _Mx0 /H _My0 ) (16)

In the formula,

i _M is the orbital inclination, Ω _M is the right ascension of the ascending node, H _Mx0 , H _My0 and H _Mz0 are the projected components of the angular momentum vector of the interceptor in the geocentric inertial coordinate system, and H _M0 is the intercepted missile in the geocentric inertial coordinate The magnitude of the angular momentum under the tie.

FIG. 3 shows a schematic diagram of the operation parameters of the interceptor provided by the embodiment of the present invention. As shown in FIG. 3 , in the embodiment of the present invention, in the orbital plane, the operational parameters of the interceptor projectile include: interceptor projectile thrust, interceptor projectile initial mass, interceptor projectile mass flow, interceptor projectile engine working time, interceptor projectile ballistic inclination, interceptor projectile Based on the position vector in the orbital plane and the angle between the interceptor's position vector and the line connecting the center of the earth to the ascending node, the dynamic model of the booster segment is established as follows:

In the formula,

V _M is the speed of the interceptor in the boost stage;

P is the thrust of the interceptor;

m ₀ is the initial mass of the interceptor;

q _m is the mass flow rate of the interceptor;

t is the working time of the interceptor engine;

g _M is the gravitational acceleration of the interceptor;

γ _M is the interceptor ballistic inclination;

r _M is the geocentric distance of the interceptor;

θ _M is the angle between the interceptor's position vector and the line connecting the center of the earth to the ascending node.

In the embodiment of the present invention, as an optional embodiment, based on the dynamic model of the booster segment, determining the end position vector and the velocity vector at the end of the booster segment of the interceptor missile, including:

Simplify the derivative of the speed of the interceptor in the booster segment in the booster segment dynamics model to obtain the simplified derivative of the speed;

Integrate the simplified derivative of the velocity to obtain the velocity at the end of the booster segment of the interceptor.

In the embodiment of the present invention, the time of the boosting section is generally short, and therefore, the change of the axial component of gravity is small and can be ignored. In this way, the derivative of the interceptor's velocity in the boost segment can be simplified to the simplified derivative of the velocity:

In the formula,

g _M0 and γ _M0 are the gravitational acceleration and the ballistic inclination at the current moment, respectively.

By integrating the above formula, the velocity expression at the end of the booster segment of the interceptor can be obtained:

V _Mbo =V _M0 -V _e [ln(1-t _bo /T)+K ₁ t _bo /T] (22)

In the formula,

V _Mbo is the speed at the end of the booster segment of the interceptor;

V _M0 is the speed of the interceptor at the current moment;

t _bo is the remaining working time of the main engine of the interceptor;

V _e , T and K ₁ are all constants, and their expressions are:

V _e =P/q _m

In the embodiment of the present invention, it is required to obtain the ballistic inclination of the interceptor at the current moment. Therefore, as an optional embodiment, the simplified derivative of the speed is integrated to obtain the speed at the end of the booster segment of the interceptor, including:

Construct an intermediate variable representing the ballistic inclination of the booster section, and obtain the derivative of the intermediate variable according to the interceptor ballistic inclination equation in the dynamic model of the booster section;

Integrate the derivative of the intermediate variable to obtain the integral term of the boost velocity and the ballistic inclination at the end of the boost segment;

Based on the obtained value of the integral term of boost speed and the ballistic inclination angle at the end of the boost segment, the velocity vector at the end of the boost segment of the interceptor is obtained.

In the embodiment of the present invention, the intermediate variable χ _M is defined as:

χ _M =ln{(1+sinγ _M )/(1-sinγ _M )} (24)

Substituting Equation (24) into Equation (18), and ignoring the influence of the change in the geocentric distance of the booster segment, the derivative of the intermediate variable can be obtained:

Integrating the above formula, the value of χ _M at the end of the booster segment can be obtained as:

In the formula,

χ _M0 is the initial value of χ _M ;

f _χ1 (t _bo ), f _χ2 (t _bo ) are the boost velocity integral terms related to the interceptor boost velocity _VM , respectively:

χ _M0 =ln{(1+sinγ _M0 )/(1-sinγ _M0 )}

By formula (24), the ballistic inclination angle at the end of the booster segment can be expressed as:

γ _Mbo = sin ^-1 [(e ^χMbo -1)/(e ^χMbo +1)] (28)

In the embodiment of the present invention, as an optional embodiment, acquiring the value of the boost speed integral term includes:

According to the velocity equation at the end of the booster segment of the interceptor, the integral term of boost velocity is calculated to obtain the boost velocity expression;

Using the Gauss-Legendre integral formula with N nodes, the boost velocity expression is solved to obtain the boost velocity integral term value.

In the embodiment of the present invention, the formula (22) is substituted into the formula (27), and the boost speed expression can be obtained:

In the formula,

为无量纲化的发动机剩余工作时间；

is the remaining working time of the non-dimensionalized engine;

为无量纲化的导弹当前速度。

is the current velocity of the dimensionless missile.

In the embodiment of the present invention, using the Gauss-Legendre integral formula of N nodes to solve the formula (30), it can be obtained:

In the formula,

ω _i is the ith integral weight;

是第i个高斯节点处的无量纲化时间。作为一可选实施例，取N＝9。

is the dimensionless time at the ith Gaussian node. As an optional embodiment, N=9 is taken.

In the embodiment of the present invention, by intercepting the angular momentum of the missile, calculating the orbital inclination and the right ascension of the ascending node, and then through algebraic derivation and Gauss-Legendre integration, the magnitude of the missile position vector at the end point of the missile booster segment is obtained, and the missile position vector Analytical formula for the angle between the center of the earth and the ascending node.

In the embodiment of the present invention, as another optional embodiment, a dynamic equation of the booster segment is established, and the end position vector and velocity vector of the booster segment are predicted, including:

B21, fit the interceptor ballistic inclination based on the derivative equation of the interceptor ballistic inclination in the dynamic model of the booster segment;

B22, based on the fitted interceptor ballistic inclination, obtain the end position equation of the interceptor booster segment and the included angle equation between the end position vector and the line connecting the center of the earth to the ascending node;

B23, based on the orbit inclination, the right ascension of the ascending node, the terminal velocity of the booster section of the interceptor, the ballistic inclination of the end point of the booster section, the end position equation and the angle equation between the end position vector and the line connecting the center of the earth to the ascending node, determine the interceptor assist The end position vector and velocity vector at the end of the push segment.

In the embodiment of the present invention, for equations (19) and (20), it is difficult to directly obtain the analytical solutions of r _M and θ _M because the trigonometric functions of the ballistic inclination are included. In the embodiment of the present invention, considering that the time of the booster segment is short, the change of the ballistic inclination angle is also small in the booster segment. The sine and cosine functions of the inclination angle are fitted to obtain the fitted interceptor ballistic inclination angle. The fitting formula is as follows:

The endpoint conditions can be solved for:

b ₁ =T(V _M0 /r _M0 -g _M0 /V _M0 )cos ² γ _M0

c ₁ = _sinγM0

c ₂ =cosγ _M0

Substitute Equation (33) into Equation (19) and Equation (20), and integrate them to obtain the end position r _Mbo of the booster segment of the interceptor and the angle θ between the end position vector of the interceptor and the line connecting the center of the earth to the ascending node _Mbo are:

In the formula, r _M0 is the center-to-center distance of the interceptor at the initial moment, and r _M,ave is the average center-to-center distance of the booster segment.

According to Equation (15), Equation (16), Equation (22), Equation (28), Equation (34) and Equation (35), the terminal position vector and velocity vector at the end of the booster segment of the interceptor can be determined.

Step 103, according to the terminal position vector and velocity vector at the end of the booster segment of the interceptor missile, and based on the strategy of the zero-control interception triangle, obtain the shutdown point parameters that satisfy the zero-control interception triangle in the taxiing segment, and the shutdown point parameters include the interceptor missile. Velocity inclination and velocity declination;

In the embodiment of the present invention, as an optional embodiment, according to the terminal position vector and velocity vector at the end of the booster segment of the interceptor, and based on the strategy of the zero-control interception triangle, the shutdown point that satisfies the zero-control interception triangle in the taxiing segment is obtained. parameters, including:

C11, applying the condition that the relative velocity of the projectile in the vertical line-of-sight direction at the time of interception is zero, and applying it to the differential equation of the relative motion velocity of the projectile in the gliding phase to obtain the interceptor's velocity inclination and velocity declination when the interceptor is turned off;

In the embodiment of the present invention, the shutdown point parameters include: the expected shutdown speed inclination angle and the speed declination angle of the interceptor missile. In order to increase the probability of the interceptor hitting the target missile and form a "zero-control interception triangle", it is necessary to make the relative velocity of the projectile in the vertical line of sight zero at the moment of interception, namely:

V _λ (t _f )=0 and V _q (t _f )=0

Among them, t _f is the interception moment.

In the embodiment of the present invention, Equation (13) is the dynamic equation of V _r , V _λ and V _q , and the boundary conditions of V _λ (t _f )=0 and V _q (t _f )=0 are applied to Equation (13 ) to solve the dynamic equation, the expressions of V _λ and V _q can be obtained. According to the expressions, the values of V _λ and V _q at the shutdown time of the interceptor can be calculated, that is, the shutdown point condition of forming a "zero-controlled interception triangle" is obtained. .

In the embodiment of the present invention, as an optional embodiment, the condition that the relative velocity of the projectile in the direction of the vertical line of sight at the interception time is zero is applied to the differential equation of the relative motion velocity of the projectile in the gliding phase to obtain the projectile at the moment when the interceptor is turned off. Relative velocity value; includes:

C111, fitting the difference in the gravitational acceleration of the projectile in the differential equation of the relative velocity of the projectile as a function of the remaining flight time;

In the embodiment of the present invention, it can be known from equation (14) that Δg _r , Δg _λ and Δg _q are coupled with other variables, which makes equation (13) difficult to solve analytically. Therefore, in the embodiment of the present invention, the gravitational acceleration differences Δg _r , Δg _λ and Δg _q are fitted as functions related to the remaining flight time t _go . In order to ensure the fitting accuracy, as an optional embodiment, a second-order polynomial is used for fitting. Since the interceptor and the target missile have equal gravitational accelerations at the moment of interception, that is, when the remaining flight time t _go = 0, Δg _r , Δg _λ and Δg _q can be respectively approximated as the following quadratic polynomials (functions) about t _go :

In the formula,

k _r1 , k _r2 , k _λ1 , k _λ2 , k _q1 and k _q2 are fitting coefficients.

In the embodiment of the present invention, using the gravity difference of the bullet and its derivative value when the interceptor is turned off, the fitting coefficient can be obtained, and the specific expression is:

In the formula,

t _gobo is the remaining flight time when the interceptor is powered off, and the other variables with subscript "bo" represent the value of the variable at the time when the interceptor is powered off.

C112, based on the relative motion equation of the projectile and the gravitational acceleration difference of the projectile, derive the function of the remaining flight time to obtain the differential equation of the gravitational acceleration difference of the projectile;

和

的表达式为：In the embodiment of the present invention, for Δg _r , Δg _λ and Δg _q in formula (14), the flight time is derived respectively, and formula (8) and formula (14) are substituted into the formula for the derivation, and the bullet can be obtained The differential equation for the difference in gravitational acceleration, namely

and

The expression is:

C113: Simplify the differential equation of the relative movement speed of the projectile to obtain the differential approximation equation of the relative movement speed of the projectile;

对式(13)所示的V_r的微分方程进行近似，得到的弹目相对运动速度微分近似方程为：In the embodiment of the present invention, for formula (13),

By approximating the differential equation of V _r shown in formula (13), the differential approximation equation of the relative velocity of the projectile obtained is:

C114, perform analytical integration on the differential approximation equation of the relative movement speed of the projectile, and obtain the analytical equation of the relative movement of the projectile about the remaining flight time;

进行解析积分，并考虑边界条件V_r(t_gobo)＝V_r,bo及r(t_gobo)＝r_bo，可得V_r及r关于t_go的弹目相对运动解析方程为：In the embodiment of the present invention, V _r,bo and r _bo are the relative velocity V _r and the relative distance r of the bullet in the line of sight direction at the shutdown point, respectively.

Carrying out analytical integration and considering the boundary conditions V _r (t _gobo )=V _r,bo and r(t _gobo )=r _bo , the analytical equations of relative motion of V _r and r about t _go can be obtained as:

In the formula,

c _r0 and c _r1 are constant coefficients whose expressions are

C115, based on the boundary condition that the angular velocity of the projectile's line of sight is zero when the remaining flight time is zero and the analytical equation of the relative motion of the projectile with respect to the remaining flight time, the analytical expression of the angular velocity of the projectile's line of sight of the zero-control interception triangle is obtained;

及

的表达式中的第二项相对于另外两项而言很小，可以忽略不计，

及

可近似为：In the embodiment of the present invention, during the interception process outside the atmosphere, the relative velocity of the projectile along the line of sight has a larger component, generally several kilometers per second, while the two components perpendicular to the line of sight are generally only one or two hundred or even Several tens of meters per second, thus, V _r >>V _λ and V _r >>V _q . In this way, the formula (13) shows

and

The second term in the expression of , is negligibly small relative to the other two terms,

and

can be approximated as:

After algebraic sorting, we can get:

In the formula,

Integrating Equation (43), the analytical equations of relative velocity of projectiles of V _λ and V _q with respect to the remaining flight time t _go can be obtained as:

In the formula,

c _λ and c _q are integral constants.

At the moment of interception, the relative distance of the projectile is 0, that is, r(0)=0. Substituting into the expression for the relative distance r of the projectile in Equation (40) can be obtained:

Considering the boundary conditions, in order to achieve the interception of the target, when t _go = 0, V _λ = 0 and V _q = 0, the analytical expressions of V _λ and V _q that satisfy the "zero-controlled interception triangle" can be obtained, that is, the expected missile The analytical expression for the relative velocity of the mesh is:

In the formula, the upper right subscript des represents the expected value of the corresponding variable.

So far, the conditions for the formation of the "zero-control interception triangle" have been obtained.

C116, obtain the value of the remaining flight time based on the fitting coefficient of the function fitted to the remaining flight time and the shutdown time;

In the embodiment of the present invention, in the process of solving Equation (48), the value of the remaining flight time t _gobo at the time of shutdown is required. Therefore, substituting Equation (37) into Equation (47) can be obtained:

In formula (50), except t _gobo , other variables can be calculated according to the predicted value of the bullet state quantity at the shutdown point. Therefore, formula (50) can be used to estimate t _gobo .

Equation (50) is a one-dimensional cubic equation about t _gobo , so it can be solved by using the root-finding formula of the one-dimensional cubic equation or the fixed-point iteration method.

C117, based on the analytical expression of the relative velocity of the projectile and the expected relative velocity of the zero-control interception triangle, obtain the expected value of the relative velocity of the projectile in the vertical line of sight at the time of shutdown.

In the embodiment of the present invention, in order to enable the interceptor to glide uncontrollably after shutdown to intercept the target missile, it is necessary to ensure that the relative velocity of the projectile at the shutdown moment can satisfy the "zero-controlled interception triangle" in the gliding segment. According to the conditions for forming a "zero-control interception triangle" shown in equations (48) and (49), the expected values of the relative velocity components of the vertical line of sight at the time of shutdown are:

C12, adjust the speed direction of the interceptor so that the shutdown speed meets the expected value of the relative speed of the projectile.

In the embodiment of the present invention, the interceptor is not provided with a thrust termination device, and its shutdown speed is difficult to adjust. Therefore, the shutdown speed can meet the expected value of the relative speed of the projectile by adjusting its speed direction.

In the embodiment of the present invention, the interceptor speed direction includes: the interceptor expected shutdown speed inclination angle and the speed declination angle, and the interceptor speed direction is obtained, including:

Obtain the declination angle expressions of the velocity component, velocity inclination and velocity declination of the interceptor's velocity vector in the local ground coordinate system;

Apply the declination angle expression to the relative motion velocity equation of the projectile to obtain the expressions of the interceptor expected shutdown speed inclination angle and velocity declination angle, and obtain the interceptor expected shutdown speed based on the expressions of the interceptor expected shutdown speed inclination angle and velocity declination angle Inclination and velocity declination.

FIG. 4 shows a schematic diagram of a three-dimensional interception in a local ground coordinate system provided by an embodiment of the present invention. The component of the interceptor's velocity vector in the local ground coordinate system can be expressed as the following expressions related to the velocity inclination and velocity declination:

为速度倾角，

为速度偏角，V_M为拦截弹的速度。In the formula,

is the velocity inclination,

is the velocity declination angle, and V _M is the velocity of the interceptor.

和速度偏角

满足拦截弹期望关机速度倾角和速度偏角的表达式：Substituting Equation (52) into Equation (9), the interceptor expected shutdown speed inclination angle

and velocity declination

The expressions that satisfy the interceptor's expected shutdown velocity inclination angle and velocity declination angle:

where V _λT,bo and V _qT,bo are the components of the target's velocity vector in the vertical line of sight at the power-off point, respectively, and _λbo and _qbo are the line-of-sight elevation angle and line-of-sight declination angle at the power-off point, respectively.

较小，可近似认为

由式(53)，可解得拦截弹期望关机速度倾角

和速度偏角

的值为：In the initial guidance stage, the interceptor will aim the launch surface at the predicted hit point. Therefore, in the middle guidance stage,

small, can be approximated as

By formula (53), the inclination angle of the expected shutdown speed of the interceptor can be obtained

and velocity declination

The value is:

In the formula: V _Mbo is the speed of the missile at the shutdown point.

Step 104, according to the shutdown point parameter, the analytical formula of the position vector and the boundary condition, and based on the preset performance index function of the ignition time of the second pulse of the interceptor, deduce the optimal ignition time of the second pulse of the interceptor;

In the embodiment of the present invention, as an optional embodiment, according to the shutdown point parameters, the position vector analytical formula and the boundary conditions, the optimal ignition timing of the second pulse of the interceptor missile is deduced, including:

D41, based on the analytical formula of the position vector and the preset boundary conditions, obtain the differential equations of the relative distance and relative velocity of the projectile at the moment of ignition of the second pulse of the interceptor;

In the embodiment of the present invention, assuming that the second pulse of the interceptor does not work, the remaining flight time at the end of the first pulse is obtained, and on the premise of the known pulse interval time, the relative distance between the projectile and the target at the ignition time of the second pulse of the interceptor is derived. Distance, relative velocity and their time derivatives to the pulse interval, so as to obtain the relative distance and relative velocity of the projectile at the moment of ignition of the second pulse of the interceptor. As an optional embodiment, based on the analytical formula of the position vector and the preset boundary conditions, the differential equations of the relative distance and relative velocity of the projectile at the time of the second pulse ignition of the interceptor projectile are obtained, including:

D411, based on the size of the position vector at the end of the first pulse of the interceptor, the projected size of the relative velocity of the projectile along the line of sight, and the projected size of the difference in the gravitational acceleration of the projectile along the line of sight, obtain when the second pulse of the interceptor does not work, the first the remaining flight time at the end of the pulse;

In the embodiment of the present invention, similar to formula (50), it is assumed that when the second pulse of the interceptor does not work, the remaining flight time at the end of the first pulse is:

In the formula, t _go0 is the remaining flight time at the end of the first pulse, r _bo1 , V _rbo1 , and Δg _rbo1 are the size of the position vector of the interceptor at the end of the first pulse, the projection of the relative velocity of the projectile along the line of sight, and the size of the projectile. The magnitude of the projection of the eye gravitational acceleration difference along the line of sight can be calculated according to the predicted value of the projectile state quantity at the moment when the first pulse is turned off. Solve the above formula according to the root-finding formula of the cubic equation in one variable or the fixed-point iteration method, and t _go0 can be obtained.

D412, based on the analytical expression of the position vector and the preset boundary conditions, obtain the analytical expressions of the relative velocity of the projectile and the relative distance of the projectile in the pulse interval section with time;

In the embodiment of the present invention, according to formula (40) and in combination with the boundary conditions V _r (t _go0 )=V _rbo1 and r(t _go0 )=r _bo1 , the relative velocity V _r,inter and the missile in the pulse interval can be obtained. The analytical expression for the time-varying relative distance r _inter is:

c _r0,inter and c _r1,inter are integral coefficients, and their specific expressions are:

D413, based on the analytical expressions of the relative velocity of the projectile and the relative distance of the projectile in the pulse interval segment changing with time, obtain the position vector and the relative velocity vector of the second pulse ignition time;

In the embodiment of the present invention, the values of V _r and r during the ignition of the second pulse can be obtained, which are respectively expressed as V _rig2 and _rig2 as:

Among them, the relationship between the remaining flight time of the second pulse ignition time of t _goig2 and the pulse interval time t _inter is:

t _goig2 = t _go0 -t _inter (59)

D414, according to the analytical equation of the relative motion of the projectile, obtain the analytical expression of the relative velocity of the projectile in the direction of the vertical line of sight in the pulse interval;

In the embodiment of the present invention, from the formula (45), the analytical expression of the relative velocity V _{λ of the bullet in the vertical line of sight direction in the pulse interval section, inter} can be obtained as:

Among them, the constant value coefficient c _λ,inter is calculated from the state quantity at the time of the first pulse shutdown, and the specific expression is:

D415, based on the analytical expression of the relative velocity of the projectile in the vertical line of sight in the pulse interval, obtain the differential equation of the relative velocity of the projectile when the second pulse is fired.

In the embodiment of the present invention, the value V _λig2 of V _λ at the time of the second pulse ignition can be obtained from the formula (60) as:

Similarly, the value V _qig2 of the second pulse ignition time V _q can be obtained as:

Taking the derivation of the relative distance and relative velocity equations of the projectile at the ignition time of the second pulse, we can get:

In the formula,

Δg _rig2 , Δg _λig2 , Δg _qig2 are the projectile gravity difference components at the second pulse ignition time, which can be obtained from equation (36):

D42, according to the differential equation of the relative velocity of the projectile and the boundary condition of the ignition time, obtain the analytical expression of the relative velocity of the projectile and the time derivative of the pulse interval in the second pulse working stage;

In the embodiment of the present invention, by establishing a differential equation of the relative velocity of the projectile including thrust, and fitting the intercepted axial acceleration and the relative term of the projectile gravity difference as a function related to the flight time, the relative distance of the projectile and the line of sight can be obtained. The analytical formula of the inclination angle and the declination angle of the line of sight can be used to derive the relative velocity of the projectile in the vertical line of sight when the second pulse is turned off and its derivative equation to the pulse interval time.

In the embodiment of the present invention, when the angle of attack is zero and the angle of sideslip is zero, the components a _MxL , a _MyL , and a _MzL of the interceptor's axial acceleration in the line of sight are respectively:

where a _M is the axial acceleration of the interceptor.

In the embodiment of the present invention, as an optional embodiment, according to the differential equation of the relative velocity of the projectile and the boundary condition of the ignition time, the analytical expression of the relative velocity of the projectile and the time derivative to the pulse interval in the second pulse working stage is obtained, including:

D421, according to the differential equation of the relative velocity of the projectile and the component of the interceptor's axial acceleration in the line-of-sight system, obtain the differential equation of the relative velocity of the projectile in the vertical line-of-sight direction of the booster section of the interceptor;

In the embodiment of the present invention, combined with formula (13), the differential equation of the relative velocity of the projectile in the vertical line of sight direction of the booster section of the interceptor projectile can be obtained as:

D422, fitting the intercepting axial acceleration and the projectile gravity difference as a function related to the flight time, and simplifying the differential equation of the relative velocity of the projectile in the vertical line of sight of the interceptor's booster segment based on the fitted function, and obtaining the interception Simplified differential equation of the relative velocity of the projectile in the direction of the vertical line of sight of the projectile booster segment;

及V_λV_qtanλ/r，并将拦截轴向加速度及弹目重力差相关项拟合为与飞行时间相关的函数，式(67)可近似为：In the embodiment of the present invention, similar to formula (42), V _r >>V _λ and V _r >>V _q , ignoring a small amount

and V _λ V _q tanλ/r, and fitting the interception axial acceleration and projectile gravity difference correlation terms as a function related to flight time, Equation (67) can be approximated as:

Among them, Q _λ (t) and Q _q (t) are the fitting coefficients of the relevant terms of the projectile gravity difference, respectively, and their expressions are:

D423, combined with the boundary conditions at the ignition time, analyze and integrate the simplified differential equation of the relative velocity of the projectile in the direction of the vertical line of sight in the booster section of the interceptor, and obtain the relative velocity equation of the projectile in the direction of the vertical line of sight when the second pulse is turned off;

In the embodiment of the present invention, formula (68) is analytically integrated and combined with the boundary conditions of the ignition timing, it can be obtained:

In the formula, V _λbo2 and V _qbo2 are the relative velocities of the projectiles in the vertical line of sight when the second pulse is turned off, and Δt _burn2 is the working time of the second pulse;

The expressions of r _ig2 , V _λig2 and V _qig2 are shown in equations (58), (62) and (63);

r _bo2 is the relative position of the projectile at the end of the second pulse of the interceptor;

t _ig2 is the ignition time of the second pulse.

In the embodiment of the present invention, in order to obtain the specific expression of the integral term in the formula (70), it is necessary to derive the fitting formula of r, Q _λ and Q _q with respect to the flight time t.

Since the interceptor has a long uncontrolled gliding segment after the second pulse is turned off, it can intercept the target missile. Therefore, for the second pulse working segment, the relative distance of the projectile is relatively large and the working time of the booster segment is shorter. , the relative distance of the projectile does not change much, and the relative distance of the projectile can be fitted as a linear function about t to ensure sufficient fitting accuracy. The specific expression is:

是助推段沿视线方向的平均弹目相对速度。In the formula, Δt=tt _ig is the working time of the booster segment; ΔV _r,burn2 is the change in the relative velocity of the projectile caused by the acceleration of the interceptor during the second pulse operation; V _rig2 is the projectile along the line of sight at the ignition time of the second pulse. The relative velocity of the mesh can be calculated by formula (58);

is the average relative velocity of the projectile along the line of sight of the boost segment.

Among them, ΔV _r,burn2 can be approximated by the following formula:

In the formula,

λ_ig2、q_ig2分别为拦截弹第二脉冲点火时刻的弹道倾角、视线仰角、视线偏角；

λ _ig2 , q _ig2 are the ballistic inclination angle, the line of sight elevation angle, and the line of sight declination angle of the interceptor’s second pulse ignition time, respectively;

ΔV _M is the velocity increment of the second pulse segment of the interceptor, and its expression is specifically:

where m ₂₀ is the initial mass of the interceptor in the second pulse segment;

P ₂ and q _m2 are the thrust and mass flow of the interceptor's second pulse, respectively.

Rewriting equation (71), we can get:

r=a _r1 (1-Δt/T ₂ )+a _r0 (74)

In the formula, T ₂ is the dimensionless factor of the working time of the second pulse of the interceptor, a _r1 and a _r0 are the proportional coefficients respectively. The specific expression is:

T ₂ =m ₂₀ /q _m2

In the second pulse working section, the relative distance of the projectiles is relatively large, so the change of the line of sight angle caused by the relative velocity of the projectiles in the vertical line of sight direction is very small, and the change of the gravity difference of the projectiles is also small, and λ, q and Δg can be ignored. Changes in _λ and Δg _q affect Q _λ and Q _q . Then λ, q and Δg _λ , Δg _q can be approximately expressed as:

In the formula, the subscript "bo1" indicates the corresponding state at the end of the first pulse of the interceptor, and the subscript "ig2" indicates the corresponding state at the ignition time of the second pulse of the interceptor.

Since the working time of the booster section is short, and the interceptor only turns under the action of gravity at zero angle of attack and zero sideslip angle, the velocity inclination angle and time interval can be approximated as a linear function as follows:

为第二脉冲工作阶段速度倾角的平均变化率，Δt为时间间隔；In the formula,

is the average rate of change of the velocity inclination in the second pulse working stage, and Δt is the time interval;

为第二脉冲点火时刻拦截弹的速度倾角，其与第一脉冲关机时速度倾角

及脉冲间隔时间t_inter有关。

is the velocity inclination of the interceptor at the second pulse ignition time, which is the same as the velocity inclination when the first pulse is turned off

It is related to the pulse interval time t _inter .

In the embodiment of the present invention, the pulse interval time is generally not long, therefore, the change of gravitational acceleration and velocity can be ignored. According to equations (24) to (28), the differential equation of the ballistic inclination angle at the ignition moment of the second pulse of the interceptor can be obtained and their analytic expressions are:

In the formula, V _Mbo1 is the speed at the end of the first pulse of the interceptor;

χ _Mbo1 and χ _Mig2 are the intermediate variables related to the ballistic inclination at the end of the first pulse and the ignition time of the second pulse of the interceptor, respectively.

始终为0。因此，Q_λ和Q_q可近似为：When flying due to zero angle of attack and zero sideslip angle

Always 0. Therefore, Q _λ and Q _q can be approximated as:

Combined with the expression of the interceptor's axial acceleration a _M =P ₂ /(m ₂₀ -q _m2 Δt), Q _λ and Q _q can be expressed as the following fitting formulas:

Among them, a _λ1 , a _λ0 , a _q1 , and a _q0 are proportional coefficients, and their expressions are:

In the formula, V _e2 is the dimensionless factor of the second pulse velocity of the interceptor.

Combining equations (74) and (82), the approximate value of the integral term in equation (70) can be obtained as

Substituting the above formula into formula (70), it can be obtained that the relative velocity equation of the projectile in the vertical line of sight at the moment when the second pulse is turned off is:

From formula (71), we can get:

D424, based on the relative velocity equation of the projectile in the vertical line-of-sight direction when the second pulse is turned off, obtain its time derivative equation with respect to the pulse interval.

In the embodiment of the present invention, through the above derivation, the relative velocities V _λbo2 and V _qbo2 of the projectile in the vertical line-of-sight direction at the moment when the second pulse is turned _off are obtained. Since the change of the sight angle of the projectile and the gravity difference of the projectile with the ignition time at the ignition time of the second pulse is very small, in order to simplify the calculation, the t _inter pair of sight angles λ _ig2 and q _ig2 and the projectile gravity difference Δg are ignored in the solution process. Effects of _λig2 and Δg _qig2 . Taking the derivation of equations (75) and (83), we can get:

The expressions of _drig2 /dt _inter and dV _rig2 /dt _inter are shown in equation (64).

Taking the derivation of equations (72) and (79), we can get:

In the formula, g _Mig2 is the gravitational acceleration at the moment of ignition of the second pulse of the interceptor.

To sum up, the derivatives of V _λbo2 and V _qbo2 to t _inter can be obtained, that is, the optimal pulse interval time derivative equation:

In the formula, χ _λ1 to χ _λ3 and χ _q1 to χ _q3 are proportional coefficients, and their expressions are:

D43, solve the relationship between the expected relative velocity of the projectile when the interceptor's second pulse is turned off and the pulse interval time, and obtain the expected relative velocity equation of the projectile in the vertical line of sight;

In the embodiment of the present invention, the remaining flight time when the second pulse is turned off is corrected, and then through step 101, the relative velocity of the interceptor in the direction of the vertical line of sight that is expected to be achieved when the second pulse is turned off and the interval between the pulses can be obtained. Derivative of time. As an optional embodiment, the relationship between the expected relative velocity of the projectile and the pulse interval time at the moment when the second pulse of the interceptor is turned off is solved, and the expected relative velocity equation of the projectile in the vertical line of sight direction is obtained, including:

D431, according to the state equation satisfied by the remaining flight time when the first pulse is turned off when the second pulse is not working, obtain the relationship equation between the remaining flight time and the pulse interval time when the second pulse is turned off;

In the embodiment of the present invention, by formula (47), when the second pulse is not working, the remaining flight time t _go0 when the first pulse is turned off satisfies:

In practical applications, since the velocity of the interceptor projectile increases after the ignition of the second pulse, the relative velocity V _r of the projectile target changes greatly. Then, the real remaining flight time when the first pulse is turned off is less than t _go0 . Neglecting the effect of gravity difference on the relative velocity V _r of the projectile in the pulse interval section and the second pulse working section, it can be obtained:

From equations (91) and (92), the relationship between the remaining flight time t _gobo2 and the pulse interval time t _inter when the second pulse is turned off can be obtained as:

为速度比，上式对t_inter求导可得：In the formula,

is the speed ratio, the above formula can be obtained by derivation of t _inter :

D432, according to the expected value equation of the relative velocity component of the projectile in the vertical line of sight at the time of shutdown, obtain the relative velocity equation of the projectile in the direction of the vertical line of sight that is expected to be achieved when the second pulse is turned off.

的方程为：In the embodiment of the present invention, it can be obtained from the formula (51), the relative velocity of the projectile in the vertical line of sight direction expected to be achieved when the second pulse is turned off

The equation is:

Taking the derivative of the above formula with respect to t _inter , we can get:

D44, based on the relative velocity equation of the projectile at the ignition time of the second pulse of the interceptor, the relative velocity of the projectile in the second pulse working stage and the equation of the time derivative of the pulse interval, and the expected relative velocity equation of the projectile in the vertical line of sight, using the variational method Find the optimal ignition timing of the interceptor's second pulse.

In the embodiment of the present invention, according to the performance index function of the ignition time of the second pulse of the interceptor, according to the property of the maximum value of the performance index function, the pulse interval time is derived, and by solving the equation with the derivative of 0, it can be solved that The optimal pulse interval time is obtained, and then the optimal ignition time of the second pulse of the interceptor is obtained.

In the embodiment of the present invention, the purpose of optimizing the ignition timing is to minimize the performance functional of the booster segment, that is, the sum of the square of the angle of attack and the sideslip angle, and the optimal ignition timing is that the booster segment can be fired at zero angle of attack after ignition. Flying can meet the ignition timing of the "zero-control interception triangle" in the taxiing segment.

In the embodiment of the present invention, the ignition timing of the second pulse of the interceptor has a great influence on the "zero-control interception triangle" of the longitudinal plane sliding section, that is, with the change of the ignition timing of the second pulse of the interceptor, the second pulse of the interceptor is turned off. When the time is perpendicular to the line of sight, the expected value and actual value of the bullet velocity component also change greatly, and the ignition time of the second pulse that makes the expected value and the actual value equal is the optimal ignition time.

In the embodiment of the present invention, the optimal ignition timing of the second pulse of the interceptor missile is the pulse interval time that minimizes the performance index function.

In the embodiment of the present invention, the performance index function J of the ignition time of the second pulse of the interceptor is:

The second pulse ignition time t _ig2 of the interceptor is in one-to-one correspondence with the pulse interval time t _inter . Therefore, solving the optimal second pulse ignition time of the interceptor can be equivalent to solving the optimal pulse interval time of the interceptor. According to the properties of the maximum value of the function, the minimum pulse interval time t _inter of the objective function, that is, the optimal pulse interval time, should satisfy:

需要同时满足以下方程：Substitute and arrange equations (95), (96), (85), and (89) to obtain the optimal pulse interval time

The following equations need to be satisfied at the same time:

Equation (100) is the constraint equation of the pulse interval segment and the time length of the gliding segment after shutdown. in,

和

分别为脉冲间隔时间的最小值和最大值；

and

are the minimum and maximum pulse interval time, respectively;

和

分别为拦截弹关机后滑行段时间的最小值和最大值。

and

They are the minimum and maximum values of the gliding period after the interceptor is turned off.

虽然与t_inter有关但其远小于1，因此，t_gobo2会随着t_inter的增大而减小。可由式(93)解出

和

对应的脉冲间隔时间

和

综合考虑式(100)中的约束，可得t_inter应满足：Equation (93) gives the functional relationship between the remaining flight time t _gobo2 and the pulse interval t _inter after the second pulse of the interceptor is turned off, where V _r,bo1 , t _go0 and Δt _burn2 are variables independent of t _inter ,

Although related to t _inter , it is much less than 1, so t _gobo2 decreases as t _inter increases. It can be solved by formula (93)

and

Corresponding pulse interval time

and

Considering the constraints in equation (100) comprehensively, it can be obtained that t _inter should satisfy:

和

分别为脉冲间隔时间的最小值和最大值。In the formula,

and

are the minimum and maximum pulse interval time, respectively.

的计算方法：The objective function J shown in Equation (97) is an approximate quadratic function form, which first decreases and then increases with the increase of t _inter , so there is only one extreme point, that is, there is only one real root in Equation (99), then The design is as follows

Calculation method:

说明

的根位于

之间，则选择

利用如下割线法计算

的值：(1) If

illustrate

The root is located at

between, choose

Use the following secant method to calculate

The value of:

说明

的根位于

之外，则选择

为

和

中使目标函数J较小的值。(2) If

illustrate

The root is located at

, select

for

and

in the value that makes the objective function J smaller.

Step 105 , based on the predicted value and expected value of the velocity inclination angle and the velocity declination angle at the time of shutdown of the interceptor missile and the optimal ignition time of the second pulse of the interceptor missile, obtain a dual-pulse optimal guidance command.

In the embodiment of the present invention, as an optional embodiment, based on the predicted value and expected value of the velocity inclination angle and the velocity declination angle at the time of shutdown of the interceptor missile and the optimal ignition time of the second pulse of the interceptor missile, the dual-pulse optimal guidance command is obtained, including:

E51, solve the first pulse optimal guidance command, where the first pulse optimal guidance command includes the optimal values of the angle of attack and the sideslip angle;

In the embodiment of the present invention, when the first pulse of the interceptor is working, the booster segment is divided into the first pulse working segment, the pulse interval segment and the second pulse working segment, and the perturbation equations of the ballistic velocity inclination and the ballistic velocity declination are established. , select the performance functional, according to the first-order necessary conditions, the functions of co-state variables and control variables can be solved, and then the approximate solution of the guidance coefficient can be obtained by the Gauss-Legendre integral formula, so as to obtain the maximum angle of attack and sideslip angle. figure of merit.

In the embodiment of the present invention, solving the first pulse optimal guidance command includes:

E511, obtain the perturbation equations of the velocity inclination angle and velocity declination angle of the interceptor in the first pulse working section, the pulse interval section, and the second pulse working section respectively;

In the embodiment of the present invention, when solving the optimal guidance command of the first pulse, due to the change of thrust, the optimal control problem to be solved is divided into three sections, namely the first pulse working section, the pulse interval section, and the second pulse working section. , the kinetic equations of each segment are different. Among them, the perturbation equations of the velocity inclination angle and velocity declination angle of each segment are:

和

分别为速度倾角及速度偏角的摄动量；In the formula,

and

are the perturbations of the velocity inclination and velocity declination, respectively;

α and β are the interceptor attack angle and sideslip angle, respectively;

P ₁ and P ₂ are the first pulse thrust and the second pulse thrust of the interceptor, respectively;

和

分别为拦截弹升力系数对攻角的导数和侧向力系数对侧滑角的导数；

and

are the derivative of the interceptor lift coefficient to the angle of attack and the derivative of the lateral force coefficient to the sideslip angle, respectively;

q is dynamic pressure;

S _ref is the pneumatic reference area;

t ₀ =0, t ₁ =t _bo1 , t ₂ =t _bo1 +t _inter and t ₃ =t _bo1 +t _inter +t _bo2 are the start and end times of each segment.

At the segmentation points t ₁ and t ₂ , the following boundary conditions must be satisfied:

In order to make the speed direction reach the desired value when the second pulse is turned off, the following endpoint constraints need to be satisfied:

和

分别为拦截弹关机时刻速度倾角和速度偏角的预测值。In the formula,

and

are the predicted values of the velocity inclination angle and velocity declination angle when the interceptor is shut down, respectively.

E512, select performance functional for perturbation equations of velocity dip and velocity declination;

In the embodiment of the present invention, in order to provide a stable control input, the weighted sum of squares of the angle of attack and the sideslip angle is selected as the performance functional, and the expression is as follows:

Among them, the weight terms (t ₁ -t) ⁿ and (t ₃ -t) ⁿ of the remaining burning time are used to shape the attack angle and sideslip angle curves. In the embodiment of the present invention, if n>0 is selected, the end values of the angle of attack and the angle of sideslip will converge to zero.

E513, based on the perturbation equations and performance functionals of the velocity inclination and velocity declination, obtain the Hamiltonian function of the optimal control problem;

From equations (103) and (106), the Hamiltonian function H of the optimal control problem can be obtained as:

和

为协态变量。根据一阶必要条件，可得协态变量的微分方程为：in,

and

is a covariate variable. According to the first-order necessary condition, the differential equation of the covariate variable can be obtained as:

It can be seen from the above formula that the covariate variables in each segment are invariant with time. At the same time, due to the need to satisfy the continuity condition at the segment point shown in Eq. (104), the covariate variable needs to satisfy the following boundary conditions at the segment point:

E514, obtain the optimal attack angle and sideslip angle equations according to the Hamiltonian function of the optimal control problem;

和

在三段内均相等。根据一阶必要条件，可得最优攻角及侧滑角方程为：In the embodiment of the present invention, the covariate variable

and

equal in all three segments. According to the first-order necessary conditions, the optimal attack angle and sideslip angle equations can be obtained as:

E515, based on the optimal attack angle and sideslip angle equations and the perturbation equations of the speed inclination angle and the speed declination angle, obtain the expressions of the speed inclination angle deviation value and the speed declination angle deviation value at the time of the second pulse shutdown;

In the embodiment of the present invention, by substituting the above formula (110) into formula (103) and integrating, the expressions of the speed inclination angle deviation value and the speed declination angle deviation value at the time of the second pulse shutdown can be obtained as follows:

E516, based on the expressions of the speed inclination deviation value and the speed declination deviation value at the time of the second pulse shutdown, and the preset end point constraint equation, obtain a covariate equation;

In the embodiment of the present invention, combined with the end point constraint equation shown in formula (105), the covariate equation can be obtained as:

和

为中间变量，表达式为：In the formula,

and

is an intermediate variable, and the expression is:

分别为拦截弹当前时刻质量、速度大小及速度倾角。In the formula, m ₀ , V _M0 and

are the mass, velocity and velocity inclination of the interceptor at the current moment, respectively.

E517, based on the co-state equation and the optimal attack angle and sideslip angle equations, obtain the optimal values of the attack angle and sideslip angle.

In the embodiment of the present invention, by substituting Equation (112) into Equation (110), the optimal values of the angle of attack and sideslip angle can be obtained:

In the formula, N _p1 and N _p2 are the guidance coefficients, and their specific expressions are:

It can be seen from the above formula that the guidance coefficient is not constant and changes with the flight time. Because the expression of the optimal guidance coefficient is too complicated, it is difficult to obtain an analytical solution. remember:

The value of each variable in the above formula can be predicted by the end position and velocity vector of the booster section in step 102, so the approximate solution of the guidance coefficients N _p1 and N _p2 can be obtained by the Gauss-Legendre integral formula:

及

分别为第i个高斯积分节点x_i对应的第一和第二脉冲工作时间；in,

and

are the working times of the first and second pulses corresponding to the ith Gaussian integration node x _i , respectively;

ω _i is the ith Gaussian integral weight coefficient;

n ₁ and n ₂ are constant coefficients, and their specific expressions are:

E52, solve the second pulse optimal guidance command, where the second pulse optimal guidance command includes the optimal values of the angle of attack and the angle of sideslip.

In the embodiment of the present invention, the process of solving the optimal guidance command of the interceptor's second pulse is similar to the process of solving the optimal guidance command of the interceptor's first pulse. The perturbation equations for angles do not need to be segmented.

In the embodiment of the present invention, as an optional embodiment, the second pulse optimal guidance command is solved, and the second pulse optimal guidance command includes the optimal values of the angle of attack and the sideslip angle, including:

E521, obtain the perturbation equations of the interceptor's ballistic inclination and ballistic declination in the second pulse stage;

E522, according to the preset performance functional and the perturbation equation of the ballistic inclination angle and the ballistic declination angle of the interceptor in the second pulse stage, obtain the Hamiltonian function of the optimal control problem;

E523, based on the Hamiltonian function and the perturbation equation of the ballistic inclination angle and the ballistic declination angle of the interceptor in the second pulse stage, obtain the expressions of the velocity inclination angle deviation value and the velocity declination angle deviation value at the time of shutdown;

E524, according to the expressions of the speed inclination angle deviation value and the speed declination angle deviation value at the time of shutdown and the preset constraint conditions, obtain the optimal values of the angle of attack and the sideslip angle.

In the embodiment of the present invention, the perturbation equations of the ballistic inclination and the ballistic declination of the interceptor in the second pulse stage are:

The endpoint constraints that need to be satisfied are:

To provide a stable control input, the following weighted sum of squares of the angle of attack and sideslip is chosen as the performance functional:

Similar to the derivation of the optimal guidance command for the first pulse, the weight term (t _bo2 -t) ⁿ of the remaining combustion time is used to shape the attack angle and sideslip angle curves. If n>0 is selected, the endpoint values of the attack angle and sideslip angle will converge to zero.

From equations (119) and (121), the Hamiltonian function of the optimal control problem is:

In the formula, λ ₁ and λ ₂ are both co-state variables. According to the first-order necessary conditions, there are:

Substituting the above formula into formula (119) and integrating it, the expressions of the speed inclination deviation value and the speed declination deviation value at the time of shutdown can be obtained as:

Combined with the endpoint constraint shown in Eq. (120), the value of the covariate can be obtained as:

In the formula, Θ ₁ and Θ ₂ are intermediate variables, and their expressions are:

Substituting Equation (126) into Equation (124), the optimal values of attack angle and sideslip angle can be obtained:

The specific expressions of N _p1 and N _p2 are:

It can be seen from the above formula that its guidance coefficient is not a constant value and changes with the flight time, and its approximate solution is obtained by the Gauss-Legendre integral formula. remember:

Similarly, the values of each variable in the above formula can be predicted by step 102 through the end position of the booster segment and the velocity vector. Then the specific values of the guidance coefficients N _p1 and N _p2 can be obtained:

为第i个高斯积分节点x_i对应的飞行时间；in,

is the flight time corresponding to the i-th Gaussian integration node x _i ;

ω _i is the ith Gaussian integral weight coefficient.

So far, the optimal guidance command for the two pulses of the dual-pulse interceptor has been derived.

The optimal mid-range guidance method for short-range interception dual-pulse based on gravity difference fitting proposed by the embodiment of the present invention is based on the working characteristics of the interceptor's dual-pulse solid rocket motor, the background of the interception outside the atmosphere, and the goal of reducing the amount of calculation. The gravitational difference of the projectile is fitted to the quadratic polynomial of the remaining flight time, so as to solve the guidance command analytically. In order to obtain the position and speed of the booster segment when the engine is shut down, the embodiment of the present invention proposes an analytical method for predicting the end position and speed of the booster segment in the outer atmosphere, which can realize the three-dimensional space for the booster segment under the premise of less computation. High-precision prediction of position and velocity at the moment of shutdown. Further, the embodiment of the present invention derives the optimal guidance law according to the first-order necessary conditions in the optimal control theory, which can satisfy the optimality of the guidance command, so that the angle of attack and the sideslip angle of the interceptor in the boosting stage are kept relatively high. Small-scale, thereby reducing the requirements for the interceptor control system and improving the interception capability and reliability of the interceptor.

FIG. 5 shows a schematic structural diagram of a dual-pulse mid-range guidance law device for short-range interception provided by an embodiment of the present invention. As shown in Figure 5, the device includes:

The differential equation building module 501 is used to establish the dynamic equation of the interceptor missile and the target missile in the taxiing section in the local ground coordinate system, and construct the line of sight coordinate system based on the dynamic equation and the coordinate transformation matrix between the line of sight coordinate system and the local ground coordinate system The differential equation of the relative motion velocity of the projectile;

In this embodiment of the present invention, as an optional embodiment, the differential equation building module 501 includes:

The geocentric distance vector acquisition unit (not shown in the figure) is used to obtain the interception respectively according to the geocentric distance of the origin of the local ground coordinate system of the taxiing segment, and the position vector of the interceptor missile and the target missile under the local ground coordinate system The geocentric distance vector of the projectile and target missile;

The gravitational acceleration vector acquisition unit is used to determine the gravitational acceleration vector of the interceptor missile and the target missile respectively in the local ground coordinate system based on the ground-to-center distance vector and the gravitational constant;

The dynamic equation building unit is used to obtain the dynamic equations of the interceptor missile and the target missile in the local ground coordinate system based on the gravitational acceleration vector;

The line-of-sight angle and line-of-sight declination expression acquisition unit is used to obtain the line-of-sight elevation angle and line-of-sight declination angle expressions of the line-of-sight coordinate system based on the component of the position vector in the dynamic equation and the relative position of the projectile between the interceptor and the target missile ;

The coordinate transformation matrix acquisition unit is used to construct the coordinate transformation matrix of the line of sight coordinate system and the local ground coordinate system according to the expressions of the line of sight elevation angle and the line of sight declination angle;

The velocity component equation obtaining unit is used to obtain the velocity components of the interceptor and the target missile in the line-of-sight coordinate system based on the coordinate transformation matrix, the velocity vector of the interceptor in the dynamic equation and the velocity vector of the target missile in the dynamic equation. equation;

The relative motion velocity equation building unit is used to construct the relative motion velocity equation of the projectile under the line-of-sight coordinate system according to the expressions of the line-of-sight elevation angle and the line-of-sight declination angle, the relative position between the interceptor and the target missile, and the respective speed component equations;

The velocity differential equation building unit is used to perform differential operation on the relative motion velocity equation of the projectile, and construct the differential equation of the relative movement velocity of the projectile under the line-of-sight coordinate system.

A prediction module 502, configured to establish a dynamic equation of the booster segment, and predict the end position vector and velocity vector of the booster segment;

In this embodiment of the present invention, as an optional embodiment, the prediction module 502 includes:

The inclination acquisition unit is used to acquire the orbital inclination of the orbital plane and the right ascension of the ascending node based on the angular momentum of the interceptor in the geocentric inertial coordinate system;

The model building unit is used to establish the dynamic model of the booster section based on the differential equation of the relative motion velocity of the projectile, the operating parameters of the interceptor and the speed of the interceptor in the orbital plane;

The vector determination unit is used to determine the terminal position vector and the velocity vector at the end of the booster segment of the interceptor based on the dynamic model of the booster segment.

In the embodiment of the present invention, as an optional embodiment, based on the dynamic model of the booster segment, determining the end position vector and the velocity vector at the end of the booster segment of the interceptor missile, including:

Simplify the derivative of the speed of the interceptor in the booster segment in the booster segment dynamics model to obtain the simplified derivative of the speed;

Integrate the simplified derivative of the velocity to obtain the velocity at the end of the booster segment of the interceptor.

In the embodiment of the present invention, as an optional embodiment, the simplified derivative of the speed is integrated to obtain the speed at the end of the booster segment of the interceptor, including:

Construct an intermediate variable representing the end time of the booster segment, and obtain the derivative of the intermediate variable according to the interceptor ballistic inclination equation in the booster segment dynamics model;

Integrate the derivative of the intermediate variable to obtain the integral term of the boost velocity and the ballistic inclination at the end of the boost segment;

Based on the obtained value of the integral term of the boost speed and the ballistic inclination at the end of the boost segment, the speed at the end of the boost segment of the interceptor is obtained.

In this embodiment of the present invention, as another optional embodiment, the prediction module 502 includes:

The fitting unit is used to fit the interceptor ballistic inclination based on the derivative equation of the interceptor ballistic inclination in the dynamic model of the booster segment;

The included angle equation acquisition unit is used to obtain the end position equation of the interceptor booster segment and the included angle equation between the end position vector and the line connecting the earth center to the ascending node based on the fitted interceptor ballistic inclination;

The vector acquisition unit is used to obtain the unit based on the orbit inclination, the right ascension of the ascending node, the terminal velocity of the booster segment of the interceptor, the ballistic inclination angle of the terminal point of the booster segment, the terminal position equation and the included angle equation between the terminal position vector and the line connecting the center of the earth to the ascending node, Determine the terminal position vector and velocity vector at the end of the interceptor's boost segment.

The shutdown point parameter acquisition module 503 is configured to obtain shutdown point parameters that satisfy the zero-control interception triangle in the taxiing segment according to the terminal position vector and velocity vector at the end of the booster segment of the interceptor, and based on the strategy of the zero-control interception triangle. Shutdown point parameters include interceptor velocity inclination and velocity declination;

In this embodiment of the present invention, as an optional embodiment, the shutdown point parameter acquisition module 503 includes:

The unit for obtaining the value of the declination angle of sight is used to apply the condition that the relative velocity of the projectile in the vertical line of sight direction at the interception time is zero, and apply it to the differential equation of the relative movement speed of the projectile in the gliding phase to obtain the declination angle of the projectile when the interceptor is turned off. speed value;

The adjustment unit is used to adjust the speed and direction of the interceptor projectile, so that the shutdown speed meets the expected value of the declination velocity value of the projectile sight line.

The derivation module 504 is used for deriving the optimal ignition time of the second pulse of the interceptor missile based on the preset performance index function of the ignition time of the second pulse of the interceptor missile according to the shutdown point parameter, the analytical expression of the position vector and the boundary condition;

In this embodiment of the present invention, as an optional embodiment, the deriving module 504 includes:

The line-of-sight declination velocity equation acquisition unit is used to obtain the line-of-sight declination velocity equation of the interceptor missile at the moment of ignition of the second pulse of the interceptor based on the analytical formula of the position vector and the preset second boundary condition;

The derivative equation obtaining unit is used to obtain the analytical expression of the relative velocity of the projectile and the derivative of the pulse interval time in the second pulse working stage according to the differential equation of the relative velocity of the projectile and the boundary conditions of the ignition time, and based on the analytical expression, the optimal solution is obtained. Pulse interval time derivative equation;

The projectile relative velocity equation acquisition unit is used to solve the relationship between the expected projectile relative velocity and the pulse interval time when the interceptor's second pulse is turned off, and obtain the projectile relative velocity equation in the vertical line of sight direction;

The optimal ignition time acquisition unit is used to solve the interception using the variational method based on the angular velocity equation of the projectile line of sight, the optimal pulse interval time derivative equation, and the relative speed equation of the vertical line of sight based on the second pulse ignition time of the interceptor. The optimal ignition time of the second pulse.

The optimal command obtaining module 505 is used to obtain the dual-pulse optimal guidance command based on the predicted value and expected value of the velocity inclination angle and the velocity declination angle at the shutdown time of the interceptor missile and the optimal ignition time of the second pulse of the interceptor missile.

In this embodiment of the present invention, as an optional embodiment, the optimal instruction obtaining module 505 includes:

a first pulse optimal guidance command obtaining unit, configured to solve the first pulse optimal guidance command, where the first pulse optimal guidance command includes the optimal values of the angle of attack and the sideslip angle;

The second pulse optimal guidance command obtaining unit is used for solving the second pulse optimal guidance command, and the second pulse optimal guidance command includes the optimal values of the angle of attack and the sideslip angle.

As shown in FIG. 6 , an embodiment of the present application provides a computer device 600 for executing the dual-pulse mid-range guidance method for short-range interception in FIG. 1 , the device includes a memory 601 and is connected to the memory 601 through a bus The processor 602 and the computer program stored on the memory 601 and running on the processor 602, wherein the above-mentioned processor 602 implements the steps of the above-mentioned dual-pulse mid-range guidance method for short-range interception when executing the above-mentioned computer program .

Specifically, the above-mentioned memory 601 and processor 602 can be general-purpose memories and processors, which are not specifically limited here. When the processor 602 runs the computer program stored in the memory 601, it can execute the above-mentioned double-pulse method for short-range interception. Guidance method.

Corresponding to the dual-pulse mid-range guidance method for short-range interception in FIG. 1 , an embodiment of the present application also provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and the computer program is processed The above-mentioned steps of the dual-pulse mid-range guidance method for short-range interception are performed when the vehicle is running.

Specifically, the storage medium can be a general storage medium, such as a removable disk, a hard disk, etc., when the computer program on the storage medium is run, the above-mentioned dual-pulse mid-range guidance method for short-range interception can be executed.

In the embodiments provided in this application, it should be understood that the disclosed system and method may be implemented in other manners. The system embodiments described above are only illustrative. For example, the division of the units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components may be combined or Can be integrated into another system, or some features can be ignored, or not implemented. On the other hand, the shown or discussed mutual coupling or direct coupling or communication connection may be through some communication interfaces, indirect coupling or communication connection of systems or units, and may be in electrical, mechanical or other forms.

The units described as separate components may or may not be physically separated, and components displayed as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution in this embodiment.

In addition, each functional unit in the embodiments provided in this application may be integrated into one processing unit, or each unit may exist physically alone, or two or more units may be integrated into one unit.

The functions, if implemented in the form of software functional units and sold or used as independent products, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application can be embodied in the form of a software product in essence, or the part that contributes to the prior art or the part of the technical solution, and the computer software product is stored in a storage medium, including Several instructions are used to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), magnetic disk or optical disk and other media that can store program codes .

It should be noted that like numerals and letters refer to like items in the following figures, so that once an item is defined in one figure, it does not require further definition and explanation in subsequent figures, Furthermore, the terms "first", "second", "third", etc. are only used to differentiate the description and should not be construed as indicating or implying relative importance.

Finally, it should be noted that the above-mentioned embodiments are only specific implementations of the present application, and are used to illustrate the technical solutions of the present application, rather than limit them. The embodiments describe the application in detail, and those of ordinary skill in the art should understand that any person skilled in the art can still modify the technical solutions described in the foregoing embodiments within the technical scope disclosed in the application. Changes can be easily conceived, or equivalent replacements are made to some of the technical features; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions in the embodiments of the present application. All should be covered within the scope of protection of this application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims (10)

1. a dual-pulse guidance method for short-range interception, is characterized in that, comprising: Establish the dynamic equations of the interceptor and target missiles in the local ground coordinate system in the gliding section, and build the differential equation of the relative motion velocity of the missile in the line of sight coordinate system based on the dynamic equation and the coordinate transformation matrix between the line of sight coordinate system and the local ground coordinate system ; Establish the dynamic equation of the booster segment, and predict the end position vector and velocity vector of the booster segment; According to the terminal position vector and velocity vector at the end of the booster segment of the interceptor missile, and based on the strategy of the zero-control interception triangle, the shutdown point parameters that satisfy the zero-control interception triangle in the gliding segment are obtained, and the shutdown point parameters include the interceptor missile speed inclination angle and speed declination; According to the parameters of the shutdown point, the analytical formula of the position vector and the boundary conditions, and based on the preset performance index function of the ignition time of the second pulse of the interceptor, the optimal ignition time of the second pulse of the interceptor is deduced; Based on the predicted value and expected value of the velocity inclination angle and velocity declination angle at the time of shutdown of the interceptor missile and the optimal ignition time of the interceptor's second pulse, the optimal guidance command of the dual-pulse is obtained. 2. method according to claim 1, is characterized in that, described establishing the dynamic equation of interceptor bomb under local ground coordinate system and target missile in gliding section, comprising: According to the geocentric distance of the origin of the local ground coordinate system of the taxiing segment, and the position vector of the interceptor and the target missile under the local ground coordinate system, the geocentric distance vectors of the interceptor and the target missile are obtained respectively; Determine the gravitational acceleration vector of the interceptor and target missile respectively in the local ground coordinate system based on the distance vector and the gravitational constant; Based on the gravitational acceleration vector, the dynamic equations of the interceptor and the target missile in the local ground coordinate system are obtained. 3. method according to claim 2, is characterized in that, described based on the coordinate transformation matrix of dynamic equation and line-of-sight coordinate system and local ground coordinate system, constructs the differential equation of relative motion velocity of projectile under line-of-sight coordinate system, comprising: Based on the component of the position vector in the dynamic equation and the relative position of the target missile between the interceptor and the target missile, obtain the expressions of the line-of-sight elevation angle and the line-of-sight declination angle of the line-of-sight coordinate system; According to the expressions of the line of sight elevation angle and the line of sight declination angle, construct the coordinate transformation matrix of the line of sight coordinate system and the local ground coordinate system; Based on the coordinate transformation matrix, the velocity vector of the interceptor in the dynamic equation and the velocity vector of the target missile in the dynamic equation, the velocity component equations of the interceptor and the target missile in the line-of-sight coordinate system are obtained respectively; According to the expressions of line-of-sight elevation angle and line-of-sight declination angle, the relative position between interceptor and target missile, and their respective velocity component equations, construct the relative motion velocity equation of the missile and target in the line-of-sight coordinate system; Differential operation is performed on the relative motion velocity equation of the projectile, and the differential equation of the relative movement speed of the projectile under the line of sight coordinate system is constructed. 4. The method according to claim 1, characterized in that, establishing the dynamic equation of the booster section to predict the end position vector and velocity vector of the booster section, comprising: Based on the angular momentum of the interceptor in the geocentric inertial coordinate system, the orbital inclination of the orbital plane and the right ascension of the ascending node are obtained; In the orbital plane, based on the differential equation of the relative motion velocity of the projectile, the operating parameters of the interceptor and the speed of the interceptor, the dynamic model of the booster section is established; Based on the dynamic model of the booster segment, the terminal position vector and velocity vector at the end of the booster segment of the interceptor are determined. 5. The method according to claim 4, characterized in that, based on the dynamic model of the booster segment, determining the terminal position vector and the velocity vector at the end of the booster segment of the interceptor, comprising: Simplify the derivative of the speed of the interceptor in the booster segment in the booster segment dynamics model to obtain the simplified derivative of the speed; Integrate the simplified derivative of the velocity to obtain the velocity at the end of the booster segment of the interceptor. 6. The method according to claim 5, wherein the simplified derivative of the velocity vector is integrated to obtain the velocity vector at the end of the booster segment of the interceptor, comprising: Construct an intermediate variable representing the end time of the booster segment, and obtain the derivative of the intermediate variable according to the interceptor ballistic inclination equation in the booster segment dynamics model; Integrate the derivative of the intermediate variable to obtain the integral term of the boost velocity and the ballistic inclination at the end of the boost segment; Based on the obtained value of the integral term of boost speed and the ballistic inclination angle at the end of the boost segment, the velocity vector at the end of the boost segment of the interceptor is obtained. 7. The method according to claim 1, characterized in that, establishing the dynamic equation of the booster section to predict the end position vector and velocity vector of the booster section, comprising: Fitting the interceptor ballistic inclination based on the derivative equation of the interceptor ballistic inclination in the dynamic model of the booster segment; Based on the fitted interceptor ballistic inclination, obtain the end position equation of the interceptor's booster segment and the included angle equation between the end position vector and the line connecting the center of the earth to the ascending node; Determine the booster segment of the interceptor missile based on the orbit inclination, the right ascension of the ascending node, the end speed of the booster segment of the interceptor, the ballistic inclination at the end of the booster segment, the end position equation, and the included angle equation between the end position vector and the line connecting the center of the earth to the ascending node. The end position vector and velocity vector at the end time. 8. A dual-pulse mid-range guidance law device for short-range interception, comprising: The differential equation building module is used to establish the dynamic equation of the interceptor missile and the target missile in the taxiing section in the local ground coordinate system. Based on the dynamic equation and the coordinate transformation matrix between the line of sight coordinate system and the local ground coordinate system, construct the line of sight coordinate system. Differential equation of relative velocity of projectile; The prediction module is used to establish the dynamic equation of the booster segment and predict the end position vector and velocity vector of the booster segment; The shutdown point parameter acquisition module is used to obtain shutdown point parameters that satisfy the zero-control interception triangle in the taxi segment according to the terminal position vector and velocity vector at the end of the booster segment of the interceptor, and based on the strategy of the zero-control interception triangle, the shutdown Point parameters include interceptor velocity inclination and velocity declination; The derivation module is used for deriving the optimal ignition time of the second pulse of the interceptor missile based on the preset performance index function of the ignition time of the second pulse of the interceptor missile according to the shutdown point parameters, the analytical expression of the position vector and the boundary conditions; The optimal command acquisition module is used to obtain the dual-pulse optimal guidance command based on the predicted value and expected value of the velocity inclination angle and the velocity declination angle at the time of shutdown of the interceptor missile and the optimal ignition time of the interceptor's second pulse. 9. A computer device, comprising: a processor, a memory, and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the computer device runs, the processor and the The memories communicate with each other through a bus, and when the machine-readable instructions are executed by the processor, the steps of the dual-pulse mid-range guidance method for short-range interception according to any one of claims 1 to 7 are performed. 10. A computer-readable storage medium, characterized in that, a computer program is stored on the computer-readable storage medium, and the computer program is executed by a processor to execute the short-range method according to any one of claims 1 to 7 when the computer program is run by a processor. The steps of the guidance method in the intercepted double pulse.

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