CN110645844A - High-speed interception guidance method with attack angle constraint - Google Patents

High-speed interception guidance method with attack angle constraint Download PDF

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CN110645844A
CN110645844A CN201910830493.4A CN201910830493A CN110645844A CN 110645844 A CN110645844 A CN 110645844A CN 201910830493 A CN201910830493 A CN 201910830493A CN 110645844 A CN110645844 A CN 110645844A
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何贤军
罗驭川
陈志华
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Nanjing Tech University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F42—AMMUNITION; BLASTING
    • F42B—EXPLOSIVE CHARGES, e.g. FOR BLASTING, FIREWORKS, AMMUNITION
    • F42B15/00—Self-propelled projectiles or missiles, e.g. rockets; Guided missiles
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Abstract

The invention discloses a high-speed interception guidance method with attack angle constraint, which comprises the following steps: taking a longitudinal plane where the missile and the target are located as an attack plane, establishing a relative motion relation between the missile and the target, and obtaining an expression of relative motion parameters; deriving an expression of zero control miss distance and zero control speed according to the relative movement parameters of the bullet; by utilizing a layered sliding mode theory, enabling zero-control miss distance and zero-control speed to be first-layer sliding mode variables, and combining the first-layer sliding modes into a second-layer sliding mode; and selecting an exponential approximation law, and enabling the exponential approximation law to be equal to the second-layer sliding mode with respect to the time derivative, so as to solve the guidance law with the falling angle constraint of the high-speed flying missile. The invention aims at the target according to the preset sight angle so as to realize the increase of the damage effect; when the target is intercepted at high speed, the target can be hit by a small miss distance, and the method has good reliability.

Description

High-speed interception guidance method with attack angle constraint
Technical Field
The invention belongs to the technical field of guidance, and particularly relates to a high-speed interception guidance method with attack angle constraint.
Background
In recent years, with the rapid development of guidance technology, the maneuverability of cruise missiles and hypersonic vehicles has also been greatly improved. The use of these high-speed, large-sized motorized aircraft presents a significant challenge to national defense systems. For such interception problem, the relative speed of the missile is high, which undoubtedly puts high requirements on the accuracy and rapidity of the novel guidance method. In order to improve the damage efficiency of the missile to the target, the missile is required to hit the target accurately and at a specific angle.
In the conventional guidance law, the proportional guidance method is a conventional and generally applicable guidance strategy, which can hit a target with good precision under the condition of knowing the relative speed of a bullet and the angular velocity of a sight line, but cannot limit the end sight line angle. The optimal guidance law with the terminal angle constraint can hit the target according to a preset line-of-sight angle, but under the condition of large maneuvering of the target, a larger miss distance occurs, which undoubtedly reduces the interception reliability.
Disclosure of Invention
The invention aims to provide a high-speed interception guidance method with attack angle constraint.
The technical solution for realizing the purpose of the invention is as follows: a high-speed interception guidance method with attack angle constraint comprises the following steps:
step 1, taking a longitudinal plane where a missile and a target are located as an attack plane, establishing a relative motion relation between the missile and the target, and obtaining an expression of relative motion parameters;
step 2, deriving an expression of zero control miss distance and zero control speed according to the relative motion parameters of the bullet;
step 3, utilizing a layered sliding mode theory, enabling zero-control miss distance and zero-control speed to be first-layer sliding mode variables, and combining the first-layer sliding modes into a second-layer sliding mode;
and 4, selecting an index approaching law, and enabling the index approaching law to be equal to the time derivative of the second-layer sliding mode in the step 3, so as to solve the guidance law with the falling angle constraint of the high-speed flying missile.
Compared with the prior art, the invention has the following remarkable advantages: (1) compared with a proportional guidance method, the method can hit the target according to a preset sight angle so as to realize the increase of the damage effect; (2) compared with the optimal guidance law, the method realizes the goal hit with smaller miss distance when the goal is intercepted at high speed, and has good reliability.
Drawings
Fig. 1 is a schematic diagram of relative motion.
Fig. 2 is a view showing a change in angle of view.
Fig. 3 is a diagram of ballistic trajectories at different line-of-sight angles.
Fig. 4 is a diagram of ballistic trajectories under different guidance law controls.
Fig. 5 is a graph of line of sight angle versus time.
Detailed Description
The invention discloses a high-speed interception guidance method with attack angle constraint, which comprises the following steps:
step 1, taking a longitudinal plane where a missile and a target are located as an attack plane, establishing a relative motion relation between the missile and the target, and obtaining an expression of relative motion parameters;
step 2, deriving an expression of zero control miss distance and zero control speed according to the relative motion parameters of the bullet;
step 3, utilizing a layered sliding mode theory, enabling the zero-control miss distance and the zero-control speed obtained in the step 2 to be variable of a first layer of sliding modes, and combining the first layer of sliding modes into a second layer of sliding modes;
and 4, selecting an index approaching law, and enabling the index approaching law to be equal to the time derivative of the second-layer sliding mode in the step 3, so as to solve the guidance law with the falling angle constraint of the high-speed flying missile.
Further, step 1 specifically comprises:
regarding the missile and the target as mass points, taking the intersection point of a missile target connecting line and the ground as an origin point, taking the horizontal direction pointing to the missile target as the X axis of an inertial coordinate system, establishing a y axis vertical to the X axis in a vertical plane passing through the X axis, taking the y axis as positive upward, and establishing the X axis of the inertial coordinate systemi_O_Yi(ii) a Taking the intersection point of the line of the bullet eyes and the ground as the origin, taking the direction of the initial line of the bullet eyes as the X axis, establishing a y axis vertical to the X axis in a vertical plane passing through the X axis, taking the upward direction as the positive, and establishing an initial sight line coordinate system XL0_O_YL0；
Subscripts M and T represent missile and target, respectively; variables V, thetaV、a、aNyRespectively representing velocity, ballistic inclination, acceleration and acceleration at the beginningA component of the starting gaze direction; thetaLIs the angle between the line of the bullet eyes and the x axis of the inertial coordinate system, r is the relative distance of the bullet eyes, ydThen representing the component of the relative distance of the bullet eyes in the y direction in the initial sight line coordinate system;
the expression of the relative speed of the bullet eyes in the component parallel to and perpendicular to the line connecting the bullet eyes is as follows:
Vr＝VT cos(θVT-θL)-VM cos(θVM-θL) (1)
Vλ＝VT sin(θVT-θL)-VM sin(θVM-θL) (2)
after the dynamic characteristics of the target and the missile are simplified into a first-order inertia link, the following can be obtained:
Figure BDA0002190539620000021
wherein the content of the first and second substances,
Figure BDA0002190539620000022
for acceleration commands of missiles, targetsM、τTIs a time constant;
in selecting a state variableIn the case of (2), the system state equation can be obtained as:
Figure BDA0002190539620000024
wherein
Figure BDA0002190539620000031
Figure BDA0002190539620000032
Represents a pair ydA derivative with respect to time;
thus, the information about t can be calculatedgoState transition matrix of (2):
wherein t isgoFor the remaining time of flight, t can be approximatedgo＝-r/Vr。
Further, step 2 is specifically
Two physical quantities for measuring the miss distance and the relative speed at the end moment can be obtained from the state transition matrix: a zero miss control amount (ZEM) and a zero speed control (ZEV), which are expressed as:
Figure BDA0002190539620000034
Figure BDA0002190539620000035
wherein ψ (x) ═ e-x+x-1，β(x)＝1-e-xAnd x is tgo/τT；
After applying the small angle linearization assumption, we find:
yd＝rsin(θL-θL0)≈r(θL-θL0) (7)
wherein, thetaL0Is the included angle between the initial bullet eye connecting line and the x axis of the inertial coordinate system;
further derivation of equation (7) yields:
Figure BDA0002190539620000036
when the guidance process is over, i.e. tgoWhen 0, equation (8) can be simplified:
Figure BDA0002190539620000037
wherein, thetaLfBy setting different theta for a predetermined end-of-line angleLfThe missile can be attacked at different anglesMarking;
substituting the formulas (7) and (8) into the formula (5) to obtain:
Figure BDA0002190539620000041
let ZEV*Is ZEV and
Figure BDA0002190539620000042
relative velocity error at end time, when ZEV*When the convergence reaches 0, the corresponding line-of-sight angle constraint is reached; so ZEV*The expression of (a) is:
Figure BDA0002190539620000043
further derivation of equations (10) and (11) can be found:
Figure BDA0002190539620000044
Figure BDA0002190539620000045
further, step 3 is specifically
Constructing a guidance law by using a layered sliding mode theory, and firstly selecting a first layer of sliding mode surface
S1＝ZEM，S2＝ZEV* (14)
The derivation of equation (14) can be:
Figure BDA0002190539620000046
Figure BDA0002190539620000047
wherein the content of the first and second substances,
Figure BDA0002190539620000049
Figure BDA00021905396200000410
Figure BDA00021905396200000411
u represents the missile acceleration command.
Further, step 4 is specifically
Selecting a second layer of slip forms S3＝c1S1+S2Wherein c is1＝c0sign(S1，S2)，c0Is a positive number;
obtaining an expression of a derivative of the sliding mode of the second layer with respect to time through the kinetic equation of the sliding mode of the first layer obtained in the step, and simplifying to obtain:
Figure BDA0002190539620000051
by selecting the exponential-approximation law,
Figure BDA0002190539620000052
wherein k and eta are both normal numbers; equation (17) is equal to the approach law, and an expression of the acceleration command is obtained:
Figure BDA0002190539620000053
the expression obtained by the formula (18) is a guidance law with a fall angle constraint based on the zero control miss amount.
The present invention will be described in detail with reference to examples.
Examples
The guidance method comprises the steps of establishing a relative motion state equation of a bullet in an initial sight line coordinate system; solving a state transition matrix related to the remaining flight time; further obtaining expressions of zero control miss distance and zero control speed on missile acceleration; and finally, deducing a sliding mode guidance law with a line-of-sight angle constraint and based on the zero control miss distance in a two-dimensional plane by adopting a layered sliding mode theory.
In order to simplify the derivation process of the guidance law, the missile and the target are regarded as particles, and the relative motion relation between the missiles as shown in figure 1 is established in the initial sight direction, wherein X is shown in the figurei_O_YiAnd XL0_O_YL0Representing an inertial coordinate system and an initial line-of-sight coordinate system; the M and T subscripts represent the missile and target, respectively; variables V, thetaV、a、aNyRespectively representing components of speed, trajectory inclination angle, acceleration and acceleration in an initial sight line direction; thetaLIs the angle of sight, r is the relative distance of the eyes, ydThen the component of the relative distance of the eyes in the initial line of sight direction is represented.
From the relative motion map, it can be further derived that the expression of the relative velocity in the direction parallel to and perpendicular to the line-of-sight component is:
Vr＝VT cos(θVT-θL)-VM cos(θVM-θL) (1)
Vλ＝VT sin(θVT-θL)-VMsin(θVM-θL) (2)
after the dynamic characteristics of the target and the missile are simplified into a truncated inertial link, the following can be obtained:
wherein the content of the first and second substances,
Figure BDA0002190539620000055
for acceleration commands of missiles, targetsM、τTIs a time constant.
Selecting state variables
Figure BDA0002190539620000056
The system state equation can be obtained as follows:
Figure BDA0002190539620000057
wherein
Thus, the information about t can be calculatedgoState transition matrix of (2):
Figure BDA0002190539620000061
wherein t isgoFor the remaining time of flight, t can be approximatedgo＝-r/Vr。
Two physical quantities for measuring the miss distance and the relative speed at the end moment can be obtained from the state transition matrix: a zero miss control amount ZEM and a zero speed control ZEV, which are expressed as follows:
Figure BDA0002190539620000063
wherein ψ (x) ═ e-x+x-1，β(x)＝1-e-xAnd x is tgo/τT。
After applying the small angle linearization assumption, we find:
yd＝rsin(θL-θL0)≈r(θL-θL0) (7)
further derivation of equation (7) yields:
when the guidance process is over, i.e. tgoWhen 0, equation (8) can be simplified:
Figure BDA0002190539620000065
wherein, thetaLfBy setting different theta for a predetermined end-of-line angleLfThe missile can attack the target at different angles, and the expected damage effect is achieved.
Substituting the formulas (7) and (8) into the formula (5) to obtain:
Figure BDA0002190539620000066
to achieve end angle constraint, let ZEV*Is ZEV andrelative velocity error at end time, when ZEV*When the convergence reaches 0, the corresponding line-of-sight angle constraint is reached, so the ZEV*The expression of (a) is:
Figure BDA0002190539620000068
Figure BDA0002190539620000071
further derivation of equations (10) and (11) can be found:
Figure BDA0002190539620000072
then, a guidance law is constructed by using a layered sliding mode theory, and a first layer of sliding mode surface is selected
S1＝ZEM，S2＝ZEV* (14)
The derivation of equation (14) can be:
Figure BDA0002190539620000073
Figure BDA0002190539620000074
wherein the content of the first and second substances,
Figure BDA0002190539620000075
Figure BDA0002190539620000077
Figure BDA0002190539620000078
u represents the missile acceleration command.
Secondly, selecting a second layer of sliding forms S3＝c1S1+S2Wherein c is1＝c0sign(S1，S2)，c0Is a positive number.
Through the kinetic equation of the sliding mode of the first layer obtained in the above, an expression of the derivative of the sliding mode of the second layer with respect to time can be obtained easily, and the expression is simplified to obtain:
Figure BDA0002190539620000079
by selecting a suitable approach law,wherein k and eta are both normal numbers. Equation (17) is equal to the approach law, and an expression of the acceleration command is obtained:
Figure BDA00021905396200000711
and the expression obtained by the formula (18) is a guidance law with a fall angle constraint based on the zero control miss amount.
The simulation calculation shows that the change trend of the line-of-sight angle is shown in fig. 2, and the guidance method provided by the invention can realize the constraint of the line-of-sight angle under the constraint of different line-of-sight angles. The ballistic trajectory of the projectile under different line-of-sight constraints is shown in figure 3. The data obtained by simulation also proves that under the constraint of different line-of-sight angles, the rocket projectile can hit the target in different tracks and directions, and the purpose of destroying the target is achieved.
Table 1 shows the values of the terminal actual line-of-sight angle and the terminal off-target amount achieved by the guidance law obtained in the present invention under the constraint of different expected line-of-sight angles, and the results show the effectiveness of the guidance strategy.
TABLE 1 simulation results
Figure BDA0002190539620000081
Subsequently, the guidance law obtained by the method is compared with the traditional guidance law and the guidance law only considering the zero control miss amount through simulation experiments. In order to visually compare the control effects of four different guidance methods, the terminal line-of-sight angles of the optimal guidance law and the guidance law proposed by the invention are set to be 10 degrees. As shown in fig. 4, PNG and OPG respectively represent a proportional guidance method and an optimal guidance law; the ZEMG is a guidance law considering only the zero control miss amount, and the ZEMZEVG is the guidance law obtained by the present invention.
As can be seen from fig. 5, when the bullet moves at a high speed and the target moves with a large motor, the OPG cannot hit the target at a specified viewing angle, and the PNG and ZEMG cannot reach the desired viewing angle due to their limitations. Table 2 compares the magnitude of the miss distance of the four guidance laws at the end of interception.
TABLE 2 comparison of simulation performance for different guidance laws
Figure BDA0002190539620000082
As can be seen from Table 2, the miss distance of PNG and OPG is far greater than that of ZEMG and ZEMZEVG under the working condition of high-speed movement; and the ZMEZEVGG guidance law with angle constraint is added on the basis of the ZEMG, so that the angle constraint is realized under the condition of sacrificing a small amount of off-target performance, and the advantages of the guidance law obtained by the method are reflected.

Claims (5)

1. A high-speed interception guidance method with attack angle constraint is characterized by comprising the following steps:
step 1, taking a longitudinal plane where a missile and a target are located as an attack plane, establishing a relative motion relation between the missile and the target, and obtaining an expression of relative motion parameters;
step 2, deriving an expression of zero control miss distance and zero control speed according to the relative motion parameters of the bullet;
step 3, utilizing a layered sliding mode theory, enabling zero-control miss distance and zero-control speed to be first-layer sliding mode variables, and combining the first-layer sliding modes into a second-layer sliding mode;
and 4, selecting an index approaching law, and enabling the index approaching law to be equal to the time derivative of the second-layer sliding mode in the step 3, so as to solve the guidance law with the falling angle constraint of the high-speed flying missile.
2. The high-speed interception guidance method with attack angle constraint according to claim 1, characterized in that the step 1 is specifically:
regarding the missile and the target as mass points, taking the intersection point of a missile target connecting line and the ground as an origin point, taking the horizontal direction pointing to the missile target as the X axis of an inertial coordinate system, establishing a y axis vertical to the X axis in a vertical plane passing through the X axis, taking the y axis as positive upward, and establishing the X axis of the inertial coordinate systemi_O_Yi(ii) a Taking the intersection point of the line of the bullet eyes and the ground as the origin, taking the direction of the initial line of the bullet eyes as the X axis, establishing a y axis vertical to the X axis in a vertical plane passing through the X axis, taking the upward direction as the positive, and establishing an initial sight line coordinate system XL0_O_YL0；
Subscripts M and T represent missile and target, respectively; variables V, thetaV、a、aNyRespectively representing components of speed, trajectory inclination angle, acceleration and acceleration in an initial sight line direction; thetaLIs the angle between the line of the bullet eyes and the x axis of the inertial coordinate system, r is the relative distance of the bullet eyes, ydThen representing the component of the relative distance of the bullet eyes in the y direction in the initial sight line coordinate system;
the expression of the relative speed of the bullet eyes in the component parallel to and perpendicular to the line connecting the bullet eyes is as follows:
Vr＝VTcos(θVT-θL)-VMcos(θVM-θL) (1)
Vλ＝VT sin(θVT-θL)-VMsin(θVM-θL) (2)
after the dynamic characteristics of the target and the missile are simplified into a first-order inertia link, the following can be obtained:
Figure FDA0002190539610000011
wherein the content of the first and second substances,
Figure FDA0002190539610000012
for acceleration commands of missiles, targetsM、τTIs a time constant;
in selecting a state variable
Figure FDA0002190539610000013
In the case of (2), the system state equation can be obtained as:
wherein
Figure FDA0002190539610000015
Figure FDA0002190539610000016
Represents a pair ydA derivative with respect to time;
thus, the information about t can be calculatedgoState transition matrix of (2):
wherein t isgoIs the remaining time of flight, approximately tgo＝-r/Vr。
3. The high-speed interception guidance method with attack angle constraint according to claim 1, characterized in that the step 2 is specifically:
two physical quantities for measuring the miss distance and the relative speed at the end moment are obtained from the state transition matrix: the expression of the zero-control miss distance ZEM and the zero-control speed ZEV is respectively as follows:
Figure FDA0002190539610000022
Figure FDA0002190539610000023
wherein ψ (x) ═ e-x+x-1，β(x)＝1-e-xAnd x is tgo/τT；
After applying the small angle linearization assumption, we find:
yd＝rsin(θL-θL0)≈r(θL-θL0) (7)
wherein, thetaL0Is the included angle between the initial bullet eye connecting line and the x axis of the inertial coordinate system;
further derivation of equation (7) yields:
when the guidance process is over, i.e. tgoWhen 0, equation (8) can be simplified:
Figure FDA0002190539610000025
wherein, thetaLfIs a preset end-of-time line-of-sight angle;
substituting the formulas (7) and (8) into the formula (5) to obtain:
let ZEV*Is ZEV and
Figure FDA0002190539610000031
relative velocity error at end time, when ZEV*When the convergence reaches 0, the corresponding line-of-sight angle constraint is reached; so ZEV*The expression of (a) is:
Figure FDA0002190539610000032
further derivation of equations (10) and (11) can be found:
Figure FDA0002190539610000033
Figure FDA0002190539610000034
4. the high-speed interception guidance method with attack angle constraint according to claim 1, characterized in that step 3 is specifically:
constructing a guidance law by using a layered sliding mode theory, and firstly selecting a first layer of sliding mode surface
S1＝ZEM，S2＝ZEV* (14)
The derivation of equation (14) can be:
Figure FDA0002190539610000035
wherein the content of the first and second substances,
Figure FDA0002190539610000037
Figure FDA0002190539610000039
u represents the missile acceleration command.
5. The high-speed interception guidance method with attack angle constraint according to claim 1, characterized in that step 4 specifically comprises:
selecting a second layer of slip forms S3＝c1S1+S2Wherein c is1＝c0sign(S1，S2)，c0Is a positive number;
obtaining an expression of a derivative of the sliding mode of the second layer with respect to time through the kinetic equation of the sliding mode of the first layer obtained in the step, and simplifying to obtain:
Figure FDA0002190539610000041
by selecting the exponential-approximation law,wherein k and eta are both normal numbers; equation (17) is equal to the approach law, and an expression of the acceleration command is obtained:
Figure FDA0002190539610000043
and the expression obtained by the formula (18) is a guidance law with a fall angle constraint based on the zero control miss amount.
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CN112113466A (en) * 2020-08-19 2020-12-22 南京理工大学 Multi-missile cooperative guidance method with limited time convergence
CN112113466B (en) * 2020-08-19 2022-07-22 南京理工大学 Multi-missile cooperative guidance method with limited time convergence
CN112286059A (en) * 2020-11-10 2021-01-29 北京航空航天大学 Second-order front angle remodeling guidance method with attack angle and field angle constraints
CN113359819A (en) * 2021-05-27 2021-09-07 北京航空航天大学 Optimal guidance law with collision angle constraint and acceleration limitation
CN113359819B (en) * 2021-05-27 2024-04-16 北京航空航天大学 Optimal guidance law with collision angle constraint and acceleration limitation
CN113758380A (en) * 2021-08-03 2021-12-07 北京航空航天大学 Guidance control integration method considering steering engine dynamic performance and attack angle constraint
CN113758380B (en) * 2021-08-03 2022-06-03 北京航空航天大学 Guidance control integration method considering steering engine dynamic performance and attack angle constraint
CN114740884A (en) * 2022-03-11 2022-07-12 北京航空航天大学 Double-pulse guidance method and device for short-range interception
CN114740884B (en) * 2022-03-11 2024-06-07 北京航空航天大学 Double-pulse middle guidance method and device for short-range interception

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Application publication date: 20200103