CN110220416B - Self-adaptive rapid trajectory tracking guidance method - Google Patents

Self-adaptive rapid trajectory tracking guidance method Download PDF

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CN110220416B
CN110220416B CN201910401301.8A CN201910401301A CN110220416B CN 110220416 B CN110220416 B CN 110220416B CN 201910401301 A CN201910401301 A CN 201910401301A CN 110220416 B CN110220416 B CN 110220416B
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易文俊
张文广
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Nanjing University of Science and Technology
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41—WEAPONS
    • F41G—WEAPON SIGHTS; AIMING
    • F41G7/00—Direction control systems for self-propelled missiles

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Abstract

The invention discloses a self-adaptive rapid trajectory tracking guidance method. The method comprises the following steps: firstly, establishing a controlled gliding missile longitudinal plane internal motion model and a longitudinal plane internal missile relative kinematics model; then, acquiring the motion parameters of the projectile body through a projectile-borne sensor, calculating the angular velocity information of the sight line, and updating the track point; designing a tracking guidance law; finally, inputting a guidance instruction into a steering engine to control the angle of the rudder sheet; and repeating the motion parameter acquisition and tracking control until the tracking is finished. The method can meet the requirement of rapidity of a battlefield, inhibit the disturbance of pneumatic parameters in control and improve the robustness of the system.

Description

Self-adaptive rapid trajectory tracking guidance method
Technical Field
The invention relates to the technical field of trajectory tracking guidance, in particular to a self-adaptive rapid trajectory tracking guidance method.
Background
The guided ammunition technology is an important development direction of the weapon science technology at present, and many guided ammunitions fly by using an accurate tracking scheme as a premise for realizing accurate striking. Due to various interferences in the atmosphere, deviation exists in measured data when a track is tracked, and the requirement on an accurate trajectory tracking technology of an aircraft is high. Scholars at home and abroad put forward a plurality of control methods aiming at the problem of trajectory tracking, and a better tracking effect is achieved. Gandolfo proposes a tracking control algorithm based on a linear algebra theory; the Zhang element accurately linearizes a guided missile particle motion model by using a feedback linearization method, and a tracking guidance law is designed based on the linearization model and a linear quadratic form optimal regulator (LQR) theory; chengyang proposes a reentry guidance method combining offline ballistic optimization and online prediction based on roll angle parameterization, and achieves good effect.
Aiming at the problem of pneumatic parameter perturbation in the trajectory tracking guidance process, Zhao Kun and the like (Zhao Kun, Cao Dongqing, Huang Wen tiger, penetration defense missile maneuver, guidance and control integrated design, system engineering and electronic technology, 2018,40(9):2040 and 2047) design an active disturbance rejection controller, and the controller uses a second-order expansion state observer to estimate uncertain items. Yi Zhongyun (Yi Zhongyun, Zhongqiang, Zhang smiling face, variable structure guidance law and its realization, proceedings of naval aviation engineering academy, 2013(1): p.6-10.) considers the influence of various interferences and deviations into the gain coefficient of the guidance law, avoids the fussy design process, and is beneficial to the engineering realization. The drawbacks of the above methods are all based on the assumption that the upper bound of the interference is known. This direct estimate of the upper bound of interference by experience is obviously crude due to the unknown flight environment and the complexity of the missile motion. In addition, the missile tracking guidance method based on speed direction correction is proposed by the Zhongyangwei and the like (Zhongyangwei, Wang Liang, Zhang Hao, a speed direction correction-based trajectory tracking guidance method research [ J ]. ballistics report, 2017.), and the defect that the real-time performance of the guidance problem is not considered is overcome.
The real-time performance is the key dynamic performance of the aircraft, and the improvement of the real-time performance of the aircraft is an effective countercheck way for dealing with the techniques of attack and target maneuver penetration. For aircraft guidance control systems, the convergence speed of a closed-loop system is an important indicator of its real-time nature. However, at present, no trajectory tracking guidance method which can simultaneously meet the requirement of battlefield rapidity, restrain pneumatic parameter disturbance in control and improve the robustness of a system exists.
Disclosure of Invention
The invention aims to provide a trajectory tracking guidance method which can meet the requirement of battlefield rapidity, inhibit pneumatic parameter disturbance in control and improve the robustness of a system.
The technical solution for realizing the purpose of the invention is as follows: an adaptive rapid trajectory tracking guidance method comprises the following steps:
step 1, establishing a controlled gliding bomb longitudinal in-plane motion model;
step 2, establishing a relative kinematics model of the bullet eyes in a longitudinal plane;
step 3, acquiring the motion parameters of the projectile body through the projectile-loaded sensor, and calculating the visual line angular velocity information;
step 4, updating the track points;
step 5, designing a tracking guidance law according to the models in the step 1 and the step 2;
step 6, inputting a guidance instruction into a steering engine to control the angle of a rudder sheet;
and 7, repeating the steps 3 to 6 until the tracking is finished.
Further, the step 1 of establishing the controlled gliding missile longitudinal plane internal motion model specifically comprises the following steps:
the motion model in the longitudinal plane of the controlled gliding missile is as follows:
Figure BDA0002059863880000021
Figure BDA0002059863880000022
Figure BDA0002059863880000023
Figure BDA0002059863880000024
Figure BDA0002059863880000025
Figure BDA0002059863880000026
Figure BDA0002059863880000027
wherein V is the velocity of the gliding missile, theta is the azimuth of velocity,
Figure BDA0002059863880000028
for pitch angle of projectile body, omegazIs pitch angular velocity, kmIs the coefficient of elasticity, JzIs moment of inertia, Cn0Is the coefficient of kinetic moment, kneIs the rudder efficiency coefficient, deltazFor the elevator deflection angle, x and y are the coordinates of the projectile, α is the angle of attack, m is the mass of the projectile, t represents time, Fx、FyIs defined as:
Fx＝kFρV2Cx,Fy＝kFρV2Cy (8)
Cx＝Cx0+kxzδz,Cy＝Cy0+kyzδz (9)
in the formula kFIs the coefficient of elasticity, ρ represents the air density, Cx、CyRespectively the total drag coefficient and the total lift coefficient of the gliding missile, Cx0Is the coefficient of body resistance, Cy0Is the coefficient of body lift, kxz、kyzFor the efficiency factor, set
Figure BDA0002059863880000031
In the formula (I), the compound is shown in the specification,
Figure BDA0002059863880000032
is kxzEstimate of, Δ kxzIs kxzError of the estimated value of (c);
Figure BDA0002059863880000033
is kyzEstimate of, Δ kyzIs kyzError of the estimated value of (c).
Further, the establishment of the model of relative kinematics of the shots in the longitudinal plane in step 2 is as follows:
establishing a relative motion equation of the missile and the track point under a polar coordinate system:
Figure BDA0002059863880000034
Figure BDA0002059863880000035
in the formula, lambda is a visual angle, r is a relative distance between missile targets,
Figure BDA0002059863880000036
in order to be able to see the angular velocity of the line of sight,
Figure BDA0002059863880000037
representing the velocity of the relative motion between the missile and the target.
Further, in step 3, the movement parameters of the projectile are acquired through the projectile loading sensor, and the line-of-sight angular velocity information is calculated, specifically as follows:
acquiring the attitude, speed and position information of a projectile body through a projectile-loaded sensor, and calculating the line-of-sight angular speed
Figure BDA0002059863880000038
Information;
angular velocity of line of sight
Figure BDA0002059863880000039
The calculation formula of (2) is as follows:
Figure BDA00020598638800000310
in the formula (x)d、yd) The coordinates of the track point are shown, and the coordinates (x and y) are the coordinates of the projectile body.
Further, the track point updating in step 4 specifically includes the following steps:
calculating the relative distance r between missile targets:
Figure BDA00020598638800000311
wherein (x)d、yd) The coordinates of the track point are shown, and the coordinates (x and y) are the coordinates of the projectile body;
comparing the residual distance r with the set minimum residual tracking distance rminIf r is>rminIf not, the track point is switched to the next coordinate in the track point sequence to be used as the track point to be tracked.
Further, the tracking guidance law designed according to the models in step 1 and step 2 in step 5 is specifically as follows:
order to
Figure BDA00020598638800000312
To pair
Figure BDA00020598638800000313
And (5) obtaining a derivative:
Figure BDA0002059863880000041
defining:
Figure BDA0002059863880000042
wherein Z is an observed value; u denotes a control signal for controlling the operation of the motor,
Figure BDA0002059863880000051
is an intermediate function, and has no specific meaning;
design sliding mode variables are:
Figure BDA0002059863880000052
in the formula k1、k2To design parameters and satisfy k1＞0，k2＞0；
Designing a tracking guidance law based on self-adaptive rapid sliding mode control:
Figure BDA0002059863880000053
in the formula: p, q are odd numbers and p>q>0；k3、k4Is a design parameter;
Figure BDA0002059863880000054
the update law of (1) is as follows:
Figure BDA0002059863880000055
Figure BDA0002059863880000056
in the formula, N1、N2Are parameters to be designed.
Compared with the prior art, the invention has the following remarkable advantages: (1) the trajectory tracking problem is converted into a guidance problem aiming at a track point sequence, a guidance law is designed based on a rapid terminal sliding mode control method, disturbance of pneumatic parameters is processed by adopting a self-adaptive control method, and the robustness of the system is improved; (2) the tracking is fast, and the requirement of the rapidity of the battlefield is met.
Drawings
Fig. 1 is a schematic flow chart of the adaptive fast trajectory tracking guidance method of the present invention.
Fig. 2 is a trajectory graph of a trajectory during a scheme of tracking in a longitudinal plane of a gliding missile in an embodiment of the invention.
FIG. 3 is a graph of a track following distance error during the glide missile tracking process in an embodiment of the present invention.
Fig. 4 is a graph of the variation of the sliding mode variable in an embodiment of the present invention.
FIG. 5 is a control command graph during tracking guidance according to an embodiment of the present invention.
FIG. 6 shows an efficiency coefficient k according to an embodiment of the present inventionxeThe updated graph of (2).
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
With reference to fig. 1, the invention provides an adaptive fast trajectory tracking guidance method, which includes the following steps:
step 1, establishing a controlled gliding bomb longitudinal plane internal movement model, which comprises the following specific steps:
the motion model in the longitudinal plane of the controlled gliding missile is as follows:
Figure BDA0002059863880000061
Figure BDA0002059863880000062
Figure BDA0002059863880000063
Figure BDA0002059863880000064
Figure BDA0002059863880000065
Figure BDA0002059863880000066
Figure BDA0002059863880000067
wherein V is the velocity of the gliding missile, theta is the azimuth of velocity,
Figure BDA0002059863880000068
for pitch angle of projectile body, omegazIs pitch angular velocity, kmIs the coefficient of elasticity, JzIs moment of inertia, Cn0Is the coefficient of kinetic moment, kneIs the rudder efficiency coefficient, deltazFor the elevator deflection angle, x and y are the coordinates of the projectile, α is the angle of attack, m is the mass of the projectile, t represents time, Fx、FyIs defined as:
Fx＝kFρV2Cx,Fy＝kFρV2Cy (8)
Cx＝Cx0+kxzδz,Cy＝Cy0+kyzδz (9)
in the formula kFIs the coefficient of elasticity, ρ represents the air density, Cx、CyRespectively the total drag coefficient and the total lift coefficient of the gliding missile, Cx0Is the coefficient of body resistance, Cy0Is the coefficient of body lift, kxz、kyzFor the efficiency factor, set
Figure BDA0002059863880000069
In the formula (I), the compound is shown in the specification,
Figure BDA0002059863880000071
is kxzEstimate of, Δ kxzIs kxzError of the estimated value of (c);
Figure BDA0002059863880000072
is kyzEstimate of, Δ kyzIs kyzError of the estimated value of (c).
Step 2, establishing a relative motion model in a longitudinal plane of the bullet, which comprises the following specific steps:
establishing a relative motion equation of the missile and the track point under a polar coordinate system:
Figure BDA0002059863880000073
Figure BDA0002059863880000074
in the formula, lambda is a visual angle, r is a relative distance between missile targets,
Figure BDA0002059863880000075
in order to be able to see the angular velocity of the line of sight,
Figure BDA0002059863880000076
representing the velocity of the relative motion between the missile and the target.
Step 3, acquiring motion parameters of the projectile body through a missile-borne sensor, such as a geomagnetic and GPS combined navigation system, measuring the posture, the speed and the position of the projectile body, and calculating the visual line angular velocity information;
acquiring the attitude, speed and position information of a projectile body through a projectile-loaded sensor, and calculating the line-of-sight angular speed
Figure BDA0002059863880000077
Information;
angular velocity of line of sight
Figure BDA0002059863880000078
The calculation formula of (2) is as follows:
Figure BDA0002059863880000079
in the formula (x)d、yd) The coordinates of the track point are shown, and the coordinates (x and y) are the coordinates of the projectile body.
And 4, updating the track points, specifically as follows:
calculating the relative distance r between missile targets:
Figure BDA00020598638800000710
wherein (x)d、yd) The coordinates of the track point are shown, and the coordinates (x and y) are the coordinates of the projectile body;
comparing the residual distance r with the set minimum residual tracking distance rminIf r is>rminIf not, the track point is switched to the next coordinate in the track point sequence to be used as the track point to be tracked.
Step 5, the model according to the step 1 and the step 2 relates to a tracking guidance law, and the following steps are specifically carried out:
order to
Figure BDA00020598638800000711
To pair
Figure BDA00020598638800000712
And (5) obtaining a derivative:
Figure BDA0002059863880000081
defining:
Figure BDA0002059863880000082
wherein Z is an observed value; u denotes a control signal for controlling the operation of the motor,
Figure BDA0002059863880000091
is an intermediate function, and has no specific meaning;
design sliding mode variables are:
Figure BDA0002059863880000092
in the formula k1、k2To design parameters and satisfy k1＞0，k2＞0；
Designing a tracking guidance law based on self-adaptive rapid sliding mode control:
Figure BDA0002059863880000093
in the formula: p, q are odd numbers and p>q>0；k3、k4Is a design parameter;
Figure BDA0002059863880000094
the update law of (1) is as follows:
Figure BDA0002059863880000095
Figure BDA0002059863880000096
in the formula, N1、N2Are parameters to be designed.
Step 6, inputting a guidance instruction into a steering engine to control the angle of a rudder sheet;
and 7, repeating the steps 3 to 6 until the tracking is finished.
The invention is described in further detail below with reference to the figures and the embodiments.
Example 1
A simulation experiment of a scheme trajectory tracking stage of a gliding missile is designed by utilizing the self-adaptive rapid trajectory tracking guidance method. The initial conditions of the simulation are set as follows: the initial conditions are v 273m/s, θ 0 °,
Figure BDA0002059863880000097
x is 0m, y is 16000m, and the set parameter error is shown in table 1.
TABLE 1 simulation parameter variation table
Figure BDA0002059863880000101
Fig. 2 is a trajectory graph of a scheme trajectory in a longitudinal plane of a glide missile in a simulation process, and it can be known that the glide trajectory can better approach the scheme trajectory.
Fig. 3 is a tracking distance error curve diagram of a gliding missile in a scheme trajectory tracking process in a simulation process. As can be seen from FIG. 3, when the residual tracking distance meets the requirement, the system automatically switches track points, and the function of the tracking distance and the time changes linearly, thereby verifying the rapidity of the invention.
Fig. 4 is a graph of variation of sliding mode variables during simulation. As can be seen from fig. 4, the sliding mode variable always obtains a value of 0 at the beginning of track point tracking, and then keeps changing flat near 0. Meanwhile, at the tracking tail end, the track of the sliding mode variable s has a steep slope phenomenon deviating from 0 value, because the value r of the tracking tail end approaches to 0, and the deviation is small because the control law in the method is nonsingular.
FIG. 5 is a graph of the instructions during tracking guidance during simulation. As can be seen from fig. 5, the control command changes smoothly without chattering.
FIG. 6 shows the efficiency coefficient k in the simulation processxeGraph of the update situation of (1). As can be seen from fig. 6, the output of the adaptive controller is not estimated from the perturbation of the parameter, but is adjusted accordingly according to the variation of the parameter, so that the system as a whole reaches a steady state.

Claims (5)

1. An adaptive rapid trajectory tracking guidance method is characterized by comprising the following steps:
step 1, establishing a controlled gliding bomb longitudinal in-plane motion model;
step 2, establishing a relative kinematics model of the bullet eyes in a longitudinal plane;
step 3, acquiring the motion parameters of the projectile body through the projectile-loaded sensor, and calculating the visual line angular velocity information;
step 4, updating the track points;
step 5, designing a tracking guidance law according to the models in the step 1 and the step 2;
step 6, inputting a guidance instruction into a steering engine to control the angle of a rudder sheet;
7, repeating the steps 3 to 6 until the tracking is finished;
the method comprises the following steps that 1, a controlled gliding missile longitudinal plane internal movement model is established, and the method specifically comprises the following steps:
the motion model in the longitudinal plane of the controlled gliding missile is as follows:
Figure FDA0003312240550000011
Figure FDA0003312240550000012
Figure FDA0003312240550000013
Figure FDA0003312240550000014
Figure FDA0003312240550000015
Figure FDA0003312240550000016
Figure FDA0003312240550000017
wherein V is the velocity of the gliding missile, theta is the azimuth of velocity,
Figure FDA0003312240550000018
for pitch angle of projectile body, omegazIs pitch angular velocity, kmIs the coefficient of elasticity, JzIs moment of inertia, Cn0Is the coefficient of kinetic moment, kneIs the rudder efficiency coefficient, deltazFor the elevator deflection angle, x and y are the coordinates of the projectile, α is the angle of attack, m is the mass of the projectile, t represents time, Fx、FyIs defined as:
Fx＝kFρV2Cx,Fy＝kFρV2Cy (8)
Cx＝Cx0+kxzδz,Cy＝Cy0+kyzδz (9)
in the formula kFIs the coefficient of elasticity, ρ represents the air density, Cx、CyRespectively the total drag coefficient and the total lift coefficient of the gliding missile, Cx0Is the coefficient of body resistance, Cy0Is the coefficient of body lift, kxz、kyzFor the efficiency factor, set
Figure FDA0003312240550000021
In the formula (I), the compound is shown in the specification,
Figure FDA0003312240550000022
is kxzEstimate of, Δ kxzIs kxzError of the estimated value of (c);
Figure FDA0003312240550000023
is kyzEstimate of, Δ kyzIs kyzError of the estimated value of (c).
2. The adaptive rapid ballistic tracking guidance method according to claim 1, wherein the establishing of the bullet relative kinematics model in the longitudinal plane in step 2 is specifically as follows:
establishing a relative motion equation of the controlled gliding missile and the track point under a polar coordinate system:
Figure FDA0003312240550000024
Figure FDA0003312240550000025
wherein λ is the viewing angle, r is the relative distance between the controlled gliding missile and the target,
Figure FDA0003312240550000026
in order to be able to see the angular velocity of the line of sight,
Figure FDA0003312240550000027
representing the speed of relative motion between the controlled gliding missile and the target.
3. The adaptive rapid trajectory tracking guidance method according to claim 2, wherein the motion parameters of the projectile body are obtained by the projectile loading sensor in step 3, and the line-of-sight angular velocity information is calculated, specifically as follows:
acquiring the attitude, speed and position information of a projectile body through a projectile-loaded sensor, and calculating the line-of-sight angular speed
Figure FDA0003312240550000028
Information;
angular velocity of line of sight
Figure FDA0003312240550000029
The calculation formula of (2) is as follows:
Figure FDA00033122405500000210
in the formula (x)d、yd) The coordinates of the track point are shown, and the coordinates (x and y) are the coordinates of the projectile body.
4. The adaptive fast ballistic tracking guidance method according to claim 3, wherein the track point update of step 4 is as follows:
calculating the relative distance r between the controlled gliding missile and the target:
Figure FDA00033122405500000211
wherein (x)d、yd) The coordinates of the track point are shown, and the coordinates (x and y) are the coordinates of the projectile body;
comparing the residual distance r with the set minimum residual tracking distance rminIf r is>rminIf not, the track point is switched to the next coordinate in the track point sequence to be used as the track point to be tracked.
5. The adaptive rapid ballistic tracking guidance method according to claim 4, wherein the model design tracking guidance law according to step 1 and step 2 in step 5 is as follows:
order to
Figure FDA00033122405500000212
To pair
Figure FDA00033122405500000213
And (5) obtaining a derivative:
Figure FDA0003312240550000031
defining:
Figure FDA0003312240550000032
wherein Z is an observed value; u denotes a control signal for controlling the operation of the motor,
Figure FDA0003312240550000041
is an intermediate function, and has no specific meaning;
design sliding mode variables are:
Figure FDA0003312240550000042
in the formula k1、k2To design parameters and satisfy k1＞0，k2＞0；
Designing a tracking guidance law based on self-adaptive rapid sliding mode control:
Figure FDA0003312240550000043
in the formula: p, q are odd numbers and p>q>0；k3、k4Is a design parameter;
Figure FDA0003312240550000044
the update law of (1) is as follows:
Figure FDA0003312240550000045
Figure FDA0003312240550000046
in the formula, N1、N2Are parameters to be designed.
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