CN111880581A - Finite time velocity tracking guidance law design method - Google Patents

Finite time velocity tracking guidance law design method Download PDF

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CN111880581A
CN111880581A CN202010803917.0A CN202010803917A CN111880581A CN 111880581 A CN111880581 A CN 111880581A CN 202010803917 A CN202010803917 A CN 202010803917A CN 111880581 A CN111880581 A CN 111880581A
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missile
guidance
guidance law
design
speed
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CN111880581B (en
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侯明哲
谭峰
石文锐
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Harbin Institute of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D13/00—Control of linear speed; Control of angular speed; Control of acceleration or deceleration, e.g. of a prime mover
    • G05D13/62—Control of linear speed; Control of angular speed; Control of acceleration or deceleration, e.g. of a prime mover characterised by the use of electric means, e.g. use of a tachometric dynamo, use of a transducer converting an electric value into a displacement

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Abstract

The invention discloses a finite time velocity tracking guidance law design method, which comprises the following steps: firstly, establishing a mathematical model of a guidance system; designing a finite time velocity tracking guidance law; step three, defining a design parameter adjusting method; and step four, checking the performance of the guidance law. The method designs a speed tracking guidance law based on a finite time control theory, and theoretically ensures that the speed tracking error angle of the missile is converged to zero in finite time, thereby ensuring that the missile accurately hits a target. The guidance law designed by the invention introduces a fractional power term, and according to the research result of the existing finite time control theory, the guidance law can have better anti-interference capability.

Description

Finite time velocity tracking guidance law design method
Technical Field
The invention belongs to the field of aerospace, relates to a speed tracking guidance law design method based on a finite time control theory, and particularly relates to a speed tracking guidance law design method capable of theoretically ensuring that a speed tracking error angle of a missile is converged to zero in finite time.
Background
Velocity tracking guidance is a guidance method widely used by many low-cost guided weapons. The basic principle is that the speed direction of the missile points to the target direction, namely the missile speed tracking error angle (namely the included angle between the speed direction and the sight line direction) is zero, so that the target is accurately hit. The traditional speed tracking guidance instruction is generally formed according to a proportional mode of a speed tracking error angle, and the method can not guarantee that the missile speed tracking error angle converges to zero theoretically. In recent years, velocity tracking guidance laws based on the Lyapunov asymptotic stability theory have appeared, but these results theoretically can only ensure that the missile velocity tracking error angle asymptotically converges to zero (i.e., the convergence time is infinite). Since the time of the last guided segment is limited, in order to achieve accurate target hit, it is objectively required that the missile velocity tracking error angle converges to zero within a limited time.
Disclosure of Invention
In order to overcome the defects of the conventional speed tracking guidance method, the invention provides a limited-time speed tracking guidance law design method. The method designs a speed tracking guidance law based on a finite time control theory, and theoretically ensures that the speed tracking error angle of the missile is converged to zero in finite time, thereby ensuring that the missile accurately hits a target.
The purpose of the invention is realized by the following technical scheme:
a finite time velocity tracking guidance law design method comprises the following steps:
step one, establishing a mathematical model of a guidance system:
assuming that the moving speeds of the missile and the target are unchanged, the mathematical model of the guidance system in the longitudinal plane is as follows:
Figure BDA0002628406670000021
Figure BDA0002628406670000022
Figure BDA0002628406670000023
wherein, the visual line inclination angle is shown, V is the speed of the missile, theta is the trajectory inclination angle of the missile, r is the missile-target relative distance, and V istRepresenting the speed of the target, thetatIndicating the trajectory inclination of the target, a indicating the missileAcceleration of (2);
step two, designing a finite time velocity tracking guidance law:
designing a missile guidance instruction according to a mathematical model of a guidance system to enable the missile speed tracking error angle lambda to be theta-to be converged to zero in a limited time, wherein: the missile guidance instructions are as follows:
Figure BDA0002628406670000024
wherein c and alpha are design parameters, c is more than 0, alpha is more than 0 and less than 1, sign (·) is a sign function, and theta0，0，λ0Initial values for θ, λ, respectively;
step three, defining a design parameter adjusting method:
the influence of the design parameters on the convergence speed of the missile velocity tracking error angle is quantitatively analyzed, and the convergence time of the missile velocity tracking error angle is as follows:
Figure BDA0002628406670000025
by increasing the design parameter c or decreasing the design parameter α, the speed tracking error angle convergence time can be decreased;
step four, checking the performance of the guidance law:
performing performance inspection of the guidance law by using a computer numerical computation simulation tool Matlab/Simulink, and finishing the design if the performance of the guidance law meets the requirements; otherwise, adjusting the design parameters of the guidance law, and re-simulating to carry out performance inspection.
Compared with the prior art, the invention has the following advantages:
1. the method can theoretically ensure that the speed tracking error angle of the missile converges to zero within a limited time, and the existing speed tracking guidance law can not theoretically ensure that the speed tracking error angle of the missile converges to zero or only ensure that the speed tracking error angle of the missile gradually converges to zero (the convergence time is infinite).
2. The guidance law designed by the invention introduces a fractional power term, and according to the research result of the existing finite time control theory, the guidance law can have better anti-interference capability.
Drawings
FIG. 1 is a flow chart of a finite time velocity tracking guidance law design according to the present invention;
FIG. 2 is a longitudinal plane intercept geometry;
FIG. 3 is a diagram showing a variation curve of the bullet-eye relative distance;
FIG. 4 is a variation curve of the acceleration command of the missile;
FIG. 5 is a velocity tracking error angle variation curve;
fig. 6 is a graph of the effect of design parameters on the convergence of velocity tracking error angles.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a finite time velocity tracking guidance law design method, as shown in figure 1, the method comprises the following steps:
step one, establishing a mathematical model of a guidance system:
the interception geometry in the longitudinal plane is shown in fig. 2, where M denotes the missile, T denotes the target, LOS denotes the line of sight, denotes the line of sight inclination, V denotes the speed of the missile, θ denotes the trajectory inclination of the missile, r denotes the missile-eye relative distance, V denotes the distance between the missile and the targettRepresenting the speed of the target, thetatRepresenting the inclination angle of the trajectory of the target, ignoring the change of the magnitude of the moving speed of the missile and the target, a representing the acceleration of the missile, atRepresenting the acceleration of the target, the mathematical model of the guidance system in the longitudinal plane is as follows:
Figure BDA0002628406670000041
Figure BDA0002628406670000042
Figure BDA0002628406670000043
secondly, designing a finite time velocity tracking guidance law:
the design task of the finite time velocity tracking guidance law can be described as follows: according to mathematical models (1) to (3) of a guidance system, guidance instructions (acceleration signals a) of the missile are designed to enable the missile speed tracking error angle (the included angle between the speed direction and the sight line direction) lambda to be theta to be converged to zero in a limited time.
In order to make λ converge to zero in a finite time, the guidance instructions are designed as follows:
Figure BDA0002628406670000044
wherein c and alpha are design parameters, c is more than 0, alpha is more than 0 and less than 1, sign (·) is a sign function, and theta0，0，λ0Respectively, as initial values of theta and lambda.
Thirdly, defining a design parameter adjusting method:
in order to clearly design the parameter adjustment method, the influence of the design parameters on the convergence speed of the speed tracking error angle needs to be quantitatively analyzed.
The velocity tracking error angle satisfies the following dynamic equation:
Figure BDA0002628406670000051
under the action of the guidance command (4), the system (5) becomes:
Figure BDA0002628406670000052
defining:
Figure BDA0002628406670000053
then:
Figure BDA0002628406670000054
wherein the content of the first and second substances,
Figure BDA0002628406670000055
from the above formula, VLλ will converge to zero within a finite time, the convergence time being:
Figure BDA0002628406670000056
it is apparent that increasing the design parameter c or decreasing the design parameter α can decrease the speed tracking error angle convergence time.
Fourthly, checking the performance of the guidance law:
in order to check the performance of the designed finite time velocity tracking guidance law, the method is applied to a non-linear guidance system of the missile in a longitudinal plane, and is carried out by means of common computer numerical calculation and simulation software such as Matlab/Simulink and the like. If the performance of the guidance law meets the requirements, the design is finished; otherwise, the design parameters of the guidance law need to be adjusted, and the performance is checked by re-simulation.
Set the target as a ground fixed target, Vt0m/s, 250m/s and initial value theta of trajectory inclination angle of missile0Initial value of bullet-mesh relative distance R of-10 DEG03000m, initial value of line of sight inclination0-30 °. And when the bullet-target relative distance is less than 1m, stopping the simulation. When the design parameter c is 0.5 and the α is 0.8, the missile-target relative distance variation curve is as shown in fig. 3, and the missile can accurately hit the target. The acceleration command curve of the missile is shown in figure 4. The velocity tracking error angle change curve of the missile is shown in figure 5, the finite time of the velocity tracking error angle of the missile is converged to zero, and the theoretical convergence time is Ts＝1/[c(1-α)]The simulation results are consistent with the theoretical results for 10 s. Fig. 6 further shows when the design parameters c-0.6, α -0.8 and c-0.6, α -In the velocity tracking error angle variation curve at 0.6, it can be seen that increasing the design parameter c or decreasing the design parameter α can decrease the velocity tracking error angle convergence time, which is also consistent with the theoretical analysis result.
The fifth step: and finishing the design.

Claims (2)

1. A finite time velocity tracking guidance law design method is characterized by comprising the following steps:
step one, establishing a mathematical model of a guidance system:
assuming that the moving speeds of the missile and the target are unchanged, the mathematical model of the guidance system in the longitudinal plane is as follows:
Figure FDA0002628406660000011
Figure FDA0002628406660000012
Figure FDA0002628406660000013
wherein, the visual line inclination angle is shown, V is the speed of the missile, theta is the trajectory inclination angle of the missile, r is the missile-target relative distance, and V istRepresenting the speed of the target, thetatRepresenting the trajectory inclination of the target, a representing the acceleration of the missile;
step two, designing a finite time velocity tracking guidance law:
designing a missile guidance instruction according to a mathematical model of a guidance system to enable the missile speed tracking error angle lambda to be theta-to be converged to zero in a limited time, wherein: the missile guidance instructions are as follows:
Figure FDA0002628406660000014
wherein c and alpha are design parameters, sign (·) is a sign function, and theta0，0，λ0Initial values for θ, λ, respectively;
step three, defining a design parameter adjusting method:
the influence of the design parameters on the convergence speed of the missile velocity tracking error angle is quantitatively analyzed, and the convergence time of the missile velocity tracking error angle is as follows:
Figure FDA0002628406660000015
by increasing the design parameter c or decreasing the design parameter α, the speed tracking error angle convergence time can be decreased;
step four, checking the performance of the guidance law:
performing performance inspection of the guidance law by using a computer numerical computation simulation tool Matlab/Simulink, and finishing the design if the performance of the guidance law meets the requirements; otherwise, adjusting the design parameters of the guidance law, and re-simulating to carry out performance inspection.
2. The finite-time velocity tracking guidance law design method according to claim 1, wherein c > 0,0 < α < 1.
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CN108416098A (en) * 2018-02-02 2018-08-17 北京航空航天大学 A kind of attack time constraint Design of Guidance Law method intercepting maneuvering target
CN109557814A (en) * 2018-12-04 2019-04-02 四川航天系统工程研究所 A kind of finite time Integral Sliding Mode Terminal Guidance Laws
CN109977613A (en) * 2019-04-19 2019-07-05 哈尔滨工业大学 A kind of adaptive sliding mode Design of Terminal Guidance Law method presetting adjustment time
CN110487132A (en) * 2019-08-30 2019-11-22 哈尔滨工业大学 A kind of angle restriction method of guidance based on nonsingular fast terminal sliding formwork control

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US6064332A (en) * 1994-04-26 2000-05-16 The United States Of America As Represented By The Secretary Of The Air Force Proportional Guidance (PROGUIDE) and Augmented Proportional Guidance (Augmented PROGUIDE)
CN104266546A (en) * 2014-09-22 2015-01-07 哈尔滨工业大学 Sight line based finite time convergence active defense guidance control method
CN108416098A (en) * 2018-02-02 2018-08-17 北京航空航天大学 A kind of attack time constraint Design of Guidance Law method intercepting maneuvering target
CN109557814A (en) * 2018-12-04 2019-04-02 四川航天系统工程研究所 A kind of finite time Integral Sliding Mode Terminal Guidance Laws
CN109977613A (en) * 2019-04-19 2019-07-05 哈尔滨工业大学 A kind of adaptive sliding mode Design of Terminal Guidance Law method presetting adjustment time
CN110487132A (en) * 2019-08-30 2019-11-22 哈尔滨工业大学 A kind of angle restriction method of guidance based on nonsingular fast terminal sliding formwork control

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丁世宏 等: "基于连续有限时间控制技术的导引律设计", 《宇航学报》 *
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