Terminal guidance strategy for hyperbola-like preposition angle remodeling based on relative distance

Abstract

The invention discloses a terminal guidance strategy for hyperbola-like preposed angle remodeling based on a relative distance. The terminal guidance strategy comprises the following steps: establishing a kinematic model of a missile for intercepting a stationary target in a two-dimensional plane; designing a guidance strategy based on a hyperbolic equation, solving geometric parameters of a hyperbolic curve according to initial conditions of a missile and a target, and obtaining an analytical equation of the guidance strategy about design parameters; and inversely solving parameters of different emission angles under the specified falling angle according to the kinematics relationship. According to the guidance strategy, equation constraint is carried out on preposed angle information, zero miss-target strike can be carried out while attack angle constraint is met, the tail end sight angle rate is converged to 0, guidance parameters are obtained through numerical integration calculation, linearization does not need to be carried out on a model, and the design of a guidance system is simplified. The applicability of the guidance system is improved, the design method is simple, and the applicability is high.

Description

Technical Field

[0001] The invention belongs to the field of missile guidance system design, and in particular relates to a terminal guidance strategy for reshaping a quasi-hyperbolic lead angle based on relative distance. Background Art

[0002] Guidance and control technology has a wide range of applications in the military and aerospace fields, such as missile guidance, UAV navigation, and satellite attitude control. Traditional guidance and control methods mainly focus on achieving zero miss distance, such as the famous proportional guidance method. However, for missiles with zero miss distance as the guidance mission, it is difficult to effectively hit the target as the target defense capability is upgraded. At this moment, it has become a key requirement to enhance the penetration capability by hitting the target at a specified angle. In addition, the viewing angle of the sensor used by the missile to detect the target in a real combat scenario cannot achieve 360° detection without blind spots. Therefore, it is necessary to design a guidance strategy with a terminal attack angle constraint and a limited viewing angle.

[0003] In recent years, guidance laws with attack angle constraints have been a hot topic of research at home and abroad, including terminal attack angle constraint guidance laws based on proportional guidance method considering bias, attack angle constraint guidance laws based on optimal theory considering the weight of remaining flight time cost, and terminal attack angle constraint guidance laws that can be controlled from any lead angle by designing non-singular sliding mode control, etc. These methods have solved the problem of impact angle to a certain extent, but there are still many challenges in practical applications, such as complex design, large amount of detection information, and some of them require linearization of missile kinematics, which is extremely inconvenient to practice in real engineering applications.

[0004] Obviously, it is very important to design a guidance strategy based on analytical equations with angle constraints and viewing angle constraints, which can simplify the design method, reduce the change of line of sight angle, and improve the applicability of the guidance system while overcoming the existing conservatism. Summary of the invention

[0005] The technical problem solved by the present invention is: with the substantial improvement of the defense capability of the target, the missile needs to attack the target at a certain angle, that is, it is necessary to design a guidance strategy with an attack angle constraint; and due to the influence of the field of view angle constraint, the lead angle of the missile under this guidance strategy cannot always exceed its maximum field of view angle. The present invention designs a terminal guidance strategy based on relative distance-based hyperbolic lead angle reshaping, and realizes the specified attack angle according to the initial condition information. Different from the existing methods, the method adopted by the present invention simplifies the design method while satisfying the missile field of view angle constraint and improving the applicability of the guidance system, and does not require linearization of the model.

[0006] To achieve the above technical objectives, the technical solution of the present invention is as follows: A terminal guidance strategy based on relative distance and hyperbolic lead angle reshaping includes the following steps: S1: Considering the two-dimensional plane where the missile and the stationary target are located as the attack plane, a kinematic model of the missile intercepting the stationary target in the attack plane is established; S2: A guidance strategy to design the lead angle equation as a hyperbolic-like expression with respect to time variation; S3: Solve the formulas for the relevant parameters of the hyperbolic expression based on the initial conditions of the missile and the target, including the distance from the origin to the displacement under the hyperbolic expression and the distance from the hyperbola vertex to the origin , get the parameter The analytical guidance strategy of is the ratio of the slope of the hyperbola asymptote to the parameter of the real semi-axis length; S4: Kinematic equations based on S1, with parameters obtained from S3 The analytical guidance strategy is based on the numerical integration method to inversely solve the parameters that change with the initial launch angle under the specified landing angle constraint. value.

[0007] Beneficial effects of the present invention: (1) The lead angle equation designed in the present invention is an attack angle constraint guidance strategy with a quasi-hyperbolic expression about time variation. It is an analytical equation design based on the missile lead angle information, involving a small amount of information and a simple method.

[0008] (2) The present invention adopts an analytical method to obtain the guidance parameters with respect to the parameters according to the initial conditions of the missile and the target. The analytical form does not require linearization of the model, and has a simple design and strong applicability.

[0009] (3) Since the field of view angle constraint is taken into consideration during the design, it is extremely practical and can achieve zero miss constraint, the terminal line of sight angular velocity converges to 0, and the specified attack angle requirement, thereby achieving better attack effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0011] Figure 1 It is a flow chart of the terminal guidance strategy of the hyperbolic lead angle reshaping based on relative distance of the present invention; Figure 2A schematic diagram of a two-dimensional attack plane for a missile to intercept a stationary target; Figure 3 It is a schematic diagram of a hyperbolic equation curve in the present invention; Figure 4 The figure is a simulation diagram of the guidance strategy of the present invention under different attack angle constraints, wherein (a) represents the flight trajectory of the missile, (b) represents the curve of the change of the missile lead angle with respect to the missile-target distance, (c) represents the curve of the change of the missile viewing angle, and (d) represents the curve of the change of the missile guidance instruction. DETAILED DESCRIPTION

[0012] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field belong to the scope of protection of the present invention.

[0013] The present invention discloses a terminal guidance strategy for reshaping a hyperbolic lead angle based on relative distance, comprising the following steps: establishing a kinematic model of a missile intercepting a stationary target in a two-dimensional plane; designing a guidance strategy based on a hyperbolic equation, solving the geometric parameters of the hyperbola according to the initial conditions of the missile and the target, and obtaining an analytical equation of the guidance strategy regarding the design parameters; inversely solving the parameters of different launch angles under a specified drop angle according to the kinematic relationship. The guidance strategy in the present invention uses equation constraints on the lead angle information, and can achieve zero miss-target strikes while satisfying the attack angle constraints, and the terminal line of sight angular rate converges to 0. The guidance parameters are obtained by numerical integration calculation, and there is no need to linearize the model, thereby simplifying the design of the guidance system. This invention improves the applicability of the guidance system, and the design method is simple and has strong applicability.

[0014] Figure 1 This is a flow chart of the terminal guidance strategy of the present invention based on the relative distance-based hyperbolic lead angle reshaping. Figure 1 Describe the specific process of this strategy. Figure 1 The specific implementation steps of this strategy are as follows: S1: Considering the two-dimensional plane where the missile and the stationary target are located as the attack plane, a kinematic model of the missile intercepting the stationary target in the attack plane is established.

[0015] like Figure 2 As shown, and Denote the missile and the target respectively. The kinematic model of the missile intercepting a stationary target in the attack plane is: (1) in, is the flight speed of the missile, is the lead angle of the missile, is the distance between the missile and the target, is the missile's ballistic inclination angle, From the missile's perspective, is the missile velocity tangential acceleration.

[0016] S2: A guidance strategy to design the lead angle equation as a hyperbolic-like expression with respect to time variation.

[0017] Lead Angle Based on Hyperbolic Expression The contour equation is: (2) in, are the parameters to be solved, which are the distance from the vertex of the hyperbola to the origin, the slope of the asymptote, and the distance from the displacement under the hyperbola to the origin, and they are all positive real numbers. is the initial missile-target distance, that is, the distance from the initial missile position to the stationary target.

[0018] To facilitate the solution, further transformation can be obtained: , Among them, the parameters .

[0019] The initial conditions of the missile and the target are as follows: The initial position of the missile is , the target location is , the missile's initial ballistic inclination is , the initial viewing angle is determined according to the following equation: .

[0020] S3: Solve the formulas for the relevant parameters of the hyperbolic expression based on the initial conditions of the missile and the target, including the distance from the origin to the displacement under the hyperbolic expression and the distance from the hyperbola vertex to the origin , get the parameter The analytical guidance strategy of It is the ratio of the slope of the hyperbola asymptote to the length parameter of the real semi-axis. The detailed implementation steps are as follows: Because the terminal lead angle needs to meet the following requirements: , And since the initial lead angle is known, we can get: , in, is the initial launch angle of the missile, It is the lead angle at the initial projectile-target distance.

[0021] From the above formula, we can get two groups of The equation is: (3) In addition, the positive and negative signs before the leading angle profile equation are determined by the sign of the emission angle. Here we consider the case when the emission angle is positive, such as Figure 3 shown.

[0022] The resulting guidance strategy is a The analytical guidance law of .

[0023] S4: Kinematic equations based on S1, with parameters obtained from S3 The analytical guidance strategy is based on the numerical integration method to solve the change of the initial launch angle under the specified landing angle constraint. value.

[0024] According to the transformation and integration of the first two equations of the kinematic equation (1), the following equation is obtained: , in, is the missile's designated landing angle, is the initial sight angle, which can be calculated based on the initial conditions.

[0025] Taylor expands the integral to N terms, and then uses the numerical integration method to iterate to calculate the specified angle of fall. Parameters for different emission angles The value of is expanded as follows: , in, is the corresponding order of terms in the summation, is the specified number of expansion items, is the first Bernoulli number, as shown below: , in, is the nth derivative of x, It is the dependent variable corresponding to this limit.

[0026] According to the numerical integration method, the inverse solution is obtained as the initial launch angle changes under the specified landing angle constraint. The process is as follows: Substitute all parameters into the above formula, where N=5. Since the expanded integral is difficult to solve, the gradient method is used here to find the integral from 0 to k. Due to monotonicity, the result of k from 0 to 1000 (when it is greater than this number, the angle does not change significantly) is in one-to-one correspondence with the k value. From this, it is calculated that when the result of the equation on the right is at the specified falling angle The corresponding k value is near .

[0027] It should be understood that all variables with dots in this article are derivatives of the variable, unless the derivative of the variable has actual physical meaning.

[0028] The following example of a missile intercepting a stationary target is used to illustrate the effectiveness of the method proposed in the present invention. The missile speed is 250 m / s, the missile initial position is (0, 0) km, the target position is (5, 0) km, the missile maximum overload limit is 10g, where g is the acceleration of gravity, and the missile maximum viewing angle constraint is 60 degrees (deg). When the initial viewing angle is specified as 60°, the attack angles are selected as: -60 degrees, -45 degrees, and -35 degrees. The parameters to be solved can be tried using the numerical integration method.

[0029] The interception simulation diagram for the stationary target is shown in the figure below: Figure 4 As shown, Figure 4 (a), (b), (c) and (d) in the figure respectively represent the missile's flight trajectory, the missile's lead angle change curve with respect to the missile-target distance, the missile's visual angle change curve, and the missile's guidance command change curve. Figure 4 It can be seen from (a) that the proposed method can effectively intercept stationary targets under the desired attack angle constraint.

[0030] According to the above analysis and description, it can be seen that the guidance strategy proposed in the present invention effectively realizes the requirements for attack angle constraints and viewing angle constraints. It does not require linearization of the model and has the characteristics of simple design method, high adaptability and flexibility, and low calculation amount.

[0031] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A terminal guidance strategy based on relative distance and hyperbolic lead angle reshaping, characterized in that: The following steps are involved: S1: Considering the two-dimensional plane where the missile and the stationary target are located as the attack plane, a kinematic model of the missile intercepting the stationary target in the attack plane is established; S2: A guidance strategy to design the lead angle equation as a hyperbolic-like expression with respect to time variation; S3: Solve the formulas for the relevant parameters of the hyperbolic expression based on the initial conditions of the missile and the target, including the distance from the origin to the displacement under the hyperbolic expression and the distance from the hyperbola vertex to the origin , get the parameter The analytical guidance strategy of is the ratio of the slope of the hyperbola asymptote to the parameter of the real semi-axis length; S4: Kinematic equations based on S1, with parameters obtained from S3 The analytical guidance strategy is based on the numerical integration method to inversely solve the parameters that change with the initial launch angle under the specified landing angle constraint. value.

2. The terminal guidance strategy of hyperbolic lead angle reshaping based on relative distance as claimed in claim 1, characterized in that: In step S1, the kinematic model of the missile intercepting a stationary target in the attack plane is: （1） in, is the flight speed of the missile, is the lead angle of the missile, is the distance between the missile and the target, is the missile's ballistic inclination angle, is the sight angle of the missile, is the missile velocity tangential acceleration.

3. The terminal guidance strategy of hyperbolic lead angle reshaping based on relative distance as claimed in claim 2, characterized in that: Step S2 includes: Lead angle based on hyperbolic expression The contour equation is: （2） in, are the parameters to be solved, which are the distance from the vertex of the hyperbola to the origin, the slope of the asymptote, and the distance from the displacement of the hyperbola to the origin, and they are all positive real numbers. is the initial missile-target distance, i.e., the distance from the initial missile position to the stationary target; Further transformation of formula (2) yields: ， Among them, the parameters .

4. The terminal guidance strategy of hyperbolic lead angle reshaping based on relative distance as claimed in claim 3, characterized in that: Step S3 includes: The distance from the origin to the displacement under the hyperbola and the distance from the hyperbola vertex to the origin The formula is: （3） in, is the initial launch angle of the missile, It is the lead angle at the initial projectile-target distance.

5. The terminal guidance strategy of hyperbolic lead angle reshaping based on relative distance as claimed in claim 4, characterized in that: In step S4, the following equation is obtained by transforming and integrating the first two equations of the kinematic equation (1): ， in, is the initial sight angle, is the missile’s designated fall angle; After Taylor expands the integral to N terms, the numerical integration method is used to iterate and calculate the specified angle of fall. Parameters for different emission angles The value of is expanded as follows: ， in, is the corresponding order of terms in the summation, is the specified number of expansion items, is the first Bernoulli number, as shown below: ， in, is the nth derivative of x, is to find the dependent variable corresponding to this limit; According to the numerical integration method, the parameters that change with the initial launch angle under the specified landing angle constraint are inversely solved. The process of calculating the value is as follows: Substitute all parameters into the above formula, take N=5, and use the gradient method to find the integral from 0 to k, thereby calculating the value when the result of the equation on the right side is at the specified falling angle The corresponding k value is near .

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