Quadratic polynomial angle constraint guidance method for field angle continuous attenuation

Abstract

The invention discloses a field angle continuous attenuation quadratic polynomial angle constraint guidance method, which comprises the following steps of: taking a two-dimensional plane where a missile and a static target are located as an attack plane, and establishing a mathematical model for intercepting the static target by the missile in the attack plane; according to the auxiliary variable based on the missile field angle and the quadratic polynomial based on the auxiliary variable, obtaining a relative distance profile of the missile and the stationary target; solving unknown parameters in the relative distance profile based on boundary conditions and attack angle constraints to obtain a semi-analytical guidance law; by limiting the missile view field angle from monotonically decreasing to 0 along with time, seeker view field angle constraint is achieved, and then an attack angle reachable domain is obtained. The method is a semi-analytical method based on the relative distance, does not need to linearize the model, does not need to perform repeated trial and error on guidance parameters, is suitable for guidance tasks with attack angle constraint and limited seeker view field, and is simple to use and high in applicability.

Description

Technical Field

[0001] The invention relates to the field of missile guidance system design, and in particular to a quadratic polynomial angle constraint guidance method with continuously attenuated field angle, which is mainly used for missile attack tasks at specific angles against stationary targets. Background Art

[0002] For the guidance system, its basic task is to generate appropriate guidance instructions to minimize the terminal miss. The guidance law design constrained by this indicator is relatively simple and the design method is mature. However, with the continuous improvement of the target defense capability, the terminal miss is no longer the only indicator to measure the effectiveness of the task completion. For targets such as tanks with composite armor and warships equipped with air defense systems, attacking at a specific attack angle can achieve greater attack effectiveness, such as attacking the relatively weak top armor of the tank. This type of application scenario puts forward new requirements for the guidance law design, that is, it is necessary to design a guidance method with attack angle constraints.

[0003] In order for the missile to lock onto the target during the flight of the missile, it is necessary to ensure that the missile's field of view angle is within the field of view of the seeker. In recent years, strapdown seekers have been widely used in engineering due to their simple structure and low cost. However, due to their narrow field of view, new guidance methods need to be designed for this type of missile weapon system. At present, the guidance law that satisfies both the attack angle constraint and the field of view constraint is a hot topic of research at home and abroad. Most of the existing guidance laws with attack angle constraints and field of view constraints require linearizing the relative motion model between the missile and the target, or are based on the remaining time estimation that may affect the stability of the system, which brings certain limitations to the designed guidance method and reduces the applicability of the method. Therefore, it is very necessary to design a guidance method with attack angle and field of view constraints, while overcoming the existing conservatism, simplifying the design method, and improving the applicability of the guidance system. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and design a guidance law with attack angle constraints and field of view angle constraints to achieve accurate strikes on stationary targets and ensure attack time constraints and field of view angle constraints. The design method of the present invention is a quadratic polynomial angle constraint guidance method with continuously decaying field of view angles, which can accurately hit targets without the need to linearize the model or to repeatedly try and match the guidance parameters. The guidance law is suitable for guidance tasks with attack angle constraints and limited field of view of the seeker, and the constraint on the attack angle is achieved by designing the parameters of the relative distance profile.

[0005] The present invention provides a quadratic polynomial angle constraint guidance method with continuous attenuation of field of view angle, comprising the following steps: S1: Considering the two-dimensional plane where the missile and the stationary target are located as the attack plane, a mathematical model for the missile to intercept the stationary target in the attack plane is established; S2: Obtain the relative distance profile between the missile and the stationary target based on the auxiliary variables based on the missile's field of view angle and the quadratic polynomial based on the auxiliary variables; S3: Solving the unknown parameters in the relative range profile obtained in step S2 based on the boundary conditions and the attack angle constraints to obtain a semi-analytical guidance law; S4: By limiting the missile field of view angle in step S2 to decrease monotonically to 0 over time, the field of view angle constraint of the seeker is realized, and then the attack angle reachable domain is obtained.

[0006] Beneficial effects of the present invention: (1) The semi-analytical guidance law based on quadratic polynomial designed in the present invention has a simple design method and strong engineering practicability, and can achieve the constraint requirements of attack angle, field of view angle and zero miss amount, thereby achieving better attack effect.

[0007] (2) The present invention adopts a method based on quadratic polynomials to construct a relative distance profile. According to the initial conditions of the missile and the target, a semi-analytical form of the guidance law can be obtained. There is no need to linearize the model or to repeatedly try out parameters. The present invention has the characteristics of simple design method and strong applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 It is a flow chart of the quadratic polynomial angle constraint guidance method with continuous attenuation of the field of view angle of the present invention; Figure 2 A schematic diagram of a two-dimensional attack plane of a missile intercepting a stationary target according to an embodiment of the present invention; Figure 3 Schematic diagram of simulation of the guidance method of an embodiment of the present invention under different attack angle constraints, wherein (a) represents the change trend of the flight trajectory of the missile, (b) represents the change trend of the normal acceleration of the missile, (c) represents the change trend of the relative distance profile between the missile and the target, and (d) represents the change trend of the sight angle of the missile; Figure 4 It is a schematic diagram of simulation of the change of the field of view angle under different attack angle constraints of the guidance method of an embodiment of the present invention. DETAILED DESCRIPTION

[0009] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0010] like Figure 1As shown, the process of the quadratic polynomial angle constraint guidance method with continuous attenuation of the field of view angle of the present invention includes the following steps: first, considering the two-dimensional plane where the missile and the stationary target are located as the attack plane, a mathematical model of the missile intercepting the stationary target in the attack plane is established; secondly, auxiliary variables based on the field of view angle are designed, and a quadratic polynomial based on the auxiliary variables is designed to obtain a relative distance profile; then, the unknown parameters in the relative distance profile are solved based on the boundary conditions and the attack angle constraint to obtain a semi-analytical guidance law; finally, by limiting the field of view angle of the missile to decrease monotonically to 0 over time, the field of view angle constraint of the seeker is realized, and then the attack angle reachable domain is obtained. From the above steps, it can be seen that the present invention adopts a method based on a quadratic polynomial to construct a relative distance profile. According to the initial conditions of the missile and the target, a semi-analytical form of the guidance law can be obtained, and there is no need to linearize the model or repeatedly try and match the parameters, which has the characteristics of simple design method and strong applicability.

[0011] It should be understood that all variables superscripted with “·” in the present invention are derivatives of the variable, unless the derivative of the variable has actual physical meaning.

[0012] The quadratic polynomial angle constraint guidance method with continuous attenuation of the field of view angle of the present invention specifically comprises the following steps: S1: Considering the two-dimensional plane where the missile and the stationary target are located as the attack plane, a mathematical model for the missile to intercept the stationary target within the attack plane is established.

[0013] like Figure 2 As shown in the figure, M and T represent the missile and the stationary target respectively. According to the kinematic and dynamic relationship between the missile and the stationary target in the two-dimensional plane, the mathematical model of the missile intercepting the stationary target in the attack plane is:

[0014] (1) in, is the flight speed of the missile, is the normal acceleration of the missile, which also needs to be designed into the guidance law. is the missile's position information, is the missile's ballistic inclination angle, is the relative distance between the missile and the stationary target, is the sight angle of the missile, is the missile’s field of view.

[0015] S2: Based on the auxiliary variables based on the missile's field of view angle and the quadratic polynomial based on the auxiliary variables, the relative distance profile between the missile and the stationary target is obtained.

[0016] The design of the relative distance profile is as follows: (2) in, , is an auxiliary variable based on the missile field of view, is non-negative ( When it is less than 0, the design method is the same). Parameters that need to be designed.

[0017] S3: Solve the unknown parameters in the relative range profile obtained in step S2 based on the boundary conditions and attack angle constraints to obtain a semi-analytical guidance law, where the boundary conditions refer to the values ​​of the relative range profile at the beginning and end of the guidance process, and the attack angle constraint refers to the line of sight angle of the missile at the interception time. Equal to the expected angle of attack , the semi-analytical guidance law refers to The specific process is as follows: First, the boundary conditions of the relative distance profile are set as follows: (3) in, When the missile is launched The initial value of , The initial field of view angle when the missile is launched, and the initial field of view angle is smaller than the maximum field of view angle of the missile seeker , is the initial relative distance, is the relative distance at the moment of interception.

[0018] Combining equation (2) and equation (3), we can get: (4) Find the value of formula (4) about The first-order derivative of , we get: (5) From formula (1) and formula (2), we can get: (6) Substituting equation (4) and equation (5) into equation (6), we can obtain: (7) Define the expected angle of attack as , the initial sight angle is , for formula (7) from arrive Integrate and we get: (8) parameter It can be obtained by numerically solving formula (8). From formula (3), we can know that , , the parameters Substituting the value of into the solution, we can get the parameter The value of .

[0019] From formula (1), we can get: (9) Will Substituting into formula (9) we can get: (10) Formula (5) and Substituting into formula (10), we get: (11) (12) S4: By limiting the missile field of view angle in step S2 to decrease monotonically to 0 over time, the seeker field of view angle constraint is realized, and then the attack angle reachable domain is obtained. The seeker field of view angle constraint means that the maximum value of the missile field of view angle is , the attack angle reachable domain refers to the expected attack angle The specific process is as follows: The seeker field of view constraint is satisfied by limiting the missile's field of view to decrease monotonically to 0 over time, that is: (13) in, is the actual impact moment, is the initial field of view angle smaller than the field of view angle constraint, is the derivative of the missile’s field of view, is the final field of view.

[0020] Combining equation (1), equation (5) and equation (13), we get: (14) Right now: (15) Note that when When (8) appears singular, Substitute into equation (7) and from arrive Integrate and we get: (16) Find the value of formula (8) about The first-order derivative of , we get: (17) And there are: (18) (19) (20) (twenty one) in, , , and They are Boundary values ​​under different conditions.

[0021] Combining equation (16) to equation (21), we get: (twenty two) in, for The safe value of and The parameters are The minimum and maximum values ​​of , .

[0022] Get the desired angle of attack The reachable domain is as follows: (twenty three) in, is the minimum value of the attack angle reachable domain, is the maximum value of the attack angle reachable range. and They are: , .

[0023] Based on the above analysis, when the desired attack angle constraint is selected within the range of equation (23), the guidance law shown in equation (11) can be used to achieve precise strikes on stationary targets while satisfying the attack angle and seeker field of view constraints.

[0024] 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 300 m / s, the missile initial position is (0, 0) km, the target position is (10, 0) km, and the missile maximum acceleration limit is 100 m / s. 2 The maximum field of view of the missile seeker is limited to 60 degrees (deg). The initial field of view of the missile needs to be set to less than 60 degrees so that the field of view of the missile meets the field of view constraint during the entire guidance process. The initial ballistic inclination of the missile is 50 degrees (deg). The interception simulation for this ground stationary target is as follows: Figure 3 As shown, the attack angle constraints of this embodiment are selected as: -55 degrees, -70 degrees, -85 degrees, and -100 degrees. Figure 3(a), (b), (c), and (d) represent the missile's flight trajectory, the change trend of the missile's normal acceleration, the missile-target relative distance profile, and the missile's line-of-sight angle change trend, respectively. Figure 4 Indicates the change trend of the missile's field of view. Figure 3 , Figure 4 It can be seen that the guidance method proposed in the present invention can enable the missile to hit the target at a desired attack angle and ensure that the field of view angle decreases monotonically to 0 over time during the flight, thereby realizing the field of view constraint of the seeker.

[0025] In summary, the guidance method proposed in the present invention effectively realizes the requirements for attack angle constraints and field of view angle constraints. It does not need to linearize the model or repeatedly try out the model parameters. It has the characteristics of simple design method and strong adaptability.

[0026] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, several modifications and improvements can be made without departing from the creative concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A quadratic polynomial angle constraint guidance method with continuous attenuation of field of view angle, 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 mathematical model for the missile to intercept the stationary target in the attack plane is established; S2: Obtain the relative distance profile between the missile and the stationary target based on the auxiliary variables based on the missile's field of view angle and the quadratic polynomial based on the auxiliary variables; S3: Solving the unknown parameters in the relative range profile obtained in step S2 based on the boundary conditions and the attack angle constraints to obtain a semi-analytical guidance law; S4: By limiting the missile field of view angle in step S2 to decrease monotonically to 0 over time, the field of view angle constraint of the seeker is realized, and then the attack angle reachable domain is obtained.

2. The quadratic polynomial angle constraint guidance method with continuous attenuation of the field of view angle according to claim 1 is characterized in that: In step S1, the mathematical model of the missile intercepting a stationary target in the attack plane is: （1） in, is the flight speed of the missile, is the normal acceleration of the missile, is the missile's position information, is the missile's ballistic inclination angle, is the relative distance between the missile and the stationary target, is the sight angle of the missile, is the missile’s field of view.

3. The quadratic polynomial angle constraint guidance method with continuous attenuation of the field of view angle according to claim 2 is characterized in that: The relative distance profile in step S2 is as follows: （2） in, is an auxiliary variable based on the missile's field of view, and is non-negative, Parameters that need to be designed.

4. The quadratic polynomial angle constraint guidance method with continuous attenuation of the field of view angle according to claim 3 is characterized in that: The semi-analytical guidance law in step S3 is as follows: （11） （12） in, is the flight speed of the missile, is the normal acceleration of the missile, is the derivative of the sight angle with respect to time, is the relative distance between the missile and the stationary target, is the initial relative distance between the missile and the stationary target, is the initial value of the auxiliary variable.

5. The quadratic polynomial angle constraint guidance method with continuous attenuation of the field of view angle according to claim 4, characterized in that: Attack angle in step S4 The reachable domains are as follows: （23） in, and They are: ， ， in, is the initial sight angle, is the minimum value of the attack angle reachable domain, is the maximum value of the attack angle reachable range.

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