An advance correction guidance method based on trajectory perspective

Abstract

The present invention proposes an advance correction guidance method based on ballistic perspective, which can be applied to artillery shells with pulse engines located at non-center of mass. The dynamic and kinematic models of the projectile are constructed and numerically solved to obtain a theoretical trajectory. Based on the actual trajectory and the theoretical trajectory, the ballistic perspective can be obtained and advance correction can be performed, which can effectively achieve trajectory tracking.

Description

Technical Field

[0001] The invention belongs to the field of guidance control, and relates to a method for realizing artillery shell guidance through advance correction of ballistic visual angle based on ballistic information, and is suitable for artillery shell guidance control with a pulse engine located at a non-center of mass. Background Art

[0002] Guided artillery shells control the flight trajectory of the projectile by designing guidance control laws. To achieve the correction of the projectile's flight trajectory, it is necessary to use an actuator to apply a certain control force to the high-speed flying projectile. As an actuator, the pulse engine is easy to control and has low cost. It can provide the control force / torque required for projectile trajectory correction, establish a large angle of attack in a very short time, and quickly change the attitude and flight trajectory of the projectile to achieve the projectile's trajectory correction. In order to ensure the effect and real-time performance of trajectory correction, projectiles based on pulse force control often use trajectory tracking guidance methods. The core idea is to pre-bind the theoretical trajectory, calculate the position deviation between the real-time trajectory and the theoretical trajectory at the same time, and then control the ignition timing of the pulse engine so that the real-time trajectory keeps approaching the theoretical trajectory. However, when the pulse engine is located at the non-center of mass of the projectile, the pulse force changes the attitude of the projectile rather than the position. Therefore, how to achieve trajectory tracking control for projectiles with pulse engines located at non-centers of mass is an urgent problem to be solved. Summary of the invention

[0003] In view of the situation that the pulse engine is located at a non-center of mass of the projectile, the present invention proposes an advance correction guidance method based on the ballistic perspective, which performs advance correction with the ballistic perspective obtained by the real-time trajectory and theoretical trajectory to realize the correction of the projectile flight trajectory.

[0004] A method for advanced correction guidance based on trajectory perspective comprises the following steps:

[0005] Step S1, constructing a projectile dynamics model and a kinematics model;

[0006] Step S2, given the structural parameters of the projectile and the external environment parameters, the fourth-order Runge-Kutta method is used to numerically solve the dynamic and kinematic models of the projectile to obtain a theoretical trajectory;

[0007] Step S3: Obtain the trajectory angle of view based on the actual trajectory and the theoretical trajectory, and calculate the error angle and pulse action azimuth angle through the trajectory angle of view and the velocity vector, specifically:

[0008] Add the shooting angle and shooting speed errors to the theoretical trajectory to simulate the actual trajectory; if the current moment is t n , then the coordinates of the projectile in the actual trajectory are In t n The coordinates of the theoretical ballistic projectile at time +T are T represents the time of advance correction, and the line connecting the two gives the trajectory sight direction v e =(x e ,y e ,z e ),in:

[0009]

[0010] The above formula gives the trajectory angle of view, that is, the trajectory sight height angle θ e and the trajectory line of sight azimuth ψ e :

[0011]

[0012] The errors of altitude and azimuth are:

[0013]

[0014] Where θ a and ψ2 represent the velocity elevation angle and velocity azimuth, respectively;

[0015] According to the above formula, we can get the error angle σ and pulse action azimuth angle γ respectively. p :

[0016]

[0017]

[0018] Step S4: perform pulse thrust equivalence, and obtain the expressions of pulse direct force and torque based on the pulse action azimuth, specifically:

[0019] The actual pulse thrust is simulated by using rectangular pulses, that is, the pulse thrust generated by the engine ignition is regarded as a constant value F imp ;

[0020] The above impulse force F imp Decompose along the coordinate axis in the projectile axis coordinate system to obtain the impulse force and the torque it generates on the center of mass of the projectile, which are:

[0021]

[0022]

[0023] In the formula, F imp_ξ 、F imp_η and F imp_ζ are the representations of the impulse force in the elastic axis coordinate system, γ p Indicates the pulse action azimuth, L imp Indicates the distance of the pulse engine from the center of mass;

[0024] After coordinate transformation, the expression of the impulse force in the velocity coordinate system is:

[0025]

[0026] Where δ1 and δ2 represent the high and low angles of attack and the azimuth angle of attack respectively;

[0027] Step S5: Use the impulse force obtained in step S4 and the torque generated on the center of mass of the projectile to control the flight of the projectile and realize trajectory correction; and use the impulse force obtained in step S4 and the torque generated on the center of mass of the projectile to correct the external forces and external torques acting on the projectile in the dynamics and kinematics model of the projectile, thereby correcting the dynamics and kinematics model of the projectile, and then continue to execute steps S2-S5 to perform the next trajectory correction.

[0028] Preferably, in step S5, the trajectory of the projectile is corrected at a set time.

[0029] Preferably, in step S4:

[0030]

[0031] Where F(t) represents the actual pulse thrust, t0 represents the start time of pulse engine ignition, t1 represents the end time of pulse engine ignition, and τ represents the pulse width of equivalent pulse thrust.

[0032] The present invention has the following beneficial effects:

[0033] The present invention proposes an advance correction guidance method based on ballistic perspective, which can be applied to artillery shells with pulse engines located at non-center of mass. The dynamic and kinematic models of the projectile are constructed and numerically solved to obtain a theoretical trajectory. Based on the actual trajectory and the theoretical trajectory, the ballistic perspective can be obtained and advance correction can be performed, which can effectively achieve trajectory tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the theoretical trajectory of the projectile;

[0035] Figure 2 It is a schematic diagram of the trajectory sight direction and velocity direction;

[0036] Figure 3 Schematic diagram of ballistic perspective and velocity vector;

[0037] Figure 4 It is a schematic diagram of equivalent pulse thrust;

[0038] Figure 5 It is a schematic diagram of the pulse force action;

[0039] Figure 6This is a schematic diagram of the trajectory correction effect. DETAILED DESCRIPTION

[0040] In order to enable relevant technical personnel to better understand the content of the present invention, the technical solution of the present invention will be accurately described below in conjunction with the drawings in the application embodiments.

[0041] An advance correction guidance method based on trajectory perspective, the specific implementation steps are as follows:

[0042] S1: Construct the projectile dynamics and kinematics model. First, construct the projectile's center of mass dynamics and kinematics equations. The projectile's center of mass motion satisfies Newton's second law, that is:

[0043]

[0044] Where m represents the mass of the projectile, v represents the velocity vector of the projectile, F is the sum of the external force vectors acting on the projectile, and t represents the time variable. is the acceleration of the projectile to the ground coordinate system. If the above formula is expressed in the velocity coordinate system, it is the sum of the velocity change rate in the velocity system and the involved motion part:

[0045]

[0046] Where ω1 represents the angular velocity of the velocity coordinate system.

[0047] Projecting all the physical quantities in the above expressions into the velocity coordinate system, the projectile center of mass dynamic equation is as follows:

[0048]

[0049] In the formula, and represents the x, y, and z components of F; θ a represents the ballistic inclination angle, and ψ2 represents the ballistic deviation angle.

[0050] Projecting the velocity vector to the ground coordinate system gives the equation of motion of the projectile's center of mass:

[0051]

[0052] Next, we need to construct the dynamic and kinematic equations of the projectile around the center of mass. The motion of the projectile around the center of mass satisfies the momentum theorem, that is:

[0053]

[0054] Where M is the sum of all external torque vectors acting on the projectile, G is the momentum moment vector of the projectile. When writing the momentum moment theorem of the projectile in the projectile axis coordinate system, the involved motion of the projectile axis coordinate system should be considered, that is:

[0055]

[0056] Where ω2 represents the angular velocity of the elastic axis coordinate system.

[0057] Projecting the above physical quantities to the missile axis coordinate system and omitting a small number of product terms, we can obtain the following dynamic equations for the projectile moving around the center of mass:

[0058]

[0059] In the formula, ω ξ ,ω η and ω ζ are the expressions of the angular velocity of the projectile in the projectile axis coordinate system, M ξ 、M η and M ζ They are the representations of external torque in the elastic axis coordinate system, C represents the polar moment of inertia, and A represents the equatorial moment of inertia.

[0060] The equations of motion of the projectile about its center of mass are as follows:

[0061]

[0062] In the formula represents the pitch angle, represents the yaw angle, and γ represents the roll angle;

[0063] The above equations (3), (4), (7) and (8) constitute the projectile flight dynamics and kinematics model.

[0064] S2: Given the structural parameters of the projectile, such as mass, length and moment of inertia, as well as the external environmental parameters, such as atmospheric density and wind speed, the fourth-order Runge-Kutta method is used to numerically solve the dynamic and kinematic models of the projectile to obtain the theoretical trajectory.

[0065]

[0066] Where f represents a series of differential equations in the projectile flight dynamics and kinematics model, y k and k+1 They represent the values ​​of the physical quantities to be solved at the current moment and the next moment respectively. h can be set by yourself, which will affect the accuracy of the model solution. The theoretical trajectory is as follows: Figure 1 shown.

[0067] S3: The ballistic angle of view is obtained based on the actual trajectory and theoretical trajectory, and the pulse action azimuth is calculated through the ballistic angle of view and velocity vector.

[0068] In this example, the shooting angle and shooting speed errors are added to the theoretical trajectory to simulate the actual trajectory, such as Figure 2 As shown, to achieve tn +T, the actual trajectory can be close to the theoretical trajectory, that is, T represents the time of advance correction. If the current time is t n , then the coordinates of the projectile in the actual trajectory are In t n The coordinates of the theoretical ballistic projectile at time +T are Connect the two to get the direction of the trajectory:

[0069] v e =(x e ,y e ,z e ),in:

[0070]

[0071] From the above formula, we can get the trajectory angle of view, that is, the trajectory sight height angle and the trajectory sight azimuth angle:

[0072]

[0073] After the pulse engine is ignited, the projectile's posture can be changed, and then the direction of the projectile's velocity can be changed. The purpose is to make the velocity direction coincide with the trajectory line of sight. The pulse action azimuth will be calculated below, such as Figure 3 As shown, the errors of the elevation angle and azimuth angle are:

[0074]

[0075] Where θ a and ψ2 represent the velocity altitude angle and velocity azimuth, respectively.

[0076] According to the above formula, the error angle and pulse action azimuth angle can be obtained as follows:

[0077]

[0078]

[0079] S4: Perform pulse thrust equivalence and obtain the expressions of pulse direct force and torque based on the pulse action azimuth.

[0080] In order to simplify the calculation, only the reaction force generated by the pulse engine ignition is considered, and the lateral jet interference generated after the engine ignition is ignored, such as Figure 4 As shown in the figure, F(t) represents the curve of the actual thrust changing with time, and the effect produced is represented by impulse I. Because the time interval Δt is very small, based on the principle of equal impulse, the actual pulse thrust can be simulated by rectangular pulse, that is, the pulse thrust generated by the engine ignition is regarded as a constant F imp ,but:

[0081]

[0082] Where t0 represents the start time of pulse engine ignition, t1 represents the end time of pulse engine ignition, and τ represents the pulse width of equivalent pulse thrust.

[0083] Since the projectile is in a high-speed rotating state and the pulse engine is fixedly connected to it, when the pulse engine is ignited, the jet airflow that reacts to the projectile is distributed in a fan shape, such as Figure 5 As shown, F t is the impulse force at the initial moment, F t+τ is the pulse force at the end moment. Because the actual pulse force is equivalent to a rectangular function force and the action time is short, it can be considered that the angular velocity of the projectile remains unchanged. Therefore, its impulse I and the direction of the average force are the direction of the angular bisector of the fan-shaped jet airflow, which is consistent with the direction of the pulse force at the midpoint of the pulse action process.

[0084] By decomposing the above impulse force along the coordinate axis in the projectile axis coordinate system, we can obtain the impulse force and the torque it generates on the center of mass of the projectile:

[0085]

[0086]

[0087] In the formula, F imp_ξ 、F imp_η and F imp_ζ are the representations of the impulse force in the elastic axis coordinate system, γ p Indicates the pulse action azimuth, L imp represents the distance between the pulse engine and the center of mass,

[0088] From formula (3), we can know that the motion equations of the projectile center of mass are all expressed in the velocity coordinate system. Therefore, after coordinate transformation, the expression of the impulse control force in the velocity coordinate system is:

[0089]

[0090] Where δ1 and δ2 represent the altitude angle of attack and azimuth angle of attack respectively.

[0091] S5: Use the pulse direct force and torque obtained in step S4 to control the flight of the projectile to achieve advance correction guidance of the ballistic perspective; and use the pulse direct force and torque obtained in step S4 to correct the external forces and external torques acting on the projectile in the dynamics and kinematics model of the projectile, thereby correcting the dynamics and kinematics model of the projectile, and then continue to execute steps S2-S5 to perform the next ballistic perspective correction guidance.

[0092] In order to verify whether the guidance method proposed above is reliable, a fixed-time correction pulse control strategy can be adopted, that is, the trajectory of the projectile is corrected at certain fixed times.

[0093] See attached Figure 6 As shown, in the present invention, as the number of pulse force actions increases, the distance between the actual ballistic landing point and the theoretical ballistic landing point gradually becomes smaller, indicating that the advance correction guidance method based on the ballistic perspective can effectively reduce the deviation between the landing point and the target point, and the trajectory tracking effect is good.

Claims

1. An advance correction guidance method based on ballistic perspective, characterized in that: The steps include: Step S1, constructing a projectile dynamics model and a kinematics model; Step S2, given the structural parameters of the projectile and the external environment parameters, the fourth-order Runge-Kutta method is used to numerically solve the dynamic and kinematic models of the projectile to obtain a theoretical trajectory; Step S3: Obtain the trajectory angle of view based on the actual trajectory and the theoretical trajectory, and calculate the error angle and pulse action azimuth angle through the trajectory angle of view and the velocity vector, specifically: Add the shooting angle and shooting speed errors to the theoretical trajectory to simulate the actual trajectory; if the current moment is t n , then the coordinates of the projectile in the actual trajectory are In t n The coordinates of the theoretical ballistic projectile at time +T are T represents the time of advance correction, and the line connecting the two gives the trajectory sight direction v e =(x e ,y e ,z e ),in: The above formula gives the trajectory angle of view, that is, the trajectory sight height angle θ e and the trajectory line of sight azimuth ψ e : The errors of altitude and azimuth are: Where θ a and ψ2 represent the velocity elevation angle and velocity azimuth, respectively; According to the above formula, we can get the error angle σ and pulse action azimuth angle γ respectively. p : Step S4: perform pulse thrust equivalence, and obtain the expressions of pulse direct force and torque based on the pulse action azimuth, specifically: The actual pulse thrust is simulated by using rectangular pulses, that is, the pulse thrust generated by the engine ignition is regarded as a constant value F imp ; The above impulse force F imp Decompose along the coordinate axis in the projectile axis coordinate system to obtain the impulse force and the torque it generates on the center of mass of the projectile, which are: In the formula, F imp_ξ 、F imp_η and F imp_ζ are the representations of the impulse force in the elastic axis coordinate system, γ p Indicates the pulse action azimuth, L imp Indicates the distance of the pulse engine from the center of mass; After coordinate transformation, the expression of the impulse force in the velocity coordinate system is: Where δ1 and δ2 represent the high and low angles of attack and the azimuth angle of attack respectively; Step S5: Use the impulse force obtained in step S4 and the torque generated on the center of mass of the projectile to control the flight of the projectile and realize trajectory correction; and use the impulse force obtained in step S4 and the torque generated on the center of mass of the projectile to correct the external forces and external torques acting on the projectile in the dynamics and kinematics model of the projectile, thereby correcting the dynamics and kinematics model of the projectile, and then continue to execute steps S2-S5 to perform the next trajectory correction.

2. The advanced correction guidance method based on trajectory perspective as claimed in claim 1, characterized in that: In step S5, the trajectory of the projectile is corrected at a set time.

3. The advanced correction guidance method based on trajectory perspective as claimed in claim 1, characterized in that: In step S4: Where F(t) represents the actual pulse thrust, t0 represents the start time of pulse engine ignition, t1 represents the end time of pulse engine ignition, and τ represents the pulse width of equivalent pulse thrust.

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