A trajectory design method for radar terminal guidance artillery projectile

Abstract

The present application belongs to the technical field of guided shell trajectory optimization, and particularly relates to a trajectory design method suitable for radar terminal guided shells, which is suitable for a shell with high initial velocity, small overload capacity and radar seeker to achieve large angle of fall attack on short range targets, and is used for providing good trajectory conditions for the radar seeker to capture targets, and increasing the angle of fall to improve the damage performance. The method takes the "anti-inclined plane attack" as the guiding ideology, comprehensively considers the overload capacity of the shell, the pitch angle at the handover time of the mid-terminal guidance and the angle of fall when hitting the target, and uses the GPOPS optimization toolbox of matlab as the design tool to optimize the design of the minimum range trajectory, which can effectively improve the minimum range capacity of the terminal guided shell, widen the attack range of the shell, avoid the problem of small terminal angle of fall and unfavorable radar seeker capture conditions caused by the conventional low stretch trajectory, and effectively improve the combat effectiveness of the weapon system, and provide a reference for the trajectory optimization design of similar terminal guided shells, and has a wide application space.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of guided shell trajectory optimization, and particularly relates to a trajectory design method suitable for radar terminal guided shells. BACKGROUND

[0002] As an important unit of modern artillery weapon systems, guided shells have the important trends of long-range attack, rapid launching and precise terminal guidance. In engineering, aerodynamic drag reduction, rocket boosting, glide range extension and trajectory optimization are important technical means to improve the long-range attack capability of guided shells. Single full charge launching provides a constant launching initial speed for the shell, which can effectively reduce the workload of firing table compilation, and has important significance for simplifying the launching process and improving the launching efficiency. Through radar seeker and precise guidance control technology, radar terminal guided shells can realize all-weather detection and precise attack on moving targets, which makes the follow-up development of artillery weapon systems have broader space for improvement and application prospects.

[0003] The minimum range is one of the overall indicators of terminal guided shells. Single full charge launching provides the maximum initial speed for the shell, thereby reducing the minimum range capability and attack range of the shell. Currently, low-stretch trajectories are mainly used in engineering to ensure that the minimum range of terminal guided shells meets the overall indicator requirements of the weapon system. For terminal guided shells, the main defects of low-stretch trajectories are two-fold. First, small drop angles can greatly reduce the damage effect of the shell, and even cause the risk of "skip shot" and inability to cause effective damage to the target. Second, the radar seeker adopts a full active detection system, which has certain requirements for the pitch angle of the shell. The small pitch angle of the low-stretch trajectory is not conducive to the scanning and tracking of the radar seeker on the target. Therefore, using the traditional trajectory design method, the radar terminal guided shell is difficult to play the advantage of the weapon system at the minimum range, and a trajectory design method needs to be researched for the minimum range to solve the above problems. SUMMARY

[0004] (I) Technical problems to be solved

[0005] The technical problem to be solved by the present application is: in view of the demand of radar terminal guided shells to attack small-range targets, how to improve the minimum range capability of the shell, broaden the attack range, and at the same time make the shell have a specific pitch angle when handing over from midcourse guidance to terminal guidance, create favorable conditions for the radar seeker to scan and search for targets, and increase the drop angle when the terminal guided shell hits the target, so as to improve the damage effect of the weapon system.

[0006] (II) Technical solutions

[0007] To solve the above technical problems, the present application provides a trajectory design method suitable for radar terminal guided artillery shell, in which the whole trajectory from the artillery shell launching to hitting the target is divided into bore acceleration section, uncontrolled flight section, mid-guided flight section and terminal-guided flight section, and the flight section mass center motion equation set is as follows:

[0008]

[0009] In the above formula, x and y are the position coordinates of the artillery shell in the launching system, V is the flight speed, θ is the speed inclination angle, S is the reference area of the projectile body, q is the dynamic pressure, m is the mass of the projectile body, C x , C y are the drag coefficient and lift coefficient of the projectile body, and α is the attack angle.

[0010] The design method of each section trajectory is as follows:

[0011] (1) Bore acceleration section

[0012] The bore acceleration section provides the initial flight speed V0 and the firing angle θ0 for the artillery shell, and the initial speed is fixed when the full charge is launched. Considering the condition limitations such as the overload capacity of the projectile body, the artillery shell is launched at a large firing angle.

[0013] (2) Uncontrolled flight section

[0014] The rudder wing mechanism of the artillery shell is folded inside the projectile body, and the projectile body is in an uncontrolled flight state. After a specific time t0, the rudder wing mechanism is controlled to open, and the uncontrolled flight section ends. The characteristic of this trajectory section is that the projectile body flies at zero attack angle and is only affected by gravity and aerodynamic drag, and the flight characteristics are described by the following formula:

[0015] α = 0, 0 ≤ t < t0 (2)

[0016] (3) Mid-guided section

[0017] The purpose of the mid-guided section is to make the artillery shell use the projectile body overload to realize the "over 90°" turn through the action of the rudder wing mechanism, so as to approach the target in a small range, and at the same time, the projectile body has a specific pitch angle when the mid-terminal guidance is handed over. When the radar seeker captures the target at time t f , the mid-guided section ends. The trajectory design method optimizes the design of the mid-guided section trajectory, and the specific design steps are as follows:

[0018] a) Determine the optimization target

[0019] Considering that the terminal guided artillery shell flies without power and has a small wing area, the available overload is limited, and it is necessary to fly at the smallest possible attack angle during flight, therefore, the following integral type optimization target function is selected:

[0020]

[0021] b) Determine the end-point constraints

[0022] In order to meet the certain missile-target relationship at the handover of midcourse guidance and terminal guidance under the minimum range condition, and to hit the target with a larger impact angle, the terminal position x f , y f and the velocity inclination angle θ f of the midcourse guidance segment need to be constrained. The terminal constraints are designed as follows:

[0023] Determine the range X t of the gun projectile, and according to the target scanning requirements of the radar seeker and the capture distance R b , the velocity inclination angle θ f at the terminal, i.e., at the handover of midcourse guidance and terminal guidance, is proposed. The terminal position of the gun projectile is calculated as follows:

[0024]

[0025] Through the above design, fixed scanning conditions are created for the radar seeker;

[0026] c) Determine the state constraints

[0027] Take V, θ, x, y as state variables, and α as the control variable. The state parameters need to always satisfy the continuous constraints of equation group (1);

[0028] The state variables and control variables at the terminal of the uncontrolled segment and the initial terminal of the midcourse guidance segment need to be equal to ensure the continuity of the system variables;

[0029] d) Determine the control quantity constraints

[0030] Considering that the overload capacity of the projectile body is limited, and in order to reduce the index requirements of the rudder, the following constraints are added to the control quantity α:

[0031] |α|<α max , t1≤t<t f (5)

[0032] The above optimization process can be summarized as follows: in the period of t1≤t<t f , the optimal α is sought to transfer the state variables from the state at t1 to the terminal state;

[0033] e) Use optimization tools to solve the optimization problem

[0034] Based on the GPOPS nonlinear optimization toolbox, the midcourse guidance trajectory is optimized. This toolbox is based on the Gauss / Radau pseudospectral method and the hp adaptive discretization grid updating technology, which can convert continuous optimization problems into discrete optimization problems, with small computational load and high solution accuracy.

[0035] (4) Terminal guidance section

[0036] After the radar seeker captures the target, the terminal guided shell is guided to fly based on the improved proportional guidance method, and has a large impact angle when hitting the target.

[0037] In the trajectory design method, the small range adopts single full charge and large angle of emission, the medium guidance section realizes rapid turning by using large overload, and the medium-terminal guidance transfer section adopts a trajectory scheme with fixed capture condition, and the trajectory is optimized and designed based on the GPOPS nonlinear optimization toolbox.

[0038] In the trajectory design method, single full charge emission provides a fixed initial speed of emission.

[0039] In the trajectory design method, by determining the terminal constraint condition of the medium guidance section, a good and stable capture condition is created for the radar seeker, and the impact angle when hitting the target is increased.

[0040] In the trajectory design method, by using the optimization objective function and the control variable constraint, the available overload requirement of the projectile body is met, and the shell stall is avoided.

[0041] In the trajectory design method, the method fully learns from the design idea of the "reverse slope attack", adopts the overall scheme of large angle of emission + large overload turning + fixed capture condition, comprehensively considers the overload capacity of the shell, the pitch angle when the medium-terminal guidance transfer is performed, and the impact angle when hitting the target, optimizes the small range trajectory, and realizes the solution of the optimization problem by taking the GPOPS optimization toolbox of matlab as a design tool, so that a nominal trajectory meeting the actual requirements is obtained.

[0042] (Three) beneficial effects

[0043] Compared with the prior art, the present application takes a certain type of radar terminal guided shell as the application background, and describes a trajectory design method suitable for a radar terminal guided shell.

[0044] The method adopts large angle of emission to form a curved trajectory with large height and long flight time, ensures that the control system has a certain working space, fully utilizes the gravity and the control system force to make the shell realize "more than 90°" turning, and the scheme can effectively improve the minimum range capability of the terminal guided shell. According to the range of the terminal guided shell and the capture condition of the radar seeker, the position and angle constraint of the end point of the medium guidance section of the shell are calculated, so that the radar seeker always has a relatively fixed missile-target relationship when searching for the target, the capture difficulty of the radar seeker is reduced, the impact angle is increased, the combat effectiveness of the weapon system is effectively improved, and reference is provided for the trajectory optimization design of similar terminal guided shells.

[0045] Figures 3-5 This indicates that the trajectory optimization results meet the design requirements. Attached Figure Description

[0046] Figure 1 This is a schematic diagram comparing the trajectory of the ballistics designed in this invention with that of a conventional low-extension ballistics.

[0047] Figure 2 This is a schematic diagram of the ballistic design principle of the present invention.

[0048] Figure 3 This is a schematic diagram of the optimized ballistic trajectory curve.

[0049] Figure 4 This is a schematic diagram of the optimized angle of attack curve.

[0050] Figure 5 This is a schematic diagram of the optimized velocity tilt angle curve.

[0051] Figure 6 This is a schematic diagram of a reverse slope ballistic trajectory. Detailed Implementation

[0052] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0053] To address the aforementioned technical problems, this invention provides a ballistic design method suitable for radar-guided projectiles, such as... Figure 1 As shown, in the ballistic design method, the entire trajectory from projectile launch to target impact is divided into an in-bore acceleration phase, an unguided flight phase, a mid-course guidance phase, and a terminal guidance phase. The equations of motion for the center of mass during the flight phase are as follows:

[0054]

[0055] In the above formula, x and y are the position coordinates of the projectile in the launching system, V is the flight velocity, θ is the velocity inclination angle, S is the reference area of ​​the projectile, q is the dynamic pressure, m is the mass of the projectile, and C is the velocity angle. x C y Let α be the drag coefficient and lift coefficient of the projectile, and α be the angle of attack.

[0056] Combination Figure 2 The design methods for each segment of the ballistic trajectory are illustrated below with specific design examples:

[0057] (1) In-bore acceleration section

[0058] The in-bore acceleration section provides the projectile with an initial flight velocity V0 and a firing angle θ0. When firing with a full charge, the initial velocity is fixed. Considering the limitations of the projectile's overload capacity and other conditions, a large firing angle is adopted.

[0059] The initial flight velocity V0=900 m / s and the angle of departure θ0are optimized;

[0060] (2) Uncontrolled flight segment

[0061] The rudder mechanism of the shell is folded inside the shell body, and the shell body is in an uncontrolled flight state. After uncontrolled flight for a specific time t0, the rudder mechanism is controlled to open, and the uncontrolled flight segment ends. The characteristic of this trajectory is that the shell body flies at zero angle of attack and is only affected by gravity and aerodynamic drag. The flight characteristics are described by the following formula:

[0062] α=0, 0≤t<t0 (2)

[0063] (3) Mid-guidance segment

[0064] The purpose of the mid-guidance segment is to make the shell use the shell body overload to achieve a "more than 90°" turn through the action of the rudder mechanism, so as to approach the target within a small range, and at the same time, the shell body has a specific pitch angle when the mid and terminal guidance shifts. When the radar seeker captures the target at time t f , the mid-guidance segment ends. The trajectory design method optimizes the design of the mid-guidance segment trajectory, and the specific design steps are as follows:

[0065] a) Determine the optimization target

[0066] Considering that the terminal guidance shell flies without power and has a small wing area, it can only provide limited available overload, and needs to fly at the smallest possible angle of attack during flight, therefore, the following integral type optimization target function is selected:

[0067]

[0068] b) Determine the endpoint constraint condition

[0069] In order to meet certain shell-target relationships at the time of mid-terminal guidance shift under the condition of minimum range, and to land at a larger angle of fall, the terminal position x f , y f and the velocity inclination angle θ f are constrained, and the terminal constraints are designed as follows:

[0070] Determine the shell range X t , and according to the target scanning requirements and capture distance R b of the radar seeker, the velocity inclination angle θ f at the terminal, i.e. the mid-terminal guidance shift, is proposed, and the terminal shell position is calculated as follows:

[0071]

[0072] Through the above design, fixed scanning conditions are created for the radar seeker;

[0073] Example set range X t = 20km, R b = 7km, θ f = -140°;

[0074] c) Determine state constraints

[0075] Take V, θ, x, y as state variables, and α as control variable, where the state parameters need to always satisfy the continuous constraints of equation group (1);

[0076] The state variables and control variables of the terminal of the uncontrolled segment and the initial terminal of the midcourse guidance segment need to be equal to ensure the continuity of the system variables;

[0077] d) Determine control quantity constraints

[0078] Considering that the overload capacity of the projectile is limited, and in order to reduce the requirements of the rudder, the following constraints are added to the control quantity α:

[0079] |α| < αmax, t1≤t < tf (5)

[0080] The above optimization process is summarized as follows: in the period of t1≤t < t f , the optimal α is obtained, so that the state variables are transferred from the state at t1 to the terminal state; where t1, t f are unconstrained and can be optimized;

[0081] In order to ensure that the artillery shell does not stall, the example sets α max = 7°;

[0082] e) Use optimization tools to solve the optimization problem

[0083] Based on the GPOPS nonlinear optimization toolbox, the midcourse guidance trajectory is optimized. This toolbox is based on Gauss / Radau pseudospectral method and hp adaptive discrete grid updating technology, which can convert continuous optimization problem into discrete optimization problem, with small calculation amount and high solving precision;

[0084] (4) Terminal guidance segment

[0085] After the radar seeker captures the target, the terminal guidance artillery shell is guided to fly based on the improved proportional guidance method, and has a large impact angle when hitting the target.

[0086] The example sets the real target position: X t ' = 18.5km, Y t ' = 0km;

[0087] The trajectory design method comprises the following steps: determining a single full charge launch to provide a fixed launch initial speed; determining a terminal constraint condition of a mid-guidance section to create a good and stable capture condition for a radar seeker and increase a falling angle when hitting a target; and determining an optimization objective function and a control variable constraint to meet a body available overload requirement and avoid a cannonball stall.

[0088] The trajectory design method comprises the following steps: determining a single full charge launch to provide a fixed launch initial speed; determining a terminal constraint condition of a mid-guidance section to create a good and stable capture condition for a radar seeker and increase a falling angle when hitting a target; and determining an optimization objective function and a control variable constraint to meet a body available overload requirement and avoid a cannonball stall.

[0089] The trajectory design method comprises the following steps: determining a single full charge launch to provide a fixed launch initial speed; determining a terminal constraint condition of a mid-guidance section to create a good and stable capture condition for a radar seeker and increase a falling angle when hitting a target; and determining an optimization objective function and a control variable constraint to meet a body available overload requirement and avoid a cannonball stall.

[0090] The trajectory design method comprises the following steps: determining a single full charge launch to provide a fixed launch initial speed; determining a terminal constraint condition of a mid-guidance section to create a good and stable capture condition for a radar seeker and increase a falling angle when hitting a target; and determining an optimization objective function and a control variable constraint to meet a body available overload requirement and avoid a cannonball stall.

[0091] The trajectory design method comprises the following steps: determining a single full charge launch to provide a fixed launch initial speed; determining a terminal constraint condition of a mid-guidance section to create a good and stable capture condition for a radar seeker and increase a falling angle when hitting a target; and determining an optimization objective function and a control variable constraint to meet a body available overload requirement and avoid a cannonball stall.

[0092] In summary, the present application belongs to the technical field of guided cannonball trajectory optimization, and particularly relates to a trajectory design method suitable for a radar terminal guidance cannonball, which is suitable for a cannonball with high initial speed, small overload capacity and a radar seeker, and is used for realizing large falling angle attack on a near range target, mainly for providing a good trajectory condition for the radar seeker to capture a target and increasing the falling angle to improve damage performance. The method takes the anti-inclined surface attack as a guiding ideology, comprehensively considers the overload capacity of the cannonball, the pitch angle when handing over the mid-terminal guidance and the falling angle when hitting a target, and optimizes the minimum range trajectory by taking the GPOPS optimization toolbox of matlab as a design tool, so that the minimum range capacity of the terminal guidance cannonball can be effectively improved, the attack range of the cannonball is widened, the problems of small terminal falling angle and unfavorable capture condition of the radar seeker caused by the conventional low stretch trajectory are avoided, the combat effectiveness of the weapon system is effectively improved, the trajectory optimization design of the similar terminal guidance cannonball is provided with reference, and the method has a wide application space.

[0093] The preferred embodiments of the present application are described above, and it should be noted that, for those skilled in the art, some improvements and modifications can be made without departing from the technical principles of the present application, and these improvements and modifications should also be considered as the protection scope of the present application.

Claims

1. A method of trajectory design suitable for radar terminal guided artillery projectiles, characterized in that, In the trajectory design method, the whole trajectory is divided into an in-bore acceleration segment, an uncontrolled flight segment, a mid-guidance flight segment, and a terminal guidance flight segment, and the equations of motion of the center of mass in the flight segments are as follows: （1） In the above formulae, is the position coordinate of the shell under the launch system, is the flight velocity, is the velocity inclination angle, is the reference area of the shell body, is the dynamic pressure, is the mass of the shell body, is the drag coefficient and the lift coefficient of the shell body, is the attack angle; The design method of each segment trajectory is as follows: (1) The in-bore acceleration segment The in-bore acceleration section provides an initial flight velocity for the projectile and the angle of fire , the initial velocity is fixed when full charge is used, and the projectile is fired at a large angle of fire considering the limitation of the overload capacity of the projectile body (2) The uncontrolled flight segment The fin mechanism of the shell is folded inside the body, the body is in uncontrolled flight, uncontrolled flight to a certain time Afterwards, the fin mechanism is controlled to open, the uncontrolled flight segment ends; the characteristic of this trajectory is that the body flies at zero angle of attack, only subject to gravity and aerodynamic drag, the flight characteristics are described by the following formula: （2） (3) The mid-guidance segment The purpose of the middle guidance section is to make the shell achieve "over 90°" turn by the action of the rudder wing mechanism, so as to approach the target in a small range, and to make the shell have a specific pitch angle when the middle and terminal guidance sections hand over, and fly to the moment when the radar seeker captures the target The trajectory design method optimizes the design of the middle guidance section trajectory, and the specific design steps are as follows: a) Determining an optimization target Considering that the terminal guidance projectile flies without power and has a small wing area, the available overload provided is limited, and the projectile needs to fly at a small attack angle during flight, therefore, the following integral optimization target function is selected; （3） b) Determining endpoint constraint conditions In order to meet the certain missile-target relation at the handover of midcourse guidance and terminal guidance under the minimum range condition and to hit the target with a larger impact angle, the terminal position and the velocity inclination angle of the midcourse guidance segment need to be constrained The terminal constraint is designed in the following method:​ Determining the range of a shell And according to the radar seeker target scanning requirements and capture distance The speed and angle of inclination of the terminal end guidance handover are proposed The terminal shell position is calculated by the following method: （4） Through the above design, fixed scanning conditions are created for the radar seeker; c) Determining state constraints With as state variables, as control variables, where the state parameters need to satisfy the continuous constraints of equation set (1) at all times; The state variables and control variables at the end of the uncontrolled segment and the beginning of the mid-guidance segment need to be equal to ensure the continuity of system variables; d) Determining control variable constraints Considering the overload capacity of the missile body is limited, and in order to reduce the index requirements of the steering engine, the control variable Add the following constraints: （5） In the above optimization process, at the time period, the optimal state variable is obtained by transferring the state at the time to the terminal state; e) Solving the optimization problem by using an optimization tool The mid-guidance segment trajectory is optimized based on the GPOPS nonlinear optimization toolbox, which can convert a continuous optimization problem into a discrete optimization problem based on the Gauss / Radau pseudospectral method and the hp adaptive discrete grid updating technology, and has a small amount of calculation and high solving accuracy; (4) The terminal guidance segment After the radar seeker captures the target, the terminal guidance projectile flies based on the improved proportional guidance method, and has a large impact angle when hitting the target.

2. The trajectory design method for radar terminal guided projectiles as claimed in claim 1, wherein, In the trajectory design method, small range is achieved by single full charge and large angle of firing, the mid-guidance segment uses large overload to achieve rapid turning, and the mid-terminal guidance transfer segment adopts a trajectory scheme with fixed capture conditions, and the trajectory is optimized based on the GPOPS nonlinear optimization toolbox.

3. The trajectory design method for radar terminal guided projectiles as claimed in claim 2, wherein, In the trajectory design method, single full charge firing provides a fixed initial firing speed.

4. The trajectory design method for radar terminal guided projectiles of claim 3, wherein In the trajectory design method, by determining the terminal constraint conditions of the mid-guidance segment, good and stable capture conditions are created for the radar seeker, and the impact angle when hitting the target is increased.

5. The trajectory design method for radar terminal guided projectiles as recited in claim 4, wherein, In the trajectory design method, the optimization target function and the control variable constraints are used to meet the available overload requirements of the projectile body and avoid projectile stall.

6. The trajectory design method for radar terminal guided projectiles of claim 4, wherein In the trajectory design method, large angle firing is adopted to form a curved trajectory with large height and long flight time, to ensure that the control system has a certain working space, and to fully utilize the gravity and control system force to make the projectile achieve a "more than 90°" turn.

7. The trajectory design method for radar terminal guided projectiles as recited in claim 4, wherein, The trajectory design method can effectively improve the minimum range capability of the terminal guidance projectile.

8. The trajectory design method for radar terminal guided projectiles of claim 4, wherein, The trajectory design method calculates the position and angle constraints of the end point of the mid-guidance segment of the projectile according to the range of the terminal guidance projectile and the capture conditions of the radar seeker, so as to ensure that the radar seeker always has a relatively fixed missile-target relationship when searching for the target, and to reduce the capture difficulty of the radar seeker. The trajectory design method can effectively improve the minimum range capability of the terminal guidance projectile. The trajectory design method calculates the position and angle constraints of the end point of the mid-guidance segment of the projectile according to the range of the terminal guidance projectile and the capture conditions of the radar seeker, so as to ensure that the radar seeker always has a relatively fixed missile-target relationship when searching for the target, and to reduce the capture difficulty of the radar seeker.

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