Ballistic trajectory design method suitable for radar terminal guided projectile

Abstract

The invention belongs to the technical field of guided projectile trajectory optimization, and particularly relates to a trajectory design method suitable for a radar terminal guided projectile, which is suitable for a projectile with high initial speed and small overload capacity and carrying a radar seeker to realize large-angle-of-fall attack on a near-range target and is used for providing a good trajectory condition for the radar seeker to capture the target. Meanwhile, the falling angle is increased to improve the damage performance. According to the method, an anti-slope attack is taken as a guiding idea, the overload capacity of the projectile, the pitch angle during middle-terminal guidance shift change and the falling angle during target hitting are comprehensively considered, a matlab GPOPS optimization tool box is taken as a design tool to carry out optimization design on the minimum range trajectory, the minimum range capacity of the terminal guidance projectile can be effectively improved, the attack range of the projectile can be widened, and the target attack rate of the terminal guidance projectile can be improved. The problems that the tail end falling angle is small and the capturing condition of a radar seeker is unfavorable due to a conventional low-stretching trajectory are solved, the combat effectiveness of a weapon system is powerfully improved, a reference is provided for trajectory optimization design of similar terminal guided projectiles, and the method has a wide application space.

Description

Technical Field

[0001] The invention belongs to the technical field of guided projectile trajectory optimization, and in particular relates to a trajectory design method suitable for radar terminally guided projectiles. Background Art

[0002] As an important unit of modern artillery weapon systems, guided artillery shells will have long-range strikes, rapid launches, and precise terminal guidance as important trends in their future development. In engineering, aerodynamic drag reduction, rocket boost, glide range extension, and trajectory optimization are important technical means to improve the long-range strike capability of guided artillery shells; the use of a single full charge launch provides a constant initial launch velocity for the shells, which can effectively reduce the workload of firing table compilation, and is also of great significance in simplifying the launch process and improving the launch efficiency; through radar seekers and precise guidance control technology, radar terminally guided artillery shells can achieve all-weather detection and precise strikes on moving targets, giving the subsequent development of artillery weapon systems a broader space for improvement and application prospects.

[0003] Minimum range is one of the overall indicators of terminally guided artillery shells. Single full charge firing provides the maximum initial velocity for the projectile, thereby reducing the minimum range capability and attack range of the projectile. At present, the main method used in engineering is to launch at a small firing angle to form a low-reach trajectory to ensure that the minimum range of the terminally guided artillery shell meets the overall indicator requirements of the weapon system. For terminally guided artillery shells, the main defects of the low-reach trajectory are two aspects. First, the small falling angle will greatly reduce the damage effect of the projectile, and even produce the risk of "bouncing" and failing to cause effective damage to the target; second, the radar seeker adopts a fully active detection system, which has certain requirements for the elevation angle of the projectile body. The small elevation angle of the low-reach trajectory is not conducive to the radar seeker scanning and tracking the target. Therefore, using the traditional trajectory design method, it is difficult for radar terminally guided artillery shells to play the advantages of the weapon system at the minimum range. It is necessary to study a trajectory design method for the minimum range to solve the above problems. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] The technical problem to be solved by the present invention is: in view of the demand for radar terminally guided projectiles to attack short-range targets, how to improve the minimum range capability of the projectiles, broaden the attack range, and make the projectile body have a specific pitch angle when the mid-terminal guidance is handed over, so as to create favorable conditions for the radar seeker to scan and search for targets, and at the same time increase the landing angle of the terminally guided projectile when hitting the target, so as to improve the damage effect of the weapon system.

[0006] (II) Technical solution

[0007] In order to solve the above technical problems, the present invention provides a trajectory design method suitable for radar terminally guided artillery shells. In the trajectory design method, from the launch of the artillery shell to hitting the target, the entire trajectory is divided into an in-bore acceleration section, an uncontrolled flight section, a mid-guidance flight section, and a terminal guidance flight section. The center of mass motion equations of the flight section are as follows:

[0008]

[0009] In the above formula, x and y are the position coordinates of the projectile in the launch system, V is the flight speed, 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 x , C y are the drag coefficient and lift coefficient of the projectile, α is the angle of attack;

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

[0011] (1) In-bore acceleration section

[0012] The acceleration section in the bore provides the projectile with an initial flight velocity V0 and a firing angle θ0. When firing with full charge, the initial velocity is fixed. Considering the limitations of the projectile's overload capacity and other conditions, a large firing angle is used.

[0013] (2) Uncontrolled flight

[0014] The rudder and wing mechanism of the projectile is folded inside the projectile body, and the projectile body is in an uncontrolled flight state. After the uncontrolled flight reaches a specific time t0, the rudder and wing mechanism is controlled to open, and the uncontrolled flight section ends; the characteristic of this section of the trajectory is that the projectile body flies without an angle of attack and is only affected by gravity and aerodynamic resistance. The flight characteristics are described by the following formula:

[0015] α=0, 0≤t<t0 (2)

[0016] (3) Mid-range guidance section

[0017] The purpose of the mid-range guidance section is to use the rudder mechanism to make the projectile use the overload of the projectile to achieve a "90°" turn, so as to approach the target within a short range. At the same time, when the mid-range and terminal guidance are handed over, the projectile has a specific pitch angle and flies to the time t when the radar seeker captures the target. f When , the mid-range guidance stage ends; the trajectory design method optimizes the trajectory of the mid-range guidance stage, and the specific design steps are as follows:

[0018] a) Determine the optimization goal

[0019] Considering that the terminally guided projectile flies without power and has a small wing area, the available overload it can provide is limited and it needs to fly at the smallest possible angle of attack during the flight. Therefore, the following integral optimization objective function is selected;

[0020]

[0021] b) Determine the endpoint constraints

[0022] In order to meet a certain missile-target relationship during the handover of mid-terminal guidance under the condition of minimum range and to hit the target at a larger angle, it is necessary to center the terminal position x of the guidance section. f ,y f and velocity inclination angle θ f The terminal constraints are designed as follows:

[0023] Determine the shell range X t , and according to the radar seeker target scanning requirements and capture distance R b The terminal speed angle θ for the mid-terminal guidance handover is proposed f , the terminal shell position is calculated as follows:

[0024]

[0025] Through the above design, a fixed scanning condition is created for the radar seeker;

[0026] c) Determine state constraints

[0027] Take V, θ, x, y as state variables and α as control variable, where the state parameters must always satisfy the continuity constraints of equation group (1);

[0028] The state variables and control variables at the end of the uncontrolled section and the beginning of the intermediate guidance section must be equal to ensure the continuity of system variables;

[0029] d) Determine the control quantity constraints

[0030] Considering the limited overload capacity of the projectile and to reduce the index requirements of the servo, the following constraints are added to the control amount α:

[0031] |α|<α max , t1≤t<t f (5)

[0032] The above optimization process can be summarized as follows: f During the time period, find the optimal α to transfer the state variable from the state at time t1 to the terminal state;

[0033] e) Use optimization tools to solve optimization problems

[0034] The trajectory of the mid-range guidance section is optimized based on the GPOPS nonlinear optimization toolbox. The toolbox is based on the Gauss / Radau pseudo-spectral method and the hp adaptive discrete grid update technology, which can transform the continuous optimization problem into a discrete optimization problem, with a small amount of calculation and high solution accuracy.

[0035] (4) Terminal guidance

[0036] After the radar seeker captures the target, the terminally guided projectile is guided based on the improved proportional guidance method and has a larger fall angle when hitting the target.

[0037] Among them, in the trajectory design method, a single full charge and large firing angle are used for short range, a large overload is used to achieve rapid turning in the mid-range guidance section, and a ballistic scheme with fixed capture conditions is adopted in the mid-terminal guidance handover section. The trajectory is optimized based on the GPOPS nonlinear optimization toolbox.

[0038] Wherein, in the trajectory design method, a single full charge launch provides a fixed initial launch velocity.

[0039] Among them, in the trajectory design method, by determining the terminal constraint conditions of the mid-range guidance section, good and stable capture conditions are created for the radar seeker, and the landing angle when hitting the target is increased.

[0040] Among them, in the trajectory design method, the optimization objective function and the control variable constraints are used to meet the available overload requirements of the projectile and avoid the stall of the projectile.

[0041] Among them, in the trajectory design method, this method fully draws on the design idea of ​​"reverse slope attack", adopts the overall plan of large shooting angle launch + large overload turning + fixed capture conditions, comprehensively considers the overload capacity of the artillery shell, the pitch angle during the handover of mid-terminal guidance and the angle of fall when hitting the target, and optimizes the design of the short-range trajectory. The GPOPS optimization toolbox of Matlab is used as the design tool to solve the optimization problem and obtain a nominal trajectory that meets actual needs.

[0042] (III) Beneficial effects

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

[0044] The method adopts a large firing angle to form a curved trajectory with a high altitude and a long flight time, ensures that the control system has a certain working space, and makes full use of gravity and the control system force to make the shell turn "more than 90 degrees". This scheme can effectively improve the minimum range capability of the terminally guided shell. According to the range of the terminally guided shell and the capture conditions of the radar seeker, the position of the end point of the guidance section in the shell and the angle constraint are calculated, so as to ensure that the radar seeker always has a relatively fixed projectile-target relationship when searching for the target, reduce the capture difficulty of the radar seeker, and at the same time help to increase the target landing angle, which effectively improves the combat effectiveness of the weapon system and provides a reference for the trajectory optimization design of similar terminally guided shells.

[0045] Figure 3 to Figure 5 It shows that the trajectory optimization results meet the design requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic diagram comparing the trajectory of the designed ballistics of the present invention and the conventional low-reaching ballistic trajectory.

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

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

[0049] Figure 4 It is a schematic diagram of the angle of attack curve obtained by optimization.

[0050] Figure 5 It is a schematic diagram of the optimized velocity inclination curve.

[0051] Figure 6 It is a schematic diagram of reverse slope trajectory. DETAILED DESCRIPTION

[0052] In order to make the purpose, content, and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below in conjunction with the accompanying drawings and examples.

[0053] In order to solve the above technical problems, the present invention provides a trajectory design method suitable for radar terminally guided projectiles, such as Figure 1 As shown, in the trajectory design method, from the launch of the shell to the hitting of the target, the entire trajectory is divided into an in-bore acceleration section, an uncontrolled flight section, a mid-range guidance flight section, and a terminal guidance flight section. The center of mass motion equations of the flight section are as follows:

[0054]

[0055] In the above formula, x and y are the position coordinates of the projectile in the launch system, V is the flight speed, 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 x , C y are the drag coefficient and lift coefficient of the projectile, α is the angle of attack;

[0056] Combination Figure 2 The design methods of each trajectory are explained with specific design examples as follows:

[0057] (1) In-bore acceleration section

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

[0059] Set the initial flight speed V0 = 900m / s, and the shooting angle θ0 is the value to be optimized;

[0060] (2) Uncontrolled flight

[0061] The rudder and wing mechanism of the projectile is folded inside the projectile body, and the projectile body is in an uncontrolled flight state. After the uncontrolled flight reaches a specific time t0, the rudder and wing mechanism is controlled to open, and the uncontrolled flight section ends; the characteristic of this section of the trajectory is that the projectile body flies without an angle of attack and is only affected by gravity and aerodynamic resistance. The flight characteristics are described by the following formula:

[0062] α=0, 0≤t<t0 (2)

[0063] (3) Mid-range guidance section

[0064] The purpose of the mid-range guidance section is to use the rudder mechanism to make the projectile use the overload of the projectile to achieve a "90°" turn, so as to approach the target within a short range. At the same time, when the mid-range and terminal guidance are handed over, the projectile has a specific pitch angle and flies to the time t when the radar seeker captures the target. f When , the mid-range guidance stage ends; the trajectory design method optimizes the trajectory of the mid-range guidance stage, and the specific design steps are as follows:

[0065] a) Determine the optimization goal

[0066] Considering that the terminally guided projectile flies without power and has a small wing area, the available overload it can provide is limited and it needs to fly at the smallest possible angle of attack during the flight. Therefore, the following integral optimization objective function is selected;

[0067]

[0068] b) Determine the endpoint constraints

[0069] In order to meet a certain missile-target relationship during the handover of mid-terminal guidance under the condition of minimum range and to hit the target at a larger angle, it is necessary to center the terminal position x of the guidance section. f ,y f and velocity inclination angle θ f The terminal constraints are designed as follows:

[0070] Determine the shell range X t , and according to the radar seeker target scanning requirements and capture distance R b The terminal speed angle θ for the mid-terminal guidance handover is proposed f , the terminal shell position is calculated as follows:

[0071]

[0072] Through the above design, a fixed scanning condition is created for the radar seeker;

[0073] Example setting 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 must always satisfy the continuity constraints of equation group (1);

[0076] The state variables and control variables at the end of the uncontrolled section and the beginning of the intermediate guidance section must be equal to ensure the continuity of system variables;

[0077] d) Determine the control quantity constraints

[0078] Considering the limited overload capacity of the projectile and to reduce the index requirements of the servo, the following constraints are added to the control amount α:

[0079] |α|<αmax, t1≤t<tf (5)

[0080] The above optimization process can be summarized as follows: f During the time period, find the optimal α to transfer the state variable from the state at time t1 to the terminal state; where t1, t f No constraints, can be optimized;

[0081] To ensure that the projectile does not stall, the sample sets α max =7°;

[0082] e) Use optimization tools to solve optimization problems

[0083] The trajectory of the mid-range guidance section is optimized based on the GPOPS nonlinear optimization toolbox. The toolbox is based on the Gauss / Radau pseudo-spectral method and the hp adaptive discrete grid update technology, which can transform the continuous optimization problem into a discrete optimization problem, with a small amount of calculation and high solution accuracy.

[0084] (4) Terminal guidance

[0085] After the radar seeker captures the target, the terminally guided projectile is guided based on the improved proportional guidance method and has a larger fall angle when hitting the target.

[0086] Example setting real target position: X t ′=18.5km,Y t ′=0km;

[0087] Among them, in the trajectory design method, a single full charge and large firing angle are used for short range, a large overload is used to achieve rapid turning in the mid-range guidance section, and a ballistic scheme with fixed capture conditions is adopted in the mid-terminal guidance handover section. The trajectory is optimized based on the GPOPS nonlinear optimization toolbox.

[0088] Wherein, in the trajectory design method, a single full charge launch provides a fixed initial launch velocity.

[0089] Among them, in the trajectory design method, by determining the terminal constraint conditions of the mid-range guidance section, good and stable capture conditions are created for the radar seeker, and the landing angle when hitting the target is increased.

[0090] Among them, in the trajectory design method, the optimization objective function and the control variable constraints are used to meet the available overload requirements of the projectile and avoid the stall of the projectile.

[0091] Among them, in the trajectory design method, this method fully draws on the design idea of ​​"reverse slope attack", adopts the overall plan of large shooting angle launch + large overload turning + fixed capture conditions, comprehensively considers the overload capacity of the artillery shell, the pitch angle during the handover of mid-terminal guidance and the angle of fall when hitting the target, and optimizes the design of the short-range trajectory. The GPOPS optimization toolbox of Matlab is used as the design tool to solve the optimization problem and obtain a nominal trajectory that meets actual needs.

[0092] In summary, the present invention belongs to the technical field of guided projectile trajectory optimization, and specifically relates to a trajectory design method suitable for radar terminal-guided projectiles, which is suitable for projectiles with high initial velocity, small overload capacity, and equipped with radar seekers to achieve large drop angle attacks on short-range targets, and is mainly used to provide good trajectory conditions for radar seekers to capture targets, while increasing the drop angle to improve damage performance. The method takes "reverse slope attack" as the guiding ideology, comprehensively considers the overload capacity of the projectile, the pitch angle during the handover of mid-terminal guidance, and the drop angle when hitting the target, and optimizes the minimum range trajectory using the GPOPS optimization toolbox of matlab as a design tool, which can effectively improve the minimum range capability of terminal-guided projectiles, broaden the attack range of projectiles, avoid the problems of small terminal drop angle and unfavorable radar seeker capture conditions caused by conventional low-reaching trajectory, effectively improve the combat effectiveness of the weapon system, and provide a reference for the trajectory optimization design of similar terminal-guided projectiles, and has a very broad application space.

[0093] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A trajectory design method suitable for radar terminally guided artillery shells, characterized in that: In the trajectory design method, from the launch of the projectile to the hitting of the target, the entire trajectory is divided into an in-bore acceleration section, an uncontrolled flight section, a mid-range guidance flight section, and a terminal guidance flight section. The center of mass motion equations for the flight section are as follows: In the above formula, x and y are the position coordinates of the projectile in the launch system, V is the flight speed, 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 x , C y are the drag coefficient and lift coefficient of the projectile, α is the angle of attack; The design method of each trajectory is as follows: (1) In-bore acceleration section The acceleration section in the bore provides the projectile with an initial flight velocity V0 and a firing angle θ0. When firing with full charge, the initial velocity is fixed. Considering the limitations of the projectile's overload capacity and other conditions, a large firing angle is used. (2) Uncontrolled flight The rudder and wing mechanism of the projectile is folded inside the projectile body, and the projectile body is in an uncontrolled flight state. After the uncontrolled flight reaches a specific time t0, the rudder and wing mechanism is controlled to open, and the uncontrolled flight section ends; the characteristic of this section of the trajectory is that the projectile body flies without an angle of attack and is only affected by gravity and aerodynamic resistance. The flight characteristics are described by the following formula: α=0, 0≤t<t0 (2) (3) Mid-range guidance section The purpose of the mid-range guidance section is to use the rudder mechanism to make the projectile use the overload of the projectile to achieve a "90°" turn, so as to approach the target within a short range. At the same time, when the mid-range and terminal guidance are handed over, the projectile has a specific pitch angle and flies to the time when the radar seeker captures the target. f When , the mid-range guidance stage ends; the trajectory design method optimizes the trajectory of the mid-range guidance stage, and the specific design steps are as follows: a) Determine the optimization goal Considering that the terminally guided projectile flies without power and has a small wing area, the available overload it can provide is limited and it needs to fly at the smallest possible angle of attack during the flight. Therefore, the following integral optimization objective function is selected; b) Determine the endpoint constraints In order to meet a certain missile-target relationship during the handover of mid-terminal guidance under the condition of minimum range and to hit the target at a larger angle, it is necessary to center the terminal position x of the guidance section. f ,y f and velocity inclination angle θ f The terminal constraints are designed as follows: Determine the shell range X t , and according to the radar seeker target scanning requirements and capture distance R b The terminal speed angle θ for the mid-terminal guidance handover is proposed f , the terminal shell position is calculated as follows: Through the above design, a fixed scanning condition is created for the radar seeker; c) Determine state constraints Take V, θ, x, y as state variables and α as control variable, where the state parameters must always satisfy the continuity constraints of equation group (1); The state variables and control variables at the end of the uncontrolled segment and the beginning of the intermediate guidance segment must be equal to ensure the continuity of system variables; d) Determine the control quantity constraints Considering the limited overload capacity of the projectile and to reduce the index requirements of the servo, the following constraints are added to the control amount α: |a|<a max , t1≤t<t f (5) The above optimization process can be summarized as follows: f During the time period, find the optimal α to transfer the state variable from the state at time t1 to the terminal state; e) Use optimization tools to solve optimization problems The trajectory of the mid-range guidance section is optimized based on the GPOPS nonlinear optimization toolbox. The toolbox is based on the Gauss / Radau pseudo-spectral method and the hp adaptive discrete grid update technology, which can transform the continuous optimization problem into a discrete optimization problem, with a small amount of calculation and high solution accuracy. (4) Terminal guidance After the radar seeker captures the target, the terminally guided projectile is guided based on the improved proportional guidance method and has a larger fall angle when hitting the target.

2. The trajectory design method for radar terminally guided projectiles as claimed in claim 1, characterized in that: In the trajectory design method, a single full charge and large firing angle are used for short range, a large overload is used to achieve rapid turning in the mid-range guidance stage, and a ballistic scheme with fixed capture conditions is adopted in the mid-terminal guidance handover stage. The trajectory is optimized based on the GPOPS nonlinear optimization toolbox.

3. The trajectory design method for radar terminally guided projectiles as claimed in claim 2, characterized in that: In the trajectory design method, a single full charge launch provides a fixed initial launch velocity.

4. The trajectory design method for radar terminally guided projectiles as claimed in claim 3, characterized in that: In the trajectory design method, by determining the terminal constraint conditions of the mid-stage guidance section, good and stable capture conditions are created for the radar seeker, and the landing angle when hitting the target is increased.

5. The trajectory design method for radar terminally guided projectiles as claimed in claim 4, characterized in that: In the trajectory design method, the objective function is optimized and the control variable constraints are used to meet the available overload requirements of the projectile and avoid the stall of the projectile.

6. The trajectory design method for radar terminally guided projectiles as claimed in claim 4, characterized in that: In the trajectory design method, the method fully draws on the design idea of ​​"reverse slope attack", adopts the overall plan of large shooting angle launch + large overload turning + fixed capture conditions, comprehensively considers the overload capacity of the artillery shell, the pitch angle during the handover of mid-terminal guidance and the landing angle when hitting the target, optimizes the design of the short-range trajectory, uses the GPOPS optimization toolbox of Matlab as a design tool to solve the optimization problem, and obtains a nominal trajectory that meets actual needs.

7. The trajectory design method for radar terminally guided projectiles as claimed in claim 4, characterized in that: In the trajectory design method, a large firing angle is adopted to form a curved trajectory with a large altitude and a long flight time, so as to ensure that the control system has a certain working space and fully utilize the gravity and the control system force to enable the projectile to achieve a "more than 90°" turn.

8. The trajectory design method for radar terminally guided projectiles as claimed in claim 4, characterized in that: The trajectory design method can effectively improve the minimum range capability of the terminally guided projectile.

9. The trajectory design method for radar terminally guided projectiles as claimed in claim 4, characterized in that: The trajectory design method calculates the position of the end point of the guidance section in the projectile and the angle constraint according to the range of the terminally guided projectile and the capture condition of the radar seeker, thereby ensuring that the radar seeker always has a relatively fixed projectile-target relationship when searching for the target, thereby reducing the capture difficulty of the radar seeker.

10. The trajectory design method for radar terminally guided projectiles as claimed in claim 4, characterized in that: The trajectory design method is conducive to increasing the impact angle, greatly improving the combat effectiveness of the weapon system, and provides a reference for the trajectory optimization design of similar terminally guided artillery shells.

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