A method and system for controlling the terminal falling speed and falling angle of an aircraft based on sliding surface

Abstract

A method and system for guiding an aircraft to meet the constraints of terminal falling speed and falling angle based on a sliding mode surface, specifically related to a method and system for guiding an aircraft to meet the constraints of terminal falling speed and falling angle based on a double sliding mode surface, aiming to solve the problem that the existing methods for guiding an aircraft to meet the constraints of terminal falling speed and falling angle in the terminal guidance process of the aircraft are complex, increasing the computational burden and resulting in a long calculation time. It constructs a kinematic model of the missile centroid and a three-dimensional attack model according to the three-dimensional attack scenario between the missile and the target; defines a sliding mode surface S1 and a sliding mode surface S2; constructs a guidance law that meets the constraints of falling speed and falling angle according to the three-dimensional attack model between the missile and the target, the sliding mode surface S1 and the sliding mode surface S2; when the aircraft is in the terminal flight, it flies according to the guidance law that meets the constraints of falling speed and falling angle until it hits the target. It belongs to the field of multi-constraint guidance of aircraft.

Description

Technical Field

[0001] The present invention relates to a method and system for constraining the terminal falling speed and falling angle of an aircraft, and in particular to a method and system for constraining the terminal falling speed and falling angle of an aircraft based on double sliding surfaces, belonging to the field of aircraft multi-constraint guidance. Background Art

[0002] With the continuous strengthening of existing defensive fortifications, the terminal guidance of the aircraft needs to ensure that the target is hit with the minimum miss, while also hitting the key or most vulnerable part of the target at a specific drop angle and drop speed to effectively penetrate. Most of the existing literature constrains the terminal drop angle, but does not consider the drop speed constraint. In the few literatures that consider the drop speed and drop angle constraints, the traditional biased proportional guidance law is used to achieve drop angle control, and the flight speed of the aircraft is controlled by parameterization of the defined variables, and then the parameters are optimized through the optimization algorithm to meet the drop speed constraint. However, this method makes the terminal guidance process of the aircraft complicated, increases the computational burden, and leads to a long calculation time. Summary of the invention

[0003] In order to solve the problem that the existing terminal guidance method of an aircraft with falling speed and falling angle constraints adopts the traditional offset proportional guidance law to realize the falling angle control, and controls the flight speed of the aircraft through parameterized control of defined variables, and then optimizes the parameters through an optimization algorithm, which makes the terminal guidance process of the aircraft complicated, increases the calculation burden, and leads to a long calculation time, and thus proposes a terminal aircraft falling speed and falling angle constraint guidance method and system based on a sliding surface.

[0004] The technical solution adopted by the present invention is:

[0005] It includes the following steps:

[0006] S1. Construct a three-dimensional attack scenario of the aircraft's missiles and attack targets;

[0007] S2. Construct a kinematic model of the missile's center of mass based on a three-dimensional attack scenario;

[0008] S3, constructing a three-dimensional attack model of the missile and the attack target according to the three-dimensional attack scenario and the kinematic model of the missile's center of mass;

[0009] S4, define sliding surface S1 and sliding surface S2;

[0010] S5, constructing a guidance law that satisfies the fall speed and fall angle constraints according to the three-dimensional attack model of the missile and the attack target, the sliding surface S1 and the sliding surface S2;

[0011] S6. When the aircraft is performing terminal flight, it flies according to the guidance law that satisfies the fall speed and fall angle constraints until it hits the target.

[0012] Furthermore, the three-dimensional attack scene in S1 includes a missile, an attack target, an inertial coordinate system, a line of sight coordinate system and a ballistic coordinate system.

[0013] Furthermore, the kinematic model of the missile center of mass in S2 is:

[0014]

[0015]

[0016]

[0017] Among them, x, y and z are the three-axis positions of the missile in the inertial coordinate system. and are the derivatives of the three-axis positions; V M is the missile's velocity, θ is the trajectory inclination, and ψ is the trajectory deviation.

[0018] Furthermore, the three-dimensional attack model of the missile and the attack target in S3 is:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Among them, r is the relative distance between the missile and the target, θ M is the pitch lead angle between the ballistic coordinate system and the line of sight coordinate system, ψ M is the offset lead angle between the ballistic coordinate system and the line of sight coordinate system, θ L is the pitch line of sight angle between the inertial coordinate system and the line of sight coordinate system, ψ L is the yaw line-of-sight angle between the inertial coordinate system and the line-of-sight coordinate system, a yM is along the ballistic coordinate system MY M The acceleration component of the axis, a zM is along the ballistic coordinate system MZ M The acceleration component of the axis, g is the acceleration due to gravity, D is the drag on the missile, ρ is the atmospheric density, S is the reference area of ​​the missile, C D is the drag coefficient, m is the mass of the missile, are r,θ respectivelyL ,ψ L ,θ M ,ψ M ,V M The derivative of .

[0026] Furthermore, the specific process of S4 is as follows:

[0027] Define sliding surface S1

[0028] S1=sinθ M -k1e θ (10)

[0029] Among them, e θ is the elevation sight angle tracking error, e θ =θ L -θ Ld , k1>0 is a parameter, and the derivative of equation (10) yields

[0030]

[0031] Substituting equation (7) into equation (11), we can obtain

[0032]

[0033] Define sliding surface S2

[0034]

[0035] Among them, e ψ is the yaw line of sight angle tracking error, e ψ =ψ L -ψ Ld , k2>0, is the expected falling speed, and the derivative of equation (13) yields:

[0036]

[0037] Substituting equation (8) into equation (14) yields

[0038]

[0039] Furthermore, the guidance law satisfying the falling speed and falling angle constraints in S5 is:

[0040]

[0041]

[0042] Among them, h0, h1, h2, and h3 all represent custom control parameters, h0>0, h1>0, h2>0, h3>0, sig γ (Si )=|S i | γ ·sign(S i ),i=1,2,γ∈(0,1),sign(·)is the sign function.

[0043] A sliding surface-based aircraft terminal fall speed and angle constraint guidance system comprises a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, any step in a sliding surface-based aircraft terminal fall speed and angle constraint guidance method is implemented.

[0044] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements any step in a method for constraining the terminal falling speed and falling angle of an aircraft based on a sliding surface.

[0045] Beneficial effects:

[0046] The present invention constructs a kinematic model of the missile's center of mass and a three-dimensional attack model of the missile and the attack target through a three-dimensional attack scenario between the missile of the aircraft and the attack target, and determines the relationship between the missile and the attack target. Define the design goal of the guidance method that takes into account the fall speed and fall angle constraints when attacking a stationary target. Define two sliding surfaces, namely sliding surface S1 and sliding surface S2. Based on the stability proof, a guidance law that meets the fall speed and fall angle constraints of the aircraft terminal guidance is constructed according to the three-dimensional attack model of the missile and the attack target, sliding surface S1 and sliding surface S2. The guidance law is used to constrain the aircraft, and the flight direction and path of the aircraft are changed to achieve accurate strikes on the attack target. Based on the design goal, the stability analysis of the guidance law that meets the fall speed and fall angle constraints is performed to ensure the stability of the flight state of the aircraft. The present invention simplifies the terminal guidance process of the aircraft by setting two sliding surfaces and a guidance law, so that when the aircraft is performing terminal flight, it only needs to fly according to the guidance law that satisfies the fall speed and fall angle constraints to meet the fall speed and fall angle constraints of the terminal guidance, so as to accurately and effectively strike the attack target. In this process, the calculation burden is significantly reduced and the calculation time is shortened. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a three-dimensional attack diagram;

[0048] Figure 2 It is the three-dimensional trajectory diagram of the simulation;

[0049] Figure 3 It is the speed curve diagram of the simulation;

[0050] Figure 4 It is a simulated two-dimensional trajectory diagram in the XY plane;

[0051] Figure 5 It is the simulated two-dimensional trajectory diagram of XZ plane;

[0052] Figure 6 It is a simulated ballistic inclination curve diagram;

[0053] Figure 7 It is the simulated ballistic deflection trajectory diagram;

[0054] Figure 8 It is the S1 curve of the simulated sliding surface;

[0055] Fig. 9 It is the S2 curve of the simulated sliding surface;

[0056] Fig.10 It is the simulated aym curve graph;

[0057] Fig.11 It is a simulated azm curve chart; DETAILED DESCRIPTION

[0058] Specific implementation method 1: Combination Figure 1 The present embodiment is described. The present embodiment is a method for controlling the terminal falling speed and falling angle of an aircraft based on a sliding surface, which comprises the following steps:

[0059] S1. Construction Figure 1 The three-dimensional attack scenario shown in the figure, where M is the missile (attack missile), T is the attack target, (X I ,Y I ,Z I ), (X L ,Y L ,Z L ), (X M ,Y M ,Z M ) represent the inertial coordinate system, the line of sight coordinate system and the ballistic coordinate system respectively. r is the relative distance between the missile and the target, θ L is the pitch line of sight angle between the inertial coordinate system and the line of sight coordinate system, ψ L is the yaw line-of-sight angle between the inertial coordinate system and the line-of-sight coordinate system, θ M is the pitch lead angle between the ballistic coordinate system and the line of sight coordinate system, ψ M It is the offset lead angle between the ballistic coordinate system and the line of sight coordinate system.

[0060] S2. When designing a multi-constraint guidance law that takes into account the aircraft's falling speed and falling angle constraints, a kinematic model of the aircraft missile's center of mass is constructed based on the three-dimensional attack scenario:

[0061]

[0062]

[0063]

[0064] Among them, x, y and z are the three-axis positions of the missile in the inertial coordinate system. and are the derivatives of the three-axis positions; V M is the missile's velocity, θ is the trajectory inclination, and ψ is the trajectory deviation.

[0065] S3. Construct a three-dimensional attack model of the missile and the attack target based on the three-dimensional attack scenario and the kinematic model of the missile's center of mass:

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] Among them, a yM is along the ballistic coordinate system MY M The acceleration component of the axis, a zM is along the ballistic coordinate system MZ M The acceleration component of the axis, g is the acceleration due to gravity, D is the drag on the missile, ρ is the atmospheric density, S is the reference area of ​​the missile, C D is the drag coefficient, m is the mass of the missile, are r,θ respectively L ,ψ L ,θ M ,ψ M ,V M The derivative of .

[0073] S4. For the guidance law design problem considering the constraints of falling speed and falling angle, the design objectives are defined as:

[0074]

[0075] Among them, t f is the total flight time of the missile, θ Ld ,ψ Ld are the desired line of sight inclination and line of sight deflection, It is the customized expected falling speed.

[0076] When attacking a stationary target, when the lead angle σ→0, the missile can be guaranteed to hit the target, and the geometric relationship between the lead angle, pitch lead angle and offset lead angle (cosσ=cosθ M ·cosψ M ) we can see that when σ→0, it means θ M →0,ψ M →0, so formula (10) can be further transformed into

[0077]

[0078] Among them, t is the flight time of the missile at a certain moment.

[0079] S5, sliding surface S1 defined as follows

[0080] S1=sinθ M -k1e θ (12)

[0081] Among them, e θ =θ L -θ Ld is the pitch line of sight angle tracking error, k1>0 is a parameter, and the derivative of equation (12) yields

[0082]

[0083] Substituting equation (7) into equation (13), we can obtain

[0084]

[0085] The sliding surface S2 is defined as follows

[0086]

[0087] Among them, e ψ is the yaw line of sight angle tracking error, e ψ =ψ L -ψ Ld , k2>0, and the derivative of equation (15) yields:

[0088]

[0089] Substituting equation (8) into equation (16), we can obtain

[0090]

[0091] S6. Based on the stability proof, the guidance law that satisfies the falling speed and falling angle constraints is constructed according to the three-dimensional attack model of the missile and the attack target, the sliding surface S1 and the sliding surface S2:

[0092]

[0093]

[0094] Among them, h0, h1, h2, and h3 all represent custom control parameters, h0>0, h1>0, h2>0, h3>0, sig γ (S i )=|S i | γ ·sign(S i ),i=1,2,γ∈(0,1),sign(·)is the sign function.

[0095] According to the relative attack dynamics model of the missile and the target and the sliding surfaces S1 and S2 shown in formulas (4)-(9), it can be determined that the proposed guidance laws (18) and (19) can achieve effective strikes on the target at the desired landing angle and speed.

[0096] Based on the design goal of S4, the stability analysis of the guidance law that meets the fall speed and fall angle constraints is carried out. Since the guidance law is derived based on stability, the flight state of the aircraft can be stabilized:

[0097] The Lyapunov function is defined as follows

[0098]

[0099] Taking the derivative of equation (20) we can get

[0100]

[0101] Substituting guidance laws (18) and (19) into equation (21), we can obtain

[0102]

[0103] Where, κ = min[h1·2 (γ+1) / 2 ,h3·2 (γ+1) / 2 ].

[0104] According to formula (22), from Lyapunov stability theory, it can be seen that the sliding surfaces S1 and S2 will converge to zero in a finite time, and the sliding surface S2 is bounded, then the velocity constraint The terminal drop speed constraint can be satisfied.

[0105] When the sliding surfaces S1 and S2 converge to zero, it can be seen from equations (12) and (15) that

[0106] sinθ M -k1e θ =0 (23)

[0107]

[0108] Select the following Lyapunov function,

[0109]

[0110] Derivative (25) and (5) and (23) yield

[0111]

[0112] Formula (26) is valid if and only if e θ = 0, it will appear According to Lyapunov stability theory, e θ will converge to zero asymptotically, and then from formula (23) we can know that when e θ = 0, sinθ M =0, by θ M From the physical definition, we know that at this time θ M = 0. From formula (24), we further select the following Lyapunov function:

[0113]

[0114] Derivative (27) and equation (6) and (24) yield:

[0115]

[0116] Formula (28) is valid if and only if e ψ = 0, it will appear According to Lyapunov stability theory, e ψ will converge to zero asymptotically, and then from formula (24), we can know that when e ψ = 0, sinψ M = 0, by ψ M From the physical definition, we know that at this time ψ M =0.

[0117] In summary, the closed-loop theoretical proof based on the Lyapunov stability theory is given above. When the sliding surface converges to zero, the attack angle error converges to zero, and then the lead tilt angle and the lead deflection angle converge to zero, which can ensure that the missile hits the target at the expected attack angle, while the traditional sliding surface cannot meet these properties; when the sliding surface is bounded, it can be guaranteed to meet the terminal drop speed constraint. Combined with the design goal of formula (11), it can be seen that the two novel sliding surfaces and multi-constraint guidance laws designed by the present invention can achieve effective attack on the target under the condition of satisfying the drop speed and drop angle constraints.

[0118] S7. When the aircraft is performing terminal flight, it flies according to the guidance law that satisfies the fall speed and fall angle constraints until it hits the attack target, thereby achieving the fall speed and fall angle constraints of the aircraft at the terminal (terminal guidance).

[0119] Specific implementation method 2: Combination Figure 1 To illustrate the present embodiment, the present embodiment describes a sliding surface-based aircraft terminal fall speed and angle constraint guidance system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements any step in a sliding surface-based aircraft terminal fall speed and angle constraint guidance method when executing the computer program.

[0120] Specific implementation method three: Combination Figure 1 To illustrate the present embodiment, the present embodiment describes a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements any step in a method for constraining the terminal fall speed and angle of fall of an aircraft based on a sliding surface.

[0121] In order to verify the effectiveness of the terminal guidance law that satisfies the falling speed and falling angle constraints, the following simulation analysis is carried out:

[0122] Set the simulation conditions as follows: the initial velocity V of the aircraft missile M (t0) = 2033 m / s, the missile's initial position (x(t0), y(t0), z(t0)) = (0, 25 km, 0), the target's position (xt, yt, zt) = (30 km, 0, -2 km), the missile's initial pitch lead angle θ M (t0) = -10°, bias lead angle error term ψ M (t0) = -3°, the expected line of sight inclination angle and line of sight deflection angle are θ Ld =-72°, ψ Ld =-5°, maximum overload is a max =20g, the initial trajectory inclination and initial trajectory deviation are θ(t0)=-0.8668rad, ψ(t0)=-0.0131rad, where t0 is the initial moment. The initial relative motion information between the missile and the target is:

[0123]

[0124] Among them, xr(t0), yr(t0), zr(t0) are the relative distances between the initial missile and the target in the inertial coordinate system, r(t0) is the initial relative distance between the missile and the target, θ L (t0),ψ L(t0) are the initial pitch sight angle and yaw sight angle respectively.

[0125] The simulation parameter settings are given as shown in Table 1

[0126] Table 1 Parameter settings for different falling speed constraints

[0127]

[0128] Depend on Figure 2-Figure 11 The simulation results show that by selecting the simulation parameters and initial simulation conditions shown in Table 1, high-precision strikes on the desired target points at different falling speeds and different desired attack angles can be achieved.

Claims

1. A method for controlling the terminal falling speed and angle of an aircraft based on a sliding surface, characterized in that: It includes the following steps: S1. Construct a three-dimensional attack scenario of the aircraft's missiles and attack targets; S2. Construct a kinematic model of the missile's center of mass based on a three-dimensional attack scenario; S3, constructing a three-dimensional attack model of the missile and the attack target according to the three-dimensional attack scenario and the kinematic model of the missile's center of mass; S4, define sliding surface S1 and sliding surface S2; S5, constructing a guidance law that satisfies the fall speed and fall angle constraints according to the three-dimensional attack model of the missile and the attack target, the sliding surface S1 and the sliding surface S2; S6. When the aircraft is performing terminal flight, it flies according to the guidance law that satisfies the fall speed and fall angle constraints until it hits the attack target; Wherein, the sliding surface S1 is defined as S1=sinθ M -k1e θ (10) Among them, e θ is the elevation sight angle tracking error, e θ =θ L -θ Ld , k1>0 is a parameter; The sliding surface S2 is defined as Among them, e ψ is the yaw line of sight angle tracking error, e ψ =ψ L -ψ Ld , k2>0, is the expected falling speed; The guidance law that satisfies the falling speed and falling angle constraints in S5 is: Among them, h0, h1, h2, and h3 all represent custom control parameters, h0>0, h1>0, h2>0, h3>0, sig γ (S i )=|S i | γ ·sign(S i ), i = 1, 2, γ∈(0, 1), sign(·) is the sign function; a yM is along the ballistic coordinate system MY M The acceleration component of the axis; a zM is along the ballistic coordinate system MZ M The acceleration component of the axis, V M is the missile's velocity, θ L is the pitch angle between the inertial coordinate system and the line of sight coordinate system, θ is the ballistic inclination angle, ψ is the ballistic deviation angle, and ψ L is the yaw line-of-sight angle between the inertial coordinate system and the line-of-sight coordinate system, ψ M is the offset lead angle between the ballistic coordinate system and the line of sight coordinate system, θ M is the pitch lead angle between the ballistic coordinate system and the line of sight coordinate system; They are θ L , ψ L , V M The derivative of .

2. The method for controlling the terminal falling speed and falling angle of an aircraft based on a sliding surface according to claim 1, characterized in that: The three-dimensional attack scene in S1 includes a missile, an attack target, an inertial coordinate system, a line of sight coordinate system and a ballistic coordinate system.

3. The method for controlling the terminal falling speed and falling angle of an aircraft based on a sliding surface according to claim 2, characterized in that: The kinematic model of the missile center of mass in S2 is: Among them, x, y and z are the three-axis positions of the missile in the inertial coordinate system. and are the derivatives of the three-axis positions; V M is the missile's velocity, θ is the trajectory inclination, and ψ is the trajectory deviation.

4. The method for controlling the terminal falling speed and falling angle of an aircraft based on a sliding surface according to claim 3, characterized in that: The three-dimensional attack model of the missile and the attack target in S3 is: Among them, r is the relative distance between the missile and the target, θ M is the pitch lead angle between the ballistic coordinate system and the line of sight coordinate system, ψ M is the offset lead angle between the ballistic coordinate system and the line of sight coordinate system, θ L is the pitch line of sight angle between the inertial coordinate system and the line of sight coordinate system, ψ L is the yaw line-of-sight angle between the inertial coordinate system and the line-of-sight coordinate system, a yM is along the ballistic coordinate system MY M The acceleration component of the axis, a zM is along the ballistic coordinate system MZ M The acceleration component of the axis, g is the acceleration due to gravity, D is the drag on the missile, ρ is the atmospheric density, S is the reference area of ​​the missile, C D is the drag coefficient, m is the mass of the missile, are r, θ L , ψ L ,θ M , ψ M , V M The derivative of .

5. The method for controlling the terminal falling speed and falling angle of an aircraft based on a sliding surface according to claim 4, characterized in that: The specific process of S4 is as follows: Define sliding surface S1 S1=sinθ M -k1e θ (10) Among them, e θ is the elevation sight angle tracking error, e θ =θ L -θ Ld , k1>0 is a parameter, and the derivative of equation (10) yields Substituting equation (7) into equation (11), we can obtain Define sliding surface S2 Among them, e ψ is the yaw line of sight angle tracking error, e ψ =ψ L -ψ Ld , k2>0, is the expected falling speed, and the derivative of equation (13) yields: Substituting equation (8) into equation (14) yields 6. A sliding surface-based aircraft terminal fall speed and fall angle constraint guidance system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

7. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

Images