CN114995495A - Time and angle constraint three-dimensional sliding mode guidance law design method under speed uncontrollable condition - Google Patents

Abstract

The invention relates to a time and angle constraint three-dimensional sliding mode guidance law design method under the condition of uncontrollable speed, and relates to the technical field of missile guidance. The guidance law designed by the invention is perpendicular to the speed direction, and the expected attack time and attack angle are realized only by changing the speed direction of the missile. In a pitching channel, a rapidly-converged nonsingular sliding mode surface and a sliding mode approach law which changes along with the distance of a missile are provided, and an expected sight elevation angle is realized; in a yaw channel, a special sliding mode surface is designed by analyzing the guidance conditions of the yaw channel, and the missile can be ensured to reach the sliding mode surface by the supercoiled sliding mode theory, so that the expected sight azimuth angle and the expected attack time are realized. Under the condition that the speed of the missile is uncontrollable, the missile strikes a target at the expected attack time and the attack angle in the three-dimensional space, the guidance law is small in miss distance, the expected attack time and the expected sight elevation angle can be accurately achieved, and the sight azimuth angle has small errors.

Description

Design method of three-dimensional sliding mode guidance law with time and angle constraints under uncontrollable speed conditions

technical field

The invention relates to the technical field of missile guidance, in particular to the design of a guidance law for controlling missile attack time and angle under the condition of uncontrollable speed.

Background technique

For the existing three-dimensional guidance law, there are mainly two guidance models. The first one is based on the line-of-sight coordinate system. After the guidance command obtained in this model is converted to the ballistic coordinate system, there is a component in the direction of velocity, which requires an aircraft Ability to control missile speed. However, in the terminal guidance stage of the missile, the missile usually has no thrust and cannot control the speed of the missile. In response to this problem, the second model is established based on the missile lead angle coordinate system, and the guidance command is perpendicular to the missile speed direction, so the speed is not controlled.

Under the condition of uncontrollable speed, the three-dimensional guidance law of missile can be divided into time constraint and angle constraint. The time-constrained guidance law is derived based on the estimation expression of the remaining time of the missile, or based on the consistency theory, by designing cooperative variables. The angle-constrained guidance law is based on the relationship between the line-of-sight angular acceleration and the overload in the model, through sliding mode control theory, optimal control theory, adaptive control theory and other methods to derive the expression of the overload command. But at present, under the condition of uncontrollable speed, there is no guidance law that can realize time constraint and angle constraint at the same time.

In the current three-dimensional guidance laws that can realize time constraints and angle constraints at the same time, they are all based on the three-dimensional model of speed control. In the terminal guidance stage of the missile, the missile usually has no thrust, and only controls the attitude of the missile through aerodynamic force. Under the condition of uncontrollable speed, the current guidance law can only achieve a single time constraint or angle constraint.

To sum up, the existing methods cannot constrain time and angle at the same time under the condition of uncontrollable speed. In order to meet the guidance requirements, there is an urgent need for a time- and angle-constrained three-dimensional sliding mode guidance law design method under the condition of uncontrollable speed. .

SUMMARY OF THE INVENTION

technical problem to be solved

Aiming at the problem that the existing three-dimensional guidance law cannot constrain the attack time and the attack angle at the same time under the condition of uncontrollable speed, the present invention proposes a time- and angle-constrained three-dimensional sliding mode guidance law design method under the condition of uncontrollable speed.

Technical solutions

The present invention designs the guidance laws of the missile pitch and yaw channels respectively:

In the pitch channel, a fast-converging non-singular sliding mode surface and a reaching law that changes with the missile distance are designed, and the derived guidance law can achieve the desired line of sight angle.

In the yaw channel, by analyzing the missile guidance conditions, a special sliding mode surface is designed, and through the super-helix sliding mode theory, it is ensured that the missile can reach the sliding mode surface, thus achieving the desired line of sight azimuth and expected attack time.

A time- and angle-constrained three-dimensional sliding mode guidance law design method under the condition of uncontrollable speed, characterized in that: after analyzing the missile guidance conditions, based on the sliding mode control method, respectively design a _my to control the missile to reach a desired line of sight inclination, a _mz is used to control the missile to reach the desired declination angle and the desired attack time;

The missile guidance model can be expressed as:

为弹道偏角，θ_L为视线高低角，

为视线方位角，σ_m表示前置角，θ_m和

为σ_m在视线坐标系下俯仰和偏航通道的分解，分别表示前置倾角和前置偏角，γ_m表示前置滚转角，V_m表示导弹速度；Among them, R is the relative distance of the projectile, θ is the ballistic inclination,

is the ballistic declination angle, θ _L is the line-of-sight angle,

is the line-of-sight azimuth, σ _m represents the lead angle, θ _m and

is the decomposition of the pitch and yaw channels of σ _m in the line-of-sight coordinate system, representing the forward inclination angle and the forward declination angle, respectively, γ _m the forward roll angle, and V _m the missile velocity;

Further derivation of the line-of-sight angle and azimuth angle can be obtained

The guidance law design method is as follows:

(1) Guidance law design for the high and low angle directions of the line of sight

First, to achieve the desired line-of-sight angle, a fast-converging non-singular sliding mode surface is designed:

λ，β均为大于0的常数，α∈[-1,1]；设计随着导弹距离变化的自适应趋近律：where x ₁ =θ _L -θ _Ld ,

λ and β are both constants greater than 0, α∈[-1,1]; the adaptive approach law is designed with the change of missile distance:

Among them, k ₁ and k ₂ are constants greater than 0, and k ₁ and k ₂ satisfy:

Finally, the guidance law of the line-of-sight direction can be obtained as

(2) Guidance law design for line of sight azimuth direction

φ＝t_d-t-ξ，并作出如下假设：Let ξ=R/V _m , e ₁ =θ _L -θ _Ld ,

φ=t _d -t-ξ, and make the following assumptions:

Assumption 1: When derivation of e ₂ , the change of cosθ _L is small, and it is regarded as a constant;

Assumption 2: During the guidance process, the time error term φ≥0 is always established;

Design the sliding surface as follows:

Taking the derivative of both ends of the sliding surface s ₂ and substituting the formula into:

The reaching law is designed based on the superhelical sliding mode control method:

Among them, l ₁ and l ₂ are both constants greater than 0, and w is an adaptive parameter of the super sliding mode to prevent chattering on the sliding mode surface. Substitute the above formula into the sliding mode surface s ₂ to obtain the control variable a _mz is:

A computer system, characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are processed by the one or more programs When the processor is executed, the one or more processors are caused to implement the above method.

A computer-readable storage medium is characterized in that computer-executable instructions are stored, and the instructions, when executed, are used to implement the above-mentioned method.

A computer program characterized by comprising computer-executable instructions which, when executed, are used to implement the above-mentioned method.

beneficial effect

The guidance law designed by the invention is perpendicular to the speed direction, and the desired attack time and attack angle can be achieved only by changing the speed direction of the missile. In the pitch channel, a fast-converging non-singular sliding mode surface and a sliding mode approach law that changes with the missile distance are proposed to achieve the desired line of sight angle; in the yaw channel, by analyzing the guidance conditions, a A special sliding mode surface, and through the super-helix sliding mode theory, ensures that the missile can reach the sliding mode surface, so as to achieve the desired line of sight azimuth and the desired attack time.

Under the condition that the speed of the missile is uncontrollable, the present invention realizes that the missile hits the target with the desired attack time and attack angle in the three-dimensional space. There are minor errors.

The innovation of the present invention is as follows:

(1) Through the sliding mode control theory, under the condition of uncontrollable speed, the sliding mode surface is designed according to the guidance conditions, and the guidance law that can hit the target at the desired time and angle at the same time is deduced, which is not achieved by other methods. of.

(2) The present invention has carried out a reasonable division of labor for the three-dimensional guidance law of the missile, wherein a _my ensures that the height angle of the missile's line of sight reaches the desired value, and a _mz ensures that the azimuth of the missile's line of sight and attack time reach the desired value.

(3) All the results of the present invention are derived based on the three-dimensional nonlinear coupled dynamics model, without considering the small angle assumption and linearization, the guidance law has high precision, wide application range, and can achieve all-round attack.

Description of drawings

The drawings are for the purpose of illustrating specific embodiments only and are not to be considered limiting of the invention, and like reference numerals refer to like parts throughout the drawings.

Figure 1: Schematic diagram of the 3D guidance model;

Figure 2: Three-dimensional trajectory map of the missile;

Figure 3: Missile estimated remaining time curve;

Figure 4: lead angle change curve;

Figure 5: Relative velocity curve;

Figure 6: The change curve of the height and low angle of the missile line of sight;

Figure 7: The change curve of the azimuth angle of the missile line of sight;

Figure 8: Variation curve of overload in the high and low angle directions of the line of sight;

Figure 9: Overload variation curve in line-of-sight azimuth direction.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

According to Figure 1, M and T represent the positions of the missile and the target respectively. In the coordinate system with the Y axis pointing upward, the three-dimensional coupled guidance model of the missile can be described as:

为弹道偏角，θ_L为视线高低角，

为视线方位角，σ_m表示前置角，θ_m和

为σ_m在视线坐标系下俯仰和偏航通道的分解，分别表示前置倾角和前置偏角，γ_m表示前置滚转角，V_m表示导弹速度。Among them, R is the relative distance of the projectile, θ is the ballistic inclination,

is the ballistic declination angle, θ _L is the line-of-sight angle,

is the line-of-sight azimuth, σ _m represents the lead angle, θ _m and

is the decomposition of the pitch and yaw channels of σ _m in the line-of-sight coordinate system, representing the forward inclination angle and the forward declination angle, respectively, γ _m the forward roll angle, and V _m the missile velocity.

(1) Guidance law design for the high and low angle directions of the line of sight

First, take the derivative of (5) and substitute equation (2), we can get

To achieve the desired line-of-sight angle, a fast-converging non-singular sliding surface is designed:

s ₁ =x ₂ +λx ₁ +βsig ^α (x ₁ ) (8)

θ_Ld为期望视线高低角，λ，β均为大于0的常数，α∈[-1,1]。为了使视线高低角能快速收敛到期望值且保持稳定，本发明提出了一种随着导弹距离变化的趋近律：where x ₁ =θ _L -θ _Ld ,

θ _Ld is the desired line-of-sight angle, λ and β are both constants greater than 0, α∈[-1,1]. In order to make the line-of-sight angle quickly converge to the desired value and keep it stable, the present invention proposes a reaching law that changes with the missile distance:

Among them, k ₁ and k ₂ are constants greater than 0, and k ₁ and k ₂ satisfy:

Taking the derivation of Equation (8) and combining Equation (7) and Equation (9), the pitch channel guidance law can be obtained as

In order to prove that the missile can achieve the desired line-of-sight angle under this guidance law, the following Lyapunov function is assumed:

Taking the derivative of this Lyapunov function, we get:

Simplify the above formula to get:

Integrating the above formula can get:

Among them, s ₁ (0) and R(0) are the sliding surface at the start time and the relative distance between the missile and the target, respectively. According to (15), there is a finite time t ^* such that the sliding surface s ₁ =0.

After reaching the sliding mode surface, the following relation can be obtained according to formula (8)

x ₂ =-λx ₁ -βsig ^α (x ₁ ) (16)

In order to prove that the line-of-sight angle of the missile can reach the expected value, the Lyapunov function is designed as:

Taking the derivative of equation (17) and substituting it into equation (16), we get:

According to equation (18), x ₁ can converge to 0 in a finite time, and the convergence time T ₁ satisfies

To sum up, the total time for the line of sight height angle to reach the desired value is the sum of the time t ^* reaching the sliding mode surface and the convergence time T ₁ of x ₁ after reaching the sliding mode surface, Tθ=t ^* +T ₁ .

(2) Guidance law design for line of sight azimuth direction

表示视线方位角误差，其中

为期望视线方位角，φ＝t_d-t-ξ。表示期望攻击时间误差。下面作如下假设：Let ξ=R/V _m , denote the estimated remaining flight time, e ₁ =θ _L -θ _Ld , denote the line-of-sight angle error,

is the line-of-sight azimuth error, where

is the desired line-of-sight azimuth, φ=t _d -t-ξ. Indicates the expected attack time error. The following assumptions are made:

Assumption 1: When differentiating _e2 , the term _cosθL changes little and treats it as a constant.

Assumption 2: During the guidance process, the time error term φ≥0 is always established.

Taking derivatives of ξ, e ₁ , e ₂ , and φ in the above formula, and substituting formulas (1)-(6), we can get:

Design an auxiliary variable Ω whose expression is:

Taking the derivative of both ends of Ω and substituting equations (20)-(23), we can get:

When the line of sight of a _my control missile reaches the desired value, according to formula (5), the following conditions will be satisfied:

In this case, equation (25) can be rewritten as

According to (27), the sliding surface is designed as follows:

Taking the derivation of both ends of the sliding surface s ₂ and substituting Equation (3) into:

In order to weaken the chattering phenomenon of the sliding mode surface and ensure that the sliding mode surface can converge quickly, the present invention designs a reaching law based on the superhelical sliding mode control method. First, formula (29) is written as:

in,

According to the superhelical sliding mode theory, the reaching law can be expressed as:

Among them, l ₁ and l ₂ are both constants greater than 0. Substituting Equation (33) into Equation (30), the control amount a _mz can be obtained as:

First, according to the super-helical sliding mode theory, the sliding mode surface can reach s ₂ =0 in a limited time. After reaching s ₂ =0, assuming that a _my also controls the missile to reach the desired line-of-sight angle, according to equations (24) and (25):

Since cosθ _m =1, according to the trigonometric formula, equations (20) and (23) can be expressed as:

First, design the following Lyapunov function:

V ₃ =0.5φ ² (38)

Taking the derivative of both ends, we have

当且仅当φ＝0时，

因此φ能够渐进收敛到0。根据假设2，在达到期望时间之前，φ≥0恒成立，假设φ＝0，根据上式可得：Since φ≥0, therefore,

If and only if φ=0,

Therefore, φ can gradually converge to 0. According to Assumption 2, before reaching the desired time, φ≥0 is always established. Assuming that φ=0, according to the above formula, we can get:

t+ξ=t _d (41)

If the missile can hit the target, when hitting the target, according to the definition, +ξ=R/V _m =0, according to formula (41), it is satisfied at this time, and t=t _d is satisfied at this time. To sum up, as long as the missile can hit the target, then the missile hits the target at the desired time and can achieve the desired line of sight azimuth.

Combining a _my and a _mz , the missile can achieve the following guidance targets:

That is, the missile can hit the target at the desired time, and can achieve the desired line of sight inclination and line of sight declination.

导弹的期望攻击时间T_d均为60s，仿真终止条件设置为r＜0.5m，导弹的最大过载为30g，仿真步长为0.001s。仿真结果如表2和图2-图9所示In order to demonstrate the feasibility and effectiveness of the time and angle constrained three-dimensional sliding mode guidance law design method under the condition of uncontrollable speed, the present invention designs a simulation verification test. The initial conditions of the missiles are shown in Table 1. The line-of-sight angle constraints of the four missiles are θ _Ld = [-35° -10° -15° -20°], and the line-of-sight azimuth is constrained by

The expected attack time T _d of the missile is 60s, the simulation termination condition is set as r<0.5m, the maximum overload of the missile is 30g, and the simulation step size is 0.001s. The simulation results are shown in Table 2 and Figure 2-Figure 9

Table 1 Missile initial conditions

Table 2 Simulation results

The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited to this. Any person skilled in the art can easily think of various equivalents within the technical scope disclosed by the present invention. Modifications or substitutions should be included within the protection scope of the present invention.

Claims (4)

1. a time and angle constraint three-dimensional sliding mode guidance law design method under uncontrollable speed conditions, is characterized in that: after analyzing the missile guidance conditions, based on the sliding mode control method, respectively design _amy for controlling the missile to reach the desired line of sight inclination , a _mz is used to control the missile to reach the desired declination angle and the desired attack time; The missile guidance model can be expressed as:

Among them, R is the relative distance of the projectile, θ is the ballistic inclination,

is the ballistic declination angle, θ _L is the line of sight height angle,

is the line-of-sight azimuth, σ _m represents the lead angle, θ _m and

is the decomposition of the pitch and yaw channels of σ _m in the line-of-sight coordinate system, representing the forward inclination angle and the forward declination angle, respectively, γ _m the forward roll angle, and V _m the missile velocity; Further derivation of the line-of-sight angle and azimuth angle can be obtained

The guidance law design method is as follows: (1) Guidance law design for the high and low angle directions of the line of sight First, to achieve the desired line-of-sight angle, a fast-converging non-singular sliding mode surface is designed:

where x ₁ =θ _L -θ _Ld ,

λ and β are both constants greater than 0, α∈[-1,1]; the adaptive approach law is designed with the change of missile distance:

Among them, k ₁ and k ₂ are constants greater than 0, and k ₁ and k ₂ satisfy:

Finally, the guidance law of the line-of-sight direction can be obtained as

(2) Guidance law design for line of sight azimuth direction Let ξ=R/V _m , e ₁ =θ _L -θ _Ld ,

φ=t _d -t-ξ, and make the following assumptions: Assumption 1: When derivation of e ₂ , the change of cosθ _L is small, and it is regarded as a constant; Assumption 2: During the guidance process, the time error term φ≥0 is always established; Design the sliding surface as follows:

Taking the derivative of both ends of the sliding surface s ₂ and substituting the formula into:

The reaching law is designed based on the superhelical sliding mode control method:

Among them, l ₁ and l ₂ are both constants greater than 0, and w is an adaptive parameter of the super sliding mode to prevent chattering on the sliding mode surface. Substitute the above formula into the sliding mode surface s ₂ to obtain the control variable a _mz is:

2. A computer system, characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more programs When executed by a plurality of processors, the one or more processors are caused to implement the method of claim 1 . 3. A computer-readable storage medium, characterized by storing computer-executable instructions that, when executed, are used to implement the method of claim 1 . 4. A computer program characterized by comprising computer-executable instructions which, when executed, are used to implement the method of claim 1 .

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