A design method of sliding mode guidance law with attack angle and convergence time control

Abstract

The application discloses a kind of attack angle and convergence time control's sliding mode guidance law design method, it includes the following steps: S1, establishes missile-target relative kinematics equation, constructs the state equation of guidance system considering attack angle constraint;S2, design convergence time controllable sliding surface and sliding mode approach law;S3, for the interference term in step S1, design fixed-time convergence disturbance observer, real-time solution interference estimation value;S4, based on sliding mode control method, according to the guidance system equation in step S1 and the sliding surface and sliding mode approach law designed in step S2, combined with the interference estimation value in step S3, design attack angle and convergence time controllable sliding mode guidance law.The application can directly set attack angle and convergence time, so that the attack angle error of missile converges at the set convergence time, and hits target with the set attack angle.

Description

Technical Field

[0001] This invention belongs to the field of missile guidance and control technology, and in particular relates to a sliding mode guidance law design method for controlling attack angle and convergence time. Background Technology

[0002] With the development of modern warfare, missile accuracy has become increasingly sophisticated, leading the industry to place new demands on missile guidance and control systems. For example, in the design of anti-ship and anti-tank missiles, there is a desire for the missile to hit the target at a specific angle, thereby maximizing the performance of the warhead and enhancing its destructive power.

[0003] Different guidance laws with attack angle constraints can be designed based on different theories. The guidance problem with attack angle constraints can be transformed into an optimal control problem with terminal constraints, and the optimal guidance law with attack angle constraints can be derived using optimal control theory. Ideally, the optimal guidance law has the best guidance performance, but it suffers from difficulties in solving and dependence on modeling accuracy. Traditional proportional guidance laws cannot meet the requirements of attack angle constraints; they are generally achieved by adding bias terms or varying proportional coefficients, resulting in simple structures and easy engineering implementation; however, the algorithms themselves are not robust, and their guidance performance is poor when intercepting maneuvering targets. Sliding mode control, due to its invariance to disturbances in the sliding mode, is widely used in guidance law design, but due to the discontinuity of control, it suffers from chattering problems. In addition, many scholars have designed inverse sliding mode composite guidance laws, circular arc guidance laws, and deep reinforcement learning guidance laws, among others. The terminal guidance phase of a missile is finite and often very short. The attack angle error and the missile-target line-of-sight angular velocity must converge rapidly before impact. Therefore, studying guidance laws that converge within a finite time has significant practical engineering implications. However, the aforementioned guidance laws do not consider the problem of finite-time convergence. Existing finite-time convergence guidance laws can only estimate the upper bound of the convergence time of the guidance system, and the convergence time is related to the guidance parameters or the initial state of the system, and cannot be directly set. Summary of the Invention

[0004] To address the problems in existing guidance law design for striking maneuvering targets with attack angle constraints and the inability to directly set the system convergence time, the present invention aims to provide a sliding mode guidance law design method for controlling the attack angle and convergence time. This method can ensure that the missile accurately hits the target at a set attack angle even in the presence of interference such as target maneuvering and system disturbances. The guidance system state converges within a finite time, and the convergence time and attack angle can be directly set.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] A sliding mode guidance law design method for controlling attack angle and convergence time, comprising the following steps:

[0007] S1. Establish the relative kinematic equations of the missile and the target, take the terminal missile-target line-of-sight angle as the attack angle, and treat the target maneuver and modeling error as interference terms to construct the state equations of the guidance system that consider the attack angle constraint.

[0008] S2. Based on the arbitrary convergence time control method, design a sliding surface with controllable convergence time and a sliding mode reaching law;

[0009] S3. For the interference term in step S1, design a fixed-time convergent interference observer to calculate the estimated value of the interference in real time.

[0010] S4. Based on the sliding mode control method, according to the guidance system state equation in step S1 and the sliding surface and sliding mode approaching law designed in step S2, and combined with the disturbance estimation value in step S3, a sliding mode guidance law with controllable attack angle and convergence time is designed.

[0011] Furthermore, in step S1 above, the relative kinematic equations of the projectile and target are as follows:

[0012]

[0013] In the formula, r is the relative distance between the missile and the target; v m θ m and a m These are the missile's speed, trajectory angle, and acceleration, respectively; v t θ t and a t These represent the target's velocity, trajectory angle, and acceleration, respectively; q is the target's line-of-sight angle.

[0014] Furthermore, in step S1 above, the terminal bullet's line-of-sight angle is used as the attack angle, and the state variable x1 = qq is defined. d , Control variable u = a m , where q d To determine the desired terminal missile-target line-of-sight angle, and considering the missile-target relative motion model, the state equation of the guidance system, taking into account the attack angle constraint, is as follows:

[0015]

[0016] in,

[0017] In the formula, Δ represents the modeling error, which mainly includes system disturbances and model uncertainties; d represents the total disturbance of the system. Due to the boundedness of the values ​​of system disturbances, missile acceleration, target acceleration, etc., d is considered to be bounded, i.e., |d|≤ξ, where ξ>0 is the upper bound of the disturbance.

[0018] Furthermore, in step S2 above, the sliding surface is...

[0019] s = x² + h(x₁)

[0020] in,

[0021] In the formula, t f1 >0 is the convergence time control parameter for system state variables x1 and x2; η1≥1 is the convergence speed control parameter, which controls the convergence speed of system state variables x1 and x2.

[0022] Furthermore, the sliding mode reaching law for step S2 above is:

[0023]

[0024] In the formula, 0 < t f2 <t f1 , t f2 η2≥1 is the convergence time control parameter for the sliding surface; η2≥1 is the convergence speed control parameter, which controls the convergence speed of the sliding surface s; sgn(s) is the sliding variable structure term; k>0 is the coefficient of the sliding variable structure term.

[0025] Furthermore, the above step S3 is defined as follows: Combined with the relative motion model of projectile and target, we obtain The designed fixed-time convergence disturbance observer is

[0026]

[0027] In the formula, This is an estimate of y; The estimation error of y; λ1, λ2, λ1, λ2, and λ3 are the design parameters of the interference observer, and their values ​​are selected to satisfy: γ1 > 1, 0 < γ2 < 1, λ1 > 0, λ2 > 0, λ3 > 0.

[0028] Furthermore, in step S4 above, the sliding mode guidance law with controllable attack angle and convergence time is as follows:

[0029]

[0030] in, Let h(x1) be the first derivative of h(x1) with respect to time.

[0031] The aforementioned guidance law mainly contains η1, η2, k, and t. f1 t f2 The parameter is adjusted by adjusting parameter t. f1 and t f2 The convergence time of the sliding surface and the system state can be adjusted by increasing parameters η1, η2, and k, and decreasing parameter t. f1 and t f2 This can improve the system's convergence speed and accuracy, but it increases the missile's required overload pressure. Since the missile's available overload is limited, a trade-off must be considered when selecting parameters. When time t approaches t... f2 At this point, the sliding surface s approaches zero, and the values ​​of the system state variables x1 and x2 are relatively small, allowing them to converge to zero in a short time. For ease of parameter setting, the relationship between the relevant parameters of the guidance law in step S4 is designed as follows:

[0032]

[0033] This ensures that the system state variables x1 and x2 converge to zero within 1 second after reaching the sliding surface, while effectively reducing the number of guidance law parameters.

[0034] Due to the adoption of the technical solution described above, the present invention has the following advantages:

[0035] This sliding mode guidance law design method, which controls the attack angle and convergence time, can effectively cope with disturbances such as target maneuvering and modeling errors, enabling the missile to accurately hit the target at the set attack angle. The missile-target line-of-sight angle and its angular rate can converge in a finite time, and the convergence time can be directly set without calculation based on guidance parameters. It can directly set the attack angle and convergence time, so that the missile's attack angle error converges at the set convergence time, and hits the target at the set attack angle. Attached Figure Description

[0036] Figure 1 This is a flowchart of the sliding mode guidance law design method for controlling the attack angle and convergence time of the present invention;

[0037] Figure 2 It is a diagram showing the relative motion between the missile and the target;

[0038] Figure 3 It shows the trajectory diagrams of the missile and the target under different attack angles with a fixed convergence time;

[0039] Figure 4 This is a graph showing the change of the sliding surface under different attack angles with a fixed convergence time;

[0040] Figure 5The curves showing the change in the line-of-sight angle of the projectile under different attack angles with a fixed convergence time;

[0041] Figure 6 The curves showing the change in the angular velocity of the projectile-eye line of sight under different attack angles with a fixed convergence time;

[0042] Figure 7 The curves showing the changes in missile acceleration under different attack angles with a fixed convergence time;

[0043] Figure 8 The trajectory diagrams of the missile and the target under different convergence times with a fixed attack angle;

[0044] Figure 9 The curves showing the change in the line-of-sight angle of the projectile under different convergence times when the attack angle is fixed.

[0045] Figure 10 The graph shows the change in the angular velocity of the projectile-eye line of sight under different convergence times when the attack angle is fixed.

[0046] Figure 11 The graph shows the missile acceleration variation under different convergence times when the attack angle is fixed.

[0047] Figure 12 This is a diagram showing the trajectory of the missile and the target when comparing the guidance law of this invention with existing guidance laws.

[0048] Figure 13 This is a graph showing the change in the line-of-sight angle between the missile and the target under the comparison of the guidance law of the present invention and the existing guidance law;

[0049] Figure 14 This is a graph showing the change in the angular velocity of the missile-eye line of sight when comparing the guidance law of this invention with existing guidance laws.

[0050] Figure 15 This is a curve showing the change in missile acceleration when comparing the guidance law of this invention with existing guidance laws. Detailed Implementation

[0051] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0052] like Figure 1 As shown, a sliding mode guidance law design method for attack angle and convergence time control includes the following steps:

[0053] S1. Establish the relative kinematic equations of the projectile and the target. The relative kinematic equations of the projectile and the target are as follows:

[0054]

[0055] In the formula, r is the relative distance between the missile and the target; vm θ m and a m These are the missile's speed, trajectory angle, and acceleration, respectively; v t θ t and a t These represent the target's velocity, trajectory angle, and acceleration, respectively; q is the target's line-of-sight angle.

[0056] Using the terminal's line-of-sight angle as the attack angle, define the state variable x1 = qq d , Control variable u = a m , where q d Given the desired terminal missile-target line-of-sight angle; considering the missile-target relative motion model, the state equation of the guidance system, taking into account the attack angle constraint, is:

[0057]

[0058] in,

[0059]

[0060] In the formula, Δ represents the modeling error, which mainly includes system disturbance and model uncertainty; d represents the total disturbance of the system. Due to the boundedness of the values ​​of system disturbance, missile acceleration, target acceleration, etc., d is considered to be bounded, i.e., |d|≤ξ, where ξ>0 is the upper bound of the disturbance.

[0061] The guidance law in this invention is achieved by controlling the missile's acceleration α. m The missile is made to fly stably, and the system states x1 and x2 converge to zero within a finite time, which satisfies the attack angle constraint and guidance accuracy requirements, and the attack angle and convergence time are controllable.

[0062] S2. Based on the arbitrary convergence time control method, design a sliding surface with controllable convergence time and a sliding mode reaching law; based on sliding mode control, the designed sliding surface is...

[0063] s=x2+h(x1) (4)

[0064] in,

[0065]

[0066] In the formula, t f1 >0, which is the convergence time control parameter for system state variables x1 and x2; η1≥1, which is the convergence speed control parameter, controlling the convergence speed of state variables x1 and x2;

[0067] The designed sliding mode convergence law is

[0068]

[0069] In the formula, 0 < t f2 <t f1 , t f2 η2≥1 is the convergence time control parameter for the sliding surface; η2≥1 is the convergence speed control parameter, which controls the convergence speed of the sliding surface s; sgn(s) is the sliding variable structure term; k>0 is the coefficient of the sliding variable structure term.

[0070] S3. For the interference term in step S1, design a fixed-time convergent interference observer to calculate the estimated value of the interference in real time.

[0071] definition Combined with the relative motion model of projectile and target, we obtain The designed fixed-time convergence disturbance observer is

[0072]

[0073] In the formula, This is an estimate of y; The estimation error of y; Let d be the estimated value of the total interference of the guidance system. γ1, γ2, λ1, λ2 and λ3 are the design parameters of the interference observer. Their values ​​must satisfy the following conditions: γ1 > 1, 0 < γ2 < 1, λ1 > 0, λ2 > 0, λ3 > 0.

[0074] S4. Based on the sliding mode control method, according to the guidance system state equation in step S1 and the sliding surface and sliding mode reaching law designed in step S2, combined with the disturbance estimation value in step S3, a sliding mode guidance law with controllable attack angle and convergence time is designed; the sliding mode guidance law with controllable attack angle and convergence time is as follows:

[0075]

[0076] in,

[0077]

[0078] in, Let h(x1) be the first derivative of h(x1) with respect to time.

[0079] The aforementioned guidance law mainly contains η1, η2, k, and t. f1 t f2 The parameter is adjusted by adjusting parameter t. f1 and t f2 The convergence time of the sliding surface and the system state can be adjusted by increasing parameters η1, η2, and k, and decreasing parameter t. f1 and t f2This can improve the system's convergence speed and accuracy, but it increases the missile's required overload pressure. Since the missile's available overload is limited, a trade-off must be considered when selecting parameters. When time t approaches t... f2 At this point, the sliding surface s approaches zero, and the values ​​of the system state variables x1 and x2 are relatively small, allowing them to converge to zero in a short time. For ease of parameter setting, the relationship between the relevant parameters of the guidance law in step S4 is designed as follows:

[0080]

[0081] This ensures that the system state variables x1 and x2 converge to zero within 1 second after reaching the sliding surface, while effectively reducing the number of guidance law parameters.

[0082] The stability and arbitrary-time convergence characteristics of the guidance law designed by the sliding mode guidance law design method of the present invention, which controls the attack angle and convergence time, are analyzed below.

[0083] Differentiating equation (4) for the sliding surface and substituting equation (8) for the guidance law, we get...

[0084]

[0085] Choose the following Lyapunov functions

[0086]

[0087]

[0088] Since t < t f2 When , g(s) and s have the same sign, therefore -sg(s) ≤ 0. The parameters are chosen to satisfy... Right now but The system is stable.

[0089] The estimation error of the interference d by equation (7) for the interference observer is generally a small value. Therefore, k is generally taken as a small value. It is also relatively small, and can be approximated as 0. Equation (12) is written as

[0090]

[0091] The analytical solution of equation (13) is

[0092]

[0093] In the formula, s0 is the value of the initial state s at time zero; For t f2 The value of time s.

[0094] As time approaches t f2 At that time, s and All approach zero, that is When t≥t f2 After that, s = 0.

[0095] When t≥t f2 When the sliding surface s converges to s = 0, equation (4) can be written as

[0096]

[0097] Its analytical solution is

[0098]

[0099] In the formula, t after reaching the sliding surface f2 The value of state x1 at time step; For t f1 The value of time x1.

[0100] As time approaches t f1 At that time, x1 and That is, x2 all approach zero, i.e. When t≥t f1 After that, x1 = 0 and x2 = 0. Therefore, the system states x1 and x2 can converge to zero in a finite time, satisfying the attack angle constraint and guidance accuracy requirements, and the convergence time can be arbitrarily set.

[0101] The following describes in further detail the sliding mode guidance law design method for controlling the attack angle and convergence time of the present invention, with reference to specific embodiments.

[0102] 1. Implementation Example Condition Settings

[0103] The embodiments of this invention were performed under computer simulation conditions, using MATLAB R2019b as the simulation software. Figure 2 As shown, taking a missile terminal guidance system as an example, the inputs to the guidance system include: the missile's flight speed v. m Initial track angle θ m (0) Expected attack angle q d , line-of-sight angle q, angular velocity of the line-of-sight angle The distance r between the projectile and the target and its rate of change Constructing a missile motion model for

[0104]

[0105] Construct the target motion model as

[0106]

[0107] The missile's initial position is set to (0m, 0m), and its velocity is v. m =500m / s, initial track angle is θ m (0) = 45°, the upper limit of missile acceleration is 100m / s² 2 The target's initial position is (8000m, 6000m), and its velocity is v. t =200m / s, initial track angle is θ t (0) = 120°. The parameters of the guidance law designed by the design method of this invention are set as η1 = η2 = 2, t f2 =t f1 -1, k = 0.01, γ1 = 1.5, γ2 = 0.4, λ1 = 20, λ2 = 50, λ3 = 10. The following three embodiments are provided to verify the effectiveness of the present invention.

[0108] Example 1

[0109] This embodiment designs the missile to strike moving targets at different attack angles. The attack angle q is set. d The angles are 60°, 70°, 80°, and 90°, with convergence times t. f1 =21s, the target moves at a constant speed. Figures 3-7 Simulation results are presented for different attack angles with a fixed convergence time.

[0110] Figure 3 The diagram shows the trajectory of the missile and the target. It can be seen that, depending on the set attack angle, under the guidance law of this invention, the missile flies with different ballistic trajectories and hits the target. The ballistic trajectory is smooth and the terminal phase is relatively straight.

[0111] Figure 4 The graph showing the variation of the sliding surface s indicates that the sliding surface can achieve the desired performance at a set t. f2 =t f1 -1 converges stably to zero at time 20s.

[0112] Figure 5 and Figure 6 The figures show the curves of the change in the projectile's line-of-sight angle and its angular velocity, respectively, at a set t... f1 =At 21s, the line-of-sight angle of the bullet can converge to the set attack angle, and at the same time, the line-of-sight angular velocity can converge to zero.

[0113] Figure 7 The diagram shows the missile overload variation curve. In the initial stage of the trajectory, the attack angle error is relatively large, resulting in a high missile acceleration, but it does not exceed the upper limit. In the terminal guidance stage, as the missile-target line-of-sight angle and its angular velocity converge, the missile acceleration also converges to zero. Because the guidance law of this invention... f1The time intervals are segmented and discontinuous, so there is a small jump in acceleration at 21s.

[0114] Example 2

[0115] This embodiment designs missiles to strike maneuvering targets with different convergence times. The desired attack angle q is set. d The angle is 60°, and the convergence time is t. f1 The time intervals are set to 15s, 16s, 17s, and 18s respectively, with a target acceleration of a. t =10m / s 2 The simulation results are as follows Figures 8-11 As shown.

[0116] Depend on Figure 8 and Figure 9 It can be seen that the missile is at an attack angle q d =60°, hitting the target with different ballistic trajectories, the projectile's line-of-sight angle can converge to the desired attack angle q at different set convergence times. d Nearby, the convergence time and attack angle were controlled.

[0117] Depend on Figure 10 It is understood that the line-of-sight angle of the projectile converges to near zero in the terminal phase, and changes to some extent when it hits the target. This is because the target is maneuvering and the relative motion between the projectile and the target changes drastically at the terminal moment, resulting in a significant change in the line-of-sight angular rate at the terminal phase.

[0118] Depend on Figure 11 It was found that the missile's acceleration converged to near zero in the terminal phase, and there was a significant change at the end of the simulation, which was caused by the change in the line-of-sight angular rate.

[0119] Example 3

[0120] This embodiment introduces an existing arbitrary-time convergence collision angle-constrained guidance law for comparative analysis. The existing guidance law takes the form of...

[0121]

[0122] Set the desired attack angle q d =60°, target serpentine maneuver, acceleration a t =30sin(πt / 10)m / s 2 The parameters of the guidance law equation (20) are set as N = 3, η = 2, t f =17, the convergence time of the guidance law of this invention is set to t. f1 =17s. Simulation results are as follows: Figures 12-15 As shown.

[0123] Depend on Figures 12-15It is known that the attack angle error of the guidance law of the present invention is less than 0.01° and the convergence time error is less than 0.01s, thus realizing the control of the attack angle and convergence time.

[0124] Depend on Figure 12 It is known that the ballistic trajectory of the guidance law of the present invention is straighter than that of the existing guidance law (20).

[0125] Depend on Figure 13 and Figure 14 It is understood that, for maneuvering targets, the guidance law of the present invention can make the line-of-sight angle of the missile converge to the desired value more smoothly and accurately, and make the line-of-sight angular rate converge to near zero. However, the existing guidance law (20) cannot make the line-of-sight angle of the missile and its angular rate converge stably, and the attack angle error is large.

[0126] Depend on Figure 15 It is understood that, in order to satisfy the finite-time convergence of the missile's line-of-sight angle and angular velocity, the missile requires a large overload in the early stage of guidance. Therefore, both guidance laws have large accelerations in the early stage. After the line-of-sight angle and angular velocity converge, the missile acceleration gradually decreases in the later stage. The missile acceleration of the guidance law of this invention gradually converges and approaches zero in the final stage of guidance, while the missile acceleration of the existing guidance law (20) still changes significantly in the final stage. Integrating the missile acceleration... As for energy consumption, the calculated energy consumption values ​​of the guidance law of the present invention and the existing guidance law (20) are 467.84 m / s and 492.73 m / s, respectively, indicating that the energy consumption of the guidance law of the present invention is less than that of the existing guidance law (20).

[0127] The simulation results of the above embodiments show that the present invention can make the missile's attack angle converge to the desired value within a set time under different target motion modes, thus meeting the requirement that the missile accurately hits the target at the desired attack angle. At the same time, the attack angle and convergence time can be directly set.

[0128] The above description is only a preferred embodiment of the present invention and not a limitation thereof. Any equivalent changes and modifications made in accordance with the scope of the present invention without departing from the spirit and scope of the present invention shall be within the scope of patent protection of the present invention.

Claims

1. A method for designing a sliding mode guidance law with attack angle and convergence time control, characterized in that: It comprises the following steps: S1, establishing a missile-target relative kinematics equation, taking the terminal missile-target line-of-sight angle as the attack angle, taking the target maneuvering and modeling error as a disturbance term, and constructing a guidance system state equation considering the attack angle constraint; S2, based on an arbitrary convergence time control method, designing a sliding mode surface and a sliding mode reaching law with controllable convergence time; The sliding mode surface is s=x2+h(x1) wherein In the formula, t f1 >0, which is the convergence time control parameter for system state variables x1 and x2; η1≥1, which is the convergence speed control parameter, controlling the convergence speed of state variables x1 and x2; The sliding mode reaching law is where 0 < t f2 < t f1 , t f2 is the convergence time control parameter of the sliding mode surface; η2≥1 is the convergence speed control parameter, which controls the convergence speed of the sliding mode surface s; sgn(s) is the sliding mode variable structure term; k > 0 is the sliding mode variable structure term coefficient; S3, for the disturbance term in step S1, designing a fixed-time convergence disturbance observer to calculate the estimated value of the disturbance in real time; S4, based on the sliding mode control method, according to the guidance system state equation in step S1, the sliding mode surface and the sliding mode reaching law designed in step S2, and the disturbance estimated value in step S3, designing a sliding mode guidance law u with controllable attack angle and convergence time, wherein q is the line-of-sight angle of the missile, θ m is the track angle of the missile, r is the relative distance between the missile and the target; v m is the velocity of the missile, v t is the velocity of the target, θ t is the track angle of the target; is the estimated value of the total disturbance d of the guidance system; is the first order derivative of h(x1) with respect to time; The relationship of the related parameters of the sliding mode guidance law u is designed as So that the set system state variables x1 and x2 converge to zero within 1s after reaching the sliding mode surface, while effectively reducing the number of guidance law parameters.

2. The attack angle and convergence time controlled sliding mode guidance law design method of claim 1, wherein: In step S1, the missile-target relative kinematics equation is where r is the relative distance between the missile and the target; v m , θ m , and a m are the velocity, the flight path angle, and the acceleration of the missile, respectively; v t , θ t , and a t are the velocity, the flight path angle, and the acceleration of the target, respectively; and q is the line-of-sight angle between the missile and the target.

3. The attack angle and convergence time controlled sliding mode guidance law design method of claim 2, wherein: In step S1, the terminal missile line-of-sight angle is used as the attack angle, and the state variable x1 = q - q d , The control variable u = a m , where q d is the desired terminal missile line-of-sight angle. Combining the relative motion model of the missile and the target, the state equation of the attack angle constraint guidance system is wherein, In the formula, Δ is the modeling error; d is the total disturbance of the system.

4. The attack angle and convergence time controlled sliding mode guidance law design method according to claim 3, characterized in that in step S3, the definition Combining the missile-target relative motion model, we have The designed fixed-time convergent disturbance observer is wherein is an estimate of y; is an estimated error of y; γ1, γ2, λ1, λ2 and λ3 are design parameters of the disturbance observer, and their values are selected to satisfy: γ1>1, 0<γ2<1, λ1>0, λ2>0, λ3>0.

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