阅读说明：本技术 一种强跟踪末制导方法 (Strong tracking terminal guidance method ) 是由 曾喆昭 于 2020-12-22 设计创作，主要内容包括：针对导弹拦截目标的末制导控制问题,本发明提出了一种强跟踪末制导控制方法。该制导控制方法的主要设计思想是以实时变化的弹目视线角为跟踪控制目标,控制拦截弹的航迹角快速跟踪弹目视线角,从而实现导弹拦截目标的强跟踪目的。为了实现该拦截目标,建立了受控弹目跟踪误差系统,据此设计了耦合PI末制导律,理论分析了弹目跟踪控制系统的鲁棒稳定性和抗扰动鲁棒性,仿真结果不仅验证了理论分析的合理性,而且表明了本发明的耦合PI末制导控制方法具有使拦截弹快速跟踪目标的强跟踪能力,在末制导控制领域具有重要的科学意义和应用价值。(The invention provides a strong tracking terminal guidance control method aiming at the terminal guidance control problem of a missile interception target. The guidance control method has the main design idea that the target line-of-sight angle of the missile which changes in real time is used as a tracking control target, and the track angle of the intercepted missile is controlled to quickly track the target line-of-sight angle, so that the aim of strongly tracking the intercepted missile is fulfilled. In order to realize the interception target, a controlled bullet tracking error system is established, a coupled PI terminal guidance law is designed according to the control method, the robustness stability and the disturbance resistance robustness of the bullet tracking control system are theoretically analyzed, the rationality of theoretical analysis is verified through simulation results, and the coupled PI terminal guidance control method has strong tracking capability for enabling the interception bullet to quickly track the target, and has important scientific significance and application value in the field of terminal guidance control.)

1. A strong tracking terminal guidance method is characterized by comprising the following steps:

1) according to the LOS angle q of the missile target and the missile track angle theta_mEstablishing a tracking error e₁And integral e of its error₀And differentialRespectively as follows:

wherein the content of the first and second substances,is the LOS angular velocity of the bullet eye, v_mIs the missile velocity, a_mIs the normal acceleration of the missile, t is the time variable;

2) in view ofThe controlled error system for tracking the LOS angle of the missile target by the missile track angle is established according to the step 1) as follows:

3) defining the proportional control force u of the terminal guidance control system according to the step 2)_pAnd the integral control force u_iRespectively as follows:

u_p＝2z_ce₁v_m，

wherein the content of the first and second substances,is a velocity factor, and alpha is more than or equal to 1 and less than or equal to 10, | u_i|≤0.5u_m，u_mIs the maximum normal acceleration of the missile, t_rIs the transition process time;

4) controlling the force u by a ratio according to step 3)_pAnd the integral control force u_iThe combination formation terminal guidance law is as follows:

wherein, | a_m|≤u_m；

5) Establishing a terminal guidance control system according to the step 2) and the step 4) as follows:

wherein the content of the first and second substances,is a bounded disturbance of unknown bullet;

6) from step 5), it can be seen that: disturbance of unknown bullet orderAny change in (b) will cause a tracking error e in the final guidance control system₁And its integral e₀Sensing in-phase changes and thereby causing a proportional control force 2z_ce₁And integral control forceForming a change of phase opposition to counteract the bullet unknown bounded disturbancesAny change of the control system makes the terminal guidance control system always in a stable equilibrium state of strong tracking.

Technical Field

The invention relates to a terminal guidance control method, in particular to a strong tracking terminal guidance control method.

Background

The use of precision guided weapons to perform precise and rapid interception of targets is a major mode of engagement in present and future warfare. The design of the terminal guidance law not only requires that the missile hit the target with a small miss distance, but also requires that the missile hit the target with a specific attack angle to achieve the maximum damage effect on the target in operation. The guidance laws that have been widely used in recent years mainly include an optimal control guidance law, a differential countermeasure guidance law, a control guidance law, a sliding mode control guidance law, and the like. When a missile flying at high speed in modern war hits a target, the time left for terminal guidance is often only dozens Of seconds, so that the Line Of Sight (LOS) angular rate Of the missile is urgently required to be quickly converged, the missile is ensured to be stabilized to an expected LOS angular direction before colliding with the target, and the guidance performance is improved. Terminal Sliding Mode Control (TSMC) ensures that the system state can converge in a finite time by introducing a nonlinear Sliding Mode surface. In recent years, the design of a guidance law aiming at a maneuvering target by adopting a TSMC (time series compensation) method is widely researched, however, the TSMC method has the singularity problem, so that a nonsingular terminal sliding mode control method is provided, for example, an integral sliding mode surface is designed in the process of researching the guidance law with attack angle constraint to avoid the singularity problem. In addition, when the system state is far away from the balance point, the TSMC convergence rate is slow, and in order to accelerate the convergence rate, a nonsingular fast terminal sliding mode control method is provided. Because the system state convergence time obtained by adopting the limited time convergence TSMC depends on the initial conditions of the system, the specific initial states of the missile and the target are usually unknown in advance in the process of designing the guidance law of the missile, and the convergence time obtained by different initial conditions is different, therefore, as the extension of a limited time stability theory, the concept of fixed-time convergence (FTC) is provided, and the FTC theory can enable the system to obtain an upper convergence time bound independent of the initial conditions. When the FTC is adopted for designing the guidance law, the upper bound of the convergence time of the system state can be preset to a fixed value independent of the initial conditions through parameter control, so that the designed guidance law is wider in application range and higher in guidance performance. For example, the nonsingular terminal sliding mode fixed time convergence guidance law design method with attack angle constraint solves the problem of singularity of a terminal sliding mode surface, and enables the sliding mode surface, the LOS angle and the LOS angle rate to be converged quickly in fixed time. Compared with the traditional fixed time convergence control method, the guidance law has a faster convergence rate.

All of the above methods are around the desired LOS angle q_dFor controlling the target, the normal acceleration a of the arresting missile is designed_mInstructions to control LOS angle q to achieve tracking of desired LOS angle q before the missile hits the target_dI.e. q → q_d. However, in the missile end guidance terminal, LOS angular acceleration is caused when the relative distance r → 0 of the missile eyesThe singular situation of (2) increases the control difficulty, and makes the design of the guidance law become very complexAnd only the index of the zero-distance hit target can be sacrificed. To this end, the invention proposes to use the missile path angle theta_mAnd (3) tracking an LOS angle q. The method is not only a guidance control method for the missile strongly tracking target, but also the guidance controller has the outstanding advantages of simple structure, small calculated amount and good real-time performance, and can realize the accurate strike of strongly tracking zero miss amount.

Disclosure of Invention

The invention provides a strong tracking terminal guidance law method which is characterized by comprising the following steps:

1) according to the LOS angle q of the missile target and the missile track angle theta_mEstablishing a tracking error e₁And integral e of its error₀And differentialRespectively as follows:

wherein the content of the first and second substances,is the LOS angular velocity of the bullet eye, v_mIs the missile velocity, a_mIs the normal acceleration of the missile, t is the time variable;

2) in view ofThe controlled error system for tracking the LOS angle of the missile target by the missile track angle is established according to the step 1) as follows:

3) defining the proportional control force u of the terminal guidance control system according to the step 2)_pAnd the integral control force u_iRespectively as follows:

u_p＝2z_ce₁v_m，

wherein the content of the first and second substances,is a velocity factor, and alpha is more than or equal to 1 and less than or equal to 10, | u_i|≤0.5u_m，u_mIs the maximum normal acceleration of the missile, t_rIs the transition process time;

4) controlling the force u by a ratio according to step 3)_pAnd the integral control force u_iThe combination formation terminal guidance law is as follows:

wherein, | a_m|≤u_m；

5) Establishing a terminal guidance control system according to the step 2) and the step 4) as follows:

wherein the content of the first and second substances,is a bounded perturbation of which the bullet is unknown.

6) From step 5), it can be seen that: disturbance of unknown bullet orderAny change in (b) will cause a tracking error e in the final guidance control system₁And its integral e₀Sensing in-phase changes and thereby causing a proportional control force 2z_ce₁And integral control forceForming a change of phase opposition to counteract the bullet unknown bounded disturbancesAny change of the control system makes the terminal guidance control system always in a stable equilibrium state of strong tracking.

Drawings

Fig. 1 longitudinal plane projectile relative motion model.

Fig. 2 strongly tracks the end guidance result, (a) an interception track, (b) a guidance instruction, (c) a missile eye relative distance, (d) an attack angle track, and (e) a LOS angle and missile track angle track.

Detailed Description

1. Model for relative movement of bullet eyes

Consider the problem of missile end guidance in a two-dimensional longitudinal plane, as shown in figure 1. Let the velocities of missile M and target T be constant, denoted v respectively_mAnd v_t(ii) a r and q respectively represent the relative distance of the bullet and the LOS angle; theta_mAnd theta_tRespectively representing the track angles of the missile and the target; a is_mAnd a_tNormal accelerations of the missile and the target are respectively represented; the bullet eye relative kinematics model is

LOS angular acceleration can be deduced according to formula (1)Is composed of

As shown in the formula (2): a is_tIs an unknown target maneuvering item, is equivalent to external disturbance and is set as total disturbanceTime varying control coefficientThe system (2) is thus effectively a non-linear time-varying perturbing system. Especially when the phases are of the order of the eyesFor the distance r → 0, d → ∞ and b → ∞ are caused, and thus LOS angular acceleration is causedThe singular case of (a). Obviously, the guidance law a of the missile is designed according to the nonlinear time-varying disturbance singular system (2)_mIs very challenging. However, the inventors believe that: by designing the guidance law a_mTo control the missile eyes LOS angle q to track the desired q_dI.e. q → q_dNot the only effective method, to this end, the inventors propose a missile trajectory angle θ with the missile aim LOS angle q as the desired target_mA tracking control method.

2. Control principle of strong tracking terminal guidance system

2.1 Strong tracking terminal guidance law design

Let θ_mAnd q is the missile track angle and the missile target LOS angle respectively, and the established tracking error and the integral thereof are respectively as follows: e.g. of the type₁＝q-θ_m，In combination with the system (1), one obtains:

wherein the LOS angular ratev_mIs the missile velocity.

In view ofThe controlled error system for tracking the LOS angle of the missile at the missile flight path angle is as follows:

defining a proportional control force u_pAnd the integral control force u_iRespectively as follows:

wherein, 0<z_c<Infinity is the speed factor and is:1≤α≤10，t_ris the transition process time.

In order to avoid overshoot and ringing due to integral saturation, it is required to limit the integral control force:

|u_i|≤0.5u_m (6)

wherein u is_mIs the maximum normal acceleration of the missile.

By proportional control of force u_pAnd the integral control force u_iCombine to form the final guidance law of

Wherein, | u_i|≤0.5u_m，|a_m|≤u_m。

2.2. Strong tracking terminal guidance system stability analysis

Theorem 1 set perturbationThe method has the following steps: epsilon is less than or equal to | d |<Infinity, then if and only if the speed factor 0<z_c<Infinity, the projectile strong tracking terminal guidance system is robust and stable in a large range, has good disturbance resistance robustness and stable errorInterception control of zero miss distance can be theoretically achieved.

And (3) proving that: terminal guidance law a defined by equation (7)_mSubstituting the controlled error system (4) to obtain the final guidance closed loop control system as follows:

as known from the system (8): disturbance of unknown bullet orderAny change in (b) will cause a tracking error e in the final guidance control system₁And its integral e₀The same-phase change is sensed, and then the proportional control force and the integral control force form reverse phase change to counteract the unknown bounded disturbance of the bulletThe last guidance control system is always in a stable balance state.

Taking Laplace transform of the system (8) and arranging the Laplace transform to obtain:

the transfer function of the terminal guidance closed-loop control system is defined as follows:

when 0 is present<z_c<Infinity, due to H(s) having a double real pole s in the left half plane of the complex frequency domain_p＝-z_c<0, so that system (10) or (8) is stable over a wide range; and because of the velocity factor 0<z_c<Infinity is independent of the model of the controlled system (1), and the closed-loop control system (10) or (8) is thus robust and stable over a wide range.

Since the system (10) has a unit impulse response of

h(t)＝(1-z_ct)exp(z_ct)，t>0 (11)

The time domain solution of the tracking error, which can be obtained from equation (9), is

Where ". x" is the convolution integral operator.

Due to disturbancesThe method has the following steps: epsilon is less than or equal to | d |<Infinity, therefore, according to equation (12), there is

Thus, according to equation (11) there is

From the formula (11): when 0 is present<t≤1/z_cWhen h (t) is more than or equal to 0; when 1/z is_c<t<Infinity, h (t)<0, and h (∞) is 0. According to the nature of the laplace transform:then there are:namely, it isThus, according to the formula (14), the

Where e is the base of the natural logarithm.

Substituting formula (15) for formula (14) to obtain

Represented by the formula (16)) As can be seen, the steady state error of the last guidance control system meets the bounded conditionAnd with the velocity factor z_cIs increased and decreased; when z is_c→ ∞ time, | e₁And (∞) | ═ 0, zero miss distance control can be realized theoretically. And because the steady-state error of the terminal guidance control system is only related to the upper bound epsilon of the LOS angular velocity and is not related to the model of the missile target relative motion system (1), the strong tracking terminal guidance system has good disturbance-resistant robustness, and the verification is finished.

2.3. Speed factor stabilizing method of strong tracking end guidance controller

Although theorem 1 indicates when the speed factor is 0<z_c<And infinity, the strong tracking coupling PI terminal guidance system is robust and stable in a large range and has good disturbance resistance robustness. However, the velocity factor z_cExcessive overshoot causes overshoot and ringing, requiring reasonable settling of the speed factor. The speed factor stabilizing method designed by the invention comprises

Wherein 1 is<α≤10，t_rThe transition process time of the terminal guidance system from the dynamic process to the steady-state process is shown.

3. Simulation results and analysis

In order to verify the effectiveness of the strong tracking terminal guidance control method, the initial distance of the missile is set as r₀10km, initial LOS angle q₀30 °; the initial path angles of the eyes are theta_m0＝60°、θ_t090 °; the speed of each bullet is v_m＝500m/s、v_t400 m/s; target mobility a_t7gsin (0.25 pi t), and the gravity acceleration g is 9.8m/s²Maximum acceleration u of the missile_m＝20g。

Defining missile attack angleAngle of view phi theta_m-q＝-e₁Let a t_rIf 1s, α is 5, and the velocity factor of the end-of-track guidance controller is z according to equation (17)_c100/s, and | u_i|≤0.4u_m＝8g，|a_m|≤u_m20 g. Therefore, according to equation (7), the strong tracking end guidance controller is

Wherein z is_c100/s, and | u_i|≤0.4u_m＝8g，|a_m|≤u_m＝20g。

In the following simulation experiments, except for different initial track angles of the missiles, the speed factor and the amplitude limiting condition of the strong tracking terminal guidance law are completely the same.

Simulation experiment 1, when the initial track angle of the missile is 60 degrees, the missile is intercepted by using the strong tracking end guidance controller (18) of the invention, and the simulation result is shown in figure 2.

As can be seen from fig. 2, the strong tracking terminal guidance control method provided by the invention intercepts the target, obtains a good intercepting effect, and shows the effectiveness of the strong tracking terminal guidance control method provided by the invention. And (3) from 1.3 seconds to the moment before the terminal attack, the missile track angle completely tracks the LOS angle of the missile, which indicates that the missile enters a strong tracking state after 1.3 seconds. Wherein, terminal attack time t_f65.929 s; the miss distance is-0.056 m, which means that the missile penetrates through the target and is actually equivalent to zero miss distance strike; the attack angle is-0.03 degrees, which represents that the missile is off-right from the back of the target by 0.03 degrees and tracks the attack strongly.

Simulation experiment 2. when the initial track angles of the missiles are respectively in the range of 0-180 degrees, the relevant technical indexes are shown in table 1 for comparison.

As can be seen from Table 1, the target can be accurately intercepted when the initial track angle of the missile is launched within the range of 0-180 degrees, which shows that the terminal guidance control method has strong tracking interception capability. In addition, when the initial track angle of the missile is too small or too large, the terminal interception time is prolonged, and when the initial track angle is emitted within the range of 60-120 degrees, the interception time is shortest; considering the field angle factor, the initial track angle of the missile should be controlled within the range of 0-60 degrees near the initial LOS angle.

TABLE.1 Main technical indices

4. Conclusion

Aiming at the interception control problem of terminal guidance, the invention provides a strong tracking terminal guidance control method, the large-range robust stability and the disturbance resistance robustness of a bullet terminal guidance control system are analyzed in a complex frequency domain, and a simulation result shows the effectiveness of the strong tracking terminal guidance control method, so that the method not only has good dynamic quality and steady-state performance, but also has the outstanding advantages of simple controller structure, small calculated amount and good robust stability of the terminal guidance control system, and is convenient for practical application.

The method has important scientific significance and application value in the field of strong tracking terminal guidance control.