Virtual point-based attitude constraint mid-terminal guidance junction section trajectory design method

Abstract

The invention discloses a virtual point-based attitude constraint mid-terminal guidance handover section trajectory design method, which comprises the following steps of: starting control after a remote guidance ammunition finishes an initial section, and entering a mid-guidance section; under the guidance of the mid-guidance law, the remote guidance ammunition passes through the virtual point, enters the mid-terminal guidance handover section, glides and flies in the mid-terminal guidance handover section and stabilizes the posture of the remote guidance ammunition, the moment when the seeker enters the pre-capture state serves as a capture point, the seeker starts to work after a target is captured, and the remote guidance ammunition enters the terminal guidance section; and finally guiding the remote guidance ammunition to hit the target. Wherein the zero miss distance guidance instruction of the mid-guidance law is used for ensuring that the remote guidance ammunition accurately passes through a virtual point, and the zero trajectory inclination angle error instruction is used for realizing angle constraint of a mid-guidance section of the remote guidance ammunition, so that stable handover of the remote guidance ammunition between the mid-guidance section and a terminal guidance section can be theoretically ensured; and meanwhile, the guidance precision in the remote guidance ammunition can be ensured by a residual flight time estimation method considering the ballistic curvature.

Description

Technical Field

[0001] The invention relates to the field of long-range guided munition trajectory design, and in particular to a mid-terminal guidance handover trajectory design method based on virtual point attitude constraints. Background Art

[0002] The smooth handover of mid-terminal guidance is one of the key issues that must be faced in the design of the long-range guided munitions' trajectory scheme. In order to ensure the smooth handover of the mid-terminal guidance section and the terminal guidance section, the engineering generally requires the long-range guided munitions to complete the mid-terminal guidance handover and the mid-terminal trajectory handover in the mid-terminal guidance handover section. Among them, the mid-terminal seeker handover refers to guiding the long-range guided munitions to the target airspace smoothly and accurately within the allowable error range, ensuring that the long-range guided munitions' seekers can successfully intercept the target and enter the terminal guidance section; the mid-terminal trajectory handover refers to the smooth transition of the long-range guided munitions' mid-terminal trajectory. There are many factors that affect the smooth handover of the mid-terminal guidance of long-range guided munitions, such as the long-range guided munitions' ballistic inclination angle, angle of attack, seeker field of view angle, and attitude disturbance motion during the flight process. Taking the trajectory inclination angle of long-range guided munitions as an example, if the trajectory inclination angle of the terminal guidance handover phase is not selected reasonably, at the very least, the long-range guided munition will require excessive overload in the terminal guidance phase to achieve a large angle of impact and hit the target, thus affecting the terminal guidance performance. At worst, it will cause the long-range guided munition seeker to fail to capture the target, resulting in a situation where the target cannot be hit. Summary of the invention

[0003] The purpose of the present invention is to provide a trajectory design method for a mid-terminal guidance transition section based on a virtual point attitude constraint, so as to ensure a smooth transition of a long-range guided munition in the mid-terminal guidance transition section.

[0004] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0005] A trajectory design method for mid-terminal guidance handover phase based on attitude constraints of virtual points, comprising:

[0006] After the long-range guided munition finishes the initial stage, it starts control and enters the mid-range guidance stage; under the guidance of the mid-range guidance law, the long-range guided munition passes through the virtual point and enters the mid-range and terminal guidance handover stage, gliding and stabilizing its own attitude in the mid-range and terminal guidance handover stage, and the moment when the seeker enters the pre-capture state is taken as the capture point. After capturing the target, the seeker starts working, and the long-range guided munition enters the terminal guidance stage, and finally guides the long-range guided munition to hit the target.

[0007] Furthermore, the position of the capture point in the long-range guided munition launch coordinate system (L C ,H C )’s horizontal and vertical coordinates satisfy:

[0008]

[0009]

[0010] Among them, L T Indicates the target position, parameter c t The value range is 0.7~0.8, L cmax represents the maximum acquisition distance of long-range guided munitions to the target, θ s represents the field of view angle of the seeker, θ d represents the desired trajectory inclination, α d is d Matching angle of attack, Represents the boundary of attitude angle disturbance of long-range guided munitions.

[0011] Furthermore, the position of the virtual point in the long-range guided munition launch coordinate system (L B ,H B )’s horizontal and vertical coordinates satisfy:

[0012]

[0013]

[0014] Among them, V B represents the terminal speed of long-range guided munitions in the mid-guidance phase, c B is a parameter not less than 2, T s is the decay time of the attitude angle disturbance of the guided munition.

[0015] Furthermore, the trajectory design scheme in the mid-terminal guidance handover section is:

[0016] a) Clarify the aerodynamic parameters, overall indicators and disturbance characteristics of long-range guided munitions during flight, and determine the boundary of attitude angle disturbance of long-range guided munitions based on the aerodynamic derivative data of long-range guided munitions during flight and the motion state of conventional flight. And the decay time T of the attitude angle disturbance of the long-range guided munition during the gliding flight s ;

[0017] b) According to the detection performance of the seeker carried by the long-range guided munition, determine the maximum capture distance L of the long-range guided munition to the target cmax , and according to the design requirements of the long-range guided munitions trajectory scheme, determine the parameter c t ;

[0018] c) Determine the expected trajectory inclination angle θ of the long-range guided munition according to the requirements of the long-range guided munition trajectory plan d , and solve the corresponding angle of attack α d , calculate the coordinates of the desired capture point in the long-range guided munition launch coordinate system (L C ,H C);

[0019] d) Based on the decay time T of the attitude angle disturbance of the long-range guided munition s and parameter c B , determine the glide distance L of long-range guided munitions in the mid-terminal guidance handover phase BC =V B T B , calculate the coordinates of the virtual point position in the launch coordinate system (L B ,H B );

[0020] e) The time when the long-range guided munition ends the initial segment is used as the start-up time of the mid-range guidance segment. Under the guidance of the mid-range guidance law, based on the determination of the virtual point, the smooth handover of the long-range guided munition in the mid-range and terminal guidance segments is achieved; the mid-range guidance law is composed of a zeroing miss amount guidance instruction based on an optimal tracking error model and a zeroing trajectory inclination angle and a desired trajectory inclination angle error guidance instruction, wherein the zeroing miss amount guidance instruction is used to ensure that the long-range guided munition passes through the virtual point accurately, and the zeroing trajectory inclination angle and the desired trajectory inclination angle error instruction is used to achieve the attitude constraint of the long-range guided munition in the mid-range guidance segment of the long-range guided munition.

[0021] Furthermore, the guidance instruction of the middle guidance law is expressed as:

[0022]

[0023] Where N is a positive constant, V M is the flight speed of long-range guided munitions, is the first-order derivative of the line-of-sight angle between the long-range guided munition and the virtual point, K is the guidance gain, t go is the remaining flight time of long-range guided munitions, ε θ is the tracking error between the trajectory inclination and the expected trajectory inclination.

[0024] Furthermore, the remaining flight time of the long-range guided munition in the guidance instruction of the medium guidance law is estimated by the following formula:

[0025]

[0026] in, is the estimated value of the remaining flight time of the long-range guided munition, R is the relative distance between the virtual point and the long-range guided munition, θ λ is the velocity error angle of long-range guided munitions.

[0027] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor is executed by a computer, the method for designing a trajectory of a terminal guidance handover segment based on a virtual point attitude constraint is implemented.

[0028] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the method for designing a trajectory in a terminal guidance handover segment based on a virtual point attitude constraint is implemented.

[0029] Compared with the prior art, the present invention has the following technical features:

[0030] 1. In the mid-terminal guidance handover trajectory design method based on virtual points considering attitude constraints provided by the present invention, the ballistic inclination angle of the long-range guided munition in the mid-terminal guidance handover section, the angle of attack corresponding to the ballistic inclination angle, the attitude disturbance boundary of the gliding flight and the field of view angle of the seeker are taken into consideration, which theoretically ensures that the long-range guided munition can accurately capture the target and smoothly enter the terminal guidance section.

[0031] 2. In the mid-terminal guidance handover trajectory design method based on virtual points considering attitude constraints provided by the present invention, virtual points are selected by analyzing the decay time of the disturbance motion of the long-range guided munition during the gliding flight, which theoretically ensures the attitude stability of the long-range guided munition in the mid-terminal guidance handover section, which is conducive to the long-range guided munition to capture the target.

[0032] 3. In the mid-terminal guidance handover trajectory design method based on virtual points considering attitude constraints provided by the present invention, the optimal mid-term guidance law based on angle constraints can ensure that the long-range guided munitions accurately pass through the virtual points at the expected trajectory inclination angle, enter the designed mid-terminal guidance handover trajectory, and achieve a smooth handover of mid-terminal guidance.

[0033] 4. In the mid-range and terminal guidance handover trajectory design method based on virtual points considering attitude constraints provided by the present invention, the mid-range guidance accuracy of long-range guided munitions is guaranteed by real-time estimation of the remaining flight time, and the influence of aerodynamic perturbations on the flight process of the mid-range guidance section is reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is the overall trajectory plan of a long-range guided munition in the launch coordinate system;

[0035] Figure 2 The design process of mid-terminal guidance handover trajectory based on virtual points considering attitude constraints;

[0036] Figure 3 It is a schematic diagram of the virtual point tracking model;

[0037] Figure 4 When there are different aerodynamic perturbations, the long-range guided munitions guided by the medium guidance law track the virtual point B: (a) virtual point trajectory diagram, (b) distance change curve from the virtual point, (c) trajectory inclination change curve, (d) line of sight angular velocity change curve, (e) acceleration response curve, and (f) flight control energy change curve.

[0038] Figure 5 When the medium guidance law guides the long-range guided munitions with different guidance gains K, the following are shown: (a) virtual point trajectory, (b) distance change curve from the virtual point, (c) trajectory inclination change curve, (d) line of sight angular velocity change curve, (e) acceleration response curve, and (f) flight control energy change curve.

[0039] Figure 6 is the desired trajectory inclination angle θ d Figure 1. (a) Tracking virtual point trajectory diagram, (b) distance change curve from the virtual point, (c) trajectory inclination change curve, (d) line of sight angular velocity change curve, (e) acceleration response curve, and (f) flight control energy change curve of the long-range guided munition guided by the medium guidance law at -50°, -65°, -75°, and -80° respectively. DETAILED DESCRIPTION

[0040] The present invention provides a trajectory design method for mid-terminal guidance handover section with attitude constraint based on virtual points. The method derives a calculation method for capturing points in the mid-terminal guidance handover section of a long-range guided munition by analyzing the process of a long-range guided munition seeker capturing a target. The calculation method for virtual points is derived by analyzing the attenuation time of attitude angle disturbance error and the flight state of the long-range guided munition during flight, thereby realizing the smooth handover of the long-range guided munition in the mid-terminal guidance section. The optimal mid-term guidance law considering attitude constraint is composed of a zero miss amount guidance instruction based on an optimal tracking error model and a zero trajectory inclination error guidance instruction, wherein the zero miss amount guidance instruction is used to ensure that the long-range guided munition passes through the virtual point accurately, and the zero trajectory inclination error instruction is used to realize the attitude constraint of the long-range guided munition in the mid-terminal guidance section. When the mid-term guidance law is used to realize the mid-terminal guidance handover trajectory scheme based on virtual points, the smooth handover of the long-range guided munition in the mid-terminal guidance section and the terminal guidance section can be theoretically guaranteed. At the same time, in order to ensure the guidance accuracy of long-range guided munitions, a remaining flight time estimation method considering the trajectory curvature was derived, thereby reducing the impact of disturbances such as aerodynamic perturbations on the flight process of the guidance segment of long-range guided munitions and ensuring the guidance performance of long-range guided munitions.

[0041] like Figure 1 As shown, a method for designing a trajectory of a mid-terminal guidance transition section based on an attitude constraint of a virtual point is disclosed, wherein, after the long-range guided munition finishes the initial section, control is started and the long-range guided munition enters the mid-terminal guidance section; under the guidance of the mid-terminal guidance law, the long-range guided munition passes through the virtual point and enters the mid-terminal guidance transition section, glides and stabilizes its own attitude in the mid-terminal guidance transition section, and the moment when the seeker enters the pre-capture state is taken as the capture point. After the target is captured, the seeker starts to work, the long-range guided munition enters the terminal guidance section, and finally guides the long-range guided munition to hit the target.

[0042] The relevant symbols and meanings in the trajectory scheme are shown in Table 1:

[0043] Table 1 Symbols and meanings in the long-range guided munitions trajectory scheme

[0044]

[0045]

[0046] From the overall trajectory plan of long-range guided munitions, we can know that when the trajectory inclination angle θ M Greater than the sight angle θ L When ∠C1CC s1 >∠C1CT, the trajectory of the long-range guided munition is in a downward state after the seeker captures the target, which is beneficial to increase the fall angle and put the long-range guided munition in a motion state that is conducive to hitting the target.

[0047] Among them, in the mid-terminal guidance handover section, the trajectory design of the present invention is as follows Figure 2 As shown, the details are as follows:

[0048] a) Clarify the aerodynamic parameters, overall indicators and disturbance characteristics of long-range guided munitions during flight, and determine the boundary of attitude angle disturbance of long-range guided munitions based on the aerodynamic derivative data of long-range guided munitions during flight and the motion state of conventional flight. And the decay time T of the attitude angle disturbance of the long-range guided munition during the gliding flight s ;

[0049] b) According to the detection performance of the seeker carried by the long-range guided munition, determine the maximum capture distance L of the long-range guided munition to the target cmax , and according to the design requirements of the long-range guided munitions trajectory scheme, determine the parameter c t ;

[0050] c) Determine the expected trajectory inclination angle θ of the long-range guided munition according to the requirements of the long-range guided munition trajectory plan d , and solve the corresponding angle of attack α d , calculate the coordinates of the desired capture point in the long-range guided munition launch coordinate system (L C ,H C );

[0051] d) Based on the decay time T of the attitude angle disturbance of the long-range guided munition s and parameter c B , determine the glide distance L of long-range guided munitions in the mid-terminal guidance handover phase BC =V B T B , calculate the coordinates of the virtual point position in the launch coordinate system (L B ,H B );

[0052] e) The time when the long-range guided munition ends the initial stage is used as the start-up time of the mid-range guidance stage; in order to adapt to the flight state of the long-range guided munition, the mid-range guidance law parameters of the long-range guided munition can be adjusted to meet the ballistic requirements of the mid-range guidance stage of the long-range guided munition.

[0053] 1. Determination of the position of the capture point in the launch coordinate system

[0054] In this scheme, the position of the capture point of the long-range guided munition in the launch coordinate system is determined as follows:

[0055] First, assume that the desired trajectory inclination angle at the mid-terminal junction is θ d , during the gliding phase of the missile body during the handover between mid-terminal guidance, the missile body forces satisfy the following relationship:

[0056] mgcosθ d =Y (1)

[0057] Among them, Y is the lift generated by the projectile, satisfying:

[0058]

[0059] In the long-range guided munitions, the expected ballistic inclination angle is θ d Flight process, corresponding angle of attack α d satisfy:

[0060]

[0061] Substituting velocity and density for dynamic pressure:

[0062]

[0063] Generally speaking, and A are mainly affected by the projectile velocity, and the related α d With θ d In addition to the projectile speed, it is also affected by speed and density. According to the overall trajectory design process, the speed of long-range guided munitions changes little during the glide process of the mid-terminal guidance handover phase. Therefore, for a certain flight speed that is approximately constant, and A are almost constant. At this time, α d With θ d is mainly affected by density, which is mainly determined by altitude, so α d With θ d The relationship can be expressed as:

[0064] α d =f(H,θ d ) (5)

[0065] Therefore, the gliding flight status of long-range guided munitions in the mid-terminal guidance transition phase, including the posture of the projectile at the capture point, can be determined.

[0066] The meanings of the symbols in the process of long-range guided munition capture point calculation are shown in Table 2.

[0067] Table 2 Meaning of symbols in the process of long-range guided munition capture point calculation

[0068]

[0069] By the attached Figure 1 It can be seen that for long-range guided munitions, when the seeker field of view angle θ s With the capture angle θ λ When they are the same, it is the optimal capture angle, that is, θ λ =θ s However, due to the existence of flight disturbances, the attitude angle of long-range guided munitions may increase, the projectile may rise, the target may move out of the capture domain, and the seeker may fail to capture the target. Therefore, it is necessary to consider the disturbance boundary of the projectile. Assume that the boundary of the attitude angle disturbance of the projectile during the gliding flight of the mid-terminal guidance handover phase is The capture angle

[0070] At this point, the geometric relationship of the overall trajectory scheme can be calculated:

[0071]

[0072] Capture height H C and the forward capture domain R C0 Respectively meet:

[0073] H C =R T sin∠CTA (7)

[0074] R C0 =R T cos∠CTA (8)

[0075] In order to ensure that the long-range guided munitions seeker can successfully capture the target, the capture distance R T Should be less than the maximum capture distance L cmax Generally speaking, R is set in engineering T =c t L cmax , c t The value range is 0.7 to 0.8.

[0076] According to the geometric relationship, the capture point C of the long-range guided munition in the overall trajectory plan is located in the launch coordinate system (L C ,H C)’s horizontal and vertical coordinates satisfy:

[0077]

[0078]

[0079] In summary, the position of the capture point of the long-range guided munition in the launch coordinate system has been determined.

[0080] 2. Determination of the position of the virtual point in the launch coordinate system

[0081] In this scheme, the position of the virtual point of the long-range guided munition in the launch coordinate system is determined as follows:

[0082] The selection of virtual points is directly determined by the mid-terminal guidance handover section of the long-range guided munition. According to the requirements of the overall ballistic plan, after the long-range guided munition ends the mid-terminal guidance section, it should enter the mid-terminal guidance handover section at the expected trajectory angle, and then achieve a smooth transition by gliding flight. Due to the existence of disturbances, the attitude of the long-range guided munition has attitude angle oscillation during the flight process. Therefore, the gliding flight time of the mid-terminal guidance handover section should be greater than the attenuation time of the disturbance attitude angle of the long-range guided munition body, so as to ensure that the attitude angle of the long-range guided munition is stable when the mid-terminal guidance handover section ends.

[0083] In reality, the gliding time of long-range guided munitions in the mid-terminal guidance handover phase is very short, and the speed change is also small. Therefore, the long-period motion of the projectile and the change of speed can be ignored in the research process. The longitudinal disturbance motion model of the long-range guided munition projectile can be expressed as:

[0084]

[0085] Among them, a α 、b α and a ω is the dynamic coefficient of the projectile. Eliminating Δα and Δθ in the projectile disturbance motion model, the projectile attitude angular motion disturbance satisfies:

[0086]

[0087] For the oscillating motion process of the projectile, the attenuation equation of the attitude angle is:

[0088]

[0089] Among them, λ i is the special solution of the characteristic equation of motion of the missile body attitude angle disturbance:

[0090] λ 2 +(b α +a ω )λ+(a α +aω b α )=0 (14)

[0091] Each λ i The corresponding perturbed motion equations have the following special solutions:

[0092]

[0093] In the transition phase between mid-range and terminal guidance, the velocity variation range of long-range guided munitions is relatively small, and the change in air density is the main factor affecting a α 、b α and a ω In order to ensure a smooth transition in the transition section, the flight time of this stage can be given, and the following is made:

[0094]

[0095] Solve for the decay time T at this time s , then the gliding time T B =c B T s , where c B Not less than 2.

[0096] Assume that the speed of the long-range guided munition at the end of the mid-guidance phase is V B Since the glide flight speed of long-range guided munitions changes little in the transition between mid-terminal guidance, the glide flight distance is L BC =V B T B At this time, according to the geometric relationship of the overall trajectory of long-range guided ammunition, the position of virtual point B in the launch coordinate system (L B ,H B )’s horizontal and vertical coordinates are:

[0097]

[0098]

[0099] In summary, the position of the virtual point B in the mid-terminal guidance handover section in the launch coordinate system is determined.

[0100] 3. Design of the Mid-Range Guidance Law

[0101] Based on the determination of the positions of the virtual point and the capture point in the launch coordinate system, the present invention provides an optimal mid-range guidance law taking into account angle constraints to ensure that long-range guided munitions can accurately pass through the virtual point at a desired angle and enter the mid-range and terminal guidance handover section.

[0102] 3.1 Establishing a virtual point tracking model for long-range guided munitions

[0103] The mid-range guidance problem is a three-dimensional problem in actual scenarios, but the lateral displacement of long-range guided munitions during flight is generally much smaller than the displacement in the pitch direction, so it can be simplified to a two-dimensional plane for research. Figure 3 The relative motion model between the long-range guided munition and the virtual point is shown in Figure 3. Among them, XOY is the inertial coordinate system, y is the relative distance between the long-range guided munition and the virtual point B along the Y axis in the inertial system XOY, and the physical meanings of the other parameters are shown in Table 3.

[0104] Table 3 Meaning of parameters of virtual point tracking model for long-range guided munitions

[0105]

[0106] In order to facilitate the design of the guidance law, the following assumptions are proposed:

[0107] Assumption 1: The speed of long-range guided munitions is constant;

[0108] Assumption 2: Ignore the influence of gravity on the virtual point tracking system during the guidance process;

[0109] Hypothesis 3: The dynamic hysteresis in the virtual point tracking system can be regarded as a first-order hysteresis link.

[0110] According to the attached Figure 3 The set relationship can be established in the reference coordinate system X R OY R The relative motion relationship between the long-range guided munition and the virtual point in :

[0111]

[0112] Among them, θ λ is the velocity direction error angle, θ λ =θ L -θ M Generally, V r =V M cosθ λ , which represents the speed of long-range guided munitions along the line of sight between the missile and the target.

[0113] The kinematic model of long-range guided munitions is:

[0114]

[0115] Equations (19) and (20) are the motion models of long-range guided munitions tracking virtual points. The design goal of the guidance law is to generate a reasonable control signal a M , guiding the long-range guided munition to pass through the virtual point B at the desired ballistic inclination.

[0116] 3.2 Establishing the optimal tracking model for long-range guided munitions

[0117] Introducing the tracking error ε(t), for the long-range guided munition tracking model, its system equation can generally be expressed as:

[0118] ε(t)=r(t)u(t) (21)

[0119] Among them, ε(t) is the tracking error, r(t) is a known time-varying function, and u(t) is the control input.

[0120] At this point, the problem of designing the mid-range guidance law for angle constraints can be transformed into selecting zero miss distance and landing angle as the expected tracking error ε(t), and then calculating the control input u(t) that satisfies equation (21) under the expected error model. r(t) is related to the selected tracking error ε(t), and since the tracking problem is controllable, r(t) is reversible, and r(t)≠0.

[0121] For guidance and tracking problems, the expected error model is generally selected as follows:

[0122]

[0123] Wherein, n is the gain for controlling the convergence speed of the tracking error, satisfying n>0.

[0124] At this time, it can be seen from formula (21) that the analytical formula of the tracking error is:

[0125]

[0126] Among them, ε(t0) is the initial tracking error.

[0127] The process of the tracking error ε(t) converging to zero is in the form of an exponential function asymptotically, and the convergence speed is related to n, and the speed increases with the increase of n. On the other hand, this error tracking model can only converge the tracking error to 0, but cannot guarantee the optimal realization of zero tracking error.

[0128] In order to achieve the optimal error tracking process, equation (22) is adjusted as follows:

[0129]

[0130] Among them, t go The remaining flight time is satisfy:

[0131]

[0132] Wherein, H(t) is a weighting function, satisfying H(t)>0.

[0133] Select the following performance indicators:

[0134]

[0135] At this time, the control input required to achieve the minimum value of the expected tracking error model (24) and the performance index (26) is:

[0136]

[0137] At this time, the tracking error model (24) using the control input formula (27) is the optimal tracking error model that can ensure that the guidance law converges in a finite time.

[0138] Comparing the general expected error model (22) and the adjusted optimal error tracking model (24), the difference between the two lies in the control gain. The control gain of the former is n, and the control gain of the optimal error tracking error model is is the remaining time t go Related time variables. At the same time:

[0139]

[0140] From formula (28), we can see that when the remaining time t go →0, time-varying control gain From the initial value to infinity, the change form is the same as related.

[0141] Let Γ(t) = H -1 (t)r 2 (t), then

[0142]

[0143] Among them, r(t) is a time-varying function related to the specific guidance problem, and the weighted function H(t) is a design parameter related to target selection. At the same time, it can be seen from formula (29) that for given r(t) and H(t), Specifically, when Γ(t) is a constant, When t→t f That is, as time increases to the last moment, Γ(t) increases, When t→t f , when Γ(t) decreases,

[0144] Next, we analyze the following two situations:

[0145] Case 1: When r(t) is a time-invariant function and the weighting function H(t) = 1, for:

[0146]

[0147] Then the optimal error tracking model (24) minimizes the performance index (31).

[0148]

[0149] Case 2: When the weighting function When N≥1,

[0150] Γ(t) is:

[0151]

[0152] at this time,

[0153]

[0154] The optimal error tracking model (24) minimizes the performance index (31).

[0155]

[0156] When r(t) = 1, N = 1, the performance index formula (34) is the performance index formula (31), and the optimal tracking error model formula (34) can be adjusted to:

[0157]

[0158] Solving equation (35), we can obtain the optimal tracking error analytical formula:

[0159]

[0160] Related to the guidance process, it needs to be selected according to the design goals.

[0161] Taking the function of the remaining flight time as the convergence mode of the tracking error, the optimal tracking error model (35) is predictable, and the optimal tracking error model (35) can be obtained by t go The simple form composed of and N is given, so this error tracking model can be applied to various guidance tracking problems that meet hardware requirements in actual engineering design.

[0162] In order to ensure the smooth completion of the mid-terminal guidance handover, the long-range guided munition is required to accurately pass through the virtual point B at the expected trajectory inclination. The tracking error includes the zeroing miss amount and the angle and landing angle constraints. Generally speaking, in order to achieve the desired angle to hit stationary targets and slow-moving targets, the guidance process can generally be achieved by adding an angle constraint term to the zeroing miss amount guidance instruction. Therefore, the tracking error model studied in this section includes the zeroing miss amount error ε r The error between the zeroing angle and the expected angle ε θ Two parts, and the guidance command can be expressed as:

[0163] a M =a r +a θ (37)

[0164] Among them, a r is the guidance instruction for zeroing the miss distance, a θ Guidance command to zero the angle error between the desired angle.

[0165] 3.3 Complete zeroing of miss error ε r The establishment and zeroing of off-target amount a r Design of mid-course guidance law

[0166] First, let R r represents the miss distance, then from the motion model of the virtual point of the long-range guided munition tracking in the mid-range guidance phase, equations (19) and (20), we can know that:

[0167] R r =R+V r t go (38)

[0168] Among them, V r is the relative velocity between the projectile and the target, which is:

[0169] V r =-V M cosθ λ (39)

[0170] Off-target amount R r Formula (39) solves the derivative with respect to time, and from the small perturbation assumption, we know that:

[0171]

[0172] Among them, a r =a Mq , is the normal acceleration of the long-range guided munition and the target, satisfying:

[0173] a r =a M cosθ λ (41)

[0174] At the same time, for the system model (21):

[0175]

[0176] Bring in R r , then the optimal tracking error model (35) can be adjusted as:

[0177]

[0178] Wherein, N is a positive constant.

[0179] At the same time, from formula (26), we can know that the performance index is:

[0180]

[0181] Substituting equation (43) into equation (40), we can obtain the optimal tracking error analytical formula:

[0182]

[0183] At the same time, from the "bullet-target" geometric relationship, we can know that:

[0184]

[0185] From equations (45) and (46), it can be seen that the guidance instruction for zeroing the miss error should be:

[0186]

[0187] 3.4 Design of trajectory inclination error guidance instructions

[0188] The final angle of the long-range guided munitions flight trajectory can be expressed as:

[0189]

[0190] Let θ d is the expected trajectory inclination, then the trajectory inclination and the expected trajectory inclination tracking error ε θ It can be expressed as:

[0191] ε θ =θ d -θ Mf (49)

[0192] Derivative of formula (49):

[0193]

[0194] By substituting equation (37) and equation (47) into equation (50), we have:

[0195]

[0196] Then for the error tracking system model (21), we have:

[0197]

[0198] Then the optimal tracking error model (35) can be adjusted as:

[0199]

[0200] Where K>1 is the designed guidance gain.

[0201] At this time, it can be seen from formula (26) that the performance index is:

[0202]

[0203] Since in formula (54), N and V M is a constant term and does not affect the trend of performance indicators. Therefore, formula (54) can be adjusted as follows:

[0204]

[0205] When K = 1, the optimal tracking error model can achieve the minimum energy. When K > 1, the acceleration command is go →0, it keeps increasing and eventually tends to infinity.

[0206] From equations (51) and (53), it can be seen that the guidance instruction for the error between the zeroed trajectory inclination angle and the expected trajectory inclination angle is:

[0207]

[0208] From equation (37), equation (47) and equation (56), we can get:

[0209]

[0210] Among them, ε θ is the solution of formula (53).

[0211] Virtual point B is a fixed point obtained by trajectory calculation, so a M It can be expressed as:

[0212]

[0213] In summary, the design of the optimal mid-range guidance law considering angle constraints is completed. Under the guidance of this mid-range guidance law, the long-range guided munition can ensure that it passes through the virtual point B accurately at the expected trajectory inclination angle, and in the process of approaching the virtual point B, the acceleration command gradually tends to 0, ensuring that the long-range guided munition can smoothly transition at the virtual point B.

[0214] In order to make the remaining flight time t go The value of is more accurate, thereby better improving the guidance effect. The present invention further provides a method for estimating the remaining flight time taking into account the trajectory curvature. The estimated flight time is obtained by this method. As t go Thus participating in the calculation of the guidance law.

[0215] 4. Estimation method of remaining flight time considering trajectory curvature

[0216] When the long-range guided munition flies along the “missile-target” line of sight angle or the speed error angle θ λ When is small, the remaining flight time can be expressed as:

[0217]

[0218] However, when the velocity vector of a long-range guided munition is not aligned with the target, the flight trajectory of the long-range guided munition under the guidance of the guidance law is a smooth curve, so it is necessary to consider the impact of the trajectory curvature on the remaining time. At the same time, from the guidance law (58) considering the angle constraint, it can be seen that the key term affecting the trajectory curvature is the zero miss distance guidance instruction term a r , that is, the proportional guidance term Therefore, the focus here is on the estimation of the remaining time for proportional guidance.

[0219] During the flight of the long-range guided munition tracking the virtual point B, the length of the ballistic trajectory is:

[0220]

[0221] Among them, t f is the flight time of the virtual point tracked by the long-range guided munition. According to the small disturbance assumption, we know that:

[0222]

[0223]

[0224] During the flight, the angular velocity of the missile-eye line of sight It can be expressed as:

[0225]

[0226] Substitute the proportional guidance law a r In, we can get:

[0227]

[0228] Substituting formula (62) into formula (64), we have:

[0229]

[0230] Let the initial values ​​y(0) = 0, y(0) = θ M0 , then formula (65) can be adjusted as follows:

[0231]

[0232] At this time, equation (66) is a first-order non-homogeneous differential equation, and its general solution is:

[0233]

[0234] Solving equation (67) for its derivative with respect to x, we have

[0235]

[0236] Using the power series expansion (60), we have

[0237]

[0238] The approximate remaining flight time is:

[0239]

[0240] From formula (70), we can see that for any time, the expression for estimating the remaining flight time of the proportional guidance item is:

[0241]

[0242] In formula (71) The physical meaning of is the remaining flight time increased by the trajectory bending under the guidance of the proportional guidance law due to the influence of the velocity direction error angle.

[0243] In summary, the present invention proposes a mid-terminal guidance handover trajectory design method based on virtual points taking into account attitude constraints, and in order to realize the mid-terminal guidance handover trajectory scheme, an optimal mid-terminal guidance law taking into account angle constraints is proposed. In the mid-terminal guidance handover trajectory design method based on virtual points, by analyzing the process of long-range guided munitions seeker capturing targets, a calculation method for the capture point of the mid-terminal guidance handover is derived, and by analyzing the attitude angle disturbance error attenuation time and flight state during the flight of long-range guided munitions, a calculation method for virtual points is given. This trajectory scheme is conducive to realizing the smooth handover of the mid-terminal guidance section of long-range guided munitions. The optimal mid-range guidance law considering angle constraints consists of the zero miss amount guidance instruction based on the optimal tracking error model and the zero trajectory inclination error guidance instruction. The zero miss amount guidance instruction is used to ensure that the long-range guided munition passes through the virtual point accurately, and the zero trajectory inclination error instruction is used to realize the angle constraint of the mid-range guidance section of the long-range guided munition. When this mid-range guidance law is used to realize the mid-range and terminal guidance handover ballistic scheme based on the virtual point, it can theoretically guarantee the smooth handover of the long-range guided munition in the mid-range guidance section and the terminal guidance section. At the same time, in order to ensure the mid-range guidance accuracy of the long-range guided munition, a method for estimating the remaining flight time considering the trajectory curvature is derived, thereby reducing the influence of disturbances such as aerodynamic perturbations on the flight process of the mid-range guidance section of the long-range guided munition, and ensuring the mid-range guidance performance of the long-range guided munition.

[0244] Experimental example:

[0245] In order to further verify the performance of the mid-terminal guidance handover trajectory design method based on virtual points considering attitude constraints provided by the present invention, this experimental example gives the control performance of the mid-term guidance law tracking the virtual point when there are different degrees of aerodynamic perturbations, different guidance gains, and expected trajectory inclinations.

[0246] Through simulation, the control performance of the mid-range guidance law tracking the virtual point of a long-range guided munition is analyzed under different degrees of aerodynamic perturbations, different guidance gains and different expected trajectory inclinations.

[0247] The initial conditions of the simulation are set as shown in the following table.

[0248] parameter Numeric Position of the start control point in the middle guidance section / m (0,11034) Virtual point position / m (14501,4273) Distance between starting point and virtual point / m 16000 Sight angle between the start control point and the virtual point in the mid-range guidance phase / (°) -25 Aircraft speed / (m / s) 400 Aircraft trajectory inclination angle / (°) -10 <![CDATA[Kinetic lag τ d > 0.4

[0249] During the simulation, the control energy is defined as:

[0250]

[0251] This experimental example analyzes the control performance of the guidance law tracking a virtual point under different degrees of aerodynamic perturbations. The aerodynamic perturbations of long-range guided munitions are: -10%, 0%, +10% and +20%, respectively. The navigation ratio N = 4, the guidance gain K = 6, and the desired trajectory inclination θ d =-65°.

[0252] This experimental example analyzes the control performance of the guidance law tracking the virtual point under different degrees of aerodynamic perturbations. The flight trajectory of the long-range guided munitions guided by the guidance law to track the virtual point B, the change in distance from the virtual point, the change in trajectory inclination, the change in line of sight angular velocity, the acceleration response and the control energy change curve are shown in the attached figure. Figure 4 As shown in the following table, the flight time of long-range guided munitions, the offset distance from the virtual point at the end of mid-range guidance, the trajectory inclination error and the total energy loss are as follows:

[0253]

[0254] The simulation results show that when there are different degrees of aerodynamic perturbations, the mid-range guidance law can accurately guide the long-range guided munition to pass through the virtual point B. The maximum offset from the virtual point B at the end of the mid-range guidance stage does not exceed 0.2368m, the final angle deviation does not exceed 0.1953°, and the total energy consumption in the mid-range guidance stage does not exceed 1.0587×10 4 (m 2 / s 3 ), the guidance law can effectively deal with the influence of aerodynamic perturbations on the guidance process and ensure that the long-range guided munitions pass through the virtual point accurately at the expected angle.

[0255] This experimental example analyzes the control performance of the long-range guided munition using different gain K in the guidance law tracking virtual point. K is selected as 4, 6, 8 and 10 respectively. The aerodynamic perturbation is +10%, the navigation ratio N = 4, and the desired trajectory inclination angle θ d =-65°.

[0256] This experimental example analyzes the control performance of the mid-range guidance law tracking the virtual point when the gain K is different. The mid-range guidance law guides the long-range guided munition to track the flight trajectory of the virtual point B, the change in distance from the virtual point, the change in trajectory inclination, the change in line of sight angular velocity, the acceleration response and the control energy change curve are shown in the attached figure. Figure 5 As shown in the following table, the flight time of long-range guided munitions, the offset distance from the virtual point at the end of mid-range guidance, the trajectory inclination error and the total energy loss are as follows:

[0257]

[0258]

[0259] The simulation results show that when different guidance gains are selected, the mid-range guidance law can accurately guide the long-range guided munition to pass through the virtual point B. The offset from the virtual point B at the end of the mid-range guidance section does not exceed 0.3922m, the final angle deviation does not exceed 0.0447°, and the total energy consumption of the mid-range guidance process does not exceed 1.2630×10 4 (m 2 / s 3 ). At the same time, it can also be seen that as the guidance gain K increases, the expected trajectory inclination convergence speed is faster, but the acceleration and control energy increase significantly.

[0260] This experimental example analyzes different expected trajectory inclination angles θ of long-range guided munitions d In the control performance of the virtual point tracking guidance law, the desired trajectory inclination angle θ is selected d They are: -50°, -65°, -75° and -80° respectively, the aerodynamic perturbation is +10%, the navigation ratio N=4, and the guidance gain K=6.

[0261] This experimental example analyzes different expected trajectory inclination angles θ d The control performance of the guidance law tracking the virtual point, the control performance of the guidance law tracking the virtual point, the flight trajectory of the long-range guided munitions tracking the virtual point B, the change of distance from the virtual point, the change of trajectory inclination, the change of line of sight angular velocity, the acceleration response and the control energy change curve are shown in the attached figure. Figure 6 As shown in the table below, the flight time of long-range guided munitions, the offset distance from the virtual point at the end of mid-range guidance, the trajectory inclination error, and the total energy loss are as follows:

[0262]

[0263]

[0264] The simulation results show that the mid-range guidance law can accurately guide the long-range guided munition to pass through the virtual point B. At the end of the mid-range guidance phase, the offset from the virtual point B does not exceed 0.0633m, the final angle deviation does not exceed 0.0069°, and the total energy consumption does not exceed 1.2622×10 4 (m 2 / s 3 ), the mid-course guidance law can realize the requirements of the mid-course guidance process for different trajectory inclination angles and ensure that the virtual point is passed accurately.

[0265] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for designing trajectory of mid-terminal guidance handover segment based on attitude constraints of virtual points, characterized in that: include: After the long-range guided munition finishes the initial stage, it starts control and enters the mid-range guidance stage; under the guidance of the mid-range guidance law, the long-range guided munition passes through the virtual point and enters the mid-range and terminal guidance handover stage, gliding and stabilizing its own attitude in the mid-range and terminal guidance handover stage, and the moment when the seeker enters the pre-capture state is taken as the capture point. After capturing the target, the seeker starts working, and the long-range guided munition enters the terminal guidance stage, and finally guides the long-range guided munition to hit the target.

2. The method for designing trajectory of mid-terminal guidance handover segment based on attitude constraint of virtual points according to claim 1 is characterized in that: The capture point is located in the long-range guided munition launch coordinate system (L C ,H C )’s horizontal and vertical coordinates satisfy: Among them, L T Indicates the target position, parameter c t The value range is 0.7~0.8, L cmax represents the maximum acquisition distance of long-range guided munitions to the target, θ s represents the field of view angle of the seeker, θ d represents the desired ballistic inclination angle, α d is d Matching angle of attack, Represents the boundary of attitude angle disturbance of long-range guided munitions.

3. The method for designing trajectory of mid-terminal guidance handover segment based on attitude constraint of virtual points according to claim 1 is characterized in that: The virtual point is located in the long-range guided munition launch coordinate system (L B ,H B )’s horizontal and vertical coordinates satisfy: Among them, V B represents the terminal speed of long-range guided munitions in the mid-guidance phase, c B is a parameter not less than 2, T s is the decay time of the attitude angle disturbance of the guided munition.

4. The method for designing trajectory of mid-terminal guidance handover segment based on attitude constraint of virtual points according to claim 1 is characterized in that: The trajectory design scheme in the mid-terminal guidance handover section is: a) Clarify the aerodynamic parameters, overall indicators and disturbance characteristics of long-range guided munitions during flight, and determine the boundary of attitude angle disturbance of long-range guided munitions based on the aerodynamic derivative data of long-range guided munitions during flight and the motion state of conventional flight. And the decay time T of the attitude angle disturbance of the long-range guided munition during the gliding flight s ; b) According to the detection performance of the seeker carried by the long-range guided munition, determine the maximum capture distance L of the long-range guided munition to the target cmax , and according to the design requirements of the long-range guided munitions trajectory scheme, determine the parameter c t ; c) Determine the expected trajectory inclination angle θ of the long-range guided munition according to the requirements of the long-range guided munition trajectory plan d , and solve the corresponding angle of attack α d , calculate the coordinates of the desired capture point in the long-range guided munition launch coordinate system (L C ,H C ); d) Based on the decay time T of the attitude angle disturbance of the long-range guided munition s and parameter c B , determine the glide distance L of long-range guided munitions in the mid-terminal guidance handover phase BC =V B T B , calculate the coordinates of the virtual point position in the launch coordinate system (L B ,H B ); e) The time when the long-range guided munition ends the initial segment is used as the start-up time of the mid-range guidance segment. Under the guidance of the mid-range guidance law, based on the determination of the virtual point, the smooth handover of the long-range guided munition in the mid-range and terminal guidance segments is achieved; the mid-range guidance law is composed of a zeroing miss amount guidance instruction based on an optimal tracking error model and a zeroing trajectory inclination angle and a desired trajectory inclination angle error guidance instruction, wherein the zeroing miss amount guidance instruction is used to ensure that the long-range guided munition passes through the virtual point accurately, and the zeroing trajectory inclination angle and the desired trajectory inclination angle error instruction is used to achieve the attitude constraint of the long-range guided munition in the mid-range guidance segment of the long-range guided munition.

5. The method for designing trajectory of mid-terminal guidance handover segment based on attitude constraint of virtual points according to claim 1 is characterized in that: The guidance instructions of the guidance law are expressed as: Where N is a positive constant, V M is the flight speed of long-range guided munitions, is the first-order derivative of the line-of-sight angle between the long-range guided munition and the virtual point, K is the guidance gain, t go is the remaining flight time of long-range guided munitions, ε θ is the tracking error between the trajectory inclination and the expected trajectory inclination.

6. The method for designing trajectory of the mid-terminal guidance handover segment based on attitude constraints of virtual points according to claim 1 is characterized in that: The remaining flight time of the long-range guided munition in the guidance instruction of the guidance law is estimated by the following formula: in, is the estimated value of the remaining flight time of the long-range guided munition, R is the relative distance between the virtual point and the long-range guided munition, θ λ is the velocity error angle of long-range guided munitions.

7. A terminal device comprising a processor, a memory and a computer program stored in the memory; characterized in that: When the processor is executed by a computer, the method for designing a trajectory in the terminal guidance handover segment based on the attitude constraint of a virtual point according to any one of claims 1 to 6 is implemented.

8. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the method for designing a trajectory in the terminal guidance handover segment based on the attitude constraint of a virtual point is implemented according to any one of claims 1 to 6.

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