A method for estimating the amplitude of proportional guidance control quantity in inertial coordinate system

Abstract

The present invention discloses a method for estimating the amplitude of the control quantity of a proportional guidance method, including 1): giving the prerequisites of the method for estimating the amplitude of the proportional guidance control quantity in an inertial coordinate system; 2): coordinate system definition, variable representation and relative motion calculation; 3): traditional proportional guidance algorithm; 4): parallel approach and guidance misalignment; 5): lead angle determination method; 6): control direction and characteristics of ideal proportional guidance; 7): control direction and characteristics of true proportional guidance; 8): control direction and characteristics of pure proportional guidance. The present invention proposes for the first time the expression relationship of the guidance control quantity of proportional guidance, pure proportional guidance and true proportional guidance described by parallel approach misalignment error, which has important theoretical guiding significance for determining the energy demand of the proportional guidance method. The parallel approach misalignment error can describe the guidance state more clearly than the line of sight angular velocity.

Description

Technical Field

[0001] The invention belongs to the technical field of precision guidance, and in particular relates to a method for estimating the amplitude of a proportional guidance control quantity based on an inertial coordinate system. Background Art

[0002] The analytical solution or closed-loop solution of the closed-loop guidance system is very important for studying the inherent characteristics of the guidance system state, the control quantity requirements, the guidance algorithm improvement, etc. It is also a difficult theoretical problem faced by the field of precision guidance (Li Hongyan, Tao Hong, Wang Jiang, He Shaoming. Three-Dimensional Optimal Guidance Without Terminal Maneuverability Advantage. Journal of Guidance Control and Dynamics, APR 2023, DOI: 10.2514 / 1.G007483). Even for traditional proportional navigation (PN Proportional Navigation), augmented proportional navigation (APN Augmented PN), pure proportional navigation PPN (Pure PN), true proportional navigation TPN (True PN), guidance based on ZEM (Zero Miss Distance) error, etc., we currently only know the stability of the closed-loop system and the analytical solution under special circumstances. In general, we can only obtain an approximate solution in a certain sense (Koray S Ererand Raziye Tekin. Impact Vector Guidance. Journal of Guidance Control and Dynamics, Oct. 2021, pp. 1892-1901).

[0003] In fact, to solve the analytical solution problem of traditional guidance, the theoretical problem of parallel approach guidance must be established first, because the concepts and theories related to parallel approach guidance play a very important guiding role in accurately describing the state of the guidance system. The main difficulty faced by parallel approach guidance is the lack of basic theoretical foundation. Although NA Shneydor's book "Missile Guidance and Pursuit: Kinematics, Dynamics and Control" (ISBN 1-898563-43-8, 1998, Horwood Publishing Limited, West Sussex, England) published in 1998 studied the problem of parallel approach guidance (see Chapter 4 "chapter 4. parallel navigation"), it did not give a guidance algorithm. Professor Yang Jun of Northwestern Polytechnical University pointed out in his book "Modern Air Defense Missile Guidance and Control Technology" (ISBN 9787561241943, 2014, Northwestern Polytechnical University Press) that the parallel approach method is difficult to apply in practice, and there are few examples of truly implementing the parallel approach method (see P50-P51). Professor Debasish Ghose of the Department of Aerospace Engineering of the Indian Institute of Science pointed out in his 2015 lecture "Guidance Theory and Applications" that proportional guidance is a reasonable way to implement the parallel approach method ("Proportional Navigation (PN) Guidance—Most logical way to implement constant bearing course", see Lecture 3, P14). Li-Chen, Wei-Der Chang, Dung-ming Chuang and others proposed a parallel approach guidance law (A Nonlinear Constant Bearing Guidance and Adaptive Autopilot Design for BTT Missiles[C]. Proceedings of the American Control Conference, Albuquerque, New Mexico June 1997, pp: 2774-2778) based on the convergence of the line of sight angular velocity exponent. However, it is theoretically impossible to prove that it meets the key guidance characteristics of the parallel approach method, and the simulation results do not match the parallel approach method and are only similar to proportional guidance.Zhigao Liu, an engineer at the Beijing Institute of Aerospace Microsystems, studied a parallel approach guidance law based on the algebraic equation with zero line-of-sight angular velocity (Constant Bearing Guidance Law for Homing Missiles[C]. 2017 10. th International Symposium on Computational Intelligence and Design (ISCID) IEEE, 2017, pp: 247-251), its simulation results are far from the parallel approach method.

[0004] With the help of parallel approach guidance related theories, proportional guidance, augmented proportional guidance, pure proportional guidance, true proportional guidance, ZEM guidance problems, etc., solving the analytical solution problem of the closed-loop system state is of great significance to precision guidance technology.

[0005] The control quantity of proportional guidance is proportional to the line-of-sight angular velocity in terms of expression, but the line-of-sight angular velocity is a distance-related quantity with a very complex range of variation. It is impossible to accurately evaluate the error characteristics of the guidance, and it is even more impossible to make an accurate judgment on the control quantity requirements of the guidance. Solving the control quantity estimation is the core content of modern guidance system design, but the problem of how to estimate has not been studied in depth, and there is a lack of reasonable estimation methods.

[0006] Therefore, this technology needs to be improved. Summary of the invention

[0007] Purpose of the invention: In order to overcome the above shortcomings, the purpose of the present invention is to provide a method for estimating the amplitude of a proportional guidance type control quantity in an inertial coordinate system, which has a simple structure, reasonable design, easy production, high degree of automation, reduced manual labor, improved work efficiency, large storage capacity and flexible application.

[0008] Technical solution: A method for estimating the amplitude of a proportional guidance control quantity in an inertial coordinate system, comprising the following steps:

[0009] 1): Give the prerequisites for the estimation method of the amplitude of the proportional guidance type control quantity in the inertial coordinate system;

[0010] 2): Coordinate system definition, variable representation and relative motion calculation;

[0011] 3): Traditional proportional guidance algorithm;

[0012] 4): Parallel approach and guidance misalignment. During the guidance process, the guidance method that can quickly return the line of sight angular velocity to zero and always maintain it at zero is called parallel approach guidance;

[0013] 5): Guidance lead angle determination method;

[0014] 6): The control direction and characteristics of the ideal proportional guidance, the ideal proportional guidance instruction is proportional to the line of sight angular velocity, the control direction vertical relative velocity, calculate the control amount and true error of the ideal proportional guidance;

[0015] 7): The control direction and characteristics of the true proportional guidance, calculate the control amount and true error of the true proportional guidance;

[0016] 8): The control direction and characteristics of pure proportional guidance, calculate the control amount and true error of pure proportional guidance.

[0017] The prerequisites for the method for estimating the amplitude of the proportional guidance control quantity in the inertial coordinate system in step 1) of the present invention are as follows:

[0018] Condition 1): All calculation methods are based on the inertial rectangular coordinate system. The so-called inertial rectangular coordinate system in the present invention can also be referred to as the inertial coordinate system, and the direction of the coordinate system body axis can be freely selected according to actual needs. The absolute position, absolute velocity vector and absolute acceleration vector of the interceptor and the target are all measured in the inertial coordinate system;

[0019] Condition 2): The relative position vector, relative velocity vector and relative acceleration vector of the interceptor and the target are defined according to their absolute position vector, absolute velocity vector and absolute acceleration vector in the inertial coordinate system; relative position, relative velocity and relative acceleration are instantaneous physical quantities;

[0020] The line of sight of the present invention refers to the line from the interceptor to the target, and the line of sight is consistent with the direction of the relative position vector of the interceptor and the target; the rotation speed of the line of sight in the inertial space is called the line of sight angular velocity;

[0021] Condition 3): Proportional navigation (PN) includes three types of guidance instruction formation methods: pure proportional navigation (PPN), ideal proportional navigation (IPN) and true proportional navigation (TPN). The acceleration instruction of the ideal proportional navigation is perpendicular to the direction of the relative velocity vector, the acceleration instruction of the true proportional navigation is perpendicular to the direction of the relative position vector (i.e., the line of sight), and the acceleration instruction of the pure proportional navigation is perpendicular to the velocity direction of the interceptor itself;

[0022] The direction of the command vector of the proportional guidance is perpendicular to the line of sight angular velocity vector, and there is a certain proportional relationship between the command vector amplitude and the line of sight angular velocity;

[0023] Condition 4): The error of the parallel approach guidance is the guidance misalignment angle; the state in which the line of sight angular velocity is not zero is called guidance misalignment.

[0024] Condition 5): The guidance lead angle is based on the line of sight direction. The angle between the interceptor velocity vector and the line of sight direction is positive when the interceptor points in the direction of target movement, and negative otherwise.

[0025] The relative position vector, relative velocity vector and relative acceleration vector between the interceptor and the target in condition 2) of the present invention are calculated as follows:

[0026] Relative position vector = target's absolute position vector - interceptor's absolute position vector;

[0027] Relative velocity vector = target's absolute velocity vector - interceptor's absolute velocity vector;

[0028] Relative acceleration vector = absolute acceleration vector of target - absolute acceleration vector of interceptor.

[0029] The step 2) of the present invention: coordinate system definition, variable representation and relative motion calculation method are as follows:

[0030] Establish inertial rectangular coordinate system F I , specifically expressed as F I (oxyz), that is, the origin of the coordinate system is o, and the three coordinate axes are ox, oy and oz respectively; the position vector of the interceptor in this coordinate system is P m , the velocity vector is V m , the acceleration vector is a m ; Similarly, the position vector of the target in this coordinate system is P t The velocity vector is represented by V t The acceleration vector is represented by a t ; Define the relative position (distance) vector between the interceptor and the target as R(t) = P t -P m , the relative velocity vector is V(t)=V t -V m , the relative acceleration vector is a=a t -a m ;

[0031] In the inertial rectangular coordinate system F I (oxyz), the relative position vector is specifically expressed as R = [xyz] T , the relative velocity vector is specifically expressed as The relative acceleration is specifically expressed as For convenience:

[0032] R=R(t)=||R(t)||, V=V(t)=||V(t)||, (1)

[0033]

[0034] V m =V m (t)=||V m (t)||,V t =V t (t)=||V t (t)||, (3)

[0035] The relative position vector R(t) of the inertial coordinate system is the sight vector, and its rotation speed in the coordinate system, that is, the sight angular velocity vector Ω(t), satisfies:

[0036]

[0037] The unit vector along the direction of vectors R(t), V(t), Ω(t) is:

[0038]

[0039] The guidance algorithms (guidance laws) of the ideal proportional guidance (IPN), true proportional guidance (TPN) and pure proportional guidance (PPN) in the present invention are methods for calculating the desired acceleration instructions of the interceptor.

[0040] Guidance command for ideal proportional guidance a IPN It is expressed as:

[0041]

[0042] Where N>0 is the navigation ratio, V ref is the reference speed, which can be selected according to the situation, such as V ref =V or

[0043] Guidance command for true proportional guidance a TPN It is expressed as:

[0044]

[0045] Guidance command for pure proportional guidance a PPN The expression is:

[0046]

[0047] The basic characteristics of the parallel approach in step 4) of the present invention are as follows:

[0048] When approaching in parallel, the line of sight angular velocity satisfies:

[0049]

[0050] When Ω(t)≠0, it is called the guidance misalignment state, and the guidance misalignment angle at this time is denoted as μ, satisfying

[0051]

[0052]

[0053] The guidance lead angle L in step 5) of the present invention is the product of the line of sight direction vector R(t) and the interceptor velocity vector V m The angle between them, if the direction is ignored, satisfies:

[0054]

[0055] The control amount and true error calculation method of the ideal proportional guidance in step 6) of the present invention are as follows:

[0056] (1) Control vector characteristics of ideal proportional guidance

[0057] The control vector of the ideal proportional guidance is V×Ω, which has the following characteristics

[0058]

[0059] in:

[0060] D CBC =I R +cosμI v ,||D CBC ||=|sinμ| (14)

[0061] Argument: Because

[0062]

[0063] The misalignment angle relationship R·V=-RVcosμ, then from formula (15) we get

[0064]

[0065] That is

[0066]

[0067] Define the optimal control direction vector as D CBC =I R +cosμI v , so the above formula can be expressed as

[0068]

[0069] Vector D CBC =I R +cosμI v ,because

[0070] ||D CBC|| 2 =I R I R +2cosμI R I v +cos 2 μI v I v (19)

[0071] Because (I R I v )=-cosμ, so the above formula becomes

[0072]

[0073] That is

[0074] |D CBC |=|sinμ| (21)

[0075] (2) Command acceleration amplitude;

[0076] For ideal proportional guidance m =NV×Ω, control instruction a m satisfy:

[0077]

[0078] Formula (22) shows that although the proportional guidance control direction is along the parallel approach method control direction, the actual error is sinμ instead of the line-of-sight angular velocity Ω, and the line-of-sight angular velocity belongs to the nominal error. In addition, sinμ≈μ when the misalignment angle is very small, so the proportional guidance performance is better only when the misalignment angle is very small. The sinμ function normalizes the misalignment angle, so that the control amount is insufficient when the misalignment angle is large. The guidance gain includes the navigation ratio adjustment factor (V / R). If the misalignment angle is not well controlled, the guidance instructions near the interception point will increase sharply.

[0079] The calculation method of the control amount and the true error of the true proportional guidance in step 7) of the present invention is as follows:

[0080] For true proportional guidance, if a m =-NVI R ×Ω, then:

[0081]

[0082] K LOS = cosμI R +I v , K LOS ⊥I R ,||K LOS ||=|sinμ| (24)

[0083]

[0084] Where K LOS Represents the sight line vector.

[0085] Argument: Because

[0086]

[0087] According to the relationship between the three vector cross products, we can get from formula (26):

[0088]

[0089] That is

[0090]

[0091] therefore

[0092]

[0093] According to the definition of misalignment angle, I R I v = -cosμ, and (I R I R )=1, so we have

[0094]

[0095] If we define K LOS = cosμI R +I v ,but

[0096]

[0097] so

[0098]

[0099] because

[0100]

[0101] therefore

[0102] K LOS = cosμI R +I v ⊥I R (34)

[0103] Now calculate K LOS = cosμI R +I v The model, obviously

[0104]

[0105] Therefore

[0106] ||K LOS ||=|sinμ| (36)

[0107] According to formula (32) and formula (36), we can get

[0108]

[0109] The results show that although the control directions of ideal proportional guidance and true proportional guidance are different, the expressions of real error and control quantity are the same, because the two guidance laws use the nominal error - line of sight angular velocity as the error; but this does not mean that the two guidance laws have the same guidance characteristics, because the guidance process has different control effects on the guidance error.

[0110] The control amount and true error calculation method of pure proportional guidance in step 8) of the present invention are as follows:

[0111] For pure proportional guidance, since the control direction is perpendicular to the interceptor's speed, it is difficult to determine the exact expression of the control quantity, but the upper bound expression of the control quantity can be obtained;

[0112] For pure proportional guidance, if a m =-NV(V m / V m )×Ω, then

[0113]

[0114] Proof: Let velocity be the unit vector because

[0115]

[0116] Previous definition is the interceptor velocity lead angle (the angle at which the velocity direction deviates from the line of sight), and then defines the interceptor velocity deviation angle for It is the angle between the interceptor velocity direction and the total relative velocity vector direction.

[0117]

[0118] Define the velocity deviation vector but

[0119]

[0120] Since the relationship in equation (41) is complicated, let’s look at the approximate relationship.

[0121]

[0122] And because Therefore

[0123] If and only if

[0124]

[0125] therefore

[0126]

[0127] and Therefore

[0128]

[0129] The control amplitude of pure proportional guidance is relatively small because the vector This is caused by the fact that it is not perpendicular to the vector Ω. It does not mean that the small control required by this guidance law itself is reasonable. The problems it has are similar to those of proportional guidance and true proportional guidance.

[0130] It can be seen from the above technical solution that the present invention has the following beneficial effects:

[0131] 1. The method for estimating the amplitude of proportional guidance control quantity in an inertial coordinate system described in the present invention analyzes the control direction vector determined by the guidance algorithm according to the proportional relationship characteristics of ideal proportional guidance, true proportional guidance and pure proportional guidance and line of sight angular velocity, and establishes the relationship or approximate equivalent relationship between the parallel approach misalignment error and the line of sight angular velocity, thereby obtaining the expression relationship of the proportional guidance control quantity with the parallel approach misalignment error as the variable. For the first time, the expression relationship of the guidance control quantity of proportional guidance, pure proportional guidance and true proportional guidance described by the parallel approach misalignment error is proposed, which has important theoretical guiding significance for determining the energy demand of the proportional guidance method. The parallel approach misalignment error can describe the guidance state more clearly than the line of sight angular velocity.

[0132] 2. The control quantity relationship expressed by the misalignment angle given by the present invention deeply reveals the essential reasons for the problems existing in proportional guidance, including slow error elimination speed and low robustness against target maneuvers.

[0133] 3. The results of the present invention also indirectly confirm that proportional guidance cannot achieve parallel approach guidance, because the guidance instruction is proportional to the inverse of the distance, which seriously affects the speed of eliminating the initial guidance error. BRIEF DESCRIPTION OF THE DRAWINGS

[0134] Figure 1 It is a flow chart of the method for estimating the amplitude of the proportional guidance type control quantity in the inertial coordinate system of the present invention;

[0135] Figure 2 Schematic diagram of the inertial coordinate system in the present invention;

[0136] Figure 3 It is a schematic diagram of the relative positions of the inertial coordinate system in the present invention;

[0137] Figure 4 It is a schematic diagram of relative velocity of the inertial coordinate system in the present invention;

[0138] Figure 5 It is a schematic diagram of relative acceleration of the inertial coordinate system in the present invention. DETAILED DESCRIPTION

[0139] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments.

[0140] Example

[0141] like Figure 1 The method for estimating the amplitude of a proportional guidance control quantity in an inertial coordinate system shown in the figure comprises the following steps:

[0142] 1): Give the prerequisites for the estimation method of the amplitude of the proportional guidance type control quantity in the inertial coordinate system;

[0143] 2): Coordinate system definition, variable representation and relative motion calculation;

[0144] 3): Traditional proportional guidance algorithm;

[0145] 4): Parallel approach and guidance misalignment. During the guidance process, the guidance method that can quickly return the line of sight angular velocity to zero and always maintain it at zero is called parallel approach guidance;

[0146] 5): Guidance lead angle determination method;

[0147] 6): The control direction and characteristics of the ideal proportional guidance, the ideal proportional guidance instruction is proportional to the line of sight angular velocity, the control direction vertical relative velocity, calculate the control amount and true error of the ideal proportional guidance;

[0148] 7): The control direction and characteristics of the true proportional guidance, calculate the control amount and true error of the true proportional guidance;

[0149] 8): The control direction and characteristics of pure proportional guidance, calculate the control amount and true error of pure proportional guidance.

[0150] The relationship between the controlled quantities profoundly reveals the essential reasons for the problems existing in proportional guidance and plays an important guiding role in the design of the guidance system.

[0151] The prerequisites for the method for estimating the amplitude of the proportional guidance control quantity in the inertial coordinate system in step 1) of this embodiment are as follows:

[0152] Condition 1): All calculation methods are based on the inertial rectangular coordinate system. The so-called inertial rectangular coordinate system in the present invention can also be referred to as the inertial coordinate system, and the direction of the coordinate system body axis can be freely selected according to actual needs. The absolute position, absolute velocity vector and absolute acceleration vector of the interceptor and the target are all measured in the inertial coordinate system;

[0153] Condition 2): The relative position vector, relative velocity vector and relative acceleration vector of the interceptor and the target are defined according to their absolute position vector, absolute velocity vector and absolute acceleration vector in the inertial coordinate system; relative position, relative velocity and relative acceleration are instantaneous physical quantities;

[0154] The line of sight of the present invention refers to the line from the interceptor to the target, and the line of sight is consistent with the direction of the relative position vector of the interceptor and the target; the rotation speed of the line of sight in the inertial space is called the line of sight angular velocity;

[0155] Condition 3): Proportional navigation (PN) includes three types of guidance instruction formation methods: pure proportional navigation (PPN), ideal proportional navigation (IPN) and true proportional navigation (TPN). The acceleration instruction of the ideal proportional navigation is perpendicular to the direction of the relative velocity vector, the acceleration instruction of the true proportional navigation is perpendicular to the direction of the relative position vector (i.e., the line of sight), and the acceleration instruction of the pure proportional navigation is perpendicular to the velocity direction of the interceptor itself;

[0156] The direction of the command vector of the proportional guidance is perpendicular to the line of sight angular velocity vector, and there is a certain proportional relationship between the command vector amplitude and the line of sight angular velocity;

[0157] Condition 4): The error of the parallel approach guidance is the guidance misalignment angle; the state in which the line of sight angular velocity is not zero is called guidance misalignment.

[0158] Condition 5): The guidance lead angle is based on the line of sight direction. The angle between the interceptor velocity vector and the line of sight direction is positive when the interceptor points in the direction of target movement, and negative otherwise.

[0159] The relative position vector, relative velocity vector and relative acceleration vector between the interceptor and the target in condition 2) in this embodiment are calculated as follows:

[0160] Relative position vector = target's absolute position vector - interceptor's absolute position vector;

[0161] Relative velocity vector = target's absolute velocity vector - interceptor's absolute velocity vector;

[0162] Relative acceleration vector = absolute acceleration vector of target - absolute acceleration vector of interceptor.

[0163] In this embodiment, step 2): coordinate system definition, variable representation and relative motion calculation method are as follows:

[0164] Establish inertial rectangular coordinate system F I , specifically expressed as F I (oxyz), that is, the origin of the coordinate system is o, and the three coordinate axes are ox, oy and oz respectively; the position vector of the interceptor in this coordinate system is P m , the velocity vector is V m , the acceleration vector is a m ; Similarly, the position vector of the target in this coordinate system is P t The velocity vector is represented by V t The acceleration vector is represented by a t ; Define the relative position (distance) vector between the interceptor and the target as R(t) = P t -P m , the relative velocity vector is V(t)=V t -V m , the relative acceleration vector is a=a t -a m ;

[0165] In the inertial rectangular coordinate system F I (oxyz), the relative position vector is specifically expressed as R = [xyz] T , the relative velocity vector is specifically expressed as The relative acceleration is specifically expressed as For convenience:

[0166] R=R(t)=||R(t)||, V=V(t)=||V(t)||, (1)

[0167]

[0168] V m =V m (t)=||V m (t)‖,V t =V t (t)=||V t (t)||, (3)

[0169] The relative position vector R(t) of the inertial coordinate system is the sight vector, and its rotation speed in the coordinate system, that is, the sight angular velocity vector Ω(t), satisfies:

[0170]

[0171] The unit vector along the direction of vectors R(t), V(t), Ω(t) is:

[0172]

[0173] The guidance algorithms (guidance laws) of the ideal proportional navigation (IPN), true proportional navigation (TPN) and pure proportional navigation (PPN) in this embodiment are methods for calculating the desired acceleration command of the interceptor.

[0174] Guidance command for ideal proportional guidance a IPN It is expressed as:

[0175]

[0176] Where N>0 is the navigation ratio, V ref is the reference speed, which can be selected according to the situation, such as V ref =V or

[0177] Guidance command for true proportional guidance a TPN It is expressed as:

[0178]

[0179] Guidance command for pure proportional guidance a PPN The expression is:

[0180]

[0181] The basic characteristics of the parallel approach in step 4) in this embodiment are as follows:

[0182] When approaching in parallel, the line of sight angular velocity satisfies:

[0183]

[0184] When Ω(t)≠0, it is called the guidance misalignment state, and the guidance misalignment angle at this time is denoted as μ, satisfying

[0185]

[0186]

[0187] In step 5) of this embodiment, the guidance lead angle L is the sum of the line of sight direction vector R(t) and the interceptor velocity vector V m The angle between them, if the direction is ignored, satisfies:

[0188]

[0189] The method for calculating the control amount and the true error of the ideal proportional guidance in step 6) of this embodiment is as follows:

[0190] (1) Control vector characteristics of ideal proportional guidance

[0191] The control vector of the ideal proportional guidance is V×Ω, which has the following characteristics

[0192]

[0193] in:

[0194] D CBC =I R +cosμI v ,||D CBC ||=|sinμ| (14)

[0195] Where K LOS Represents the sight line vector.

[0196] Argument: Because

[0197]

[0198] The misalignment angle relationship R·V=-RVcosμ, then from formula (15) we get

[0199]

[0200] That is

[0201]

[0202] Define the optimal control direction vector as D CBC =I R +cosμI v , so the above formula can be expressed as

[0203]

[0204] Vector D CBC =I R +cosμI v ,because

[0205] ||D CBC || 2 =I R I R +2cosμI R I v +cos 2 μI v I v (19)

[0206] Because (I R I v )=-cosμ, so the above formula becomes

[0207]

[0208] That is

[0209] |D CBC |=|sinμ| (21)

[0210] (2) Command acceleration amplitude;

[0211] For ideal proportional guidance m =NV×Ω, control instruction a m satisfy:

[0212]

[0213] Formula (22) shows that although the proportional guidance control direction is along the parallel approach method control direction, the actual error is sinμ instead of the line-of-sight angular velocity Ω, and the line-of-sight angular velocity belongs to the nominal error. In addition, sinμ≈μ when the misalignment angle is very small, so the proportional guidance performance is better only when the misalignment angle is very small. The sinμ function normalizes the misalignment angle, so that the control amount is insufficient when the misalignment angle is large. The guidance gain includes the navigation ratio adjustment factor (V / R). If the misalignment angle is not well controlled, the guidance instructions near the interception point will increase sharply.

[0214] The following conclusions are drawn about the ideal ratio guidance:

[0215] The control command of the ideal proportional guidance (space vector form) is in the optimal control direction;

[0216] The error of the ideal proportional guidance is equivalent to sinμ, and since |sinμ|≤1, it normalizes the misalignment angle by the sine function; the command amplitude of the ideal proportional guidance is NV(V / R)|sinμ|, which is proportional to the sine function of the misalignment angle.

[0217] The factor (V / R) is the main reason for the delay in the correction of long-range errors in ideal proportional guidance.

[0218] If the factor (V / R) is introduced into the navigation ratio of the ideal proportional guidance, the deficiencies in the ideal proportional guidance performance can be corrected and the optimal guidance objective can be achieved.

[0219] The calculation method of the control amount and the true error of the true proportional guidance in step 7) of this embodiment is as follows:

[0220] For true proportional guidance, if a m =-NVI R ×Ω, then:

[0221]

[0222] K LOS= cosμI R +I v , K LOS ⊥I R ,||K LOS ||=|sinμ| (24)

[0223]

[0224] Argument: Because

[0225]

[0226] According to the relationship between the three vector cross products, we can get from formula (26):

[0227]

[0228] That is

[0229]

[0230] therefore

[0231]

[0232] According to the definition of misalignment angle, I R I v = -cosμ, and (I R I R )=1, so we have

[0233]

[0234] If we define K LOS = cosμI R +I v ,but

[0235]

[0236] so

[0237]

[0238] because

[0239]

[0240] therefore

[0241] K LOS = cosμI R +I v ⊥I R (34)

[0242] Now calculate K LOS = cosμIR +I v The model, obviously

[0243]

[0244] Therefore

[0245] ||K LOS ||=|sinμ| (36)

[0246] According to formula (32) and formula (36), we can get

[0247]

[0248] The results show that although the control directions of ideal proportional guidance and true proportional guidance are different, the expressions of real error and control quantity are the same, because the two guidance laws use the nominal error - line of sight angular velocity as the error; but this does not mean that the two guidance laws have the same guidance characteristics, because the guidance process has different control effects on the guidance error.

[0249] The method for calculating the control amount and true error of pure proportional guidance in step 8) of this embodiment is as follows:

[0250] For pure proportional guidance, since the control direction is perpendicular to the interceptor's speed, it is difficult to determine the exact expression of the control quantity, but the upper bound expression of the control quantity can be obtained;

[0251] For pure proportional guidance, if a m =-NV(V m / V m )×Ω, then

[0252]

[0253] Proof: Let velocity be the unit vector because

[0254]

[0255] Previous definition is the interceptor velocity lead angle (the angle at which the velocity direction deviates from the line of sight), and then defines the interceptor velocity deviation angle for It is the angle between the interceptor velocity direction and the total relative velocity vector direction.

[0256]

[0257] Define the velocity deviation vector but

[0258]

[0259] Since the relationship in equation (41) is complicated, let’s look at the approximate relationship.

[0260]

[0261] And because Therefore

[0262] If and only if

[0263]

[0264] therefore

[0265]

[0266] and Therefore

[0267]

[0268] The control amplitude of pure proportional guidance is relatively small because the vector This is caused by the fact that it is not perpendicular to the vector Ω. It does not mean that the small control required by this guidance law itself is reasonable. The problems it has are similar to those of proportional guidance and true proportional guidance.

[0269] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be regarded as within the protection scope of the present invention.

Claims

1. A method for estimating the amplitude of a proportional guidance control quantity in an inertial coordinate system, characterized in that: The following steps are involved: 1): Give the prerequisites for the estimation method of the amplitude of the proportional guidance type control quantity in the inertial coordinate system; 2): Coordinate system definition, variable representation and relative motion calculation; 3): Traditional proportional guidance algorithm, that is, calculating the guidance instructions a of the ideal proportional guidance respectively IPN , guidance command for true proportional guidance a TPN and guidance command a for pure proportional guidance PPN , where the guidance algorithms of ideal proportional guidance, true proportional guidance and pure proportional guidance are methods for calculating the desired acceleration command of the interceptor; 4): Judgment of parallel approach and guidance misalignment. During the guidance process, the guidance method that can quickly return the line of sight angular velocity to zero and always maintain it at zero is called parallel approach guidance; 5): Determine the leading angle; 6): Analyze the control direction and characteristics of the ideal proportional guidance, the ideal proportional guidance instruction is proportional to the line of sight angular velocity, the control direction vertical relative velocity, and calculate the control amount and true error of the ideal proportional guidance; 7): Analyze the control direction and characteristics of the true proportional guidance, and calculate the control amount and true error of the true proportional guidance; 8): Analyze the control direction and characteristics of pure proportional guidance, and calculate the control amount and true error of pure proportional guidance; The method for calculating the control amount and true error of the ideal proportional guidance in step 6) is as follows: (1) Control vector characteristics of ideal proportional guidance The control vector of the ideal proportional guidance is V×Ω, which has the following characteristics Where: The optimal control direction vector is defined as D CBC D CBC =I R +cosμI v ,||D CBC ||=|sinμ| (2) In the formula, the unit vector along the direction of vectors R(t) and V(t) is I R ,I v ; (2) Command acceleration amplitude; Ideal Proportional Guidance m =NV×Ω, control instruction a m satisfy: The calculation method of the control amount and the true error of the true proportional guidance in step 7) is as follows: For true proportional guidance, a m =-NVI R ×Ω, then: K LOS =cosμI R +I v ,K LOS ⊥I R ,||K LOS ||=|sinμ| (5) Where N>0 is the navigation ratio, the line of sight angular velocity is Ω, the guidance misalignment angle is μ, and K LOS represents the sight line vector; The control amount and true error calculation method of pure proportional guidance in step 8) are as follows: For pure proportional guidance, since the control direction is perpendicular to the interceptor's speed, it is difficult to determine the exact expression of the control quantity, but the upper bound expression of the control quantity can be obtained; For pure proportional guidance, a m =-NV(V m / V m )×Ω, then 2. The method for estimating the amplitude of proportional guidance control quantity in an inertial coordinate system according to claim 1, characterized in that: The prerequisites for the method for estimating the amplitude of the proportional guidance type control quantity in the inertial coordinate system in step 1) are as follows: Condition 1): All calculation methods are based on an inertial rectangular coordinate system; the absolute position, absolute velocity vector and absolute acceleration vector of the interceptor and the target are measured in this inertial coordinate system; Condition 2): The relative position vector, relative velocity vector and relative acceleration vector of the interceptor and the target are defined according to their absolute position vector, absolute velocity vector and absolute acceleration vector in the inertial coordinate system; relative position, relative velocity and relative acceleration are instantaneous physical quantities; Condition 3): Proportional guidance includes three types of guidance instruction formation methods: pure proportional guidance, ideal proportional guidance and true proportional guidance. The acceleration instruction of the ideal proportional guidance is perpendicular to the relative velocity vector direction, the acceleration instruction of the true proportional guidance is perpendicular to the relative position vector direction, and the acceleration instruction of the pure proportional guidance is perpendicular to the velocity direction of the interceptor itself; The direction of the command vector of the proportional guidance is perpendicular to the line of sight angular velocity vector, and the amplitude of the command vector is proportional to the line of sight angular velocity; Condition 4): The error of the parallel approach guidance is the guidance misalignment angle; The state in which the line-of-sight angular velocity is not zero is called guidance misalignment; Condition 5): The guidance lead angle is based on the line of sight direction. The angle between the interceptor velocity vector and the line of sight direction is positive when the interceptor points in the direction of target movement, and negative otherwise.

3. The method for estimating the amplitude of proportional guidance control quantity in an inertial coordinate system according to claim 2, characterized in that: The relative position vector, relative velocity vector and relative acceleration vector between the interceptor and the target in condition 2) are calculated as follows: Relative position vector = target's absolute position vector - interceptor's absolute position vector; Relative velocity vector = target's absolute velocity vector - interceptor's absolute velocity vector; Relative acceleration vector = absolute acceleration vector of target - absolute acceleration vector of interceptor.

4. The method for estimating the amplitude of proportional guidance control quantity in an inertial coordinate system according to claim 2, characterized in that: The step 2): coordinate system definition, variable representation and relative motion calculation method are as follows: Establish inertial rectangular coordinate system F I , specifically expressed as F I (oxyz), that is, the origin of the coordinate system is o, and the three coordinate axes are ox, oy and oz respectively; the position vector of the interceptor in this coordinate system is P m , the velocity vector is V m , the acceleration vector is a m ; Similarly, the position vector of the target in this coordinate system is P t The velocity vector is represented by V t The acceleration vector is represented by a t ; Define the relative position vector of the interceptor and the target as R(t)=P t -P m , the relative velocity vector is V(t)=V t -V m , the relative acceleration vector is a=a t -a m ; In the inertial rectangular coordinate system F I (oxyz), the relative position vector is specifically expressed as R(t) = [xyz] T , the relative velocity vector is specifically expressed as The relative acceleration is specifically expressed as remember: R=R(t)=||R(t)||, V=V(t)=||V(t)||, (8) V m =V m (t)=||V m (t)||,V t =V t (t)=||V t (t)||, (10) The relative position vector R(t) of the inertial coordinate system is the sight vector, and its rotation speed in the coordinate system, that is, the sight angular velocity vector Ω(t), satisfies: The unit vector along the direction of vectors R(t), V(t), Ω(t) is:

5. The method for estimating the amplitude of proportional guidance control quantity in an inertial coordinate system according to claim 2, characterized in that: The guidance algorithms of ideal proportional guidance, true proportional guidance and pure proportional guidance are the methods of calculating the desired acceleration command of the interceptor; Guidance command for ideal proportional guidance a IPN It is expressed as: Where N>0 is the navigation ratio, V ref is the reference speed, V ref =V or Guidance command for true proportional guidance a TPN It is expressed as: Guidance command for pure proportional guidance a PPN The expression is:

6. The method for estimating the amplitude of proportional guidance control quantity in an inertial coordinate system according to claim 2, characterized in that: The basic characteristics of the parallel approach in step 4) are as follows: When approaching in parallel, the line of sight angular velocity satisfies: When Ω(t)≠0, it is called the guidance misalignment state, and the guidance misalignment angle at this time is μ, satisfying 7. The method for estimating the amplitude of proportional guidance control quantity in an inertial coordinate system according to claim 2, characterized in that: In step 5), the guidance lead angle L is the sum of the line of sight direction vector R(t) and the interceptor velocity vector V m The angle between them, regardless of direction, satisfies:

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