Guidance method and equipment with falling angle constraint suitable for high-speed aircraft
By establishing a final guidance model and optimal guidance method suitable for high-speed aircraft, the problem of insufficient end strike capabilities is solved, precise control of collision angles and warhead power is achieved, and the combat effectiveness of the weapon system is improved.
Patent Information
- Application Number
- CN202510250074.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-04
- Publication Date
- 2025-07-08
AI Technical Summary
The terminal strike capability of the medium and medium-speed aircraft in the prior art is insufficient, making it difficult to accurately control the collision angle to maximize the power of the warhead.
By establishing kinematic and dynamic models of the final guidance section, using optimal theory and linear relative motion equations, a guidance method with corner constraints suitable for high-speed aircraft is designed, including establishing performance indicators and Hamilton's function, solving the optimal guidance law analytical solution, and through simulation optimization processing, a differential countermeasure guidance law with feedback was finally obtained.
It improves the precise strike capability at the end of the high-speed aircraft, meets the corner constraints, and enhances the combat effectiveness of the weapon system.
Smart Images
Figure CN120277799A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of terminal guidance, and particularly relates to a guidance method and device with impact angle constraint applicable to high-speed aircraft. Background Art
[0002] High-speed aircraft fly at high speeds, have strong penetration capabilities, and possess a strong terminal strike ability. They can be used to break through the interception of anti-missile systems and achieve precise strikes with high-speed aircraft. The terminal guidance technology of aircraft is one of the most important links for weapon systems to exert their effectiveness, and it has a great impact on the damage effect of the terminal miss distance. At the same time, accurately controlling the impact angle can maximize the power of the warhead. Through the research on differential game theory, a guidance method with impact angle constraint applicable to high-speed aircraft is designed, which is of great significance for improving the combat effectiveness of weapon systems. Summary of the Invention
[0003] Aiming at the defects existing in the prior art, the technical problem solved by the present invention is: to provide a guidance method with impact angle constraint applicable to high-speed aircraft, which improves the terminal precise strike ability of high-speed aircraft.
[0004] To achieve the above object, in a first aspect, an embodiment of the present application provides a guidance method with impact angle constraint applicable to high-speed aircraft, characterized in that the method includes the following steps:
[0005] S1: Establish a kinematic model and a dynamic model for the terminal guidance section according to the ballistic inclination angles θ of the aircraft and the target, the speeds V of the aircraft and the target, and the relative distance r between the aircraft and the target;
[0006] The expression of the dynamic model is:
[0007]
[0008] θ M and θ T are the ballistic inclination angles, respectively representing the angles between the speeds of the aircraft and the target and the X-axis of the inertial system; I axis;
[0009] q is the line-of-sight angle;
[0010] M represents the aircraft, and T represents the target;
[0011] V M and V T are the magnitudes of the speeds of the aircraft and the target, respectively;
[0012] The expression of the kinematic model is: where x i represents the state vector of the internal dynamic characteristics of the aircraft or the target, and Ai , C i is the coefficient matrix related to the states of the aircraft and the target itself, B i , d i is the coefficient matrix related to the commanded acceleration;
[0013] S2: Based on the small-angle assumption at the end stage, after processing the kinematic model and the dynamic model, a linear relative motion equation convenient for analysis is established in the direction perpendicular to the line of sight. The vector expression form of this equation is:
[0014] S3: Based on the linear relative motion equation in S2, performance indexes are established according to the combat target and requirements. Based on the established performance indexes, the analytical solution of the optimal guidance law is solved according to the optimal theory. The expression of the performance index J is:
[0015]
[0016] Combined with the first aspect, in an implementation manner, X is defined I -O I -Y I as an inertial reference frame;
[0017] q is the angle between the line connecting the aircraft and the target and the X I axis;
[0018] Define X - O - Y as the initial line-of-sight coordinate system, the initial line of sight LOS0 is the X axis, and the Y axis is perpendicular to the initial line of sight;
[0019] a M and a T are the magnitudes of the accelerations of the aircraft and the target respectively, and the directions are perpendicular to the velocity directions;
[0020] Specifically, the above kinematic model is obtained from the projections of r and the relative velocity v in the line-of-sight coordinates, and the calculation formula is:
[0021]
[0022] Taking the derivative of r gives:
[0023]
[0024] The projection of the relative velocity v in the line-of-sight coordinates is:
[0025]
[0026] Combined with the first aspect, in one implementation, when the magnitudes of the speeds of the aircraft and the target are basically unchanged in the terminal guidance section, the overload is perpendicular to the direction of the speed, and we get:
[0027]
[0028]
[0029] Combined with the first aspect, in one implementation, according to the aircraft dynamic characteristic equation, the maneuvering accelerations a of the aircraft and the target are obtained i For the control input u i The transfer function of:
[0030] G i (s) = C i (sI - A i ) -1 B i + d i
[0031] Given the initial remaining range r0 and the initial approach speed between the aircraft and the target The terminal interception time is expressed as:
[0032]
[0033] Ignoring the changes in the magnitude and direction of the speed in the terminal guidance section, with the initial time being 0, then
[0034] For the remaining flight time t at any interception moment go It is expressed as:
[0035]
[0036] Combined with the first aspect, in one implementation, the establishment process of the linear relative motion equation includes:
[0037] The dynamic models of the aircraft and the target are expressed as:
[0038] a MN = k CM a M = k CM C M x M + k CM d M u M
[0039] a TN = k CT a T = k CT C T xT +k CT d T u T
[0040] Considering the terminal miss distance and angle constraints, let the state variables be:
[0041] x γ =θ M +θ T ;
[0042] Establish the relative motion equation in the direction perpendicular to the line of sight LOS0:
[0043]
[0044] The vector expression of the relative motion equation is:
[0045]
[0046] Combined with the first aspect, in one implementation, after establishing the linear relative motion equation, S2 further includes the following steps: projecting the current state to the interception moment using the state transition matrix for order reduction processing:
[0047]
[0048] The state transition matrix satisfies:
[0049]
[0050] Deriving the zero-effort miss distance term gives:
[0051]
[0052] The zero-effort state Z and its derivative term both contain the calculation method of EΦ(t f ,t), Φ(t f ,t) is:
[0053] Φ(t f ,t) = L -1 [(sI - A) -1
[0054] Then Where:
[0055]
[0056] is the inverse Laplace operator for the variable t go ;
[0057] The derivative of the zero control state variable can be expressed as:
[0058]
[0059] Where:
[0060]
[0061] t go can be expressed as can be expressed as:
[0062]
[0063]
[0064] Also Then:
[0065]
[0066] Combined with the first aspect, in one implementation, the establishment process of the performance index J includes:
[0067]
[0068] In the formula, a, b, η T are all non - negative. When a→∞, a zero - miss - distance interception guidance law can be obtained; when b→∞, an interception guidance law without collision angle error can be obtained, and η T is the estimated value of the maneuverability of the target relative to the interceptor missile;
[0069] At the interception moment, if x1(t f ) = Z1(t f ), x γ (t f ) = Z2(t f ), then the expression in S3 can be obtained.
[0070] Combined with the first aspect, in one implementation, the process of solving the analytical solution of the optimal guidance law based on the established performance index according to the optimal theory includes:
[0071] Based on the performance index and the optimal theory, establish the Hamiltonian function:
[0072]
[0073] From the co - state equation, we can get:
[0074]
[0075] From the transversality condition, we can get:
[0076]
[0077] The expression of the co-state variable is:
[0078]
[0079] From the control equation it can be obtained that:
[0080]
[0081] Also the differential game control equation of the aircraft and the target can be obtained:
[0082]
[0083] It can be obtained that:
[0084]
[0085] By integrating, we get:
[0086]
[0087] Among them:
[0088]
[0089] After arranging it into the form of we get:
[0090]
[0091] Using Cramer's rule to solve, we get:
[0092]
[0093] In the formula, detΛ = Λ 11 Λ 22 -Λ 12 Λ 21 , when aet Λ≠0;
[0094] The relationship between the current state and the co-state variable is obtained as:
[0095]
[0096] A set of differential game guidance laws in feedback form is obtained. The control quantity of the aircraft is linearly related to the final miss distance and the collision angle, and is expressed as:
[0097]
[0098] Combined with the first aspect, in one implementation, the method further includes the following steps:
[0099] S4. Optimize the analytical solution of the optimal guidance law according to the simulation results.
[0100] In a second aspect, an embodiment of the present application provides a guidance device with impact angle constraints applicable to high-speed aircraft. The guidance device with impact angle constraints applicable to high-speed aircraft includes a processor, a memory, and a guidance program with impact angle constraints applicable to high-speed aircraft stored on the memory and executable by the processor. When the guidance program with impact angle constraints applicable to high-speed aircraft is executed by the processor, the method provided in the first aspect is implemented.
[0101] Compared with the prior art, the advantages of the present invention are as follows:
[0102] Through the independently developed guidance method with impact angle constraints applicable to high-speed aircraft, the present invention can be directly applied to high-speed aircraft under constraints, improving the terminal precision strike ability of high-speed aircraft. BRIEF DESCRIPTION OF THE DRAWINGS
[0103] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.
[0104] Figure 1 Schematic diagram of the relative position relationship between the aircraft and the target in the embodiment of the present invention;
[0105] Figure 2 Schematic diagram of the simulation trajectories with three impact angle constraints of -60°, -70°, and -80° at the terminal in the embodiment of the present invention;
[0106] Figure 3 Schematic diagram of the overload conditions with three impact angle constraints of -60°, -70°, and -80° at the terminal in the embodiment of the present invention;
[0107] Figure 4 Schematic diagram of the hardware structure of the guidance device with impact angle constraints applicable to high-speed aircraft involved in the solution of the embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0108] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the following will clearly and completely describe the technical solutions in the embodiments of this application with reference to the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are some, but not all, of the embodiments of this application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in this application without creative efforts shall fall within the scope of protection of this application.
[0109] The flowcharts shown in the accompanying drawings are only illustrative, and do not necessarily include all the content and operations / steps, nor do they necessarily need to be executed in the described order. For example, some operations / steps can also be decomposed, combined, or partially merged, so the actual execution order may change according to the actual situation.
[0110] To make the objectives, technical solutions, and advantages of this application clearer, the following will further describe the embodiments of this application in detail with reference to the accompanying drawings.
[0111] In a first aspect, an embodiment of this application provides a guidance method with a fall angle constraint applicable to a high-speed aircraft, and the steps of this method include:
[0112] S1: Establish a kinematic model and a dynamic model for the terminal guidance section based on the ballistic inclination angles of the aircraft and the target, the speeds of the aircraft and the target, and the relative distance between the aircraft and the target;
[0113] The expression of the dynamic model is:
[0114]
[0115] See Figure 1 As shown, X I -O I -Y I is an inertial reference frame:
[0116] θ M and θ T are the ballistic inclination angles, respectively representing the angles between the speeds of the aircraft and the target and the X I axis of the inertial system;
[0117] q is the line-of-sight angle, that is, the angle between the line connecting the aircraft and the target and the X I axis.
[0118] X - O - Y is the initial line-of-sight coordinate system, the initial line of sight LOS0 is the X axis, and the Y axis is perpendicular to the initial line of sight;
[0119] M represents the aircraft, and T represents the target;
[0120] V M and V TThe magnitudes of the velocities of the aircraft and the target respectively;
[0121] a M 、a T The magnitudes of the accelerations of the aircraft and the target respectively, with the direction perpendicular to the velocity direction; r is the relative distance between the aircraft and the target.
[0122] The expression of the kinematic model is: where x i represents the state vector of the internal dynamic characteristics of the aircraft or the target, A i , C i are the coefficient matrices related to the self-states of the aircraft and the target, B i , d i is the coefficient matrix related to the command acceleration.
[0123] Specifically, the above kinematic model is obtained from the projections of r and the relative velocity v in the line-of-sight coordinate, and the calculation formula is:
[0124]
[0125] Taking the derivative of r gives:
[0126]
[0127] The projection of the relative velocity v in the line-of-sight coordinate is:
[0128]
[0129] In this way, the above dynamic model can be obtained.
[0130] In addition, since the magnitudes of the velocities of the aircraft and the target are basically unchanged in the terminal guidance section and the overload is perpendicular to the velocity direction, we get:
[0131]
[0132]
[0133] Furthermore, according to the aircraft dynamic characteristic equation, the maneuvering accelerations a of the aircraft and the target can be obtained i The transfer function with respect to the control input u i is:
[0134] G i (s) = C i (sI - A i ) -1 B i + d i
[0135] For the problem of terminal guidance interception, given the initial remaining range \(r_0\) and the initial closing velocity between the vehicle and the target The terminal interception time can be approximately expressed as:
[0136]
[0137] Ignoring the changes in the magnitude and direction of the velocity in the terminal guidance section, with the initial time being 0, the above equation can be further simplified to:
[0138]
[0139] For the remaining flight time \(t\) at any interception moment go It can be expressed as:
[0140]
[0141] S2: Based on the small-angle assumption in the terminal section, after linearizing the non-linear relative position relationship between the missile and the target (i.e., simplifying the kinematic model and dynamic model in S1), a linear relative motion equation convenient for analysis is established in the direction perpendicular to the line of sight. The vector expression form of this equation is:
[0142]
[0143] Specifically, the establishment process of the above linear relative motion equation includes:
[0144] Since the relative motion relationship between the vehicle and the target on the initial line of sight axis is fixed; therefore, the relative motion relationship between the vehicle and the target can be represented by the relative motion equation in the direction perpendicular to the initial line of sight.
[0145] The dynamic model of the vehicle and the target can be expressed as:
[0146] a MN =k CM a M =k CM C M x M +k CM d M u M
[0147] a TN =k CT a T =k CT C T x T +k CT d T uT
[0148] Considering the terminal miss distance and angular constraints, let the state variables be:
[0149] x γ = θ M + θ T ;
[0150] Establish the relative motion equation in the direction perpendicular to the line of sight LOS0:
[0151]
[0152] The vector expression of the relative motion equation is:
[0153]
[0154] Meanwhile, after S2 establishes the linear relative motion equation, it also includes the following steps:
[0155] Since the system order is relatively high and direct solution is relatively complex, the current state of the system is projected to the interception moment using the state transition matrix, and the system is reduced in order, reducing the five-dimensional linear equation system to a two-dimensional scalar equation:
[0156]
[0157] For a given linear system, since its A matrix is known, we can obtain:
[0158]
[0159] Then the state transition matrix satisfies:
[0160]
[0161] Taking the derivative of the zero-effort miss distance term, we can obtain:
[0162]
[0163] The zero-effort state Z and its derivative term both contain the calculation method of EΦ(t f , t), Φ(t f , t) is:
[0164] Φ(t f , t) = L -1 [(sI - A) -1
[0165] Then
[0166] Where:
[0167]
[0168] is for the variable t go of the inverse Laplace operator.
[0169] The derivative of the zero-control state quantity can be expressed as:
[0170]
[0171] Where:
[0172]
[0173] t go can be expressed as Therefore can be expressed as:
[0174]
[0175] Also Then the above formula can be expressed as:
[0176]
[0177] S3: Based on the linear relative motion equation in S2, establish performance indicators according to the combat target and requirements, and solve the analytical solution of the optimal guidance law based on the established performance indicators. The expression of the performance indicator J is:
[0178]
[0179] Specifically, the establishment process of the above performance indicators includes:
[0180] Considering the miss distance, collision angle, and energy constraint, the following performance indicator J can be established:
[0181]
[0182] In the formula, a, b, η T are all non-negative. In the ideal case, a→∞ can obtain a zero-miss-distance interception guidance law, b→∞ can obtain an interception guidance law without collision angle error, and η T is the estimated value of the target's maneuverability relative to the interceptor missile.
[0183] At the interception moment, x1(t f ) = Z1(t f ), x γ (t f ) = Z2(t f) Then the above formula (the formula of J) can be rewritten as the expression in S3.
[0184] Furthermore, the process of solving the analytical solution of the optimal guidance law based on the established performance index according to the optimal theory in S3 includes:
[0185] Based on the performance index and the optimal theory, establish the Hamiltonian function:
[0186]
[0187] From the co-state equation, we can get:
[0188]
[0189] From the transversality condition, we can get:
[0190]
[0191] It can be known that the expression of the co-state variable is:
[0192]
[0193] From the control equation we can get:
[0194]
[0195] Also we can get the differential game control equation of the aircraft and the target:
[0196]
[0197] We can get:
[0198]
[0199] Integrating the above formula directly, we can get:
[0200]
[0201] where:
[0202]
[0203] It can be arranged into in the form, where:
[0204]
[0205] Using Cramer's rule to solve, we can get:
[0206]
[0207] where detΛ = Λ 11 Λ 22 -Λ 12 Λ 21 , when detΛ ≠ 0, the above equation has a unique solution.
[0208] The relationship between the current state and the co-state variables can be obtained as:
[0209]
[0210] Finally, a set of differential game guidance laws in feedback form can be obtained. The control quantity of the aircraft is linearly related to the final miss distance and the collision angle, and can be expressed as:
[0211]
[0212] S4. Optimize the analytical solution of the optimal guidance law according to the simulation situation. Since the overload limit and structural limit are not considered in the design process of the guidance law, the guidance parameters need to be iteratively optimized according to the simulation situation until the actual functional requirements are met.
[0213] The effectiveness of the above method is verified by an example below.
[0214] For a stationary target, assuming that the aircraft and the target have ideal characteristics, then:
[0215]
[0216] Substituting it in, the optimal control equation of the aircraft can be obtained.
[0217]
[0218] Table 1. State settings for terminal guidance simulation
[0219]
[0220] Figure 2 、 Figure 3 The simulation trajectories and overload conditions for three impact angle constraints of -60°, -70°, and -80° at the end are given. It can be seen that the guidance law proposed by the present invention can be directly applied to high-speed aircraft under constrained conditions.
[0221] In the second aspect, an embodiment of the present application provides a guidance device with impact angle constraints applicable to high-speed aircraft. The guidance device with impact angle constraints applicable to high-speed aircraft can be a device with data processing functions such as a personal computer (PC), a laptop computer, a server, etc.
[0222] Referring to Figure 4 , Figure 4This is a schematic diagram of the hardware structure of a guidance device with impact angle constraints applicable to high-speed aircraft in the solution of the embodiment of the present application. In the embodiment of the present application, the guidance device with impact angle constraints applicable to high-speed aircraft may include a processor, a memory, a communication interface, and a communication bus.
[0223] Among them, the communication bus can be of any type and is used to interconnect the processor, the memory, and the communication interface.
[0224] The communication interface includes interfaces such as input / output (I / O) interfaces, physical interfaces, and logical interfaces for interconnecting components inside the guidance device with impact angle constraints applicable to high-speed aircraft, as well as interfaces for interconnecting the guidance device with impact angle constraints applicable to high-speed aircraft with other devices (such as other computing devices or user devices). The physical interface can be an Ethernet interface, a fiber optic interface, an ATM interface, etc.; the user device can be a display, a keyboard, etc.
[0225] The memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical memory, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.
[0226] The processor can be a general-purpose processor, and the general-purpose processor can call the guidance program with impact angle constraints applicable to high-speed aircraft stored in the memory and execute the guidance method with impact angle constraints applicable to high-speed aircraft provided by the embodiment of the present application. For example, the general-purpose processor can be a central processing unit (CPU). Among them, the method executed when the guidance program with impact angle constraints applicable to high-speed aircraft is called can refer to the various embodiments of the guidance method with impact angle constraints applicable to high-speed aircraft of the present application, which will not be elaborated here.
[0227] Those skilled in the art can understand that Figure 4 the hardware structure shown in does not constitute a limitation to the present application, and may include more or fewer components than shown in the figure, or combine some components, or have different component arrangements.
[0228] In a third aspect, an embodiment of the present application further provides a computer-readable storage medium.
[0229] Stored on the computer-readable storage medium of the present application is a guidance program with impact angle constraint applicable to a high-speed aircraft. When the guidance program with impact angle constraint applicable to a high-speed aircraft is executed by a processor, the steps of the guidance method with impact angle constraint applicable to a high-speed aircraft as described above are implemented.
[0230] Among them, the method implemented when the guidance program with impact angle constraint applicable to a high-speed aircraft is executed can refer to various embodiments of the guidance method with impact angle constraint applicable to a high-speed aircraft of the present application, which will not be elaborated here.
[0231] It should be noted that the serial numbers of the above embodiments of the present application are only for description and do not represent the superiority or inferiority of the embodiments.
[0232] Through the description of the above embodiments, those skilled in the art can clearly understand that the above embodiment methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art can be embodied in the form of a software product. This computer software product is stored in a storage medium as described above (such as ROM / RAM, magnetic disk, optical disc) and includes several instructions for causing a terminal device to execute the methods described in various embodiments of the present application.
[0233] The terms "including" and "having" and any variations thereof in the specification, claims and drawings of the present application are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally further includes steps or units not listed, or optionally further includes other steps or units inherent to these processes, methods, products or devices. The descriptions of terms such as "first", "second" and "third" are used to distinguish different objects, etc., and do not represent a sequence, nor do they limit that "first", "second" and "third" are different types.
[0234] In the description of the embodiments of the present application, terms such as "exemplary", "for example" or "for instance" are used to indicate examples, illustrations or explanations. Any embodiment or design solution described as "exemplary", "for example" or "for instance" in the embodiments of the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Exactly speaking, the use of terms such as "exemplary", "for example" or "for instance" is intended to present relevant concepts in a specific manner.
[0235] In the description of the embodiments of the present application, unless otherwise specified, " / " means "or". For example, A / B may mean A or B. The "and / or" in the text is merely a description of the relationship between associated objects, indicating that there can be three relationships. For example, A and / or B may mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of the present application, "a plurality of" means two or more than two.
[0236] In some processes described in the embodiments of the present application, there are multiple operations or steps that appear in a specific order. However, it should be understood that these operations or steps may not be executed in the order in which they appear in the embodiments of the present application or may be executed in parallel. The serial numbers of the operations are only used to distinguish different operations, and the serial numbers themselves do not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed in sequence or in parallel, and these operations or steps may be combined.
[0237] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-described embodiment methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium as described above (such as ROM / RAM, magnetic disk, optical disc) and includes several instructions for causing a terminal device to execute the methods described in the various embodiments of the present application.
[0238] The above is only the specific implementation manner of the embodiments of the present invention, but the protection scope of the embodiments of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed in the embodiments of the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of the embodiments of the present invention. Therefore, the protection scope of the embodiments of the present invention should be subject to the protection scope of the claims.
Claims
1. A guidance method with impact angle constraint applicable to high-speed aircraft, characterized in that, The method includes the following steps: S1: Establish the kinematic model and dynamic model of the terminal guidance section according to the ballistic inclination angle θ of the aircraft and the target, the speeds V of the aircraft and the target, and the relative distance r between the aircraft and the target; The expression of the dynamic model is: θ M 、 θ T are the ballistic inclinations, respectively representing the angles between the velocities of the aircraft and the target and the X-axis of the inertial system; I axis; q is the line-of-sight angle; M represents the aircraft and T represents the target; V M 、V T are the magnitudes of the velocities of the aircraft and the target, respectively; The expression of the kinematic model is: where x i represents the state vector of the internal dynamic characteristics of the aircraft or target, A i , C i are coefficient matrices related to the state of the aircraft and the target itself, B i , d i are coefficient matrices related to the commanded acceleration; S2: Based on the small-angle assumption at the end stage, after processing the kinematic model and the dynamic model, establish a linear relative motion equation convenient for analysis in the direction perpendicular to the line of sight. The vector expression form of this equation is: S3: Based on the linear relative motion equation in S2, establish performance indicators according to the combat target and requirements, and solve the analytical solution of the optimal guidance law according to the optimal theory based on the established performance indicators. The expression of the performance indicator J is:
2. The guidance method with impact angle constraint applicable to high-speed aircraft as described in claim 1, characterized in that: Define X I -O I -Y I is an inertial reference frame; q is the angle between the line connecting the aircraft and the target and the X I axis; Define X-O-T as the initial line-of-sight coordinate system, with the initial line of sight LOS0 as the X-axis and the T-axis perpendicular to the initial line of sight; a M and T are the magnitudes of the accelerations of the aircraft and the target respectively, and the directions are perpendicular to the velocity directions; Specifically, the above kinematic model is obtained according to the projections of r and the relative velocity v in the line-of-sight coordinates, and the calculation formula is: Taking the derivative of r gives: The projection of the relative velocity v in the line-of-sight coordinates is:
3. The guidance method with angle-of-descent constraint applicable to high-speed aircraft as claimed in Claim 2, wherein: When the speeds of the aircraft and the target are basically unchanged in the terminal guidance section, the overload is perpendicular to the velocity direction, and we get:
4. The guidance method with impact angle constraint applicable to high-speed aircraft according to claim 3, characterized in that: According to the dynamic characteristic equation of the aircraft, the maneuvering accelerations a of the aircraft and the target are obtained i For the control input u i The transfer function of G i (s) = C i (sI - A i ) -1 B i +d i Given the initial remaining range r0 and the initial closing speed between the aircraft and the target The end-game interception time is expressed as: Ignoring the changes in the magnitude and direction of the velocity in the terminal guidance section, if the initial time is 0, then For the remaining flight time t at any interception moment go It is expressed as:
5. The guidance method with impact angle constraint applicable to high-speed aircraft according to claim 4, characterized in that, The establishment process of the linear relative motion equation includes: The dynamic model of the aircraft and the target is expressed as: a MN = k CM a M = k CM C M x M + k CM d M u M a TN = k CT a T = k CT C T x T + k CT d T u T Considering the terminal miss distance and angle constraints, let the state variables be: Establish a relative motion equation in the direction perpendicular to the line of sight LOS0: The vector expression of the relative motion equation is:
6. The guidance method with impact angle constraint applicable to high-speed aircraft as described in claim 5, characterized in that After S2 establishes the linear relative motion equation, it also includes the following steps: Use the state transition matrix to project the current state to the interception moment for order reduction processing: The state transition matrix satisfies: Taking the derivative of the zero-control miss distance term gives: Zero control state Z and its derivative terms Both contain EΦ(t f ,t), Φ(t f ,t) is calculated as follows: φ(t f , t) = L -1 [(sI - A) -1 Then Where: is for the variable t go inverse Laplace operator; The derivative of the zero-control state quantity can be expressed as: Where: t go can be expressed as can be expressed as: Also Then:
7. The guidance method with impact angle constraint applicable to high-speed aircraft according to claim 6, characterized in that, The establishment process of the performance indicator J includes: where a, b, and η T are all non-negative. When a → ∞, a zero-miss intercept guidance law can be obtained. When b → ∞, an intercept guidance law with no collision angle error can be obtained. η T is an estimated value of the maneuverability of the target relative to the intercept missile; At the interception moment, x1(t f ) = Z1(t f ), x γ (t f ) = Z2(t f ), the expression in S3 can be obtained.
8. The guidance method with impact angle constraint applicable to high-speed aircraft according to claim 7, characterized in that, The process of solving the analytical solution of the optimal guidance law according to the optimal theory based on the established performance indicators includes: Based on the performance indicators and the optimal theory, establish the Hamiltonian function: From the co-state equation, we can get: From the transversality condition, we can get: The expression of the co-state variable is: From the governing equations it can be obtained that: Again The differential game control equations of the aircraft and the target can be obtained: We can get: Performing integration gives: Where: Sorted into to obtain the following form: Using Cramer's rule for solution gives: where detΛ = Λ 11 Λ 22 -Λ 12 Λ 21 , when detΛ ≠ 0; The relationship between the current state and the co-state variable is obtained as: A set of differential game guidance laws in feedback form is obtained. The control quantity of the aircraft is linearly related to the final miss distance and the collision angle, and is expressed as:
9. The guidance method with impact angle constraint applicable to high-speed aircraft according to any one of claims 1 to 8, characterized in that, The method also includes the following steps: S4. Optimize the analytical solution of the optimal guidance law according to the simulation situation.
10. A guidance device with angle-of-fall constraint applicable to high-speed aircraft, characterized in that, The guidance device applicable to high-speed aircraft with impact angle constraints includes a processor, a memory, and a guidance program applicable to high-speed aircraft with impact angle constraints stored on the memory and executable by the processor. When the guidance program applicable to high-speed aircraft with impact angle constraints is executed by the processor, the steps of the guidance method applicable to high-speed aircraft with impact angle constraints as described in any one of claims 1 to 7 are implemented.