A guidance and control integrated design method considering flight state constraints

Abstract

The invention relates to the field of missile interception, and specifically discloses a guidance and control integrated design method considering flight state constraints, comprising S1: establishing a three-dimensional guidance and control integrated model; S2: designing a maneuvering target attack or interception algorithm at a desired angle based on the model of S1; S3: designing a guidance and control algorithm under state constraints based on the algorithm of S2, establishing a six-degree-of-freedom guidance and control integrated model according to an aircraft kinematic model, a dynamic model and a three-dimensional missile-target relative kinematic model, avoiding the influence of inconsistent time constants of inner and outer loop dynamic models on guidance efficiency, taking flight condition constraints such as flight attack angle and attitude angular rate into consideration through the scheme, designing a state-constrained guidance and control integrated method based on safety constraint control theory, and effectively improving the flight safety and stability of the interceptor missile.

Description

Technical Field

[0001] The invention relates to the technical field of missile interception, and in particular to a guidance and control integrated design method taking flight state constraints into consideration. Background Art

[0002] With the development of aerospace weapon system technology, the penetration, stealth and maneuvering escape capabilities of high-speed maneuvering targets are constantly improving, and the tactical and technical indicators of intercepting missiles present a multi-dimensional demand, which brings great challenges to traditional defense systems. The design of the terminal guidance law of the missile directly determines the terminal trajectory and interception accuracy of the missile. Therefore, it is of great significance to study a new terminal guidance law that can adapt to battlefield needs and intercept high-speed maneuvering targets. Since Germany first applied the V-2 ballistic missile to actual combat in the 1940s, scholars at home and abroad have carried out a series of studies on the control laws of missiles. The proportional guidance law (PN) is one of the most widely used guidance laws in engineering. It has the advantages of requiring less guidance information and being easy to implement in engineering. According to different guidance command design directions, traditional proportional guidance laws can be divided into pure proportional guidance (PPN) and true proportional guidance (TPN). In PPN, the guidance command of the interceptor missile is designed to be perpendicular to the missile speed direction; while in TPN, the guidance command of the interceptor missile is perpendicular to the line of sight of the missile and the target. In subsequent research work, domestic and foreign scholars have conducted extensive research on these two guidance laws and proposed a series of improvement methods such as IPN, GTPN, OPPN, and RTPN.

[0003] Although the traditional PN-based guidance law has a wide range of engineering applications, with the changes in battlefield environment and the improvement of target mobility, it is hoped that the guidance law will meet more complex terminal constraints. For example, for targets such as stealth fighters and stealth cruise missiles that use special aerodynamic shapes and absorbing materials, due to their small radar reflection cross-section, they can usually only be identified at certain specific angles, which requires the missile to have the ability to intercept from different directions in space. For high-speed moving targets, since modern interceptors usually use kinetic killing to intercept, the terminal guidance time of the interceptor is very short, which requires the terminal guidance law of the interceptor to have a fast convergence capability. In order to solve the above problems, relevant scholars have adopted nonlinear control theories, such as model predictive control, sliding mode control, inversion control, etc., to design guidance algorithms with different convergence speeds, which can enable the interceptor to quickly converge to the desired line of sight angle within a limited time, a fixed time, and a preset time, thereby completing the interception and strike mission. For targets with large maneuverability to escape, since the targets usually take high-frequency maneuvers to evade, the unknown time-varying target maneuvers are the key to the successful interception of missiles, which requires the missile to have the ability to handle unknown target maneuvers. In order to solve the external disturbance problem caused by target maneuvers, the common solution is to use nonlinear disturbance observers or extended state observers to estimate the external disturbance of the model online and compensate for it in the guidance law, but this type of method often requires the establishment of a more accurate aircraft dynamics model, which restricts its application scope in actual engineering.

[0004] In addition, most of the existing guidance law design methods use the three-degree-of-freedom missile-target relative kinematic model for research. This type of method works better when the aircraft speed is low. However, with the increase in the speed and maneuverability of the interceptor missile, the outer loop kinematic model and the inner loop attitude dynamics model of the aircraft no longer meet the spectrum separation conditions. The time constant between the attitude system as a fast-changing subsystem and the outer loop slow-changing kinematic subsystem is inconsistent, resulting in reduced guidance accuracy. In order to avoid the occurrence of this phenomenon, a common method is to establish an integrated guidance and control model, and directly design the inner loop rudder angle command under the given expected strike angle condition. Therefore, the integrated guidance and control design method has attracted the attention of more and more scholars. In order to improve the transient and steady-state control effects of the aircraft in the guidance stage, a type of guidance and control method based on preset performance has been proposed. By introducing a new error conversion function in the guidance system, the line of sight angle can be quickly converged to the expected value within a given interval. In response to the saturation problem of the aerodynamic control surface, relevant scholars have designed a new auxiliary system. When the actuator saturation occurs in the system, the control input size is adjusted to effectively alleviate the actuator saturation phenomenon. At present, most of the solutions to the problem of integrated guidance and control of interceptor missiles use nonlinear theory combined with disturbance observer technology to achieve interception or attack of maneuvering targets in three-dimensional space. Most of the existing guidance and control methods do not consider flight state constraints, such as flight angle of attack and attitude angle constraints. However, in actual flight environments, excessive flight angle of attack will lead to decreased aerodynamic efficiency. For thrust-powered aircraft, excessive flight angle of attack will also cause unstable operation of the engine or even surge. Therefore, it is necessary to constrain the flight state of the aircraft to improve the flight stability and safety of the interceptor missile.

[0005] Through the above analysis, it can be seen that although there are a lot of research results on the integrated guidance and control methods, the existing literature often does not consider the flight state constraints, which brings huge safety risks to the stable flight of the six-freedom interceptor missile. In addition, the interceptor missile faces a variety of constraints in the real flight environment, such as input saturation constraints, unknown external disturbance constraints, flight state constraints, strike angle constraints, etc. There are few studies on the integrated guidance and control design methods under complex constraints in the existing literature. In order to solve the above problems, the present invention introduces barrier Lyapunov functions, first-order auxiliary anti-saturation subsystems and adaptive inversion control technologies to design a new integrated guidance and control strategy, which can intercept or strike three-dimensional maneuvering targets at a desired angle while ensuring that the flight state constraints and input saturation constraints are met. Summary of the invention

[0006] In order to solve the problems existing in the background technology, the invention takes the interception of three-dimensional maneuvering targets by six-degree-of-freedom aircraft as the research background, and considers the influence of angle constraints on guidance performance. The invention proposes a guidance and control integrated design method considering flight state constraints. Under the condition of satisfying the flight angle constraints, the six-degree-of-freedom interceptor missile intercepts the maneuvering target, avoiding the influence of large attack angle and large attitude angle on the guidance performance in the initial stage of guidance. The safety constraint control theory is used to design a new guidance and control integration strategy to improve the flight stability and safety of the interceptor missile. The method of this scheme includes the following steps:

[0007] S1: Establish a three-dimensional guidance and control integrated model;

[0008] S2: Design an algorithm to strike or intercept maneuvering targets at a desired angle based on the model in S1;

[0009] S3: Design a guidance control algorithm under state constraints based on the algorithm in S2.

[0010] The specifics of this plan are:

[0011] The first step is to establish a six-degree-of-freedom guidance and control integrated model based on the aircraft kinematic model, dynamic model and three-dimensional missile-target relative kinematic model to avoid the influence of inconsistent time constants of the inner and outer loop dynamic models on the guidance effectiveness;

[0012] The second step is to use nonlinear backstepping control theory, nonlinear disturbance observer and other technologies to design a guidance and control integration strategy to achieve spatial strike angle constraints, so that the expected line of sight angle tracking error converges to zero within a limited time.

[0013] The third step is to consider the state constraints such as flight angle and attitude angular rate, and introduce the obstacle Lyapunov function into the traditional nonlinear control method to design a new guidance and control integrated instruction considering the state constraints;

[0014] The fourth step is to prove the stability of the designed method based on Lyapunov stability control theory, ensuring that all error states of the closed-loop system converge to a small neighborhood of zero within a finite time, ensuring that the flight state constraints are met.

[0015] The present invention has at least the following beneficial effects:

[0016] 1. Different from the three-degree-of-freedom guidance model used in the existing literature, the present invention takes the six-degree-of-freedom interceptor missile model as the research object, which effectively avoids the problem of reduced guidance accuracy caused by the inconsistency of the time constants of the guidance and control loops;

[0017] 2. Different from the existing guidance law literature that uses overload or acceleration as the interceptor missile input command, the guidance and control integration method proposed in the present invention directly generates the control command of the rudder surface deflection, which can give full play to the performance advantages of the six-degree-of-freedom interceptor missile and has a wider range of model application;

[0018] 3. The guidance and control strategy designed by the present invention takes into account flight condition constraints such as flight angle of attack and attitude angular rate. Based on the safety constraint control theory, an integrated method of constraint guidance and control taking the state into consideration is designed, which effectively improves the flight safety and stability of the interceptor missile. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a schematic diagram of the three-dimensional interception geometry of the present invention;

[0020] Figure 2 It is a schematic diagram of the three-dimensional simulation result of the present invention;

[0021] Figure 3 This is a schematic diagram of the simulated projectile-target distance change of the present invention;

[0022] Figure 4 Schematic diagram of the change of the sight angle of the interceptor missile of the present invention;

[0023] Figure 5 This is a diagram showing the change in the flight angle of the interceptor missile of the present invention;

[0024] Figure 6 is a graph showing the change in attitude angular rate of the interceptor missile of the present invention;

[0025] Figure 7 It is the interceptor missile control input diagram of the present invention. DETAILED DESCRIPTION

[0026] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0027] Example

[0028] See also Figure 1-Figure 7 , a guidance and control integration method considering flight state constraints, comprising the following steps:

[0029] (1) Establishing a three-dimensional guidance model and a six-degree-of-freedom model of the interceptor missile:

[0030] 1) Define the coordinate system, including

[0031] Ground coordinate system: A coordinate system fixed to the surface of the earth is the ground coordinate system. The center of mass of the instantaneous interceptor missile is selected as the origin of the coordinate system. , the intersection line of the ballistic plane and the horizontal plane is selected as Axis, the direction pointing to the target is positive; Axis and The axis is vertical and points upwards, The axes are given by the right-hand rule, thus determining the coordinate system .

[0032] Projectile coordinate system: It is fixed to the projectile and moves and rotates in space with the projectile. It is a dynamic coordinate system. Usually its coordinate origin is Select the center of mass of the interceptor missile. The axis is usually parallel to the symmetry axis of the missile body or the mean aerodynamic chord of the missile wing, and is positive when pointing to the head. The axis is located in the left-right symmetric plane of the projectile. Axis and The axes are vertical and contain the origin, The axis is positive; The axes are determined according to the right-hand rule.

[0033] Ballistic coordinate system: coordinate system origin It is selected at the center of mass of the interceptor missile (target), and it is a dynamic coordinate system that moves in space with the center of mass of the interceptor missile. The velocity vector of the axis and the center of mass of the interceptor missile The same direction, The axis passes through In the vertical plane of the axis and Vertically, the direction away from the center of the earth is positive; The axes are determined by the right-hand rule.

[0034] Line of sight coordinate system: Select the missile sight as Axis, where the coordinate origin The interceptor missile is selected at the center of mass. The direction of the interceptor missile pointing to the target is positive. Axis and The axis is vertical and located at the On the vertical plane of the axis, Positive is pointing upwards. The axis is determined by the right-hand rule. The relative motion equation between the interceptor missile and the target in the line of sight direction is mainly established in the line of sight coordinate system. The interceptor missile and the target are fixed to the line of sight coordinate system, which is a moving coordinate system.

[0035] 2) Establish a 3D guidance and control integrated model

[0036] The relative kinematic relationship between the interceptor missile and the target is usually described in the line-of-sight coordinate system. is the distance between the projectile and the target, and Represents the line of sight inclination and line of sight deflection. and are the speeds of the interceptor missile and the target, respectively. and is the lead angle of the interceptor missile in the line of sight. and is the lead angle of the target in the line of sight. and are the components of the interceptor missile and target acceleration vector in the line of sight, respectively. The missile-target relative kinematic model is described as

[0037] (1)

[0038] (2)

[0039] (3)

[0040] (4)

[0041] (5)

[0042] (6)

[0043] (7)

[0044] By deriving formulas (1) to (3), and combining formulas (4) and (7), the following three-dimensional guidance model can be obtained:

[0045] (8)

[0046] in , are the acceleration components of the interceptor missile and the target in the line of sight system respectively.

[0047] The interceptor missile is in the line of sight coordinate system and ballistic coordinate system The acceleration components of satisfy the following relationship:

[0048] (9)

[0049] The acceleration coordinate transformation matrix is:

[0050] (10)

[0051] in:

[0052] ,

[0053] .

[0054] Further:

[0055] (11)

[0056] in:

[0057]

[0058] The acceleration vectors of the interceptor and the target in the velocity system and Projected to the line of sight coordinate system respectively, the three-dimensional guidance model can be rewritten as:

[0059] (12)

[0060] In the formula and To intercept the lift force and lateral force, the expression is:

[0061] (13)

[0062] Where: , , are the interceptor mass, reference area and flight pressure respectively. , are angle of attack and sideslip angle respectively.

[0063] The attitude dynamics equation of the interceptor missile with STT configuration can be described as:

[0064] (14)

[0065] in is the roll angle, is the attitude angular rate, is the three-axis moment of inertia of the interceptor missile, is the aerodynamic torque, It is the rudder input.

[0066] set up are the desired line of sight inclination and declination, , , , , , In order to facilitate the design of guidance and control laws, the interceptor missile kinematic equations and attitude dynamics equations are rewritten as follows:

[0067] (15)

[0068] in It is external interference, and there are:

[0069] , ,

[0070] , ,

[0071] , ;

[0072] .

[0073] The goal of the guidance control algorithm designed in this invention is to achieve the strike or interception of a three-dimensional maneuvering target at a desired angle while ensuring that the flight state of the interceptor missile meets the safety constraints. The mathematical equation can be expressed as:

[0074] (16)

[0075] 3) Integrated design of guidance and control considering state constraints

[0076] First, define the following sliding surface:

[0077] (17)

[0078] in Status The virtual control law is , The amplitude is The saturation function of Produced by:

[0079] (18)

[0080] in .

[0081] Sliding surface Derivative, we have:

[0082] (19)

[0083] Virtual Control Law Designed for:

[0084] (20)

[0085] in , Yes The estimate of , and satisfies:

[0086] (twenty one)

[0087] variable The kinetic equation is:

[0088] (twenty two)

[0089] in .

[0090] make , , and take the derivative of the sliding surface:

[0091] (twenty three)

[0092] The virtual control law is designed as:

[0093] (twenty four)

[0094] in Yes The estimate of , and satisfies:

[0095] (25)

[0096] in , .

[0097] variable The kinetic equation is:

[0098] (26)

[0099] in .

[0100] To avoid the parameters Take the derivative and design the following first-order filter:

[0101] (27)

[0102] Nominal virtual control law Designed for , The amplitude is saturation function.

[0103] Define the third sliding surface as , and its derivative is:

[0104] (28)

[0105] The guidance law instructions are designed as follows:

[0106] (29)

[0107] in Yes The estimate of , and satisfies:

[0108] (30)

[0109] in , .

[0110] variable The kinetic equation is:

[0111] (31)

[0112] in .

[0113] 4) Proof of Stability of Guidance and Control Algorithm

[0114] Before conducting controller stability analysis, the following lemma is given:

[0115] Lemma 1: For any constant and , the following inequality holds:

[0116] (32)

[0117] Lemma 2: For any and satisfaction relationship The constant of , the following inequality holds:

[0118] (33)

[0119] First, define the following variables:

[0120] (34)

[0121] By taking the derivative of formula (34), we can get:

[0122] (35)

[0123] Then from formula (19) we get:

[0124] (36)

[0125] Similarly, there are:

[0126] (37)

[0127] Substituting the virtual control laws (20), (24) and (29) into the above equation, we obtain:

[0128] (38)

[0129] Define the external disturbance estimation error . Construct the following Lyapunov function with the BLF function:

[0130] (39)

[0131] right The derivatives are:

[0132] (40)

[0133] Substituting formula (38) into the above formula, we can get:

[0134] (41)

[0135] According to Young's inequality, the above formula can be written as:

[0136] (42)

[0137] in .

[0138] Substituting equations (21), (25) and (30) into the above equation, we can obtain from Lemma 1:

[0139] (43)

[0140] Same reason

[0141] (44)

[0142] in is the maximum value of the unknown external disturbance.

[0143] Substituting and into the equation, we get:

[0144] (45)

[0145] Select the following controller parameters:

[0146] (46)

[0147] At the same time, , then inequality (45) can be rewritten as:

[0148] (47)

[0149] The analytical solution of the above formula is:

[0150] (48)

[0151] Therefore, the closed-loop system control error changes with time , , the control target can be achieved.

[0152] 5) Guidance and control algorithm simulation verification

[0153] In order to verify the effectiveness of the algorithm of the present invention, a simulation scenario is designed in which a six-degree-of-freedom interceptor missile intercepts a constant maneuvering target. The initial state of the target is:

[0154]

[0155] The target constant maneuver amplitude is:

[0156]

[0157] The initial state of the interceptor missile is:

[0158]

[0159] The desired line of sight angle at the interceptor terminal is , the sight angle is The flight angle constraint is , the maximum attitude angular rate is , the maximum rudder surface deflection angle is ,Right now:

[0160]

[0161] The controller parameters are selected as follows:

[0162]

[0163] In summary, this plan:

[0164] 1. Based on the aircraft kinematic model, dynamic model and three-dimensional missile-target relative kinematic model, a six-degree-of-freedom guidance and control integrated model is established to avoid the influence of inconsistent time constants of the inner and outer loop dynamic models on the guidance effectiveness;

[0165] Second, by using nonlinear backstepping control theory, nonlinear disturbance observer and other technologies, a guidance and control integration strategy for realizing spatial strike angle constraints is designed to achieve the desired line of sight angle tracking error converging to zero within a finite time;

[0166] Third, considering the state constraints such as flight angle and attitude angular rate, a new guidance and control integrated instruction considering the state constraints is designed by introducing the obstacle Lyapunov function into the traditional nonlinear control method;

[0167] Fourth, based on the Lyapunov stability control theory, a proof of the stability of the designed method is given to ensure that all error states of the closed-loop system converge to a small neighborhood of zero within a finite time, ensuring that the flight state constraints are met.

[0168] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0169] While the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that many changes, modifications, substitutions and variations can be made to the embodiments without departing from the principles and spirit of the invention.

Claims

1. A guidance and control integrated design method considering flight state constraints, including defining a coordinate system, Features: S1: Establish a three-dimensional guidance and control integrated model; S2: Design an algorithm to strike or intercept maneuvering targets at a desired angle based on the model in S1; S3: Design a guidance control algorithm under state constraints based on the algorithm in S2; The guidance control algorithm under the design state constraint includes the following steps: First, define the following sliding surface: (17) in Status The virtual control law is , The amplitude is The saturation function of Produced by: (18) in ; Sliding surface Derivative, we have: (19) Virtual Control Law Designed for: (20) in , Yes The estimate of , and satisfies: (21) variable The kinetic equation is: (22) in ; make , , and take the derivative of the sliding surface: (23) The virtual control law is designed as: (24) in Yes The estimate of , and satisfies: (25) in , ; variable The kinetic equation is: (26) in ; To avoid the parameters Take the derivative and design the following first-order filter: (27) Nominal virtual control law Designed for , The amplitude is The saturation function of Define the third sliding surface as , and its derivative is: (28) The guidance law instructions are designed as follows: (29) in Yes The estimate of , and satisfies: (30) in , ; variable The kinetic equation is: (31) in .

2. The guidance and control integrated design method considering flight state constraints according to claim 1, characterized in that: set up is the distance between the projectile and the target, and Represents the line of sight inclination and line of sight deflection, and are the speeds of the interceptor missile and the target, respectively. and is the lead angle of the interceptor missile in the line of sight. and is the lead angle of the target in the line of sight, and are the components of the interceptor missile and target acceleration vector in the line of sight, respectively. The missile-target relative kinematic model is described as: (1) (2) (3) (4) (5) (6) (7) By taking the derivatives of equations (1) to (3), and combining equations (4) and (7), the following three-dimensional guidance model can be obtained: (8) in , are the acceleration components of the interceptor missile and the target in the line of sight system respectively; The interceptor missile is in the line of sight coordinate system and ballistic coordinate system The acceleration components of satisfy the following relationship: (9) The acceleration coordinate transformation matrix is: (10) in: ， ， Further: (11) in: ； The acceleration vectors of the interceptor and the target in the velocity system and Projected to the line of sight coordinate system respectively, the three-dimensional guidance model can be rewritten as: (12) In the formula and To intercept the lift force and lateral force, the expression is: (13) Where: , , are the interceptor mass, reference area and flight pressure respectively. , are angle of attack and sideslip angle respectively.

3. The guidance and control integrated design method considering flight state constraints according to claim 1, characterized in that: Designing an algorithm to strike or intercept a maneuvering target at a desired angle includes the following steps: First, the interceptor missile attitude dynamics equation can be described as: (14) in is the roll angle, is the attitude angular rate, is the three-axis moment of inertia of the interceptor missile, is the aerodynamic torque, is the rudder deviation input; Then, suppose are the desired line of sight inclination and declination, , , , , , ; In order to facilitate the design of guidance and control laws, the interceptor missile kinematic equations and attitude dynamics equations are rewritten as follows: (15) in For external interference, there are: ， ， ， ， ， ； ， Finally, under the premise of ensuring that the interceptor missile's flight state meets the safety constraints, the three-dimensional maneuvering target can be hit or intercepted at the desired angle, which can be expressed as: (16)。

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