A method for sliding mode guidance of aircraft terminal predetermined time
In the predetermined time sliding molding guide method at the end of the aircraft, a fixed time disturbance observer model in the three-dimensional coupled environment is used to design the sliding molding guide law, and the problem of uncontrollable guidance accuracy and convergence time of the aircraft intercepting maneuver target in the three-dimensional environment in the prior art is solved, and high-precision interception within the predetermined time is achieved.
Patent Information
- Application Number
- CN202410232226.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-03-01
- Publication Date
- 2025-04-08
- Estimated Expiration
- 2044-03-01
AI Technical Summary
The guidance law design of existing aircraft intercepting maneuver targets is difficult to effectively consider terminal angle constraints in a three-dimensional environment, resulting in reduced guidance accuracy and uncontrollable convergence time.
The sliding molding guide method of the last-stage aircraft is adopted. In a three-dimensional coupled environment, the fixed-time disturbance observer model and the predetermined time convergence performance are used to design the sliding molding guide law to ensure that the system converges within the predetermined time and estimate external disturbances.
It achieves high-precision intercepting maneuver targets within a predetermined time, improves guidance accuracy and system convergence performance, and can effectively estimate external disturbances.
Smart Images
Figure CN119247757B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of control or regulation of non-electrical variables, and in particular to a sliding mode guidance method for a predetermined time in the terminal stage of an aircraft. Background Art
[0002] Due to the complex characteristics of aerial targets, the design of the guidance law for an aircraft when intercepting a maneuvering target not only needs to achieve the minimum interception miss amount, but more importantly, the aircraft needs to achieve dynamic interception of the maneuvering target at the desired terminal angle according to mission requirements.
[0003] Compared with the traditional proportional guidance (PNG), the guidance law design based on sliding mode variable structure control is invariant to the external disturbance caused by the target maneuver, and there is no need to know the precise maneuver information of the target in advance. Therefore, the design based on sliding mode variable structure control has been greatly promoted. Since the time taken by the aircraft to intercept the target is short in the terminal guidance stage, the guidance law designed with asymptotic stability will be difficult to meet the guidance requirements in actual scenarios. Therefore, in the design process of the guidance law, the convergence of the system is a key indicator to measure the performance of the designed guidance law.
[0004] In order to realize the finite time guidance law, a continuous attack angle guidance law is designed based on the second-order sliding mode and finite time convergence disturbance observer. At the same time, in order to solve the singularity problem of the sliding mode guidance law, an adaptive non-singular fast terminal sliding mode guidance law is designed, which not only avoids the singularity problem but also achieves the convergence of the system in a finite time. In order to further improve the convergence performance of the guidance law, a super-twisting spiral with fixed time convergence is proposed to achieve the convergence of the vehicle-target line of sight angle to the desired angle in a fixed time. Since the aircraft intercepting the target is a three-dimensional dynamic tracking process, the above-mentioned guidance methods all decompose it into two mutually perpendicular planes when designing the guidance law, and design the guidance law separately. Since the aircraft and the target are in a three-dimensional space during the process of intercepting the maneuvering target, decomposing it into two mutually orthogonal two-dimensional models and then designing the guidance law separately will ignore the cross-coupling terms in the three-dimensional space model established by the aircraft and the target, reduce the performance of the guidance law, and thus reduce the guidance and interception accuracy when the aircraft intercepts the target, which is not conducive to actual interception applications; and although this method can improve the convergence performance of the guidance law to a certain extent at a fixed time, it also has the defect that the convergence time of the guidance law cannot be directly obtained, and fixed-time convergence must be achieved through multi-parameter design. Summary of the invention
[0005] The technical problem to be solved by the present invention is to provide a sliding mode guidance method for the terminal stage of an aircraft at a predetermined time. In a three-dimensional coupling environment, the terminal angle constraint is considered, a fixed-time disturbance observer model and the predetermined-time convergence performance are utilized, and a sliding mode guidance law for intercepting a maneuvering target at a predetermined time is designed. The system can be ensured to converge within the set predetermined time. At the same time, the fixed-time disturbance observer model can realize the estimation of the external disturbance caused by the target, and has a high hit accuracy.
[0006] The present invention is achieved through the following technical solutions:
[0007] A method for sliding mode guidance of a predetermined time in the terminal phase of an aircraft comprises the following steps:
[0008] A1: Establish a three-dimensional coupled relative motion model for the terminal guidance of the aircraft intercepting the target;
[0009] A2: Convert the guidance problem with terminal angle constraint into a guidance problem with line of sight angle constraint, so that the pitch angle of the aircraft target line of sight relative to the inertial coordinate system and the azimuth angle of the aircraft target line of sight relative to the inertial coordinate system converge to the desired angle within a predetermined time;
[0010] A3: Constructing a guidance law design target, so that the guidance law satisfies the terminal sight angle constraint under the sight line of sight of the aircraft target when the three-dimensional aircraft intercepts the maneuvering target, and simplifying the three-dimensional coupled relative motion model of step A1 to obtain a simplified three-dimensional coupled relative motion model;
[0011] A4: Define the predetermined time sliding surface, and obtain the predetermined time guidance law model according to the designed predetermined time reaching law;
[0012] A5: using a fixed-time disturbance observer model to estimate the disturbance vector of the target, and using the simplified three-dimensional coupled relative motion model obtained in step A3 to estimate the external disturbance caused by the acceleration of the target, and then solving the predetermined time guidance law according to the predetermined time guidance law model obtained in step A4;
[0013] A6: According to the predetermined time guidance law obtained in step A5, numerically solve the simplified three-dimensional coupled relative motion model in step A3 to obtain the motion state information of the aircraft;
[0014] A7: The aircraft control system controls the aircraft to track the target according to the aircraft motion state information obtained in step A6 and the guidance law of the last predetermined time obtained in step A5.
[0015] The optimized three-dimensional coupled relative motion model of the terminal guidance of the aircraft intercepting the target established in step A1 is formula (1):
[0016] (1);
[0017] in: Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, represents the speed of the target, Indicates the target's velocity relative to the pitch angle of the aircraft's target line of sight, Indicates the azimuth of the target's velocity relative to the aircraft's target line of sight, represents the speed of the aircraft, Indicates the pitch angle of the aircraft speed relative to the aircraft's target line of sight, Indicates the azimuth of the aircraft speed relative to the aircraft's target line of sight, Indicates the acceleration of the aircraft in the pitch channel, represents the acceleration of the aircraft in the yaw channel, Indicates the acceleration of the target in the pitch channel, Indicates the acceleration of the target in the yaw channel.
[0018] In the optimized step A2, the guidance problem with the terminal angle constraint is transformed into the guidance problem with the sight angle constraint according to equation (2), so that the pitch angle of the aircraft target sight line relative to the inertial coordinate system and the azimuth angle of the aircraft target sight line relative to the inertial coordinate system converge to the desired angle within a predetermined time:
[0019] (2);
[0020] in: Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, Indicates the pitch angle of the target's velocity relative to the target's sight line direction of the aircraft. Indicates the azimuth of the target's velocity relative to the target's line of sight of the aircraft. Indicates the pitch angle of the aircraft speed relative to the aircraft's target line of sight, Indicates the azimuth of the aircraft speed relative to the aircraft's target line of sight, Indicates the acceleration of the aircraft in the pitch channel, represents the acceleration of the aircraft in the yaw channel, Indicates the acceleration of the target in the pitch channel, Indicates the acceleration of the target in the yaw channel.
[0021] Optimized, in step A3, the guidance law design target is constructed according to equation (3), so that the three-dimensional aircraft intercepts the maneuvering target and satisfies the guidance of the end sight angle constraint of the aircraft target sight line:
[0022] (3);
[0023] in: Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, represents the desired pitch angle of the aircraft to intercept the target, Indicates the desired azimuth angle for the aircraft to intercept the target.
[0024] Furthermore, the simplified three-dimensional coupled relative motion model obtained in step A3 is formula (4):
[0025] (4);
[0026] in: The state variable representing the angle tracking of the line of sight coordinate system, Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, Indicates the pitch angle of the target's velocity relative to the target's sight line direction of the aircraft. Indicates the azimuth of the target's velocity relative to the target's line of sight of the aircraft. Indicates the pitch angle of the aircraft speed relative to the aircraft's target line of sight, Indicates the azimuth of the aircraft speed relative to the aircraft's target line of sight, Indicates the acceleration of the target in the pitch channel, represents the acceleration of the target in the yaw channel, It indicates the maximum maneuverability that the aircraft's actuator can provide during the guidance process. Indicates the aircraft target sight information, represents the perturbation vector of the target, Indicates aircraft information. represents the predetermined time guidance law, Indicates the acceleration of the aircraft in the pitch channel, Indicates the acceleration of the aircraft in the yaw channel.
[0027] Optimized, the predetermined time sliding surface is defined in step A4 as equation (5), and equation (6) is obtained by differentiating equation (5):
[0028] (5);
[0029] (6);
[0030] in: represents the sliding surface at the predetermined time, Represents the sliding surface The initial state value is , represents the initial time of the system, represents a positive constant for the tuning parameter, represents a control gain greater than 0, Indicates adjustable A normal number to a power, Indicates the system state used to adjust the sliding surface A normal number to a power, represents a normal number that can be artificially controlled. represents the predetermined time for achieving convergence of the sliding surface, represents the scheduled time of the sliding surface, The state variable representing the aircraft target sight angle tracking, Represents a symbolic function.
[0031] Optimally, the predetermined time approaching law designed in step A4 is formula (7):
[0032] (7);
[0033] in: represents the control gain, Indicates the scheduled time set in the reaching law.
[0034] The optimized, predetermined time guidance law model obtained in step A4 is formula (8):
[0035] (8);
[0036] in: The perturbation vector of the target Observed value of .
[0037] The optimized fixed-time disturbance observer model in step A5 is formula (9):
[0038] (9);
[0039] in: Express The estimated value of To control the gain, represents adjustable gain, is an adjustable parameter, is a controllable parameter, is the gain to be adjusted.
[0040] Further, obtaining the motion state information of the aircraft and the target in step A5 includes the following steps:
[0041] A51: Calculate the target disturbance vector according to formula (9) Observed value ;
[0042] A52: The perturbation vector of the calculated target Observed value Substitute into the guidance law model of the predetermined time (8) to solve the guidance law of the predetermined time , and the guidance law for the predetermined time It is limited according to formula (10);
[0043] (10);
[0044] in: It indicates the maneuvering force provided by the aircraft actuator during the guidance process. represents the saturation function of the maneuvering force provided by the aircraft actuator during the guidance process;
[0045] A53: The solved predetermined time guidance law Substitute it into equation (1) and solve it, and the motion state information of the aircraft is obtained as equation (11):
[0046] (11);
[0047] in: express The rate of change of the aircraft's motion state at any moment, express The rate of change of the aircraft's motion state at any moment, express The rate of change of the aircraft's motion state at any moment, Indicates the rate of change of the aircraft motion state at the terminal point of the time period, represents the simulation step length, express The independent variable at time, express The value of the aircraft's motion state at any moment, express The numerical value of the aircraft's motion state at the moment.
[0048] Beneficial effects of the invention:
[0049] The present invention provides a sliding mode guidance method for a predetermined time in the terminal stage of an aircraft. In a three-dimensional coupling environment, the terminal angle constraint is considered, a fixed-time disturbance observer model and the predetermined-time convergence performance are utilized, and a sliding mode guidance law for intercepting a maneuvering target at a predetermined time is designed. The method can ensure that the system converges within the set predetermined time. Meanwhile, the fixed-time disturbance observer model can realize the estimation of the external disturbance caused by the target, and has a high hit accuracy. BRIEF DESCRIPTION OF THE DRAWINGS
[0050] Figure 1 It is a schematic diagram of the process of the present invention.
[0051] Figure 2 It is a schematic diagram of the three-dimensional relative motion model of the aircraft-target of the present invention.
[0052] Figure 3 The aircraft and the target of the present invention are in the inertial coordinate system Schematic diagram of the motion trajectory.
[0053] Figure 4 The figure is a schematic diagram of a curve showing a change in the distance between the aircraft and the target over time according to the present invention.
[0054] Figure 5 is the pitch angle of the target sight line of the aircraft of the present invention relative to the inertial coordinate system Schematic diagram of the curve of change over time.
[0055] Figure 6 is the azimuth of the target sight line of the aircraft of the present invention relative to the inertial coordinate system Schematic diagram of the curve of change over time.
[0056] Figure 7 is the acceleration of the aircraft of the present invention in the pitch channel Schematic diagram of the curve of change over time.
[0057] Figure 8 is the acceleration of the aircraft of the present invention in the yaw channel Schematic diagram of the curve of change over time. DETAILED DESCRIPTION
[0058] The present invention is a method for sliding mode guidance of an aircraft at the terminal stage with a predetermined time, and the specific flow chart is as follows: Figure 1 As shown, it includes the following steps:
[0059] A1: Establish a three-dimensional coupled relative motion model for the terminal guidance of the aircraft intercepting the target;
[0060] Specifically, the established three-dimensional coupled relative motion model for the terminal guidance of the aircraft intercepting the target can be expressed as formula (1):
[0061] (1);
[0062] in: Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, represents the speed of the target, Indicates the target's velocity relative to the pitch angle of the aircraft's target line of sight, Indicates the azimuth of the target's velocity relative to the aircraft's target line of sight, represents the speed of the aircraft, Indicates the pitch angle of the aircraft speed relative to the aircraft's target line of sight, Indicates the azimuth of the aircraft speed relative to the aircraft's target line of sight, Indicates the acceleration of the aircraft in the pitch channel, represents the acceleration of the aircraft in the yaw channel, Indicates the acceleration of the target in the pitch channel, It represents the acceleration of the target in the yaw channel. Since the terminal guidance phase of the aircraft takes a short time, it can be assumed that the speeds of the aircraft and the target are constant during the terminal interception phase.
[0063] The three-dimensional coupled relative motion model of the terminal guidance of the aircraft intercepting the target can ensure that the terminal predetermined time sliding mode guidance method of the aircraft provided by the present invention is carried out in a three-dimensional coupling environment, and will not ignore the cross-coupling items in the three-dimensional space model established between the aircraft and the target, thereby providing a prerequisite for ensuring the guidance and interception accuracy when the aircraft intercepts the target.
[0064] A2: Convert the guidance problem with terminal angle constraint into a guidance problem with line of sight angle constraint, so that the pitch angle of the aircraft target line of sight relative to the inertial coordinate system and the azimuth angle of the aircraft target line of sight relative to the inertial coordinate system converge to the desired angle within a predetermined time;
[0065] Specifically, step A2 can transform the guidance problem with the terminal angle constraint into the guidance problem with the line of sight angle constraint according to formula (2), so that the pitch angle of the aircraft target line of sight relative to the inertial coordinate system and the azimuth angle of the aircraft target line of sight relative to the inertial coordinate system converge to the desired angle within a predetermined time, which can further provide a strong guarantee for the guidance and interception accuracy when the aircraft intercepts the target.
[0066] (2);
[0067] in: Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, Indicates the pitch angle of the target's velocity relative to the target's sight line direction of the aircraft. Indicates the azimuth of the target's velocity relative to the target's line of sight of the aircraft. Indicates the pitch angle of the aircraft speed relative to the aircraft's target line of sight, Indicates the azimuth of the aircraft speed relative to the aircraft's target line of sight, Indicates the acceleration of the aircraft in the pitch channel, represents the acceleration of the aircraft in the yaw channel, Indicates the acceleration of the target in the pitch channel, Indicates the acceleration of the target in the yaw channel.
[0068] A3: Constructing a guidance law design target, so that the guidance law satisfies the terminal sight angle constraint under the sight line of sight of the aircraft target when the three-dimensional aircraft intercepts the maneuvering target, and simplifying the three-dimensional coupled relative motion model of step A1 to obtain a simplified three-dimensional coupled relative motion model;
[0069] Specifically, in step A3, the guidance law design target can be constructed according to formula (3), so that the three-dimensional aircraft intercepts the maneuvering target and satisfies the guidance of the line of sight angle constraint at the end of the aircraft target line of sight:
[0070] (3);
[0071] in: Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, represents the desired pitch angle of the aircraft to intercept the target, It represents the expected azimuth angle of the aircraft to intercept the target, and defines the state variable of the line of sight coordinate system angle tracking as , , is the pitch angle tracking error of the aircraft target line of sight, is the aircraft target line of sight azimuth tracking error.
[0072] Further, combined and , and By differentiating, the simplified three-dimensional coupled relative motion model can be obtained as formula (4):
[0073] (4);
[0074] in: The state variable representing the angle tracking of the line of sight coordinate system, Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, Indicates the pitch angle of the target's velocity relative to the target's sight line direction of the aircraft. Indicates the azimuth of the target's velocity relative to the target's line of sight of the aircraft. Indicates the pitch angle of the aircraft speed relative to the aircraft's target line of sight, Indicates the azimuth of the aircraft speed relative to the aircraft's target line of sight, Indicates the acceleration of the target in the pitch channel, represents the acceleration of the target in the yaw channel, It indicates the maximum maneuverability that the aircraft's actuator can provide during the guidance process. Indicates the aircraft target sight information, represents the perturbation vector of the target, Indicates aircraft information. represents the predetermined time guidance law, Indicates the acceleration of the aircraft in the pitch channel, Indicates the acceleration of the aircraft in the yaw channel.
[0075] A4: Define a predetermined time sliding surface, and obtain a predetermined time guidance law model according to the designed predetermined time reaching law; specifically, the predetermined time sliding surface defined in step A4 can be formula (5), and formula (6) can be obtained by differentiating formula (5):
[0076] (5);
[0077] (6);
[0078] in: represents the sliding surface at the predetermined time, Represents the sliding surface The initial state value is , represents the initial time of the system, represents a positive constant for the tuning parameter, represents a control gain greater than 0, Indicates adjustable A normal number to a power, Indicates the system state used to adjust the sliding surface A normal number to a power, Represents a normal number that can be artificially controlled and must satisfy , , represents the predetermined time for achieving convergence of the sliding surface, , , represents the scheduled time of the sliding surface, The state variable representing the aircraft target sight angle tracking, represents the gamma function, Represents a symbolic function.
[0079] Specifically, the predetermined time approaching law designed in step A4 can be expressed as formula (7):
[0080] (7);
[0081] in: represents the control gain, Indicates the scheduled time set in the reaching law.
[0082] Specifically, the predetermined time guidance law model obtained in step A4 is formula (8):
[0083] (8);
[0084] in: The perturbation vector of the target Observed value of .
[0085] A5: using a fixed-time disturbance observer model to estimate the disturbance vector of the target, and using the simplified three-dimensional coupled relative motion model obtained in step A3 to estimate the external disturbance caused by the acceleration of the target, and then solving the predetermined time guidance law according to the predetermined time guidance law model obtained in step A4;
[0086] Specifically, assuming and is bounded, continuous and differentiable. and As an external disturbance, set , The perturbation vector representing the target The size of is known to have an upper bound.
[0087] Then the fixed time disturbance observer model in step A5 is formula (9):
[0088] (9);
[0089] in: Express The estimated value of To control the gain, represents adjustable gain, and Need to meet , is an adjustable parameter and must satisfy , is a controllable parameter and must satisfy , is the gain to be adjusted and must satisfy .
[0090] Further, obtaining the motion state information of the aircraft and the target in step A5 includes the following steps:
[0091] A51: Calculate the target disturbance vector according to formula (9) Observed value ;
[0092] A52: The perturbation vector of the calculated target Observed value Substitute into the guidance law model of the predetermined time (8) to solve the guidance law of the predetermined time Considering the problem of limited input of the aircraft controller in the terminal guidance phase, the guidance law of the predetermined time can be It is limited according to formula (10);
[0093] (10);
[0094] in: It indicates the maneuvering force provided by the aircraft actuator during the guidance process. represents the saturation function of the maneuvering force provided by the aircraft actuator during the guidance process;
[0095] A53: The solved predetermined time guidance law Substitute it into equation (1) and solve it, and the motion state information of the aircraft is obtained as equation (11):
[0096] (11);
[0097] in: express The rate of change of the aircraft's motion state at any moment, express The rate of change of the aircraft's motion state at any moment, express The rate of change of the aircraft's motion state at any moment, Indicates the rate of change of the aircraft motion state at the terminal point of the time period, represents the simulation step length, express The independent variable at time, express The value of the aircraft's motion state at any moment, express The numerical value of the aircraft's motion state at the moment.
[0098] A6: According to the predetermined time guidance law obtained in step A5, numerically solve the simplified three-dimensional coupled relative motion model in step A3 to obtain the motion state information of the aircraft;
[0099] A7: The aircraft control system controls the aircraft to track the target according to the aircraft motion state information obtained in step A6 and the guidance law of the last predetermined time obtained in step A5.
[0100] The specific embodiments are as follows:
[0101] Assume that the initial position of the aircraft is (-18600, 1500, 0) and the initial speed of the aircraft is 850 , the initial for , the aircraft is initially for The maximum acceleration that the aircraft can provide is 500 , assuming the target's initial position is (0, 0, 9000) and the target's initial velocity is 510 , the acceleration of the target is , , the initial target for , the initial target for , the desired pitch angle of the aircraft to intercept the target for , the desired azimuth of the aircraft to intercept the target ;
[0102] The parameters in the predetermined time guidance law model (8) are set as , , , , , , the predetermined time sliding surface in formula (5) , ;
[0103] The parameters in the fixed-time disturbance observer model (9) are set as , , , , .
[0104] Figure 2 is a schematic diagram of the three-dimensional relative motion model of the aircraft and the target, where represents the inertial reference coordinate system, is the aircraft velocity coordinate system, is the target velocity coordinate system, Indicates the distance between the aircraft and the target.
[0105] Figure 3 The aircraft and the target are in the inertial coordinate system Schematic diagram of the motion trajectory, from Figure 3 It can be seen that the designed predetermined time guidance law has good performance and can ensure that the aircraft can intercept the target under the initial conditions.
[0106] Figure 4 Figure 1 is a schematic diagram of the curve of the distance between the aircraft and the target changing with time. It can be seen that the time it takes for the aircraft to intercept the target is approximately 15.77 seconds.
[0107] Figure 5 is the pitch angle of the aircraft target line of sight relative to the inertial coordinate system Schematic diagram of the curve of change over time. From the figure, we can see At the preset time The expected sight value has been reached before .
[0108] Figure 6 is the azimuth of the aircraft target line of sight relative to the inertial coordinate system The schematic diagram of the curve of change over time shows that Achieve the expected value within the scheduled time Intercept the target.
[0109] Figure 7 is the acceleration of the aircraft in the pitch channel Schematic diagram of the curve of change over time, Figure 8 is the acceleration of the aircraft in the yaw channel Schematic diagram of the change curve over time, from Figure 7 and Figure 8 It can be seen that the acceleration of the aircraft in the pitch channel and the yaw channel can be stabilized within the predetermined time.
[0110] In summary, the present invention proposes a sliding mode guidance method for the terminal stage of an aircraft at a predetermined time. In a three-dimensional coupling environment, the terminal angle constraint is considered, and a fixed-time disturbance observer model and a predetermined-time convergence performance are utilized to design a sliding mode guidance law for intercepting a maneuvering target at a predetermined time. This method can ensure that the system converges within the set predetermined time. At the same time, the fixed-time disturbance observer model can realize the estimation of the external disturbance caused by the target, and has a higher hit accuracy.
[0111] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.
Claims
1. A method for sliding mode guidance of a predetermined time in the terminal phase of an aircraft, characterized in that: The steps include: A1: Establish a three-dimensional coupled relative motion model for the terminal guidance of the aircraft intercepting the target; A2: Convert the guidance problem with terminal angle constraint into a guidance problem with line of sight angle constraint, so that the pitch angle of the aircraft target line of sight relative to the inertial coordinate system and the azimuth angle of the aircraft target line of sight relative to the inertial coordinate system converge to the desired angle within a predetermined time; A3: Constructing a guidance law design target, so that the guidance law satisfies the terminal sight angle constraint under the sight line of sight of the aircraft target when the three-dimensional aircraft intercepts the maneuvering target, and simplifying the three-dimensional coupled relative motion model of step A1 to obtain a simplified three-dimensional coupled relative motion model; A4: Define the predetermined time sliding surface, and obtain the predetermined time guidance law model according to the designed predetermined time reaching law; Define the predetermined time sliding surface as equation (5), and differentiate equation (5) to obtain equation (6): （5）； （6）； in: represents the sliding surface at the predetermined time, Represents the sliding surface The initial state value is , represents the initial time of the system, represents a positive constant for the tuning parameter, represents a control gain greater than 0, Indicates adjustable A normal number to a power, Indicates the system state used to adjust the sliding surface A normal number to a power, represents a normal number that can be artificially controlled. represents the predetermined time for achieving convergence of the sliding surface, represents the scheduled time of the sliding surface, The state variable representing the angle tracking of the line of sight coordinate system, represents a symbolic function; The design schedule reaching law is as follows: （7）； in: represents the control gain, It represents the predetermined time set in the approaching law; The obtained predetermined time guidance law model is formula (8): （8）； in: The perturbation vector of the target The observed value of Indicates the aircraft target sight information, Indicates aircraft information; A5: using a fixed-time disturbance observer model to estimate the disturbance vector of the target, and using the simplified three-dimensional coupled relative motion model obtained in step A3 to estimate the external disturbance caused by the acceleration of the target, and then solving the predetermined time guidance law according to the predetermined time guidance law model obtained in step A4; A6: According to the predetermined time guidance law obtained in step A5, numerically solve the simplified three-dimensional coupled relative motion model in step A3 to obtain the motion state information of the aircraft; A7: The aircraft control system controls the aircraft to track the target according to the aircraft motion state information obtained in step A6 and the guidance law of the last predetermined time obtained in step A5.
2. A method for sliding mode guidance of a predetermined time in the terminal stage of an aircraft according to claim 1, characterized in that: The three-dimensional coupled relative motion model of the terminal guidance of the aircraft intercepting the target established in step A1 is formula (1): （1）； in: Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, represents the speed of the target, Indicates the pitch angle of the target's velocity relative to the aircraft's target line of sight, Indicates the azimuth of the target's velocity relative to the aircraft's target line of sight, represents the speed of the aircraft, Indicates the pitch angle of the aircraft speed relative to the aircraft's target line of sight, Indicates the azimuth of the aircraft's velocity relative to the aircraft's target line of sight, Indicates the acceleration of the aircraft in the pitch channel, represents the acceleration of the aircraft in the yaw channel, Indicates the acceleration of the target in the pitch channel, Indicates the acceleration of the target in the yaw channel.
3. The method for sliding mode guidance of a predetermined time at the terminal stage of an aircraft according to claim 1, characterized in that: Step A2 converts the guidance problem with terminal angle constraint into the guidance problem with sight angle constraint according to equation (2), so that the pitch angle of the aircraft target sight line relative to the inertial coordinate system and the azimuth angle of the aircraft target sight line relative to the inertial coordinate system converge to the desired angle within a predetermined time: （2）； in: Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, Indicates the pitch angle of the target's velocity relative to the target's sight line direction of the aircraft. Indicates the azimuth of the target's velocity relative to the target's line of sight of the aircraft. Indicates the pitch angle of the aircraft speed relative to the aircraft's target line of sight, Indicates the azimuth of the aircraft's velocity relative to the aircraft's target line of sight, Indicates the acceleration of the aircraft in the pitch channel, represents the acceleration of the aircraft in the yaw channel, Indicates the acceleration of the target in the pitch channel, Indicates the acceleration of the target in the yaw channel.
4. The method for sliding mode guidance of a terminal predetermined time of an aircraft according to claim 1, characterized in that: In step A3, the guidance law design target is constructed according to formula (3), so that the guidance of the three-dimensional aircraft intercepting the maneuvering target satisfies the constraint of the end line of sight angle of the aircraft target: （3）； in: Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, represents the desired pitch angle of the aircraft to intercept the target, Indicates the desired azimuth angle for the aircraft to intercept the target.
5. The method for sliding mode guidance of a predetermined time at the terminal stage of an aircraft according to claim 1, characterized in that: The simplified three-dimensional coupled relative motion model obtained in step A3 is formula (4): （4）； in: The state variable representing the angle tracking of the line of sight coordinate system, Indicates the distance between the aircraft and the target. It represents the pitch angle of the aircraft target line of sight relative to the inertial coordinate system. Indicates the azimuth of the aircraft target line of sight relative to the inertial coordinate system, Indicates the pitch angle of the target's velocity relative to the target's sight line direction of the aircraft. Indicates the azimuth of the target's velocity relative to the target's line of sight of the aircraft. Indicates the pitch angle of the aircraft speed relative to the aircraft's target line of sight, Indicates the azimuth of the aircraft's velocity relative to the aircraft's target line of sight, Indicates the acceleration of the target in the pitch channel, represents the acceleration of the target in the yaw channel, It indicates the maximum maneuverability that the aircraft's actuator can provide during the guidance process. Indicates the aircraft target sight information, represents the perturbation vector of the target, Indicates aircraft information. represents the predetermined time guidance law, Indicates the acceleration of the aircraft in the pitch channel, Indicates the acceleration of the aircraft in the yaw channel.
6. The method for sliding mode guidance of a predetermined time at the terminal stage of an aircraft according to claim 1, characterized in that: The fixed-time disturbance observer model in step A5 is formula (9): （9）； in: Express The estimated value of To control the gain, represents adjustable gain, is an adjustable parameter, is a controllable parameter, is the gain to be adjusted.
7. A method for sliding mode guidance of a terminal predetermined time of an aircraft according to claim 6, characterized in that: Acquiring the motion status information of the aircraft and the target in step A5 includes the following steps: A51: Calculate the target disturbance vector according to formula (9) Observed value ; A52: The perturbation vector of the calculated target Observed value Substitute into the guidance law model of the predetermined time (8) to solve the guidance law of the predetermined time , and the guidance law for the predetermined time It is limited according to formula (10); （10）； in: It indicates the maneuvering force provided by the aircraft actuator during the guidance process. represents the saturation function of the maneuvering force provided by the aircraft actuator during the guidance process; A53: The solved predetermined time guidance law Substitute it into equation (1) and solve it, and the motion state information of the aircraft is obtained as equation (11): （11）； in: express The rate of change of the aircraft's motion state at any moment, express The rate of change of the aircraft's motion state at any moment, express The rate of change of the aircraft's motion state at any moment, Indicates the rate of change of the motion state of the aircraft at the terminal point of the time period, represents the simulation step length, express The independent variable at time, express The value of the aircraft's motion state at any moment, express The numerical value of the aircraft's motion state at the moment.