A guidance method with field of view angle and impact angle constraints for variable speed aircraft

Abstract

The application discloses a guidance method with field of view angle and impact angle constraints suitable for variable-speed aircrafts and belongs to the technical field of precise guidance of aircrafts. The application realizes the method as follows: the end impact angle γ f of the aircraft under the proportional guidance is predicted, the difference δ between the expected end impact angle γ d and the end impact angle prediction value γ f is defined as the impact angle control error, and when the impact angle control error δ converges to zero, γ f γ d . The expected change rate of the impact angle control error δ is designed to ensure that δ converges to zero before hitting the target and to meet the field of view angle limitation of the guidance head; the feedback structure of the biased proportional guidance is adopted, the biased item is designed, the impact angle control error δ of the aircraft follows the designed expected change rate, and then the aircraft meets the impact angle and field of view angle constraints while precisely hitting the target, thereby realizing the guidance of the aircraft with the field of view angle and impact angle constraints. In the case that the speed of the aircraft is time-varying, the application can still guarantee the impact angle control performance and meet the field of view angle constraints.

Description

Technical Field

[0001] This invention relates to a guidance method with landing angle constraints, and more particularly to a guidance method with field of view and landing angle constraints applicable to variable speed aircraft, belonging to the field of precision guidance technology for aircraft. Background Technology

[0002] Modern battlefield operations are becoming increasingly complex. In certain scenarios, such as attacking armored vehicles, underground bunkers, and surface ships, aircraft need to attack targets at specific angles to enhance their destructive effectiveness. Angle-constrained guidance methods can improve combat effectiveness without significantly increasing aircraft costs, making them of great research significance.

[0003] Some research has been conducted on guidance methods with angle-of-arrival constraints. Most existing research can only guarantee the asymptotic convergence of the angle-of-arrival control error. However, the terminal guidance time of an aircraft is often short, and asymptotic convergence cannot guarantee that the angle-of-arrival control error will converge before the aircraft hits the target, thus affecting the terminal angle-of-arrival control performance. Designing a guidance method with angle-of-arrival constraints that ensures the angle-of-arrival control error converges before target impact can effectively improve the aircraft's angle-of-arrival control performance. During guidance, the aircraft relies on a guidance and detection device to obtain target information. Therefore, it is necessary to consider the field-of-view limitation of the seeker and ensure that the target remains within the seeker's field of view throughout the guidance process. Furthermore, due to factors such as gravity and drag, the aircraft's velocity is often time-varying. When designing a guidance method with angle-of-arrival constraints, it is necessary to ensure that the angle-of-arrival control performance is unaffected by changes in the aircraft's velocity.

[0004] Considering the above factors, it is essential to design a guidance method with a landing angle constraint that can ensure the convergence of landing angle control error for aircraft with varying flight speeds and limited field of view of the seeker. Summary of the Invention

[0005] To address the problem that existing angle-of-view constraint guidance methods struggle to ensure the convergence of angle-of-view control errors and simultaneously satisfy field-of-view constraints, the main objective of this invention is to provide a guidance method with both field-of-view and angle-of-view constraints suitable for variable-speed aircraft. This method can adapt to the angle-of-view control requirements under varying aircraft speeds and ensure that the angle-of-view control error converges before hitting the target while simultaneously satisfying the seeker's field-of-view constraints, enabling the aircraft to accurately strike the target at a predetermined angle.

[0006] The objective of this invention is achieved through the following technical solution.

[0007] This invention discloses a guidance method with field-of-view and angle-of-arrival constraints suitable for variable-speed aircraft, wherein the terminal angle γ of the aircraft is determined by proportional guidance. f To make a prediction, the expected terminal landing angle γ is...d and the predicted end angle γ f The difference δ is defined as the landing angle control error; when the landing angle control error δ converges to zero, γ f =γ d This means achieving control over the aircraft's landing angle. A desired rate of change is designed for the landing angle control error δ. To ensure that δ converges to zero before hitting the target, while simultaneously satisfying the seeker's field of view limitations, a feedback structure using offset proportional guidance is employed. By designing the offset term, the aircraft's angle of impact control error δ follows the designed desired rate of change. This ensures that the aircraft accurately hits the target while meeting the constraints of the angle of impact and field of view, achieving guidance with both angle of impact and field of view constraints. Meeting the angle of impact constraint allows for precise strikes at a predetermined angle, improving the aircraft's damage effectiveness. Meeting the field of view constraint ensures that the target remains within the seeker's field of view during guidance, preventing target loss and guidance failure. Even with varying aircraft speeds, this invention maintains accurate angle of impact control and meets the field of view constraints, making it more suitable for practical engineering needs.

[0008] This invention discloses a guidance method with field of view and angle of impact constraints suitable for variable-speed aircraft, comprising the following steps:

[0009] Step 1: Establish the relative motion equations between the aircraft and the target, and predict the terminal landing angle of the aircraft under proportional guidance, so as to facilitate the construction of a guidance method with field of view and landing angle constraints in Step 3.

[0010] The equation of relative motion between the aircraft and the target is expressed as follows:

[0011]

[0012]

[0013]

[0014]

[0015] Where r represents the relative distance between the aircraft and the target, σ represents the line-of-sight angle, γ represents the trajectory tilt angle of the aircraft, η represents the field of view angle of the aircraft, and V M a represents the speed of the aircraft. M This indicates the normal acceleration command for the aircraft.

[0016] The normal acceleration command for proportional guidance is:

[0017]

[0018] Where N represents the navigation ratio, which is a positive constant.

[0019] Under proportional guidance, the terminal angle of the aircraft upon hitting the target is...

[0020]

[0021] Based on equation (6), the terminal landing angle of the aircraft under proportional guidance is predicted, which facilitates the construction of a guidance method with field of view and landing angle constraints in step three.

[0022] Step 2: Determine the desired end angle γ d And the predicted end landing angle γ obtained in step one f The difference δ is defined as the landing angle control error. The expected rate of change is designed for the landing angle control error δ. The feedback structure employing the bias proportional guidance method, through the design of the bias term, ensures that the aircraft's landing angle control error δ follows the designed desired rate of change. To ensure that the angle of impact control error δ converges before the aircraft hits the target, the angle of impact control is achieved to improve the aircraft's damage effectiveness against the target. At the same time, the aircraft meets the field of view constraint to avoid target loss and guidance failure.

[0023] Step 2.1: Determine the expected rate of change of the landing angle control error δ

[0024] The landing angle control error δ represents the desired landing angle γ at the end of the landing. d and the predicted end angle γ f The difference. When the control δ converges to zero, γ d and γ f Equal values ​​allow for control of the aircraft's landing angle. From the definition of the landing angle control error δ, we obtain...

[0025] δ=γ d -γ f (7)

[0026] Because the terminal guidance process is relatively short, it is crucial to ensure that the angle of impact control error δ converges to zero before the aircraft hits the target. Simultaneously, the aircraft needs to meet the seeker's field of view limitations during guidance to avoid target loss. To achieve these objectives, the expected rate of change of the angle of impact control error δ is constructed as follows:

[0027]

[0028] Among them, sig m ()=sign()|| m `sign()` represents the sign function, where α > 0, β > 0, 0 < m < 1, n > 1, and t goIndicates the remaining flight time of the aircraft. η represents the field of view of the aircraft, η max Let represent the maximum field of view of the aircraft. f(x) is an adjustment function used to adjust the aircraft's field of view to ensure that the field of view constraint is met; its form is f(x) = 1 - |x| d (d>0), defined on [-1,1] and satisfying f(-1)=f(1)=0, f(0)=1.

[0029] Step 2.2: Determine the bias term of the guidance method so that the landing angle control error δ follows the expected rate of change in equation (8), thereby achieving field-of-view and landing angle constrained guidance for the aircraft.

[0030] Using a bias-proportional guidance feedback structure, the following guidance method with field-of-view and landing angle constraints is designed.

[0031] a M =a P +a I (9)

[0032] Among them, a P This indicates a proportional guidance term used to ensure zero miss distance; a I The term represents the bias term, which is used to ensure that δ satisfies the expected rate of change in equation (8), thereby satisfying the field of view and landing angle constraints.

[0033] From equations (3), (6), and (7), we get

[0034]

[0035] Substituting equations (2), (5), and (9) into equation (10) yields

[0036]

[0037] According to equations (8) and (11), the bias term is:

[0038]

[0039] Combining equations (5), (9), and (12), we obtain the normal acceleration command with landing angle and field of view constraints, so that the landing angle control error δ of the aircraft satisfies the expected rate of change in equation (8), thereby ensuring that the landing angle control error δ converges to zero before the end of the guidance process, and at the same time, the aircraft satisfies the seeker's field of view constraints throughout the entire guidance process.

[0040] Step 3: Based on the characteristics of the closed-loop guidance model, determine the method for estimating the remaining flight time of the aircraft, and construct a guidance method with line-of-sight angle and impact angle constraints. This ensures that the constructed guidance method can ensure that the trajectory shape of the aircraft is independent of its speed when used to strike stationary targets, thereby guaranteeing the applicability of the guidance method to variable-speed aircraft.

[0041] The shape of the aircraft's trajectory is determined by the relative distance r and the line-of-sight angle σ. Let s represent the arc length along the aircraft's trajectory, then we have...

[0042]

[0043] The method for calculating the remaining flight time of an aircraft is as follows:

[0044]

[0045] Differentiate the relative distance r, line-of-sight angle σ, field of view angle η, and landing angle error δ with respect to the trajectory arc length s, and substitute equations (5), (9), and (12) into the equations to obtain the following results.

[0046]

[0047]

[0048]

[0049]

[0050] The right-hand side of equations (15)-(18) does not include the speed magnitude V of the aircraft. M Therefore, the changes in the variables relative distance r, line-of-sight angle σ, field of view angle η, and landing angle error δ will not be affected by the aircraft's speed V. M Therefore, it is known that under the guidance method described above, the trajectory shape of the aircraft will not be affected by the aircraft speed V. M The effect of this principle, when applied to variable-speed aircraft, ensures that the angle of fall control performance is unaffected by changes in speed.

[0051] Step 4: Provide real-time feedback on the current status of the aircraft, and deduce the normal acceleration command for the next moment based on the guidance method constructed in Step 3, until the aircraft hits the target at the desired angle of impact, thus completing the guidance and control of the target and the precision strike.

[0052] Beneficial effects:

[0053] (1) The present invention discloses a guidance method with field of view and angle of impact constraints for variable speed aircraft. It adopts a feedback structure of bias proportional guidance. By designing the bias term, the angle of impact control error of the aircraft follows the designed expected rate of change, thereby ensuring that the aircraft meets the angle of impact and field of view constraints while accurately hitting the target. This realizes guidance of the aircraft with field of view and angle of impact constraints, improves the damage effectiveness of the aircraft to the target, and avoids the loss of the target leading to guidance failure.

[0054] (2) The present invention discloses a guidance method with field of view and landing angle constraints applicable to variable speed aircraft. Based on the finite time control theory, the expected rate of change of landing angle control error δ is designed to ensure that the landing angle error converges to zero before the end of the guidance process, thereby improving guidance accuracy and efficiency.

[0055] (3) The present invention discloses a guidance method with field of view and angle of impact constraints applicable to variable speed aircraft. By analyzing the characteristics of the closed-loop guidance model, the remaining flight time estimation method of the aircraft is determined. When striking a stationary target, the guidance method disclosed in the present invention can ensure that the trajectory shape of the aircraft is independent of its speed, thereby ensuring that the angle of impact control performance and field of view constraints are not affected by changes in the speed of flight, thus ensuring the applicability of the guidance method to variable speed aircraft, which is more in line with the actual engineering needs of precision guidance and efficient strike. Attached Figure Description

[0056] Figure 1 This is a flowchart of a guidance method with field of view and landing angle constraints applicable to variable speed aircraft according to the present invention;

[0057] Figure 2 This is a schematic diagram illustrating the relative motion relationship between the aircraft and the target upon which this invention is based;

[0058] Figure 3 This is a flight trajectory diagram of an aircraft according to an embodiment of the present invention;

[0059] Figure 4 This is a graph showing the variation of the aircraft's landing angle error according to an embodiment of the present invention;

[0060] Figure 5 This is a diagram showing the change in the landing angle of the aircraft according to an embodiment of the present invention;

[0061] Figure 6 This is a diagram showing the change in the field of view of the aircraft according to an embodiment of the present invention;

[0062] Figure 7 This is a diagram showing the variation of the aircraft guidance commands according to an embodiment of the present invention;

[0063] Figure 8 This is a graph showing the change in the aircraft speed according to an embodiment of the present invention. Detailed Implementation

[0064] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0065] To verify the effectiveness of the proposed guidance method with field-of-view and landing angle constraints, the following embodiments will simultaneously consider numerical simulations of a real aircraft model and a constant-speed aircraft model. The velocity change of the aircraft can be described as...

[0066]

[0067] Where, m c Let g represent the mass of the aircraft, and g represent the acceleration due to gravity, where g = 9.81 m / s². 2 T m T represents the magnitude of the thrust of the aircraft and has the following condition when 0 ≤ t ≤ 4s. m =2000N; when t>4s, T m =0N. D represents the drag experienced by the aircraft and has

[0068]

[0069] Where ρ represents air density, C D Let N represent the drag coefficient, and S represent the reference area. Simulation parameters are set as follows: N = 3, α = β = 2, m = 0.8, n = 1.2, d = 6, m c =90kg, S=0.2m 2 The initial position of the target is (x... T ,y T ,z T The initial conditions of the spacecraft are (x) = (0,0)m. T ,y T ,z T )=(5000,0)m. Three sets of desired landing angles are set as follows: 1)γ d = -30°; 2) γ d =-90°; 3)γ d = -120°. The maximum field of view of the aircraft is set to σ. max =50°. The speeds of aircraft 1, 2, and 3 change according to the law of equation (19), and the initial speed V M,0 =250m / s. The speeds of aircraft 4, 5, and 6 are set to constant values ​​and V... M =250m / s. For each set of desired landing angles, two aircraft are specified: aircraft 1 and 4 are considered under landing angle condition 1), aircraft 2 and 5 are applied under landing angle condition 2), and aircraft 3 and 6 are applied under landing angle condition 3.

[0070] like Figure 1 As shown in the figure, this embodiment discloses a guidance method with field of view and landing angle constraints suitable for variable speed aircraft. The specific implementation steps are as follows:

[0071] Step 1: The relative motion between the aircraft and the target, such as... Figure 2As shown, M and T represent the aircraft and target, respectively. During guidance, based on the current states of the aircraft and target, such as their positions, the aircraft's velocity, and the trajectory angle, the predicted terminal angle of the aircraft is calculated using the following formula under proportional guidance.

[0072]

[0073] Step 2: Determine the desired landing angle γ based on task requirements. d In this embodiment, three sets of desired landing angles are set as follows: 1) γ d = -30°; 2) γ d =-90°; 3)γ d = -120°. The current landing angle control error δ is calculated using the following formula:

[0074] δ=γ d -γ f

[0075] Based on the current state of the aircraft and the target, the proposed normal acceleration command with field of view and landing angle constraints is calculated using the following formula:

[0076] a M =a P +a I

[0077]

[0078]

[0079] The remaining flight time is

[0080] By providing real-time feedback on the aircraft's current flight status, and using the current status as a starting condition, the acceleration command for the next moment is derived to adjust the aircraft's flight trajectory, ultimately guiding the aircraft to hit the target at the desired angle of impact.

[0081] Guidance results as follows Figures 3 to 8 As shown. The trajectories of aircraft 1 to 6 are as follows. Figure 3 As shown. By Figure 3 As can be seen, all aircraft successfully hit their targets. Furthermore, for each angle of impact, the shape of the trajectory of the aircraft with the time-varying velocity is the same as that of the aircraft with the constant velocity. This verifies that under the guidance method disclosed in this invention, the trajectory shape of the aircraft is unaffected by changes in its velocity, ensuring angle of impact control performance when applied to variable-speed aircraft. Figure 4 and Figure 5 As can be seen, before finally hitting the target, the landing angle error converged to zero in all three landing angle constraint cases, and the required landing angle was achieved. Figure 6 As shown, under these three landing angle constraints, no aircraft's field of view exceeded the maximum field of view during the entire guidance process. These results verify the effectiveness of the guidance method with field of view and landing angle constraints proposed in this invention.

[0082] The above implementation process and exemplary examples have provided a detailed description of the present invention; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and implementation methods of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention.

Claims

1. A guidance method for variable-speed aircraft with field-of-view and angle-of-fall constraints, characterized in that: Includes the following steps, Step 1: Establish the relative motion equations between the aircraft and the target, and predict the terminal landing angle of the aircraft under the proportional guidance method, so as to facilitate the construction of a guidance method with field of view and landing angle constraints in Step 3. Step 2: Determine the desired end angle. And the predicted end landing angle obtained in step one The difference Defined as landing angle control error; is the landing angle control error Design expected rate of change The feedback structure employing the bias proportional guidance method, through the design of bias terms, reduces the aircraft's landing angle control error. Follow the designed expected rate of change To ensure the accuracy of the landing angle control error The convergence is completed before the aircraft hits the target, and the angle of impact is controlled to improve the aircraft's damage effectiveness against the target. At the same time, the aircraft meets the field of view constraint to avoid target loss and guidance failure. Step 3: Based on the characteristics of the closed-loop guidance model, determine the method for estimating the remaining flight time of the aircraft, and construct a guidance method with line-of-sight angle and impact angle constraints. This ensures that the constructed guidance method can ensure that the trajectory shape of the aircraft is independent of its speed when used to strike stationary targets, thereby guaranteeing the applicability of the guidance method to variable-speed aircraft. Step 4: Provide real-time feedback on the current status of the aircraft, and deduce the normal acceleration command for the next moment based on the guidance method constructed in Step 3, until the aircraft hits the target at the desired angle of impact, thus completing the guidance and control of the aircraft and the precise strike on the target. The implementation method for step one is as follows: The equation of relative motion between the aircraft and the target is expressed as follows: in, Indicates the relative distance between the aircraft and the target. Indicates the viewing angle. Indicates the trajectory inclination angle of the aircraft. Indicates the field of view of the aircraft. Indicates the speed of the aircraft. This indicates the normal acceleration command for the aircraft; The normal acceleration command for proportional guidance is: in, The navigation ratio is a positive constant. Under proportional guidance, the terminal angle of the aircraft upon hitting the target is... According to the formula Predicting the terminal landing angle of an aircraft under proportional guidance facilitates the construction of a guidance method with field of view and landing angle constraints in step three.

2. The guidance method with field of view and angle of fall constraints applicable to variable-speed aircraft as described in claim 1, characterized in that: The second step is implemented as follows: Step 2.1: Determine the landing angle control error Expected rate of change ; Drop angle control error Indicates the expected terminal angle and predicted end angle The difference; when controlling When it converges to zero, and Equal values ​​allow for control of the aircraft's landing angle; the landing angle controls the error. The definition is Because the terminal guidance process is relatively short, it is crucial to ensure the accuracy of the landing angle control error. It is crucial that the aircraft converges to zero before hitting the target; simultaneously, the aircraft needs to meet the seeker's field of view limitations during guidance to avoid target loss; to achieve these objectives, an impact angle control error is constructed. The expected rate of change is shown in the following formula: in, , Represents a symbolic function. , , , , Indicates the remaining flight time of the aircraft. , Indicates the field of view of the aircraft. Indicates the maximum field of view of the aircraft; Let be the adjustment function used to adjust the field of view of the aircraft to ensure that the field of view constraint is met. Its form is: ( ), defined in And satisfy , ; Step 2.2: Determine the guidance method bias term to control the angle of landing error. Follow The expected rate of change in the data enables constrained guidance of the aircraft with both field of view and angle of impact. Using a bias-proportional guidance feedback structure, the following guidance method with field-of-view and landing angle constraints is designed. in, This indicates a proportional guidance term used to ensure zero miss distance; Indicates the bias term, used to ensure Satisfaction The expected rate of change in the field of view, thereby satisfying the constraints of the field of view angle and the angle of fall; From the formula and have to The formula and Substitution have to According to the formula and The bias term is obtained as Combined and This means obtaining a normal acceleration command with landing angle and field of view constraints, thereby reducing the aircraft's landing angle control error. Satisfaction The expected rate of change in the value, thereby ensuring the control error of the landing angle. The guidance process converges to zero before the end of the guidance process, and the spacecraft satisfies the seeker's field of view constraint throughout the entire guidance process.

3. The guidance method with field of view and angle of impact constraints applicable to variable-speed aircraft as described in claim 2, characterized in that: The method for implementing step three is as follows: The trajectory shape of the aircraft is determined by the relative distance and line of sight Jointly decided; defined Let the arc length along the trajectory of the aircraft be denoted as , then we have The method for calculating the remaining flight time of an aircraft is as follows: relative distance line of sight Field of view and landing angle error For trajectory arc length Differentiate and express and Substitution Mode - The right end does not include the speed of the aircraft. Therefore, the relative distance of the variables line of sight Field of view and landing angle error The change will not be affected by the aircraft's speed Therefore, it is known that under the guidance method described above, the trajectory shape of the aircraft will be unaffected by the aircraft speed. The effect of this principle, when applied to variable-speed aircraft, ensures that the angle of fall control performance is unaffected by changes in speed.

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