Aircraft track prediction method based on simplified model

Abstract

The invention provides an aircraft track prediction method based on a simplified model, belongs to the field of aircraft navigation, guidance and control, and aims to solve the problems that the prediction precision is reduced due to the fact that an attitude control system is ignored in the traditional prediction based on a three-degree-of-freedom model, and the calculation amount is sharply increased in the prediction based on a six-degree-of-freedom model. The method comprises the following steps: firstly, establishing a mass center dynamics simplified model, and simplifying aerodynamic model calculation to reduce calculation complexity so as to describe the mass center motion of the aircraft; secondly, simplifying the attitude control system into a second-order link, and converting the second-order link into a state equation to obtain an equivalent model of the attitude control system so as to describe aircraft attitude motion; then constructing a least square matrix and an observation matrix based on historical flight data, and identifying equivalent model parameters by using a least square method; and finally, combining the mass point dynamics model with the attitude control system equivalent model to obtain a simplified six-degree-of-freedom model of the aircraft, and realizing trajectory recursion by adopting a numerical integration method. According to the method, on the basis of ensuring the prediction precision, the complete process from dynamic modeling to trajectory prediction is realized by simplifying the dynamic model, and support is provided for efficient flight trajectory calculation.

Description

1. Technical Field

[0001] The present invention relates to a flight path prediction method, in particular to a flight path prediction method for an aircraft based on a simplified model, belonging to the fields of aircraft navigation, guidance, and control. 2. Background Art

[0002] Flight path prediction of an aircraft is not only an important technical means to ensure flight safety and reduce air traffic congestion, but also has important application value in aspects such as airspace optimization management and flight plan scheduling. Currently, in trajectory prediction algorithms, the method based on the kinematic model does not deeply consider the influence of aerodynamic force, thrust, etc. during the flight of a fighter plane. For complex flight states, the prediction accuracy will be affected; the method based on the dynamic model faces the problems of slow calculation speed and large calculation amount; the method based on deep learning overly relies on complete data sets and training techniques and is difficult to cope with complex and changeable scenarios in sequence prediction tasks.

[0003] In the article "Research on Aircraft Near-Ground Collision Avoidance Technology Based on Multi-Trajectory Prediction" (Bai Yang, Mi Yufeng, Liu Yunfei, Zhang Xue, "Aircraft Design", Vol. 43, No. 4, 2023), the prediction of multiple escape trajectories of an automatic collision avoidance system is carried out based on the six-degree-of-freedom dynamic model of an aircraft, which solves the problem of realizing the safe and optimal selection of multiple paths of the aircraft and improves the success rate of terrain avoidance of the aircraft. However, in actual engineering applications, the real-time calculation based on the six-degree-of-freedom dynamic model of an aircraft will occupy a large amount of on-board computing resources, and the engineering implementation is difficult. 3. Summary of the Invention

[0004] The technical solution adopted by the present invention to solve its technical problems: A flight path prediction method based on a simplified model, characterized by including the following steps:

[0005] Step 1: Since when the aircraft adopts an augmentation system, the sideslip angle is maintained at a small value close to zero through feedback control, and the flight path roll angle can be approximated as the attitude roll angle, the aircraft centroid dynamic model can be simplified to

[0006]

[0007] In the formula, x, y, and z are the positions of the aircraft in the earth-fixed coordinate system; V is the airspeed of the aircraft; α is the angle of attack; γ, χ, and μ are the flight path inclination angle, flight path azimuth angle, and flight path roll angle respectively; T is the engine thrust; L and D are the aerodynamic lift and drag respectively; m is the mass of the aircraft; g is the acceleration due to gravity.

[0008] Step 2: Calculate α, L, and D in formula (1). First, simplify α to

[0009] α = θ - γ (2)

[0010] In the formula, θ is the pitch angle.

[0011] Secondly, simplify L and D to

[0012]

[0013] where ρ is the air density; are simplified aerodynamic parameters.

[0014] Model the variation law of the aerodynamic lift coefficient with the angle of attack as a linear function, i.e.,

[0015]

[0016] where, is given by fitting the aerodynamic interpolation table.

[0017] At the same time, model the variation law of the aerodynamic drag coefficient with the angle of attack as a quadratic function, i.e.,

[0018]

[0019] where, is given by fitting the aerodynamic interpolation table.

[0020] Step 3: Since the attitude control system is not considered in the aircraft centroid dynamics model, a low-order equivalent model is constructed to equivalently replace the attitude control system. First, simplify the attitude control response to a second-order transfer function, i.e.,

[0021]

[0022] where: φ is the aircraft roll angle; φ

[0025] , nθ , , r , , φ , φ , nφ ,

[0024] ,

[0022] , φ , ,

[0021] , θ , , nθ , , φ , nφ , , r ,

[0023] , is the roll angle step command; θ r is the pitch angle step command; k nφ , k nθ are the second-order system gains of the roll and pitch channels respectively; ω nφ , ω nθ are the undamped natural frequencies of the roll and pitch channels respectively; ξ φ , ξ θ are the damping ratios of the roll and pitch channels respectively.

[0023] By transforming Equation (6) into the state-space form, an equivalent model for roll angle control can be established as

[0024]

[0025] where, is the state variable of the equivalent model for roll angle control. A φ , B φ , C φ can be expressed as

[0026]

[0027] Establish the equivalent model of pitch angle control as

[0028]

[0029] Wherein, is the state variable of the equivalent model of pitch angle control. A θ , B θ , C θ can be expressed as

[0030]

[0031] Step 4: Through the discrete sequence data of the aircraft's historical flight, use the least square method to identify the parameters k nφ , k nθ , ω nφ , ω nθ , ξ φ , ξ θ in the equivalent models (8) and (9). Set the sampling period as T s , select the historical control commands {φ r (1), φ r (2), …, φ r (N)}, {θ r (1), θ r (2), …, θ r (N)} at N moments, as well as the historical control responses {φ(1), φ(2), …, φ(N)}, {θ(1), θ(2), …, θ(N)}, and construct the least square matrices Φ φ , Φ θ

[0032]

[0033] Secondly, construct the observation matrices Z φ , Z θ

[0034]

[0035] Then the model parameters identified based on the least square method are

[0036]

[0037] The equivalent model parameters of roll angle control are calculated as follows

[0038]

[0039] The equivalent model parameters for pitch angle control are calculated as follows

[0040]

[0041] Step 5: According to Equations (1), (7), and (8), the six-degree-of-freedom simplified model of the aircraft can be obtained

[0042]

[0043] wherein, is the state variable, is the input variable

[0044] Given the initial state value X0 of the aircraft through the navigation system and the aircraft control instruction U0 received by the attitude control system, the trajectory within a future period of time is recursively derived in the form of fourth-order Runge-Kutta numerical integration. Denote the trajectory at the nth moment as x n = x(nh), y n = y(nh), z n = z(nh), where h is the sampling and integration time. Select the numerical integration method as fourth-order Runge-Kutta integration, and use the following formula to implement the trajectory recursion

[0045]

[0046] wherein, is the Runge-Kutta integration term, and is calculated as the following formula

[0047] 4. Description of the Drawings

[0048] Figure 1 Shows the flowchart of the aircraft trajectory prediction method based on the simplified model provided by the specific embodiment of the present invention 5. Specific Embodiment

[0049] Referring to Figure 1 the specific steps of the trajectory prediction method of the present invention based on the simplified model are as follows

[0050] Step 1: Since when the aircraft adopts a stability augmentation system, the sideslip angle is maintained at a small value close to zero through feedback control, and the trajectory roll angle can be approximated as the attitude roll angle, the aircraft centroid dynamics model can be simplified to

[0051]

[0052] where \(x\), \(y\), and \(z\) are the positions in the aircraft's earth-fixed coordinate system; \(V\) is the aircraft's airspeed; \(\alpha\) is the angle of attack; \(\gamma\), \(\chi\), and \(\mu\) are the flight path inclination angle, flight path azimuth angle, and flight path roll angle, respectively; \(T\) is the engine thrust; \(L\) and \(D\) are the aerodynamic lift and drag, respectively; \(m\) is the aircraft mass; and \(g\) is the acceleration due to gravity. Select the F16 fighter as the object and set the model parameters as \(m = 288.98\ kg\), \(g = 9.8\ m\) 2 / s.

[0053] Step 2: Regarding how to calculate \(\alpha\), \(L\), and \(D\) in Equation (1), first simplify \(\alpha\) to

[0054] \(\alpha=\theta - \gamma\ (17)\)

[0055] where \(\theta\) is the pitch angle.

[0056] Secondly, simplify \(L\) and \(D\) to

[0057]

[0058] where \(\rho\) is the air density; are simplified aerodynamic parameters.

[0059] Model the variation law of the aerodynamic lift coefficient with the angle of attack as a linear function, that is

[0060]

[0061] where is given by fitting the aerodynamic interpolation table. Set

[0062] At the same time, model the variation law of the aerodynamic drag coefficient with the angle of attack as a quadratic function, that is

[0063]

[0064] where is given by fitting the aerodynamic interpolation table. Set

[0065] Step 3: Since the attitude control system is not considered in the aircraft's center-of-mass dynamics model, a low-order model is constructed to equivalently replace the attitude control system. First, simplify the attitude control response to a second-order transfer function, that is

[0066]

[0067] where: \(\varphi\) is the aircraft's roll angle; \(\varphi\) r is the roll angle step command; \(\theta\) r is the pitch angle step command; \(k\) nφ 、\(k\) nθare the second-order system gains of the roll and pitch channels; ω nφ , ω nθ are the undamped natural frequencies of the roll and pitch channels; ξ φ , ξ θ are the damping ratios of the roll and pitch channels respectively.

[0068] By transforming Equation (6) into the state-space form, an equivalent model for roll angle control can be established as

[0069]

[0070] where is the state variable of the equivalent model for roll angle control. A φ , B φ , C φ can be expressed as

[0071]

[0072] An equivalent model for pitch angle control is established as

[0073]

[0074] where is the state variable of the equivalent model for pitch angle control. A θ , B θ , C θ can be expressed as

[0075]

[0076] Step 4: Through the discrete sequence data of the aircraft's historical flight, use the least squares method to identify the parameters k nφ , k nθ , ω nφ , ω nθ , ξ φ , ξ θ in the equivalent models (8) and (9). Set the sampling period as T s = 0.01 s, select the historical control commands {φ r (1), φ r (2), …, φ r (N)}, {θ r (1), θ r (2), …, θ r (N)} at N = 1000 moments, as well as the historical control responses {φ(1), φ(2), …, φ(N)}, {θ(1), θ(2), …, θ(N)}, and construct the least squares matrices Φ φ , Φ θ

[0077]

[0078] Secondly, construct the observation matrix Z φ 、Z θ

[0079]

[0080] Then the model parameters identified based on the least squares method are

[0081]

[0082] The equivalent model parameters for roll angle control are calculated as follows

[0083]

[0084] The equivalent model parameters for pitch angle control are calculated as follows

[0085]

[0086] After calculation, we can obtain k nφ = 1.02, ω nφ = 0.25, ξ φ = 1.26, k nθ = 1.01, ω nθ = 0.28, ξ θ = 1.96.

[0087] Step 5: According to equations (1), (7), and (8), the six-degree-of-freedom simplified model of the aircraft can be obtained

[0088]

[0089] where is the state variable, is the input variable.

[0090] The initial state value X0 = [\(0m\), \(0m\), \(15000m\), \(450m / s\), \(-5.875126608018265°\), \(0°\), \(0°\), \(0\), \(0°\), \(0\)] is given by the navigation system T , and the aircraft control command U0 = [\(10000N\), \(20°\), \(60°\)] accepted by the attitude control system. Using the form of fourth-order Runge-Kutta numerical integration, the trajectory in the future period is recursively derived. Denote the trajectory at the \(n\)th moment as \(x\) n = \(x(nh)\), \(y\) n = \(y(nh)\), \(z\) n = \(z(nh)\), where \(h = 0.01s\) is the integration step size. The numerical integration method selected is fourth-order Runge-Kutta integration, and the trajectory recursion is realized using the following formula

[0091]

[0092] Among them, is the Runge-Kutta integration term, which is calculated as follows

[0093]

[0094] The parts not described in detail in the present invention belong to the common general knowledge of those skilled in the art.

Claims

1. A flight path prediction method for an aircraft based on a simplified model, characterized in that, The described flight path prediction method includes: 1). Establish an aircraft particle dynamics model based on position and flight path angle; 2). Model the lift coefficient and drag coefficient as first - order and second - order functions of the angle of attack respectively to achieve simplification; 3). Based on a second - order link, establish a low - order equivalent model of the attitude control system; 4). Use historical flight data to identify the parameters of the equivalent model of the attitude control system based on the least - squares method; 5). Combine the aircraft particle dynamics model and the equivalent model of the control system, and use the numerical integration method to predict the future flight path.

2. The trajectory prediction method according to claim 1, wherein: Since when the aircraft adopts an augmentation system, the sideslip angle is maintained at a small value close to zero through feedback control, the flight path roll angle can be approximated as the attitude roll angle. Therefore, the aircraft centroid dynamics model can be simplified to where x, y, and z are the positions of the aircraft in the earth - fixed coordinate system; V is the airspeed of the aircraft; α is the angle of attack; γ, χ, and μ are the flight path inclination angle, flight path azimuth angle, and flight path roll angle respectively; T is the engine thrust; L and D are the aerodynamic lift and drag respectively; m is the mass of the aircraft; g is the acceleration due to gravity.

3. The track prediction method according to claim 1, characterized in that: Regarding how to calculate α, L, and D in Equation (1), first simplify α to α = θ - γ (2) where θ is the pitch angle. Secondly, simplify L and D to Where ρ is the air density; is to simplify the aerodynamic parameters. Model the variation law of the aerodynamic lift coefficient with the angle of attack as a linear function, that is In the formula, is given by fitting an air pressure interpolation table. Meanwhile, model the variation law of the aerodynamic drag coefficient with the angle of attack as a quadratic function, that is In the formula, is given by fitting an air pressure interpolation table.

4. The track prediction method according to claim 1, characterized in that: Since the attitude control system is not considered in the aircraft particle dynamics model, a low - order equivalent model is constructed to equivalently replace the attitude control system. First, simplify the attitude control response to a second - order transfer function, that is where: φ is the aircraft roll angle; φ r is the roll angle step command; θ r is the pitch angle step command; k nφ and k nθ are the second-order system gains of the roll and pitch channels respectively; ω nφ and ω nθ are the undamped natural frequencies of the roll and pitch channels respectively; ξ φ and ξ θ are the damping ratios of the roll and pitch channels respectively. By transforming Equation (6) into the state - space form, the equivalent model of roll - angle control can be established as Among them, is the state variable of the roll angle control equivalent model. A φ , B φ , C φ can be expressed as Establish the equivalent model of pitch - angle control as Among them, is the state variable of the pitch angle control equivalent model. A θ , B θ , C θ can be expressed as 5. The track prediction method according to claim 1, wherein: Based on the discrete sequence data of the historical flights of the aircraft, the parameters k nφ 、k nθ 、ω nφ 、ω nθ 、ξ φ 、ξ θ in the equivalent models (8) and (9) are identified by using the least - squares method. Set the sampling period as T s . Select the historical control commands {φ r (1), φ r (2), …, φ r (N)}, {θ r (1), θ r (2), …, θ r (N)} at N moments, as well as the historical control responses {φ(1), φ(2), …, φ(N)}, {θ(1), θ(2), …, θ(N)}, and construct the least - squares matrices Φ φ 、Φ θ Next, construct the observation matrix Z φ , Z θ The model parameters identified based on the least squares method are The parameters of the equivalent model of roll - angle control are calculated as follows The parameters of the equivalent model of pitch - angle control are calculated as follows 6. The track prediction method according to claim 1, characterized in that: According to Equations (1), (7), and (8), a six - degree - of - freedom simplified model of the aircraft can be obtained Among them, is a state variable, is an input variable. Given the initial state value X0 by the navigation system and the aircraft control command U0 received by the attitude control system, the trajectory within a certain period in the future is recursively derived in the form of fourth-order Runge-Kutta numerical integration. Denote the trajectory at the nth moment as x n = x(nh), y n = y(nh), z n = z(nh), where h is the sampling and integration time. The numerical integration method is selected as fourth-order Runge-Kutta integration, and the trajectory recursion is realized by the following formula Among them, is the Runge-Kutta integration term, which is calculated as follows

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