A method for improving the deep stall state of an aircraft at a large angle of attack

Abstract

The invention discloses a method for improving a deep stall state of an aircraft at a large angle of attack, belongs to the field of aircraft motion characteristic analysis, proposes a frequency domain response method of a nonlinear system combined with bifurcation analysis, is used to analyze the dynamic characteristics of an aircraft at a large angle of attack, expands the application form of bifurcation analysis, regards the nonlinear system as a harmonic forced system and adopts a frequency domain method to perform analysis, combines with a continuous algorithm in the bifurcation analysis, finds the periodic response of the nonlinear system to the harmonic forced input, and presents the result in the form of a nonlinear Bode diagram, obtains the motion characteristics of the aircraft at a large angle of attack, and obtains a suitable frequency to make the aircraft escape from the deep stall state.

Description

Technical Field

[0001] The invention belongs to the field of aircraft motion characteristic analysis, and in particular relates to a method for improving a deep stall state of an aircraft at a large angle of attack. Background Art

[0002] For some aircraft with relaxed static stability design, the trim point may appear at a high angle of attack. After such aircraft enters a deep stall, the elevator control efficiency is severely reduced and sufficient pitch restoring torque cannot be generated. The aircraft will be locked in a deep stall, causing the aircraft to drop rapidly. The deep stall flight state is stable and dangerous. After the aircraft enters a dangerous deep stall state, this unfavorable stable state needs to be destroyed as soon as possible. The most common way to recover is through a stick shaker. The amplitude and frequency of the stick shaker affect the recovery efficiency. It is crucial to find the appropriate stick shaker amplitude and frequency. It is necessary to analyze the dynamic characteristics of the aircraft at a high angle of attack.

[0003] Bifurcation analysis based on branching and catastrophe theory has been shown to be a powerful tool for studying nonlinear dynamics. Since this method can predict many nonlinear phenomena and provide valuable insights, it has become a popular choice for studying the dynamics of nonlinear systems. Despite its many advantages, bifurcation analysis currently implemented on nonlinear systems cannot capture the nonequilibrium elements in nonlinear dynamics.

[0004] In linear system theory, a harmonic input produces a harmonic output of the same frequency, whereas the output of a nonlinear system may contain multiple frequencies. Furthermore, in a linear system a smooth change in the forcing frequency or the forcing amplitude produces a smooth change in the amplitude and phase of the response. In a nonlinear system, the response depends on both the forcing frequency and the amplitude and may produce a bistable solution. For example, a smooth change in the input frequency may result in a sudden change in amplitude and phase, known as a jump phenomenon. Forced vibrations of nonlinear systems have been intensively studied, but their applications are mainly limited to structural engineering. Summary of the invention

[0005] The present invention provides a method for improving the deep stall state of an aircraft at a large angle of attack. Based on the branch and catastrophe theory and the linear frequency domain response, the bifurcation analysis is extended to the nonlinear frequency domain response analysis to obtain the appropriate stick shaker amplitude and frequency.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for improving a deep stall state of an aircraft at a high angle of attack comprises the following steps:

[0008] Establish a nonlinear mathematical model of the aircraft;

[0009] Taking the rudder deflection angle as the external forced input and the aircraft's motion state as the observed response, the Bode diagram between the aircraft's various motion states and the rudder deflection angle frequency is plotted, the nonlinear characteristics are analyzed, the aircraft's motion characteristics at large angles of attack are obtained, and the appropriate frequency is obtained to make the aircraft escape from a deep stall state.

[0010] Beneficial effects: The present invention provides a method for improving the deep stall state of an aircraft at a large angle of attack, proposes a frequency domain response method of a nonlinear system combined with bifurcation analysis, which is used to analyze the dynamic characteristics of an aircraft at a large angle of attack, expands the application form of bifurcation analysis, regards the aircraft nonlinear system as a harmonic forced system and adopts a frequency domain method to analyze it, takes the rudder deflection angle as an external forced input, takes the motion state of the aircraft as an observed response, draws a Bode diagram between each motion state of the aircraft and the rudder deflection angle frequency, combines the continuous algorithm in the bifurcation analysis, finds the periodic response of the aircraft nonlinear system to the harmonic forced input, and presents the result in the form of a "nonlinear Bode diagram". Unlike the linear Bode diagram, the nonlinear Bode diagram does not involve any linearization of the system motion equation, thereby allowing some nonlinear elements to be directly reflected in the diagram; analyzes the nonlinear characteristics, obtains the motion characteristics of the aircraft at a large angle of attack, and obtains a suitable frequency to make the aircraft escape from the deep stall state. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 A schematic diagram of the vertical coordinate definition of a nonlinear Bode diagram in an embodiment of the present invention;

[0012] Figure 2 Schematic diagram of nonlinear frequency domain response results at different amplitudes and frequencies obtained by performing nonlinear frequency domain analysis on a fighter system in an embodiment of the present invention, wherein (a) is an amplitude gain curve when A=1°; (b) is an amplitude gain curve when A=8°; (c) is an amplitude gain curve when A=25°; and (d) is a partial amplitude gain curve when A=25°;

[0013] Figure 3 Schematic diagram of the input of the aircraft for high angle of attack trimming when sinusoidal signals of different frequencies are used as the condition of A=25° in an embodiment of the present invention;

[0014] Figure 4 Schematic diagram of the time domain variation of the aircraft angle of attack obtained by using sinusoidal signals of different frequencies as inputs for aircraft trimming at high angles of attack under the condition of A=25° in an embodiment of the present invention. DETAILED DESCRIPTION

[0015] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments:

[0016] A method for improving a deep stall state of an aircraft at a high angle of attack comprises the following steps:

[0017] Establish a nonlinear mathematical model of the aircraft,

[0018] In deriving the nonlinear equations of motion for the aircraft, the following assumptions were made:

[0019] 1. Assume that the earth is flat, ignoring the curvature and rotation of the earth;

[0020] 2. Assume that the aircraft is a rigid body, and do not consider the influence of elastic deformation and rotating parts of the aircraft;

[0021] 3. Assume that the atmosphere is a static standard atmosphere and do not consider the influence of wind;

[0022] 4. Assume that the mass of the aircraft remains unchanged, that is, ignore the change in the mass of the fighter due to fuel consumption;

[0023] The nonlinear model of the aircraft consists of two parts: dynamics and kinematics, as follows:

[0024] (1) Center of mass dynamics equation

[0025] The description of the motion of the center of mass of an aircraft is described by Newton's second law of motion:

[0026]

[0027] Where m is the mass of the aircraft, V is the flight velocity vector of the aircraft, and F is the resultant force vector of the external force acting on the center of mass of the aircraft. For a general moving coordinate system, the absolute acceleration of the center of mass can be expressed as:

[0028]

[0029] In the formula ω is the acceleration when the angular velocity of the moving system is zero; ω×V is the acceleration due to the existence of angular velocity ω The acceleration caused by the change in the direction of V relative to the moving coordinate system; dV / dt is the absolute acceleration of the center of mass. From the above formula, the center of mass dynamics vector form expressed in the moving coordinate system is:

[0030]

[0031] (2) Kinematic equation of center of mass

[0032] In order to determine the flight trajectory of the aircraft in space, it is necessary to establish the center of mass motion equation of the aircraft. Since the velocity components of the ground coordinate system are the differentials of the center of mass space coordinates, the center of mass kinematic equation can be obtained from the transformation matrix from the track coordinate system to the ground coordinate system:

[0033]

[0034] Where γ is the track inclination angle, χ is the track deviation angle;

[0035] (3) Rotational dynamics equation

[0036] From theoretical mechanics, we know that the rotational motion of an aircraft around its center of mass can be described by the momentum theorem, namely:

[0037]

[0038] Where H is the momentum moment of the aircraft about the origin of the coordinate system, and M is the resultant moment of the external force acting on the aircraft about the origin, where:

[0039] H=∫r×(ω×r)dm

[0040] The radius vector r and the angular velocity ω After using the projection component in the coordinate system to insert into the above equation, we can get:

[0041]

[0042] Where I x , I y and I z is the inertia moment of the aircraft about the Ox axis, Oy axis and Oz axis, and I xy , I yz and I zx are the inertia products of the aircraft about the Ox axis and the Oy axis, the Oy axis and the Oz axis, and the Oz axis and the Ox axis respectively;

[0043] When specifically studying the rotation law of the aircraft around the center of mass, the angular momentum derivative dH / dt can be expressed as dH / dt=δH / δt+ω×H, and the dynamic equation of the aircraft's rotation around the center of mass expressed in the moving coordinate system is obtained:

[0044]

[0045] Because most aircraft are symmetrical about the XOZ plane, the inertia product I xy =I yz =0, the above formula can be simplified to:

[0046]

[0047] (4) Rotational kinematic equations

[0048] The attitude of the aircraft in space is represented by the three Euler angles (ψ, θ, φ) of the body axis system relative to the ground axis system. In the process of converting from the ground coordinate system to the body coordinate system, the projection of the rotational angular velocity (p, q, r) on the body axis can be written as:

[0049]

[0050] Solving this equation gives the rotational kinematic equation:

[0051]

[0052] The specific expression of the aerodynamic model of the aircraft is as follows:

[0053] Expressions for lift coefficient, drag coefficient and side force coefficient:

[0054]

[0055] The specific expressions of the rolling aerodynamic moment coefficient, the pitching aerodynamic moment coefficient and the yaw aerodynamic moment coefficient are:

[0056]

[0057] In the above expressions of aerodynamic force and aerodynamic moment, c is the chord length of the wing and b is the span length of the wing;

[0058] Taking the rudder deflection angle as the external forced input and the aircraft's motion state as the observed response, the Bode diagram between the aircraft's various motion states and the rudder deflection angle frequency is drawn, the nonlinear characteristics are analyzed, and the aircraft's motion characteristics at large angles of attack are obtained;

[0059] When drawing the Bode diagram of a nonlinear system, the ordinate of the Bode diagram is defined as follows:

[0060]

[0061] Phase(degree)=(X1-X3)×360

[0062] Among them, X i and Y i are the x and y coordinates of the corresponding points of the peak and trough in a complete cycle, such as Figure 1 shown.

[0063] In order to find the appropriate stick shaker amplitude and frequency for deep stall recovery, a nonlinear frequency domain analysis is now performed on the fighter system. The elevator deflection angle is used in the form of A sinωt to generate a forced oscillation signal. The nonlinear frequency domain response results at different amplitudes and frequencies are shown in the following figure. Figure 3 As shown, the thinner dotted line represents the amplitude gain curve of the linearized model, the thicker black curve represents the nonlinear gain curve, the solid line represents the stable solution, and the dotted line represents the unstable solution.

[0064] From the frequency domain response of the linear system, it can be observed that when the frequency of the system input is 1.32rad / s, there is a peak in the frequency domain response of the system, which means that the system responds most violently at this frequency, and it is possible to make the aircraft recover from a stable deep stall state. However, the aircraft is a nonlinear system. Figure 2 It can be seen that the nonlinear system has a system softening phenomenon, and with the increase of the input amplitude, the number of peaks in the frequency domain response of the nonlinear system also increases. The maximum amplitude gain at certain frequencies is higher than that of the linear system, and there is also an unstable periodic oscillation response, which means that using forced vibration inputs at these frequencies can enable the aircraft to get out of the stable deep stall state as soon as possible.

[0065] In order to verify the above judgment, Figure 3 As shown in the figure, under the condition that the external forced input amplitude is A = 25°, two sinusoidal signals with frequencies of 1 rad / s and 1.32 rad / s are used as the input of the aircraft during high angle of attack trim, and the time domain change of the aircraft angle of attack is obtained as shown in Figure 4 As shown, it can be seen that when the elevator oscillation frequency is 1 rad / s, the aircraft's angle of attack diverges faster. At 15 seconds, the angle of attack diverges to about 10°, which is exactly what we expect to see when recovering from a deep stall.

[0066] In actual flight, once the aircraft recovers from a high angle of attack trim state and descends to a suitable angle of attack, the pilot can stop shaking the stick and control the aircraft to fly at a normal angle of attack.

[0067] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for improving a deep stall state of an aircraft at a large angle of attack, characterized in that: The following steps are involved: Establish a nonlinear mathematical model of the aircraft, which consists of two parts: dynamics and kinematics; The center of mass dynamic vector of the aircraft in the moving coordinate system is: Where m is the mass of the aircraft, V is the flight velocity vector of the aircraft, F is the resultant force vector of the external forces acting on the center of mass of the aircraft, and ω is the acceleration when the angular velocity of the dynamic system is zero; ω×V is the acceleration caused by the change in the direction of V relative to the moving coordinate system due to the angular velocity ω; In order to determine the flight trajectory of the aircraft in space, it is necessary to establish the center of mass motion equation of the aircraft. Since the velocity components of the ground coordinate system are the differentials of the center of mass space coordinates, the center of mass kinematic equation can be obtained from the transformation matrix from the track coordinate system to the ground coordinate system: Where γ is the track inclination angle, χ is the track deviation angle; The dynamic equation of the aircraft rotating around the center of mass expressed by the aircraft in the moving coordinate system is: Where H is the momentum moment of the aircraft about the origin of the coordinate system, and M is the resultant moment of the external force acting on the aircraft about the origin; The rotational kinematic equation is: In the formula, (ψ, θ, φ) are the three Euler angles of the aircraft's body axis system relative to the ground axis system, and (p, q, r) are the rotational angular velocity that can be written in the process of converting from the ground coordinate system to the body coordinate system; The specific expression of the aircraft's aerodynamic model is as follows: Expressions for lift coefficient, drag coefficient and side force coefficient: The specific expressions of the rolling aerodynamic moment coefficient, the pitching aerodynamic moment coefficient and the yaw aerodynamic moment coefficient are: In the aerodynamic force and aerodynamic moment expressions, c is the chord length of the wing, and b is the span length of the wing; Taking the rudder deflection angle as the external forced input and the aircraft's motion state as the observed response, the Bode diagram between the aircraft's various motion states and the rudder deflection angle frequency is plotted, the nonlinear characteristics are analyzed, the aircraft's motion characteristics at large angles of attack are obtained, and the appropriate frequency is obtained to make the aircraft escape from a deep stall state.

2. The method for improving the deep stall state of an aircraft at a large angle of attack according to claim 1, characterized in that: The aircraft is symmetrical about the XOZ plane, so the inertia product I xy =I yz =0, we get:

3. The method for improving the deep stall state of an aircraft at a large angle of attack according to claim 1, characterized in that: When drawing the Bode diagram between the various motion states of the aircraft and the frequency of the rudder deflection angle, the vertical axis of the Bode diagram is defined as follows: Phase(degree)=(X1-X3)×360 Among them, Xi and Yi are the x- and y-axis coordinates of the corresponding points of the peak and trough in a complete cycle.

4. The method for improving the deep stall state of an aircraft at a large angle of attack according to claim 1, characterized in that: The fighter system is subjected to nonlinear frequency domain analysis, and the elevator deflection angle is adopted Asinωt The form of is used to generate forced oscillation signals, and the nonlinear frequency domain response results at different amplitudes and frequencies are obtained. According to the response results, the forced vibration input that can make the aircraft leave the stable deep stall state as soon as possible is determined.

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