A method for analyzing instability motion based on bifurcation theory and freedom release experiment

Abstract

The present invention discloses a method for analyzing instability motion based on bifurcation theory and degree-of-freedom release experiment. First, a degree-of-freedom release experiment system is built in a wind tunnel. Then, by introducing bifurcation theory into the degree-of-freedom release experiment, a continuous algorithm based on control is established to search for branch equilibrium points and periodic closed orbits. Non-invasive control is adopted to transform the branch search process into an optimization process in which the feedback control quantity tends to zero, so that the feedback control can change the stability of the equilibrium branch while maintaining its equilibrium branch position. Thus, stable and unstable equilibrium solutions can be continuously tracked in the experiment to obtain the global stability characteristics of the aircraft, providing a brand-new experimental method for the research on the dynamic characteristics of the aircraft and enabling accurate prediction of the stall departure characteristics of the aircraft.

Description

Technical Field

[0001] The present invention relates to the technical field of ground tests for aircraft, and particularly to a method for analyzing instability motion based on bifurcation theory and degree-of-freedom release experiments. Background Art

[0002] Modern fighter jets, in pursuit of high maneuverability, often enter the large angle of attack region, where their motion may exhibit severe nonlinearity at large angles of attack, making them extremely prone to stall departure and even at risk of entering a spin. The study of such instability problems is not only related to flight safety but also to the combat capabilities of modern high-performance aircraft. Due to factors such as the severe nonlinearity of aerodynamic forces and moments, longitudinal and lateral aerodynamic cross-coupling, the influence of unsteady characteristics, and obvious aerodynamic hysteresis phenomena in the stall departure region, it has brought great difficulties and risks to the prediction and flight test of aircraft stall departure.

[0003] Most of the current means for studying stall departure and stall departure criteria are based on conventional wind tunnel experiment data, which have limitations in reflecting nonlinear aerodynamic characteristics. Moreover, when the nonlinear system is in the critical state of stall departure, there will be non-negligible errors between the analysis results and the actual system response. Therefore, it is of great significance to develop new research methods for aircraft stall departure problems. Summary of the Invention

[0004] The purpose of the present invention is to solve the technical problems existing in the prior art and provide a method for analyzing instability motion based on bifurcation theory and degree-of-freedom release experiments.

[0005] To achieve the above purpose, the technical solution provided by the present invention is: a method for analyzing instability motion based on bifurcation theory and degree-of-freedom release experiments, including building a set of degree-of-freedom release experimental systems in a wind tunnel; first, by introducing bifurcation theory into the degree-of-freedom release experimental system, establishing a continuous algorithm based on control to search for branch equilibrium points and periodic closed orbits; using a non-invasive control method to transform the branch search process into an optimization process where the feedback control quantity tends to zero, so that the feedback control not only changes the stability of the equilibrium branch but also maintains its equilibrium branch position, thereby continuously tracking the equilibrium solution in the experiment and crossing the "inflection point" on the branch, and experimentally tracking the unstable equilibrium solution to obtain the global stability characteristics of the aircraft.

[0006] Further, the method specifically includes the following steps:

[0007] (1) Through the degree-of-freedom release experimental system, study the nonlinear dynamic phenomena of the experimental model;

[0008] (2) Through the ramp input of the elevator, obtain the characteristics and mutation characteristics of the experimental model on different stable motion branches without feedback control;

[0009] (3) Introduce the simple feedback control of the experimental model rudder surface on the attitude. Study the effectiveness of the feedback control in enhancing the stability of the experimental model;

[0010] (4) Construct a tracking command control law based on the simple control law obtained in the previous step, and track the stable and unstable branches through a continuous algorithm based on control to obtain the complete bifurcation characteristics.

[0011] Furthermore, the degree-of-freedom release experimental system includes an experimental model, a degree-of-freedom release mechanism, and a ground control center. The degree-of-freedom release mechanism fixes the experimental model in the wind tunnel. A flight control system is embedded in the experimental model, and the ground control center is connected to the flight control system through wireless communication.

[0012] Furthermore, the continuous algorithm based on control includes: directly tracking the steady-state response of the system with parameter changes through physical experiments. The continuous algorithm based on control depends on control to reach the specified state point; adopt the nonlinear dynamic inversion method based on PI feedback as the control law to track the angular rate command Ω c ={p c , q c , r c} and the output command The control method is as shown in Equation

[0013]

[0014] where, Ω c is the angular velocity command, I is the identity matrix, p c is the roll angular rate command, q c is the pitch angular rate command, r c is the yaw angular rate command, is the roll angular acceleration output command, is the pitch angular acceleration output command, is the yaw angular acceleration output command.

[0015] Furthermore, the control signal of the non-invasive control method is expressed as:

[0016] u(t) = g(x * (t) - x(t))

[0017] In the formula, u(t) is the control signal, x(t) is the actual response, and x * (t) is the tracking command; in the experiment, u(t) is continuously made to approach zero through a continuous algorithm based on control, so as to achieve non-invasive control.

[0018] Advantages of the present invention:

[0019] The present invention builds a degree-of-freedom release experimental system in a wind tunnel; then, by introducing bifurcation theory in the degree-of-freedom release experiment, a continuous algorithm based on control is established to search for branch equilibrium points and periodic closed orbits; non-invasive control is adopted to transform the branch search process into an optimization process in which the feedback control quantity tends to zero, so that the feedback control maintains the equilibrium branch position while changing the stability of the equilibrium branch, thereby continuously tracking stable and unstable equilibrium solutions in the experiment, obtaining the global stability characteristics of the aircraft, providing a new experimental method for the research of the dynamic characteristics of the aircraft, and enabling accurate prediction of the stall deviation characteristics of the aircraft. Brief Description of the Drawings

[0020] The drawings described herein are used to provide a further understanding of the present invention, and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention.

[0021] Figure 1 Schematic diagram of the degree-of-freedom release experimental system of the present invention;

[0022] Figure 2 Schematic diagram of the command tracking controller in the continuous algorithm based on control;

[0023] Figure 3 Schematic diagram of the process of the continuous algorithm based on control;

[0024] Figure 4 Schematic diagram of the iterative process of non-invasive control;

[0025] Figure 5 General flowchart of the experimental process of the present invention;

[0026] Figure 6 Open-loop elevator-angle of attack equilibrium bifurcation diagram provided by the embodiment of the present invention;

[0027] Figure 7 Open-loop elevator-sideslip angle equilibrium bifurcation diagram provided by the embodiment of the present invention;

[0028] Figure 8 Closed-loop elevator-angle of attack equilibrium bifurcation diagram provided by the embodiment of the present invention;

[0029] Figure 9 Closed-loop elevator-sideslip angle equilibrium bifurcation diagram provided by the embodiment of the present invention.

[0030] Annotation of the drawings:

[0031] 1 - Experimental model, 2 - Degree-of-freedom release mechanism, 3 - Flight control system, 4 - Ground control center. Detailed Embodiments

[0032] This section will describe in detail specific embodiments of the present invention. Preferred embodiments of the present invention are shown in the accompanying drawings, and the function of the drawings is to supplement the description in the text part of the specification, enabling people to intuitively and vividly understand each technical feature and the overall technical solution of the present invention. However, it should not be construed as a limitation on the protection scope of the present invention.

[0033] Referring to Figures 1 - 9 , a preferred embodiment of the present invention, a method for analyzing instability motion based on bifurcation theory and degree-of-freedom release experiment, includes building a set of degree-of-freedom release experimental systems in a wind tunnel; first, by introducing bifurcation theory into the degree-of-freedom release experimental system, establishing a continuous algorithm based on control to search for branch equilibrium points and periodic closed orbits; adopting a non-invasive control method to transform the branch search process into an optimization process where the feedback control quantity tends to zero, so that the feedback control not only changes the stability of the equilibrium branch but also maintains its equilibrium branch position, thereby continuously tracking the equilibrium solution in the experiment and crossing the "inflection point" on the branch, experimentally tracking the unstable equilibrium solution, and obtaining the global stability characteristics of the aircraft.

[0034] As a preferred embodiment of the present invention, it may also have the following additional technical features:

[0035] In this embodiment, the method specifically includes the following steps:

[0036] (1) Through the degree-of-freedom release experimental system, study the nonlinear dynamic phenomena of experimental model 1.

[0037] (2) Through the ramp input of the elevator, obtain the characteristics and mutation characteristics of experimental model 1 on different stable motion branches without feedback control.

[0038] (3) Introduce the simple feedback control of the rudder surface of experimental model 1 to the attitude; study the effectiveness of the feedback control in enhancing the stability of experimental model 1.

[0039] (4) Based on the simple control law obtained in the previous step, construct a tracking command control law, and track the stable and unstable branches through a continuous algorithm based on control to obtain the complete bifurcation characteristics.

[0040] In this embodiment, the degree-of-freedom release experimental system includes experimental model 1, degree-of-freedom release mechanism 2, and ground control center 4. The degree-of-freedom release mechanism 2 fixes the experimental model 1 in the wind tunnel. A flight control system 3 is embedded in the experimental model 1, and the ground control center 4 is connected to the flight control system 3 through wireless communication.

[0041] In this embodiment, the continuous algorithm based on control includes: directly tracking the steady-state response of the system with parameter changes through physical experiments. The continuous algorithm based on control relies on control to reach the specified state point; adopting the nonlinear dynamic inversion method based on PI feedback as the control law to track the angular rate command Ω c ={p c , q c , r c} and the output command The control method is as shown in Equation

[0042]

[0043] where Ω c is the angular velocity command, I is the identity matrix, p c is the roll angular rate command, q c is the pitch angular rate command, r c is the yaw angular rate command, is the roll angular acceleration output command, is the pitch angular acceleration output command, is the yaw angular acceleration output command.

[0044] In this embodiment, the control signal of the non-invasive control method is expressed as:

[0045] u(t) = g(x * (t) - x(t))

[0046] where u(t) is the control signal, x(t) is the actual response, and x * (t) is the tracking command; in the experiment, through the continuous algorithm based on control, u(t) continuously approaches zero, thereby realizing non-invasive control.

[0047] Specifically

[0048] such as Figure 1 , the degree-of-freedom release system includes: experimental model 1, degree-of-freedom release mechanism 2, flight control system 3, and ground control center 4. Experimental model 1 is a controllable model with fully maneuverable control surfaces; the degree-of-freedom release mechanism 2 fixes the experimental model 1 in the wind tunnel and provides rotational motion in three degrees of freedom: roll, pitch, and yaw for the experimental model 1; the flight control system 3 is embedded in the experimental model 1 and can realize functions such as servo control of the experimental model 1, measurement of rudder deflection angle, measurement of model attitude angle and angular velocity, execution of control laws, and data recording; the ground control center 4 serves as the center for system configuration, system testing, operation status detection, data recording, and data transmission, and is connected to the flight control system 3 through wireless communication.

[0049] such as Figure 2, in the instruction tracking controller of the continuous algorithm based on control, its closed-loop transfer function is

[0050]

[0051] It can be known from the standard second-order dynamic system that

[0052] K i = ω 2 (2)

[0053] K p = 2ξω (3)

[0054] where q(s) is the Laplace transform of the actual response of the pitch rate, q c (s) is the Laplace transform of the pitch rate command, K i is the integral gain, K p is the proportional gain, ω is the natural frequency, and ξ is the damping ratio.

[0055] Such as Figure 3 , the process of the continuous algorithm based on control includes:

[0056] u(t) = g(x * (t) - x(t)) (4)

[0057] In the formula, u(t) is the control signal, x(t) is the actual response, and x * (t) is the tracking command; in the experiment, it is assumed that the tracking command and the actual response can be expressed by the corresponding Fourier expansion:

[0058]

[0059]

[0060] In the formula, A0, A j , B j are the coefficients of the Fourier expansion of the actual response x(t). are the coefficients of the Fourier expansion of the tracking command x*(t).

[0061] Similarly, the control signal can also be written in the following form

[0062]

[0063] In the formula, is the basic signal coefficient of the control signal u(t), are the coefficients of the Fourier expansion of the high-frequency part of the control signal u(t).

[0064] The main part of the control signal will make the model perform harmonic motion, while the high-frequency part of the signal represents the additional feedback required to keep the model's motion accurate; thus, the key is to make the high-frequency part of the control signal less than δ, so as to provide non-invasive feedback control and enable the model to obtain corresponding motion responses under the basic control. under which, corresponding motion responses are obtained.

[0065] For example Figure 4 , the iterative process of non-invasive control includes:

[0066] First, starting from the initial zero value, increase the value of the command tracking signal. The controller makes corresponding parameter updates according to the command signal. At this time, the experimental model makes a response. When the model response converges to a steady state, judge the feedback control quantity.

[0067] If the feedback quantity is less than the error value δ (generally not zero, but a very small value), record the current experimental point. At this point, it is considered that the applied control is non-invasive, and the position of the aircraft's response in the equilibrium topological structure is the same as that in the uncontrolled experiment.

[0068] If the feedback quantity does not meet the condition, correct the command tracking signal to reduce the error so that u(t) ≤ δ is satisfied.

[0069] Repeat the above process until the tracking command traverses the maximum angle of attack that the aircraft can reach, thereby plotting the complete equilibrium branch curve of the aircraft.

[0070] For example Figure 5 , shows the overall experimental flow chart of the instability motion analysis method based on bifurcation theory and degree-of-freedom release experiment, including:

[0071] (1) Through the degree-of-freedom release experimental system, study the nonlinear dynamic phenomena of experimental model 1.

[0072] (2) Through the ramp input of the elevator, obtain the characteristics and mutation characteristics of experimental model 1 on different stable motion branches under no feedback control.

[0073] (3) Introduce the simple feedback control of the experimental model 1's rudder surface on the attitude, and study the effectiveness of the feedback control in enhancing the stability of experimental model 1.

[0074] (4) Based on the simple control law obtained in the previous step, construct a tracking command control law; track the stable and unstable branches through a continuous algorithm based on control to obtain the complete bifurcation characteristics.

[0075] To introduce in more detail a method for analyzing instability motion based on bifurcation theory and degree-of-freedom release experiments provided by the embodiments of the present invention, the stall departure characteristics of a blended wing-body aircraft under longitudinal and lateral-directional coupling effects are studied below. First, the open-loop characteristics of three degrees of freedom are analyzed. By continuously changing the elevator, the response of the angle of attack is determined, and based on the changes in parameters such as the roll angle and roll rate, an open-loop equilibrium bifurcation diagram of three degrees of freedom is plotted. Then, a closed-loop experimental method is adopted. By using a continuous algorithm based on control, the equilibrium points of the three-degree-of-freedom motion are captured and compared with the open-loop results for analysis to determine the complete equilibrium bifurcation diagram, thereby predicting the stall departure characteristics of the blended wing-body aircraft.

[0076] Experiment 1: Analysis of three-degree-of-freedom open-loop experiment. In the open-loop experiment, the ailerons and rudder of the model are kept in the neutral state (aileron δa = 0°, rudder δr = 0°). Then, the ground control center 4 sends an elevator ramp input signal to the experimental model 1, causing the model to make a slow nose-up motion. At the same time, the attitude angle and angular velocity information of the experimental model 1 are recorded. Since periodic oscillations occur during the motion, the periodic oscillation data needs to be processed when plotting the equilibrium bifurcation diagram. By selecting the maximum and minimum values in each oscillation period, the maximum and minimum amplitudes of the oscillatory motion are obtained, and a scatter plot is formed by combining them with the elevator deflection corresponding to each oscillation period. Then, the equilibrium bifurcation curve is obtained by fitting these data points. Figure 6 and Figure 7 are the elevator-angle-of-attack equilibrium bifurcation diagram under open-loop and the elevator-side-slip-angle equilibrium bifurcation diagram under open-loop, respectively.

[0077] From Figure 6 and Figure 7 it can be seen that for the equilibrium bifurcation diagram of the three-degree-of-freedom open-loop experiment, there is a Hopf bifurcation point H3(-6.2°, 7.4°). When the angle of attack is less than 7.4°, the motion of the aircraft is a stable equilibrium branch; when the angle of attack exceeds 7.4°, the aircraft undergoes a Hopf bifurcation at H3, and the original stable equilibrium state becomes unstable, bifurcating into a periodic motion corresponding to the periodic oscillations of the angle of attack and the side-slip angle.

[0078] Experiment 2: Analysis of three-degree-of-freedom closed-loop experiment. In the closed-loop experiment analysis, an angle-of-attack ramp command signal is sent to the experimental model 1, and at the same time, stability augmentation control in the lateral-directional is carried out to slowly increase the angle of attack, and the curves of the changes of various parameters with time history are recorded. Taking the elevator deflection as the variable parameter, the closed-loop equilibrium bifurcation curve is obtained. Figure 7 and Figure 8 are the elevator-angle-of-attack equilibrium bifurcation diagram under closed-loop and the elevator-side-slip-angle equilibrium bifurcation diagram under closed-loop, respectively.

[0079] Figure 8There is a limit point, a BP bifurcation point and a section of unstable equilibrium branch in it; among them, the limit point is LP9(-9°, 13.3°), and the BP bifurcation point is BP(-8.5°, 16°); within the angle of attack range of 0° to 13.3°, the angle of attack increases with the decrease of the elevator deflection, while within the angle of attack range corresponding to LP9 and BP, that is, 13.3° to 16°, the angle of attack increases with the increase of the elevator deflection, and the aircraft is in a stable equilibrium branch within the 16° angle of attack range; while at the BP point, the angle of attack begins to increase sharply, and the aircraft changes from a stable branch to an unstable branch.

[0080] In summary, for Figure 8 and Figure 9 Analysis shows that the stability of the aircraft in the closed-loop experiment analysis mainly undergoes a mutation at the BP bifurcation point. The type of mutation is manifested as roll instability with the rapid divergence of the roll angle and roll angle rate. At this time, the corresponding angle of attack is the critical instability angle of attack for roll divergence, and this angle is 16°. At the same time, comparing with the results of the three-degree-of-freedom open-loop experiment analysis, the Hopf bifurcation point H3 in the open-loop experiment is transformed into an equilibrium point, and the corresponding periodic oscillatory motions of the angle of attack and sideslip angle are also transformed into equilibrium branches.

[0081] The present invention builds a set of degree-of-freedom release experimental system in a wind tunnel; then, by introducing bifurcation theory in the degree-of-freedom release experiment, a continuous algorithm based on control is established to search for branch equilibrium points and periodic closed orbits; non-invasive control is adopted to transform the branch search process into an optimization process in which the feedback control quantity tends to zero, so that the feedback control can change the stability of the equilibrium branch while maintaining its equilibrium branch position, thereby continuously tracking stable and unstable equilibrium solutions in the experiment, obtaining the global stability characteristics of the aircraft, and providing a brand-new experimental method for the research of the dynamic characteristics of the aircraft, and can realize the accurate prediction of the stall deviation characteristics of the aircraft.

[0082] On the premise of no conflict, those skilled in the art can freely combine and superimpose the above-mentioned additional technical features.

[0083] The above is only the preferred implementation mode of the present invention, and all technical solutions that achieve the purpose of the present invention by basically the same means fall within the protection scope of the present invention.

Claims

1. A method for analyzing instability motion based on bifurcation theory and degree-of-freedom release experiment, characterized in that: It includes building a degree-of-freedom release experimental system in a wind tunnel; first, by introducing bifurcation theory into the degree-of-freedom release experimental system, a continuous algorithm based on control is established to search for branch equilibrium points and periodic closed orbits; the non-invasive control method is used to transform the branch search process into an optimization process where the feedback control quantity tends to zero, so that the feedback control can change the stability of the equilibrium branch while maintaining its equilibrium branch position, thereby continuously tracking the equilibrium solution in the experiment, crossing the "inflection point" on the branch, experimentally tracking the unstable equilibrium solution, and obtaining the global stability characteristics of the aircraft; The method specifically includes the following steps: (1) Through the degree-of-freedom release experimental system, study the nonlinear dynamic phenomena of the experimental model; (2) Through the ramp input of the elevator, obtain the characteristics and mutation characteristics of the experimental model on different stable motion branches without feedback control; (3) Introduce the simple feedback control of the experimental model rudder surface on the attitude, and study the effectiveness of the feedback control in enhancing the stability of the experimental model; (4) Construct a tracking command control law based on the simple control law obtained in the previous step, and track the stable and unstable branches through a continuous algorithm based on control to obtain the complete bifurcation characteristics; The degree-of-freedom release experimental system includes an experimental model, a degree-of-freedom release mechanism, and a ground control center. The degree-of-freedom release mechanism fixes the experimental model in the wind tunnel. A flight control system is embedded in the experimental model, and the ground control center is connected to the flight control system through wireless communication; The described continuous algorithm based on control includes directly tracking the steady-state response of the system with parameter changes through physical experiments. The continuous algorithm based on control relies on control to reach the specified state point. The nonlinear dynamic inversion method based on PI feedback is used as the control law to track the angular rate command Ω c ={p c , q c , r c} and the output command The control method is as shown in the formula where, Ω c is the angular velocity command, I is the identity matrix, p c is the roll rate command, q c is the pitch rate command, r c is the yaw rate command, is the roll angular acceleration output command, is the pitch angular acceleration output command, is the yaw angular acceleration output command; The control signal of the non-invasive control method is expressed as: u(t) = g(x * (t) - x(t)) where u(t) is the control signal, x(t) is the actual response, and x * (t) is the tracking command, and g is the PI feedback control law; in the experiment, u(t) is continuously driven to approach zero through a continuous algorithm based on control, thereby achieving non-invasive control.

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