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Research Papers

Prediction and Recovery of Aircraft Unstable Nonlinear Phenomena Using Bifurcation Analysis and Backstepping Method

[+] Author and Article Information
Qi Xin

School of Automation,
Northwestern Polytechnical University,
Xi'an 710072, China
e-mail: jiufengxin@126.com

Zhongke Shi

Professor
School of Automation,
Northwestern Polytechnical University,
Xi'an 710072, China
e-mail: shizknwpu@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 6, 2015; final manuscript received June 21, 2016; published online July 22, 2016. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 11(6), 061007 (Jul 22, 2016) (12 pages) Paper No: CND-15-1410; doi: 10.1115/1.4034049 History: Received December 06, 2015; Revised June 21, 2016

To protect the aircraft flight safety across the envelope of angle of attack, bifurcation analysis and backstepping method are investigated to predict and suppress the unstable nonlinear flight phenomena. By applying bifurcation analysis and continuation method to the flight motion, the onsets of both the chaotic phenomenon called falling leaf motion and the catastrophe phenomenon named coupled jump behavior are derived. To stabilize these unstable motions, a backstepping and disturbance observer based flight controller is designed. According to the main function of the control surface, we divide the flight controller into the airspeed subsystem and the flight path subsystem, where the airspeed subsystem is regulated by an adaptive dynamic inversion controller while the flight path subsystem is stabilized by a third-order compound controller. Considering the parametric uncertainties of aerodynamics, three sliding mode disturbance observers are presented as compensators to approximate the compound uncertainties. Simulations demonstrate that the proposed controller can recover the aircraft from falling leaf motion or coupled jump behavior to straight level flying.

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References

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Figures

Grahic Jump Location
Fig. 1

Dynamics of aircraft [8,9]

Grahic Jump Location
Fig. 2

The equlibrium paths of the aircraft longitudinal states and the eigenvalues versus δe with δt = 0.1007: (a) airspeed, (b) angle of attack, and (c) pitch angle

Grahic Jump Location
Fig. 3

The Hopf bifurcation diagrams of δr and flight states versus δa: (a) rudder deflection, (b) angle of attack, (c) sideslip angle, and (d) roll rate

Grahic Jump Location
Fig. 4

The properties of the damped elliptical oscillation: (a) sideslip angle versus angle of attack, (b) roll rate versus angle of attack, (c) time history of angle of attack, and (d) oscillation period

Grahic Jump Location
Fig. 5

The characteristics of the falling leaf motion: (a) sideslip angle versus angle of attack, (b) roll rate versus angle of attack, (c) time history of angle of attack, and (d) oscillation period

Grahic Jump Location
Fig. 6

Maximum LE for F/A-18 with different pitch rates

Grahic Jump Location
Fig. 7

Time responses for coupled jump behavior: (a) angle of attack and sideslip and (b) angular rate

Grahic Jump Location
Fig. 8

The state equlibrium paths and the eigenvalues versus δe with δt = 0.1007, δa = −0.2942, and δr = −0.3737: (a) angle of attack and (b) real part of the eigenvalues

Grahic Jump Location
Fig. 9

The architecture of the flight controller

Grahic Jump Location
Fig. 10

Comparisons of the free and controlled responses of the falling leaf motion: (a) airspeed, (b) flight path angle, (c) ground track angle, (d) angle of attack, and (e) sideslip angle

Grahic Jump Location
Fig. 11

Responses comparisons of the falling leaf motion stabilization under different uncertainties: (a) airspeed, (b) flight path angle, (c) ground track angle, (d) elevator deflection, (e) aileron deflection, (f) rudder deflection, (g) throttle setting, (h) airspeed compound uncertainty, (i) flight path angle compound uncertainty, (j) ground track angle compound uncertainty, (k) roll rate compound uncertainty, (l) pitch rate compound uncertainty, and (m) yaw rate compound uncertainty

Grahic Jump Location
Fig. 12

Comparisons of the free and controlled responses of the coupled jump behavior: (a) airspeed, (b) flight path angle, (c) ground track angle, (d) angle of attack, and (e) sideslip angle

Grahic Jump Location
Fig. 13

Comparisons of responses in the suppression of coupled jump behavior under different uncertainties: (a) airspeed, (b) flight path angle, (c) ground track angle, (d) elevator deflection, (e) aileron deflection, (f) rudder deflection, and (g) throttle setting

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