Extending Nonlinear Frequency Analysis to Flight Dynamics and Control Problems

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


Unforced bifurcation analysis has proven to be a powerful method for nonlinear fixed-wing aircraft flight dynamics analysis in the past 40 years. On the other hand, the use of harmonically-forced bifurcation analysis in fixed-wing flight dynamics studies is almost unexplored. The advantage of this method is its ability to capture non-stationary nonlinearities, including but not limited to rate limiting, nonlinear damping, controller gain scheduling, and modal coupling. These phenomena are of great importance in flight dynamics analysis, especially as current and future aircraft continue to push the operating envelope and incorporate more nonlinear features in their designs.

In this thesis, it is proposed that harmonically-forced bifurcation analysis be exploited and the outputs visualised in the form of a nonlinear Bode plot. This approach provides the capability to assess the non-stationary nonlinearities, which cannot be reflected using conventional (unforced) bifurcation methods and linear frequency analysis. A wide range of promising applications is discussed in this thesis. In all cases, the nonlinear Bode plot not only accurately reflects aircraft’s transient dynamics in the time-domain, but also uncovers many interesting phenomena that may otherwise be undetected.

Nonlinear frequency response can reveal regions where the closed-loop performance deteriorates considerably comparing to the linear-based prediction. Furthermore, a dedicated study on the link between actuator saturation and pilot-induced oscillation reveals that rate saturation can create a pair of fold bifurcations, resulting in 180o jump in phase lag. It is also shown that harmonic forcing of the elevator can excite the aircraft’s natural resonance frequency, leading to a divergent oscillation that can be used to escape a locked-in deep stall. Additionally, the method verifies that unsteady aerodynamic effects have a negative impact on the aircraft flying qualities. The final study investigates the sub- and super-harmonic resonances, which presents a more theoretical analysis into the frequency-domain nonlinearities in a flight dynamics model.
Date of Award2 Dec 2021
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorSimon A Neild (Supervisor) & Mark H Lowenberg (Supervisor)

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