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Stability Analysis of Nonlinear Periodically Time-Varying Dynamic Systems By Studying Typical Insect-Like Flapping Wing

Kamankesh, Zahra | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49260 (45)
  4. University: Sharif University of Technology
  5. Department: Aerospace Engineering
  6. Advisor(s): Banazadeh, Afshin
  7. Abstract:
  8. Designing Nonautonomous periodic systems such as helicopters, multirotors, monocopters or the dynamics of flapping wings requires stability analysis and careful examination in order to identify and determine their dynamic behaviour. In practice, analysis and design are interdependent and the design of nonlinear control systems involves an iterative process. To know the importance of identifying and to accurately implement methods to analyse this kind of systems in the field of aerospace, the flapping wing can be a good example. The issue of stability and the control of the flapping wings have not yet had a clear solution, and the current research including controller design based on linear analysis is carried out by averaging, despite the lack of stability studies on flapping wings. Regarding this issue, this study attempts to reach a general understanding in the stability analysis of such systems by investigating these methods on the mass-spring-pendulum system, Duffing equation and aerospace systems such as Hummingbird and Hawk-Moth flapping wing models. The supplementary arguments to using Lyapunov theory of Nonautonomous systems, the periodic Lyapunov equation and dynamic-Routh’s method are developed. Using Floquet theory, kinetic energy integration as well as phase portrait for the insect-like Hummingbird indicates the instability of hovering flight and requires the expansion of force equations in order to determine the impact of parameters on increasing the level of total kinetic energy. This analysis is carried out in the extended model of the Hawk-Moth. Moreover, these analyses are carried out by determining the stability range as well as further increasing it by changing the parameters of the system during the design process, which then facilitates the controller design. To this end, after adjusting the hinge location of Hawk-Moth’s wing and other parameters to create hover trim, the range of mean angle of attack to achieve the specified stability is determined by the averaging and linearization methods while investigating the results with the phase portrait and energy analysis on the other equivalent dynamics in order to detect the instability origin. Applying stability range to the Nonautonomous periodic dynamic system and the use of Floquet theory shows the instability and the creation of strange attractor in the system
  9. Keywords:
  10. Flapping Wing ; Stability Analysis ; Dynamical Systems ; Nonlinear Dynamical System ; Duffing Differential Equation ; Floquet Eigenfunctions ; Integral Energy ; Phase Plane ; Nonautonomous Periodically Dynamic System ; Stronge Attractor

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