Loading...

Study on Periodic Orbits in Nonlinear Fractional Order Systems Via Perturbation Methods

Yazdani Jahromi, Masoud | 2010

771 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40934 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Salarieh, Hassan
  7. Abstract:
  8. Using fractional order calculus to model complex phenomena with combined behavior (i.e., dissipative, capacitive and inertia behavior) is one of the most recent research fields in the world. These accurate models lead to better understanding of the phenomena. For example, consider viscoelastic materials. In early models, dissipative behavior is separated from capacitive behavior but by using fractional order models, these two behaviors are considered simultaneously thus the complexity of the model would be reduced. To use fractional order models in real-life engineering applications, it is important to investigate the dynamics of these systems. Unfortunately, there are a few proper analytical tools to do such investigations. This deficiency is more significant when study of steady state behavior of nonlinear fractional order systems is considered. it is coming from this fact that the methods usually used in investigation of integer order systems do not work properly in these systems therefore these methods should be revised to use in such systems. In this research, the existence of periodic orbits in steady state condition of a fractional order system is proved, and the harmonic balance method is modified and utilized for extracting the periodic orbits. Then some classical perturbation methods have been modified to estimate the periodic orbits of a fractional order system. Finally a Homotopy-based method is developed to find the periodic solutions of nonlinear fractional order systems. Many case studies have been examined to study the effectiveness of the presented methods, and the limitations of each method have been described via examples.
  9. Keywords:
  10. Fractional Order System ; Nonlinear System ; Periodic Behaviour ; Perturbation Method ; Homotopy Analysis Method

 Digital Object List

  • محتواي پايان نامه
  •   view

 Bookmark

No TOC