As a perturbation method, averaging is a mathematical tool for dynamic analysis of time-periodic and space-periodic dynamical systems, including those governed by partial differential equations. The control design procedure presented in this work uses averaging techniques, the well-developed linear control strategies, and finite element methods. The controller is designed based on the linear averaged dynamics of a time- or space-periodic system. The controller is then used for trajectory tracking or stabilization of the periodic system. The applicability and performance of the suggested method depend on different physical parameters of the periodic system and the control parameters of the controller. The effects of these parameters are discussed in this work. Numerical simulations show acceptable performance of the proposed control design strategy for two linear and nonlinear time- and space-periodic systems, namely, the one-dimensional heat equation and the Chafee-Infante equation with periodic coefficients. / M.S. / Dynamic analysis and control of dynamical systems with varying parameters is a challenging task. It is always of great help if one can perform the analyses for an approximate system with constant parameters and use the results to study and control the original system with varying parameters. Averaging is a mathematical tool that is used to approximate a system with periodic parameters with a ``simpler'' system with constant parameters. In this research averaging is used for design of controllers for systems with periodic parameters. First, an approximate system with constant parameters, called the averaged system, is determined. The averaged system is used for design of a controller which can be then be used for the original system with periodic parameters.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/116574 |
| Date | 04 October 2023 |
| Creators | Tahmasian, Sevak |
| Contributors | Mathematics, Borggaard, Jeff, Abaid, Nicole, Staples, Anne E. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf, application/pdf |
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