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|Title:||Stochastic Stability and Nonlinear Control in Mechanical Systems|
|Doctoral Committee Chair(s):||Namachchivaya, N. Sri|
|Department / Program:||Aeronautical and Astronautical Engineering|
|Discipline:||Aeronautical and Astronautical Engineering|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|Abstract:||Almost-sure asymptotic stability of 3 and 4 dimensional co-dimension two dynamical systems under small intensity stochastic excitations is investigated. The method of stochastic averaging is used to derive a set of approximate Ito equations which are then examined to obtain the almost-sure stability conditions. The sample properties of the process are based on the boundary behavior of the associated scalar diffusion process of the amplitude Ito equations. This method is then applied to a linear, gyroscopic problem of a rotating shaft with a random loading demonstrating the conservative nature of mean square stability. In addition to stochastic excitations, many systems also undergo harmonic loading. The almost-sure stability of two degree-of-freedom systems subjected to both random and harmonic excitation is then investigated. In this analysis, stochastic averaging followed by a perturbation theoretic approximation is used to facilitate the solution of the multi-dimensional diffusive Markov process.
The emerging field of nonlinear control theory has attempted to alleviate the problem associated with applying linear control theory to nonlinear problems. A segment of nonlinear control theory, called exact feedback linearization, has proven useful in a class of problems satisfying certain controllability and integrability constraints. Approximate feedback linearization has enlarged this class by weakening the integrability conditions, but application of both these techniques remains limited to problems in which a series of linear partial differential equations can easily be solved. By use of the idea of normal forms, from dynamical systems theory, a method of obtaining the necessary coordinate transformation and nonlinear feedback rules is given. This method, algebraic in nature, is valid for any dimensional system and any order nonlinearity provided it meets the approximate feedback linearization conditions.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1993.
|Date Available in IDEALS:||2014-12-17|