Vibrational control: Application to a laser-illuminated reaction and extension to nonlinear functional differential equations

Vibrational Control method is an open-loop control technique which utilizes zero mean parametric excitations to modify the behavior of dynamical systems in a desired manner. It may be used where conventional methods such as feedback or feedforward techniques fail due to restricted sensing and/or actuation. There are two major goals in this thesis. The first goal is to implement vibrational control technique in a physical system to verify its potential applicability as an alternative to feedback. The second goal is to extend vibrational control theory to a more general class of systems, namely nonlinear systems with finite time delays. To achieve the first goal, the laser illuminated thermochemical reaction, $S\sb2O\sb6F\sb2$ $\rightleftharpoons$ 2 $SO\sb3F\cdot$, was chosen. Numerical simulation and experimental work were carried out for the case of a rectangular wave oscillating incident laser power. It was shown experimentally that such parametric vibrations can indeed induce asymptotically stable operating regimes with averages located at initially unstable steady states as predicted by vibrational control theory. Hence, vibrational control is demonstrated to be a feasible stabilizing strategy for laser induced reactions that needs no on-line measurements and complex actuators. For the second goal, three problems of control of nonlinear systems with time delays were addressed: (i) an existence and a synthesis of parametric vibrations for their stabilization, (ii) the transient behavior analysis of the vibrationally controlled nonlinear systems with time lags, and (iii) the robustness analysis of this class of systems with respect to the vibration parameters. Stabilizability conditions for two vibration types are formulated and procedures for the synthesis of the corresponding stabilizing vibrations are proposed. The method for the transient behavior analysis of vibrationally controlled systems on a finite time interval is developed as well. Several examples are given to support the theory presented. The robustness analysis of the type of vibrations considered has shown that linear multiplicative vibrations do result in totally robustly stable equilibrium point, whereas vector additive vibrations result only in robust stabilizability within a known margin of the order O(ε).

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Fakhfakh, Jamel

Contributors dc:contributor

• Bentsman, Joseph

• Engineering, Mechanical

Statement dc:rights

• Copyright 1990 Fakhfakh, Jamel

Language dc:language

eng

Identifier

AAI9114232
(UMI)AAI9114232

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/20573