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Gain Analysis and Stability of Nonlinear Control Systems Open Access


Other title
Nonlinear Control Systems
Nonlinear Systems
Type of item
Degree grantor
University of Alberta
Author or creator
Zahedzadeh, Vahid
Supervisor and department
Chen, Tongwen
Marquez, Horacio J.
Examining committee member and department
Lynch, Alan F.
Khorasani, Khashayar
Ben-Zvi, Amos
Tavakoli, Mahdi
Department of Electrical and Computer Engineering

Date accepted
Graduation date
Doctor of Philosophy
Degree level
The complexity of large industrial engineering systems such as chemical plants has continued to increase over the years. As a result, flexible control systems are required to handle variation in the operating conditions. In the classical approach, first the plant model should be linearized at the nominal operating point and then, a robust controller should be designed for the resulting linear system. However, the performance of a controller designed by this method deteriorates when operation deviates from the nominal point. When the distance between the operating region and the nominal operating point increases, this performance degradation may lead to instability. In the context of traditional linear control, one method to solve this problem is to consider the impact of nonlinearity as “uncertainty” around the nominal model and design a controller such that the desired performance is satisfied for all possible systems in the uncertainty set. As the size of uncertainty increases, conservatism occurs and at some point, it becomes impossible to design a controller that can provide satisfactory performance. One of the methods proposed to overcome the aforementioned shortcomings is the so-called Multiple Model approach. Using Multi-Models, local designs are performed for various operating regions and membership functions or a supervisory switching scheme is used to interpolate or switch among the controllers as the operating point moves among local regions. Since the Multiple Model method is a natural extension of the linear control method, it inherits some benefits of linear control such as simplicity of analysis and implementation. However, all these benefits are valid locally. For example, the multiple model method may be vulnerable when global stability is taken into account. The core objective of this thesis is to develop new tools to study stability of closed-loop nonlinear systems controlled by local controllers in order to improve design of multiple model control systems. For example, one of the aims of this work is to investigate how to determine the region where closed loop system is stable. A secondary objective is to study the effects of the exogenous signals on stability of such systems.
License granted by Vahid Zahedzadeh ( on 2009-07-07T17:28:01Z (GMT): Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of the above terms. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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