Date of Award

2016

Document Type

Dissertation - Open Access

Degree Name

Doctor of Philosophy in Engineering Physics

Department

Physical Sciences

Committee Chair

Dr. Sergey V. Drakuno, Ph.D.

First Committee Member

Dr. William MacKunis, Ph.D.

Second Committee Member

Dr. Bogdan Udrea, Ph.D.

Third Committee Member

Dr. Matthew Zettergren, Ph.D.

Abstract

Many processes in nature and industry can be described by partial differential equations. PDEs employ quantities such as density, temperature, velocity, etc. and their partial derivatives to model these phenomena. However, in the case of distributed parameter systems, it is not always possible to have access to the states of the systems due to technical difficulties such as lack of sensors. Therefore, there is the need for state observers to estimate the states of the system only having the output of the system available. In this research, the theory of sliding mode and variable structure systems are employed in order to design observers for different classes of distributed parameter systems such as advection equation, Burgers’ equation, Euler equations, etc. Some contributions of this research are: suggesting the state transformation which allows the arbitrary design of sliding manifold in sliding mode observer, developing some formulae for observer gain, discussing the shock wave situation and its properties and solutions, designing sliding mode observer and anomaly detection system for a system of advection equations.

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