Date of Award

Summer 2014

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computational Analysis and Modeling

First Advisor

Katie Evans


In this work we analyze a one dimensional model for a flexible wing micro aerial vehicle which can undergo heaving motion. The vehicle is modeled with a non-local type of internal damping known as spatial hysteresis as well as viscous external damping. We present a rigorous theoretical analysis of the model proving that the linearly approximated system is well-posed and the first order feedback system operators generate exponentially stable C0–semigroups.

Furthermore, we present numerical simulations of control designs used on the linearly approximated model to control the associated nonlinear model in two different strategies. The first strategy used to control the system is a target tracking strategy. The second strategy used in this work is morphing the system to a target state over time. The controllers used in this work include Linear Quadratic Regulator, Linear Quadratic Gaussian, and central control.

In light of the theory of this work we have incorporated the appropriate Riccati equation solutions into the control design for a system with a mode problem (i.e. zero eigenvalue for stiffness operator). This work remains consistent with the literature that concerns multiple component structures with a mode problem.