Author

Derek Hoffman

Date of Award

3-19-2018

Document Type

Dissertation - Open Access

Degree Name

Doctor of Philosophy in Engineering Physics

Department

Physical Sciences

Committee Chair

Dr. Mahmut Reyhanoglu

First Committee Member

Dr. William Mackunis

Second Committee Member

Dr. Ylechiel Crispin

Third Committee Member

Dr. Anthony Reynolds

Abstract

It is the purpose of this document to elaborate on the control of systems that are underactuated or otherwise constrained. To do so, local- and global-coordinate formulations are implemented to generate well-defined system dynamics for a multitude of scenarios. These dynamics are shown to lie on manifolds defined by mathematical restrictions, allowing for singularity-free modeling for global considerations. Feed-back controllers by extension share these benefits, facilitating singularity-free control algorithms as a result. Further, unactuated degrees of freedom can be treated as additional constraints, resulting in an embedded manifold upon the original dynamics. A transformation between a provided set of dynamical equations containing one or more unactuated degrees of freedom to a new set of coupled dynamics avoiding their perturbation will be shown. The necessary background is included with procedures outlining the solution of similarly-structured classes of systems. For complete insight, a Langragian formulation of the dynamical equations of motion is elaborated on, although differential geometric techniques do not demand restrictions on the dynamical methods applied. Examples are provided to demonstrate the proposed techniques. Appropriate controllers are then designed and proven to be effective at obtaining the control objective, initially through mathematical rigor. Following such proofs, simulational and experimental benchmark systems are given with corresponding MATLAB/Simulink plots for numerical analysis.

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