ASU Electronic Theses and Dissertations
This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.
In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.
Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.
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- All Subjects: Applied Mathematics
- Creators: Rogers, Bradley
Description
The field of prostheses and rehabilitation devices has seen tremendous advancement since the ’90s. However, the control aspect of the said devices is lacking. The need for mathematical theories to improve the control strategies is apparent. This thesis attempts to bridge the gap by introducing some dynamic system analysis and control strategies.Firstly, the human gait dynamics are assumed to be periodic. Lyapunov Floquet theory and Invariant manifold theory are applied. A transformation is obtained onto a simple single degree of freedom oscillator system. The said system is transformed back into the original domain and compared to the original system. The results are discussed and critiqued. Then the technique is applied to the kinematic and kinetic data collected from healthy human subjects to verify the technique’s feasibility. The results show that the technique successfully reconstructed the kinematic and kinetic data.
Human gait dynamics are not purely periodic, so a quasi-periodic approach is adopted. Techniques to reduce the order of a quasi-periodic system are studied. Lyapunov-Peron transformation (a surrogate of Lyapunov Floquet transformation for quasi-periodic systems) is studied. The transformed system is easier to control. The inverse of the said transformation is obtained to transform back to the original domain. The application of the techniques to different cases (including externally forced systems) is studied.
The reduction of metabolic cost is presented as a viable goal for applying the previously studied control techniques. An experimental protocol is designed and executed to understand periodic assistive forces' effects on human walking gait. Different tether stiffnesses are used to determine the best stiffness for a given subject population. An estimation technique is introduced to obtain the metabolic cost using the center of mass's kinematic data.
Lastly, it is concluded that the mathematical techniques can be utilized in a robotic tail-like rehabilitation device. Some possible future research ideas are provided to implement the techniques mentioned in this dissertation.
ContributorsBhat, Sandesh Ganapati (Author) / Redkar, Sangram (Thesis advisor) / Sugar, Thomas G (Committee member) / Rogers, Bradley (Committee member) / Arizona State University (Publisher)
Created2021
Description
The inherent behavior of many real world applications tends to exhibit complex or chaotic patterns. A novel technique to reduce and analyze such complex systems is introduced in this work, and its applications to multiple perturbed systems are discussed comprehensively. In this work, a unified approach between the Floquet theory for time periodic systems and the Poincare theory of Normal Forms is proposed to analyze time varying systems. The proposed unified approach is initially verified for linear time periodic systems with the aid of an intuitive state augmentation and the method of Time Independent Normal Forms (TINF). This approach also resulted in the closed form expressions for the State Transition Matrix (STM) and Lyapunov-Floquet (L-F) transformation for linear time periodic systems. The application of theory towards stability analysis is further demonstrated with the system of Suction Stabilized Floating (SSF) platform. Additionally, multiple control strategies are discussed and implemented to drive an unstable time periodic system to a desired stable point or orbit efficiently and optimally. The computed L-F transformation is further utilized to analyze nonlinear and externally excited systems with deterministic and stochastic time periodic coefficients. The central theme of this work is to verify the extension of Floquet theory towards time varying systems with periodic coefficients comprising of incommensurate frequencies or quasi-periodic systems. As per Floquet theory, a Lyapunov-Perron (L-P) transformation converts a time-varying quasi-periodic system to a time-invariant form. A class of commutative quasi-periodic systems is introduced to demonstrate the proposed theory and its applications analytically. An extension of the proposed unified approach towards analyzing the linear quasi-periodic system is observed to provide good results, computationally less complex and widely applicable for strongly excited systems. The computed L-P transformation using the unified theory is applied to analyze both commutative and non-commutative linear quasi-periodic systems with nonlinear terms and external excitation terms. For highly nonlinear quasi-periodic systems, the implementation of multiple order reduction techniques and their performance comparisons are illustrated in this work. Finally, the robustness and stability analysis of nonlinearly perturbed and stochastically excited quasi-periodic systems are performed using Lyapunov's direct method and Infante's approach.
ContributorsCherangara Subramanian, Susheelkumar (Author) / Redkar, Sangram (Thesis advisor) / Rogers, Bradley (Committee member) / Sugar, Thomas (Committee member) / Arizona State University (Publisher)
Created2021