Modeling and design optimization of coupled and undermodeled dynamical systems

This dissertation is concerned with investigating the behavior of dynamical systems that consist of coupled components, some of which may be poorly understood and undermodeled, where the topology of coupling constitutes an essential ingredient in the system composition, may be available for purposeful design, or suggests a natural decomposition in experimental testing. The work seeks to explore nontrivial consequences of network topology, design dynamical systems that leverage network topology, contribute to control-theoretic methods for experimental study, and describe potential applications to physical sensor designs. The first two of these objectives are formulated in the context of resonant dynamics of networks of linearly coupled, weakly damped, linear and/or nonlinear self-sustained mechanical oscillators; triggered by external harmonic excitation in systems with a unique stable free response or due to external triggers and slowly varying internal parameters in the case of a class of bistable systems. A dynamic substructuring technique known as real-time hybrid testing is reviewed with particular emphasis on the use of root-finding techniques for eliminating the effects of inevitable time delays in physical experiments, and a model-reference adaptive control framework is derived for locating and tracking unknown periodic responses in such experiments on systems with known forms of nonlinearity but uncertain parameters. Finally, the use of root-finding techniques is also proposed as an element of a sensor design that couples in-silico components to physical elements, for example, microcantilevers for ultrasensitive mass sensing in viscous environments. The inclusion of self-sustained oscillators is here inspired by the emergence of self-organization in complex biological systems because of endogenous energy sources. Nonlinearity and self-organization allow such systems to achieve a collective response to exogenous signals that is less dependent on exact resonance than linear systems. With bistability comes the further possibility of hysteretic dynamics, as a response is sustained also after an exogenous signal is removed and the system progressively adapts to its own response. In this dissertation, networks with Van der Pol oscillators with only quadratic nonlinearities in the damping coefficient are shown to exhibit qualitative transitions between the behavior associated with networks of all linear and all nonlinear oscillators, respectively, under continuous variations in damping ratios. Perturbation analysis is used to derive general results and to explore means of suppressing the influence of 1:1 and 1:3 internal resonances in an asymptotic limit. For networks with Van der Pol oscillators with quadratic and quartic nonlinearities in the damping coefficient, this dissertation describes the intentional design of slow-fast dynamics that separate fast oscillations of the network nodes from slow variations in the damping ratios, driven by local feedback laws assigned to individual nodes. Again, perturbation results establish a rigorous asymptotic behavior that is then explored using parameter continuation techniques away from the asymptotic limit. In the context of real-time hybrid testing, this dissertation shows how adaptive control strategies developed to track stable and unstable periodic orbits in experiments may be generalized to the case where decomposition results in parametric excitation of the physical experiment, rather than additive excitation that can be handled already with existing techniques. The analysis also illustrates how such control-based continuation may be implemented to support model-free design optimization using a technique of successive continuation.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Mao, Yu

Contributors dc:contributor

• Dankowicz, Harry
• Vakakis, Alexander
• Allison, James
• Chamorro, Leonardo

• Coupled dynamical systems
• Nonlinear dynamics
• Sensor design
• Hybrid testing
• Adaptive control
• Control-based continuation

Statement dc:rights

• Copyright 2022 Yu Mao

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/115447

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115447