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Dissertation
Surgical Manipulation of the Modal Dynamics of Networks
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2021
DOI:
https://doi.org/10.7273/000003348
Handle:
https://hdl.handle.net/2376/122105
Abstract
This dissertation is concerned with surgical manipulation of dynamical networks, i.e. estimation or control of specific network dynamical properties using limited actuation and sensing. We focus specifically on manipulation of modal (eigenvalue, eigenvector) properties of a linear network model. Three directions are pursued: 1) design of local feedback controllers to block observability/controllability, 2) error analysis of mode estimators, and 3) small-disturbance analysis of droop-controlled microgrids.
First, we study the design of local feedback controllers to block observability for a set of remote measurement nodes in a linear network process. This study is motivated by the increasing interest in designing control systems for secure management of critical infrastructures, when multiple stakeholders have access. For the purpose of design, conditions and techniques for surgical eigenstructure assignment, where a subset of key eigenvectors and all eigenvalues are placed, are developed by extending the classical results on full eigenstructure assignment. This result is then used in tandem with graph-theoretic and control-theoretic approaches to design sparser and regional feedback-based observability-blocking controls, in a way that exploits the network's graph topology. The dual problem -- the design of controllability-blocking controls -- is also addressed.
Second, motivated by network mode monitoring applications, we pursue the development of lower bounds on impulse-response-based mode estimates for a single-input single-output linear dynamical system. Specifically, we derive expressions for general Barankin-type bounds as well as some simplified bounds for pole and residue estimates. These bounds are tighter than the well-known Cramer-Rao bounds, particularly at low signal-to-noise ratios. These studies also highlight the inefficacy of unbiased estimators for mode estimation at high noise.
Third, motivated by stability issues observed in microgrids with substantial resistive losses, we seek to assess and design the small-disturbance responses of droop-controlled inverter-based microgrids. We begin by deriving a structure-preserving small-signal model for a lossy microgrid which uses new rotated-droop controls. We then provide several graph-theoretic conditions that guarantee angle and voltage stability regardless of filtering or droop parameters, and undertake design of the rotated droop controls. The formal results are verified and illustrated by simulating transient responses of standard IEEE test systems.
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Details
- Title
- Surgical Manipulation of the Modal Dynamics of Networks
- Creators
- Abdullah Al Maruf
- Contributors
- Sandip Roy (Advisor)Ali Saberi (Committee Member)Anamika Dubey (Committee Member)Bernard Lesieutre (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Electrical Engineering and Computer Science, School of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 379
- Identifiers
- 99900652104001842
- Language
- English
- Resource Type
- Dissertation