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This paper proposes a method to efficiently compute the voltage and current along a transmission line which can be “damaged”; that is its electrical properties can be unevenly distributed. The method approximates a transmission line by a self-similar circuit network and leverages our previous work regarding the frequency response for that class of networks. The main motivation arises from research for railway track circuit systems where transmission line models are often employed. Determining deviations from baseline properties of the railway circuit is important for health monitoring of the system and furthermore, changes in circuit properties due to a train occupying a segment of the track also is of great interest as a means to ensure safety. Thus, in addition to monitoring the integrity of the railway circuit, our approach also could provide a means for safe operation in that it can be used to detect segments of the rail system that are occupied by trains.
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Frequency Response and Transfer Functions of Large Self-Similar Networks
Abstract Large-scale dynamical systems, no matter whether possessing interconnected appearances, are frequently modeled as networks. For instance, graphs, multi-agent systems, and materials' intricate behaviors are often treated as networked dynamical systems. However, only a few studies have approached the problem in the frequency domain, mostly due to the complexity of evaluating their frequency response. That gap is filled by this paper, which proposes algorithms computing a general class of self-similar networks' frequency response and transfer functions, no matter they are finite or infinite, damaged or undamaged. In addition, this paper shows that for infinite self-similar networks, even when they are damaged, fractional-order and irrational dynamics naturally come into sight. Most importantly, this paper illustrates that for a network under different operating conditions, its frequency response would form a set of neighboring plants, which sets the basis of applying robust control methods to dynamic networks.
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- Award ID(s):
- 1826079
- PAR ID:
- 10431426
- Date Published:
- Journal Name:
- Journal of Dynamic Systems, Measurement, and Control
- Volume:
- 144
- Issue:
- 8
- ISSN:
- 0022-0434
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4054645
