Topics in Modeling and Control of Spatially Distributed Systems
- Degree Grantor:
- University of California, Santa Barbara. Electrical and Computer Engineering
- Degree Supervisor:
- Bassam Bamieh
- Place of Publication:
- [Santa Barbara, Calif.]
- Publisher:
- University of California, Santa Barbara
- Creation Date:
- 2014
- Issued Date:
- 2014
- Topics:
- Engineering, Mechanical and Engineering, Electronics and Electrical
- Keywords:
- Distributed-parameter systems,
Optimal Periodic Contol,
Thermoacoustics,
Thermoacoustic Instabilities,
Control Engineering, and
Rijke Tube - Genres:
- Online resources and Dissertations, Academic
- Dissertation:
- Ph.D.--University of California, Santa Barbara, 2014
- Description:
This dissertation consists of three parts centered around the topic of spatially distributed systems.
The first part treats a specific spatially distributed system, the so-called Rijke tube, an experiment illustrating the unstable interplay of heat exchange and gas dynamics. The experiment is described in detail and it is demonstrated how closed-loop system identification tools can be applied to obtain a transfer function model, before a spatially distributed model is developed and analyzed. The model in its most idealized form can be described in the frequency domain by a matrix of non-rational transfer functions, which facilitates analysis with classical methods such as the root locus.
The second part considers the following problem: for a given plant and cost function, could there be a finite-length periodic trajectory that achieves better performance than the optimal steady state? Termed optimal periodic control (OPC), this problem has received attention over several decades, however most available methods employ state-space based methods and hence scale very badly with plant dimension. Here, the problem is approached from a frequency-domain perspective, and methods whose complexity is independent of system dimension are developed by recasting the OPC problem for linear plants with certain memoryless polynomial nonlinearities as the problem of minimizing a polynomial.
Finally, the third part extends results for a special class within spatially distributed systems, that of spatially invariant systems, from systems defined on [special character omitted]2 (square-integrable) spaces to systems whose state space is an inner-product Sobolev space as they arise when considering systems of higher temporal order. It is shown how standard results on exponential stability, stabilizability and LQ control can be generalized by carefully keeping track of spatial frequency weighting functions related to the Sobolev inner products, and simple recipes for doing so are given.
- Physical Description:
- 1 online resource (161 pages)
- Format:
- Text
- Collection(s):
- UCSB electronic theses and dissertations
- Other Versions:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3682897
- ARK:
- ark:/48907/f3gf0rpp
- ISBN:
- 9781321567724
- Catalog System Number:
- 990045118200203776
- Copyright:
- Jonathan Epperlein, 2014
- Rights:
- In Copyright
- Copyright Holder:
- Jonathan Epperlein
File | Description |
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Access: Public access | |
Epperlein_ucsb_0035D_12445.pdf | pdf (Portable Document Format) |