Approximating a MIMO, 1D Diffusion System to a Low Order, State-Space Form in Order to Facilitate Controller Design
Chemical distribution is an important factor in many biological systems, driving the phenomenon known as chemotaxis. In order to properly study the effects of various chemical inputs to an in vitro biological assay, it is necessary to have strict control over the spatial distribution of these chemic...
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| Format: | Article |
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ASME International
2018
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| Online Access: | http://hdl.handle.net/1721.1/118779 https://orcid.org/0000-0002-9898-2377 https://orcid.org/0000-0003-3155-6223 |
| _version_ | 1811076864815398912 |
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| author | Schor, Alisha R Asada, Haruhiko |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Schor, Alisha R Asada, Haruhiko |
| author_sort | Schor, Alisha R |
| collection | MIT |
| description | Chemical distribution is an important factor in many biological systems, driving the phenomenon known as chemotaxis. In order to properly study the effects of various chemical inputs to an in vitro biological assay, it is necessary to have strict control over the spatial distribution of these chemicals. This distribution is typically governed by diffusion, which by nature is a distributed parameter system (DPS), dependent on both space and time. Much study and literature within the controls community has been devoted to DPS, whose dynamics are marked by partial differential equations or delays. They span an infinite-dimensional state-space, and the mathematical complexity associated with this leads to the development of controllers that are often highly abstract in nature. In this paper, we present a method of approximating these systems and expressing them in a manner that makes a DPS amenable to control using a very low order model. In particular, we express the PDE for one-dimensional chemical diffusion as a two-input, two-output state-space system and show that standard controllers can manipulate the outputs of interest, using pole placement and integral control via an augmented state model. Copyright © 2010 by ASME. |
| first_indexed | 2024-09-23T10:29:14Z |
| format | Article |
| id | mit-1721.1/118779 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T10:29:14Z |
| publishDate | 2018 |
| publisher | ASME International |
| record_format | dspace |
| spelling | mit-1721.1/1187792022-09-30T21:29:07Z Approximating a MIMO, 1D Diffusion System to a Low Order, State-Space Form in Order to Facilitate Controller Design Schor, Alisha R Asada, Haruhiko Massachusetts Institute of Technology. Department of Mechanical Engineering Schor, Alisha R Asada, Haruhiko Chemical distribution is an important factor in many biological systems, driving the phenomenon known as chemotaxis. In order to properly study the effects of various chemical inputs to an in vitro biological assay, it is necessary to have strict control over the spatial distribution of these chemicals. This distribution is typically governed by diffusion, which by nature is a distributed parameter system (DPS), dependent on both space and time. Much study and literature within the controls community has been devoted to DPS, whose dynamics are marked by partial differential equations or delays. They span an infinite-dimensional state-space, and the mathematical complexity associated with this leads to the development of controllers that are often highly abstract in nature. In this paper, we present a method of approximating these systems and expressing them in a manner that makes a DPS amenable to control using a very low order model. In particular, we express the PDE for one-dimensional chemical diffusion as a two-input, two-output state-space system and show that standard controllers can manipulate the outputs of interest, using pole placement and integral control via an augmented state model. Copyright © 2010 by ASME. Singapore-MIT Alliance for Research and Technology (SMART) Massachusetts Institute of Technology (Presidential Fellowship) Massachusetts Institute of Technology (Martin Fellowship in Design) 2018-10-25T17:21:35Z 2018-10-25T17:21:35Z 2010-09 2018-10-23T13:37:19Z Article http://purl.org/eprint/type/ConferencePaper 978-0-7918-4417-5 http://hdl.handle.net/1721.1/118779 Schor, Alisha R., and H. Harry Asada. “Approximating a MIMO, 1D Diffusion System to a Low Order, State-Space Form in Order to Facilitate Controller Design.” ASME 2010 Dynamic Systems and Control Conference, Volume 1, 12-15 September, Cambridge, Massachusetts, 2010, ASME, 2010, pp. 333–40. https://orcid.org/0000-0002-9898-2377 https://orcid.org/0000-0003-3155-6223 http://dx.doi.org/10.1115/DSCC2010-4071 ASME 2010 Dynamic Systems and Control Conference, Volume 1 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf ASME International ASME |
| spellingShingle | Schor, Alisha R Asada, Haruhiko Approximating a MIMO, 1D Diffusion System to a Low Order, State-Space Form in Order to Facilitate Controller Design |
| title | Approximating a MIMO, 1D Diffusion System to a Low Order, State-Space Form in Order to Facilitate Controller Design |
| title_full | Approximating a MIMO, 1D Diffusion System to a Low Order, State-Space Form in Order to Facilitate Controller Design |
| title_fullStr | Approximating a MIMO, 1D Diffusion System to a Low Order, State-Space Form in Order to Facilitate Controller Design |
| title_full_unstemmed | Approximating a MIMO, 1D Diffusion System to a Low Order, State-Space Form in Order to Facilitate Controller Design |
| title_short | Approximating a MIMO, 1D Diffusion System to a Low Order, State-Space Form in Order to Facilitate Controller Design |
| title_sort | approximating a mimo 1d diffusion system to a low order state space form in order to facilitate controller design |
| url | http://hdl.handle.net/1721.1/118779 https://orcid.org/0000-0002-9898-2377 https://orcid.org/0000-0003-3155-6223 |
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