On approximate dynamic inversion and proportional-integral control
Approximate dynamic inversion (ADI) has been established as a method to control minimum-phase, nonaffine-in-control systems. Previous results have shown that for single-input nonaffine-in-control systems, every ADI controller admits a linear proportional-integral (PI) realization that is largely ind...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2010
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| Online Access: | http://hdl.handle.net/1721.1/52566 https://orcid.org/0000-0001-8576-1930 |
| _version_ | 1811092308150452224 |
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| author | Teo, Justin How, Jonathan P. Lavretsky, Eugene |
| author2 | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics |
| author_facet | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Teo, Justin How, Jonathan P. Lavretsky, Eugene |
| author_sort | Teo, Justin |
| collection | MIT |
| description | Approximate dynamic inversion (ADI) has been established as a method to control minimum-phase, nonaffine-in-control systems. Previous results have shown that for single-input nonaffine-in-control systems, every ADI controller admits a linear proportional-integral (PI) realization that is largely independent of the nonlinear function that defines the system. This paper extends these previous results in three ways. First, we present an extension of ADI that renders the closed loop error dynamics independent of the reference model dynamics. It is then shown that the equivalence between the ADI and PI controllers only holds for the time response when applied to the exact system. Finally, key robustness properties of the two control approaches are compared using linear system techniques. These results indicate that the PI realization is preferable when accurate knowledge of the nonlinear system dynamics is not available, and that the ADI realization would be preferred if time delays are the major limitations in the system. |
| first_indexed | 2024-09-23T15:16:20Z |
| format | Article |
| id | mit-1721.1/52566 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:16:20Z |
| publishDate | 2010 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/525662022-09-29T13:47:13Z On approximate dynamic inversion and proportional-integral control Teo, Justin How, Jonathan P. Lavretsky, Eugene Massachusetts Institute of Technology. Department of Aeronautics and Astronautics How, Jonathan P. Teo, Justin How, Jonathan P. Approximate dynamic inversion (ADI) has been established as a method to control minimum-phase, nonaffine-in-control systems. Previous results have shown that for single-input nonaffine-in-control systems, every ADI controller admits a linear proportional-integral (PI) realization that is largely independent of the nonlinear function that defines the system. This paper extends these previous results in three ways. First, we present an extension of ADI that renders the closed loop error dynamics independent of the reference model dynamics. It is then shown that the equivalence between the ADI and PI controllers only holds for the time response when applied to the exact system. Finally, key robustness properties of the two control approaches are compared using linear system techniques. These results indicate that the PI realization is preferable when accurate knowledge of the nonlinear system dynamics is not available, and that the ADI realization would be preferred if time delays are the major limitations in the system. 2010-03-15T12:08:54Z 2010-03-15T12:08:54Z 2009-07 2009-06 Article http://purl.org/eprint/type/ConferencePaper 978-1-4244-4523-3 0743-1619 INSPEC Accession Number: 10775974 http://hdl.handle.net/1721.1/52566 Teo, J., J.P. How, and E. Lavretsky. “On Approximate Dynamic Inversion and Proportional-Integral control.” American Control Conference, 2009. ACC '09. 2009. 1592-1597. https://orcid.org/0000-0001-8576-1930 en_US http://dx.doi.org/10.1109/ACC.2009.5160598 Proceedings of the 2009 American Control Conference Attribution-Noncommercial-Share Alike 3.0 Unported http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers author/dept web page |
| spellingShingle | Teo, Justin How, Jonathan P. Lavretsky, Eugene On approximate dynamic inversion and proportional-integral control |
| title | On approximate dynamic inversion and proportional-integral control |
| title_full | On approximate dynamic inversion and proportional-integral control |
| title_fullStr | On approximate dynamic inversion and proportional-integral control |
| title_full_unstemmed | On approximate dynamic inversion and proportional-integral control |
| title_short | On approximate dynamic inversion and proportional-integral control |
| title_sort | on approximate dynamic inversion and proportional integral control |
| url | http://hdl.handle.net/1721.1/52566 https://orcid.org/0000-0001-8576-1930 |
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