Gradient projection anti-windup scheme
Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2011
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| Online Access: | http://hdl.handle.net/1721.1/63043 |
| _version_ | 1811069440258736128 |
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| author | Teo, Chun Sang Justin |
| author2 | Jonathan Patrick How. |
| author_facet | Jonathan Patrick How. Teo, Chun Sang Justin |
| author_sort | Teo, Chun Sang Justin |
| collection | MIT |
| description | Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011. |
| first_indexed | 2024-09-23T08:10:32Z |
| format | Thesis |
| id | mit-1721.1/63043 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T08:10:32Z |
| publishDate | 2011 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/630432022-01-13T07:54:11Z Gradient projection anti-windup scheme Teo, Chun Sang Justin Jonathan Patrick How. Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Aeronautics and Astronautics. Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011. Cataloged from PDF version of thesis. Includes bibliographical references (p. 205-217). It is a well-recognized fact that control saturation affects virtually all practical control systems. It leads to controller windup, which degrades/limits the system's closed-loop performance, and may cause catastrophic failures if it induces instability. Anti-windup compensation is one of two main approaches to mitigate the effects of windup, and is conceptually and practically attractive. For the idealized case of constrained linear time invariant (LTI) plants driven by LTI controllers, numerous anti-windup schemes exist. However, most practical control systems are inherently nonlinear, and anti-windup compensation for nonlinear systems remains largely an open problem. To this end, we propose the gradient projection anti-windup (GPAW) scheme, which is an extension of the conditional integration method to multi-input-multi-output (MIMO) nonlinear systems, using Rosen's gradient projection method for nonlinear programming. It achieves controller state-output consistency by projecting the controller state onto the unsaturated region induced by the control saturation constraints. The GPAW-compensated controller is a hybrid controller defined by the online solution to either a combinatorial optimization subproblem, a convex quadratic program, or a projection onto a convex polyhedral cone problem. We show that the GPAW-compensated system is obtained by modifying the uncompensated system with a passive operator. Qualitative weaknesses of some existing anti-windup results are established, which motivated a new paradigm to address the anti-windup problem. It is shown that for a constrained first order LTI plant driven by a first order LTI controller, GPAW compensation can only maintain/enlarge its region of attraction (ROA). In this new paradigm, we derived some ROA comparison and stability results for MIMO nonlinear as well as MIMO LTI systems. The thesis is not that the GPAW scheme solves a centuries-old open problem of immense practical importance, but rather, that it provides a potential path to a solution. We invite the reader to join us in this quest at the confluence of nonlinear systems, hybrid systems, projected dynamical systems, differential equations with discontinuous right-hand sides, combinatorial optimization, convex analysis and optimization, and passive systems. by Chun Sang Justin Teo. Sc.D. 2011-05-23T18:07:35Z 2011-05-23T18:07:35Z 2011 2011 Thesis http://hdl.handle.net/1721.1/63043 722800079 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 217 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Aeronautics and Astronautics. Teo, Chun Sang Justin Gradient projection anti-windup scheme |
| title | Gradient projection anti-windup scheme |
| title_full | Gradient projection anti-windup scheme |
| title_fullStr | Gradient projection anti-windup scheme |
| title_full_unstemmed | Gradient projection anti-windup scheme |
| title_short | Gradient projection anti-windup scheme |
| title_sort | gradient projection anti windup scheme |
| topic | Aeronautics and Astronautics. |
| url | http://hdl.handle.net/1721.1/63043 |
| work_keys_str_mv | AT teochunsangjustin gradientprojectionantiwindupscheme |