Robustness analysis and optimally robust control design via sum-of-squares

Andrei Dorobantu, Luis G. Crespo, Peter J. Seiler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

A control analysis and design framework is proposed for systems subject to paramet- ric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, defined as inequality con- straints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, cal- culated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggre- gate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.

Original languageEnglish (US)
Title of host publicationCollection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
StatePublished - 2012
Event53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference - Honolulu, HI, United States
Duration: Apr 23 2012Apr 26 2012

Publication series

NameCollection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
ISSN (Print)0273-4508

Other

Other53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
CountryUnited States
CityHonolulu, HI
Period4/23/124/26/12

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