TY - GEN

T1 - Robustness analysis and optimally robust control design via sum-of-squares

AU - Dorobantu, Andrei

AU - Crespo, Luis G.

AU - Seiler, Peter J.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:84881434732

SN - 9781600869372

T3 - Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

BT - Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

T2 - 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

Y2 - 23 April 2012 through 26 April 2012

ER -