Sum-of-Squares-Based Region of Attraction Analysis for Gain-Scheduled Three-Loop Autopilot

Original Paper
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Abstract

A conventional method of designing a missile autopilot is to linearize the original nonlinear dynamics at several trim points, then to determine linear controllers for each linearized model, and finally implement gain-scheduling technique. The validation of such a controller is often based on linear system analysis for the linear closed-loop system at the trim conditions. Although this type of gain-scheduled linear autopilot works well in practice, validation based solely on linear analysis may not be sufficient to fully characterize the closed-loop system especially when the aerodynamic coefficients exhibit substantial nonlinearity with respect to the flight condition. The purpose of this paper is to present a methodology for analyzing the stability of a gain-scheduled controller in a setting close to the original nonlinear setting. The method is based on sum-of-squares (SOS) optimization that can be used to characterize the region of attraction of a polynomial system by solving convex optimization problems. The applicability of the proposed SOS-based methodology is verified on a short-period autopilot of a skid-to-turn missile.

Keywords

Sum-of-squares optimization Nonlinear stability analysis Region of attraction Autopilot 

Notes

Acknowledgements

This work was supported by “Core Technology Research for the Next Generation of Precision Guided Munitions” Project funded by LIG Nex1.

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Copyright information

© The Korean Society for Aeronautical & Space Sciences and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Pangyo R&D Center of LIG Nex1 Corp.SeongnamRepublic of Korea
  2. 2.Department of Aerospace EngineeringKAISTDaejeonRepublic of Korea

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