Journal of the Institute of Electronics and Information Engineers (전자공학회논문지)

The Institute of Electronics and Information Engineers (대한전자공학회)
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Robust and Non-fragile H∞ Controller Design Algorithm for Time-delayed System with Randomly Occurring Uncertainties and Disturbances )

임의발생 불확실성 및 외란을 고려한 시간지연시스템의 강인비약성 H∞ 제어기 설계 알고리듬

  • Yang, Seung Hyeop (School of Electronics Engineering, the College of IT Engineering, Kyungpook National University) ;
  • Paik, Seung Hyun (School of Electronics Engineering, the College of IT Engineering, Kyungpook National University) ;
  • Lee, Jun Yeong (School of Electronics Engineering, the College of IT Engineering, Kyungpook National University) ;
  • Park, Hong Bae (School of Electronics Engineering, the College of IT Engineering, Kyungpook National University)
  • 양승협 (경북대학교 IT대학 전자공학부) ;
  • 백승현 (경북대학교 IT대학 전자공학부) ;
  • 이준영 (경북대학교 IT대학 전자공학부) ;
  • 박홍배 (경북대학교 IT대학 전자공학부)
  • Received : 2015.08.03
  • Accepted : 2015.12.01
  • Published : 2015.12.25
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Abstract

This paper provides a robust and non-fragile $H_{\infty}$ controller design algorithm for time-delayed systems with randomly occurring polytopic uncertainties and disturbances. First, we design time-delayed system considering randomly occurring uncertainties and disturbances. Next, The sufficient condition for the existence of robust and non-fragile $H_{\infty}$ controller is presented by LMI(linear matrix inequality) using Lyapunov stability analysis and $H_{\infty}$ performance measure. Since the obtained condition can be expressed as a PLMI(parameterized linear matrix inequality) by changes of variables and Schur complement, all solutions including controller gain, degrees of controller satisfying non-fragility, $H_{\infty}$ norm bound ${\gamma}$ can be calculated simultaneously. Finally, numerical examples are given to illustrate the performance and the effectiveness of the proposed robust and non-fragile $H_{\infty}$ controller compared with the deterministic uncertainty model even though there exists randomly occurring uncertainties, disturbances and time delays.

본 논문에서는 임의적으로 발생하는 폴리토프 불확실성과 외란을 고려한 시간지연시스템의 강인비약성 $H_{\infty}$ 제어기설계 알고리듬을 다룬다. 먼저 임의적으로 발생하는 불확실성과 외란을 가지는 시간지연시스템을 설계하고, Lyapunov 안정성 분석과 $H_{\infty}$ 성능지수를 기반으로 강인비약성 $H_{\infty}$ 제어기가 존재하기 위한 충분조건을 선형행렬부등식(LMI, linear matrix inequality)의 형태로 제시한다. 구한 충분조건은 변수치환과 슈어 여수(Schur complement) 정리를 바탕으로 파라미터의 함수를 포함한 파라미터화 선형행렬부등식(PLMI, parameterized linear matrix inequality)으로 표현할 수 있으므로 PLMI의 모든 해로부터 제어기이득과 비약성을 만족하는 제어기 섭동영역 및 $H_{\infty}$ 성능을 만족하는 노옴 한계치 ${\gamma}$를 한번에 구할 수 있다. 마지막으로 예제와 모의실험에서 제안한 강인비약성 $H_{\infty}$ 제어기가 임의적으로 발생하는 불확실성 및 외란, 시간지연이 있더라도 폐루프시스템을 안정화시키고 $H_{\infty}$ 성능을 보장함을 확인하고 확정적인 불확실성을 기반으로 설계한 제어기와 성능을 비교한다.

Keywords

Acknowledgement

Supported by : 경북대학교

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