Journal of the Korea Convergence Society (한국융합학회논문지)

Korea Convergence Society (한국융합학회)
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The Control of Spring-Mass-Damper Convergence System using H∞ Controller and μ-Synthesis Controller

H∞ 제어와 μ-합성 제어를 이용한 스프링-질량-감쇠 융합시스템 제어

  • 정성훈 (초당대학교 항공학부 드론학과)
  • Received : 2017.02.14
  • Accepted : 2017.05.20
  • Published : 2017.05.28
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Abstract

With a given spring-mass-damper system, $H_{\infty}$ and ${\mu}$-synthesis control methods are used to build system controllers which minimize vibrations at two major natural frequencies in two cases; without uncertainty; with 20% uncertainty. In order to check the stability and performance of two controllers, those are examined using GM and PM values. The signal strength of output responses is compared using the concept of central numerical differentiation and then results are quantified using the RMS method. Lastly, 40 random samples of $H_{\infty}$ and ${\mu}$-synthesis controllers are obtained for three different $W_{per\;f1}$ weighting functions and drawn in the time domain in order to compare the stability. Overall, ${\mu}$-synthesis controller manages the vibrations much better than $H_{\infty}$ controller according to the robust stability and performance values obtained by simulating random samples of 40 plant models.

$H_{\infty}$ 제어와 뮤-합성 제어 방법을 사용하여 두 가지 상황, 즉 불확실성이 포함되지 않았을 때와 20% 불확실성이 포함되었을 때, 하에서 스프링-매스-댐퍼 시스템의 진동을 최소화하였다. 두 컨트롤러의 안정성 및 성능 파악을 위해 GM와 PM 값을 사용하여 분석되었다. 중앙 수치 미분법과 RMS 방법을 사용하여 출력 응답의 신호 강도가 비교되었다. 끝으로, 안정성 비교를 위하여 3가지 다른 $W_{per\;f1}$ 가중함수의 경우에 대해 총 40개의 $H_{\infty}$ 제어기와 뮤-합성 제어기 무작위 표본이 생성되었다. 전반적으로, 40개 플랜트 모델에서 얻어진 결과 값의 견고한 안정성과 성능 값에 따르면, 뮤-합성 제어기가 $H_{\infty}$ 제어기보다 진동 관리에 효과적임이 입증되었다.

Keywords

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