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State weighted model reduction based on frequency weighted gramians and its application to micro inertial sensors

서울대학교 대학원
Publication Date
  • Model Reduction
  • 모델 축소
  • Balanced Structure
  • 평형 구조
  • Frequency Weighted Gramians
  • 주파수 가중 그래미언
  • Rebalance Loop
  • 상태 가중 모델 축소
  • Micro Inertial Sensor
  • 오차 노옴 상한
  • 재평형루프
  • Computer Science


<B3EDB9AE20C7A5C1F62E687770> Abstract In this dissertation, the novel frequency weighted Gramians and two state weighted model reduction algorithms are proposed. The frequency weighted Gramians are defined in frequency domain which have frequency weighting fac- tors to accentuate the input-output behavior of each state individually in any given frequency range. The Gramians can be obtained using similar Lyapunov equations to the case of the conventional time domain Gramians, which means that the proposed Gramians can reflect the controllability and observability of the system, and have similar properties to the conventional Gramians. The state weighted model reduction algorithm is based on state weighting technique with the use of frequency weighted Gramians. It is more flexi- ble and useful than other algorithms that only put weightings on inputs or outputs. With the proposed state weighted model reduction algorithm, the interested state can be made to have more influence on the reduced system in the specified frequency range, resulting in small model reduction errors with little sacrifice in performance, especially in some concerned frequency range. Furthermore, the stability of the reduced system is guaranteed by choosing Copyright(c)2002 by Seoul National University Library. All rights reserved.( 2003/08/21 17:52:19 reasonable weighting functions, and the infinity norm error bound is provided. Unfortunately, the state weighted model reduction algorithm cannot guar- antee the stability of the reduced model for the arbitrary weighting function. Moreover, the proposed infinity norm error bound is somewhat conservative. These shortcomings can be overcome using the modified state weighted model reduction algorithm proposed in this dissertation. The modified state weighted model reduction algorithm is to truncate unimportant states whose Gramians are small, or equivalently, which are less controllable and observa

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