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지진 하중을 받는 구조물의 능동 모달 퍼지 제어시스템

2004 년도 대한토목학회 정기 학술대회 보광 휘닉스파크 200 4 년 10 월 21 일. 지진 하중을 받는 구조물의 능동 모달 퍼지 제어시스템. 최강민 , 한국과학기술원 건설 및 환경공학과 조상원 , 한국과학기술원 건설 및 환경공학과 김춘호 , 중부대학교 토목공학과 이인원 , 한국과학기술원 건설 및 환경공학과. Outline. Introduction Proposed Method Numerical Example Conclusions. Introduction.

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지진 하중을 받는 구조물의 능동 모달 퍼지 제어시스템

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  1. 2004년도 대한토목학회 정기 학술대회 보광 휘닉스파크 2004년 10월 21일 지진 하중을 받는 구조물의능동 모달 퍼지 제어시스템 최강민, 한국과학기술원 건설 및 환경공학과 조상원,한국과학기술원 건설 및 환경공학과 김춘호, 중부대학교 토목공학과 이인원, 한국과학기술원 건설 및 환경공학과

  2. Outline • Introduction • Proposed Method • Numerical Example • Conclusions

  3. Introduction • Fuzzy theory has been recently proposed for the active structural control of civil engineering systems. • The uncertainties of input data from the external loads and structural responses are treated in a much easier way by the fuzzy controller than by classical control theory. • If offers a simple and robust structure for the specification of nonlinear control laws.

  4. Input Values (state variables) 입력을 퍼지 제어시스템 내에서 정의되는 퍼지 변수들에 대한 확실성의 정도로 나타내는 퍼지값으로 변환 퍼지규칙표에 따라 퍼지화과정을 통하여 결정되는 입력퍼지값들을 출력에 해당하는 퍼지값으로 변환시켜주는 역할 Fuzzification Fuzzy Inference 이러한 입력에 대한 퍼지값으로의 사상관계를 나타내는 것이 소속함수 퍼지 출력값을 물리적인 의미를 갖는 출력정보로 역환산하는 과정 Defuzzification Output Values

  5. Modal control algorithm represents one control class in which the vibration is reshaped by merely controlling some selected vibration modes. • Because civil structures has hundred or even thousand DOFs and its vibration is usually dominated by first few modes, modal control algorithm is especially desirable for reducing vibration of civil engineering structure.

  6. Conventional Fuzzy Controller • One should determine state variables which are used as inputs of the fuzzy controller. - It is very complicated and difficult for the designer to select state variables used as inputs among a lot of state variables. • One should construct the proper fuzzy rule. - Control performance can be varied according to many kinds of fuzzy rules.

  7. Objectives • Development of active fuzzy controller on modal coordinates - An active modal-fuzzy control algorithm can be magnified efficiency caused by belonging their’ own advantages together.

  8. Proposed Method • Modal Approach • Equations of motion for MDOF system • Using modal transformation • Modal equations (1) (2) (3)

  9. Displacement where • State space equation where (4) (5)

  10. Control force • Modal approach is desirable for civil engineering structure (6) - Involve hundred or thousand DOFs- Vibration is dominated by the first few modes

  11. Active Modal-fuzzy Control System Modal Structure Structure Fuzzy controller Force output

  12. Input variables : mode coordinates • Output variable : desired control force • Modal-fuzzy control system design Fuzzification Output variables Input variables Fuzzy inference Defuzzification • Fuzzy inference : membership functions, fuzzy rule

  13. Numerical Example • Six-Story Building (Jansen and Dyke 2000)

  14. 104 102 • Frequency Response Analysis • Under the scaled El Centro earthquake 6th Floor 1st Floor PSD of Displacement PSD of Velocity PSD of Acceleration

  15. In frequency analysis, the first mode is dominant. • The responses can be reduced by modal-fuzzy control using the lowest one mode.

  16. Active Modal-fuzzy Controller Design • input variables : first mode coordinates • output variable : desired control force • Fuzzy inference • Membership function • - A type : triangular shapes (inputs: 5MFs, output: 5MFs) • - B type : triangular shapes (inputs: 5MFs, output: 7MFs)  A type : for displacement reduction B type : for acceleration reduction

  17. Fuzzy rule - A type - B type

  18. - Fuzzy rule surface (A type)

  19. Input Earthquakes El Centro (PGA: 0.348g) Accel. (m/sec2) California (PGA: 0.156g) Accel. (m/sec2) Kobe (PGA: 0.834g) Accel. (m/sec2) Time(sec)

  20. Evaluation Criteria Normalized maximum floor displacement Normalized maximum inter-story drift Normalized peak floor acceleration Maximum control force normalized by the weight of the structure • This evaluation criteria is used in the second generation linear • control problem for buildings (Spencer et al. 1997)

  21. Control Results Fig. 1 Peak responses of each floor of structure to scaled El Centro earthquake

  22. Normalized Controlled Maximum Response due to • Scaled El Centro Earthquake Fuzzy A type B type J1 J2 J3

  23. High amplitude (the 120% El Centro earthquake) Fuzzy A type B type

  24. Low amplitude (the 80% El Centro earthquake) Fuzzy A type B type

  25. Scaled Kobe earthquake (1995) Fuzzy A type B type

  26. Scaled California earthquake (1994) Fuzzy A type B type

  27. Conclusions • A new active modal-fuzzy control strategy for seismic response reduction is proposed. • Verification of the proposed method has been investigated according to various amplitudes and frequency components. • The performance of the proposed method is comparable to that of conventional method. • The proposed method is more convenient and easy to apply to real system

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