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모달 퍼지 이론을 이용한 지진하중을 받는 구조물의 능동제어

2004 년도 한국전산구조공학회 춘계 학술발표회 국민대학교, 서울 200 4 년 4월 1 0 일. 모달 퍼지 이론을 이용한 지진하중을 받는 구조물의 능동제어. 최강민 , 한국과학기술원 건설 및 환경공학과 조상원 , 한국과학기술원 건설 및 환경공학과 오주원 , 한남대학교 토목공학과 이인원 , 한국과학기술원 건설 및 환경공학과. Outline. Introduction Proposed Method Numerical Example Conclusions. Introduction.

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모달 퍼지 이론을 이용한 지진하중을 받는 구조물의 능동제어

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  1. 2004년도 한국전산구조공학회 춘계 학술발표회 국민대학교, 서울 2004년 4월 10일 모달 퍼지 이론을 이용한 지진하중을 받는 구조물의 능동제어 최강민, 한국과학기술원 건설 및 환경공학과 조상원,한국과학기술원 건설 및 환경공학과 오주원, 한남대학교 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. 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.

  5. 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.

  6. 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.

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

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

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

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

  11. 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

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

  13. 104 102 • Frequency Response Analysis • Under the scaled El Centro earthquake 6th Floor 1st Floor PSD of Displacement PSD of Velocity PSD of Acceleration

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

  15. 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

  16. Fuzzy rule - A type - B type

  17. - Fuzzy rule surface (A type)

  18. 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)

  19. 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)

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

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

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

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

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

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

  26. 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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