1. Structural Dynamics & Vibration Control Lab. 1 Kang-Min Choi, Ph.D. Candidate, KAIST, Korea Jung-Hyun Hong, Graduate Student, KAIST, Korea Ji-Seong Jo, Section Manager, POSCO E&C, Korea In-Won Lee, Professor, KAIST, Korea Active Control for Seismic Response Reduction Using Modal-Fuzzy Approach The 18 th KKCNN Symposium (2005) Kaohsiung, Taiwan Dec. 20-21, 2005

2. Structural Dynamics & Vibration Control Lab., KAIST, Korea 2 CONTENTS Introduction Proposed Method Numerical Example Conclusions

3. Structural Dynamics & Vibration Control Lab., KAIST, Korea 3 Introduction Death : 14,491 Magnitude : 7.4 Sumatra, Indonesia (2004) Recent Earthquakes Death : 5,400 Magnitude : 7.2 Kobe, Japan (1995) Death : 283,106 Magnitude : 9.0 Gebze, Turkey (1999) Kashmir, Pakistan (2005) Death : 30,000 Magnitude : 7.6  To increase the safety and reliability, structural control is required.

4. Structural Dynamics & Vibration Control Lab., KAIST, Korea 4 Passive control system - Vibration control without external power - Energy dissipation of structure - No adaptability to various external load - Large deformation of devices - Examples: Lead rubber bearing, Viscous damper Active control system - Vibration control with external power - Adaptability to various loading conditions - Large external power - Examples: Active mass damper, Hydraulic actuator

5. Structural Dynamics & Vibration Control Lab., KAIST, Korea 5 Control Algorithms Active control algorithms - Linear optimal control algorithm - Sliding mode control algorithm - Adaptive control algorithm - Fuzzy control algorithm - Modal control algorithm

6. Structural Dynamics & Vibration Control Lab., KAIST, Korea 6 Fuzzy control algorithm 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. It offers a simple and robust structure for the specification of nonlinear control laws.

7. Structural Dynamics & Vibration Control Lab., KAIST, Korea 7 Modal control algorithm represents one control class in which the vibration is reshaped by merely controlling some selected vibration modes. Civil structures has hundred or even thousand DOFs. its vibration is usually dominated by first few modes, modal control algorithm is especially desirable for reducing vibration of civil structure.

8. Structural Dynamics & Vibration Control Lab., KAIST, Korea 8 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.

9. Structural Dynamics & Vibration Control Lab., KAIST, Korea 9 Objective Development of active fuzzy control algorithm on modal coordinates

10. Structural Dynamics & Vibration Control Lab., KAIST, Korea 10 Proposed Method Modal Algorithm - Equation of motion for MDOF system (2) - Using modal transformation (3) - Modal equation (4)

11. Structural Dynamics & Vibration Control Lab., KAIST, Korea 11 (5) (6) - Displacement - State space equation Controlled displacement Residual displacement

12. Structural Dynamics & Vibration Control Lab., KAIST, Korea 12  Modal algorithm is desirable for civil structure. - Civil structure involves tens or hundreds of thousands DOFs. - Vibration is dominated by the first few modes.

13. Structural Dynamics & Vibration Control Lab., KAIST, Korea 13 Active Modal-fuzzy Control System Structure Fuzzy Controller Modal Structure

14. Structural Dynamics & Vibration Control Lab., KAIST, Korea 14 Modal-fuzzy control system Input variables Output variables Fuzzification Defuzzification Fuzzy inference Fuzzy inference : membership functions, fuzzy rule Input variables : mode coordinates Output variable : desired control force

15. Structural Dynamics & Vibration Control Lab., KAIST, Korea 15 - Development of fuzzy controller on modal coordinates - Easy to select fuzzy input variables - Use of information of all DOFs - Serviceability of modal approach - Easy to treat the uncertainties of input data - Robustness of fuzzy controller Characteristics

16. Structural Dynamics & Vibration Control Lab., KAIST, Korea 16 Six-Story Building (Jansen and Dyke 2000) Numerical Example - System data Mass of each floor : 0.277 N/(cm/sec 2 ) Stiffness : 297 N/cm Damping ratio : 0.5% for each mode

17. Structural Dynamics & Vibration Control Lab., KAIST, Korea 17 Frequency Response Analysis - Under the scaled El Centro earthquake 1 st Floor 6 th Floor Frequency, Hz  10 3  10 4  10 2  10 5  10 7  10 6 12 8 4 10 8 6 4 2 86428642 5432154321 5432154321 86428642 PSD PSD of Displacement PSD of Velocity PSD of Acceleration

18. Structural Dynamics & Vibration Control Lab., KAIST, Korea 18 In frequency analysis, the first mode is dominant. - The responses can be reduced by modal-fuzzy control using the lowest one mode.

19. Structural Dynamics & Vibration Control Lab., KAIST, Korea 19 Active Optimal Controller Design (LQR) Cost function (7) where Q : placing a weighting 9000(cm -2 ) on the relative displacements of all floors

20. Structural Dynamics & Vibration Control Lab., KAIST, Korea 20 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 

21. Structural Dynamics & Vibration Control Lab., KAIST, Korea 21 - Membership functions NLNSZEPSPL -xx0 Input membership function Output membership function NLNSZEPSPM -yy0 NM PL : Negative Large : Negative Small : Zero : Positive Small : Positive Large NL NS ZE PS PL : Negative Large : Negative Medium : Negative Small : Zero : Positive Small : Positive Medium : Positive Large NL NM NS ZE PS PM PL

22. Structural Dynamics & Vibration Control Lab., KAIST, Korea 22 Fuzzy rule - A type NLNSZEPSPL NLPL PMPSZE NSPLPMPSZENS ZEPMPSZENSNM PS ZENSNMNL PLZENSNMNL - B type NLNSZEPSPL NLPL PS ZE NSPLPS ZENS ZEPS ZENS PS ZENS NL PLZENSNL

23. Structural Dynamics & Vibration Control Lab., KAIST, Korea 23 Accel. (m/sec 2 ) El Centro (PGA: 0.348g) Input Earthquakes Medium amplitude (100% El Centro earthquake) High amplitude (120% El Centro earthquake) Low amplitude (80% El Centro earthquake)

24. Structural Dynamics & Vibration Control Lab., KAIST, Korea 24 Normalized maximum floor displacement Normalized maximum inter-story drift Normalized peak floor acceleration Maximum control force normalized by the weight of the structure - Evaluation criteria are used in the second generation linear control problem for buildings (Spencer et al. 1997) Evaluation Criteria

25. Structural Dynamics & Vibration Control Lab., KAIST, Korea 25 Control Results Fig. 1 Peak responses of each floor of structure to scaled El Centro earthquake Peak interstory drift (cm) Floor of structure Peak absolute acceleration (cm/s 2 ) Floor of structure

26. Structural Dynamics & Vibration Control Lab., KAIST, Korea 26 - Though the proposed Type A performs significantly better than other systems restricted within the interstory drift, but the performance of peak acceleration is not good. - A well designed proposed Type B balances the benefits of the different objectives within the requirements of the specific design scenario. Observations

27. Structural Dynamics & Vibration Control Lab., KAIST, Korea 27 Control strategyJ1J1 J2J2 J3J3 J4J4 Optimal LQR Active Modal-fuzzy control (A type) Active Modal-fuzzy control (B type) 0.479 0.343 0.548 0.626 0.562 0.635 0.685 1.186 0.601 0.0178 0.0134 Medium amplitude

28. Structural Dynamics & Vibration Control Lab., KAIST, Korea 28 - Performance of proposed Type B is comparable to optimal control. - Control force is relatively small compared to those of other controllers. Observations J1J1 J2J2 J3J3 Evaluation criteria Reduction factor J 4 ×10

29. Structural Dynamics & Vibration Control Lab., KAIST, Korea 29 Control strategyJ1J1 J2J2 J3J3 J4J4 Optimal LQR Active Modal-fuzzy control (A type) Active Modal-fuzzy control (B type) 0.479 0.374 0.607 0.610 0.594 0.623 0.912 1.545 0.701 0.0178 0.0134 High amplitude J1J1 J2J2 J3J3 Evaluation criteria Reduction factor J 4 ×10

30. Structural Dynamics & Vibration Control Lab., KAIST, Korea 30 Low amplitude Control strategyJ1J1 J2J2 J3J3 J4J4 Optimal LQR Active Modal-fuzzy control (A type) Active Modal-fuzzy control (B type) 0.474 0.289 0.504 0.657 0.573 0.624 0.586 1.386 0.773 0.0178 0.0134 J1J1 J2J2 J3J3 Evaluation criteria Reduction factor J 4 ×10

31. Structural Dynamics & Vibration Control Lab., KAIST, Korea 31 - Proposed method Type B gives comparable performance to optimal controller. - Moreover, it is much easier to design control system than optimal controller. Observations - Control force is relatively small compared to those of other controllers.

32. Structural Dynamics & Vibration Control Lab., KAIST, Korea 32 - Phase plane trajectory (Battaini et al. 1998) Technique to reflect graphically the dynamic properties of control system in phase plane. - Stability test for worst case of floor displacement Stability of proposed control system Displacement (cm) Time (sec)

33. Structural Dynamics & Vibration Control Lab., KAIST, Korea 33 - Stability test for worst case of floor acceleration - Stability test for worst case of control force  Proposed control system is stable. Acceleration (g) Time (sec) Control force (N) Time (sec)

34. Structural Dynamics & Vibration Control Lab., KAIST, Korea 34 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 amplitude earthquakes.

35. Structural Dynamics & Vibration Control Lab., KAIST, Korea 35 The performance of proposed method is comparable to optimal controller. The proposed method is convenient, simple and easy to apply to real civil structures.

36. Structural Dynamics & Vibration Control Lab., KAIST, Korea 36 Thank you for your attention!