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Modified Bang-Bang Control of Seismically Excited Structures Using MR Dampers

KAIST-Kyoto Univ. Joint Seminar Daejeon, Korea February 25, 2002. Modified Bang-Bang Control of Seismically Excited Structures Using MR Dampers. Sang-Won Cho* : Ph.D. Student, KAIST Ji-Sung Jo : Ph.D. Student, KAIST In-Won Lee : Professor, KAIST. CONTENTS. Introduction

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Modified Bang-Bang Control of Seismically Excited Structures Using MR Dampers

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  1. KAIST-Kyoto Univ. Joint Seminar Daejeon, Korea February 25, 2002 Modified Bang-Bang Control of Seismically Excited Structures Using MR Dampers Sang-Won Cho* : Ph.D. Student, KAIST Ji-Sung Jo : Ph.D. Student, KAIST In-Won Lee : Professor, KAIST

  2. CONTENTS • Introduction • Semi-Active Control • Proposed Control Algorithm • Numerical Example • Conclusions and Further Studies Structural Dynamics & Vibration Control Lab., KAIST, Korea

  3. Introduction • Recent Earthquakes • Kobe, Japan (1995) 5,400 of death and 1.5 trillion won of damage • Gebze, Turkey (1999) 14,491 of death and 13 trillion won of damage • Chi-Chi, Taiwan (1999) 2,161 of death and 9.2 trillion won of damage To increase the safety and reliability, structural control is required Structural Dynamics & Vibration Control Lab., KAIST, Korea

  4. Structural Control Strategies • Active control • Use external control force to reduce the responses • Large external power • The problem of reliability under earthquake • Active Mass Damper (AMD) • Passive control • Increase the capacity of energy dissipation of structure • No external power • No adaptability to various external load • Lead Rubber Bearing (LRB) Structural Dynamics & Vibration Control Lab., KAIST, Korea

  5. Semi-active control • Change the characteristics of control devices • Small external power • Reliability of passive system with adaptability of active system • Variable-orifice damper, MR/ER damper Structural Dynamics & Vibration Control Lab., KAIST, Korea

  6. Semi-Active Control Devices • Variable-orifice damper Feng and Shinozuka (1990), Kawashima et al. (1992) • Variable-friction damper Akbay and Aktan (1990), Kannan et al. (1995) • Semi-active impact damper Masri and Yang (1973), Papalou and Masri(1996) Structural Dynamics & Vibration Control Lab., KAIST, Korea

  7. Controllable fluid damper • Electrorheorogical fluid damper (ER damper) Ergott and Masri(1992) • Magnetorheorogical fluid damper (MR damper) Carlson et al. (1994) Table 1 Properties of MR and ER Fluids Structural Dynamics & Vibration Control Lab., KAIST, Korea

  8. MR Damper • Characteristics of MR fluid With Magnetic Fields Without Magnetic Fields Wires to Electromgnet Diaphragm MR Fluid Coil Bearing & Seal Accumulator Structural Dynamics & Vibration Control Lab., KAIST, Korea

  9. x (1) • Modeling of MR damper • Model of the parallel-plate MR damper (Jansen et al. 2000) f c0 • Voltage dependence of the damper parameters (2) v : commanded voltage Indirect control command is used Structural Dynamics & Vibration Control Lab., KAIST, Korea

  10. Objective and Scope To develop an efficient semi-active control strategies considering the characteristics of MR damper Structural Dynamics & Vibration Control Lab., KAIST, Korea

  11. Semi-Active Control • Semi-Active Control Algorithms • Karnopp et al. (1974) “Skyhook” damper control algorithm • Feng and Shinozukah (1990) Bang-Bang controller for a hybrid controller on bridge • Brogan (1991), Leitmann (1994) Lyapunov stability theory for ER dampers • McClamroch and Gavin (1995) Decentralized Bang-Bang controller Structural Dynamics & Vibration Control Lab., KAIST, Korea

  12. Inaudi (1997) : Modulated homogeneous friction algorithm for a variable friction device • Sack et al. (1994), Dyke (1996) : Clipped optimal controllers for semi-active devices Structural Dynamics & Vibration Control Lab., KAIST, Korea

  13. Clipped-Optimal Control (Dyke et al. 1996) • Optimal control with clipped algorithm • Optimal control • State-space equation • Cost function (3) (4) Structural Dynamics & Vibration Control Lab., KAIST, Korea

  14. (5) • Optimal control algorithm K : solution of Ricatti equation (6) • Control force is linear to the state of structure- No consideration of saturation Structural Dynamics & Vibration Control Lab., KAIST, Korea

  15. Clipped algorithm • Indirect control command to MR damper • Control voltage v , instead of control force (7) fc : calculated optimal control force fi : control force of MR damper H : Heaviside step function vi : control voltage Structural Dynamics & Vibration Control Lab., KAIST, Korea

  16. Proposed Control Strategy : Clipped Decentralized Bang-Bang Control (CDBBC) • Decentralized Bang-Bang Control • To use full capacity of MR damper • To consider the saturation of MR damper • High speed switching control command • Clipped algorithm • Indirect control command Structural Dynamics & Vibration Control Lab., KAIST, Korea

  17. Decentralized Bang-Bang Control (McClamroch and Gavin, 1995) • Based on Lyapunov stability theory • Lyapunov function V(z) • Derivative of Lyapunov function (8) (9) Structural Dynamics & Vibration Control Lab., KAIST, Korea

  18. (10) • Control law which minimize Eq.(9) • Approximate sign function • Modified decentralized bang-bang control (11) (12) where Structural Dynamics & Vibration Control Lab., KAIST, Korea

  19. Clipped algorithm • Indirect control command to MR damper • Control voltage v , instead of control force (13) fc : calculated CMBB Control force fi : control force of MR damper (nonlinear) H : Heaviside step function vi : control voltage Structural Dynamics & Vibration Control Lab., KAIST, Korea

  20. Block diagram of proposed control algorithm Structure MR Damper ` Clipped Algorithm Modified DBB Control Clipped Modified Decentralized Bang-Bang Control (CMDBBC) Structural Dynamics & Vibration Control Lab., KAIST, Korea

  21. Numerical Examples • Three-Story Building (Dyke at al. 1996) v f Control Computer Structural Dynamics & Vibration Control Lab., KAIST, Korea

  22. System matrices Structural Dynamics & Vibration Control Lab., KAIST, Korea

  23. Damper modeling and parameters Bouc-Wen c0 c0 k1 k1 c1 c1 k0 k0 Modified Bouc-Wen Model Structural Dynamics & Vibration Control Lab., KAIST, Korea

  24. 3 Modes of MR damper • Passive-off : input Voltage = 0 V • Passive-on : input Voltage = 2.5 V • Semi-Active : switching on and off according to control algorithm Structural Dynamics & Vibration Control Lab., KAIST, Korea

  25. Structural responses by CMDBBC (Under El Centro Earthquake, at 3rd floor) Uncontrolled CMDBBC Structural Dynamics & Vibration Control Lab., KAIST, Korea

  26. Peak responses under El Centro Earthquake Structural Dynamics & Vibration Control Lab., KAIST, Korea

  27. Discussions • Performance of CMDBBC • Measured control forces • Capacity of MR damper : 3000N (104% of total weight) Unsaturated condition !! Structural Dynamics & Vibration Control Lab., KAIST, Korea

  28. Peak responses under scaled El Centro earthquake Structural Dynamics & Vibration Control Lab., KAIST, Korea

  29. Conclusions • Proposed Clipped modified decentralized bang-bang control reduce the structural responses from the uncontrolled value • Performance of proposed is not better than clipped optimal control under unsaturated condition • For the strong earthquake (i.e. saturated condition), proposed control is superior in reducing the responses Structural Dynamics & Vibration Control Lab., KAIST, Korea

  30. Further Studies • Clipped Modified Decentralized Bang-Bang Control • Improve the performance • Apply to full-scale MR damper • Experimental Studies • Shaking table test • Full-scale MR damper test Structural Dynamics & Vibration Control Lab., KAIST, Korea

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