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

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

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) 능동제어기법은 외부제어력으로 구조물의 응답을 감소시키는 ‘방식’이다. 따라서 대규모의 외부 전력이 필요하다 그러므로 지진시에 전력차단과 같은 신뢰성에 문제가 있다. 이에 비해서 수동제어 방식은 구조물의 에너지 소산능력을 증가시키는 방식이다. 따라서 외부입력전원이 필요가 없다. Structural Dynamics & Vibration Control Lab., KAIST, Korea

Change the characteristics of control devices Small external power 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

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

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 Property MR Fluids ER Fluids Response Time milliseconds Operable Temp. Range -40 to 150°C +10 to 90°C Stability Unaffected by most impurities Cannot tolerate impurities Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

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

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

Modulated homogeneous friction algorithm for a 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

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

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

Indirect control command to MR damper 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

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

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

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

Indirect control command to MR damper 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

` 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

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

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

Modified Bouc-Wen Model Damper modeling and parameters Value coa 21.0 Nsec/cm a 140 N/cm cob 3.50 Nsec/cmV b 695 N/cmV ko 46.9 N/cm  363 cm-2 c1a 283 Nsec/cm  c1b 2.95 Nsec/cmV A 301 k1 5.00 N/cm n 2 xo 14.3 cm  190 sec-1 Bouc-Wen c0 c0 k1 k1 c1 c1 k0 k0 Modified Bouc-Wen Model Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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

Peak responses under El Centro Earthquake Control Strategy Uncont. Passive- Off On Clip.-Opt. CMBBC xi (cm) 0.538 0.820 0.962 0.211 0.357 0.455 0.076 0.196 0.306 0.114 0.185 0.212 0.080 di 0.319 0.201 0.153 0.103 0.158 0.110 0.090 0.101 0.111 (cm/sec2) 856 1030 1400 420 480 717 281 494 767 696 739 703 310 507 772 F (N) - 258 979 941 982 Structural Dynamics & Vibration Control Lab., KAIST, Korea

Discussions Performance of CMDBBC Measured control forces Capacity of MR damper : 3000N (104% of total weight) Unsaturated condition !! Control Strategy Uncont. Passive- Off On Clip.-Opt. CMBBC F(N) - 258 979 941 982 Structural Dynamics & Vibration Control Lab., KAIST, Korea

Peak responses under scaled El Centro earthquake Control Strategy Uncont. Passive- Off On Clip.-Opt. CMDBBC xi (cm) 2.742 4.179 4.863 3.209 4.211 4.869 0.859 1.474 1.862 1.321 2.223 2.818 0.864 1.503 1.876 di 1.591 1.014 1.935 1.632 0.646 0.394 1.035 0.805 0.642 0.373 4399 5342 7053 14276 9321 11354 2235 2574 2741 5986 4711 5599 2126 2532 2598 f (N) - 1500 Structural Dynamics & Vibration Control Lab., KAIST, Korea

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

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