A Survey on State Feedback AMD Control

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Presentation transcript:

A Survey on State Feedback AMD Control ICSSD 2000 A Survey on State Feedback AMD Control Kyu-Hong Shim: Postdoctoral Researcher, KAIST Dong-Hyawn Kim: Postdoctoral Researcher,KAIST Kyu-Sik Park: Doctoral Candidate, KAIST In-Won Lee: Professor, KAIST

Table of Contents  State Feedback Control  Numerical Example Introduction  State Feedback Control  Numerical Example  Conclusions Structural Dynamics & Vibration Control Lab., KAIST, Korea

Introduction Optimal Feedback Control X _ u G .. Structure xg X: state xg: ground accel. G: optimal gain u: control force .. Further reduction of vibration is impossible ! Structural Dynamics & Vibration Control Lab., KAIST, Korea

Previous Studies • Spencer Jr. et al. (1996) - made experimental model of three-story building. - developed simulation program for benchmark. • Chase and Smith (1999) - solved actuator saturation problem. - implemented it for real building in Tokyo, Japan. • Wu and Soong (1994) - studied Bang-Bang control to reduce peak-response. Structural Dynamics & Vibration Control Lab., KAIST, Korea

Pole Placement Control • Advantage : can speed up response reduction. • Drawback : more power may be consumed. • Remark : powerful actuator is needed. Pole placement control has not been studied yet. Structural Dynamics & Vibration Control Lab., KAIST, Korea

Apply pole placement control to a building structure. Objective Apply pole placement control to a building structure. Compare it with optimal control. Structural Dynamics & Vibration Control Lab., KAIST, Korea

State Feedback Control Equation of Motion (1) : mass matrix : damping matrix : stiffness matrix : actuator vector : displacement : ground accel. : control force : direction of earthq. Structural Dynamics & Vibration Control Lab., KAIST, Korea

State Space Equation (2) (3), (4) (5), (6) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Optimal Control Minimizing Cost (7) Feedback Rule (8) Riccati Equation (9) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Sub-Optimal Control Pole Placement (10) (11) (12) Structural Dynamics & Vibration Control Lab., KAIST, Korea

Numerical Example < Three Story Building with AMD > Structural Dynamics & Vibration Control Lab., KAIST, Korea

Parameters Structure AMD mass : 200 kg (story) stiffness : 2.25105 N/m (inter-story) damping ratios : 0.6, 0.7, 0.3% (modal) AMD mass : 18 kg (3% of building total mass) stiffness : 3.71103 N/m damping ratio : 8.65% Structural Dynamics & Vibration Control Lab., KAIST, Korea

• Excitation input: El Centro earthquake • Sub-optimal gains: and • Weighting matrices: Structural Dynamics & Vibration Control Lab., KAIST, Korea

Free Vibration of Third Floor Structural Dynamics & Vibration Control Lab., KAIST, Korea

Earthquake Response of Third Floor Structural Dynamics & Vibration Control Lab., KAIST, Korea

Free Vibration of AMD Structural Dynamics & Vibration Control Lab., KAIST, Korea

Earthquake Response of AMD Structural Dynamics & Vibration Control Lab., KAIST, Korea

Conclusions • Optimal control(Gopt) and pole placement control(0.5Gopt) showed the same responses. • Therefore, pole placement is better than optimal control because pole placement requires smaller control force. Structural Dynamics & Vibration Control Lab., KAIST, Korea