1. 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

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

3. 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

4. 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

5. 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

6. 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

7. 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

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

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

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

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

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

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

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

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

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

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

18. 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