1. 지진 하중을 받는 구조물의 능동 모달 퍼지 제어시스템
2004년도 대한토목학회 정기 학술대회
보광 휘닉스파크
2004년 10월 21일
지진 하중을 받는 구조물의 능동 모달 퍼지 제어시스템
최강민, 한국과학기술원 건설 및 환경공학과
조상원, 한국과학기술원 건설 및 환경공학과
김춘호, 중부대학교 토목공학과
이인원, 한국과학기술원 건설 및 환경공학과

2. Outline Introduction Proposed Method Numerical Example Conclusions
Due to the time constraints on today’s presentation, I will talk about the MR damper experiment. This includes the experimental setup, damper design considerations and some experimental results. Also, I will talk about quasi-static modeling of MR dampers, dynamic modeling of the MR damper system, and a naval application – reduced ramp stress levels using semi-active devices.

3. Introduction
Fuzzy theory 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.
If offers a simple and robust structure for the specification of nonlinear control laws.

4. Input Values (state variables) Fuzzification Fuzzy Inference
입력을 퍼지 제어시스템 내에서 정의되는 퍼지 변수들에 대한 확실성의 정도로 나타내는 퍼지값으로 변환
퍼지규칙표에 따라 퍼지화과정을 통하여 결정되는 입력퍼지값들을 출력에 해당하는 퍼지값으로 변환시켜주는 역할
Fuzzification
Fuzzy Inference
이러한 입력에 대한 퍼지값으로의 사상관계를 나타내는 것이 소속함수
퍼지 출력값을 물리적인 의미를 갖는 출력정보로 역환산하는 과정
Defuzzification
This slides shows the schematic of the MR damper. When the piston moves, the MR fluids flow through the by-pass duct. The magnetic choke is utilized to control the magnetic field in the by-pass area, thus, the damper force.
Output Values

5. Modal control algorithm represents one control class in which the vibration is reshaped by merely controlling some selected vibration modes.
Because civil structures has hundred or even thousand DOFs and its vibration is usually dominated by first few modes, modal control algorithm is especially desirable for reducing vibration of civil engineering structure.
This slides shows the schematic of the MR damper. When the piston moves, the MR fluids flow through the by-pass duct. The magnetic choke is utilized to control the magnetic field in the by-pass area, thus, the damper force.

6. 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.
The prototype 20-ton large-scale MR damper was designed and built under the partnership between the University of Notre Dame and the Lord Corporation. This damper has a diameter of 20 cm and a stroke of 16 cm. The damper is double-ended. Therefore, the rod-volume compensator does not need to be incorporated into the damper. However, a small pressurized accumulator is provided to accommodate thermal expansion of the fluid. The electromagnetic coils are wound in three sections on the piston, resulting in four effective valve regions.

7. Development of active fuzzy controller on modal coordinates
Objectives
Development of active fuzzy controller on modal coordinates
- An active modal-fuzzy control algorithm can be magnified efficiency caused by belonging their’ own advantages together.
The flow gap runs between the outside edge of the piston and the inside surface of the cylinder housing. The fully-assembled damper is approximately 1 m long, has a mass of 250 kg, and contains approximately 6 liters of MR fluids.
Along the way, there are a number of hurdles that had to be overcome before tests to characterize damper behavior could begin. I would like to tell you about three of them that were quite critical to the success of this work.

8. Proposed Method Modal Approach Equations of motion for MDOF system
Using modal transformation
Modal equations
(1)
(2)
This figure shows the force-displacement test results under a triangular excitation with a velocity of 6 cm/sec. As can be seen, the MR damper force increases as the applied current increases. Moreover, the area enclosed by the force-displacement loop also enlarges, and more energy is dissipated.
(3)

9. Displacement where State space equation (4) (5)
These figures show the force-displacement and force-velocity relationships when the damper is subjected to a 1-inch, 0.5-Hz sinusoidal displacement excitation. As can be seen, the damper behavior is quite stable and consistent.

10. Modal approach is desirable for civil engineering structure
Control force
Modal approach is desirable for civil engineering structure
(6)
- Involve hundred or thousand DOFs - Vibration is dominated by the first few modes

11. Active Modal-fuzzy Control System
Modal Structure
Structure
To test the MR damper, an experimental setup was constructed. The damper is attached to a 3-inch-thick plate grouted on the strong floor. The damper is driven by a 125-kip actuator in conjunction with two Moog servo valves. A Houston Scientific position sensor (string pot) is used to measure the damper displacement, and a load cell is utilized to measure the damper force. The hydraulic system is controlled by a Schenck-Pegusus 5910 servo controller in displacement feedback mode.
Fuzzy controller
Force output

12. Modal-fuzzy control system design
Fuzzification
Input variables
Fuzzy inference
Output variables
Defuzzification
Here is a short video taken during the damper testing.
Input variables : mode coordinates
Output variable : desired control force
Fuzzy inference : membership functions, fuzzy rule

13. Numerical Example
Six-Story Building (Jansen and Dyke 2000)

14. Frequency Response Analysis
Under the scaled El Centro earthquake
102
6th Floor
104
1st Floor
PSD of Displacement PSD of Velocity PSD of Acceleration

15. In frequency analysis, the first mode is dominant.
The responses can be reduced by modal-fuzzy control using the lowest one mode.
The dynamic model of the MR damper system is necessary for simulation of damper behavior and structural vibration control simulation with MR dampers.
A new dynamic model of the overall MR damper system is proposed; this model is comprised of two parts. The first is the dynamic model of the current driver, i.e. a power source in which the current rather than the voltage is commanded. The current driver has been shown to be more effective than the common voltage-driven power supply in improving MR damper response time. The second part is a dynamic model of the MR damper based on the Bouc-Wen hysteresis model.

16. 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)
This is the transfer function block diagram of the current driver. Here is the governing equation derived from the transfer function block diagram. The identified dynamic model for the current driver is shown here.
 A type : for displacement reduction
B type : for acceleration reduction

17. Fuzzy rule - A type - B type NL NS ZE PS PL NL NS ZE PS PL PM NM
This figure compares the measured and predicted current using the dynamic model of the current driver. This figure provides a close-up of the current fast-changing region. As shown here, the dynamic model can predict the current very well.

18. - Fuzzy rule surface (A type)
This figure compares the measured and predicted current using the dynamic model of the current driver. This figure provides a close-up of the current fast-changing region. As shown here, the dynamic model can predict the current very well.

19. Input Earthquakes El Centro (PGA: 0.348g) California (PGA: 0.156g)
Accel. (m/sec2)
California
(PGA: 0.156g)
Accel. (m/sec2)
For the purposes of this discussion, the damper response can be divided into three regions. At the beginning of region I, the velocity changes in sign from negative to positive; the velocity is quite small and flow direction reverses. At this stage, the MR damper force is below the yield level, and the displacement measurement is behind the command signal. Because the servo controller uses displacement feedback, the controller tends to command a large valve opening to facilitate the damper movement. Therefore, a substantial increase in acceleration is observed. After the MR force exceeds the yield level, the acceleration drops to its normal sinusoidal trajectory, as shown at the end of region I. Because the inertial component of the damper force is related to the acceleration, a force overshoot, as shown in the figure, appears to be attributed to this peak response in acceleration during the test.
In region II, the acceleration decreases; the velocity continues to increase while still remaining positive. In general, the plastic-viscous force increases faster than the inertial force decreases. Therefore, a slight net force increase is observed.
In region III, both the velocity and acceleration decrease. Note that the damper velocity approaches zero at the end of this region, and the plastic viscous force drops more rapidly due to the fluid shear thinning effect. Therefore, a force roll-off is observed. Note that the force overshoot occurs only in region I; two clockwise loops are observed in the force-velocity plot…
Kobe
(PGA: 0.834g)
Accel. (m/sec2)
Time(sec)

20. Evaluation Criteria Normalized maximum floor displacement
inter-story drift
Normalized peak
floor acceleration
Maximum control force
normalized by the
weight of the structure
This is the transfer function block diagram of the current driver. Here is the governing equation derived from the transfer function block diagram. The identified dynamic model for the current driver is shown here.
This evaluation criteria is used in the second generation linear
control problem for buildings (Spencer et al. 1997)

21. Control Results
…as shown here.
Fig. 1 Peak responses of each floor of structure to scaled El Centro earthquake

22. Normalized Controlled Maximum Response due to
Scaled El Centro Earthquake
Control strategy J1 J2 J3 J4
Active Modal-fuzzy control (A type)
Active Modal-fuzzy control (B type)
Active Fuzzy control
0.343
0.548
0.600
0.562
0.635
0.756
1.186
0.601
0.660
0.0178
0.0134
Fuzzy
A type
B type
Here is the schematic of the proposed dynamic model based on the Bouc-Wen hysteresis model. In this model, the damper force is governed by this equation, where z is the evolutionary variable given by this equation, C is the post-yield damping term, assumed to satisfy this equation. Note that this equation is a mono-decreasing function used to describe the MR fluid shear thinning effect. Also, a mass element is used to accommodate the fluid inertial effect. Moreover, the accumulator stiffness is represented by k, and the friction force is taken into account by f0. J1 J2 J3

23. High amplitude (the 120% El Centro earthquake)
Control strategy J1 J2 J3 J4
Active Modal-fuzzy control (A type)
Active Modal-fuzzy control (B type)
Active fuzzy control
0.449
0.729
0.745
0.727
0.762
0.885
1.856
0.842
0.939
0.0178
0.0134
Fuzzy
A type
B type
This slide compares the experimentally-obtained and predicted damper response under a sinusoidal displacement excitation. As can be seen, the proposed model captures the damper force-displacement response very well. Moreover, the proposed model capsures the damper force-velocity behavior very well in all regions, including the force roll-off at low velocities and additional loops at velocity extremes.

24. Low amplitude (the 80% El Centro earthquake)
Control strategy J1 J2 J3 J4
Active Modal-fuzzy control (A type)
Active Modal-fuzzy control (B type)
Active fuzzy control
0.231
0.403
0.473
0.467
0.509
0.640
1.110
0.619
0.531
0.0178
0.0134
Fuzzy
A type
B type

25. Scaled Kobe earthquake (1995)
Control strategy J1 J2 J3 J4
Active Modal-fuzzy control (A type)
Active Modal-fuzzy control (B type)
Active fuzzy control
0.294
0.360
0.430
0.321
0.366
0.402
0.677
0.660
0.614
0.0178
0.0134
Fuzzy
A type
B type
To generalize the model for fluctuating input current to the damper, six parameters in the model are assumed to vary with the input current. Also, a first-order low-pass filter is utilized to accommodate the dynamics involved in the MR fluid reaching rheological equilibrium.

26. Scaled California earthquake (1994)
Control strategy J1 J2 J3 J4
Active Modal-fuzzy control (A type)
Active Modal-fuzzy control (B type)
Active fuzzy control
0.175
0.173
0.178
0.485
0.268
0.244
1.144
0.561
0.260
0.0100
0.0070
0.0076
Fuzzy
A type
B type
These figures show the displacement excitation and input current of the tested damper.

27. 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 amplitudes and frequency components.
The performance of the proposed method is comparable to that of conventional method.
The proposed method is more convenient and easy to apply to real system