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REAL-TIME HYBRID TESTING OF A STEEL-STRUCTURE EQUIPPED WITH LARGE-SCALE MAGNETO-RHEOLOGICAL DAMPERS APPLYING SEMI-ACTIVE

CONTROL ALGORITHMS

Eunchurn PARK/Dankook Unv. Sung-Kyung LEE/Dankook Unv. Heon-Jae LEE/Samsung Eng. Seok-Joon MOON/KIMM Hyung-Jo JUNG/KAIST

Byoung-Wook MOON/Dankook Unv. Kyung-Won MIN/Dankook Unv.

Proceedings of SMASIS08 ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems

October 28-30, 2008, Ellicott City, Maryland, USA

SMASIS2008-488

ABSTRACT

This study introduces the quantitative evaluation of the seismic performance of a building structure equipped with MR dampers by using real-time hybrid testing method (RT-HYTEM). A real-scaled 5-story building is used as the numerical substructure, and MR dampers corresponding to an experimental substructure is physically tested by using UTM. First, the force required to drive the displacement of the story, at which the MR damper is located, is measured from the load cell attached to UTM. Then, the measured force is returned to a control computer to calculate the response of the numerical substructure. Finally, the experimental substructure is excited by UTM with the calculated response of the numerical substructure. The RT-HYTEM implemented in this study is validated for that the real-time hybrid testing results obtained by application of sinusoidal and earthquake excitations and the corresponding analytical results obtained by using the Bouc-Wen model as the control force of the MR damper respect to input currents were in good agreement. Furthermore, semi-active control algorithms were applied to the MR damper. The comparison results of experimental and numerical responses demonstrated that using RT-HYTEM was more reasonable in semi-active devices such as MR dampers having strong nonlinearity.

INTRODUCTION A wide variety of structural control strategies for civil

engineering structures such as bridges and buildings have been proposed by structural engineers. Various types of active and semi-active control dampers also have been developed to enhance the performance of passive control devices. Analytical and experimental studies on these control devices working with

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MR dampers have been performed in an effort to reduce the structural responses, mainly due to their intrinsic stability and low power consumption. Also, semi-active control strategies using the MR damper were compared extensively [1]. In analytical studies, the Bingham, Bouc-Wen, and phenomenological models were proposed as the analytical model for describing the hysteretic behavior of the MR damper [2-3]. Although these models are useful in the design of the MR damper, they are inappropriate for characterizing the behavior of the MR damper under the excitation of irregular loads such as earthquakes and winds because of its strong nonlinearities due to its dependency on the loading rate and the amplitude of excitations. Also, the performance of the MR damper is not guaranteed according to its current providing devices. Moreover, when the MR damper behaves as a semi-active control device, the hysteretic model varying with the applied current is unreliable [4]. For these reasons, there may be disagreement between the actual responses of a building installed with an MR damper applying the semi-active control strategy and the corresponding analytical results.

In this study, the investigation of the hysteretic behavior of an MR damper itself and the quantitative evaluation of the seismic performance of a building structure installed with an MR damper are carried out experimentally by using the real-time hybrid testing method (RT-HYTEM). RT-HYTEM is a structural testing technique, in which the numerical integration of the equation of motion of a numerical substructure and the physical testing of an experimental substructure with severe nonlinear characteristics are carried out simultaneously in real-time. Since the development of this method primarily for the application to large-scale structures and for the use of the base-isolator by Nakashima [5, 6], several researches have been

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performed both experimentally and analytically on the real-time substructuring technique to overcome the difficulties in the testing of large-scale structures. This technique is especially useful for evaluating the performance of the control device itself as well as that of the integrated system, incorporated with the control device [7].

OUTLINE OF METHODOLOGY Fig. 1 shows the concept of the real-time hybrid testing

method (RT-HYTEM), which is experimentally implemented in this study. As shown in Fig. 1 (a), the structural response of a building model with n-degrees-of-freedom subjected to base input motion, , is controlled by an MR damper, which is typically located in the first story to reduce the maximum shear force of a bare structure. The whole system is divided into experimental and numerical substructures (Fig. 1 (b)). The MR damper was used as an experimental substructure because it was very difficult to numerically predict its exact dynamic behavior under seismic load, due to its strong nonlinear characteristic of the dependency of the damper force on the loading rate and amplitude. The remaining parts, that is, the structure without MR damper, were analytically calculated. As depicted in Fig. 1 (c), three procedures associated with the measurement of force, numerical calculation of analytical parts, and loading of the experimental substructure were used to implement RT-HYTEM for the whole structural control system [8]. First, the force acting at the interface between experimental and numerical substructures, here the control force generated by the MR damper, was measured by the load cell attached to an actuator. Then, this value of this measured control force was returned to the control computer for use in the calculation of the displacement constraint condition, which should be satisfied by both the experimental and numerical substructures. Finally, the MR damper physically tested in the laboratory was loaded by an actuator with respect to the displacement response of the story installed with the MR damper.

nm

1−nm

1m( )tY1

( )tYn 1−

( )tYn

( )txg&& (a) structural control

system

nm

1−nm

1m( )tY1

( )tYn 1−

( )tYn

( )txg&&

( )f t ( )f t

(b) experimental and

numerical substructures

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force measuring

MR damper actuator

( )tYnnm

1−nm

1m

(

( )tY1

)tYn 1−

( )txg&&

loading

calculating

control computer

( )f t

( ) ( ) ( ) ( ) ( )g et t t x t f t

(c) implementation of real-time hybrid testing method

Figure 1. Conceptual view of real-time hybrid testing method for a building with an MR damper

The numerical substructure that is surrounded by dotted

line in Fig. 1 (c) is calculated based on the equation of motion for the building model subjected to ground input acceleration and, for structural control, equipped with an MR damper, which is represented by

+ + = − +Mx Cx Kx MΓ H&& & &&

, M C K n n×( )t

1n

(1)

where, and represent the structural mass, damping, and stiffness matrices, respectively. x is the × vector of the relative structural displacement to the

ground input motion, . is the 0 ( )y t Γ 1n× vector of the ground input motion influence coefficients. is the nH 1× vector that represents the location of the MR dampers. x ( )g t&&

( )e

is the ground input acceleration. f t

( ) ( ) ( )( ) ( ) ( )

s s s

s s s

t t tt t t

is the control force exerted by the MR damper on the structure, in which subscript “ e ” stands for the “experimentally” measured control force.

To perform RT-HYTEM, Eq. (1) is transformed into its state-space representation, which definitely specifies the relationship between the input and output of the numerical substructure, and it can be written as

= += +

z A z B uY C z D u&

( ) { ( ), ( )}Ts t t t=z x x& 2 1n×

( ) { ( ), ( )}Te gt f t x t=u && 2 1×

( ) ( )s t t

(2)

where, is the system state vector.

is the system input vector and =Y x 1n is the 2 2n n× system output vector. The ×

system state matrix, sA 2 2n×, and the location matrix of system input, sB

1 1n n

s×− −

, both associated with the system state variables, are represented by

⎡ ⎤

= ⎢ ⎥− −⎣ ⎦

0 IA

M K M C1 11

n ns

× ×−

⎡ ⎤= and ⎢ ⎥− −⎣ ⎦

0 0M H Γ

B (3)



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and the system out matrix, n n× sC , and the 2n× direct transmission matrix , sD , both related to the system output variables, are given by

s =C I and 1s n×=D 0 (4)

In Eqs. (3) and (4), is the unit matrix. Also, and are the and zero matrices,

respectively. Note that, in the actual implementation of RT-HYTEM, the system output vector, , in Eq. (2) should be designated as the story-drifts where the MR dampers were installed and also Eq. (4) be modified because these story-drifts affect the system output vector.

I n n×n×

( )s tY

n n×0 1n×0 n n× 1

CONTROLLER STRATEGIES FOR RT-HYTEM

Experimental setup In general, the successful experimental implementation of

RT-HYTEM with high accuracy depends strongly on the dynamic performance of the actuators used to excite the experimental substructure in the test. Namely, the actuators used in the test should promptly react upon applied command signals and load the experimental substructure. In this study, a universal testing machine (UTM), which is commonly used for the performance test of various structural materials, was utilized as an actuator to load the experimental part. Fig. 2 shows the experimental set-up using UTM with the maximum loading capacity of 200 kN and excitation frequency range of 0~10 Hz (Model name STL-HU10T). An MR damper, which can develop a control force ranging 3~12 kN , was connected to this system.

Figure 2. Configuration of experimental system As shown in Fig. 3, three apparatuses, whose functions are

interconnected, were equipped on the experimental set-up to perform RT-HYTEM. The main task of the signal generator is

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to generate the current signal, by which an MR damper is operated and control force is exerted on UTM. The control computer with a digital signal processing (DSP) board calculates the responses of the numerical substructure by using the input, that is, the control force measured from a load cell of UTM, and sends the command signal to the UTM console computer. The primary task of the UTM console computer is to transfer the command signal generated by the control computer, according to the control algorithm for implementing RT-HYTEM, to the UTM. Finally, UTM excites the experimental part according to this control signal.

analog output

control computercontrol computer

controlsignal

signal generatorsignal generator

constant voltage

Experimentalsubstructure

currentamplifier

commandsignal

controlforce

UTM console computerUTM console computer

control algorithm

for implementing

RTHTM

currentsignal

(a) building model installed withan MR damper

(b) UTM installed with an MR damper (c) experimental instrumentation

calculated current

Figure 3. Schematic view of experimental set-up

Numerical substructure A real-scaled five-story steel frame building was

considered as the model of the numerical substructure to use in the structural modal testing of this study, as shown in Fig. 4.

Figure 4. Five-story building structure This building has the height of 6 m in all stories and 6x6 m

in plan. To investigate its modal characteristics, a forced-vibration test was performed using a hybrid mass damper


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(HMD) located on the fourth floor. The building was excited by a white-noise signal with frequency components of 0~10 Hz, and then the corresponding acceleration responses were measures at each floor. Using these measured acceleration data, transfer functions in the frequency domain were obtained, as shown in Fig. 5 by the dotted lines. Finally, the structural damping and stiffness matrices were identified based the experimentally obtained transfer functions, as shown in Fig. 5 by the solid lines. The estimated mass and the identified damping and stiffness matrices are given in Eqs. (5)~(7), respectively, which results in 0.52, 1.76, 2.95, 3.67 and 5.38 Hz for each mode.

0 1 2 3 4 5 6 7 810

-4

10-2

100

Mag

nitu

de

Frequency (Hz)

(a) fifth floor acceleration magnitude

0 1 2 3 4 5 6 7 810

-4

10-2

100

Mag

nitu

de

Frequency (Hz)

(b) third floor acceleration magnitude

0 1 2 3 4 5 6 7 810

-4

10-2

100

Mag

nitu

de

⎤⎥⎥⎥⎥⎥⎥⎦

⎤⎥⎥⎥⎥⎥⎥⎦

Frequency (Hz)

(c) first floor acceleration magnitude

Figure 5. Measured and identified transfer functions with the HMD acceleration (dotted line : experiment,

solid lines : identification)

5

19365.5 0 0 0 00 19365.5 0 0 0

kg0 0 19365.5 0 00 0 0 19365.5 00 0 0 0 19365.5

⎡⎢⎢⎢=⎢⎢⎢⎣

M (5)

5

14.184 5.015 0.084 0.789 0.1015.015 14.990 6.397 0.822 1.145

0.084 6.397 15.830 6.120 0.9250.789 0.822 6.120 14.065 6.3830.101 1.145 0.925 6.383 9.750

− −⎡⎢− −⎢⎢= − −⎢− −⎢⎢ − − −⎣

C−−−

kN sec/m⋅ (6)

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5

7473.953 4860.497 1295.606 908.262 432.1624860.497 9640.722 6637.235 2446.225 926.951

1295.606 6637.235 10861.354 6005.863 748.607908.262 2446.225 6005.863 9132.066 4852.783

432.162 926.951 748.607 4852.783

− −− − −

= − −− − −

− −

K kN m

4543.854

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

( ) ( ) ( )( ) ( ) ( )

n n n n

n n n n

t t tt t t

(7)

When these identified structural properties are incorporated in the numerical substructure, Eqs. (2)~(4) can be rewritten by Eqs. (8)~(10), respectively.

= += +

z A z B uY C z D u&

1 5 1 5( ) { ( ) ~ ( ), ( ) ~ ( )}Tn t x t x t x t x t=z & & 10 1

(8)

where, is the × system state vector. is the ( ) { ( ), ( )}T

e gt f t x t=u && 2 1× system input vector and ( ) ( ) ( ),~{ 51 txtxtn =Y ( ) ( ),~ 51 txtx &&

( ) ( )}~ 51 tXtX &&&& 15 1×10 10

is the system output vector. The × system state matrix, , and the 10nA 2× location

matrix of system input, , are represented by Eq.(9) nB

5 51 1

5 5 5 5n

×− −

⎡ ⎤

= ⎢ ⎥− −⎣ ⎦

0 IA

M K M C5 1 5 1

15 5 5

n× ×−

⎡ ⎤= ⎢ ⎥− −⎣ ⎦

0 0M H Γ

15 10

and B (9)

and the × system out matrix, , and the 155C 2×

direct transmission matrix , , are given by Eq.(10). 5D

5 5

5 51 1

5 5 5 5

n

×

×− −

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥− −⎣ ⎦

I 0C 0 I

M K M C

5 1 5 1

5 1 5 11

5 5 5 1

n

× ×

× ×−

×

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥−⎣ ⎦

0 0D 0 0

M H 0

I 5 5×5 5

and (10)

In Eqs. (9) and (10), is the unit matrix. Also,

×0 5 1 and ×0 5 5× 5 1 are the and × zero matrices, respectively.

Controller design of UTM In order to properly push a load the experimental

substructure, according to the control algorithm of RT-HYTEM, by an actuator, the dynamic property of the actuator itself between the command signal and the measured response should be appropriately compensated. Without this compensation, the experimental results can have problems such as chattering problems or the operating performance of the testing system can be degraded. Especially, in structural testing associated with vibration control issues, the control force often acts as an external load, and as a result, the experimental system can become unstable.

To experimentally measure the dynamics of UTM, white noise with frequency ranging 0~10Hz was used as the command signal, as shown in Fig. 3, and then the corresponding displacement of UTM that was driven by this



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signal was measured. Using these input and output data sets in the time domain, the transfer function in the frequency domain, which corresponds to the dynamics of the UTM itself, was obtained, as shown in Fig. 6. The figure shows that the amplitude of the transfer function is nearly one for all frequency ranges, while that of the phase curve varies with the increase of frequency. This means that the measured displacement of UTM is identical to the command signal with respect to amplitude but it is delayed with respect to phase in comparison to the command signal.

10-1

1000

0.5

1

1.5

2

Frequency (Hz)

Mag

nitu

de

(a) Magnitude

10-1

100-60

-50

-40

-30

-20

-10

0

Frequency (Hz)

Phas

e

(b) Phase angle (degree)

Figure 6. Measured transfer function from the command signal to the displacement of UTM

The phase delay was compensated by using the inverse

transfer function (ITRF, [7, 9]), in which the relation between the input and output in the transfer function is reversed. Accordingly, the measured ITRF is obtained with the input of the measured displacement of UTM and the output of the command signal, as shown in Fig. 7 by the dotted lines. This measured ITRF should be incorporated in the control computer as part of the control algorithm in Fig. 3 to compensate the phase delay of UTM and to correctly excite the experimental substructure. The measured ITRF was approximated by using the ‘invfreqs’ command in MATLAB [10], which finds the real numerator and denominator coefficient vectors of the approximated transfer function in the form of a fractional expression by adopting the damped Gauss-Newton method for iterative search, which minimizes the sum of the squared error between the measured and the approximated frequency response points [11]. The approximation result shown in Fig. 7 by the solid line is given by the following second order linear analog filter


1.05

1

0.95

1 2 3 4 50.85

0.9

Frequency (Hz)

Mag

nitu

de

measuredcalculated

(a) Magnitude

80

1 2 3 4 50

20

40

60measured

Frequency (Hz)

Pha

se (d

eg. °

)

calculated

(b) Phase angle

Figure 7. Measured and approximated inverse transfer function from the displacement of UTM to the

command signal

21

2

7.1945 636.4862 27368.6533( )412.4726 27758.6756

s sG ss s

− + +=

+ + (11)

s , equals iwhere, the Laplace variable, ω with the imaginary constant, . i

( ) ( ) ( )( ) ( ) ( )

s i s i

i s i

t = t + r tc t = t + D r t

y A y BC y

&

Fig. 7 shows that, at 5 Hz, compensation on phase lag was attainted only by 20 degree with the approximated ITRF, while phase lag of 60 degree is observed in the measured ITRF. Further compensation would be possible with use of other filters. However, further compensation was excluded here since it would have resulted in an unstable ITRF.

Eq. (11) is converted into the following state space realization for implementation in the control computer.

(12)

where, sy ( )r t ( )c t 2 1×1 1

, and are the state vector, the × reference signal, and the command signal of UTM,

respectively. , , and are the 1 1×

iA iB iC iD 2 2× , 2 1× , 1 2× and 1 1× system matrices, respectively.

EXPERIMENTAL IMPLEMENTATION

Integrated controller of the numerical substructure and UTM

The numerical substructure and the approximated inverse transfer function explained were incorporated in the control computer as an integrated controller to implement RT-HYTEM, as shown in Fig. 8 by the shaded area. First, when the constant current sent from signal generator for passive control test and the calculated current of semi-active control algorithms sent



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from analog output for semi-active control test are applied to the MR damper, the control force proportional to the magnitude of the current signal is developed and transferred to the UTM. Then, the drift response, 1( )x t , of the first story where the MR damper is positioned is calculated from the numerical substructure, given by Eq. (8), with two inputs, namely, the control force, ( )ef t , measured from the load cell attached to UTM and the ground input acceleration, ( )gx t&& , given by the user. The motion of the UTM is so driven by the controller using the inverse transfer function, represented by Eq. (12), such that the UTM itself operates as the first story where the MR damper is located, and excites the MR damper that should be physically tested. In the actual experimental implementation of RT-HYTEM, the continuous filters involved in Fig. 8 were converted into discrete filters with a time interval of 0.01 sec, and MATLAB Simulink[12] with Real-Time Windows Target[13] were used as the control system

controlforce

analog outputcontrol signal

command signal

UTM console computUTM console computerer

currentdriver

control computercontrol computer

ground inputacceleration, ( )gx t&&

numerical substruc( ) ( )( ) ( )

n n n

n n n

t tt t= += +

z A zY C z&

ture( )( )

n

n

tt

B uD u

ITRF( ) ( )( ) ( )s i s

i s i

t = t +c t = t + D ry A y

C y& ( )

( )ir t

tB

force measuring, ( )ef t

1st story drift 1( )x t

current signal

UTM

actuator

load-cell

MR damper

UTM systemUTM system

( )nei fSv z,=Control algorithm

Full state feed-back

Figure 8. Integrated controller for implementing RT-

HYTEM

Experimental verification (Simple Bouc-Wen Model) RT-HYTEM with a sinusoidal wave excitation was carried

out to investigate the hysteretic behavior of the MR damper used and to verify the RT-HYTEM experimentally implemented in this study. A current of 0 [A] was applied to the MR damper and a sine wave with the frequency of 0.52 Hz, which corresponds to the fundamental frequency of the numerical substructure, and with the amplitude of 5 cm was used as the ground input acceleration in Fig. 8.

Then, parametric identification was performed to find the numerical model of the MR damper on a basis of the experimentally measured hysteretic loop. Bouc-Wen model is widely used for modeling of various hysteretic loops [14]. The control force by the MR damper also can be specified by using this model. The force described by this model is represented by

1MR MR 1 0( ) ( ) ( ) ( )MRf t z t c x t k x t fα= + + +& (13)

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where, MRk and MRc

0

are the stiffness and viscosity of the MR damper. f is the initial friction force. is a dimensionless valuable introduced to describe the hysteresis, and

z

α is a variable that regulates the effect of on z ( )MRf tz

and it depends on the magnetic field. is given by the following differential equation.

1

1 1 1( ) ( ) ( ) ( ) ( ) ( ) ( )n nz t x t z t z t x t z t Ax tγ β−= − − +& & && (14)

where, γ , β , A and the superscript are the coefficients determining the shape of the hysteretic curve.

n

0, , , , , , MR MRc k f nThe eight parameters in Eqs. (13) and (14),

α γ β and A were identified using least-squares optimization to minimize the performance index defined as

( ) [ ]2

1{ } ( ) ({ }, )

N

e MRk

p f k t f p k t=

= ⋅Δ − ⋅Δ∑

( )e

J (15)

f k twhere, ⋅Δ k

}p 8×

0{ , , , , , , , }MR MRc k f n A

is the force data measured at the -th sampling time. { is the 1 vector of the identification parameter, α γ β . f ({ }, )MR p k t⋅ Δ

k{ }p

295.497,804.335518058.3,377.471409

10.6,/456.16647/582.81418,/130,13288

2

20

==

==

==

is the force obtained at the -th calculating time from Eqs. (13) and (14) using the parameter .

This procedure was carried out by using MATLAB subroutines [15], and the identified parameters are given by

⋅==

−

−

Amnm

NfmNkmsNcmN

MR

MR

β

γ

α (16)

A comparison between the calculated and experimental

responses is provided in Fig. 9. The displacement and velocity in Figs. 9 (b) and (c) corresponds to the first story drift and velocity responses, respectively. The Bouc-Wen model represents the force-displacement and the force-velocity hysteretic behaviors of the damper well.

4000

80 81 82 83 84 85 86 87 88 89 90-4000

-2000

0

2000

ExperimentCalculation

Time(sec)

forc

e(N

)

(a) Time history of force


erms of Use: http://asme.org/terms

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-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

1st story velocity(m/s)

dam

per f

orce

(N)


(b) Force-velocity relation

-4 -3 -2 -1 0 1 2 3 4x 10

-3

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

1st story drift(m)

dam

per f

orce

(N)


(c) Force-displacement relation

Figure 9. Comparison between calculated and

experimentally measured responses for Bouc-Wen model

RT-HYTEM implemented in this study was verified by

experiment using the excitation of historical seismic measurements. Four different records of earthquake acceleration measurements of El Centro, Hachinohe, Kobe and Northridge were used as ground input acceleration in Fig. 8 by multiplying them by 0.05, respectively. Also, the current of 0 [A] was applied to an MR damper in the same manner as the sinusoidal excitation test above. In addition to the measurement of the control force produced by an MR damper, given by Eqs. (8)~(10), structural displacement, velocity and absolute acceleration responses were obtained from RT-HYTEM for earthquake excitations. Fig. (10) compare the responses measured from RT-HYTEM such as Fig. 8 with those calculated from the 5-story building model installed with an MR damper with the identified parameters such Eq. (16) to compute the control force.


0 5 10 15-0.2

-0.1

0

0.1

0.2 Experiment

1st s

tory

(m/s

2 )

Calculation

0.2

0 5 10 15-0.2

-0.1

0

0.1

3rd

stor

y (m

/s2 )

0.2

0.1

0

-0.1

0-0.2

5 10 15Time (sec)

5th

stor

y (m

/s2 )

(a) Absolute acceleration responses

0 5 10 15 20 25

2 x 10-3

30-3

-2

-1

0

1

1st s

tory

, x1(m

)


0.01

0 5 10 15 20 25 30-0.01

-0.005

0

0.005

3rd

stor

y, x

3 (m)

0.01

0.005

0

-0.005

0-0.01

5 10 15 20 25 30Time (sec)

5th

stor

y, x

5 (m)

(b) Displacement responses

Figure 10. Comparison between calculated and

experimentally measured responses to El Centro wave

Also, the measured and calculated hysteretic behaviors

were compared for El Centro seismic excitations in Fig. (11). Fig. (10) show that the two results agree well with each other. Fig. (11) shows that the overall hysteretic behaviors are well predicted with the Bouc-Wen model.



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-0.01 -0.005 0 0.005 0.01 0.015-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

1st story velocity (m/s)

forc

e (N

)


-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

4000

x 10-3

-4000

-3000

-2000

-1000

0

1000

2000

3000

1st story drift (m)

forc

e (N

)


(a) Force-displacement curve (b) Force-velocity curve Figure 11. Comparison between calculated and

experimentally measured hysteresis under El Centro wave excitation

Applied Semi-active control algorithms 1. Optimization of Bouc-Wen Parameter by input

currents In order to compare the numerical and the semi-active RT-

HYTEM result, identification of Bouc-Wen parameter corresponding to input currents is required. In this study, sine-wave excitation test was implemented and Bouc-Wen parameter ( MRcA,,α ) were identified.

Fig.12 shows the comparison of test model and the identified Bouc-Wen model with respect to different input currents. Fig.12(a) and (b) the optimal parameter of Bouc-Wen model was established by force-velocity and force-displacement relationships as shown in Fig.12 (a) and (b). For implementing semi-active control of MR damper, three parameters which were assumed to be polynomial exponential function of input current are identified by using least square method.

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04-1.5

-1

-0.5

0

0.5

1

1.5x 10

4

Velocity (m/sec)

MR

Dam

per F

orce

(N)

physical modelnumerical model

0A

1A

2A3A

(a) force-velocity relation


-0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

1.5x 10

4

0.025-1.5

-1

-0.5

0

0.5

1

Stroke (m)

MR

Dam

per F

orce

(N)

physical modelnumerical model

0A

1A2A3A

( ) 40.35477785.0exp03.324576 +−

(b) Force-displacement relation

Figure 12. Identified Bouc-Wen parameter and the

numerical model of MR damper Identified Bouc-Wen parameters are as follow Eqs.(17) to

(19)

(17) x=α −( ) 96.603304.1exp17.44567 +− (18) = − xcMR

( ) ( )xxA 3321.0exp5.222476.5exp7.854 (19) = − + −where, x is input current (A) 2. Clipped-optimal control algorithm From an implementation point of view, this control

strategy seem to be the most direct on because it can take advantage of the great amount of experimental and practical studies that have been conducted on active control strategies. The clipped-optimal algorithm that has been shown to be effective for use with the MR damper is proposed by Dyke, et al (1996). The clipped-optimal control approach is to design a linear optimal controller K that calculates a vector of desired control forces f based on the measured structural responses

( )sc

[ ]Tcnccc fff K,, 21=y and the measured control

force vector applied to the structure, i.e., f

( )⎭⎬⎫

⎩⎨⎧

⎭⎬⎫

⎩⎨⎧

−= −

fy

Kf LL scc1

(20)

{}⋅L

cif

i

is the Laplace transform. where, Because the force generated in the MR damper is

dependent on the local responses of the structural system, the desired optimal control force cannot always be produced

by the MR damper. Only the control voltage v can be directly controlled to increase or decrease the force produced by the device. Thus, a force feedback loop is incorporated to



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induce the MR damper to generate approximately the desired optimal control force . cif

i V=

To induce the MR damper to generate approximately the corresponding desired optimal control force , the command

signal is selected as follows. When the ith MR damper is providing the desired optimal force, the voltage applied to the damper should remain at the present level. If the magnitude of the force produced by the damper is smaller than the magnitude of the desired optimal force and the two forces have the same sign, the voltage applied to the current driver is increased to the maximum level so as to increase the force produced by the damper to match the desired control force. Otherwise, the commanded voltage is set to zero. The algorithm for selecting the command signal for the ith MR damper is stated as Eq. (21). [1]

cif

iv

{ }( )iici fffH −

=c

v max (21) Although a variety of approaches may be used to design

the optimal controller, LQR methods are advocated because of their successful application. The optimal gain of state vector based on the target building model with MR damper is used as follow

K [-98301479.1 110902868.9 -36659599.6

24569454.5 -12841877.0 -4926535.9 -3813412.5 -331115.5 -1239172.8 -1309155.8]

For implementing the RT-HYTEM experiment, the

integrated MATLAB Simulink controller was designed as shown in Fig.13. In field testing application of this control law, it is required to obtain full structural state vector using such as Obserber/Kalman filter estimation method. However, because RT-HYTEM uses the structural model as numerical model, this method has an advantage to using structural state variable easily in experiment.

Damper force

Earthquake

U U(E)

state variable

y(n)=Cx(n)+Du(n)x(n+1)=Ax(n)+Bu(n)

inverse Transfer Function

damper force

fd

fc

Out1

clippedalgorithm1

y(n)=Cx(n+1)=

UNISON M

x(n)+Du(n)Ax(n)+Bu(n)

odal Testing Tower

In1 Out1

DAQ Subsystem

K*u

Gainkobe.mat

Earthquake

0.5

EQ gain1

-K-

EQ gain

-K-

Disp CoefficientAnalogOutput

Analog OutputNational Instruments

DAQCard-6036E [auto]

AnalogInput

Analog InputNational Instruments


U U(E)

1F Disp

Figure 13. Clipped-optimal and RT-HYTEM integrated

controller 3. Modulated Homogeneous Friction algorithms This control strategy was developed originally for a

variable-friction damper. In this approach, at every occurrence of local extremes in the deformation of the device, the normal force applied to the frictional interface is updated to a new

nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 04/02/2014 Te

value. At each local minimum or maximum in the deformation the normal force ( )tNi is chosen to be proportional to the absolute value of the semi-active damper deformation. The control law is written as Eq. (22) [16]

) ( )[ ]( tPgtN iii Δ=

ig

(22)

[ ]where, is a positive gain and the operator ⋅P as the prior-local-peak operator is defined as [ ( )] ( )stt ii −Δ=ΔP where { }( ) (0:0min =−Δ≥= xtxs & defining )st −Δ

( )

as the most recent local extreme in the deformation.

Because this algorithm was developed for variable friction devices, the following modifications are needed when applying it to MR dampers.

i) There is often no need to check if the force is greater than the static friction, because MR dampers have no static friction.

ii) A force feedback loop is used to induce the MR damper to produce approximately the frictional force corresponding to the required normal force. Thus, the goal is to generate a required control force with a magnitude

[ ] ( )[ ] (23) tPgtPgf iniiini Δ=Δ= μ

nigmmN /

where, the proportionality constant has unit of stiffness

. As in the clipped-optimal control law, because the force

produced by the MR damper cannot be directly commanded, a force feedback loop is used. The measured force is compared to the desired force determined by Eq. (18), and the resulting control law is

( )inii ffHVv −= max

maxV

nig nif

nig

nigmkN /150

(24)

where, is the maximum current value that can offer the MR damper.

An appropriate choice of will keep the force within the operating envelope of each MR damper a majority of the time, allowing the MR damper forces to closely approximate the desired force of each device. However, the optimal value of is dependent on the amplitude of the ground acceleration. In this study value was chosen as

based on 3 earthquakes excitation. Additionally, notice that this control law is quite

straightforward to implement because it requires only measurement of applied force and the relative displacements of the control device.

For applying the RT-HYTEM experiment, the integrated MATLAB Simulink controller was designed as shown in Fig.14.



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DAMPER FORCE

Earthquakegn


UNISON Modal Testing Tower

state variable

In1Out1

current out subsystem

In1Out1

MHF Subsystem

In1 Out1

DAQ SubsystemDamper force

-K-

north.mat

Earthquake

-K-

EQ gain

-K-

Disp Coefficient


inverse transfer function

AnalogOutput

Analog OutputNational Instruments


AnalogInput

Analog InputNational Instruments

DAQCard-6036E [auto]|u|

Abs

|u|

Abs

U U(E)

1F Disp

0.5

1/2

Figure 14. MHF and RT-HYTEM integrated controller

TESTING RESULT

Passive control performance RT-HYTEM illustrated in Fig. 8 was implemented to

evaluate the seismic performance of the passive-controlled MR damper used in this study. Except for the variation of the applied current to the MR damper, in the same manner as the above, four earthquake records were also given as the ground accelerations in Fig. 8. The tests for the controlled case were carried out by increasing the current applied to the MR damper from 0 A to 3 A. In Fig. 8, the test for the uncontrolled case was performed by removing the feedback loop of the control force generated by an MR damper into the control computer. Therefore, the numerical substructure was excited only by the ground input acceleration, even though the current of 0 A was applied to the MR damper.

Figs. (15)~(16) compares, for the selected floors, the time histories of experimentally measured structural displacement responses to the excitation of two earthquake waves, as the current applied to the MR damper was varied. Remarkable control effects are observed between the uncontrolled and the passive-off case, but were not observed in the other passive-on cases with the increase of the applied current.

0 5 10 15 20 25 30 35 40 45 50-5

0

5x 10

-3

Time (second)

1st F

loor

Dis

plac

emen

t (m

)

0 5 10 15 20 25 30 35 40 45 50-0.02

-0.01

0

0.01

Time (second)

3rd

Floo

r Dis

plac

emen

t (m

)

0 5 10 15 20 25 30 35 40 45 50-0.015

-0.01

-0.005

0

0.005

0.01

0.015

Time (second)

5th

Floo

r Dis

plac

emen

t (m

)

El Centro

uncontrolled0.0A1.0A2.0A3.0A

Figure 15. Experimental results in the time domain under El Centro earthquake excitation at different

applied currents


0.015

0.01

0.005

0

-0.005

-0.01

-0.0150 5 10 15

Time (second)

1st F

loor

Dis

plac

emen

t (m

)

20 25

0.04

0.03

0.02

0.01

0

-0.01

-0.02

-0.030 5 10 15

Time (second)

3rd

Floo

r Dis

plac

emen

t (m

)

20 25

0.06

0 5 10 15 20 25-0.04

-0.02

0

0.02

0.04

5th

Floo

r Dis

plac

emen

t (m

)

Northridge

uncontrolled0.0A1.0A2.0A3.0A

Time (second)

Figure 16. Experimental results in the time domain under Northridge earthquake excitation at different

applied currents Also, the displacement responses in the frequency domain

to four earthquake excitations at different applied currents were compared for the 1st floors in Fig.17. The figures show that the peak in the uncontrolled case appears at 0.52 Hz corresponding to the fundamental frequency of the numerical substructure under consideration, but the peak is shifted to the vicinity of 0.62 Hz as the applied current increases. This small amount of frequency shifting was due to the stiffening effect of the MR damper used in this study as the applied current was increased.

3 7

(a) El Centro (b) Kobe

(c) Northridge (d) Hachinohe

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5 6

Frequency (Hz)

1st S

tory

Dis

plac

emen

t Mag

nitu

de

5

4

3

2

1

00 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Frequency (Hz)

1st S

tory

Dis

plac

emen

t Mag

nitu

de

3.5 1.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

Frequency (Hz)

1st S

tory

Dis

plac

emen

t Mag

nitu

de

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

uncontrolled0.0A1.0A

Frequency (Hz)

1st S

tory

Dis

plac

emen

t Mag

nitu

de

2.0A3.0A

Figure 17. First story displacement in the frequency

domain at different applied currents Semi-active control performance Fig.18 show the comparison result of numerical and

experimental the clipped-optimal control under El Centro earthquake excitation based on identified Bouc-Wen parameters. Fig.18(a) shows the reasonable control



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performance in numerical analysis, however as shown in Fig.18 (b), there are different currency between experimental and numerical results. Moreover, because the peak responses are very important to evaluate seismic performance, it is critical to have large differences between the experimental and numerical results. These results are due to the nonlinearity of MR dampers which varies the numerical model corresponding to frequencies of piston and nonlinear reaction velocity of input currents. As a result, these results prove that using the RT-HYTEM is more reasonable in nonlinear damper model such as MR dampers.

0 5 10 15 20 25 30 35 40 45 50-5

0

5x 10-3

Time (second)

Dis

plac

emen

t (m

)

uncontrolled (numerical)clipped-optimal controlled (numerical)

0 5 10 15 20 25 30 35 40 45 50-5

0

5x 10-3

Time (second)

Dis

plac

emen

t (m

)

uncontrolled (numerical)clipped-optimal controlled (numerical)

(a) Numerical analysis result

0 5 10 15 20 25 30 35 40 45 50-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10 -3

Time (second)

Dis

plac

emen

t (m

)

RTHTM experimental clipped-optimal controlnumerical clipped-optimal control

0 5 10 15 20 25 30 35 40 45 50-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10 -3

Time (second)

Dis

plac

emen

t (m

)

RTHTM experimental clipped-optimal controlnumerical clipped-optimal control

(b) Comparison of numerical and experimental result

Figure 18. Comparison of numerical and experimental result under El Centro earthquake excitation.

Fig.19 compares, for the 1st floors, the time histories of

experimentally measured structural displacement responses to the excitation of three earthquake waves, as the current applied to the MR damper was varied corresponding to each semi-active control algorithms. Remarkable control effects are observed between the uncontrolled and the passive control case, but were not observed in the each semi-active control cases of El Centro as shown in Fig.19(a). In Fig.19(c) the clipped optimal control algorithms shows the remarkable performances in controlling displacement response.

0 2 4 6 8 10 12 14 16 18 20

-4

-3

-2

-1

0

1

2

3

4

x 10-3

Time (second)

1st F

loor

Displ

acem

ent (

m)

uncontrolledpassive onClipped OptimalModulated Homogenous Friction

(a) El Centro earthquake

nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 04/02/2014 Term

0.01

6 8 10 12 14 16 18 20 22 24 26-0.01

-0.005

0

0.005

uncontrolledpassive

1st F

loor

Dis

plac

emen

t (m

)

Clipped OptimalModulated Homogenius Friction

Time (second)

(b) Kobe earthquake

0.015

0.01

0 2 4 6 8 10 12 14 16 18 20-0.015

-0.01

-0.005

0

0.005

1st F

loor

Dis

plac

emen

t (m

)

Time (second)

(c) Northridge earthquake Figure 19. Passive and semi-active RT-HYTEM

experimental result (Time domain) Also, the displacement responses in the frequency domain

to three earthquake excitations applied to uncontrolled, passive and semi-active controlled RT-HYTEM were compared for the 1st floor in Fig.20. The figures show that overall best control performance is when the clipped-optimal control algorithms applied to the structure. However, all the result shows insignificant control performance against the passive control. These results were led by long period model structure having 0.52Hz and scale downed excitation load due to the UTM capacity. As the passive result, the peak response is shifted to the vicinity of 0.62 Hz in semi-active controlled result. This small amount of frequency shifting was due to the stiffening effect of the MR damper used in this study as the applied current was increased as passive control results.

120 250

0 1 2 3 4 50

20

40

60

80

100

(a) El CentroFrequency (Hz)

5th

Acc

eler

atio

n M

agni

tude

200

150

100

50

00 1 2 3 4 5

Frequency (Hz)

5th

Acce

lera

tion

Mag

nitu

de

0 1 2 3 4 50

20

40

60

80

100

120

140

uncontrolled

Frequency (Hz)

5th

Acce

lera

tion

Mag

nitu

de

passive controlClipped OptimalModulated Homogenous Friction

(b) Kobe

(c) Northridge Figure 20. Passive and semi-active RT-HYTEM

experimental result (Frequency domain)


s of Use: http://asme.org/terms

Down

CONCLUDING REMARKS In this study, the investigation of the hysteretic behavior of

an MR damper itself and the seismic performance evaluation of a building structure, installed with an MR damper were experimentally implemented by using the real-time hybrid testing method. In the tests, the building model that was identified from the force-vibration test results of a real-scaled 5-story building was adopted as a numerical substructure in this study. Also, an MR damper that corresponds to an experimental substructure was physically tested by using a universal testing machine (UTM). The Bouc-Wen model was used to calculate the control force of the MR damper used in this study, and its parameters were identified based on the experimental results from the RT-HYTEM, which used a sinusoidal wave as the ground input acceleration. RT-HYTEM was validated because the real-time hybrid testing results from the sinusoidal and earthquake excitations and the corresponding analytical results agreed well with each other. Especially, the RT-HYTEM was highly reliable with the impulse-like seismic excitation such as that of the Northridge earthquake. To compare RT-HYTEM and numerical result, Bouc-Wen model parameters was identified by each input currents. This comparison result showed that the RT-HYTEM was the more reasonable than numerical analysis due to nonlinear variation of reaction velocity and excitation frequency. The experimental results from RT-HYTEM for the passive on control showed that structural responses were not decreased further by excessive control force, but was decreased with the increase of the current applied to the MR damper. Also the semi-active controlled result showed insignificant control performance than passive controlled result. It seems that passive control force of MR damper already reached to the optimal friction force by proportional shear force of 1st floor. For the better performance of semi-active control algorithms, more loading capacity of UTM of which the optimal friction force of the structure can be laid in the maximum and minimum force of MR damper is required. All results indicated that the seismic performance of a building structure installed with an MR damper can be indirectly evaluated by the RT-HYTEM, in which only the MR dampers are physically tested. For further study, various applications of semi-active algorithms and more minimizing technique of the time delay in RT-HYTEM would be required.

ACKNOWLEDGMENTS The work presented in this paper was supported by the

Ministry of Education & Human Resources Development through the Second Stage of BK21.

REFERENCES [1] Jansen L. M., Dyke S. J., “Semi-Active Control strategies

for MR Dampers : A Comparative Study”, ASCE Journal of Engineering Mechanics, Vol. 126, No. 8, pp.795-803.

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[2] Yang G., Spencer Jr. B. F., Jung H.-J., Carlson J. D. (2004). “Dynamic Modeling of Large-Scale Magnetorheological Damper Systems for Civil Engineering Applications”, J. Engrg. Mech., Vol. 130, No. 9, pp. 1107-1114.

[3] Spencer Jr. B. F., Dyke S. J., Sain M. K. and Carlson J. D. (1997). “Phenomenological Model for Manetorheological Dampers”, J. Engrg. Mech., Vol. 123, No. 3, pp.230-238

[4] Lee H.-J., Yang. G., Jung H.-J., Spencer Jr. B. F., and Lee I.-W. (2006). “Semi-active neurocontrol of a base-isolated benchmark structure”, Struct. Control Health Monit., Vol. 13, pp.682-692

[5] Nakashima M., Kato H. and Takaokas E. (1992). “Development of real-time pseudo dynamic testing”, Earthquake Engineering and Structural Dynamics, Vol. 21, pp. 79-92

[6] Pan P., Nakashima M. and Tomofuji H. (2005). “Online test using displacement-force mixed control”, Earthquake Engineering and Structural Dynamics, Vol. 34, pp. 869-888

[7] Lee S.-K., Park E. C., Min K.-W., Lee S.-H. Chung L. and Park J.-H. (2007), “Real-time hybrid shaking table testing method for the performance evaluation of a tuned liquid damper controlling seismic response of building structures”, J. of Sound and Vibration, Vol. 302, pp.596-612

[8] Blakeborough A., Williams M. S., Darby A. P. and Williams D.M. (2001). “The development of real-time substructure testing”, Philosophical transactions. Series A, Mathematical, physical and engineering sciences, Vol. 359, No. 1786, 2001, pp. 1869-1892

[9] Lee S.-K., Park E. C., Min K.-W. and Park J.-H. (2007), “Real-time substructuring technique for the shaking table test of upper substructures”, Engineering Structures, Vol. 29, pp.2219-2232

[10] The MathWorks (2007). Signal Processing Toolbox User’s Guide, The MathWorks,

[11] Dennis J.E., Jr., and Schnabel R. B., Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Englewood Cliffs, NJ: Prentice-Hall, 1983

[12] The MathWorks, Inc, (2007). Simulink Reference, MATLAB®SIMULINK®

[13] The MathWorks, Inc, (2007). Real-Time Windows Target 3 User’s Guide, MATLAB®SIMULINK®

[14] Wen Y. K. (1976). “Method of random vibration of hyteretic systems”, J. Engrg. Mech. Div., ASCE, 102(2), pp.249-263

[15] The MathWorks, (1999), Optimization Toolbox User’s Guide, The MathWorks

[16] Inaudi J. A. (1997), “Modulated Homogeneous Friction : a Semi-active Damping Strategy”, Earthquake Engineering and Structural Dynamics, Vol. 26, pp.361-376.



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