Literature 1

1An Experimental Study of MR Dampers for Seismic Protection

S.J. Dyke,1 B.F. Spencer Jr.,2 M.K. Sain3 and J.D. Carlson4

AbstractIn this paper, the efficacy of magnetorheological (MR) dampers for seismic response reduc-

tion is examined. To investigate the performance of the MR damper, a series of experiments wasconducted in which the MR damper is used in conjunction with a recently developed clipped-opti-mal control strategy to control a three story test structure subjected to a one-dimensional groundexcitation. The ability of the MR damper to reduce both peak responses, in a series of earthquaketests, and rms responses, in a series of broadband excitation tests is shown. Additionally, becausesemi-active control systems are nonlinear, a variety of disturbance amplitudes are considered toinvestigate the performance of this control sytstems over a variety of loading conditions. For eachcase, the results for three clipped-optimal control designs are presented and compared to the per-formance of two passive systems. The results indicate that the MR damper is quite effective forstructural response reduction over a wide class of seismic excitations.

1.0 IntroductionIn the last three decades or so, there has been a great deal of interest in the use of control sys-

tems to mitigate the effects of dynamic environmental hazards such as earthquakes and strongwinds on civil engineering structures. A variety of control systems have been considered for theseapplications that can be classified as either passive, active, semi-active, or hybrid (combinationsof the previous types). Passive control systems, such as viscoelastic dampers, tuned mass damp-ers, frictional dampers, tuned liquid dampers, and base-isolation systems, were developed as ameans of augmenting the damping in a structure [30]. Passive systems impart forces on the struc-ture by reacting to the localized motion of the structure, primarily acting to dissipate the vibratoryenergy in the structural system. These systems are now widely accepted as a viable means ofreducing the responses of a structure. However, passive systems are limited because they cannotadapt to varying loading conditions. Thus, passive systems may perform well in subjected to theloading conditions for which they were designed, but may not be effective in other situations.

To develop a more versatile alternative, the concept of active control was introduced by Yaoin 1972 [38]. Active control systems operate by using external energy supplied by actuators toimpart forces on the structure, generally depending on a sizeable power supply. The appropriatecontrol action is typically determined based on measurements of the structural responses and/orthe disturbance. Because the control forces are not entirely dependent on the local motion of thestructure (although there is some dependence on the local response due to the effects of control-structure interaction), the control systems are considerably more flexible in their ability to reducethe structural responses for a wide variety of loading conditions. Extensive research has been

1. Dept. of Civil Engineering, Washington University, St. Louis, MO 63130, U.S.A.2. Dept. of Civil Engineering and Geol. Sci., University of Notre Dame, Notre Dame, IN 46556, U.S.A.3. Dept. of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, U.S.A.4. Mechanical Products Division, Lord Corporation, Cary, NC 27511, U.S.A.

To appear in Smart Materials and Structures: Spe-cial Issue on Large Civil Structures.

2done on active structural control [1623, 29], and these systems have been installed in overtwenty commercial buildings and more than ten bridges (during construction) [16, 23]. However,there are still a number of questions that must be addressed before this technology is widelyaccepted, including questions of stability, cost effectiveness, reliability, power requirements, etc.For instance, active systems have the ability to input mechanical energy into the structural system,making them capable of generating instabilities due to unmodeled dynamics and nonlinearities, orequipment failure (e.g., power source, sensors, control hardware/software, etc.). Additionally, theneed for sizeable power supplies and large control forces may make them quite costly to installand maintain.

Semi-active systems offer another alternative in structural control. A variety of semi-activecontrol devices have been proposed, including variable orifice dampers, variable friction devices,adjustable tuned liquid dampers, and controllable fluid dampers. These systems have attractedmuch attention recently because they possess the adaptability of active control systems, yet areintrinsically stable and operate using very low power. Typically, a semi-active control device isdefined as one that cannot increase the mechanical energy in the controlled system (i.e., includingboth the structure and the device), but has properties that can be dynamically varied. Becausethese devices are adaptable, they are expected to be quite effective for structural response reduc-tion over a wide range of loading conditions. Additionally, semi-active control devices do notrequire large power sources such as those associated with active control systems, making themquite attractive for seismic applications. Moreover, semi-active devices are inherently stable (in abounded input - bounded output sense), which makes it possible to implement high authority con-trol strategies which, in practice, may result in performances that can surpass that of comparableactive systems.

One semi-active device that appears to be particularly promising for seismic protection is themagnetorheological (MR) damper [4, 5, 1115, 3234]. MR dampers use MR fluids to producecontrollable dampers. MR fluids are the magnetic analogs of electrorheological (ER) fluids [17,18, 25, 27, 28, 36], and like ER fluids, the essential characteristic of the MR fluids is their abilityto reversibly change from a free-flowing, linear viscous fluid to a semi-solid in milliseconds whenexposed to a magnetic field (or in the case of ER fluids, an electric field). A typical MR fluid con-sists of 2040% by volume of relatively pure, soft iron particles, e.g. carbonyl iron, suspended inan appropriate carrier liquid such as mineral oil, synthetic oil, water or a glycol. Particle diameteris typically 3 to 5 microns. A variety of proprietary additives similar to those found in commerciallubricants are commonly added that discourage gravitational settling and promote particle suspen-sion, enhance lubricity, modify viscosity, and inhibit wear. The ultimate strength of a MR fluiddepends on the square of the saturation magnetization of the suspended particle [3, 5, 19, 20], andthe key to a strong MR fluid is to choose a particle with a large saturation magnetization. Pureiron particles, the best practical choice, have a saturation magnetization of 2.15 Tesla [5] and MRfluids made from iron particles exhibit a yield strength of 50100 kPa for an applied magneticfield of 150250 kA/m.

Although the characteristics of MR and ER fluids are similar in some respects, devices whichare based on MR fluids appear to have a number of advantages, making them extremely promis-ing for civil engineering applications [1, 2]. For example, the achievable yield stress of MR fluidsis an order of magnitude greater than its ER counterpart, making it possible to develop deviceswhich are capable of generating larger forces. Additionally, MR fluids are not highly sensitive tocontaminants or impurities such as are commonly encountered during manufacture and usage.Further, because the magnetic polarization mechanism is not affected by the surface chemistry of

3surfactants and additives, it is relatively straightforward to stabilize MR fluids against particle-liq-uid separation in spite of the large density mismatch. Antiwear and lubricity additives can also beincluded in the formulation without affecting strength and power requirements. Devices employ-ing the MR fluid can be controlled with a low power (e.g., less than 50 watts), low voltage (e.g.,~1224V), current-driven power supply outputting only ~12 amps, which could be readily sup-plied by batteries. MR fluids have been used to develop semi-active control devices for a varietyof applications, including braking devices in exercise equipment, and actuators in vehicular seatsuspension systems [14]. MR fluid technology appears to be scalable to the size required forseismic control applications. To demonstrate the feasibility of producing forces required for full-scale structures, Lord Corporation has recently designed and built a 20-ton MR damper. Testingon the full-scale MR damper is currently underway at the University of Notre Dame [4, 5].

Because MR dampers are intrinsically nonlinear, one of the challenges is to develop appro-priate control algorithms to take advantage of the unique characteristics of the device. Variousapproaches have been proposed in the literature for the control of semi-active systems (see, forexample, refs. [12, 13, 24, 25, 28]). To be implementable, the algorithms must use readily avail-able measurements, such as accelerations, in determining the control action. Previously, a numberof active control experiments have been conducted to demonstrate the efficacy of accelerationfeedback control strategies based on /LQG techniques [7, 9, 10, 13]. For semi-actively con-trolled structures, Dyke et al. [11 15] have extended these results to develop a clipped-optimalcontrol strategy based on acceleration feedback, and shown the effectiveness of this approach.

The focus of this paper is to experimentally demonstrate the ability of the MR damper toreduce structural responses over a wide range of loading conditions. Following a description ofthe experimental setup, the procedure used to identify a model of the integrated MR damper/struc-ture is described. A clipped-optimal control algorithm recently developed for use with the MRdamper [1115], is then discussed. In the experiments, the ability of the system to reduce both thepeak responses, in the case of the earthquake excitation, and rms response, in the case of thebroadband excitation, is studied. Due to the intrinsic nonlinear behavior of the MR damper, theperformance of the control system will vary with the magnitude of the disturbance. Thus, theamplitude of the disturbance was also varied in the tests. The performance of the semi-activelycontrolled structure is compared to that of two cases in which the MR damper is used in a passivemode, designated passive-off and passive-on. The results reported herein indicate that this semi-active control system is quite effective for seismic response reduction over a wide range of seis-mic excitations.

2.0 Experimental SetupFigure 1 is a diagram of the semi-actively controlled, three-story, model building at the

Structural Dynamics and Control/Earthquake Engineering Laboratory at the University of NotreDame (http://www.nd.edu/~quake/). The test structure used in this experiment is designed to be ascale model of the prototype building discussed in Chung, et al. [6] and is subjected to a one-dimensional ground motion. The building frame is constructed of steel, with a height of 158 cm.The floor masses of the model weigh a total of 227 kg, distributed evenly between the threefloors. The time scale factor is 0.2, making the natural frequencies of the model approximatelyfive times those of the prototype. More information on this test structure is available in [35].

H2

4In this experiment, a single magne-torheological (MR) damper is installedbetween the ground and the first floor, asshown in Fig. 1. The MR damperemployed here is a prototype device,shown schematically in Fig. 2 obtainedfrom the Lord Corporation for testing andevaluation [33] (see also http://www.mrfluid.com). The damper is 21.5cm long in its extended position and has a

cm stroke. The main cylinder is 3.8cm in diameter and houses the piston, themagnetic circuit, an accumulator and 50ml of MR fluid. The magnetic field pro-duced in the device is generated by asmall electromagnet in the piston head.The current for the electromagnet is sup-plied by a linear current driver which gen-erates a current that is proportional to theapplied voltage. The peak power requiredis less than 10 watts. The system, includ-ing the damper and the current driver, hasa response time of typically less than 10 msec.

A nu,mber of sensors are installed in themodel building for use in determining the controlaction. Accelerometers located on each of thethree floors provide measurements the absoluteaccelerations, , an LVDT (linear vari-able differential transformer) measures the dis-placement of the MR damper, and a forcetransducer is placed in series with the MR damperto measure the control force being applied to thestructure. Note that only these five measurementsare used in the control algorithm. However, toevaluate the performance of the control strategies,LVDTs are attached to the base and to each floorof the structure to measure the relative displace-ments of the structure.

Implementation of the discrete controller wasperformed using the Spectrum Signal ProcessingReal-Time Digital Signal Processor (DSP) Sys-tem. A discussion of the specific capabilities ofthis board which make it suitable for use in struc-tural control systems is provided in Quast, et al. [37].

xg

xa1 xd,

xa2

xa3

Figure 1. Diagram of MR DamperImplementation.

f

ControlComputer

CurrentDriver

2.5

Figure 2. Schematic of MR Damper.

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MR Fluid

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Wires toElectromagnet

Wires toElectromagnet

Bearing & Seal

MR Fluid

Coil

Diaphragm

Accumulator

AnnularOrifice

xa1 xa2 xa3

xd

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53.0 System IdentificationOne of the most important and challenging tasks in control synthesis and analysis is the

development of an accurate mathematical model of the structural system under consideration,including both the structure and the associated control devices. The approach to system identifica-tion of semi-actively controlled structures outlined in [32] is employed. In this approach, theproblem is simplified by decoupling the identification of the nonlinear semi-active device fromthat of the primary structure. If the semi-active controller is assumed to be adequate to keep theresponse of the primary structure in the linear range, then standard linear system identificationtechniques can be used to develop a model for the primary structure. Nonlinear identificationmeans must still be employed to identify the semi-active control device. Additionally, thisapproach is attractive because the identification of the semi-active system requires only measure-ments which are available for controlling the responses of the structure.

The approach consists of four steps: (i) modeling and identification of the semi-active controldevice, (ii) identification of a model of the primary structure, (iii) integration and optimization ofthe device and structural models, and (iv) validation of the integrated model of the system. Thesesteps are briefly described in the subsequent sections.Modeling and Identification of the MR Damper

The first step in the identification process is to develop an input/output model for the MRdamper. The simple mechanical idealization of the MR damper depicted in Fig. 3 has been shownto accurately predict the behavior of a prototype MR damper over a broad range of inputs [31,33]. The equations governing the force predicted by this model are given by

(1)

(2)

(3)

fc0

k0c1

k1

Figure 3. Simple Mechanical Model of the MR Damper.

Bouc-Wen xd

y

ff c1 y k1 xd x0( )+=

z xd y z zn 1

xd y( ) z n A xd y( )+=

y 1c0 c1+---------------- z c0 xd k0 xd y( )+ +{ }=

6where is an evolutionary variable that accounts for the history dependence of the response. Themodel parameters depend on the voltage to the current driver as follows

, , (4)

where is given as the output of the first-order filter

(5)Eq. (5) is necessary to model the dynamics involved in reaching rheological equilibrium and indriving the electromagnet in the MR damper [31, 33].

A nominal set of parameters was obtained based on the response of the MR damper in aseries of displacement-controlled tests. A hydraulic actuator was employed to drive the MRdamper, and the displacement and force generated in the MR damper were measured, as describedin [31, 33]. A typical response of the MR damper for a sinusoidal input in shown in Fig. 4. Aleast-squares output-error method was employed in conjunction with a constrained nonlinear opti-mization to obtain the 14 model parameters in Eqs. (15). The optimization was performed usingthe sequential quadratic programming algorithm available in MATLAB [26]. A representativecomparison of the response predicted by this model and the experimentally measured response forthe MR damper is shown in Fig. 4. The resulting parameters were used to initialize the identifica-tion of the integrated system model, presented subsequently.

zv

a bu+= c1 c1a c1bu+= c0 c0a c0bu+=

u

u u v( )=

Figure 4. Comparison of the Model Results and the ExperimentalData for the Random Displacement, Random Voltage Test.

Time (sec)

Velocity (cm/sec)Displacement (cm)

Forc

e (N

)Fo

rce (N

)

a) Force vs. Time

b) Force vs. Displacement c) Force vs. Velocity

ExperimentalPredicted

0 0.5 1 1.52000

1000

0

1000

2000

1 0.5 0 0.5 12000

1000

0

1000

2000

40 0 402000

1000

0

1000

2000

7Identification of the Primary StructureThe next step in identifying a model of the integrated system is to develop an input/output

model of the structure. Because the structure itself is assumed to remain in the linear region, thefrequency domain approach to linear system identification discussed in Dyke, et al. [7, 9, 10, 13]and Spencer and Dyke [32] is used to identify a mathematical model of the test structure.

A block diagram of the structural system to be identified is shown in Fig. 5. There are twoinputs to the structural system, including the ground excitation and the applied control force .The four measured system outputs are the displacement of the structure at the attachment pointof the MR damper, and the absolute accelerations, , , , of the three floors of the teststructure (i.e., ). Thus, a transfer function matrix must be identi-fied to describe the characteristics of the system in Fig. 5.

The first step in the identification of the structure is to experimentally determine the transferfunctions from each of the system inputs to each of the outputs. The eight transfer functions aredetermined by independently exciting each of the inputs of the structure with a random input andmeasuring the structural responses. The transfer functions from the ground acceleration to each ofthe measured responses were obtained by exciting the structure with a band-limited white noiseground acceleration (0-50 Hz). During this test, the MR damper is not connected to the structure,thus making . Similarly, the experimental transfer functions from the applied control forceto each of the measured outputs are determined. To this end, the MR damper is replaced with ahydraulic actuator to apply a band-limited white noise (0-50 Hz) force to the structure while thebase of the structure is held fixed. The force transducer, mentioned previously, is placed in serieswith the hydraulic actuator to directly measure the applied force. A representative transfer func-tion from the ground acceleration to the third floor absolute acceleration is shown in Figure 6.This transfer function was obtained using twenty averages. The three distinct, lightly-dampedpeaks occurring at 5.88, 17.5, and 28.3 Hz correspond to the first three modes of the structuralsystem.

Once the experimental transfer functions have been obtained, the next step in the systemidentification procedure is to model each transfer function as a ratio of two polynomials in theLaplace variable s. This task is accomplished via a least squares fit of the ratio polynomials, eval-uated on the axis, to the experimentally obtained transfer functions. For this structure, thedecision was made to focus control efforts on reducing the structural responses in the first threemodes. Thus, the model is required to be accurate below 35 Hz. Six poles are necessary to modelthe input/output behavior of each of the transfer functions in the frequency range of interest.

xg fxd

xa1 xa2 xa3y xd xa1 xa2 xa3[ ]= 4 2

Figure 5. System Identification Block Diagram.

f

xgxdxa1xa2xa3

Structure

Primary

f 0=

j

8The system is then assembled in state space form using the analytical representation of thetransfer functions (i.e., the poles, zeros and gain). Because all of the transfer functions requiredsix states, the combined system has a total of twelve poles. A model reduction is performed toachieve a minimal realization of the system; thus, the twelve state system was reduced to a sixstate system, resulting in a reduced-order model of the form

(6)

where v represents the measurement noise vector.A representative comparison of the reduced-order model to the experimental transfer func-

tions is shown in Fig. 6. Additional details regarding this frequency domain identificationapproach can be found in Dyke, et al. [710, 13].Development of an Integrated System Model

The next step in identifying a model of the integrated structural system is to optimize the setof parameters for the MR damper model (Eqs. 15) for the case when it is installed in the teststructure, and combine the models of the device and structure to form the integrated system model(shown in Fig. 7). Updating the parameters of the MR damper model is necessary because the MRdamper may function at a different operating point when installed in the test structure than in theinitial tests in which the damper was driven with a hydraulic actuator [32].

xr Axr Bf E xg,+ +=y Cyxr Dy f v,+ +=

Figure 6. Comparison of Reduced-Order Model and Experimental TransferFunction: Ground Acceleration to Third Floor Absolute Acceleration.

0 5 10 15 20 25 30 35 40 45 50200

100

0

100

200

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40

20

0

20

40

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Frequency (Hz)

Mag

nitu

de (d

B)Ph

ase

(deg)

Model

Experimental

9To update the parameters of the MR damper model, a series of tests was conducted to mea-sure the response of the structure with the MR damper in place in the test structure (see Fig. 1). Inthese tests, the structure was excited at the base, while various voltages were applied to the cur-rent driver of the MR damper. The recorded system responses included the force generated in theMR damper, absolute accelerations of each floor, displacement of the floors of the structure, dis-placement of the base, and displacement of the three floors of the structure. Optimized parameterswere determined to fit the generalized model of the MR damper to the experimental data. Theresulting parameters are: = 8 N sec/cm, = 6 N sec/cm/V, = 50 N/cm, = 290N sec/cm, = 5N sec/cm/V, = 12 N/cm, = 14.3 cm, =100, = 450 V1, = 363cm2, = 363 cm2, = 301, = 2, = 190 sec1.

The integrated system model is then formed by connecting the models of the MR damper(Eqs. 15) and structure (Eq. 6) as shown in Fig. 7. Verification of this integrated system model isprovided in the following section.

Experimental Validation of the Integrated System ModelTo verify that the identified model is adequate for control synthesis and analysis, the pre-

dicted response and experimental response were compared in one controlled case (Controller A asdescribed in the following section). A representative comparison of the experimental and pre-dicted responses for the relative displacement and absolute acceleration of the third floor is shownin Fig. 8 for a broadband excitation (0-20 Hz) with an rms ground acceleration of 0.20 g. Goodagreement is obtained.

4.0 Clipped-Optimal Control AlgorithmOne of the main challenges in semi-active control is the development of an appropriate con-

trol algorithm that can take advantage of the features of the control device to produce an effectivecontrol system. An important requirement of the control algorithm is that it be implementable infull-scale applications. To be implementable, the algorithm should use available measurements,such as accelerations, in determining the control action. Dyke, et al. [11, 12] have proposed aclipped-optimal control strategy based on acceleration feedback for the MR damper. Analyticalstudies demonstrated that the MR damper, used in conjunction with the clipped optimal controlalgorithm, was effective for controlling a multi-story structure with a single MR damper. In this

v

c0a c0b k0 c1a c1b k1 x0 a b A n

xdxa1xa2xa3

Figure 7. Block Diagram of the Identified Integrated Structural System.

fxg

vMR Damper Primary

Structure

xd

ModelModel

10

section, the approach to the design of the clipped-optimal controller is provided. The discussionof the control algorithm considers the general case in which there are multiple devices present tocontrol the structure, although in this experiment only a single MR damper is employed.

In the clipped-optimal controller, the approach is to append n force feedback loops to induceeach MR damper to produce approximately a desired control force. The desired control force ofthe ith MR damper is denoted . A linear optimal controller is designed that calculates a

vector of desired control forces, , based on the measured structural re-sponse vector and the measured control force vector , i.e.,

(7)

where { } is the Laplace transform. Although the controller can be obtained from a vari-ety of synthesis methods, /LQG strategies are advocated herein because of the stochastic na-ture of earthquake ground motions and because of their successful application in other civilengineering structural control applications [7, 9, 10, 13].

Figure 8. Experimental and Predicted Responses of the Semi-Actively Controlled System (Controller A): Third Floor Relative

Displacement and Absolute Acceleration.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 52000

0

2000

Time (sec)

Third

Flo

or A

bsol

ute

Acc

eler

atio

n (cm

/sec2 )

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.6

0

0.6

Third

Flo

or R

elat

ive

Disp

lace

men

t (cm

) PredictedExperimental

f ci Kc s( )

fc f c1 f c2 f cn =y f

fc L1 Kc s( )L

yf

=

L Kc s( )H2

11

To discuss the algorithm used for determining the control action, consider the ith MR damperused to control the structure. Because the response of the MR damper is dependent on the relativestructural displacements and velocities at the point of attachment of the MR damper, the forcegenerated by the MR damper cannot be commanded; only the voltage applied to the currentdriver of the ith MR damper can be directly controlled. To induce the MR damper to generateapproximately the corresponding desired optimal control force , the command signal isselected as follows. When the ith MR damper is providing the desired optimal force (i.e.,

), the voltage applied to the damper should remain at the present level. If the magnitudeof the force produced by the damper is smaller than the magnitude of the desired optimal forceand the two forces have the same sign, the voltage applied to the current driver is increased to themaximum level so as to increase the force produced by the damper to match the desired controlforce. Otherwise, the commanded voltage is set to zero. The algorithm for selecting the commandsignal for the ith MR damper is graphically represented in Fig. 9 and can be concisely stated as

(8)

where is the voltage to the current driver associated with saturation of the MR effect in thetested device, and ( ) is the Heaviside step function. A block diagram of this semi-active controlsystem is shown in Fig. 10. In the block diagram, the dependence of the MR damper forces on thestructural responses is indicated by the link feeding back the vectors and , which contain therelative structural displacements and velocities at the attachment points of the MR damper. For in-stance, if three MR dampers were rigidly attached between the first three floors of a structure, thisvector would be .

One of the attractive features of this control strategy is that the feedback for the controller isbased on readily obtainable acceleration measurements, thus making them quite implementable.In addition, the proposed control design does not require a model for the MR damper, althoughthe model of the damper is important to system analysis.

vi

f ci vif i f ci=

vi Vmax=

fci

f ivi 0=

vi 0=

vi 0=

vi 0=

Figure 9. Graphical Representation ofAlgorithm for Selecting the Command Signal

vi Vmax=

vi Vmax H ( f ci f i{ } f i)=

V maxH

xr xr

xr x1 x2 x1 x3 x2 =

12

5.0 Experimental ResultsTo evaluate the performance of the semi-active control system employing the MR damper,

eight controllers with various performance objectives were designed based on the identifiedmodel of the integrated structure/MR damper system and implemented in the laboratory. Theresults of three semi-active control designs, denoted AC, are presented herein. Controller A wasdesigned by placing a high weighting on the third floor relative displacement. Controllers B, andC were designed by placing a low and high weighting, respectively, on the third floor accelera-tion. In the results, is the displacement of the th floor relative to the ground, is the inter-story drift (i.e., ), is the absolute acceleration of the th floor, and is the measuredcontrol force.

In addition to the results for semi-active controllers, two passive cases are considered. Pas-sive-off and passive-on refer to the cases in which the voltage to the MR damper is held at a con-stant value of and Volts, respectively. The uncontrolled responserefers to the case in which the MR damper is not attached to the structure.

Two types of experiments were conducted to evaluate the performance of the control designs.In the first set of tests, the three story model structure was subjected to a scaled 1940 El Centroearthquake and the peak values of the measured responses were determined. In these tests, theearthquake was reproduced at five times the recorded speed to satisfy the similitude relations. Inthe second set of tests, the three story model structure was subjected to a 200 second broadbandsignal (020 Hz) and rms values of the measured responses were calculated.

Because the MR damper is a nonlinear device, its performance will vary for different excita-tion levels. Thus, the earthquake tests were performed at two different excitation amplitudes (80%and 120% of the recorded El Centro earthquake) and the broadband tests were conducted at threedifferent input amplitudes including excitations with rms values of 0.06 g (low), 0.13 g (medium),and 0.20 g (high).

Because in some cases the excitation levels used in the passive and controlled tests were quitelarge for the test structure, exciting the uncontrolled structure with the same excitation could have

Figure 10. Block Diagram of the Semi-ActiveControl System.

f

fc

v

xr xr,

MRDampers Structure

xg

Kc

s( )Eq. (8) f

y

Control Law

f

xi i dixi xi 1 xai i f

V 0= V Vmax 2.25= =

13

been destructive. Therefore, the uncontrolled results presented herein were obtained by using anexcitation with 50% of that used in the controlled tests, and then scaling the uncontrolled struc-tural responses up to represent the response of the structure to the full excitation. Thus the uncon-trolled results represent the response of the structure if it were to remain linear throughout thetests.

The experimental results are summarized in the following sections.El Centro Earthquake Results

Table 1 summarizes the results of the high and low amplitude El Centro earthquake excita-tion tests. Notice that both the passive-off and passive-on systems are able to achieve a reasonablelevel of performance at high and low excitation levels. Because the MR damper is capable of gen-erating larger damping forces in the passive-on case than in the passive-off case, one might pre-dict that the passive-on system would achieve larger reductions in the responses. However, fromthe results it is shown that a number of the responses of the passive-on system are actually largerthan those of the passive-off system. For instance, in the low amplitude tests, the third floor dis-placement, maximum interstory displacement, and maximum floor acceleration of the passive-onsystem are 11.3%, 10.9% and 19.0% larger, respectively, than the responses of the passive-offsystem. In the high amplitude tests, the passive-on controller performs better than the passive-off

Table 1: Experimental Peak Responses due to the El Centro Earthquake.

ControlStrategy Uncontrolled Passive-Off Passive-On

Clipped-OptimalController A

Clipped-OptimalController B

Clipped-OptimalController C

High Amplitude: Responses due to the 120% El Centro Earthquake

(cm)0.7101.0681.249

0.2360.3620.436

0.1260.3120.420

0.1270.2290.318

0.1570.2640.335

0.1510.2130.280

(cm)0.7100.3620.205

0.2360.1670.106

0.1260.1960.110

0.1270.1390.092

0.1570.1390.081

0.1510.1230.087

(cm/sec2)87911101500

666714804

920808897

711642786

874673653

957859748

(cm) 0.214 0.095 0.112 0.133 0.133 (N) 258 1030 696 668 754

Low Amplitude: Responses due to the 80% El Centro Earthquake

(cm)0.4730.7120.833

0.1190.1970.240

0.0740.1960.267

0.0840.1570.213

0.0870.1480.192

0.0890.1360.184

(cm)0.4730.2410.137

0.1190.0990.067

0.0740.1320.083

0.0840.0860.066

0.0870.0850.060

0.0890.0770.059

(cm/sec2)5867401000

388481500

595546594

462457482

542579521

657759545

(cm) 0.112 0.049 0.063 0.071 0.071 (N) 224 768 537 580 630

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controller in reducing the peak third floor displacement and maximum interstory displacement,but an increase in the absolute accelerations is still observed.

The results presented in Table 1 show that all of the semi-active control systems perform sig-nificantly better that the passive systems. In the high amplitude tests, Controller A achieves a24.3% reduction in the peak third floor displacement and a 29.1% reduction in the maximuminterstory displacement over the best passive responses. Furthermore, these reductions wereobtained while achieving a modest reduction in the maximum acceleration. Additional reductionin the peak third floor relative displacement over the best passive case is achieved with ControllerC (33.3%), although with an increase in the maximum acceleration. Notice that for all of the semi-actively controlled systems, these performance gains are achieved while requiring significantlysmaller control forces than are required in the passive-on case.

At low excitation amplitudes, the performance of the semi-active controllers is still superiorto that of the passive controllers, although not to as great an extent. The third floor relative dis-placement, maximum interstory displacement, and maximum absolute acceleration are reducedover the best passive case by 11.3%, 27.8%, and 3.6%, respectively, with Controller A. Again,additional reduction in the third floor relative displacement is achieved with Controllers B (20%),and C (23.3%), although the maximum acceleration response is increased in these cases.

Figure 11 shows the uncontrolled and semi-actively controlled (using Controller A) responsesfor the tested structure. The effectiveness of the proposed control strategy is clearly seen, withpeak third floor displacement being reduced by 74.5% and the peak third floor acceleration beingreduced by 47.6% over the uncontrolled responses.

UncontrolledControlled

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 51.3

0

1.3

x3

(cm)

xa

3(cm

/sec2 )

Figure 11. Controlled and Uncontrolled StructuralResponses due to 120% El Centro Earthquake (Controller A).

time (sec)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

1500

0

1500

15

Random Excitation ResultsThe rms values of the structural responses in the random excitation test are provided in Table

2. Here, the passive systems are able to achieve reasonable reduction in the structural responses atall excitation levels. In the high amplitude tests, most of the rms responses of the passive-on sys-tem are better than those of the passive-off system. However, at lower excitation levels, the rmsresponses of the passive-on system are often larger than. those of the passive-off system. For

Table 2: Experimental RMS Responses Due to the Random Excitations.

ControlStrategy Uncontrolled Passive-Off Passive-On

Clipped-OptimalController A

Clipped-OptimalController B

Clipped-OptimalController C

High Amplitude: Responses to the High Amplitude Random Excitation

(cm)0.2500.3820.467

0.0700.1120.139

0.0270.0700.103

0.0360.0660.091

0.0360.0650.088

0.0380.0660.089

(cm)0.2500.1560.123

0.0700.0480.035

0.0270.0490.036

0.0360.0390.031

0.0360.0360.027

0.0380.0360.029

(cm/sec2)1020576999

274184292

226178292

228159250

209153223

225176241

(cm) 0.066 0.020 0.033 0.032 0.034 (N) 112 311 219 209 220

Medium Amplitude: Responses to the Medium Amplitude Random Excitation

(cm)0.1640.2480.304

0.0360.0590.077

0.0180.0490.073

0.0220.0430.062

0.0220.0430.060

0.0230.0440.061

(cm)0.1630.1010.080

0.0360.0280.022

0.0180.0350.026

0.0220.0280.022

0.0220.0260.020

0.0230.0270.021

(cm/sec2)663374649

168112176

162134208

154115174

149113162

161126172

(cm) 0.031 0.010 0.018 0.019 0.020 (N) 105 237 174 161 170

Low Amplitude: Responses to the Low Amplitude Random Excitation

(cm)0.0750.1150.140

0.0130.0260.035

0.0090.0260.037

0.0090.0240.034

0.0100.0230.033

0.0100.0230.033

(cm)0.0750.0470.037

0.0130.0160.012

0.0090.0200.014

0.0090.0170.012

0.0100.0160.012

0.0100.0170.012

(cm/sec2)306173300

88.368.392.5

11488.1113

10278.3102

10276.895.6

10578.796.9

(cm) 0.017 0.007 0.010 0.012 0.014 (N) 85.0 140 121 111 113

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instance, in both the low and medium amplitude tests, the maximum rms acceleration is larger inthe passive-on case than in the passive-off case. Additionally, in the low amplitude test, the maxi-mum interstory displacement is 25% larger in the passive-on case than in the passive-off case.This demonstrates that using a passive device which is capable of generating large control forcesis not always the best approach.

The results indicate that the semi-active control systems perform significantly better at reduc-ing the rms structural responses than the passive systems. At all excitation levels, the three semi-active controllers are able to reduce not only the rms third floor relative displacements and inter-story displacements, but also the maximum rms floor accelerations, well below those obtainedwith the passive systems. Controller B achieves the best performance of the three semi-activecontrol designs, reducing the third floor displacement, maximum interstory displacement, and themaximum floor absolute acceleration, by 14.6%, 26.5%, and 23.6%, respectively, over the bestpassive case in the high amplitude tests, and by 17.8%, 30.0% and 8.0%, in the medium amplitudetests. Even at low amplitudes, a modest reduction in the structural responses is observed. Again,notice that the semi-active controllers achieve these performance levels while using significantlyless force than the passive-on system

6.0 ConclusionThe efficacy of the MR damper in reducing the structural responses for a wide range of load-

ing conditions has been demonstrated in a series of experiments conducted at the StructuralDynamics and Control/Earthquake Engineering Laboratory at the University of Notre Dame. Inthese experiments, the MR damper was used in conjunction with a clipped-optimal control algo-rithm to control the responses of a three story test structure. The clipped-optimal control algo-rithm is implementable in that it uses readily available measurements of the structural responses,primarily absolute accelerations, to perform the control calculations.

The MR damper was shown to effectively reduce both the peak and rms responses due to abroad class of seismic excitations. Three different clipped-optimal control designs were consid-ered, and each of the control designs achieved excellent results. In all cases, the semi-active con-trollers performed significantly better than both of the passive systems considered in reducing thestructural responses. Reductions in both acceleration and displacement responses were observedwith the semi-actively controlled systems. Additionally, the semi-active control systems wereable to achieve these performance gains while using smaller control forces than in the passive-onsystem. Moreover, the capabilities of the MR damper have been shown to mesh well with therequirements and constraints associated with the seismic response reduction in civil engineeringstructures.

Note that algorithms that explicitly incorporate actuator dynamics and control-structure inter-action into the control design process may offer additional controlled performance gains [8].Efforts are currently underway to investigate this possibility.

AcknowledgmentThis research is supported in part by National Science Foundation Grant Nos. CMS 93

01584 and CMS 9500301. In addition, the authors from Notre Dame and Washington Universitywould like to express their appreciation to Lord Corporation of Cary, North Carolina for provid-ing the prototype magnetorheological damper.

17

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