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An experimental study of MR dampers for seismic protection
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Smart Mater. Struct. 7 (1998) 693703. Printed in the UK PII: S0964-1726(98)96181-X
An experimental study of MR
dampers for seismic protection
S J Dyke, B F Spencer Jr, M K Sain and J D Carlson
Department of Civil Engineering, Washington University, St Louis, MO 63130,
USA Department of Civil Engineering and Geological Science, University of NotreDame, Notre Dame, IN 46556, USA Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN46556, USAMechanical Products Division, Lord Corporation, Cary, NC 27511, USA
Received 13 March 1997, accepted for publication 23 June 1997
Abstract. In this paper, the efficacy of magnetorheological (MR) dampers forseismic response reduction is examined. To investigate the performance of the MRdamper, a series of experiments was conducted in which the MR damper is used inconjunction with a recently developed clipped-optimal control strategy to control athree-story test structure subjected to a one-dimensional ground excitation. Theability 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, because semi-active control systems are nonlinear, a variety ofdisturbance amplitudes are considered to investigate the performance of this controlsystem over a variety of loading conditions. For each case, the results for threeclipped-optimal control designs are presented and compared to the performance oftwo passive systems. The results indicate that the MR damper is quite effective forstructural response reduction over a wide class of seismic excitations.
1. Introduction
In the last three decades or so, there has been a great deal of
interest in the use of control systems to mitigate the effects
of dynamic environmental hazards such as earthquakes and
strong winds on civil engineering structures. A variety of
control systems have been considered for these applications
that can be classified as either passive, active, semi-active
or hybrid (combinations of the previous types). Passive
control systems, such as viscoelastic dampers, tuned mass
dampers, frictional dampers, tuned liquid dampers and
base-isolation systems, were developed as a means of
augmenting the damping in a structure [30]. Passive
systems impart forces on the structure by reacting to
the localized motion of the structure, primarily acting to
dissipate the vibratory energy in the structural system.
These systems are now widely accepted as a viable means
of reducing the responses of a structure. However, passive
systems are limited because they cannot adapt to varying
loading conditions. Thus, passive systems may performwell subjected to the loading 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 Yao in 1972 [38].
Active control systems operate by using external energy
supplied by actuators to impart forces on the structure,
generally depending on a sizeable power supply. The
appropriate control action is typically determined based
on measurements of the structural responses and/or the
disturbance. Because the control forces are not entirely
dependent on the local motion of the structure (although
there is some dependence on the local response due to
the effects of controlstructure interaction), the control
systems are considerably more flexible in their ability to
reduce the structural responses for a wide variety of loading
conditions. Extensive research has been done on active
structural control [1623, 29], and these systems have been
installed in over twenty 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 widely accepted, 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,
or equipment failure (e.g., power source, sensors, control
hardware/software etc). Additionally, the need for sizeablepower supplies and large control forces may make them
quite costly to install and maintain.
Semi-active systems offer another alternative in
structural control. A variety of semi-active control devices
have been proposed, including variable orifice dampers,
variable friction devices, adjustable tuned liquid dampers
and controllable fluid dampers. These systems have
attracted much attention recently because they possess the
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adaptability of active control systems, yet are intrinsically
stable and operate using very low power. Typically, a
semi-active control device is defined as one that cannot
increase the mechanical energy in the controlled system
(i.e., including both the structure and the device), but
has properties that can be dynamically varied. Because
these devices are adaptable, they are expected to be quite
effective for structural response reduction over a wide range
of loading conditions. Additionally, semi-active control
devices do not require large power sources such as those
associated with active control systems, making them quite
attractive for seismic applications. Moreover, semi-activedevices are inherently stable (in a bounded inputbounded
output sense), which makes it possible to implement high
authority control strategies which, in practice, may result
in performances that can surpass that of comparable active
systems.
One semi-active device that appears to be particularly
promising for seismic protection is the magnetorheological
(MR) damper [4, 5, 1115,3234]. MR dampers use MR
fluids to produce controllable 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 ability to reversibly
change from a free-flowing, linear viscous fluid to a semi-
solid in milliseconds when exposed to a magnetic field (or
in the case of ER fluids, an electric field). A typical MR
fluid consists of 2040% by volume of relatively pure,
soft iron particles, e.g. carbonyl iron, suspended in an
appropriate carrier liquid such as mineral oil, synthetic
oil, water or a glycol. Particle diameter is typically 3
to 5 microns. A variety of proprietary additives similar
to those found in commercial lubricants are commonly
added that discourage gravitational settling and promote
particle suspension, enhance lubricity, modify viscosity
and inhibit wear. The ultimate strength of a MR fluid
depends on the square of the saturation magnetization of
the suspended particle [3,5, 19, 20], and the key to a strong
MR fluid is to choose a particle with a large saturationmagnetization. Pure iron particles, the best practical choice,
have a saturation magnetization of 2.15 T [5] and MR fluids
made from iron particles exhibit a yield strength of 50
100 kPa for an applied magnetic field of 150250 kA m1.
Although the characteristics of MR and ER fluids
are similar in some respects, devices which are based
on MR fluids appear to have a number of advantages,
making them extremely promising for civil engineering
applications [1, 2]. For example, the achievable yield stress
of MR fluids is an order of magnitude greater than its ER
counterpart, making it possible to develop devices which
are capable of generating larger forces. Additionally, MR
fluids are not highly sensitive to contaminants or impuritiessuch as are commonly encountered during manufacture
and usage. Further, because the magnetic polarization
mechanism is not affected by the surface chemistry of
surfactants and additives, it is relatively straightforward
to stabilize MR fluids against particleliquid separation
in spite of the large density mismatch. Antiwear and
lubricity additives can also be included in the formulation
without affecting strength and power requirements. Devices
employing the MR fluid can be controlled with a low power
(e.g., less than 50 watts), low voltage (e.g., 1224 V),
current-driven power supply outputting only 12 amps,
which could be readily supplied by batteries. MR fluids
have been used to develop semi-active control devices
for a variety of applications, including braking devices
in exercise equipment, and actuators in vehicular seat
suspension systems [14]. MR fluid technology appears
to be scalable to the size required for seismic 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.Testing on the full-scale MR damper is currently under way
at the University of Notre Dame [4, 5].
Because MR dampers are intrinsically nonlinear, one of
the challenges is to develop appropriate control algorithms
to take advantage of the unique characteristics of the
device. Various approaches have been proposed in the
literature for the control of semi-active systems (see,
for example, [12,13, 24,25, 28]). To be implementable,
the algorithms must use readily available measurements,
such as accelerations, in determining the control action.
Previously, a number of active control experiments have
been conducted to demonstrate the efficacy of acceleration
feedback control strategies based on H2/LQG techniques
[7, 9, 10, 13]. For semi-actively controlled structures, Dyke
et al [1115] have extended these results to develop
a clipped-optimal control 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 to reduce structural responses
over a wide range of loading conditions. Following a
description of the experimental setup, the procedure used
to identify a model of the integrated MR damper/structure
is described. A clipped-optimal control algorithm, recently
developed for use with the MR damper [1115], is then
discussed. In the experiments, the ability of the system
to reduce both the peak responses, in the case of the
earthquake excitation, and rms response, in the case ofthe broadband excitation, is studied. Due to the intrinsic
nonlinear behavior of the MR damper, the performance of
the control system will vary with the magnitude of the
disturbance. Thus, the amplitude of the disturbance was
also varied in the tests. The performance of the semi-
actively controlled structure is compared to that of two
cases in which the MR damper is used in a passive mode,
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 seismic excitations.
2. Experimental setup
Figure 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 Notre Dame (http://www.nd.edu/quake/).
The test structure used in this experiment is designed to
be a scale model of the prototype building discussed in
Chung et al [6] and is subjected to a one-dimensional
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Figure 1. Diagram of MR damper implementation.
Figure 2. Schematic of MR damper.
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
three floors. The time scale factor is 0.2, making the natural
frequencies of the model approximately five times those ofthe prototype. More information on this test structure is
available in [35].
In this experiment, a single magnetorheological (MR)
damper is installed between the ground and the first floor,
as shown in figure 1. The MR damper employed here is a
prototype device, shown schematically in figure 2, obtained
from the Lord Corporation for testing and evaluation [33]
(see also http://www.mrfluid.com). The damper is 21.5 cm
long in its extended position and has a 2.5 cm stroke.
The main cylinder is 3.8 cm in diameter and houses the
piston, the magnetic circuit, an accumulator and 50 ml
of MR fluid. The magnetic field produced in the device
is generated by a small electromagnet in the piston head.The current for the electromagnet is supplied by a linear
current driver which generates a current that is proportional
to the applied voltage. The peak power required is less than
10 watts. The system, including the damper and the current
driver, has a response time of typically less than 10 ms.
A number of sensors are installed in the model building
for use in determining the control action. Accelerometers
located on each of the three floors provide measurements
Figure 3. Simple mechanical model of the MR damper.
of the absolute accelerations, xa1 xa2 xa3, an LVDT (linear
variable differential transformer) measures the displacement
xd of the MR damper, and a force transducer is placed in
series with the MR damper to measure the control force
f being applied to the structure. Note that only these five
measurements are used in the control algorithm. However,
to evaluate the performance of the control strategies, LVDTs
are attached to the base and to each floor of the structure
to measure the relative displacements of the structure.
Implementation of the discrete controller was per-
formed using the Spectrum Signal Processing Real-TimeDigital Signal Processor (DSP) System. A discussion of
the specific capabilities of this board which make it suit-
able for use in structural control systems is provided in
Quast et al [37].
3. System identification
One 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 theassociated control devices. The approach to system
identification of semi-actively controlled structures outlined
in [32] is employed. In this approach, the problem is
simplified by decoupling the identification of the nonlinear
semi-active device from that of the primary structure. If the
semi-active controller is assumed to be adequate to keep the
response of the primary structure in the linear range, then
standard linear system identification techniques can be used
to develop a model for the primary structure. Nonlinear
identification means must still be employed to identify the
semi-active control device. Additionally, this approach
is attractive because the identification of the semi-active
system requires only measurements which are available for
controlling the responses of the structure.
The approach consists of four steps: (i) modeling
and identification of the semi-active control device, (ii)
identification of a model of the primary structure, (iii)
integration and optimization of the device and structural
models and (iv) validation of the integrated model of the
system. These steps are briefly described in the subsequent
sections.
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Figure 4. Comparison of the model results and the experimental data for the random displacement, random voltage test.
3.1. Modeling and identification of the MR damper
The first step in the identification process is to develop
an input/output model for the MR damper. The simple
mechanical idealization of the MR damper depicted in
figure 3 has been shown to accurately predict the behavior
of a prototype MR damper over a broad range of inputs
[31, 33]. The equations governing the forcef predicted by
this model are given by
f =c1y+ k1
xd x0
(1)
z= |xd y|z|z|n1
xd t
|z|n +A
xd y
(2)
y =1
c0+ c1z+c0xd+ k0xd y (3)
where z is an evolutionary variable that accounts for the
history dependence of the response. The model parameters
depend on the voltage v to the current driver as follows
= a + bu c1 = c1a+ c1bu c0 = c0a + c0bu
(4)
whereu is given as the output of the first-order filter
u= (uv). (5)
Equation (5) is necessary to model the dynamics involved
in reaching rheological equilibrium and in driving the
electromagnet in the MR damper [31, 33].A nominal set of parameters was obtained based on the
response of the MR damper in a series of displacement-
controlled tests. A hydraulic actuator was employed to
drive the MR damper, and the displacement and force
generated in the MR damper were measured, as described
in [31, 33]. A typical response of the MR damper for
a sinusoidal input is shown in figure 4. A least-squares
output-error method was employed in conjunction with a
constrained nonlinear optimization to obtain the 14 modelparameters in equations (1)(5). The optimization was
performed using the sequential quadratic programming
algorithm available in MATLAB [26]. A representative
comparison of the response predicted by this model and
the experimentally measured response for the MR damper
is shown in figure 4. The resulting parameters were used to
initialize the identification of the integrated system model,
presented subsequently.
3.2. Identification of the primary structure
The 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, the frequency 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 figure 5. There are two inputs to the structural
system, including the ground excitation xg and the applied
control forcef. The four measured system outputs are the
displacement xd of the structure at the attachment point
of the MR damper, and the absolute accelerations, xa1,
xa2, xa3, of the three floors of the test structure (i.e.,
y = [xdxa1 xa2 xa3]). Thus, a 4 2 transfer function
matrix must be identified to describe the characteristics ofthe system in figure 5.
The first step in the identification of the structure is to
experimentally determine the transfer functions from each
of the system inputs to each of the outputs. The eight
transfer functions are determined by independently exciting
each of the inputs of the structure with a random input and
measuring the structural responses. The transfer functions
from the ground acceleration to each of the measured
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Figure 5. System identification block diagram.
responses were obtained by exciting the structure with a
band-limited white noise ground acceleration (050 Hz).
During this test, the MR damper is not connected to the
structure, thus making f = 0. Similarly, the experimental
transfer functions from the applied control force to each
of the measured outputs are determined. To this end,
the MR damper is replaced with a hydraulic actuator to
apply a band-limited white noise (05 Hz) force to the
structure while the base of the structure is held fixed. The
force transducer, mentioned previously, is placed in series
with the hydraulic actuator to directly measure the applied
force. A representative transfer function from the ground
acceleration to the third floor absolute acceleration is shownin figure 6. This transfer function was obtained using
twenty averages. The three distinct, lightly damped peaks
occurring at 5.88, 17.5 and 28.3 Hz correspond to the first
three modes of the structural system.
Once the experimental transfer functions have been
obtained, the next step in the system identification
procedure is to model each transfer function as a ratio
of two polynomials in the Laplace variable s. This
task is accomplished via a least-squares fit of the ratio
polynomials, evaluated on the jaxis, to the experimentally
obtained transfer functions. For this structure, the decision
was made to focus control efforts on reducing the structural
responses in the first three modes. Thus, the model isrequired to be accurate below 35 Hz. Six poles are
necessary to model the input/output behavior of each of
the transfer functions in the frequency range of interest.
The system is then assembled in state space form using
the analytical representation of the transfer functions (i.e.,
the poles, zeros and gain). Because all of the transfer
functions required six states, the combined system has a
total of twelve poles. A model reduction is performed
to achieve a minimal realization of the system; thus, the
twelve-state system was reduced to a six-state system,
resulting in a reduced-order model of the form
xr = Axr + Bf +Exg
y = Cyxr + Dyf + v(6)
wherev represents the measurement noise vector.
A representative comparison of the reduced-order
model to the experimental transfer functions is shown in
figure 6. Additional details regarding this frequency domain
identification approach can be found in Dyke et al [7
10,13].
3.3. Development of an integrated system model
The next step in identifying a model of the integrated
structural system is to optimize the set of parameters for the
MR damper model (equations (1)(5)) for the case when it
is installed in the test structure, and combine the models
of the device and structure to form the integrated system
model (shown in figure 7). Updating the parameters of the
MR damper model is necessary because the MR damper
may function at a different operating point when installed
in the test structure than in the initial tests in which the
damper was driven with a hydraulic actuator [32].
To update the parameters of the MR damper model, a
series of tests was conducted to measure the response of the
structure with the MR damper in place in the test structure
(see figure 1). In these tests, the structure was excited at the
base, while various voltages v were applied to the current
driver of the MR damper. The recorded system responses
included the force generated in the MR damper, absolute
accelerations of each floor, displacement of the floors of
the structure, displacement of the base and displacement
of the three floors of the structure. Optimized parameters
were determined to fit the generalized model of the MR
damper to the experimental data. The resulting parameters
are: c0a = 8 N s cm1, c0b = 6 N s cm
1 V1, k0 =
50 N cm1, c1a = 290 N s cm1, c1b = 5 N s cm1 V1,k1 = 12 N cm
1, x0 = 14.3 cm, a =100, b = 450 V1,
= 363 cm2, = 363 cm2, A = 301, n = 2,
= 190 s1.
The integrated system model is then formed by
connecting the models of the MR damper (equations (1)
(5)) and structure (equation (6)) as shown in figure 7.
Verification of this integrated system model is provided in
the following section.
3.4. Experimental validation of the integrated system
model
To verify that the identified model is adequate forcontrol synthesis and analysis, the predicted response and
experimental response were compared in one controlled
case (controller A as described in the following section).
A representative comparison of the experimental and
predicted responses for the relative displacement and
absolute acceleration of the third floor is shown in figure 8
for a broadband excitation (020 Hz) with an rms ground
acceleration of 0.20 g . Good agreement is obtained.
4. Clipped-optimal control algorithm
One of the main challenges in semi-active control is
the development of an appropriate control algorithmthat can take advantage of the features of the control
device to produce an effective control system. An
important requirement of the control algorithm is that
it be implementable in full-scale applications. To
be implementable, the algorithm should use available
measurements, such as accelerations, in determining the
control action. Dykeet al [11, 12] have proposed a clipped-
optimal control strategy based on acceleration feedback for
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Figure 6. Comparison of reduced-order model and experimental transfer function: ground accelertion to third floor absoluteacceleration.
Figure 7. Block diagram of the identified integrated structural system.
Figure 8. Experimental and predicted responses of the semi-actively controlled system (controller A): third floor relativedisplacement and absolute acceleration.
the MR damper. Analytical studies demonstrated that the
MR damper, used in conjunction with the clipped optimal-
control algorithm, was effective for controlling a multi-
story structure with a single MR damper. In this section, the
approach to the design of the clipped-optimal controller is
provided. The discussion of the control algorithm considers
the general case in which there are multiple devices present
to control the structure, although in this experiment only a
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single MR damper is employed.
In the clipped-optimal controller, the approach is to
appendn force feedback loops to induce each MR damper
to produce approximately a desired control force. The
desired control force of the i th MR damper is denoted fci .
A linear optimal controller Kc(s) is designed that calculates
a vector of desired control forces, fc = [fc1fc2. . . f cn],
based on the measured structural response vector y and the
measured control force vector f, i.e.,
fc = L1
Kc(s)Ly
f (7)where L{} is the Laplace transform. Although the
controllerKc(s) can be obtained from a variety of synthesis
methods, H2/LQG strategies are advocated herein because
of the stochastic nature of earthquake ground motions
and because of their successful application in other civil
engineering structural control applications [7, 9, 10, 13].
To discuss the algorithm used for determining the
control action, consider the i th MR damper used to control
the structure. Because the response of the MR damper
is dependent on the relative structural displacements and
velocities at the point of attachment of the MR damper, the
force generated by the MR damper cannot be commanded;
only the voltage vi applied to the current driver of theith MR damper can be directly controlled. To induce the
MR damper to generate approximately the corresponding
desired optimal control force fci , the command signal vi is
selected as follows. When thei th MR damper is providing
the desired optimal force (i.e.,fi =fci ), 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 i th MR damper is graphically represented infigure 9 and can be concisely stated as
vi =VmaxH
fci fi
fi
(8)
where Vmax is the voltage to the current driver associated
with saturation of the MR effect in the tested device, and
H () is the Heaviside step function. A block diagram of
this semi-active control system is shown in figure 10. In the
block diagram, the dependence of the MR damper forces on
the structural responses is indicated by the link feeding back
the vectors xr and xr , which contain the relative structural
displacements and velocities at the attachment points of
the MR damper. For instance, if three MR dampers were
rigidly attached between the first three floors of a structure,this vector would be xr =[x1x2x1x3 x2]
.
One of the attractive features of this control strategy
is that the feedback for the controller is based 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,
although the model of the damper is important to system
analysis.
Figure 9. Graphical representation of algorithm forselecting the command signal.
Figure 10. Block diagram of the semi-active controlsystem.
5. Experimental results
To evaluate the performance of the semi-active control
system employing the MR damper, eight controllers with
various performance objectives were designed based on
the identified model of the integrated structure/MR damper
system and implemented in the laboratory. The results
of three semi-active control designs, denoted AC, are
presented herein. Controller A was designed by placing
a high weighting on the third floor relative displacement.
Controllers B and C were designed by placing a low and
high weighting, respectively, on the third floor acceleration.
In the results, xi is the displacement of thei th floor relative
to the ground, di is the interstory drift (i.e., xi xi1), xaiis the absolute acceleration of the ith floor and f is the
measured control force.
In addition to the results for semi-active controllers, two
passive cases are considered. Passive-off and passive-on
refer to the cases in which the voltage to the MR damper is
held at a constant value ofV =0 and V =Vmax = 2.25 V,respectively. Theuncontrolled response refers to the case
in which the MR damper is not attached to the structure.
Two types of experiment 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 Centro earthquake and the peak values of
the measured responses were determined. In these tests,
the earthquake was reproduced at five times the recorded
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speed to satisfy the similitude relations. In the second set
of tests, the three-story model structure was subjected to a
200 second broadband signal (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 excitation 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 three different input amplitudes including excitations
with rms values of 0.06 g (low), 0.13 g (medium) and
0.20g (high).Because in some cases the excitation levels used in
the passive and controlled tests were quite large for the
test structure, exciting the uncontrolled structure with the
same excitation could have been destructive. Therefore,
the uncontrolled results presented herein were obtained
by using an excitation with 50% of that used in the
controlled tests, and then scaling the uncontrolled structural
responses up to represent the response of the structure to
the full excitation. Thus the uncontrolled results represent
the response of the structure if it were to remain linear
throughout the tests.
The experimental results are summarized in the
following sections.
5.1. El Centro earthquake results
Table 1 summarizes the results of the high and low
amplitude El Centro earthquake excitation tests. Notice
that both the passive-off and passive-on systems are able
to achieve a reasonable level of performance at high and
low excitation levels. Because the MR damper is capable of
generating larger damping forces in the passive-on case than
in the passive-off case, one might predict that the passive-
on system would achieve larger reductions in the responses.
However, from the results it is shown that a number of
the responses of the passive-on system are actually larger
than those of the passive-off system. For instance, in the
low amplitude tests, the third floor displacement, maximum
interstory displacement and maximum floor acceleration
of the passive-on system are 11.3%, 10.9% and 19.0%
larger, respectively, than the responses of the passive-
off system. In the high amplitude tests, the passive-on
controller performs better than the passive-off 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 significantly better
than the passive systems. In the high amplitude tests,
controller A achieves a 24.3% reduction in the peak
third floor displacement and a 29.1% reduction in themaximum interstory displacement over the best passive
responses. Furthermore, these reductions were obtained
while achieving a modest reduction in the maximum
acceleration. Additional reduction in the peak third floor
relative displacement over the best passive case is achieved
with controller C (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 significantly smaller control forces
than are required in the passive-on case.
At low excitation amplitudes, the performance of
the semi-active controllers is still superior to that of
the passive controllers, although not to as great an
extent. The third floor relative displacement, maximum
interstory displacement and maximum absolute acceleration
are reduced over 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) responses for the tested
structure. The effectiveness of the proposed control strategy
is clearly seen, with peak third floor displacement being
reduced by 74.5% and the peak third floor acceleration
being reduced by 47.6% over the uncontrolled responses.
5.2. Random excitation results
The 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 at all excitation levels. In the high
amplitude tests, most of the rms responses of the passive-
on system are better than those of the passive-off system.
However, at lower excitation levels, the rms responses of
the passive-on system are often larger than those of the
passive-off system. For instance, in both the low and
medium amplitude tests, the maximum rms acceleration
is larger in the passive-on case than in the passive-off
case. Additionally, in the low amplitude test, the maximum
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
forces is not always the best approach.
The results indicate that the semi-active control systems
perform significantly better at reducing the rms structuralresponses 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
interstory displacements, but also the maximum rms floor
accelerations, well below those obtained with the passive
systems. Controller B achieves the best performance of
the three semi-active control designs, reducing the third
floor displacement, maximum interstory displacement and
the maximum floor absolute acceleration, by 14.6%, 26.5%
and 23.6%, respectively, over the best passive case in the
high amplitude tests, and by 17.8%, 30.0% and 8.0% in
the medium amplitude tests. 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 significantly less force than
the passive-on system.
6. Conclusion
The efficacy of the MR damper in reducing the structural
responses for a wide range of loading conditions has been
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Table 1. Experimental peak responses due to the El Centro earthquake.
Clipped-optimal Clipped-optimal Clipped-optimalUncontrolled Passive-off Passive-on controller A controller B controller C
High amplitude: responses due to the 120% El Centro earthquakexi 0.710 0.236 0.126 0.127 0.157 0.151(cm) 1.068 0.362 0.312 0.229 0.264 0.213
1.249 0.436 0.420 0.318 0.335 0.280
di 0.710 0.236 0.126 0.127 0.157 0.151(cm) 0.362 0.167 0.196 0.139 0.139 0.123
0.205 0.106 0.110 0.092 0.081 0.087
xai 879 666 920 711 874 957(cm s2) 1110 714 808 642 673 859
1500 804 897 786 653 748
xd (cm) 0.214 0.095 0.112 0.133 0.133
f (N) 258 1030 696 668 754
Low amplitude: responses due to the 80% El Centro earthquakexi 0.473 0.119 0.074 0.084 0.087 0.089(cm) 0.712 0.197 0.196 0.157 0.148 0.136
0.833 0.240 0.267 0.213 0.192 0.184
di 0.473 0.119 0.074 0.084 0.087 0.089(cm) 0.241 0.099 0.132 0.086 0.085 0.077
0.137 0.067 0.083 0.066 0.060 0.059
xai 586 388 595 462 542 657(cm s2) 740 481 546 457 579 759
1000 500 594 482 521 545
xd (cm) 0.112 0.049 0.063 0.071 0.071
f (N) 224 768 537 580 630
Figure 11. Controlled and uncontrolled structural responses due to 120% El Centro earthquake (controller A).
demonstrated in a series of experiments conducted at the
Structural Dynamics and Control/Earthquake EngineeringLaboratory at the University of Notre Dame. In these
experiments, the MR damper was used in conjunction
with a clipped-optimal control algorithm to control the
responses of a three-story test structure. The clipped-
optimal control algorithm 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 a broad class of seismicexcitations. Three different clipped-optimal control designs
were considered, and each of the control designs achieved
excellent results. In all cases, the semi-active controllers
performed significantly better than both of the passive
systems considered in reducing the structural responses.
Reductions in both acceleration and displacement responses
were observed with the semi-actively controlled systems.
Additionally, the semi-active control systems were able
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Table 2. Experimental rms responses due to the random excitations.
Clipped-optimal Clipped-optimal Clipped-optimalUncontrolled Passive-off Passive-on controller A controller B controller C
High amplitude: responses to the high amplitude random excitationxi 0.250 0.070 0.027 0.036 0.036 0.038(cm) 0.382 0.112 0.070 0.066 0.065 0.066
0.467 0.139 0.103 0.091 0.088 0.089
di 0.250 0.070 0.027 0.036 0.036 0.038(cm) 0.156 0.048 0.049 0.039 0.036 0.036
0.123 0.035 0.036 0.031 0.027 0.029
xai 1020 274 226 228 209 225(cm s2) 576 184 178 159 153 176
999 292 292 250 223 241
xd (cm) 0.066 0.020 0.033 0.032 0.034
f (N) 112 311 219 209 220
Medium amplitude: responses to the medium amplitude random excitationxi 0.164 0.036 0.018 0.022 0.022 0.023(cm) 0.248 0.059 0.049 0.043 0.043 0.044
0.304 0.077 0.073 0.062 0.060 0.061
di 0.163 0.036 0.018 0.022 0.022 0.023(cm) 0.101 0.028 0.035 0.028 0.026 0.027
0.080 0.022 0.026 0.022 0.020 0.021
xai 663 168 162 154 149 161(cm s1) 374 112 134 115 113 126
649 176 208 174 162 172
xd (cm) 0.031 0.010 0.018 0.019 0.020
f (N) 105 237 174 161 170
Low amplitude: responses to the low amplitude random excitationxi 0.075 0.013 0.009 0.009 0.010 0.010(cm) 0.115 0.026 0.026 0.024 0.023 0.023
0.140 0.035 0.037 0.034 0.033 0.033
di 0.075 0.013 0.009 0.009 0.010 0.010(cm) 0.047 0.016 0.020 0.017 0.016 0.017
0.037 0.012 0.014 0.012 0.012 0.012
xai 306 88.3 114 102 102 105(cm s1) 173 68.3 88.1 78.3 76.8 78.7
300 92.5 113 102 95.6 96.9
xd (cm) 0.017 0.007 0.010 0.012 0.014
f (N) 85.0 140 121 111 113
to achieve these performance gains while using smaller
control forces than in the passive-on system. Moreover,
the capabilities of the MR damper have been shown to
mesh well with the requirements and constraints associated
with the seismic response reduction in civil engineering
structures.
Note that algorithms that explicitly incorporate actuator
dynamics and controlstructure interaction into the control
design process may offer additional controlled performance
gains [8]. Efforts are currently under way to investigate this
possibility.
Acknowledgment
This research is supported in part by National Science
Foundation grant Nos CMS 93-01584 and CMS 95-00301.
In addition, the authors from Notre Dame and Washington
University would like to express their appreciation to
Lord Corporation of Cary, NC for providing the prototype
magnetorheological damper.
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