Dyke, Spencer, Sain & Carlson August 1, 1996 1
Modeling and Control of Magnetorheological Dampers
for Seismic Response Reduction
S.J. Dyke,
1
B.F. Spencer Jr.,
2
M.K. Sain
3
and J.D. Carlson
4
1
Dept. of Civil Engrg., Washington University, St. Louis, MO 63130
2
Dept. of Civil Engrg. and Geo. Sci., Univ. of Notre Dame, Notre Dame, IN 46556
3
Dept. of Electrical Engrg., Univ. of Notre Dame, Notre Dame, IN 46556
4
Mechanical Products Division, Lord Corporation, Cary, NC 27511
Abstract
Control of civil engineering structures for earthquake hazard mitigation represents a relative-
ly new area of research that is growing rapidly. Control systems for these structures have unique
requirements and constraints. For example, during a severe seismic event, the external power to a
structure may be severed, rendering control schemes relying on large external power supplies in-
effective. Magnetorheological (MR) dampers are a new class of devices that mesh well with the
requirements and constraints of seismic applications, including having very low power require-
ments. This paper proposes a clipped-optimal control strategy based on acceleration feedback for
controlling MR dampers to reduce structural responses due to seismic loads. A numerical exam-
ple, employing a newly developed model that accurately portrays the salient characteristics of the
MR dampers, is presented to illustrate the effectiveness of the approach.
Introduction
The tragic consequences of the recent earthquakes in Kobe, Japan and in Los Angeles, Cali-
fornia have underscored, in terms of both human and economic factors, the tremendous impor-
tance of the way in which buildings and bridges respond to earthquakes. In the last decade,
significant effort has been devoted to the possibility of employing various control strategies in the
design of engineering structures to increase their safety and reliability against strong earthquakes
[20, 22–24, 39]. These control approaches are often termed protective systems and offer the ad-
vantage of being able to modify dynamically the response of a structure in a desirable manner.
Moreover, structural control systems can be an effective means by which existing structures can
be retrofitted or strengthened to withstand future seismic activity.
To date, active structural control has been successfully applied in over twenty commercial
buildings and more than ten bridges (during erection) [20]. Yet there are a number of serious chal-
lenges that remain before active control can gain general acceptance by the engineering and con-
struction professions at large. These challenges include: (i) reduction of capital cost and
maintenance, (ii) eliminating reliance on external power, (iii) increasing system reliability and ro-
bustness, and (iv) gaining acceptance of nontraditional technology by the profession. Semi-active
Dyke, Spencer, Sain & Carlson August 1, 1996 2
control strategies appear to be particularly promising in addressing a number of these challenges
[43].
Semi-active control devices potentially offer the reliability of passive devices, yet maintain
the versatility and adaptability of fully active systems. According to presently accepted defini-
tions, a semi-active control device is one which cannot input energy into the system being con-
trolled. Such devices typically have extremely low power requirements, which is particularly
critical during seismic events when the main power source to the structure may fail.
Various semi-active devices have been proposed which utilize forces generated by surface
friction or viscous/viscoelastic-plastic fluids to dissipate vibratory energy in a structural system.
Examples of such devices that have been considered for civil engineering applications include:
variable orifice dampers [9, 26, 29, 34, 36, 38], controllable friction braces [1, 10], controllable
friction isolators [19], variable stiffness devices [27], and electrorheological (ER) dampers [2, 17,
18, 21, 30, 32]. The effectiveness of one semi-active control system employing a variable stiffness
system has already been proven in a low-rise building in Japan [28].
Magnetorheological (MR) dampers are new semi-active control devices that use MR fluids to
provide controllable dampers that are quite promising for civil engineering applications [8, 15,
42]. They offer highly reliable operation at a modest cost and can be viewed as fail-safe in that
they become passive dampers should the control hardware malfunction. This paper first presents a
recently developed model for a prototype MR damper [42] that has been studied in the Structural
Dynamics and Control / Earthquake Engineering Laboratory (http://www.nd.edu/~quake/) at the
University of Notre Dame. Then a clipped-optimal acceleration feedback control strategy is pro-
posed for controlling the MR damper. The effectiveness of the proposed algorithm and the useful-
ness of MR dampers for structural response reduction are demonstrated through a numerical
example employing a seismically excited three story model building.
MR Damper Behavior and Modeling
Magnetorheological fluids recently developed by the Lord Corporation [3–7] (see also http://
www.rheonetic.com/mrfluid/) have many attractive features, including high yield strength, low
viscosity and stable hysteretic behavior over a broad temperature range. MR fluids are the mag-
netic analogs of electrorheological (ER) fluids and typically consist of micron-sized, magnetically
polarizable particles dispersed in a carrier medium such as mineral or silicone oil. When a mag-
netic field is applied to the fluids, particle chains form, and the fluid becomes a semi-solid, exhib-
iting plastic behavior similar to that of ER fluids. Transition to rheological equilibrium can be
achieved in a few milliseconds, providing devices with high bandwidth. Additionally, the achiev-
able yield stress of modern MR fluids is in excess of 80 kPa, allowing for devices capable of gen-
erating large forces such as are required for full-scale installations. In fact, MR dampers with a
capacity of 20 tons have been designed, with testing to begin in the summer of 1996 [8]. More-
over, MR fluids can operate at temperatures from –40 to 150
o
C with only slight variations in the
yield stress. Consequently, devices based on MR fluids are viable candidates for installation in
both exterior civil infrastructure applications (e.g., bridges, towers, etc.) as well as enclosed appli-
cations (e.g., buildings, secondary systems, etc.).
To evaluate the potential of MR dampers in structural control applications and to take full ad-
vantage of the unique features of these devices, a model must be developed that can accurately re-
produce the behavior of the MR damper. A prototype MR damper has been considered, which
was obtained for evaluation from the Lord Corporation and is comprised of a fixed orifice damper
Dyke, Spencer, Sain & Carlson August 1, 1996 3
filled with an MR fluid [42]. The damper is 21.5 cm long in its extended position, and the main
cylinder is 3.8 cm in diameter. The main cylinder houses the piston, the magnetic circuit, an accu-
mulator and 50 ml of MR fluid, and the damper has a cm stroke. As shown in Fig. 1, 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 running off of 120 V AC,
which generates a 0–1 amp current that is proportional to an applied DC input voltage in the range
0–3 V. The peak power required is less than 10 watts, which could allow the damper to be operat-
ed continuously for more than an hour on a small camera battery. Forces of up to 3000 N can be
generated with the device. The force is stable over a broad temperature range, varying less than
10% in the range of –40 to 150 degrees Celsius. The rise time (defined as the time required to go
from 10% to 90% of the final value) in the force generated by the MR damper during a constant
velocity test when a step in the voltage is applied to the current driver is approximately 8 msec.
This behavior is primarily due to the time the MR fluid in the damper takes to reach rheological
equilibrium and the time lag associated with the dynamics of driving the electromagnet in the MR
damper.
The response of the MR damper due to a 2.5 Hz sinusoid with an amplitude of 1.5 cm is
shown in Fig. 2 for four constant voltage levels, 0 V, 0.75 V, 1.5 V, and 2.25 V, being applied to
the current driver for the device. These voltages correspond to 0 A, 0.25 A, 0.5 A and 0.75 A, re-
spectively. Saturation of the MR effect begins in the tested device when the applied voltage is 2.25
V (0.75 A). Thus, attention is restricted to voltages between 0 and 2.25 V. The measured forces
are shown as a function of time in Fig. 2a, the force-displacement loops are shown in Fig. 2b, and
the force-velocity loops are shown in Fig. 2c. The force-displacement loops in Fig. 2b progress
along a clockwise path with increasing time, whereas the force-velocity loops in Fig. 2c progress
along a counter-clockwise path with increasing time. Note that the nonzero mean force produced
by the MR damper is due to the accumulator (see Fig. 1).
2.5±
Figure 1. Schematic of MR Damper.
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MR Fluid
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Electromagnet
Dyke, Spencer, Sain & Carlson August 1, 1996 4
In Fig. 2, the effects of changing the magnetic field are readily observed. At 0 V the MR
damper primarily exhibits the characteristics of a viscous device (i.e., the force-displacement rela-
tionship is approximately elliptical, and the force-velocity relationship is nearly linear). However,
as the voltage increases, the force required to yield the fluid increases and produces behavior asso-
ciated with a plastic material in parallel with a viscous damper, i.e., Bingham plastic behavior
[37].
The simple mechanical idealizations of the MR damper depicted in Fig. 3 has been shown to
accurately predict the behavior of the prototype MR damper over a broad range of inputs [42].
The applied force predicted by this model is given by
(1)
or equivalently
(2)
where the evolutionary variable is governed by [45]
(3)
and
(4)
Figure 2. Experimentally Measured Force for 2.5 Hz Sinusoidal
Excitation with an Amplitude of 1.5 cm.
Time (sec)
Velocity (cm/sec)Displacement (cm)
Force (N)Force (N)
a) Force vs. Time
b) Force vs. Displacement
c) Force vs. Velocity
−2 −1 0 1 2
−1500
−1000
−500
0
500
1000
1500
−10 −5 0 5 10
−1500
−1000
−500
0
500
1000
1500
0 V
0.75 V
1.5 V
2.25 V
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
−1500
−1000
−500
0
500
1000
1500
f
f αzc
0
x˙ y˙–()k
0
xy–()k
1
xx
0
–()+++=
fc
1
y˙ k
1
xx
0
–()+=
z
z˙ γ x˙ y˙– zz
n 1–
– β x˙ y˙–()z
n
– Ax˙ y˙–()+=
y˙
1
c
0
c
1
+()
---------------------
αzc
0
x˙ k
0
xy–()++{}=
Dyke, Spencer, Sain & Carlson August 1, 1996 5
Here, the accumulator stiffness is represented by , the viscous damping observed at larger ve-
locities by . A dashpot, represented by , is included in the model to introduce the nonlinear
roll-off in the force-velocity loops that was observed in the experimental data at low velocities,
is present to control the stiffness at large velocities, and is the initial displacement of spring
associated with the nominal damper force due to the accumulator. By adjusting the parameters of
the model , and , one can control the shape of the hysteresis loops for the yielding element.
To account for the dependence of the force on the voltage applied to the current driver and the
resulting magnetic current, Spencer, et al. [42] have suggested
(5)
(6)
(7)
where is given as the output of a first-order filter given by
(8)
and is the commanded voltage sent to the current driver. Eq. (8) is necessary to model the dy-
namics involved in reaching rheological equilibrium and in driving the electromagnet in the MR
damper.
A constrained nonlinear optimization was used to obtain the 14 model parameters in Eqs. (1–
8). The optimization was performed using the sequential quadratic programming algorithm avail-
able in MATLAB [31]. Optimized parameters were determined to fit the generalized model to the
experimental data in a variety of tests. The resulting parameters are given in Table 1.
f
c
0
k
0
c
1
k
1
Figure 3. Simple Mechanical Model of the MR Damper.
Bouc-Wen
xy
k
1
c
0
c
1
k
0
x
0
k
1
γβ A
ααu() α
a
α
b
u+==
c
1
c
1
u() c
1a
c
1b
u+==
c
0
c
0
u() c
0a
c
0b
u+==
u
u˙ η uv–()–=
v
