Modeling and Control of Magnetorheological Dampers for Seismic Response Reduction

TL;DR: In this paper, a clipped-optimal control strategy based on acceleration feedback for controlling magnetorheological dampers is proposed to reduce structural responses due to seismic loads, and a numerical example, employing a newly developed model that accurately portrays the salient characteristics of the MR dampers, is presented to illustrate the effectiveness of the approach.

Abstract: Control of civil engineering structures for earthquake hazard mitigation represents a relatively 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 ineffective. 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 requirements. 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 example, employing a newly developed model that accurately portrays the salient characteristics of the MR dampers, is presented to illustrate the effectiveness of the approach.

Summary

Introduction

• The tragic consequences of the recent earthquakes in Kobe, Japan and in Los Angeles, California have underscored, in terms of both human and economic factors, the tremendous importance of the way in which buildings and bridges respond to earthquakes.
• 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 challenges that remain before active control can gain general acceptance by the engineering and construction professions at large.
• Semi-active control devices potentially offer the reliability of passive devices, yet maintain the versatility and adaptability of fully active systems.

MR Damper Behavior and Modeling

• Magnetorheological fluids recently developed by the Lord Corporation [3–7] (see alsohttp:// www.rheonetic.com/mrfluid/) have many attractive features, including high yield strength, low viscosity and stable hysteretic behavior over a broad temperature range.
• Moreover, MR fluids can operate at temperatures from –40 to 150oC with only slight variations in the yield stress.
• 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 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].
• A constrained nonlinear optimization was used to obtain the 14 model parameters in Eqs. (1– 8).

Clipped-Optimal Control Algorithm Development

• Previous researchers have found semi-active control systems can potentially achieve the majority of the performance of fully active systems [25, 33, 35, 44].
• To date, most of the current active structural control strategies for aseismic protection have been based on either full-state feedback (i.e., all structural displacements and velocities) or on velocity feedback.
• Consider a seismically excited structure controlled with a single MR damper.
• The measurement equation is given by (10) where is the vector of measured outputs, and is the measurement noise vector.
• When the MR damper is providing the desired optimal force (i.e., ), the voltage applied to the damper should remain at the present level.

Numerical Example

• The performance of the clipped-optimal control algorithm presented in the previous section is now evaluated through numerical simulation.
• The structural measurements used for calculating the desired control force include the absolute accelerations of the three floors of the structure, and the displacement of the MR damper (i.e., ).
• The peak structural responses to the El Centro earthquake are given in Table 2.
• Notice that these performance gains are achieved by the semi-active controller while requiring smaller control forces than are required in the passive-on case.
• Interestingly, the forces applied by the MR damper operating in semi-active mode are often smaller than those corresponding to the damper operating in the passive-on mode, again indicating that larger damping forces do not always produce better results.

Conclusions

• The performance of a semi-active control system based on newly developed magnetorheological (MR) fluid dampers has been studied.
• A recently reported model for the MR damper was presented which is capable of predicting the response of the MR damper over a wide range of loading conditions and command voltages, and a clipped-optimal controller was proposed for control implementation.
• Excellent results were obtained when this strategy was applied to control a model of a seismically excited three-story scaled building model.
• Similar results have been obtained experimentally [11, 16].
• Finally, note that the algorithms that explicitly incorporate actuator dynamics and controlstructure interaction into the control design process may offer additional controlled performance gains [12].

Figures

Table 1: Parameters for the MR Damper Model

Figure 4. Inputs to MR Damper During the Random Displacement, Random Voltage Test.

Figure 5. Comparison of the Model Results and the Experimental Data for the Random Displacement, Random Voltage Test.

Figure 8. Diagram of MR Damper Implementation.

Figure 11. Command Signal and Control Force Applied in the Clipped-Optimal Case, and Reaction Force for the Passive-On Case due to the El Centro Earthquake.

Figure 1. Schematic of MR Damper.

Figure 10. Structural Responses of Uncontrolled and ClippedOptimal Systems due to the El Centro Earthquake.

Figure 2. Experimentally Measured Force for 2.5 Hz Sinusoidal Excitation with an Amplitude of 1.5 cm.

Table 2: Peak Responses due to the El Centro Earthquake.

Figure 9. Time Scaled NS Component of the Ground Acceleration for the 1940 El Centro Earthquake.

Figure 6. Graphical Representation of Algorithm ( i.e., Eq. 12) for Selecting the Command Signal.

Figure 7. Block Diagram of the Semi-Active Control System.

Figure 3. Simple Mechanical Model of the MR Damper.

Full text

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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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
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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

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Modeling and control of magnetorheological dampers for seismic response reduction" ?

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 example, employing a newly developed model that accurately portrays the salient characteristics of the MR dampers, is presented to illustrate the effectiveness of the approach. 

Q2. What have the authors stated for future works in "Modeling and control of magnetorheological dampers for seismic response reduction" ?

Efforts are currently underway to investigate this possibility. 

Q3. What is the force-velocity relationship of the MR damper?

At 0 V the MR damper primarily exhibits the characteristics of a viscous device (i.e., the force-displacement relationship is approximately elliptical, and the force-velocity relationship is nearly linear). 

Q4. How long can the damper be operated?

The peak power required is less than 10 watts, which could allow the damper to be operated continuously for more than an hour on a small camera battery. 

Q5. What are the advantages of semi-active control devices?

Semi-active control devices potentially offer the reliability of passive devices, yet maintain the versatility and adaptability of fully active systems. 

Q6. What is the description of MR dampers?

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. 

Q7. How many buildings have been successfully constructed?

To date, active structural control has been successfully applied in over twenty commercial buildings and more than ten bridges (during erection) [20]. 

Q8. What is the displacement of the MR damper?

Because the MR damper is attached between the first floor and the ground, its displacement is equal to the displacement of the first floor of the structure relative to the ground, i.e., in Eqs. (1–4). 

Q9. Why did the semi-active controller perform better than the passive-off and passive-on control?

Because the semi-active system has the ability to vary its properties to more effectively control the structure, the clipped optimal controller performed better than both the passive-off and passive-on control systems. 

Q10. Why is the MR damper unable to be operated continuously for more than an hour?

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. 

Q11. How long does the MR damper take to rise?

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. 

Q12. What is the way to induce the MR damper to produce the desired control force?

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. 

Q13. What are some of the common types of semi-active devices?

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. 

Q14. What is the performance of the semi-active control system?

The performance of the semi-active control system employing the MR damper was found to be modestly better in reducing peak displacements than that of the linear active controller, indicating that the semi-active control system is capable of not only approaching, but surpassing, the performance of linear active control system, while only requiring a small fraction of the power that is required by the active controller. 

Q15. What is the way to control the MR damper?

When the MR damper is providing the desired optimal force (i.e., ), the voltage applied to the damper should remain at the present level. 

Q16. What is the way to measure the displacement of a structure?

Because accelerometers can readily provide reliable and inexpensive measurement of accelerations at arbitrary points on the structure, development of control methods based on acceleration feedback is an ideal solution to this problem and will be presented subsequently. 

Q17. What are the structural measurements used for calculating the desired control force?

The structural measurements used for calculating the desired control force include the absolute accelerations of the three floors of the structure, and the displacement of the MR damper (i.e., ). 

Q18. What is the definition of a semi-active control device?

According to presently accepted definitions, a semi-active control device is one which cannot input energy into the system being controlled. 

Q19. What is the equation of motion for a MR damper?

Assuming that the forces provided by the MR damper are adequate to keep the response of the primary structure from exiting the linear region, then the equations of motion can be written as(9)ż