State-of-the-art recent developments of large magnetorheological (MR) dampers: a review

Abstract

Large MR (MR) dampers are popular due to their higher damping force capabilities which makes them suitable in the field
of civil engineering, structural engineering, suspension bridge structure, mining engineering, and agricultural engineering
applications. This paper presents a comprehensive review of large MR dampers. The classifications and applications of large
MR dampers, the principle of operation, different fluid models, their structural design and control systems are classified and
reviewed in this paper. The large MR dampers have higher damping force controllability than conventional MR dampers.
The review indicates that the large MR dampers have enough vibration mitigation ability and higher damping performances

Full text

Vol.:(0123456789)
1 3
Korea-Australia Rheology Journal (2022) 34:105–136
https://doi.org/10.1007/s13367-022-00021-2
REVIEW ARTICLE
State‑of‑the‑art recent developments oflarge magnetorheological
(MR) dampers: areview
MohammadAbdulAziz1 · SakibMuhammadMohtasim2· RubelAhammed2
Received: 10 January 2022 / Revised: 10 January 2022 / Accepted: 16 January 2022 / Published online: 19 April 2022
© The Author(s) 2022, corrected publication 2022
Abstract
Large MR (MR) dampers are popular due to their higher damping force capabilities which makes them suitable in the field
of civil engineering, structural engineering, suspension bridge structure, mining engineering, and agricultural engineering
applications. This paper presents a comprehensive review of large MR dampers. The classifications and applications of large
MR dampers, the principle of operation, different fluid models, their structural design and control systems are classified and
reviewed in this paper. The large MR dampers have higher damping force controllability than conventional MR dampers.
The review indicates that the large MR dampers have enough vibration mitigation ability and higher damping performances.
Keywords Magnetorheological (MR) damper· MR fluid· MR fluid model· Large MR damper· Control algorithm
List of symbols
a
Acceleration
a, b, c Damper characterization
parameters
Ae
Effective area of the piston
a
Velocity adjustment co-
efficient of coulomb damping
force
Ap
,
Am
State matrices
Bp
,
Bm
Input matrices
Ci
Damping coefficient
Cpost
Post-yield damping
c
Viscous coefficients
c1
Pre-yield viscous
ck
Viscous damping for force
roll off
cl
Viscous damping at large
velocities
co(x)
Post yield plastic damping
coefficient
cb
Roll off phenomenon of
MR damper at low motion
velocities
cmax
Maximum damping
coefficients
cmin
Minimum damping
coefficients
Cp
,
Cm
Output matrices
D′
Mean diameter of the damp-
ing gap
di
and
do
Input and output disturbances
es
Sprung mass displacement
error
F
Damping force
fc
Frictional force
Fpost
Post-yield damping force
Fy
Yield force
fpy
Positive or negative force
Fpre
Pre-yield damping force
f0
Damper force when the
damper velocity is zero
fm
Damper force when the
damper velocity is maximum
fd
Damper force offset
Fc
Coulomb friction force
Fd
Coulomb force
F𝜏
Shear stress
fk
Damper force caused by seals
and measurement bias
* Mohammad Abdul Aziz
m.abdulaziz@uqconnect.edu.au
1 School ofMechanical andMining Engineering, The
University ofQueensland, StLucia, QLD4072, Australia
2 Department ofMechanical Engineering, Rajshahi University
ofEngineering andTechnology (RUET), 6204Rajshahi,
Bangladesh

106 M.Abdul Aziz et al.
1 3
F𝜂
Viscous stress
Fb
Control force
f
Measured force
G
Influence vector
g
Positive gain coefficient
h
Heaviside step function
H0
Strength of the magnetic field
I
Current
k
Stiffness coefficients
kl
Stiffness at large velocities
ka
Accumulator stiffness
ks
Linear spring constant
kc
Consistency index
Kc
Linear optimal controller
k1
Pre-yield stiffness
kH
Shape coefficient
kx
,
kwa
and
kwb
Hysteresis loop controlling
parameter
l
Effective length of the piston
L Laplace transform
M
Mass
m0
Mass acceleration
n
Power law index
N(t)
Controllable contact force
q0,q1,q2,q3,ro,r1,r2and r3
Optimal co-efficient of the
polynomial equation for con-
trol signal
R
State vector.
Rp
,
Rm
N × 1 plant state vector
nm
×
1 model state vector
Δ(t)
Damping deformation
u
Dimensionless displacement
ur
Relative velocity
u0
Harmonic motion with an
amplitude
ua
Absolute displacement of the
single degree of freedom
up
M × 1 input control vector
um
M × 1 input command vector
V(z)
Lyapunov function
Vn
Velocity of the piston
Vref
Reference velocity
vo
Input voltage to the current
driver
vi
Measured noise vector
Vmax
Maximum allowable voltage
𝜔2
Angular speed of the upper
lever
𝜔
Frequency
x
Displacement of MR damper
x0
Displacement initial mass
x0
Initial mass velocity
x
Velocity
xi
Spring initial displacement
xH
Hysteretic velocity
xc
Characteristics displacement
xv
Displacement value when
damping force was zero
xs0
Sprung mass displacement
xs
Vertical displacement

x+
t
or x
−
t.
Tangential curve velocity
xg
Ground acceleration
yp
Plant output
ym
Model output
yj
Measured output vector
||z||p
Norm of the state
𝛼,𝛽,𝛿,𝛾,n
Model parameters
a1,a2,p
Positive constants
𝜂
Dynamical viscosity
𝜏y
Yield shear stress
𝜇
Coefficient of friction
𝛼1
,
𝛼2
Angular position
Pi,j
,
Aj,Bj
System matrices
𝜂
Dynamic viscosity of MR
fluid
𝛾
Strain rate
Г Column vector
λ Vector
Φ
Convergence rate of sliding
mode control
1 Introduction
Magnetorheological (MR) fluid which is a smart material
was first developed by Jacob Rainbow in the 1940s [1]. MR
damper [2] is a vibration control device that uses MR fluid
for its operating environment was first developed by Lord
Corporation in the early 1940s [3, 4]. Since then MR fluid
has become an important engineering field to develop. MR
fluid contains suspended iron particles in oil or carrier fluid
[5, 6]. In the presence of a magnetic field the rheological
properties (yield stress) of MR fluid change within milli-
seconds [7]. The iron particles in MR fluid align along the
direction of the magnetic field and form a chain structure
thus transform it from viscous into a semi-solid state [8].
In an MR damper, the magnetic field is generated and con-
trolled using an external power source that supplies current
to the piston coil [9]. Thus controllable damping force can
be achieved [10]. This controllable mechanical properties
of MR fluid attracted many researchers to develop different
MR devices [11–14] through the years. MR damper based
semi-active control system came to the attention of many
researchers and has been developing as a shock reducing
device due to its controllable damping force [15], simple
design [16], low power usage [17] and cost-effectiveness

107State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
[18]. MR damper has been practically utilized in different
engineering applications. It has been developed for automo-
bile suspension [19, 20], railway vehicles [21, 22], helicopter
landing gear systems [23, 24], civil infrastructure [25–27],
cable bridge [28, 29], and vibration isolation system [30].
MR dampers were commercially applied on vehicle sus-
pension system [31] as it reacts to vibration motion quickly
and provides sufficient damping force. Thus, human comfort
during riding is achieved. Desai etal. [32] examined the
damping performance of the RD-8040-1 MR damper for seat
suspension that ensured better damping range and rides com-
fort. Whereas, Du etal. [33] proposed an MR damper-based
suspension system using an adaptive skyhook control that
improved the vehicle ride performance further. Besides, MR
damper is commercially implemented by many researchers
on the washing machine [34, 35], prosthetic knee [36, 37]
applications also. The required damping force is less in these
cases.
Different damping devices are used against earthquake
and wind-induced structural vibration. Passive control
devices were incorporated inside the building structure to
absorb energy from earthquake vibration. Among them, fluid
viscous dampers [38, 39], viscoelastic dampers [40, 41],
hysteretic dampers [42, 43], metallic and friction devices
[44] are mostly used. But the use of these damping devices
reduces due to higher cost, high nonlinear response, fluid
leakage and less reliability issue [44]. MR damper is also
proposed to use in different structural areas where higher
damping force is required to isolate the large-frequency
vibration. The first large MR damper with 300KN capacity
was developed by Sanwa Tekki Corporation in 2001 and
installed at Tokyo National Museum of Emerging Science
and Innovation for protection against seismic excitation
[45]. Later in 2003, a 400KN MR damper was used in a
residential building at Keio University in Japan developed
by Sanwa Tekki Corporation [46, 47]. As MR damper has
better response control over passive dampers, researchers
[48–53] have been developing large-scale MR damper for
bridge, railway bridge, building structure through the years.
Heo etal. [54] developed a sliding mode control with
optimal polynomial control based MR damper (30KN)
system with lumped mass to mitigate pounding between
spans and abutment under seismic load. The experimental
result showed it could mitigate the pounding of the bridge
span effectively whereas the damage of bridge piers was
experimentally reduced by Heo etal. [55] using a hybrid
seismic response control based MR damper (1000KN)
system. The active systems consume more energy in earth-
quake or wind vibration reduction [56]. To decrease the
power consumption, semi-active or adaptive systems were
developed for reducing the wind and earthquake induced
structural vibration [57–59]. Yeganehfallah and Attari [60]
proposed a robust controller and simulated the response
phenomenon of the cable-stayed bridge structure with an
MR damper (1000KN)-based semi-active control system.
For the same control system, Bathaei etal. [61] proposed
two different types of Fuzzy logic controller (FLC) where
the type-2 FLC was proven more effective in reducing the
response time of bridge structure, whereas six semi-active
fuzzy controllers were devised by Hormozabad and Tanha
[62]. A similar study was also examined using a building
model by Bathaei etal. [63] with a tuned mass system with
an MR damper(1000KN) where the type-2 FLC controller
was also worthwhile in performance. As the fuzzy control-
lers have some lacking, Bozorgvar and Zahrai [64] designed
an adaptive neuro-fuzzy interference system (ANFIS) for
MR damper to reduce the response time of building struc-
ture. The system had better efficiency than other control-
lers. Bhaiya etal. [65] developed a control system for MR
damper-based building structure and showed that it is less
effective when subjected to near field earthquake. Fu etal.
[66] developed two control system and experimentally
showed that a 20KN capacity MR damper-based isolation
system in a concrete structure responds quickly against a dif-
ferent level of a large earthquake. Gong etal. [67] developed
a 10 kN capacity MR damper with a pseudo-negative-stiff-
ness (PSN) control system. Experimental results showed that
under different level of earthquake it performs better than
other control systems. Cruze etal. [68] proposed a multi
coil large MR damper and experimentally validated that it
can generate sufficient damping force of 5.83kN for seismic
mitigation of building structure.
This paper aims to review a literature on large MR
damper, their classification and application, their design
strategy, implementation, and development over the years.
This paper also presents the classification of large MR
damper based on different mathematical models and con-
trol systems.
2 Applications ofMR dampers
Both active and passive suspension systems can be sum-
marized by MR dampers thus attracted the attention of
many researchers to use MR damper in different applica-
tions. Besides, the high damping force and durability of MR
damper replaced other vibration control devices in many
engineering applications. Several MR damper systems and
their applications are presented in Table1.
Different MR fluid-based devices application are shown
in Table2.
2.1 Classifications
The optimization in design can enhance the performance
by changing the number of the coil-like single-coil [108],

108 M.Abdul Aziz et al.
1 3
double coil [109], multi-coil [110]. The classifications of
MR dampers depend on their design, coils turn number, pis-
ton coils, bypass valve, control valve, and power-producing
capacity.
The main two basic types of MR dampers are monotube
[111, 112] and twin-tube [112, 113] which are either can be
double-ended [114, 115] or single-ended [116] MR dampers.
Monotube MR damper contains one fluid reservoir while
the twin-tube has two reservoirs [117]. MR damper with a
single-ended structure has one piston rod while the double-
ended structure has an extended piston rod from both ends
of the cylinder. MR damper can either have inner or outer
coils mechanism. In an inner coil mechanism, the coils are
wounded inside the piston of the MR damper [118] while
the external coils [119] are wounded on the outer structure
of the damper. The piston incorporates a different number
of coils that can be a single coil, double coils or multi coils.
Based on control valves, the flow mode in MR damper
can be categorized as single flow mode [120] and mixed
flow mode [121]. Single flow mode MR dampers can be
characterized as flow mode [122], shear mode [123], and
squeeze mode [124] MR dampers.
Based on different flow channel MR dampers can be clas-
sified as inner bypass or outer bypass which either can be
single-ended [125], double-ended [126], or piston bypass
[125, 127] type. The outer bypass MR dampers can be cat-
egorized as outer tube bypass [128, 129], double-ended
bypass [129], bypass MR valve [130], meandering type valve
[131] and bypass spool valve [132] MR dampers. According
to the size, MR dampers can be classified into three types
such as short stroke, long stroke and large MR dampers. In
the short stroke and long stroke MR dampers, the stroke
length varies from 55 to 74mm [133] while for large stroke
MR dampers, stroke length varies from 160 to 300mm.
2.2 Working principle ofMR damper
The working system of conventional MR damper is shown
in Fig.1. The MR damper device is installed with other
sensor and power system that provides information about
controlling damping force. An external power source is uti-
lized to supply current to the piston coil while the piston
reciprocates to and fro within the cylinder chamber [134].
This current induces a magnetic field around the fluid flow
path and under the interaction with magnetic field the fluid
changes its phase from liquid to solid state [135]. The system
controller takes data from sensors that is connected to the
system where damping force is required. Thus, the current
driver delivers different level of current as per requirement
and controllable damping force obtained. A typical MR
damper is shown in Fig.2.
2.3 Operation modes
The MR dampers are a type of MR dampers that utilize the
larger stroke into a shear stress development in the MRFs
region. The principles of operation of large MR dampers
are based on shear mode operation, flow mode operation,
squeeze mode and mixed-mode operation. MR damper
Table 1 MR dampers and their application
Field of application References
Civil infrastructure [69, 70]
Automobiles [71, 72]
Battery recoil system [73, 74]
Semi active vibration isolation systems [75–77]
Railway vehicles [78, 79]
Helicopters applications [80, 81]
Gun recoil systems [82, 83]
Military vehicles [84]
Optical polishing [85]
Fluid clutches [86, 87]
MR powertrain mount [88, 89]
Polishing industry [90]
Engine mounts and clutch systems [91, 92]
Table 2 MR devices and their
application MR devices Applications References
MR damper Shock absorber, heavy-duty, washing machine,
robot, haptic devices, cable bridge
[34, 93]
MR-based elastomers Engine mounting system, sensors [94, 95]
MR valves MR damper, actuator [96, 97]
Seals Rotating shaft of a machine [98, 99]
Hydraulic valves Actuator, converters [100, 101]
Composite structure Building structure, beams, panels, plate [102–104]
Flexible structure Turbine blades [105]
Pneumatic motion control system Linear resistance component [30]
Braking system Suspension device, aerospace applications [106, 107]

109State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
operations are divided into three parts namely single flow
mode [137], mixed-mode [138], and multimode [139]. The
combined operation of the valve and direct shear mode is
called mixed mode. On the other hand, the squeeze mode
[140], direct shear mode [141] and valve mode [142] are
called multi-mode operations.
Particularly, when the fluid is translated parallel to the
wall are called shear mode (Fig.3a) [143]. In the flow mode
MR damper, the bi-fold mode causes high-pressure differ-
ences to develop higher damping force in a small volume.
This is also illustrated in (Fig.3b) [37].
Figure4a presents the mixed-mode MR damper as a
combined working mode of shear and squeeze mode. In
the mixed-mode operation, the MR damper generates a
higher damping force in comparison with the MR damper
[127, 144, 145]. Figure4b presents the squeeze mode MR
damper which transpires due to the wall sliding movement
and squeezing out the fluid [146].
Among the three-damping operation, mixed-mode MR
dampers are more controllable and generate a higher damp-
ing force.
Fig. 1 Schematic diagram of
MR damper-based semi-active
control system [17]
Fig. 2 MR damper structure [136]
Fig. 3 a Shear mode operation [143], b flow mode operation in MR damper [37]

110 M.Abdul Aziz et al.
1 3
3 Applications oflarge MR dampers
Table3 shows the applications of different large MR damper.
3.1 Large MR damper working principle
Large MR damper works similarly to conventional MR
damper. Large MR damper consists of a piston, piston rod,
cylinder, electromagnetic coil, seal, shaft bearing, MR fluid
and accumulator [160]. An external power supply is used
to supply sufficient current to the coil that produces a mag-
netic field. Figure5 shows the schematic diagram of large
MR damper. The sensors and controller are used to detect
the displacement of the structure. During piston movement,
the MR fluid in the cylinder flows through the orifice of the
piston and the fluid transforms its phase from liquid to semi-
solid due to the presence of the magnetic field [160]. Thus,
required damping force obtained and vibration controlled.
Figure5 shows the large MR damper components.
4 MR Damper numerical models
To design an efficient semi-active control system for MR
dampers several fluid models are required. Till to date, a
Fig. 4 a Mixed-mode [145] and b squeeze mode of MR damper [146]
Table 3 Large MR damper system and their applications
MR damper system Applications References
MR damper Heavy truck, knee prosthetics of limbs, a humanoid robot, haptic devices, motion
master, shock absorber
[36, 147, 148]
MR damper-based suspension system Railway suspension, Tracked vehicle suspension [21, 149]
MR damper-based structure Seismic and wind loading, earthquake mitigation, wind vibration reduction [10, 45, 150]
Scissor jack braced MR damper Wind turbine seismic load control [151]
MR valves Actuator [152–154]
Smart outrigger MR damper Reduction of the dynamic response of tall buildings [155]
MR damper-based bridge structure Pounding mitigation of multi-span bridge [156, 157]
MR damper-based pipeline Reduction of low-frequency pipeline vibration [158]
Rotary MR damper Vibration control of stay cables [159]
Semi-active MR damper system The cable-stayed bridge, Building structure [62]
Fig. 5 Schematic of large MR damper [160]

111State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
group of researchers developed different mathematical mod-
els for analyzing behavior and characteristics of MR damp-
ers performances. To predict the response of physical MR
damper, several techniques, parametric models, and reliable
approach has designed already, and those models can predict
non-linear response. Table4 shows the different fluid models
for MR dampers. Among these, the Bingham model, the
Bouc-Wen and the Modified Bouc-Wen models are some of
the most common models utilized to predict the characteris-
tics of MR dampers [161]. In this regards, large MR dampers
are one of the categories of MR dampers.
5 Large MR damper classication
5.1 Monotube Large MR damper (single‑ended)
The first monotube large-scale MR damper was developed
by Lord Corporation [193] in the 1990s. In 2005s the second
generation of large MR damper was also developed by Lord
Corporation [193].
5.1.1 Bingham model‑based monotube large MR damper
(single‑ended)
Sodeyama etal. [194] developed the Bingham model-based
three types of MR dampers having capacity of 2 kN, 20 kN,
and 200 kN (Fig.6a) which included two types of MR flu-
ids, and two hysteretic models. The damping forces versus
displacement showed a significant increment as frequency
and trial product #104 by Bando Chemical than conven-
tional MRF-132LD by Lord Corporation. A typical involu-
tion model was developed to characterize force–velocity as
shown in Fig.6b presents the involution model for large MR
damper (Eq.1).
In the Fig.7a–7d presents several large MR damper
applications and their real-world application. Figure7a–7c
shows that large MR damper connected to the structure as a
Table 4 MR dampers fluid
models Modelling technique MR damper Models
Bingham models Original Bingham model [56]
Modified Bingham model [162]
Gamota and Filisko model [163]
Updated Bingham model [164]
Herschel-Bulkley model [165]
Bi-viscous models Nonlinear bi-viscous model [166]
Nonlinear hysteretic bi-viscous model [167]
Nonlinear hysteretic arctangent model [168]
Lumped parameter bi-viscous model [169, 170]
Visco-elastic–plastic models General visco-elastic–plastic models [171]
Visco-elastic–plastic model [172]
Stiffness-viscosity-elasto-slide (SVES)
model
[171, 173]
Maxwell models BingMax model [174]
Maxwell nonlinear slider model [175]
Bouc-Wen models Simple Bouc-Wen model [56]
Modified Bouc-Wen model [56]
Bouc-Wen model for shear mode dampers [176, 177]
Bouc-Wen model for large-scale dampers [50]
Current dependent Bouc-Wen model [178]
Current-frequency-amplitude dependent [179, 180]
Non-symmetrical Bouc-Wen model [181]
Dahl models Modified Dahl model [182]
Viscous Dahl model [182]
LuGre models Modified LuGre model [183, 184]
Modified LuGre model [185, 186]
Hyperbolic tangent models [187]
Sigmoid models [188]
Equivalent models [189]
Phase transition models [190–192]

112 M.Abdul Aziz et al.
1 3
vibration support device for seismic vibration control. Fig-
ure7d shows regenerative large MR damper used in struc-
ture support for vibration control.
(1)
F=CiVn
where F,
Ci
and
Vn
are the damping force, damping coef-
ficient and velocity of the piston.
Stanway etal. [198] investigated the electrorheologi-
cal (ER) damper and proposed a mechanical model. This
model is known as the Bingham plastic model. This model
Fig. 6 a Cross-sectional view of 200KN large MR damper and b Involution model of MR damper [194]
Fig. 7 a, b MR damper (structure support) [195] c MR damper (structure support) [196] and d MR damper (cable structure) [197]

113State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
combines a viscous damper a dashpot and a coulomb friction
element which are placed in parallel as shown in Fig.8. The
nonlinear Bingham plastic model (Eq.2) usually used for
characterizing MR dampers force from Fig.8a
where,
Ci
and
fc
represents the damping coefficient and fric-
tional force connected to the fluid yield stress and
sgn
for
signum function.
xandF
are the displacement of MR damper
and damping force [28].
However, the Bingham behavior of an MR damper can
also be derived from the Bingham plastic model for MR
fluids given by Eq.(1) through the study of an axisymmetric
model of the MR fluid flow [30]. Wereley etal. [93] investi-
gate the Bingham model where the parallel plate geometry
or axisymmetric model is used to develop an MR damper
model using shear force mechanism and supports the several
MR dampers models [93, 106, 108]. The following equations
are as follows:
where,
Cpost
is the post-yield damping and
Fy
is the yield
force and
x
is velocity.
The model is given by Eq.(3) assumes that, in the pre-
yield condition, the material is rigid and does not flow;
hence, when |
F(t)
|<
Fy
the shaft velocity
x
=0. Once the force
applied to the damper exceeds the yield force, then the fluid
begins to flow and the material is essentially a Newtonian
fluid with nonzero yield stress. In this constitutive model,
the yield force is obtained from the post-yield force ver-
sus velocity asymptote intercept with the force axis. The
Bingham model accounts for MR fluid behavior beyond the
yield point, i.e., for fully developed fluid flow or sufficiently
(2)
F=Cix+fcsgn(x)
(3)
F
(t)=
⎧
⎪
⎨
⎪
⎩
Cpost x+Fy,x>
0
−Fy<F(t)<Fy,x=
0
Cpost x−Fy,x<
0
high shear rates. However, it assumes that the fluid remains
rigid in the pre-yield region. Thus, the Bingham model does
not describe the fluid elastic properties at small deforma-
tions and low shear rates, which are necessary for dynamic
applications [113]. Considering that the width of the hys-
teretic loop with the Bingham model is relatively narrow,
Weng etal. [127] constructed a more complicated model to
represent the wider hysteretic loop and the updated model
can be expressed by Eq.(4). The following equation can be
written as:
where
kH
,
xH
and
a
are the represents the shape coefficient,
hysteretic velocity and acceleration.
kH
and
xH
are the func-
tions of applied current
I
A 400KN large MR damper (Fig.9) was developed by
Fujitani etal. [47] using Bingham visco-plastic model for
civil structural vibration control. Several research groups
developed large MR damper using the Bingham model for
time delay reduction [164, 198, 199] and they investigated
time delays in the case of control systems, electrical parts,
and mechanical parts of the dampers.
(4)
F
(t)=C0a+
2
𝜋
fcarct an
{
kH
[
a−xHsgn(x)
]}
+f
0
Fig. 8 Bingham plastic model:
a Coulomb friction element in
parallel with a viscous dashpot
[28] and b the piecewise con-
tinuous model for MR dampers
[93]
Fig. 9 400KN bypass type MR damper [47]

114 M.Abdul Aziz et al.
1 3
5.1.2 Maxwell Nonlinear Slider (MNS) model‑based
monotube large MR damper (single‑ended)
Chen etal. [200] developed a monotube large MR damper
(Fig.10) based on Maxwell Nonlinear Slider (MNS) model
for real-time hybrid simulation. The MR fluid behavior (pre-
yield and post-yield region) was characterized by the MNS
model by utilizing Hershel–Bulkley fluid model. Bouc-Wen
model, hyperbolic tangent model and MNS model were
compared with experimental results as shown in Fig.11.
Maximum damping forces were found for the MNS model
and this damper was specially developed for seismic vibra-
tion control three-storied building structure.
To overcome the dynamics of a large MR damper, a vari-
able current controller was then developed for the similar
MNS model. The response time using the variable current
MNS model showed an improved accuracy using RTHS
[200]. The MNS model [175] has pre-yield and post-yield
regions. The pre-yield and post-yield regions can be sepa-
rated independently according to their behavior. The details
of the MNS model can be found in Fig.12 and Fig.13
where
x,yandz
presents the degree of freedom responsible
for damper deformation, pre-yield and post-yield region
variables.
MR damper model [175].
The pre-yield region damping force behavior can be
solved using Eq.(5) which is known as the Maxwell ele-
ment model differential equation
where
c
and
k
are viscous and stiffness co-efficient.
When the damper is in pre-yield mode,
y
is equal to the
damper velocity
x
. The initial value of y is set to be equal to
x
; thus Eq.(5) can be solved in terms of
z
for a given
x
and
the damper force is then determined. The values of
c
and
k
for the Maxwell element are obtained from the force–veloc-
ity relationship observed in damper characterization tests,
selecting two appropriate points on the hysteretic response
curve, and then applying visco-elasticity theory. Assuming
the Maxwell element is subjected to a harmonic motion with
an amplitude of
u0
and circular excitation frequency of
𝜔
,
the coefficients
c
and
k
are calculated from Eqs.(6) and (7)
which are as follows:
(5)
F=k(y−z)=cz
(6)
c
=
1
u
0
𝜔
f
2
0+f
2
m
f
0
Fig. 10 Schematic of large-scale MR damper [200]
Fig. 11 Model comparisons of Large MR damper (Quasi-static behavior) using sinusoidal test results: a I = 0.0 A and b I = 2.5 A [200]
Fig. 12 Proposed phenomenological MR damper model: Maxwell
Nonlinear Slider (MNS)

115State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
where
f0
and
fm
are the damper force when the damper
velocity is zero and a maximum value, respectively. In the
post-yield mode,
x
defined as velocity. Post-yield curves are
defined as the Herschel-Bulkley model [201] and tangential
curve velocity is
x+
tor x−
t.
The mathematical model (Eqs.8,
9, 10) can be written as follows:
where
a,bandc
are damper characterization parameters
and
at
=
bn|
|
x+
t
|
|
n−1
and
f+
t=a+b|x|n
. However, in Eq.(9)
the post-yield damping force
Fpost
can be written as
where,
fpy
and
m0
are positive or negative force and mass
acceleration which is predicted force by the MNS model. If
the mode is changed from post-yield to pre-yield in the MNS
model, then the equation can be written as
where
Fpre
is the pre-yield force.
5.1.3 Hyperbolic tangent function‑based mono tube
single‑ended large MR damper
Based on hysteresis and linear function, Kwok etal. [187]
proposed the force of hyperbolic tangent function model
(7)
k
=
1
u0𝜔
f
2
0+f
2
m
f0
(8)
f+
py(x)=
{
a+b
|
x
|n
if x≥x
+
t
a
t(
x−x+
t)
+f+
t
if x<x
+
t
(9)
F
post =
{
fpy(x)if x.x≥0
f
py
(x)+m
0
x
otherwise
(10)
|
|
|
Fpre
|
|
|
=fpy(x
)
where they analyzed viscous and stiffness of the MR damper
(Fig.14). To define the MR damper hysteretic force–veloc-
ity behavior, a strategy was deployed where a simple model
is proposed here to model the hysteretic viscous damping
(dashpot), spring stiffness and a hysteretic component as
shown in Fig.15. Equation(11, 12) shows the mathematical
expression of the hyperbolic tangent function model [187].
The following equations are as follows:
where
𝛼,𝛽,𝛿,𝛾,n
are model parameters,
c
and
k
are the vis-
cous and stiffness coefficients,
z
the hysteretic variable given
by the hyperbolic tangent function and
fd
is the damper
force offset. This model is applicable for parameter iden-
tification and subsequent inclusion in controller design and
implementation.
Figure15b presents the component building hysteresis
which describes force–velocity response using the effects
of the parameter. The components building up the hyster-
esis are depicted in Fig.15b which illustrates the effects of
the parameters on the damper force–velocity response. The
basic hysteretic loop, which is the smaller one is shown in
Fig.15b, which is determined by β. This coefficient is the
scale factor of the damper velocity defining the hysteretic
slope. Thus, a steep slope results from a large value of β. The
scale factor δ and the sign of the displacement determine the
width of the hysteresis through the term δ sign(x), a wide
hysteresis corresponds to a large value of δ. The overall hys-
teresis (the larger hysteretic loop shown in Fig.15b is scaled
(11)
F=cx+kx +𝛼z+fd
(12)
z=𝛿x−𝛽x|z|n−𝛾z|x||z|n−1
Fig. 13 Pre-defined post-yield curves for MNS model [175]
Fig. 14 MR damper structure [187]

116 M.Abdul Aziz et al.
1 3
by the factor α determining the height of the hysteresis. The
overall hysteretic loop is finally shifted by the offset
fd
.
After hyperbolic tangent function development, Gamota
and Filisko [163] developed viscous and coulomb-based
damping mechanisms and later Gavin [202] proposed a
hyperbolic tangent model-based electro-rheological fluid
damper. Bass and Christenson [203] developed a hyper-
bolic tangent model-based 200KN MR damper for structural
vibration control where over-driven clipped optimal con-
trol (ODCOC) was used. Two simplified elements (spring-
dashpot elements) constitute the hyperbolic tangent model as
illustrated in Fig.16. The following equations are as follows:
(13)

x0
x
0
=

0

−k
0
−k
1
∕m
i
1

−c
0
−c
1
∕m
i
x0
x
0
+

0
k
1
∕m
i
1
c
1
∕m
i
x
x

+

0
−1∕m
i
Fytanh

x0

Vref

The inertial mass element resists motion employing a
Coulomb friction element. The displacement and velocity
of the inertial mass relative to a fixed base,
x0
, and
x0
, and
displacement and velocity of damper piston end relative to
the inertial mass,
x1
and
x1
, are summed together resulting
in the displacement and velocity across the damper,
x
and
x
.
The pre-yield visco-elastic behavior is modelled by
k1
and
c1
. The post-yield visco-elastic behavior is modelled by
k0
(14)
F
=

−k1−c1

x0
x
0
+

k1c1

x
x

Fig. 15 a Hysteresis model—component-wise additive approach and b hysteresis parameters [187]
Fig. 16 Hyperbolic tangent function-based dynamic model for a MR dampers [203] and b MR dampers [187]

117State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
and
k1
. The term
mi
represents the inertia of both the fluid
and the moving piston. The parameter
Fy
is the yield force
and
Vref
is a reference velocity, which affects the shape of
the transition from the elastic to the plastic region of the
function. Figure17 show the large MR damper fast hybrid
test setup in three different floors.
The error for frequency-amplitude combination and error
for larger current across the large MR damper is 17% and
5%, respectively. The hyperbolic tangent model was imple-
mented to capture the silent behavior of a large MR damper.
In another research studied hyperbolic tangent function-
based large MR damper. In terms of convergence and sta-
bility, the hyperbolic tangent function model can run up to
12/1024 (0.012) s while the RMS error at 1/2048 (0.0005)
s for the hyperbolic tangent model converges. The hyper-
bolic tangent model is much slower than other models except
the Bouc-Wen model. The hyperbolic tangent shows better
accuracy where RMS error at numerical time step equal to
1/1024 (0.001) [204]. The schematic of a large-scale semi-
active damper shows in Fig.18.
Phillips etal. [51] developed a large 596KN MR damper
for building structure control using the hyperbolic tangent
function model and four control strategies. The RTHS
predicts the performance of large MR damper and force
tracking controller found to be higher in performance. Equa-
tion(15) expresses the structural behavior of building which
is as follows:
where,
m,c,k,GL,F,x
and
xg
are the mass, damping, stiff-
ness, influence vectors, force, displacement vector and
ground acceleration.
5.2 Monotube large MR damper (double‑ended)
5.2.1 Modified Bouc‑wen model‑based Monotube Large
MR damper (double‑ended)
Yang and Cai [205] developed a mixed-mode control sys-
tem using a 20KN capacity MRD 9000 (Fig.19) [206] to
attenuate the vibration of the suspension bridge generated
from vehicle braking force and earthquake. A total of seven
control strategies were investigated to get the maximum
efficiency. A combination of semi-passive on control and
fuzzy control strategies was analyzed that showed better per-
formance on vibration reduction. Figure19 shows the MR
damper installed on bridge.
The damping force can be expressed in Eqs.(16, 17, 18)
using the modified Bouc-wen model which can be written as
where z and y are expressed by
where
cl
is the viscous damping at large velocities,
ck
is the
viscous damping for force roll off at low velocities,
ka
is the
accumulator stiffness,
kl
stiffness at large velocities,
xi
spring
(15)
mx+cx+kx =GF −mL xg
(16)
F
=c
k
y+k
a(
x−x
i)
=𝛼z+c
l
(x−y)+k
a
(x−y)+k
a(
x−x
i)
(17)
z=−𝛾|x−y|z|z|n−1−𝛽(x−y)|z|n+A(x−y)
(18)

y
=
1
C
l+
C
k
[𝛼z+clx+kl(x−y
)
Fig. 17 A schematic of the large MR damper fast hybrid test setup
showing the computer structure model and the three physical MR
dampers [203]
Fig. 18 Schematic of large-scale semi-active damper [204]
Fig. 19 MRD 9000 by Lord corporation [206]

118 M.Abdul Aziz et al.
1 3
initial displacement and A,
𝛽
,
𝛾
, and n are constant. But the
application of this control system was limited to low vibra-
tion. During the excessive earthquake, this control system
fails to protect the pier and bearing damage to the bridge.
To save the bridge members under excessive earthquakes
a real-time semi-active control algorithm based on the dam-
age of bridge members (RTSD) was proposed using a similar
20KN large MR damper [207] by Li etal.[208]. Figure20
shows the MRF-04K damper. This proposed model ensured
that it can reduce the chance of damage to the bearing and
pier more effectively and can set the damping force in a dif-
ferent range. The nonlinearity of the damper was measured
using the modified Bouc-wen model.
5.2.2 Phenomenological Bouc–Wen model‑based
monotube large MR damper (Double‑ended)
Yang etal. [209] developed a 200 KN large MR damper
(Fig.21) for structural vibration control using the Bouc-
Wen model. They found higher damping force using a small
amount of energy and quicker response time (damper coils)
using parallel coil connection.
Sanwa Tekki Cooperation (Japan) [210] and Lord Cor-
poration [133] jointly developed a 300 KN MR damper for
seismic vibration control application while in 2003 they also
developed a 400 KN MR damper for residential building
applications [46, 47]. In 2003, 312 SD-1005 MR dampers
were installed at Dongting Lake Bridge in Hunan and Ou
etal. [48] developed several large MR dampers for Binzhou
Yellow River Bridge China. Meanwhile, Binzhou Yellow
River Bridge used several MR dampers for world longest
cable-stayed bridge [211]. They used 6000 KN, 12 large MR
dampers for vibration control.
In the Fig.22a–d presents several large MR damper appli-
cations in suspension Fig.22a–d also shows that large MR
damper with control system and sensor network.
In 2011, Tu etal. [52] developed a sedimentation
proof500 KN large MR damper (Fig.23) using a modified
Fig. 20 Cross section of MRF-04K damper [207]
Fig. 21 Schematic of the large-scale 200KN MR damper [209]
Fig. 22 a Dongting Lake
Bridge-China (Large MR
damper) [48], b, c Cable-stayed-
Eiland Bridge (Netherlands)
equipped with large MR damper
[212] and d Earthquake-proof
large MR damper [213]

119State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
Bingham plastic model which was used for parameter
identification.
Yang etal. [50] proposed a Bouc-Wen model-based dou-
ble ended large-scale MR damper for structural vibration
mitigation. Fluid inertial and shear-thinning effects were also
analyzed using the Bouc–Wen model and it is found from
the experiment that the current driven power supply is suit-
able for quicker response time. Cha etal. [214, 215] investi-
gated the time delay of large MR damper using semi-active
algorithms for 200KN MR damper to address robustness.
Four types of control algorithms were used for semi-active
control using the Bouc–Wen model where decentralized out-
put feedback passive controller were more robust for time
delay calculation than the clipped-optimal controller.
Bahar etal. [216] proposed a Bouc–Wen hysteresis model
based large MR damper for real-time hybrid simulation
using a parameter identification algorithm. They also studied
large MR damper for benchmark building using parameter
identification algorithm [217].
A similar large scale practical MR damper (Fig.24)
developed by Dyke etal. [218] and Rodríguez etal. [219]
developed seismic vibration control MR damper (Fig.25)
using Bouc–Wen model and used clipped-optimal control
algorithm for real-time applications and similar model and
algorithm used by Zapateiro etal. [220] where real-time
hybrid testing (RTHT) utilized for time delays and MR
damper dynamics control [220].
Bouc–Wen model-based shear mode large MR damper
developed for seismic vibration of a five-storied build-
ing where they used Bang-Bang, the Lyapunov and
Clipped-Optimal controllers [221]. Other research groups
developed MR damper integrated with base isolation system
for large structure vibration control where they used Lyapu-
nov controller [222].
Chen etal. [223] minimized actuator time delay using
the CR algorithm and demonstrated the RTHS technique
for experimental validation. Other research group used El-
Centro, Kobe and Northridge seismic protection large MR
damper numerical and experimental analysis investigation
done by Bouc–Wen model and Clipped Optimal Control
strategies. They found that the property of the damper can
cope with normal natural frequencies and placement of
the MR dampers were sensitive cases which include floor
optimum location also [224]. The long term reliability of
large scales MR dampers such as response time, dissipative
capacity, control technique and force response are the criti-
cal point of MR damper applications in seismic vibration
control [225].
A large MR damper RTHS was done for seismic vibration
protection using the Bouc–Wen model where they used a
semi-active neuro controller (SA-NC) and found that SA-NC
is capable of reducing acceleration and displacement [226].
A similar SA-NC based study was proposed by Chae etal.
[227] and Moon etal. [228].
The Bouc–Wen model-based MR damper was pro-
posed by Spencer etal. [56], which is known as modified
Bouc–Wen model. The Bouc–Wen model proposed by Bouc
[229, 230]and later generalized by Wen [230] for MR damp-
ers numerical investigations such as hysteresis behaviour.
The damper force is given by Eq.(19) which can be written
as:
where the evolutionary variable z is governed by Eq.(20)
which is as follows:
(19)
F−fc=m

x+co(

x)

x+kax+
𝛼
z
(20)
z=−𝛾|x|z|z|n−1−𝛽x|z|n+Ax
Fig. 23 Main parts of full-scale MR damper [52]
Fig. 24 Schematic of MR damper [218]
Fig. 25 Detail structure of MR damper [219]

120 M.Abdul Aziz et al.
1 3
In this model, m = equivalent mass which represents the
MR fluid stiction phenomenon and inertial effect;
ka
=accu-
mulator stiffness and MR fluid compressibility;
fc
damper
friction force due to seals and measurement bias; and
co(x)=
post-yield plastic damping coefficient.
To describe the MR fluid shear thinning effect which
results in the force roll-off of the damper resisting force
in the low-velocity region, the damping coefficient
c(x)
is defined as a mono decreasing function with respect to
absolute velocity
|x|.
The post-yield damping coefficient is
expressed in Eq.(21). The post-yield damping coefficient
can be written as:
where
a1,a2
, and
p=
positive constants.
Besides the proposed phenomenological model (Fig.26),
two other types of dynamic models (Fig.27) based on the
Bouc–Wen model are also investigated. One is the simple
Bouc–Wen model with the mass element (Fig.27a). Note
that the damping coefficient is set to be a constant in this
model. The other one is the phenomenological model [56]
with the mass element (Fig.27(b)). To assess their ability
(21)
c(
x
)
=a
1
e
−a
2
|

x|p
to estimate the MR damper behaviour, these three dynamic
models are employed to fit the damper response under a 1
in., 0.5Hz sinusoidal displacement excitation at an input
current of 2 A. As can be seen, all models can describe the
damper force–displacement behaviour very well. However,
the simple Bouc–Wen model fails to capture the force roll-
off in the low-velocity region. The damping force is shown
in Eq.(22) and the damper force is as follows:
where
x
is the velocity of the piston,
c
is the damping co-
efficient and
ks
is the linear spring constant.
5.2.3 Phenomenological Dhel friction model based
monotube large MR damper (Double‑ended)
Dhel friction model [231] was developed by Dahl [231] to
characterize the frictional behaviour and a differential equa-
tion was used for stress–strain curve modeling. Let x be the
displacement,
fc
the friction force and
Fc
the Coulomb fric-
tion force. Figure28 presents the typical solid friction force
function.
Solid friction mathematical model (Eq.23), in terms of
time rate of change of solid friction can be written as
where
F(x)
is a solid friction force (function of displacement
x
). When
x
is positive then friction force will be +
Fc
and in
case of reverse force,
x<0
and
F(x)
will be negative that
is
−Fc
. Though
x
changes then the friction function slope
dF(x)
dx
, remains positive. The friction slope functions can be
expressed from Eqs.(24, 25, 26, 27) and will be simulated
(22)
F
(t)=mx+cx+k
s(
x−x
0)
+𝛼
z
(23)
dF(x)
dt
=
dF(x)
dx
dx
dt
Fig. 26 The proposed phenomenological model of MR dampers [50]
Fig. 27 Two other types of phenomenological models of MR dampers based on Bouc–Wen hysteresis model [56]

121State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
with hysteresis behavior. The following equations are as
follows:
For positive velocities
sgn x
=
+1
, then the dimensionless
ratio
r
=
F
F
c
With
where
u=
x
xc
is a dimensionless displacement variable, and
xc
is a characteristics displacement which can be written as
(24)
dF(x)
dx =𝜎
|
1−F
F
c
sgn x
|
sgn(1−F
F
c
sgn 
x
)
(25)
r=1−[1−(1−i)u]
1
∕
1−
i
(26)
u
<
(
1
∕
1−i
)
for i>
1
(27)
x
c=
Fc
𝜎
The modified Dahl model proposed by Zhou and Qu
[162] is shown in Fig.29. This model is used to simulate
Coulomb force and avoid too many parameters. The damp-
ing force can be written as:
where
k,
Ci,Fd,x,fkand Z
are stiffness, damping coefficient,
Coulomb force modulated by the applied magnetic field, dis-
placement of MR damper, damper force caused by seals and
measurement bias and nondimensional hysteretic variable
governed by [231] the following equation:
where
sgn
determines hysteretic loop shape and
𝜎
is the rest
stiffness or slope of the displacement curve.
After modified Dahl model, Ikhouane and Dyke [182]
developed a viscous Dahl model for the shear mode MR
damper (Figs.30, 31).
The viscous dry friction model for MR dampers can be
written as
Here
z
is a no dimensional hysteretic variable and the
constants
𝛼
and c depend on voltage.
(28)
F=kx +Ci
x+FdZ−fk
(29)
z=𝜎x(1−Zsgn( x))
(30)
F(t)=cx+𝛼z
Fig. 28 Typical solid friction force function [231]
Fig. 29 Modified Dahl model of MR damper [162]
Fig. 30 Shear mode MR damper [182]
Fig. 31 Viscous + Dahl model for the MR damper [182]

122 M.Abdul Aziz et al.
1 3
Using the viscous Dahl model, Rodriguez etal. [232]
proposed a large MR damper for vibration mitigation using
Bouc-Wen and Dahl frictional model [233]. The proposed
model verified the viscous term which was smaller than
hysteresis one and modified identification technique. They
found Dahl friction model [233] generated higher error than
Bouc–Wen model. Bouc–Wen model was more suitable for
large MR fluid damper modeling. Dhel friction model was
used for three-storied building vibration reduction while for
larger storied was not considered. The issue of high pay-
load, particle sedimentation and magnetic flux distribution
was not considered also. Jiang and Christenson [204] inves-
tigated the Dahl friction model using Aguirre etal. [234]
viscous plus Dahl model. It was found from the RTHS that
the Dahl friction model is more sensitive during the change
of numerical integration time step than algebraic model and
viscous plus Dahl models follows the simpler equations
modeling the force behavior.
5.2.4 Bingham model‑based Monotube Large MR damper
(double‑ended)
Kui etal. [235] proposed a large 1400N MR damper to miti-
gate the unwanted pipeline vibration using Bingham plastic
non-linear fluid model and linear quadratic regulator (LQR)
control algorithm. The use of an LQR control system and
magnetism insulator ensures the high magnetic flux density
that results in high damping performance. Figure32 shows
the 3D model of the MR damper. The damping force is given
in Eq.(32). The damping force using the Bingham plastic
non-linear model can be expressed as
where,
F𝜏
is the shear stress,
F𝜂
is the viscous stress,
𝜂
is the
dynamic viscosity of MR fluid, h is the width of damping
gap,
Ae
is the effective area of the piston,
l
is the effective
(31)
F
=F𝜂+F𝜏+Ff=
12𝜂lA
2
p
𝜋D
�
h
3ur+
(
3l𝜏yAe
h
+Ff
)
sgn[ ur
]
length of the piston,
ur
is the relative velocity of the piston
and cylinder and
D′
is the mean diameter of the damping
gap. The dynamic range of MRF damper can be written as
5.2.5 Herschel‑Bulky model‑based Monotube Large MR
damper (double‑ended)
A semi-active control system incorporating a large 200KN
MR damper was proposed by Peng and Zhang [236] to
understand the full operating environment of the system for
control structure. The Herschel-Bulky model was employed
to understand the MR fluid characteristic. The simulation
results match well with the experimental data. Figure33
shows the MR damper.
The features of Herschel-Bulkley model (Eqs.(33, 34)
defines both Bingham plastic model and power law model.
The rheological behavior of MR fluids using Herschel-Bulk-
ley model can be written as
where
𝜂
,
kc,𝜏y
n
and
𝛾
are the dynamical viscosity, consist-
ency index, yield shear stress, power law index and strain
rate.
Finally, the Herschel-Bulkley fluid model [237] can be
written as
where
H0
is the strength of the magnetic field.
(32)
β= F
𝜂
+F
𝜏
+F
f
F
𝜂
+F
f
=1+F𝜏
F
𝜂
+F
f
(33)
𝜂
=
𝜏y
𝛾
+kc
(
𝜏y
𝛾
)n−1
(34)
𝜏
=

𝜏y

H0

+K

𝛾

1
m

sgn( 𝛾
)
Fig. 32 3D model of MR damper [235]
Fig. 33 Shear value modal MR damper [236]

123State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
5.2.6 Double sigmoid model‑based Monotube MR damper
(double‑ended)
A semi-active control system base MR damper is proposed
by Ji etal. [158] to reduce the low-frequency vibration in
the pipeline by introducing three different control modes.
Results showed that the sliding mode variable structure
control mode had better vibration reducing proficiencies
than PID control at high frequency level. A double-sigmoid
model was developed to express the damping force of the
MR damper shown in Eq.(35) which can be written as
where,
Fc
is the adjustable coulomb damping force,
xv
is the
displacement value when damping force was zero,
x
and
x
are relative displacement and velocity of MR damper piston
and cylinder,
Ci
is the viscous damping coefficient and
a
is the velocity adjustment co-efficient of coulomb damping
force.
5.3 Twin tube large MR damper (single‑ended)
5.3.1 Bingham model‑based twin tube large MR damper
Zolfagharian etal. [238] developed an unsteady analytical
model combined with quasi-static analysis and experimen-
tally investigated the MR fluid flow behavior through the
piston annular channel of a twin-tube MR damper. Figure34
presents single ended twin tube large MR damper structure.
The result showed that the new unsteady analytical model
can measure the phase difference more effectively than other
models which also results in higher damping force. The non-
Newtonian fluid characteristic was described through the
Bingham plastic model, where the developed shear stress
(Eq.36) can be written as
where,
F𝜏
is the shear stress,
𝜏y
is the yield stress,
H
mag-
netic field amplitude,
𝛾
shear strain rate and
𝜂
is the viscosity
of MRFs.
5.4 Twin tube large MR damper (double‑ended)
5.4.1 Phenomenological Bouc‑wen model‑based twin tube
large MR damper (double‑ended)
A new phenomenological model was proposed by Spencer
etal. [56] and applied by Wang etal. [239] to improve the
long-term operation capability of the MR damper by ana-
lyzing the mechanical characteristic of the dampers which
(35)
F
=Fc
1−e
−a(x−x
v
sign(x))
1+e
−a(x−xvsign(x))+Ci

x
(36)
F𝜏=𝜏y(H)sign(𝛾 )+𝜂 𝛾
were in operation for a long time in cable bridge. Figure35
presents schematic of twin-tube large MR damper.
The modified model is shown in Fig.36. The final damp-
ing force (Eq.37) of the model can be written as
Fig. 34 Single ended twin-tube MR damper [238]
Fig. 35 Twin-tube large MR damper [239]

124 M.Abdul Aziz et al.
1 3
where
cb
is used to model the roll off phenomenon of MR
damper at low motion velocities,
k
is the stiffness of the accu-
mulator,
x
is the displacement of the piston,
xi
is the initial
displacement of the spring and
A1
and
A2
are the modified
co-efficient for the bottom right part and top left part of the
displacement damping force loop..
The experimental results showed that the used dampers
were a lack in efficiency due to the leakage problem of MR
fluid and the new proposed model had a better effect on the
mechanical properties of the dampers.
(37)
F
mmr =





cb
y+k

x−xi

+A1x
x
cb
y+kx−xi−A2x
x
cb
y+k

x−xi

6 Control algorithm strategies oflarge MR
dampers
Several control strategies were taken last decades to mini-
mize response time, time delays, dissipative energy capac-
ity, force responses, robustness and excessive cost etc. The
control techniques of large MR dampers are passive, active,
and semi-active [46]. Passive control techniques are used
in base-isolators, elastomeric and frictional dampers, and
tuned-mass dampers while active control systems are used
in active bracing/tendon systems, active-mass drivers, and
active variable-stiffness devices [240]. A semi-active control
system combines both passive and active control strategies
which is especially used in large force requirements using
lesser power [241]. Semi-active device used in variable fric-
tion/stiffness dampers and controllable-fluid dampers (elec-
trorheological (ER) and MR (MR) fluid dampers) [242]. The
semi-active control methods are model-based control and
soft computing-based control. Model-based control tech-
niques are bang–bang control, back-stepping control, sliding
mode control,
H2
and
H
∞ control, adaptive/non-linear con-
trol, and bilinear control while soft computing-based control
are neural network-based control, fuzzy logic control, and
genetic algorithm-based control [53, 214, 243].
6.1 Skyhook control algorithm
Karnopp etal. [244] proposed a ‘skyhook’ damper control
algorithm (Fig.37a) for a vehicle suspension system [135,
Fig. 36 Phenomenological mechanical model [56]
Fig. 37 a The skyhook damper
system [244] b configuration of
MR damper [246]

125State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
245]. An MR damper [246] with skyhook control system for
vehicle suspension system is shown in Fig.37b.
The skyhook control law can be written as.
Where
Fb
is the control force,
c
and
k
viscous and stiff-
ness co-efficient.
6.2 Decentralized bang‑bang control
Other research group such as McClamroch and Gavin [247]
proposed decentralized bang-bang control law using the
Lyapunov control algorithm. They reported that this control
system is accurately working for ER dampers application
with maximum and minimum dissipation rate. The control
law can be represented as
where
vo
, is the input voltage to the current driver,
Vmax
is
the maximum allowable voltage and
h
is the Heaviside step
function.
6.3 Clipped‑optimal control (COC)
Acceleration feedback-based Clipped-optimal control (COC)
(Fig.38) was proposed by Dyke etal. [248] to overcome the
full-state feedback or on velocity feedback control system.
Accelerometers based COC can provide a reliable and inex-
pensive solutions. COC algorithm needed to design a linear
optimal controller
Kc
which will provide control force
Fb
based on measured response
y
i.e.:
(38)
Fb=+c(

x−

x0)++k(

x−

x0)
(39)
Fb=cx+k(x−x0)
(40)
vo
=V
max
h(− x
t
Λf
)
where L is Laplace transform,
f
is the measured force,
yj
is
measured output vector,
vi
is the measured noise vector and
the control law can be written as.
where
Vmax
,
H
, are the voltage to the current driver related
to the saturation of the magnetic field in the MR damper and
Heaviside step function.
Heo etal. [249] proposed an MR damper (Fig.39) using
clipped optimal control system for a cable stayed bridge to
control seismic vibration.
6.4 Homogeneous friction controller
Inaudi [251] proposed a Homogeneous friction controller for
semi-active control of structures. This controller system is
also known as modulated homogeneous friction (MHF) con-
troller. This proposed controller shows quadratic dissipation
of energy per cycle in the deformation amplitude, maximum
dissipation efficiency for resistance-force level proportional
to deformation, and simple and accurate linearization. In
addition, a modified type of modulated homogeneous fric-
tion controller proposed by He etal. [252] that is capable of
increasing the performance of MR dampers. The proposed
control law is shown in Eqs.(43, 45, 46) which can be writ-
ten as
(41)
F
b=L−1
(
−Kc(s)L
(
yj
f
))
(42)
vi
=V
max
H(
[
F
b
−f
]
f
)
(43)
N(t)=g|P[Δ(t)]|
Fig. 38 Block diagram of the semi-active control system [248]
Fig. 39 Large MR Damper (COC based) [249] and b COC based
large MR damper [250]

126 M.Abdul Aziz et al.
1 3
where,
N(t)
is controllable contact force,
Δ(t)
is damping
deformation,
𝜇
is coefficient of friction,
g
is the positive gain
coefficient and
Δ(t−s)
is local peak of deformation signal.
6.5 Semi‑active control algorithms
Xu etal. [199] proposed semi-active control algorithms
which is based on neural networks applied for MR dampers
structures. The control algorithm can be written as [253]
(44)
P[Δ(t)]=Δ
(t−s)
(45)
f[Δ(t)]=g𝜇
|
P[Δ(t)]
|
sgn
(
dΔ(t)
dt
)
if dΔ(t)
dt ≠
0
(46)
−
g𝜇
|
P[Δ(t)]
|
≤f[Δ(t)]≤g𝜇
|
P[Δ(t)]
|
if
dΔ(t)
dt
=
0
(47)
Msx+Csx+Ksx=𝜆Fb−MsΓxg
where, x is the vector of relative displacement of the floors
of the structure,
xg
is one-dimensional ground acceleration,
Fb
is measured control force, Г is column vector of ones, λ
is the vector determined by the position of MR damper. An
MR damper with semi active control system [199] based on
neural network is shown in Figs.40 and 41.
6.6 Quasi‑bang‑bang control algorithm
The quasi-bang-bang control algorithm (Eq.48) proposed
by Barroso etal. [254] for MR dampers structures and pro-
posed controllers considered static equilibrium conditions.
The equation can be written as follows [255]
where
Vmax
is the maximum voltage.
(48)
V
i=
{
Vmax
if moving away from the center
0 if moving towards the center
Fig. 40 Structure of neural
network controller [199]
Fig. 41 Schematic diagram of MR damper [199]Fig. 42 Schematic of MR damper [256]

127State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
6.7 Lyapunov control theory
To provide higher performance Spencer and Nagarajaiah
[46] proposed Lyapunov control theory-based damping
control system for MR dampers. The control law (Eq.49)
for Lyapunov control theory can be written as
where
cmax
and
cmin
are maximum and minimum damp-
ing coefficients, respectively, and
𝜔n=√k∕m
, and
ua(t)
is
the absolute displacement of the single degree of freedom
(DOF) and
ur
is the relative velocity.
A Lyapunov control system-based MR damper [256] and
the control block diagram is shown in Figs.42 and 43.
6.8 Decentralized Output feedback polynomial
controller (DOFPC)
Cha and Agrawal [257] investigated decentralized output
feedback polynomial controller (DOFPC) for both active
and semi-active controls of the highway suspension bridge.
The control strategy is expressed in terms of velocity and
displacement across MR dampers using 3rd order polynomial
equation. The equation can be written as
where
v
is the control signal,
xand x
are the inter-
story drift and interstory velocity, respectively,
q0,q1,q2,q3,ro,r1,r2andr3
are optimal co-efficient of the
polynomial equation for control signal.
(49)
c
(t)=
{
cmax
(
𝜔nua+ua
)
ur>
0
c
max(
𝜔
n
u
a
+u
a)
u
r
<
0
(50)
v
=
(
q
0
+qx +q
2
x
2
+q
3
x
3)
+(r
o
+r
1
x+r
2
x
2
+r
3
x
3)
6.9 Maximum energy dissipation controller
Jansen and Dyke [176] proposed maximum energy dissipa-
tion controller for six story building using MR dampers and
considered Lyapunov controller. Maximum Energy Dissipa-
tion Controller specialized for multi-input control system.
The equation can be written as [255]
where,
V(z)
is Lyapunov function,
||z||p
=
p norm of the state
and P = real symmetric, positive define matrix.
6.9.1 Simple‑passive control (SPC)
Zhang [258] proposed simple-passive control (SPC) system
for seismic MR damper where zero-displacement positions
are available. MR damper can cope with large control force
with its zero-displacement position. The simple-passive con-
troller formulation can be written as
where
Vb
,
x
are the control voltage to the ith MR damper
and inter-story displacement.
x1,x2,x3
,
v1,v2
and
v3
are the
design parameter which can be determined by optimization
process.
6.9.2 Back‑stepping control
Back-stepping control provides higher performance and
accuracy which was proposed by Zapateiro etal. [259] for
the vehicle suspension system. Primarily Back stepping
Controller used Dahl model and a proposed Back-stepping
Controller for seismic protection and vehicle neural network
for MR dampers. The neural network can achieve inverse
(51)
V
(z)=
1
2||
z
||2
p
(52)
V
b=
⎧
⎪
⎨
⎪
⎩
v
1
�x�<x
1
v2x1≤�x�<x1+x2
v3x1+x2≤
�
x
�
<x1+x2+x
3
0
x
1+
x
2+
x
3
≤
�
x
�
Fig. 43 Block diagram of the control scheme [256]
Fig. 44 MR Damper [260]

128 M.Abdul Aziz et al.
1 3
dynamics or reproduce using Back stepping Controller in the
MR damper. A back-stepping technique-based MR damper is
shown in Fig.44 [260]. The control law is shown in Eqs.(53,
54, 55). The following equation can be written as
where,
𝛼1
,
𝛼2
are the angular position,
F
is the generated
damping force,
𝜔2
is the angular speed of the upper lever,
Vb
is the control voltage and
kx
,
kwa
and
kwb
are hysteresis loop
controlling parameter.
(53)
F
=−
(
𝛼1−𝛼2
)(
1+h1h2
)
+
(
h1+h2
)
𝜔2+f
g
(54)
F
=k
x
x+[k
wa
+k
wb
V
b
]
w
(55)
V
b=−
(
𝛼1−𝛼2eq
)(
1+h1h2
)
+
(
h1+h2
)
𝜔2+f−g(kxx+

kwbw
)
kwbwg
6.9.3 Sliding mode controller
The sliding mode controller (Fig.45) was used for driving
the response trajectory along with a sliding surface [261]
and particularly applied in nonlinear and hysteretic struc-
tures while several research group used for MR/ER damp-
ers (Fig.46) for seismic structures [262, 263]. The required
equation can be written as
xs0
is sprung mass displacement,
es
is sprung mass dis-
placement error,
xs
is the vertical displacement and
Φ
is con-
vergence rate of sliding mode control.
(56)
s=es(t)+Φes(t)
(57)
es(t)=xs(t)+xs0(t)
Fig. 45 Schematic diagram of
SSMC-based MR quarter-vehi-
cle suspension system [264]
Fig. 46 Schematic of MR damper [265]
Fig. 47 Block diagram of adaptive control system [267]

129State-of-the-art recent developments oflarge magnetorheological (MR) dampers: areview
1 3
6.9.4 Non‑linear closed‑loop controller
Kane etal. [266] proposed non-linear closed-loop control-
ler for MR damper structures. The advantages of nonlinear
controller over linear controller are controlling the dynamic
force saturation limit and agent-based control structure. The
control equation can be written as
where
W
j
_

Z
i
FZ

=
n
i=1𝜇pi,j(Z
i
FZ
)
and
𝜇
p
i,j
(Z
i
FZ )
is the grade
of membership of Z
i
FZ
in
Pi,j
,
Aj,Bj
are system matrices and
R
is state vector.
6.9.5 A non‑linear/adaptive control
A non-linear/adaptive control (Fig.47) was proposed by
Bitaraf etal. [267] after combining the study of simple adap-
tive control method [268] and genetic-based fuzzy control
method. An adaptive control-based MR damper [269] for
seat suspension is shown in Fig.48. A nonlinear or adaptive
controller can controlboth displacement, acceleration and
response time effectively. Fuzzy logic control method is a
combination of several control methods such as sliding mode
and genetic algorithm control or combined method of fuzzy
logic and neural network where neural network models [270]
and black box model [271] are used. Fuzzy logic algorithm
was proposed in civil structure [272–275] and MR dampers
modeling [276–279]. Equation(59–62) shows the control
law of the system. The equation are as follows:
(58)

R
=
N
r
j
N
r
q=1Wj

Zi
FZ

⋅
Wq

Zi
FZ

Aj+BjKq
R

Nr
j

Nr
q=1Wj

Zi
FZ

Wq

Zi
FZ

where,
Ap
Am
are state matrices,
Bp
,
Bm
are input matrices,
Cp
,
Cm
are the output matrices,
Rp
,
Rm
are the n × 1 plant state
vector
nm
× 1 model state vector,
yp
is plant output,
ym
is the
model output,
up
is the m × 1 input control vector,
um
is the
m × 1 input command vector and
di
and
do
are the input and
output disturbances.
7 Conclusion
Large MR dampers have been developing for large vibra-
tion control systems. The review presents different struc-
tural design, mathematical models, their applications, clas-
sifications and different control system used for large MR
dampers. Large MR dampers are developed by modifying
the conventional MR dampers both in internal and external
design structure. The main feature of a large MR damper
over normal MR damper is its higher damping force and
large frequency vibration control capability. The mono tube
large MR damper with single ended and double ended struc-
ture are mostly developed over the years due to its cost-
effectiveness and availability while the twin-tube large MR
damper are less developed.
Among different mathematical model, the phenomeno-
logical bouc-wen model-based mono tube MR damper was
mostly developed due to its fast response time, resistance to
particle sedimentation, lower energy consumption and effec-
tive in both low and high frequency vibration control system.
Whereas the Phenomenological Dhel friction model-based
monotube large MR damper had more error in efficiency
and not suitable for large scale MR damper modeling due
to its high sedimentation, low magnetic flux distribution
problems.
It is essential to react fast when subjected to large fre-
quency vibration in case of large vibration mitigation. Large
MR damper requires faster response time and better reli-
ability for long-term large vibration control system. Among
different control system the non-linear or adaptive control
system was proved to be the most effective in case of better
response, displacement and acceleration control. It is a com-
bination of adaptive control and fuzzy control method which
(59)

Rp
(t)=A
p
R
p
(t)+B
p
u
p
(t)+d
i
(t
)
(60)
yp(t)=CpRp(t)+d0(t)
(61)

Rm
(t)=A
m
R
m
(t)+B
m
u
m
(t
)
(62)
ym(t)=CmRm(t)
Fig. 48 MR Damper [269]

130 M.Abdul Aziz et al.
1 3
are used for many civil engineering applications where large
damping force requires.
Acknowledgements The authors would like to convey their gratitude
to the Abdal Engineering Limited (C-146474/2018), Bangladesh, for
providing their facilities and research support.
Author contributions MAA: Formal analysis, writing—original draft,
methodology, review-editing, and supervision. SMM: Formal analysis,
Writing—original draft. RA: Writing, review & editing.
Funding Open Access funding enabled and organized by CAUL and
its Member Institutions.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source,
provide a link to the Creative Commons licence, and indicate if changes
were made. The images or other third party material in this article are
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otherwise in a credit line to the material. If material is not included in
the article's Creative Commons licence and your intended use is not
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need to obtain permission directly from the copyright holder. To view a
copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.
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