19-04-2012, 04:58 PM
New control strategies for active tuned mass damper systems
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Introduction
The most commonly used active control device for
civil engineering structures is the active tuned mass
damper (ATMD). As Li et al. [11] commented, the high
efficiency is the major advantage of ATMD, in which a
relatively small mass can be used to reduce structural
response. Meanwhile an active control force is applied to
move this small mass efficiently in order to achieve
further response reduction. Thus, a relatively small active
control force can significantly reduce structural response
by 40–50% or more [2]. On the other hand, unlike
some other active control devices, ATMD can be installed
in many kinds of structures: buildings, towers
and bridges.
Three kinds of ATMDs have been developed over the
last two decades. They are the hybrid mass damper
(HMD), the active mass damper (AMD) and DUOX
(Figs. 1 and 2). A significant difference between a HMD
and an AMD is that the stiffness and damping of HMD
are provided by a tuned mass damper, while the stiffness
or/and damping of an AMD is provided by the active
force [13]. The so-called ‘‘DUOX’’ system is composed
of three parts, a small mass, a tuned mass damper and
an active force [2]. The active force, mainly used to reduce
the stroke of the TMD in the DUOX system, is
applied to the TMD through the action of the small
mass
Extensive theoretical and experimental studies on
AMD devices have been conducted by many researchers
e.g., [1–8,12–14,16]. The first practical application of an
AMD device in the world was realized in Japan in 1989,
when two AMDs were installed on the 11th floor of a
commercial office building, Kyobashi Seiwa Building in
Tokyo by Kajima Cooperation. The objective of
installing the AMDs is to control the lateral and torsional
vibration of the building subjected to earthquakes
and frequent strong winds. Since then, the active tuned
mass dampers have been installed in several buildings,
towers and bridges [3].
Corresponding author.
E-mail address: bcqsli[at]cityu.edu.hk (Q.S. Li).
0045-7949/$ - see front matter 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compstruc.2004.05.010
Computers and Structures 82 (2004) 2341–2350
www.elsevierlocate/compstruc
As is well known, all active structural control
strategies are rooted in the modern control theory. The
simplest and most popular strategy is the linear quadratic
regulator (LQR) method. However, an active
control strategy for an ATMD has its own specifications
and limitations. Cao [2] has shown that highly
nonlinear control strategies, such as bang–bang control,
may not be suitable for ATMD applications. New
control strategies, which are based on linear feedback
control, are proposed in this paper from a response parameter
analysis. Unlike the traditional LQR method, the
new strategies do not need to solve the Riccati equation.
Furthermore, a simplified method for ATMD
design is presented based on the proposed strategies.
As a main feature, the equivalent damping induced
by an ATMD can be easily determined by the simplified
method. In order to check the effectiveness of
the proposed formulas and the active control strategies,
numerical simulations are conducted for three
examples. The numerical results show that the present
strategies result in a better reduction on structural
acceleration responses than the LQR method. It is also
observed from the numerical examples that the results
determined from the simplified design method are in
good agreement with those obtained from the present
strategies and the LQR method.
Equations of motion
As introduced above, a DUOX system is composed
of three parts, a small mass, a tuned mass damper and
an active force, as shown in Fig. 2. The equations of
motion of a structure with a DUOX system
Conclusions
The active tuned mass dampers have many advantages,
such as high efficiency and flexibility. In this
paper, a different structural control approach is developed.
Instead of solving the Riccati equation, new
control strategies are developed from a response
parameter analysis and based on the linear feedback
control for the design of ATMD systems under dynamic
excitations. Based on the proposed strategies, a simplified
method for ATMD design is presented. The equivalent
damping induced by an ATMD can be easily
determined by the simplified method. When the equivalent
damping ratio is given, one can easily evaluate the
response reduction caused by the ATMD. The numerical
examples show that the present strategies result in a
better reduction on acceleration response than the LQR
method. It is also shown through a numerical example
that the results determined from the simplified design
method are in good agreement with those obtained from
the present strategies and the LQR method.