INTRODUCTION
Buildings in modern cities are often built closely to each other due to limited
space available. These buildings, in most cases, are separated without any structural
connections. Hence, earthquake resistant capacity of each building mainly depends
on itself. To improve the earthquake resistance of these buildings, the concept
of using control devices to link adjacent buildings has been presented (Bhaskararao
and Jangid, 2006).
Passive control strategies have been studied for both highrise and lowrise
buildings. Kamagata et al. (1996) have studied
the case of coupling tall flexible structures with passive devices, while Luco
and De Barros (1998), Xu et al. (1999) studied
connecting lowrise structures to mediumrise structures with passive devices.
Active control strategies have been studied extensively for flexible structures
by Seto (1996).
Semi active coupled building control has been proposed by Christenson
et al. (2000). These studies have presented various coupled building
configurations and identified coupled building design guidelines. The studies
have also experimentally verified active coupled building control, employing
acceleration feedback. Zhu et al. (2001) has
also proposed semi active coupled building control. They considered coupling
two singledegreeof freedom masses with a semi active connector with positive
results.
In addition to these theoretical activities, fullscale applications are being
implemented in the Kajima Intelligent Building complex that was constructed
in Tokyo, Japan in 1989. This complex coupled the 5storey and 9storey towers
of a lowrise office complex with passive yielding devices connected at the
5th floor. The general contracting firm, Konoike, has implemented four substructure
coupling projects in recent years and in 1998, coupled two of their headquarter
buildings in Osaka, Japan, with passive viscoelastic dampers (Lynch,
1998).
A type of semiactive device, the magnetorheological (MR) damper, is composed
of a hydraulic cylinder filled with MR fluid, a suspension of micronsized magnetically
polarizable particles in water, glycol, mineral or synthetic oil. The damping
capabilities of this device can be controlled by the introduction and/or variation
of a magnetic field that can change the fluid from viscous to semisolid in
milliseconds. These control devices have been successfully employed as shock
absorbers, suspension systems in vehicle seats, brakes in aerobic exercise equipment
and more recently, in prosthetics and seismic and wind mitigation (Fujitani
et al., 2002).
Several control algorithms have been proposed for use with the MR dampers.
The most commonly used is the clippedoptimal control proposed by Dyke
et al. (1996). Control strategies based on Lyapunov functions (Jansen
and Dyke, 2000; Yi et al., 2001), stochastic
control (Ying and Zhu, 2006), Continuous Sliding Mode
(CSM) control (Lu et al., 2008), linear quadratic
Gaussian with loop transfer recovery (LQG/LTR) control (Zhang
and Roschke, 1999) and intelligent control have also been successfully employed
(Jung et al., 2004). Algorithms in the area of
intelligent control have the advantage of not requiring a model of the system.
Examples include neural networks based control (Xu and Zhang,
2002) and fuzzy control (Zhou et al., 2002;
Wilson and Abdullah, 2005).
Fuzzy control is based on “IFTHEN” rules that correlate the controller
inputs to the desired outputs. These controllers are composed of three steps
(Aldawod et al., 2001): (1) Fuzzification, where
the inputs are converted to fuzzy linguistic values using membership functions;
(2) Decision making, this uses “ifthen” rules to determine the linguistic
value of the output and (3) Defuzzification, where the fuzzy output is converted
to a crisp value.
In this study a new TS fuzzy controller was developed to regulate the damping properties of the MR damper so that both floor displacement and acceleration are reduced in seismically excited buildings. Furthermore the output time histories of applied voltage or current to MR dampers became almost constant.
MODELING OF ADJACENT STRUCTURES
Figure 1 shows the structural model under consideration depicting
multidegreeoffreedom shear models with rigid floors. In this Fig.
1, the lstory building connected through 1000 kN MR dampers at different
floors to the adjacent mstory building (l≤m), whereas 20 ton MR dampers
are installed at different floors in mstory building. The masses in these models
are assumed to be lumped at each floor level and the stiffness is provided by
axially inextensible massless columns. Both buildings are assumed to receive
the same earthquake ground motion in horizontal direction. The soilstructure
interaction effects are not taken into consideration. These adjacent buildings
are connected at different floor levels by 1000 kN MR dampers. The 20 ton MR
dampers are installed in building 2 to serve as energy dissipation mechanism.

Fig. 1: 
Model of connected adjacent buildings 
The 20 ton MR dampers were modeled according to the phenomenological model
proposed by Spencer et al. (1997). Values for
parameters of the 20 ton MR damper are presented in Yang
et al. (2002). The parameters of the 1000 kN MR damper used in this
study are based on the identified model of a shearmode prototype MR damper
tested at Washington University (Yi et al., 2001).
Table 1: 
Control rules for 1000kN MR damper 

Table 2: 
Control rules for 20 ton MR damper 

FUZZY CONTROLLER
The fuzzy control diagram is shown in Fig. 3.The input variables to the fuzzy controller for 20 ton MR damper were chosen as floor displacement (x) and velocity (x) and for 1000 kN MR damper as floor displacements (X_{k1} and X_{k2}) and velocities (X_{k1} and X_{k2}) that k≤l and the output as the applied current to the 20 ton MR damper (i) and applied voltage to the 1000 kN MR damper (v). The membership functions for the inputs were defined on the normalized universe of discourse [1, 1] and selected as three identical Gaussian membership functions (Fig. 2). The labels N, Z, P refer to negative, zero and positive, respectively. Those for the output were defined on the universe of discourse [0, 1] and selected as three linear levels (m_{f1} = 0, m_{f2} =0.5, m_{f3} = 1). Rules for computing the desired current and voltage are presented in Table 1 and 2. The Sugeno fuzzy method is selected for this study. Because of the linear dependence of each rule on the input variables of a system, the Sugeno method is ideal for acting as an interpolating supervisor of multiple linear controllers that are to be applied, respectively, to different operating conditions of dynamic nonlinear or linear systems. Since the output’s universe of discourse was normalized, a defuzzifier factor was required and chosen as Ku = 5 for 20 ton MR damper and Ku = 80 for 100 ton MR damper . The fuzzifier factors that are used to convert the inputs into fuzzy variables were defined as Kd = 32 and Kv = 3.3, for displacements and velocities, respectively (Fig. 3). One of the main advantages of this proposed fuzzy controller is that the outputs’ time histories (applied current and voltage) are very smooth and are almost constant (Fig. 410).
NUMERICAL EXAMPLE
The seismic response of two adjacent SDOF structures and two adjacent multistoried
buildings,connected using MR dampers is investigated here.

Fig. 4: 
Applied voltage and current to MR dampers to El Centro earthquake
for 2 SDOF adjacent buildings 

Fig. 5: 
Building 1 response to El Centro earthquake for 2 SDOF adjacent
buildings 

Fig. 6: 
Building 2 response to El Centro earthquake for 2 SDOF adjacent
buildings 
In this approach the multidegreeoffreedom shear models of the adjacent
buildings are used, with 1000 kN MR damper between structures and 20 ton MR
dampers in one building at different floor levels.

Fig. 7: 
Applied voltage and current to MR dampers to Kobe earthquake
for 2 SDOF adjacent buildings 

Fig. 8: 
Building 1 response to Kobe earthquake for 2 SDOF adjacent
buildings 

Fig. 9: 
Building 2 response to Kobe earthquake for 2 SDOF adjacent
buildings 

Fig. 10: 
Applied voltage and current to MR dampers to El Centro earthquake
for 5 and 10 storey buildings 
The earthquake motions selected for this study are El Centro and Kobe earthquakes.
Two SDOF adjacent buildings: Building 1, selected for this study, has a mass (m) of 593500 kg, a stiffness (k) of 22.45x10^{7} N m^{1} and a damping ratio of 2% and Building 2, has a mass (m) of 345600 kg, a stiffness (k) of 3.4x10^{7} N m^{1} and a damping ratio of 2%. Building 2 is equipped with two 20 ton MR dampers and the two structures are connected with a 1000 KN MR damper and are subjected to the northsouth acceleration of two earthquakes widely used in structural control research: El Centro and Kobe.
Time responses of the floor displacement and acceleration under different seismic
excitations are presented in Fig. 49. Figure
4 and 7 show the applied voltage and current to MR dampers
for the two selected earthquakes. It is clear that the variations of applied
input for both earthquakes are very small and negligible and almost constant.
Figure 59 compare the building responses
in both controlled and uncontrolled states under El Centro and Kobe earthquakes.
It is seen that both displacement and acceleration are greatly decreased specially
in building 2.
All the results are summarized in Table 3 for better comparison. These results show that the proposed control algorithms were very successful in reducing both building responses under the different earthquake loads. It can also be observed that they were more effective in reducing floor displacements than floor accelerations for all loading cases.
Table 3: 
Maximum building responses to earthquakes selected for 2
SDOF adjacent buildings 

Table 4: 
Relevant stiffness of buildings (kN m^{1}) 

Table 5: 
Number of dampers in building 2 


Fig. 11: 
Building 1 response to El Centro earthquake for 5 and 10 storey
buildings 
Two MDOF adjacent buildings: For the purpose of numerical analysis, two adjacent structures with 5 and 10 storey are considered. The floors mass of structures 1 and 2 are 593.5 and 207 ton, respectively. The stiffness of structures is listed in Table 4. A damping ratio of 2% is considered for both structures in all modes of vibration. Building 2 is equipped with eleven 20 ton MR dampers and the number of dampers in different storeys is shown in Table 5. The two structures are connected with a 1000 kN MR damper in the 5th storey.
The time history of top floor acceleration and displacement for 5 and 10storey
adjacent buildings for unconnected and connected cases under northsouth acceleration
of two El Centro and Kobe earthquakes are indicated in Fig. 1015.

Fig. 12: 
Building 2 response to El Centro earthquake for 5 and 10 storey
buildings 

Fig. 13: 
Applied voltage and current to MR dampers to Kobe earthquake
for 5 and 10 storey buildings 
Maximum displacements and accelerations are presented in Table 6. These responses were also greatly reduced by the proposed control algorithm employed.
Table 6: 
Maximum building responses to earthquakes selected for 5
and 10 storey buildings 


Fig. 14: 
Building 1 response to Kobe earthquake for 5 and 10 storey
buildings 

Fig. 15: 
Building 2 response to Kobe earthquake for 5 and 10 storey
buildings 
Again like the two SDOF systems both displacements and accelerations are reduced greatly with an almost constant voltage and current input. The responses of building 2 (taller building) are reduced more than the smaller building which shows the effectiveness of coupling newly built buildings to adjacent existing buildings in reducing building responses and therefore construction costs and increasing building safety.
CONCLUSIONS
The seismic reduction response of adjacent structures connected with MR dampers is investigated, when one of the structures (the taller) is equipped with 20 tons MR dampers. Coupled building control and proposed control algorithms were very successful in reducing both building responses under the different earthquake loads.
Significant reduction in the peak displacements and simultaneously in the peak accelerations are achieved by introducing MR dampers at the floor levels of adjacent structures. The MR dampers are helpful in avoiding the pounding consequences.
It is shown that one of the main advantages of this proposed fuzzy controller is that the outputs time histories of applied current and voltage are very smooth and are almost constant.
ACKNOWLEDGMENT
We hereby thank Dr. Freidon Amini for helping us in this research.