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between pre-yielding and post-yielding regions;
v
and
u
are input and output voltages of a first-
order filter, respectively; and
η
is the time constant
of the first-order filter. Note that nonlinear phe-
nomena occur when the highly nonlinear MR
dampers are applied to structural systems for ef-
fective energy dissipation. Such an integrated
structure-MR damper system behaves nonlin-
early although the structure itself is usually as-
sumed to remain linear. Therefore, the develop-
ment of an effective control algorithm for the
nonlinear behavior of the structure-MR damper
system would play a key role in semiactive con-
trol system design: a solution can be found in a
model-free brain limbic system-based control
algorithm.
drift response. Selected time history and inter-
story responses are provided.
Figure 8, Figure 9, and Figure 10 show the
time history responses at the top floor of the
smart structures subjected to the 1940 El-Centro
earthquake with the intensity of 0.5, 1.0, and 1.5,
respectively. As seen, the proposed neuromorphic
control algorithm produces the best control per-
formance over the passive, PID, and LQG control
systems as far as the displacement responses of
each floor are investigated. Also, all of the control
algorithms have better performance than the pas-
sive control system. To further investigate of the
control performances, the maximum interstory
responses of the smart structure employing dif-
ferent control strategies are shown in Figure 11,
Figure 12, and Figure 13. From the figure, it is
apparent that the proposed neuromorphic control
algorithm has the best performance over other
control systems for most of cases. However, it is
shown that the performances of the LQG and the
neuromorphic control systems are similar for the
case of 50% intensity of earthquake disturbance
case. It is demonstrated from the simulation results
that the proposed neuromorphic control algorithm
is very effective in reducing vibration of the seis-
mically excited building structure employing an
MR damper.
Simulation
In this chapter, the performances of four control-
lers (i.e., passive, PID, LQG, and neuromorphic
controls) are compared to demonstrate the ef-
fectiveness of the proposed hybrid neuromorphic
controller for hazard mitigation of civil structures
while the uncontrolled structure is used as a base-
line. Properties of the three-story building employ-
ing an MR damper are adopted from a benchmark
model (Dyke et al. 1996). The mass of each floor
m m m
1
= = =
. kg,
the stiffness of each
story
k
1
= 516,000 N/m,
k
2
= 684,000 N/m, and
k
3
= 684,000 N/m; and the damping of each floor
c
1
= 125 Ns/m,
c
2
= 50 Ns/m, and
c
3
= 50 Ns/m.
The parameters of the comparative controllers
are: (1) the learning rates for the amygdala and
orbitofrontal cortex of the BELBIC algorithm are
adopted as a = 1 and
b
= 1 (2) w
1
= 2, w
2
= 1, w
3
= 2, and w
4
= 1 (3) the PID control gains are
K
P
= 120,
K
I
=100, and
K
D
= 10, respectively (4) the
parameters of the LQG control system are ad-
opted from Dyke et al. (1996). The input signal
to be fed through the each controller is the 1
st
floor
98 3
2
3
FUTURE RESEARCH DIRECTIONS
It is recommended that the applications of the
proposed neuromorphic controllers to a variety
of uncertain cases be studied to demonstrate the
robustness of the proposed approach. Additionally,
the stability analysis of the neuromorphic control
will be conducted for analytical demonstration of
the given novel control strategy.
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