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Figure 30. Base isolator and third-floor displacement and acceleration responses under Big Bear earth-
quake for dynamic inversion based MR damper monitoring
pra, 2005). Therefore SDOF models provide good
approximation to these systems for quick calcula-
tion under ground motion. The integrator back-
stepping based algorithm is developed assuming
a SDOF system with mass equal to the total mass
of the three storey base isolated building and
stiffness equal to that of the base stiffness. The
tolerances for the simulation studies with back-
stepping are set to
tol
1
The third floor displacement has also been
minimized from 0.0020m in uncontrolled (simple
isolation) condition to 0.0007m in MR damper
controlled (hybrid isolation) case and at the same
time it has managed to keep the acceleration re-
sponse reduced (2.2361 m/s
2
in uncontrolled case
Figure 31. Voltage input and control force under
Big Bear earthquake for dynamic inversion based
MR damper monitoring
−
5
= ×
1 10
m
for isolator
displacement and
tol
2
= ×
−
for isolator
5
1 10
velocity.
Figure 32 shows the time histories of the
uncontrolled (simple isolation) and controlled
system (hybrid isolation) responses of base isola-
tor and at the third floor. The peak displacement
response of the isolator is reduced from 0.1229m
to 0.0061m by the integral backstepping monitored
MR damper. The isolator acceleration has been
observed to increase from 2.3214m/s
2
to 3.326m/
s
2
with backstepping control, which is a smaller
increase in comparison to that obtained through
DI control.
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