Nonlinear Structural Control Using Magnetorheological Damper - Design Optimization of Active and Passive Structural Control Systems - page 323

analysis at 2% of the critical. The MR damper
parameters taken for the present analysis are given
in Table 1. The maximum input voltage allowed
for the damper is 5V. The damper can provide a
maximum force of ±2250 N.
Numerical simulations are carried out for
micro-GA optimized FLC, clipped optimal con-
trol, dynamic inversion based MR damper
monitoring and with integrator backstepping
control of MR damper voltage input.
Results for GAFLC are shown in Figures 14
and 15. Figure 26 shows the displacement and ac-
celeration time histories at the base and at the third
storey of the building. Both the uncontrolled and
controlled time histories are shown in same plot
for better comparison of the responses. The peak
displacement response of the isolator in simple
isolation condition is found to be 0.1229m, which
is reduced to 0.0015m and the third floor drift is
decreased from 0.0020m in uncontrolled condition
to 0.0015m in MR damper controlled case. Since
the MR damper decreases the isolator displace-
ment, the isolator acceleration goes up. The base
acceleration of 2.3214m/s 2 in uncontrolled case
is increased to 7.7440m/s 2 in the MR controlled
case but the third floor acceleration is decreased
from 2.3631 m/s 2 in uncontrolled case to 2.0381m/
s 2 . Figure 27 shows the voltage time history and

the corresponding control force supplied by the
MR damper.
A LQR based clipped optimal control strategy
is considered for the comparison purposes. The
LQR is designed with the weights same as con-
sidered for the dynamic inversion based control
case. The matrix Q

= × 5 10 3 × I

8 8 and

×

R = × − 1 10 4 are considered for the study. I 8 ×

is an identity matrix of dimension (8×8).
Figure 28 shows the time histories of the un-
controlled and controlled system responses (dis-
placement and acceleration) of base isolator and
at the third floor. The peak displacement response
of the isolator in simple isolation condition has
been found to be 0.1229m, which is reduced to
0.0010m. The third floor time histories also show
decrease displacement responses from 0.0020m in
uncontrolled condition to 0.0016m in MR damper
controlled case, which is a slight decrease in dis-
placement response when compared with other
control techniques.
Since the MR damper decreases the isolator
displacement, the isolator acceleration increases.
The base acceleration of 2.3214m/s 2 in uncon-
trolled case is increased to 8.2796m/s 2 in the MR
controlled case. The third floor acceleration is

Figure 25. Seismic input excitation: Big Bear earthquake (Frequency content up to 30 Hz)