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by Eqn. 2.9 and Eqn. 2.12, respectively, based on the estimated states obtained by the EKF
4. DAMAGE EVALUATION CRITERIA
In order to compare the performance of various control strategies, some criteria should be given. The
damage of the hysteretic structures subjected to strong earthquake is the most critical criteria to
evaluate the performance of the structures. Lots of damage evaluation criteria have been given for
hysteretic structures (Cosenza et al 2000). As a whole, the peak value of the interstory drift, the energy
dissipation, and the damage index are the most common criteria to indicate the destroy and collapse of
structures. The Park and Ang's damage index will be employed in this study.
In addition, the control force that is related with the power for active control devices will be another
criteria. The ratio of the energy dissipation supplied by the control devices to that by the structural
hysteretic characteristics is also a criterion to evaluate the efficiency of the control strategy.
5. NUMERICAL STUDIES
5.1 Full State-Feedback Controller
Consider a 5-story shear building model with active control devices attached at each floor. The
uniform lumped mass and floor stiffness are 2000kg and 10 6 N/m so that the first period of the linear
structure is 0.99s. The critical damping ratio is 0.02 for the first two modes and the Rayleigh damping
matrk keep constant regardless of whether the structure is linear or nonlinear. The parameters to
describe the hysteretic characteristics are assumed to be ,4 = 1,a = 0.05,^ = 0.5 and 7 = 0.5. The yield
displacement is 2cm, ultimate displacement is 14cm and £ =0 15 used in Park and Ang's damage
index is assumed. The control forces in Eqns. 2.12 and 2.5 with the weighing matrix in Eqn. 2.7, and in
Eqn. 2,11 are used in the numerical example, and the additional damping ratio in Eqn. 2.10 is assumed
to be 0.03, 0.08, 0.13 and 0.18. The matrix R in Eqn. 2.12 and 2.5 was determined according to the
demand of identical control force for three control strategies. EL Centro, Kobe and Northridge ground
motion records with peak values 3.417m/s 2 , 8.18m/s 2 and 8.27m/s 2 , respectively, are used as inputs.
The earthquake intensity is changed by multiplying coefficient ranged from 0.05 to 3.5 for EL Centro
earthquake and 0.05 to 2 for Northridge and Kobe earthquakes with increment 0.1.
The interstory drifts of the building subjected to various intensity earthquakes are shown in Fig. 5.1. It
was shown that the response reduction of the first story drift is the nearly same by the three control
strategies, MC, MM and LQR for small and moderate intensity EL Centro, however, the further
reduction for the first story drift was established by the proposed control strategy (MC) than that
achieved by MM and LQR for high intensity EL Centro, Furthermore, the proposed control strategy
(MC) established significant further reduction of the 1 st and 5 th story drifts than MM and LQR by using
the same value of control force for both Northridge and Kobe earthquakes over all intensity range,
especially more significant further reduction established over high intensity range.
Fig. 5.2 show the 1 st floor damage index under Northridge earthquake. The results indicate that MC
strategy decreased the damage of the structures more significantly than MM and LQR.