An iterative output feedback controller-design strategy for energy-to-peak structural vibration control

Figures & data

Figure 1. El Centro 1940 ground-acceleration seismic record.

Table 1. $\mathit{\gamma }$for each iteration step.

step i	0	1	2	3	4	5
${\gamma }_{{\mathit{k}}^{\left(\mathit{i}\right)}}$	0.5949	0.0759	0.0757	0.0756	0.0755	0.0755

Figure 2. Maximum singular values of the FRFs. (a) overall view. (b) close view.

Figure 3. Maximum inter-story drifts.

Figure 4. Maximum absolute displacements.

Figure 5. Maximum absolute accelerations.

Figure 6. Maximum control forces.

Table 2. Partial record of seismic dynamic response results.

Stories	Inter-story drifts(cm)				Absolute accelerations(m/s^2)
	Case1	Case2	Case3	Case4	Case1	Case2	Case3	Case4
1	5.55	2.71	2.66	2.63	6.30	4.21	4.22	4.25
2	5.29	2.63	2.59	2.58	7.12	5.68	4.88	5.03
3	4.80	2.35	2.43	2.46	8.32	6.67	5.47	5.11
4	4.13	2.44	2.36	2.35	8.01	6.33	5.61	5.68
5	3.70	2.37	2.20	2.16	9.47	6.31	6.48	6.54
6	3.08	2.08	1.86	1.79	12.12	8.29	7.83	7.76
7	2.22	1.53	1.35	1.28	12.45	9.00	8.35	8.22
8	1.22	0.84	0.72	0.68	13.02	9.51	8.54	8.26

Figure 7. The time-history curves of the inter-story drift in the top layer.

Figure 8. The time-history curves of the absolute acceleration in the top layer.

Table 3. Results of evaluation indicators for different control strategies.

	State feedback	Output feedback	Iterative output feedback
$J_1$	0.488	0.479	0.473
$J_2$	0.731	0.655	0.635