A semi-active H∞ control strategy with application to the vibration suppression of nonlinear high-rise building under earthquake excitations

Yan, Guiyun; Chen, Fuquan; Wu, Yingxiong

doi:10.1186/s40064-016-2635-1

SpringerPlus

Table 2 Evaluation criteria for evaluated control systems

From: A semi-active H∞ control strategy with application to the vibration suppression of nonlinear high-rise building under earthquake excitations

Earthquake intensity	Semi-active H∞					Semi-active MPC					Clipped-LQG control
	El Centro	Hachi.	Northrdg.	Kobe	Max value	El Centro	Hachi.	Northrdg.	Kobe	Max value	El Centro	Hachi.	Northrdg.	Kobe	Max value
	0.5/1.0/1.5	0.5/1.0/1.5	0.5/1.0	0.5/1.0	Max value	0.5/1.0/1.5	0.5/1.0/1.5	0.5/1.0	0.5/1.0	Max value	0.5/1.0/1.5	0.5/1.0/1.5	0.5/1.0	0.5/1.0	Max value
J ₁ Peak drift ratio	0.5870 0.5883 0.5896	0.7581 0.7576 0.8058	0.6648 0.9209	0.5016 0.5360	0.9209	0.6704 0.6628 0.6632	0.7832 0.7891 0.8114	0.7487 0.8741	0.5996 0.5990	0.8741	0.6957 0.6450 0.6007	0.7867 0.7707 0.8180	0.691 0.906	0.5495 0.5324	0.906
J ₂ Peak acceleration	0.5129 0.5093 0.5235	0.5235 0.5275 0.5996	0.6208 0.7866	0.4315 0.6561	0.7866	0.617 0.6334 0.6493	0.7572 0.7561 0.8518	0.7427 0.8266	0.5411 0.77	0.9271	0.6149 0.5568 0.6156	0.8171 0.7673 0.8175	0.7167 0.8195	0.6228 0.741	0.8195
J ₃ Peak base shear	0.7061 0.7063 0.8266	0.9923 0.9884 1.0194	0.9320 1.0302	0.7264 1.0430	1.0430	0.857 0.8197 0.9306	1.0907 1.0466 1.0733	0.9373 1.0136	0.9629 1.0378	1.0907	0.8145 0.8283 0.9612	1.0519 1.0507 1.0623	1.0019 1.0777	0.766 1.0793	1.0793
J ₄ Norm drift ratio	0.5247 0.5232 0.5277	0.7512 0.7526 0.7697	0.4862 1.0809	0.3771 0.1427	1.2809	0.569 0.577 0.5866	0.7928 0.7994 0.8198	0.5814 1.0175	0.4762 0.1867	1.0175	0.5568 0.5261 0.5206	0.7761 0.7553 0.7649	0.4557 1.1881	0.3563 0.1716	1.1881
J ₅ Norm acceleration	0.3255 0.3251 0.3351	0.4571 0.4576 0.4689	0.3508 0.4513	0.3080 0.4448	0.4689	0.4786 0.4815 0.4328	0.7025 0.6348 0.5525	0.4739 0.5401	0.5342 0.5717	0.7025	0.5656 0.4833 0.462	0.6647 0.59 0.5699	0.4043 0.4909	0.4237 0.548	0.6647
J ₆ Norm base shear	0.5865 0.5847 0.5889	0.7456 0.7462 0.7580	0.5146 0.7295	0.4545 0.6498	0.7580	0.6693 0.6516 0.6568	0.7946 0.7749 0.7848	0.6261 0.7984	0.5845 0.7626	0.7984	0.6733 0.6303 0.6179	0.823 0.784 0.7831	0.5091 0.7429	0.4395 0.6352	0.823
J ₇ Ductility	0.6839 0.66847 0.6399	0.9310 0.9303 0.8969	0.7174 0.9423	0.4193 0.5606	0.9423	0.6747 0.6689 0.6253	0.9245 0.9231 0.8789	0.6603 0.9012	0.5763 0.6818	0.9245	0.6992 0.7098 0.6533	0.9569 0.9367 0.8999	0.6837 0.9276	0.4292 0.4985	0.9569
J ₈ Dissipated energy	– – 0	– – 0.2548	0.0561 0.3065	0 0.0983	0.3065	– – 0	– – 0.2422	0.0254 0.3936	0.024 0.1109	0.3936	– – 0	– – 0.2567	0.0351 0.2546	0 0.0719	0.2567
J ₉ Plastic connection	– – 0	– – 0.3256	0.2917 0.6354	0 0.3810	0.6354	– – 0	– – 0.4186	0.2292 0.8021	0.1538 0.7024	0.8021	– – 0	– – 0.3256	0.2083 0.6979	0 0.5833	0.6979
J ₁₀ Norm ductility	0.5847 0.5832 0.5207	0.7350 0.7360 0.7990	0.3976 1.2573	0.3871 0.1447	1.2573	0.6324 0.6426 0.5793	0.7632 0.7716 0.8125	0.4821 1.0805	0.4919 0.2522	1.0805	0.6136 0.5875 0.5137	0.7519 0.7288 0.8343	0.3858 1.2044	0.3394 0.207	1.2044
J ₁₁ Control force	0.0016 0.0032 0.0048	0.0017 0.0033 0.0049	0.0051 0.0090	0.0045 0.0090	0.0090	0.0017 0.0033 0.0044	0.0017 0.0033 0.0043	0.0044 0.0069	0.0046 0.0084	0.0084	0.002092 0.00382 0.005435	0.002315 0.004334 0.006041	0.00647 0.009429	0.007067 0.009408	0.009429
J ₁₂ Device stroke	0.0680 0.0680 0.0687	0.0746 0.0746 0.0792	0.0792 0.1036	0.0947 0.1030	0.1036	0.0667 0.0655 0.0661	0.0739 0.0737 0.0781	0.0724 0.0965	0.1113 0.1096	0.1113	0.07083 0.07125 0.07095	0.07562 0.07395 0.07793	0.07372 0.09833	0.08558 0.08767	0.09833
J ₁₃ Control power	0.000065 0.000033 0.000023	0.000066 0.000033 0.000024	0.000018 0.000015	0.000023 0.000016	0.000066	0.000065 0.000033 0.000023	0.000066 0.000033 0.000024	0.000018 0.000015	0.000023 0.000016	0.000066	0.000009 0.000009 0.00001	0.000011 0.000011 0.000012	0.000009 0.00001	0.000011 0.000013	0.000013
J ₁₄ Norm control power	0.000065 0.000033 0.000023	0.000066 0.000033 0.000024	0.000018 0.000015	0.000023 0.000016	0.000066	0.000065 0.000033 0.000023	0.000066 0.000033 0.000024	0.000018 0.000015	0.000023 0.000016	0.000066	0.000001 0.000001 0.000001	0.000001 0.000001 0.000001	0 0	0 0	0.000001
J ₁₅ Control devices	65				65	65				65	65				65
J ₁₆ Sensors	25				25	5				5	25				25
J ₁₇ Computational resolution	20				20	20				20	20				20
J ₁₈ Maximum permanent drift	– – 0	– – 0.8389	0.1845 1.0926	0 0.0225	1.0926	– – 0.0022	– – 0.8338	0.0308 1.028	0.0779 0.0902	1.028	– – 0	– – 1.3284	0.1438 1.2149	0 0.1398	1.3284
J ₁₉ Total permanent drift	– – 0	– – 0.4006	0.0832 0.7249	0 0.0174	0.7249	– – 0.0037	– – 0.5005	0.0152 0.7468	0.0292 0.1334	0.7468	– – 0	– – 0.7127	0.0598 0.7214	0 0.1057	0.7214

^aNote that uncontrolled structure does not yield in some cases such as 0.5/1.0 scale El Centro earthquake and 0.5/1.0 scale Hachi. earthquake

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