LQR Control of Wind Excited Benchmark Building Using Variable Stiffness Tuned Mass Damper

Table 1

Performance criteria: STLC compared with ALC and STSC, for 0% and ±15% structural stiffness variations.

RMS response				Peak response
Criterion	0%	15%	−15%	Criterion	0%	15%	−15%
𝐽1	0.44	0.45	0.45	𝐽7	0.44	0.51	0.52
	{0.37}	{0.37}	{0.39}		{0.38}	{0.41}	{0.49}
	[0.47]	[0.46]	[0.50]		[0.45]	[0.50]	[0.57]
𝐽2	0.44	0.45	0.45	𝐽8	0.45	0.50	0.55
	{0.42}	{0.41}	{0.44}		{0.43}	{0.44}	{0.54}
	[0.46]	[0.45]	[0.50]		[0.46]	[0.47]	[0.57]
𝐽3	0.58	0.50	0.70	𝐽9	0.71	0.64	0.81
	{0.58}	{0.49}	{0.71}		{0.72}	{0.61}	{0.77}
	[0.60]	[0.51]	[0.74]		[0.71]	[0.62]	[0.84]
𝐽4	0.58	0.50	0.71	𝐽10	0.71	0.65	0.82
	{0.58}	{0.49}	{0.71}		{0.73}	{0.61}	{0.78}
	[0.60]	[0.51]	[0.74]		[0.72]	[0.62]	[0.85]
𝐽6 (kNm/s)	5.35	4.33	6.83	𝐽12 (kNm/s)	35.7	27.0	52.1
	{12.0}	{8.46}	{16.6}		{72.0}	{52.7}	{118}
𝐽^∗6 (kNm/s)	2.37	2.18	2.46	𝐽^∗12 (kNm/s)	2.33	2.24	2.82
	{2.37}	{2.03}	{2.62}		{2.34}	{2.02}	{2.67}
	[2.38]	[2.05]	[2.49]		[2.26]	[2.08]	[2.65]
𝜎𝑢 (kN)	22.7	19.2	28.3	max|𝑢(𝑡)| (kN)	94.2	83.1	106
	{34.1}	{28.3}	{44.3}		{118}	{106}	{164}
𝜎𝑥drel (cm)	22.8	19.5	25.3	max𝑥drel (cm)	76.8	70.6	93.1
	{23.0}	{18.4}	{27.5}		{74.3}	{59.8}	{91.6}
	[22.3]	[17.9]	[25.0]		[69.6]	[58.0]	[84.3]