Conclusions

Chapter 3 Multi-Degree-of-Freedom Systems

3.6 Conclusions

This chapter carries out a comprehensive study on the response of MDOF AIC systems under earthquake ground motions. Based on the analytical and numerical results obtained in the preceding sections, the following conclusions are drawn:

1. Use of either the NC or MC approaches can substantially reduce the number of con- figurations needed to be examined in each sampling interval. For an N-story building, the reduction is from 2N to 2N and 2 for the NC and MC approaches, respectively.

2. Of the three AIC algorithms examined in MDOF systems, no single algorithm gives the best overall control efficiency in both NC and the MC approaches. In terms of re- ducing the maximum story drift, the OCS algorithm achieves the best control effec- tiveness in the MC approach, the AID algorithm gives the second best control results in both the NC and the MC approaches, and the A VS algorithm yields the best control efficiency in the NC approach. In terms of reducing the maximum absolute accelera- tion at the top floor of the building, the OCS and AID algorithms performed better than the A VS algorithm in both NC and the MC approaches. In the MC approach, the best control result is found in the case in which the measurement and control decision are both made at the ^1st story level of the building.

3. An AS with a smaller mass, a smaller damping, and a larger stiffness is more effective in controlling the response of the PS. However, the effects of the mass, damping, and stiffness of the AS are less noteworthy in MDOF systems than in SDOF systems.

4. The OCS algorithm is much more sensitive to the sampling interval than the AID and A VS algorithms. A finer sampling interval is often needed in the MC approach than in the NC approach. Since the OCS algorithm is sensitive to high frequency motion, relatively better control effect is obtained in the RRS case than in the ELC case for the OCS algorithm.

5. fu contrast to the NC approach, the robustness of AIC algorithms with respect to time delays in MDOF systems are improved in the MC approach. Compared to the system performance in SDOF systems, more deterioration and instability are observed in MDOF systems. The AID algorithm is more robust than the OCS and AVS algo- rithms with respect to time delays in MDOF systems.

6. The predictive scheme shows great promise in compensating time delays for the A VS algorithm in both NC and MC approaches, and for the AID algorithm in the MC ap- proach. However, it is only effective in compensating short time delays (0.02 and 0.04 seconds) for the OCS algorithm in the NC and MC approaches.

7. The control results obtained from SDOF AIC systems in Chapter 2 provide a good qualitative approximation of the dynamic behavior of MDOF AIC systems. However, the hypothetical sinusoidal mode shape assumed in the SDOF model generally under- estimates the actual story drift distribution in MDOF systems.

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_{2 4}

^"

_{6 8 10}

Time (second)

Figure 3.3.12: 8th story absolute acceleration responses of the PS excited by the RRS ground motion uncontrolled and controlled by the OCS, AID, and A VS algorithms in the MC approach

...

...

-...l

:E 0

.-.-AID --AVS

~ 10² .9 en

=

co

!E 0

10°

1o-·~ ~~~~w

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10⁴

~~~~--.--.--.--,,---~~~~

... Uncontrolled

ocs

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~wF=.

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en

~

10°~----~--~--~~~~~~----~----~L_~~~~ 10-' . ' . . ,

10° ^10'

10⁴~-~-~~~~~--~--.-~~~~~

0 ~

~ 10²

en,~ .9

... -,..

=

....

1~

10~-~----~~~~~~~--~--~~~~

10°

Frequency (Hz)

10'

Figure 3.3.13: Fourier Amplitude Spectra of the 1^5\ 4th, and 8th story drift responses of the PS excited by the ELC ground motion un- controlled and controlled by the OCS, AID, and A VS algo- rithms in the MC approach

€ ^.-.-AID _---AVS

0

~ ^{102 r---_..}

U5

~ . / \ I

v

1~ ,.

10~ 1~ 1~

10⁴ ~~~--.---...--.--

... Uncontrolled

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€ 0

~ 10² .9 en

.c :¢

..,·-·-.

--

10° "

10-' 10° 10'

10·,-~-...-...~~...,,---~-...-...~~...-.--,

0 €

~ 10²

a =

.... .;

- . - . ""'. ·I ... ... ^~

/ \ .

/ ·/

1~ '

1~ 10°

Frequency (Hz)

10'

Figure 3.3.14: Fourier Amplitude Spectra of the 1^5\ 4th, and 8th story drift responses of the PS excited by the RRS ground motion un- controlled and controlled by the OCS, AID, and A VS algo- rithms in the MC approach

,...

,...

00

7 6

~5 cn4 .9

3 2

...

'\ ...

\ \

\ I I

;i

\

' '

\

... Uncontrolled

ocs

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1L---~----~--L-~----~--~----~--~~--~

7

6

~5 cn4 .9

3 2

0 0.5

\

2 3

1.5 2 2.5

Maximum Story Drift (em)

(b)

\

\

3 3.5

... Uncontrolled

ocs

---AID .:..."-.AVS

4

\

\

I

' ' ' ' ' ' 1

4 5 6 7 8 9 10

Maximum Story Drift (em)

Figure 3.3.15: Maximum story drift distribution of the PS excited by the (a) ELC and (b) RRS ground motions uncontrolled and con- trolled by the OCS, AID, and A VS algorithms in the MC approach (control decision made in the 1⁵¹ story)

7 6

~5 .9 cn4

3 2

I ·. . ... Uncontrolled

ocs

---AID .-.-AVS

1~~~---L----~----~--~~--~--~~--~

0 5 10 15 20 25 30 35 40

Maximum Story Drift (em)

(b)

8~----~----~~--~----~----~r---r---~

\ ·.

I . 71- I !

1-I I 6 .

a4

~5

3 2

I I II I"

I· I I ~

II II

lj

1~~--~----~----~----~----~~----~----U

0 10 20 30 40 50 60 70

Maximum Story Drift (em)

Figure 3.3.16: Maximum story drift distribution of the PS excited by the (a) ELC and (b) RRS ground motions uncontrolled and con- trolled by the OCS, AID, and A VS algorithms in the MC approach (control decision made in the 3rd story)

...

...

\0

7 6 2:-5 (1)4 .9

3 2

' '

\

I I

...: ...

....

/

....

...

Cts

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...-- · -:::.~AVS

...

...

' '

1~--~--~~~--~~--~--~~-L--~----~~

0 0.5 1 .5 2 2.5 3 3.5 4 4.5 5

Maximum Story Drift (em)

(b)

8r---~~---~~----~---,---r----~

7

6 2:-5 (1)4 .9

3 2

' '

^\

\

\

\

\

\

\

\

\

\

... Uncontrolled

ocs

---AID

1~----~---~--~--~----~---~~--~

0 2 4 6 8 10 12

Maximum Story Drift (em)

Figure 3.3.17: Maximum story drift distribution of the PS excited by the (a) ELC and (b) RRS ground motions uncontrolled and con- trolled by the OCS, AID, and A VS algorithms in the MC approach (control decision made in the 5th story)

7

6 2:-5 (1)4 .9

3 2

'

\

\

\

\

\

I ^I

\

\

/

~·

/

ocs

1~--~---L~--~----~--~~--~--~-L--~

0 0.5 1.5 2 2.5 3 3.5 4

Maximum Story Drift (em)

(b)

8 ' I I~ ^{I I I ' ·}

I

I '- · ...

Uncortlcolled

7 6 2:-5 (1)4 .9

3 2

' ' '

^\

\

\

\

\

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I

\

\

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^.... _....

....

_os;.s· ...--

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1~----~---L---~----~--~---L~--~

0 2 4 6 8 10 12

Maximum Story Drift (em)

Figure 3.3.18: Maximum story drift distribution of the PS excited by the (a) ELC and (b) RRS ground motions uncontrolled and con- trolled by the OCS, AID, and A VS algorithms in the MC approach (control decision made in the gth story)

...

N 0

7

6

'f

2:'5 cn4 .s

3

I·

1

l I

\ 2

I I I

1 \

0 I \

0.5 1.5 2 2.5 3

Maximum Story Drift (em)

(b)

... Uncontrolled

ocs

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3.5 4

81

1 \ \ 1 \ I I I I I

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I

... Uncontrolled

7 6

c:-5 .s cn4

3 2

\

\

2 l I

\

\

\

\

3

)

I

\

\

\

\

\

4

\

\

5 6 7

Maximum Story Drift (em) 8

ocs

---AID .:..."-.f>:VS

9 10

Figure 3.3.19: Maximum story drift distribution of the PS excited by the (a) ELC and (b) RRS ground motions uncontrolled and con- trolled by the OCS, AID, and A VS algorithms in the MC approach (uncertainties in the mass of the AS)

'

7 6

c:-5

cn4 .s

3

2

'

_'\ ^\

\ \

\ \ l I /,·

I!

/·

I I

\

\ l

... Uncontrolled

ocs

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1~--~~--~~--~----~----~----~----~--~

0 0.5 1.5 2 2.5 3 3.5 4

Maximum Story Drift (em)

(b)

8.---~~r---.---.-~.---.---.---.---.---.---.

7

6

c:-5 .s cn4

3 2

\

\

\ l

\

\

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... Uncontrolled

ocs

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1L---~--~--L-L-L-~L---L---L---~--~--~~

0 2 3 4 5 6 7 8 9 10

Maximum Story Drift (em)

Figure 3.3.20: Maximum story drift distribution of the PS excited by the (a) ELC and (b) RRS ground motions uncontrolled and con- trolled by the OCS, AID, and A VS algorithms in the MC approach (uncertainties in the stiffness of the AS)

>-' N

>-'

3.5 '[ 3

=

;§ 2.5

.e ~ 2

Cl)

E ~ 1.5

-~

::2:

0.5

...

.-

- . - - - -

---·-·-·-·-·-·-·-·-

ocs ---AID .-.-AVS

--

^:;·

/ /

OL---~----~----~----~---L----~----~--~

4 6 8 10 12 14 16 18 20

Number of Stories

(b) 12

... Uncontrolled

10

E ~

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--

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2

,.,.. -~~-.-.-.-.-.-. /

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0 4 6 8 10 12 14 16 18 20

Number of Stories

Figure 3.4.1: SDS of the PS excited by the (a) ELC and (b) RRS ground motions uncontrolled and controlled by the OCS, AID, and A VS algorithms in the NC approach

3.5

E

³

~

=

;§ 2.5

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Cl)

§ 1.5 -~ E ::2:

0.5

/

/

-·-·-·-·-.

/

/ """:"-···.._

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... ; / · / ..

/ / /

- - - -

OL---~----~----~----~--~----~---L--~

E ~

€ 0

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E ::J

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4 6

12 10 8 6

4

L ...---_:.. ....

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8 10 12 14

Number of Stories

(b)

/ /

,.,.,.·-·-·-·-·- /

16 18

... Uncontrolled ocs ---AID

· . / . ...._ .-.-AVS / . · ... ··

'

^...

...

- - - - --

20

'

OL---~----~----~----~--~~--~----~--~

4 6 8 10 12 14 16 18 20

Number of Stories

Figure 3.4.2: SDS of the PS excited by the (a) ELC and (b) RRS ground motions uncontrolled and controlled by the OCS, AID, and A VS algorithms in the MC approach

...

~

5

^_Aipha=5%

~ ---Alpha= 10%

€ 3 .-.-Alpha= 15%

Cl :·:··: ~~~a: 20'ro · · • . . . .

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^=. = · - ...

:..:~...:..

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E 1

"§

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o~----L---~----~----~----~---~----~--~

4 6 8 10 12 14 16 18 20

(b) Effect of the damping of the AS (ELC)

4.----.---.---.---.---.----.---.---~

E

~

€3 Cl

£2 ~ 00

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_ Damping = 2%

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· · · · .•.•.. , J?ampi~Q.;. ~0%

- . - . - . - . ..... "'""-::.~.·--·.·.:._·: :__· ...

~..:..::::;.·.-=r.:.-:...:.~···--·:.a.::

0~--~~--~----~----~----~----~----~--~

4 6 8 10 12 14 16 18 20

(c) Effect of the stiffness of the AS (ELC)

~4.----.r----.---.---.---.----.---,---~

~ E Gamma=0.5

--Gamma= 1

E3b?-.-Gamma=2 ~

0 ... ^Gamma=4

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£2 ~~-=-·==· . : ... · ... ·.~·--=-..:...-:-_ ···~ ... :-:- ..

~ ··· ·-·-.-·-·-·-·

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4 6 8 10 12 14 16 18 20

Number of Stories

Figure 3.4.3: SDS of the PS excited by the ELC ground motion controlled by the OCS algorithm in the NC approach (effects of the mass, damping, and stiffness of the AS)

~ E _Aipha=5%

---Alpha= 10%

€ .-.-Alpha=)§% . . . · - . _ . - . _

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4 6 8 10 12 14 16 18 20

(b) Effect of the damping of the AS (RRS)

~ 15.----.---.---.---.---.----.---.---,

~ E .t=

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a

~

§ 5

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_ Damping = 2%

---Damping= 10%

.-.- Damping = 20%

... Da~P.ing~·

0~--~----~----~----L---~----~----~--~

4 6 8 10 12 14 16 18 20

(c) Effect of the stiffness of the AS (RRS)

15.----.---.---.---.---.---.----.---,

~

e

.t=

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~ 00 £

E ::I

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4 6 8 10 12 14 16 18 20

Number of Stories

Figure 3.4.4: SDS of the PS excited by the RRS ground motion controlled by the OCS algorithm in the NC approach (effects of the mass, damping, and stiffness of the AS)

...

N w

~

€ 02 2:-

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6 8 10 12 14 16 18 20

(b) Effect of the damping of the AS (ELC)

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=

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4 6 8 10 12 14 16 18 20

(c) Effect of the stiffness of the AS (ELC)

3.---~--.----r---~---r---~----·

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a

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/ / /

:20~--~----~----~----~--~~--~---L--~

4 6 8 10 12 14 16 18 20

Number of Stories

Figure 3.4.5: SDS of the PS excited by the ELC ground motion controlled by the OCS algorithm in the MC approach (effects of the mass, damping, and stiffness of the AS)

~ 8 --- Alpha = 1 0%

·c: 0 2:- 6

.e

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5

5

2:- 6

a

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::l

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4 6 8 10 12 14 16

(b) Effect of the damping of the AS (RRS)

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---Damping= 10%

.-.-Damping= 20%

... Damping = 40%

""--~--·---··-=:--

18 20

0~--~---L----J---~--~~--~----~--~

4 6 8 10 12 14 16

(c) Effect of the stiffness of the AS (RRS)

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5

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2:- 6

Gamma=0.5 --Gamma= 1 .-.-Gamma= 2 ... Gamma=4

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0~--~---L----~----~--~---L----~--~

4 6 8 10 12 14 16 18 20

Number of Stories

Figure 3.4.6: SDS of the PS excited by the RRS ground motion controlled by the OCS algorithm in the MC approach (effects of the mass, damping, and stiffness of the AS)

...

N .j:::..

81

·~.

- --

7 6 i:=-5

0

i'i54 3 2

··· dt = 0.010 s .-.- dt = 0.005 s - - dt = 0.002 s dt= 0.001 s

<.;.. :-...

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:/

:-

l:c....:....:.. ..

. --. ...,· ...

1 . . .

0 0.5 1.5

(b) AID (ELC)

2 2.5

~f

^I

',z,·

^{I I}

ⁱ

6 ~

... dt = o.010s .-.- dt = 0.005 s --- dt = 0.002 s dt = 0.001 s

... dt = 0.010 s .-.- dt = 0.005 s --- dt = 0.002 s

~:-:.001 s

~ /.

\ ..

I

/

1.5 Maximum Story Drift (em)

7

2 2.5

2 2.5

Figure 3.5.1: Maximum story drift distribution of the PS excited by the ELC ground motion controlled by the OCS algorithm in the NC approach (effect of the sampling interval)

7 6 i:=-5

a4

... .., ...

. . ... ^{ ...

'·'

.... _{: .} \

' -

^-:-_-..

3 ... dt=0.010s ---·-:::::: ·..::::-. _ .

.-.-dt=0.005s - _ ,

2 ---dt=0.002s · · · . . . . ":"",.._-

_dt=0.001 s .. · .~

1 .. ·

0 1 2 3 4 5 6 7 8 9 10

(b) AID (RRS)

8~~~~~~~~~~~~

7 6

'

i:=-5 W4 ~

3 2

~

'

~

... dt=0.010s .-.- dt = 0.005 s --- dt = 0.002 s dt= 0.001 s

\

\

1~---L----~--~--~~~~----~--~----~---4--~

0 2

... dt= 0.010 s .-.- dt = 0.005 s --- dt = 0.002 s dt = 0.001 s

3 4 5 6

(c) AVS (RRS)

6 Maximum Story Drift (em)

7 8 9 10

7 8 9 10

Figure 3.5.2: Maximum story drift distribution of the PS excited by the RRS ground motion controlled by the OCS algorithm in the NC approach (effect of the sampling interval)

...

N Ul.

6 ' '

~· ^{' "}

^{... I}

W4 .s

... dt = 0.010 s .-.- dt = 0.005 s - - dt = 0.002 s .::-::.001 s

0.5 /

\

\

/

'

/ /

>

'

_I

1.5 (b) AID (ELC)

2 2.5

8r---~---~---,,---r---,

7 6 2::'5 W4 .s

3 2

... dt= 0.010s .-.- dt = 0.005 s

--- dt = 0.002 s I

I ^Ul = u.uu I ;) ' : I

1 ^{I I} I ^{I· I I}

di=0AA•-

0 0.5 1 1.5 2 2.5

(c) AVS (ELC)

8~--~----~~c.=~----~--~

7 6

.s ~5

W4 3 2

1 u•-u;uv•o

1 1

\· ••• \ 1

I 1

... dt = 0.010s .-.- dt = 0.005 s --- dt = 0.002 s dl= 0 AA.-

0 0.5 2 2.5

Maximum Story Drift (em)

Figure 3.5.3: Maximum story drift distribution of the PS excited by the ELC ground motion controlled by the OCS algorithm in the MC approach (effect of the sampling interval)

6

~r \~

.

. .

'

~· ^{\'' 1}

W4 3 2

... dt= 0.010 s .-.- dt = 0.005 s - - dt = 0.002 s dt= 0.001 s

\

\

1L---~---~~~--~----~---~----~

0 2 3 4 5 6

(b) AID (RRS)

8r---.~~--~---r---r---.---,

7 6 2::'5 W4 .s

3 2

... dt= 0.010s .-.- dt = 0.005 s --- dt = 0.002 s dt= 0.001 s

1L---~---~---~--~~~---~----~

0 2 3

(c) AVS (RRS)

8 ~

7 6

.s ~5

W4 3 2

... dt=0.010S .-.- dt = 0.005 s --- dt = 0.002 s

4 5 6

'

'I

I _ul::;:v.vv•::, \ I

1 I I I I · I

dt= 0 AA.-

0 2 3 4 5 6

Maximum Story Drift (em)

Figure 3.5.4: Maximum story drift distribution of the PS excited by the RRS ground motion controlled by the OCS algorithm in the MC approach (effect of the sampling interval)

...

1:--.) 0"1

I

¹⁰

€

0 0

.9 2:-

(/)

t5 -10

TD= Os --- TO = 0.02 s .-.- TD = 0.04 s

-20 . ,.

0 2 3 4 5

(b) AID

6 7 8 9 10

4.---.---~---.---,----.---,----r--~---~

I

!t:

0 0 .9 2:-

(/)

t5 -2

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0 2 3 4 5 6 7 8 9 10

(c) AVS

2.---.----.---,,---.----.---.----.----.---.----.

E' ~

€

0 0

i

_{t5 -1}

TD=Os

-2L---~--~---L--~----~--~--~--~----~~

0 2 3 4 5 6 7 8 9 10

Time (second)

Figure 3.5.5: ^1st story drift responses of the PS excited by the ELC ground motion controlled by the OCS, AID, and A VS algorithms in the NC approach (effect of the time delay)

TD=Os --- TD = 0.02 s

:e

~ ₀₄

... ....

.9 ~ (/) E

21 ..-- __.. -.

-~ ~ ---~

~

04~~~~~~~-=--~--~--~--J

6 8 10 12 14 16 18 20

(b) AID

~6.----..----.---.---.---.---.----.---.

~ E :§ 04

TO=Os ---TO = 0.02 s . .-.-TO= 0.04 s · ... TO= 0.06 s."

i ~2e~--~---

-~ ---.:.-.

~ -~

0 4

I I

6 8 10

I

12 (c)AVS

I

14

_...

...

...

_...

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..:

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16 18 20

~6.----.,----.---.---.---.----.---.----.

~ E

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a

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1

E

~

TO=Os

OL---~L---~---L----~---L----~----~--~

4 6 8 10 12 14 16 18 20

Number of Stories

Figure 3.5.6: SDS of the PS excited by the RRS ground motion controlled by the OCS, AID, and A VS algorithms in the NC approach (effect of the time delay)

...

~

1

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:E

0 0

.9 2:-

(/)

iii -2

TD=Os ..

__ TD = 0.04 s

t.

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rtf

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(b) AID

6 7 8 9 10

2.---~---r--~----.---~---r--~----.---,----,

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0 2 3 4 5 6 7 8 9 10

(c) AVS

-2L---~--~--~----~--~--~--~----L---~--~

0 2 3 4 5 6 7 8 9 10

Time (second)

Figure 3.5. 7: ^1st story drift responses of the PS excited by the ELC ground motion controlled by the OCS, AID, and A VS algorithms in the MC approach (effect of the time delay)

~• E

l

^{ro-o. .}

j

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(§ 4 ... TD = 0.06 ~

f

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4 6 8 10 12 14 16 18 20

(b) AID

~6.----,,----.---.---.---.----.---.---.

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1

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TD=Os --- TD = 0.02 s .-.- TD = 0.04 s ... TD=0.06s

-·-·-·-

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4 6 8 10 12

(c) AVS

14 16 ¹⁸ 20

~6,----.---.---.---.----.---.---.---.

1 -=

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TD=Os

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Figure 3.5.9: 1st story drift responses of the PS excited by the ELC ground motion controlled by the OCS, AID, and A VS algorithms in the NC approach with time delay compensation

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Figure 3.5.10: SDS of the PS excited by the RRS ground motion controlled by the OCS, AID, and A VS algorithms in the NC approach with time delay compensation

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