Semi-active control devices in structural control implementation

SEMI-ACTIVE CONTROL DEVICES IN STRUCTURAL CONTROLIMPLEMENTATION

J. Y. XU1, J. TANG2 AND Q. S. LI2*1 Department of Civil Engineering, Wuhan University of Technology, Wuhan, PR China

2 Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong

SUMMARY

A semi-active control device for structural control implementations is presented and discussed in this paper. Basedon two passive control devices, the mass pump and the hydraulic mass system, a new passive control system, themass damper pump (MDP), is introduced. It is found that the MDP system is more effective in vibration controlthan the other two passive control systems. It is then shown that the passive control MDP can be modified to bea semi-active control device and is very effective in structural control. Through theoretical analysis and numeri-cal simulations, it is found that the proposed semi-active control device MDP is more suitable for structures withordinary height or the magnitude of earthquake excitations is not very large (because the control force providedby the semi-active control is limited). Under these situations, the maximum response of a controlled structure canbe reduced by one-third to one-half. Also, it is found that multiple MDP is more effective in reducing structuralresponse than a single MDP when they are placed in appropriate locations. Copyright © 2005 John Wiley & Sons,Ltd.

1. INTRODUCTION

As large civil engineering structures such as tall buildings, high-rise towers and large-span bridgesbecome lighter and more flexible, their dynamic responses to wind, earthquake and other extraordi-nary loads are of great concern. To keep these structures functioning safely, effective vibration controldevices have been developed to reduce the vibration response of these kinds of structures to environ-mental loads (Abe, 1996; Polak et al., 1994; Yang et al., 1995; Symans and Constantinou, 1997a,1997b, 1999; Loh and Ma, 1996; Dupont et al., 1997; Wang et al., 1994; Ricciardelli et al., 2000).

There are three major classes of control systems (Symans and Constantinou, 1999):

(1) passive control system that does not require an external power source for operation and utilizesthe motion of the structure to provide the control forces;

(2) active control system that requires a large power source for operation of electro-hydraulic orelectromechanical actuates which supply control forces to the structure;

(3) semi-active control system that typically requires a small external power source for operation (e.g.a battery) and utilizes the motion of the structure to develop the control forces, the magnitude ofwhich can be adjusted by the external power source.

For structural control under earthquake action, due to the fact that in most places an earthquakemay not occur for a very long period of time or even during the whole design lifetime, or in some

THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGSStruct. Design Tall Spec. Build. 14, 165–174 (2005)Published online in Wiley Interscience (www.interscience.wiley.com). DOI:10.1002/tal.270

Copyright © 2005 John Wiley & Sons, Ltd. Received May 2004Accepted May 2004

*Correspondence to: Qiu Sheng Li, Department of Building and Construction, City University of Hong Kong, 83 Tat CheeAvenue, Kowloon, Hong Kong. E-mail: [email protected]

cases the control system gets destroyed during strong earthquake action or energy supply is stopped,the function of active control in these situations may not be realized. On the other hand, in these situations, passive control may not be able to achieve the specified targets or level of control. Thus,in these situations, semi-active control systems may be the most suitable choice.

Semi-active control systems maintain the reliability of passive control systems (can operate withouta large power source, acting like passive control) while also taking advantage of the adjustability ofan active control system. Therefore, they are becoming increasingly popular in practical applications,especially for civil engineering structures.

Semi-active control systems have only recently been developed for structural control applications.A semi-active control system generally originates from a passive control system that has been subse-quently modified to allow for the adjustment of mechanical properties.

In this paper, based on two passive control devices, the mass pump and the hydraulic mass system(HMS), a new passive control system, the mass damper pump (MDP) is introduced first. It is foundthat the passive MDP system is more effective than the other two passive control systems. It is thenshown that the passive control system MDP can be modified to be a semi-active control device andis effective in structural control.

Examples are provided to demonstrate the implementation of the proposed passive and semi-activecontrol devices. Results show that the proposed devices, both passive and semi-active, are very effec-tive in reducing structural vibration.

2. THE PASSIVE CONTROL DEVICES

In order to understand the proposed semi-active control device, it is necessary to become familiar withliquid passive control devices first.

2.1 Liquid passive control devices

The first liquid passive control device to be introduced is shown in Figure 1 and is called a mass pump.Through the vibration of the liquid inside the duct, the control force in the system is enlarged by the

166 J. Y. XU ET AL.

Copyright © 2005 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. 14, 165–174 (2005)

Figure 1. Mass pump

corrugated pipe, thus controlling the vibration of the structure. For a single degree of freedom system,the equation of motion is

(1)

where v = b sinj, b = A/a, and m and c0 are the mass and damping coefficient of the liquid; A and aare cross-sections of the corrugated pipe and duct, respectively; j is the supporting angle; M, k and care mass, stiffness and damping coefficient of the structure; and is the acceleration of earthquakeground movement.

It is seen that after installation of the mass pump:

(1) the natural frequencies of the structure are reduced;(2) generalized load is reduced;(3) critical damping ratio is increased.

Thus, the mass pump can effectively control the response of the structure.

2.2 Hydraulic mass vibration control system

The second passive control system, the hydraulic mass vibration control system (HMS), is shown inFigure 2. This is a relatively recently developed liquid control system. Through our experiments, it isfound that it can effectively control the response of some flexible floors (especially the bottom floor).

For a single degree of freedom system, its equation of motion is

(2)

wherea = A/a, b = A/A0 and Dm2 is the mass of the liquid inside the vertical pipes.

M m M x c c x kx M m M xg+ +( ) + +( ) + = - - -( )a b a a b2 20

20 2 0˙̇ ˙ ˙̇D

˙̇xg

M v m x c v c x kx M mv xg+( ) + +( ) + = - -( )2 20˙̇ ˙ ˙̇

SEMI-ACTIVE CONTROL DEVICES 167


Figure 2. Hydraulic mass system

This system has the following features:

(1) included vertical and horizontal pipes;(2) inside the horizontal pipes there is a sliding block, which plays an important role in the structural

control;(3) through the use of the hydraulic pump, the control force increases;(4) effective disturbing forces are greatly reduced. Also, the control effect can be adjusted to coun-

teract the input of the earthquake;(5) the system’s effective damping and mass are increased.

Now, let us compare HMS with the mass pump. In Equation (1), let

and let = sinqt, then the dynamic coefficient is determined by

(3)

In Equation (2), let

then, the dynamic coefficient is

(4)

It can be proved that:

(1) m2 < m1, so the vibration control provided by HMS is more effective than that of the mass pump;(2) m1 and m2 are both less than the dynamic coefficient for the case without any control system; there-

fore both controls are effective.

However, the installation of HMS in a multi-storey structure is relatively troublesome, especiallyin regard to the vertical pipes and sliding blocks. The sliding blocks may occupy some useful space;the liquid mass in the vertical pipe is small in comparison with the structural mass M. Thus, the slidingblocks and horizontal liquid pipes are better installed in the bottom or top floor or other appropriateplace. For most buildings, of course, the spaces between each storey are relatively large; therefore,the installation of HMS in these structures is suitable.

2.3 Mass damper pump

Based on the two passive control systems introduced above, a new system, the mass damper pump(MDP) has been developed and is shown in Figure 3.

m hq

wqxw2 2

2

2 2

2

2

20 5

1 4= - ÊË

ˆ¯

ÊËÁ

ˆ¯̃

+ ÊË

ˆ¯

È

ÎÍÍ

˘

˚˙˙

- ◊

ha b

22 0=

- -M m m

Ma

D

M M m Mk

M

c c

kMa

a a

= + + = =+

a b w xa2 2

0 2 2

20

4, , ,

m hqw

qxw1 1

1

2 2

1

1

20 5

1 4= - ÊË

ˆ¯

ÊËÁ

ˆ¯̃

+ ÊË

ˆ¯

È

ÎÍÍ

˘

˚˙˙

- ◊

˙̇xg

w x h1 2 1

20

2 1 24=

+=

++( )

=-+

k

M mv

c v c

k M mv

M mv

M mv, ,

168 J. Y. XU ET AL.


Let

Then, the equation of motion is

(5)

where x is the displacement of the floor; d is the displacement of the separating plate of the corru-gated pipe; z is the relative displacement of the liquid in the duct; A and a are the cross-sections ofthe corrugated pipe and duct, respectively; P and N are the liquid pressure and supporting axial force,respectively; and m and c¢0 are the mass and damping coefficient of the liquid, respectively.

Now, we will compare these three systems, i.e., mass pump, HMS and MDP.

(1) Comparison between MDP and mass pump:

Loading: M(1 - lv) = M - (m + M0)v < M - mv.Mass: M(1 + l(v - 1)v) = M + v(v - 1)(m + M0) > M + v2m.

Damping: and are identical.

Frequency: the frequency of the mass pump system is relatively large; in selection of a system thathas a lower frequency than that of external disturbances, the response of the MDP system is less thanthat of the mass pump.

(2) Comparison between MDP and HMS:

Loading: M(1 - lv) = M - (m + M0)v = M - bcosj(m + M0), which is basically the same as M -

(A/A0 < b).

Mass: M(1 + l(v - 1)v) = M + v(v - 1)(m + M0) = M + v2m - vM0, which is basically the same as

M mA

AM+ - Ê

Ëˆ¯b

0

2

0 .

bDmA

AM2

00-

c c v

M v m

+ ¢+

02

2

c c v

M v v

+ ¢+ -( )[ ]

02

1 1 l

M v v x c c v x kx M v xg1 1 102+ -( )[ ] + + ¢( ) + = - -( )l l˙̇ ˙ ˙̇

d xA

az d N P v

m M

M= = = = = =

+( )cos , , , , cos ,j b b b b j l 0



Figure 3. Mass damper pump

Damping: c + c¢0v2 > c + b2c (c¢0 includes damping provided by the mass pump and horizontal pipes).Frequency: the two are very close.

Therefore, the MDP system is more effective than the HMS system. For the MDP system, let

Then, the dynamic coefficient is m = mw /w 20.

It can be proved that

(6)

From Equation (6) it is observed: when l or v increases, the response decreases; normally, v canbe as high as tens or hundreds, while l can be appropriately selected, usually lv £ 1. Thus, l is rel-atively small. When lv = 1, the external disturbances are completely eliminated.

In addition, when

the dynamic coefficient reaches its maximum.

Example 1

The controlled structure under consideration in this example is shown in Figure 3, in which x = 0·05,lc = 2; then l ≥ 0·01, v £ l-1 £ 100. If we select lv = 0·8, then the results are given in Table 1.

From Table 1 it is observed that the dynamic coefficients of the controlled structure with MDP aresensitive to the variations of v and qw; therefore, the design of the control system plays an importantpart in the implementation of MDP.

3. THE SEMI-ACTIVE CONTROL DEVICE

In Figure 3, if the liquid pump is big, then a = A/a will be very large. On the other hand, one canopen a lot of small orifices in the piston and according to the control requirement regularly open andclose these orifices. This therefore produces additional damping, thus forming a semi-active controldevice.

Under these conditions, the damping is

ql x l

lw =- 2 0

2c

v

∂m∂l

∂m∂

w w< <0 0,v

m l mw = -( ) -1 11v

m l q x l qw w12 2

02 2 2

0 5

1 1 1 4 1= - + -( )( )[ ] + +( ){ } ◊v v vc

w ww

lq

qw

l lw02 2 0

2

0

0 0

1 11= =

+ -( )= =

¢> =

+K

M v v

c

c

M m

Mc, , , ,

C c c v M v v C v M vc c1 02 2

0 022 1 1 1 2 1= + ¢ = + -( )[ ] = +( ) = +( )xw l l x w l

170 J. Y. XU ET AL.


where d is the outside diameter of the piston; D is the inside diameter of the oil pump; l is the lengthof the piston; and h is the dynamic viscosity.

Thus, Equation (5) becomes

(7)

It can be seen that, when the frequency of the system is far away from the external disturbing fre-quency, the damping is increased dramatically. The stiffness is also increased accordingly and thedynamic coefficient is reduced greatly.

It is noted that if a spring is used to connect the mass block and the system in Figure 3, the controldevice is similar to a tuned mass damper (TMP); this device will therefore be called a tuned massdamper pump (TMDP). It can be shown that the TMDP is a more effective control device than theMDP.

3.1 MDP for multi-degrees of freedom structures

For a structure that has two degrees of freedom, the equation of motion is

(8)

where

Kk k k

k kF

M vm

M vMx M M mg=

+ --

ÈÎÍ

˘˚̇

= -+-

ÈÎÍ

˘˚̇

= +1 2 2

2 2 20, ˙̇ ,

MM v M v v m

v M M v v MC

c c c v c c v

c c v c c v=

+ - -( )- + -( )

ÈÎÍ

˘˚̇

=+ + - -

- - +ÈÎÍ

˘˚̇

12

22

1 2 02

2 02

2 02

2 02

1

1,

MX CX KX F DU˙̇ ˙+ + = +

M v v x C x kx M v x v Cxg1 1 122+ -( )[ ] + + = - -( ) -l l˙̇ ˙ ˙̇ ˙D

tD

dd =

Cl

tc c C c

d1 2

6

1=

-( )+ + = +

phD D



Table 1. Dynamic coefficients (mw) of the controlled structure with MDP

qw

v 0·1 0·2 0·3 0·4 0·5 0·6 1

20 0·226 0·3 0·207 0·102 0·06 0·039 0·01340 0·226 0·171 0·079 0·042 0·026 0·018 0·00660 0·201 0·103 0·048 0·027 0·017 0·0123 0·00480 0·169 0·073 0·034 0·019 0·012 0·009 0·003

100 0·135 0·056 0·026 0·015 0·01 0·007 0·002

where c0 is the damping of the liquid (does not include damping from the piston hole); U is the semi-active damping force produced from the piston hole; D is the location matrix of the control force; hereD = [0, 1]T.

According to the optimal control design, we have

(9)

where B, P, Z can be determined by the parameters of the system, k1, k2, M0, m, v.

Example 2

For the implementation of the hydraulic semi-active control system, we can use the system shown inFigure 3 (it is also suitable for high-rise structures, but the semi-active control device should be placedwhere the amplitudes are relatively large). Mechanical oils are used in this system. The followingparameters are used in this example:

M1 = 2·73kNs2/m, M2 = 1·85kNs2/m, k1 = 1·76 ¥ 104 kN/m, k2 = 1·21 ¥ 104 kN/m, C1 = C2 = 2·43Ns/m.Under the El Centro earthquake action, through the structural control design (e.g. Li et al., 1999, 2001),we determined the parameters of the control device as:

The responses of the structure with and without the control device are summarized in Table 2 forcomparison purposes.

From Table 2 it is seen that the reduction of the structural response is quite obvious using the MDP,suggesting the MDP is effective in reducing structural responses.

Example 3

Figure 4 shows a seven-storey building. It is assumed that M1~M6 = 450 t, M7 = 350 t, k1~k6 = 5·5 ¥104 kN/m, k7 = 4 ¥ 104 kN/m. Assume the structure damping ratio is xi = 0·04.

Under the El Centro earthquake action, through the structural control design (e.g. Li et al., 1999,2001), we have determined the control devices used in two different situations:

(1) Only the top floor is installed with MDP; the parameters are selected as l = 0·1, v = 80, h = 4·5¥ 105 Ns/m2, M0 = 0·35 t.

(2) MDPs are installed on the sixth and seventh floors; the selected parameters are the same as in (1).

The structural responses are summarized in Table 3 for comparison purposes.

l h= ◊ = = ◊ ¥ = ◊ = ◊ = [ ]01 80 4 5 10 0 34 2 0 0 15 20, , , , , ,v M M D

TNs m KNs m KNs m2 2

h r= ( ) = ◊ ¥ ◊ ¥ = ◊ = ◊17 100 1 445 10 8 5 10 1 02 0 34 5 2~ ~ , ,Ns m mt ld

U r BPZ= - -1

172 J. Y. XU ET AL.


Table 2. Structural responses for Example 2

Max. (x1) (cm) Max. (x2) (cm)

Without control With control Reduction Without control With control Reduction

0·612 0·393 36% 0·954 0·586 39%

From Tables 2 and 3, we can see that:

(1) Liquid semi-active control can reduce the response of the structure by about one-third. It seemsthat it is an effective control device, but active control can usually reduce the response by aboutone-half.

(2) Rationally installing multi-MDP is more effective in reducing structural response than a singleMDP.

4. CONCLUSIONS

A semi-active control strategy for structural control implementations is presented in this paper. Basedon two passive control devices, the mass pump and the hydraulic mass system (HMS), a new passivecontrol system, the mass damper pump (MDP), is developed. It is found that the MDP system is moreeffective than the other two passive control systems. It is then shown that the passive control MDPcan be modified to be a semi-active control device and is very effective in reducing structuralresponses.

The proposed liquid semi-active control system, the MDP, in fact is an on-and-off semi-activecontrol device. However, because there are many orifices in the piston, by regularly opening the ori-fices in the piston according to the rule of optimal control it is possible to produce continuous dampingand also approach optimal control.



Figure 4. Semi-active control MDP

Table 3. Structural responses for Example 3

Max. (x7) (cm) Max. (x6) (cm)

Without control 2·1 Reduction 1·81 ReductionSituation (1) 1·41 33% 1·25 31%Situation (2) 1·22 42% 1·13 38%

Through theoretical analysis and numerical simulation, it is found that the semi-active control strat-egy is more suitable for structures of ordinary height (non-super high-rise building, such as below 20storeys) or when magnitude of the earthquake action is not very large (because the control force pro-vided by the semi-active control is limited). Under these situations, the structural response can bereduced by one-third to one-half, and multiple MDP is more effective in vibration control than a singleMDP if they are placed in appropriate locations.

REFERENCES

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Li QS, Cao H, Li GQ, Li SJ, Liu DK. 1999. Optimal design of wind-induced vibration control of tall buildingsand high rise structures. Wind Structures 2(1): 69–83.

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Symans MD, Constantinou MC. 1997b. Seismic testing of a building structure with a semi-active fluid dampercontrol system. Earthquake Engineering and Structural Dynamics 26: 759–777.

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Wang KW, Kim YS, Shea DB. 1994. Structural vibration control via electrorheological-fluid-based actuators withadaptive viscous and frictional damping. Journal of Sound and Vibration 177(2): 227–237.

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Semi-active control devices in structural control implementation