SEMI-ACTIVE MR DAMPERS FOR SEISMIC CONTROL OF STRUCTURES

Transcription

1 157 SEMI-ACIVE MR DAMPERS FOR SEISMIC CONROL OF SRUCURES Jagadh G. Kor 1 and R.S. Jangd 2 SUMMARY Magnotorheologal (MR) damper have been demontrated to be more effetve n redung the trutural repone due to earthquake ung only a mall amount of external power. he performane of MR damper depend upon type of ontrol law ued and the damper fore dretly depend on the nput ommand voltage. he purpoe of th tudy to evaluate the effetvene of nput ommand voltage on MR damper ytem agant reently propoed ontrol law under dfferent earthquake. he magntude of ontrol fore nreae wth the nreae n the nput ommand voltage of MR damper, however for the dfferent damper loaton and onfguraton maxmum ommand voltage to the urrent drver may not alway effetve n redung the trutural repone. o nvetgate the effetve performane of the MR damper, dfferent ontrol algorthm wth multple MR damper loaton are ondered n th tudy. A phenomenologal model of a hear- mode MR damper, baed on a Bou Wen element, employed n the analy of the ontrolled buldng. he ontrol algorthm are teted on a fve-tory framed buldng and parametr tudy on varaton n the nput ommand voltage onduted for dfferent real earthquake ground moton. he numerally evaluated optmum parametr value are ondered for the analy of the dfferent damper loaton n the buldng n order to redue the dplaement, aeleraton and the bae hear of the buldng. It hown numerally that the performane of the MR damper ha a great potental n uppreng trutural vbraton over a wde range of em nput by eletng approprate optmum nput ommand voltage. KEY WORDS Strutural ontrol, em-atve ontrol, MR damper, earthquake, ontrol algorthm 1. INRODUCION Mot of the vl engneerng truture have very lttle dampng apablty; hene extenve damage and even trutural falure are ommon under em load. o dpate energy from earthquake and redue vbraton n truture, thereby redung human and materal loe, ontrol deve have been developed and mplemented n vl engneerng truture. he trutural ontrol deve are lafed a pave, atve and em-atve ontrol (Houner et al. 1997), (Datta 2003). One of the more promng among the ontrol deve the em-atve ontrol deve n em ontrol of truture known for t mplty, relablty and mall power requrement. herefore the em-atve ontrol deve have attrated a great deal of attenton n reent year. Many of thee ytem an operate on battery-power alone, provng advantageou durng em event when the man power oure to the truture may fal. Alo, beaue ematve deve annot njet energy nto the trutural ytem, they do not have the potental to detablze the ytem (Spener and Nagarajaah 2003). he em-atve ontrol deve are lafed a em-atve varable-tffne ytem, em-atve frton ontrol deve, varable orfe damper and ontrollable flud deve. One of the type of ontrollable flud deve the magnetorheologal (MR) damper, whh ont of a hydraul ylnder ontanng a oluton that, n the preene of a magnet feld, an reverbly hange from a free-flowng, lnear vou flud to a em-old tate wth ontrollable yeld trength. Intenve theoretal and expermental reearhe have been made on the dynam behavour and potental applaton of MR damper (Syman and Contantnou 1999). he effetve ontrol of trutural ytem hghly dependent on the ontrol method ued for degnng the MR damper ontrol law (Dyke and Spener 1997). he MR damper an be ontrolled wth low power (e.g., le than 50 W), low voltage (e.g., V), urrent-drven power upply outputtng only (e.g., 1 2 A), whh ould be uppled by battere and are apable of generatng large ontrol fore requred for full-ale applaton (Dyke et al. 1998). he MR damper are gnfantly hndered by ther nherently hyteret and hghly non-lnear dynam. Hene an approprate modelng of MR damper very mportant for ther applaton. Many tude on MR damper have been onduted analytally a well a expermentally for vbraton reduton under wnd and earthquake. Spener et al. (1996), Dyke et al. (1996, 1998) and Janen and Dyke (2000) ued MR damper to redue the em vbraton of model buldng truture. Yang et al. (2002) have developed a large-ale MR damper deve that ould be applable to realt vl and arhtetural truture. Yohoka et al. (2002), (Faruque Al and Ramawamy 2009) norporated an MR damper wth a bae olaton ytem uh that the olaton ytem would be effetve under both trong and moderate earthquake. Yohda and Dyke (2004) appled em-atve ontrol ytem ung MR damper to a non-lnear model of a full-ale buldng to verfy t effetvene n redung repone when non-lnear behavour ondered. Ohtor et al. (2004) ued a model of a full-ale 20-tory buldng model developed for 1 Prnpal Sarawat College of Engneerng, Kharghar, Nav-Mumba (Inda) 2 Profeor Department of Cvl Engneerng, Indan Inttute of ehnology Bombay, Powa, Mumba (Inda) (e-mal: rjangd@vl.tb.a.n) BULLEIN OF HE NEW ZEALAND SOCIEY FOR EARHQUAKE ENGINEERING, Vol. 42, No. 3, September 2009

2 158 the benhmark ontrol problem for emally exted nonlnear buldng. Yohda and Dyke (2005) nvetgated the plaement heme of MR damper baed on genet algorthm (GA). Sonej and Jangd (2006) tuded the effetvene of em-atve MR damper n redung the em repone of able-tayed brdge. Several model have been propoed to derbe the behavour of the MR damper. hee nlude the phenomenologal model baed on a Bou Wen hytere model propoed by Spener et al. (1997), neural network model developed by Chang and Rohke (1998), voelat plat model (Wereley et al., 1998), fuzzy model (Shurter and Rohke, 2000), (Huang et al., 2009), polynomal model (Cho et al., 2001). Among thee MR model, the phenomenologal model an aurately derbe the behavour of the MR damper. Neural network and fuzzy model an be ued for the MR damper, but the eleton of network truture and tranng data are eental n order to obtan aurate reult. In the voelat plat model the nvere dynam of the MR damper are often dffult to obtan due to ther nonlnear haratert. he lmtaton of polynomal model that t annot haraterze the MR behavour favorably at the relatvely low veloty regon. In th paper, the model ontng of a Bou Wen element n parallel wth a vou damper predt the behavour of a hear-mode MR damper propoed by (Yohda and Dyke, 2004) ued. he deve ont of two teel parallel plate. he magnet feld produed n the deve generated by an eletromagnet ontng of a ol at one end of the deve. Fore are generated when the movng plate, oated wth thn foam aturated wth MR flud, lde between the two parallel plate. he damper fore nreae wth nreang magnet feld and dependent on the ommand voltage. he maxmum ommand voltage fxed wth repet to the aturaton of magnet feld n the MR flud damper. he fore generated by the MR flud damper annot be ommanded dretly; only the ommand voltage appled to the urrent drver of the MR flud damper an be dretly ontrolled. he repone of the MR damper dependent on the loal moton of the truture and alo on the maxmum nput ommand voltage to the urrent drver. Hene t mportant to know the optmum nput ommand voltage, o that reultng MR damper fore n a trutural ytem aue a reduton n the trutural repone. he optmum ommand voltage an be any value between 0 and V max. So far, the effet of ommand voltage on the MR damper and the evaluaton of optmal value baed on the dfferent onfguraton of damper loaton under dfferent earthquake loadng have not been nvetgated. he am of th paper to ompare ome of the MR damper ontrol algorthm by ondutng a rtal parametr tudy n the vbraton ontrol of truture. Here the nfluene of varaton n ommand voltage of the MR damper for the em repone of a truture ondered for dfferent earthquake ground moton. he prmary objetve of th tudy an be ummarzed a: () to nvetgate the effet of ommand voltage n a em-atve MR damper, whh rtal n determnng the effetvene to trutural vbraton ontrol, () to dentfy the optmal value of ommand voltage for the bet poble trutural ontrol onfguraton wth dfferent damper deployment, () to evaluate analytally the dynam of em-atve MR damper for varou em-atve ontrol algorthm, that an provde better performane wth the hange n nput ommand voltage and (v) to ugget effetve gudelne for the ue of em-atve MR damper n vbraton ontrol of truture baed on the parametr tudy. 2. MODEL OF MAGNEORHEOLOGICAL DAMPER he MR damper how dynamally non-lnear fore-veloty behavour, hene a more aurate dynam model of MR damper neeary. Alo modelng of the ontrol deve eental for the adequate predton of the behavour of the ontrolled ytem. he Bou-Wen model propoed by Wen (1976) that numerally tratable and ha been ued extenvely for modelng the hyteret ytem and ha been ondered for derbng the behavour of the MR damper. he Bou-Wen model extremely veratle and an exhbt a wde varety of hyteret behavour. A hemat of the hearmode MR damper model hown n Fgure 1(a). k 5 k 4 k 3 k 2 k 1 Fgure 1. Model of hear-mode MR damper and fve-tory buldng wth MR damper. he model ontng of a Bou Wen element n parallel wth a vou damper predt the behavour of a hear-mode MR damper. he expreon governng the fore predted by th model a follow n 1 0 Bou-Wen (a) m 5 m 4 m 3 m 2 m 1 (b) f = x& + α z z& = γ x& z z βx& z + Ax& n 0 (1) x f f 2 f 1 x 5 & x& g x 4 x 3 x 2 x 1 (2)

3 159 where z an evolutonary varable that aount for the htory dependene of the repone and x the damper dplaement. he parameter 0, α, β, γ, n and A are alled the hape or haratert parameter of the model. he model parameter α and 0 depend on the voltage to the urrent drver a follow α=α +α u, a b 0 0a 0b = + u (3) whle the fltered voltage u determned by the appled voltage v a follow & (4) u = η( u v) where η a ontant. Equaton 4 neeary to model the dynam nvolved n reahng rheologal equlbrum and n drvng the eletromagnet n the MR damper. 3. GOVERNING EQUAIONS OF MOION Conder a mult-tory buldng equpped wth em-atve MR damper a hown n Fgure 1(b). he notaton m, k and x n Fgure 1(b) repreent the ma, tffne and dplaement relatve-to-the-ground of the -th floor. Aumng that the fore provded by the MR damper are adequate to keep the repone of the prmary truture from extng the lnear regon, and then the equaton of moton an be wrtten a M & x where C x& + K x = Λ f M Γx & g + (5) M the ma matrx, C the dampng matrx, K the tffne matrx, x the vetor of floor dplaement, x& and & x& are floor veloty and aeleraton vetor, repetvely, Λ a matrx of zero and one, where one wll ndate where the MR damper fore beng appled, f = [ f 1, f 2,... f n ] the vetor of ontrol fore produed by the damper, Γ a vetor of one and g the aeleraton due to an earthquake. For the unontrolled ae, the fore f produed by the MR damper zero. Ung the tate-pae repreentaton Equaton 5 take the followng form z & + & y = Az y + Bf Exg (6) = Cz + Df v (7) y y + & where z y = [x x] the tate vetor, y = [ x x] the vetor of meaured output, and v the meaurement noe vetor. he ytem matre are defned a follow 0 I A =, 1 1 M K M C 0 0 B =, = M 1 Λ Γ 1 M K C = I M & & x& E (8) 1 0 C, M D = 0 1 Λ 4. SEMI-ACIVE CONROL ALGORIHM Sem-atve ontrol ytem are typally hghly non-lnear. One of the man hallenge n em-atve ontrol the development of an approprate ontrol algorthm that an take advantage of the feature of the ontrol deve to produe an effetve ontrol ytem. o evaluate the performane of ematve ontrol algorthm, here three veratle and effetve ontrol algorthm are eleted n the urrent tudy. hee three ontrol algorthm; the bang-bang ontroller, the Lyapunov ontroller and Clpped-Optmal ontroller are derbed n th eton. Bang-bang ontrol algorthm In th approah, requre meaurement of the floor velote and appled fore. he ontrol trategy baed on Lyapunov funton to repreent the total vbratory energy n the truture and th ontrol algorthm determne the urrent ent to the th MR damper a follow = & + & (10) v V max H ( ( x Γx where H ( ) the Heavde tep funton. Here Λ the th olumn of the Λ matrx. g ) Λ Lyapunov tablty theory ontrol algorthm h approah requre the ue of a Lyapunov funton; even though number of Lyapunov funton are avalable, but here Lyapunov dret approah ued, n whh a potve defnte matrx P found wth eleted potve emdefnte matrx Q P by ung the followng Lyapunov equaton. A P + PA = Q (11) P he ontrol law determne the urrent ent to th MR damper a follow v f ) (9) = Vmax H (( z y ) PB f ) (12) Clpped-optmal ontrol algorthm he lpped-optmal ontrol trategy baed on aeleraton feedbak for ontrollng the MR damper. In th approah a lnear optmal ontroller, K () degned that alulate ' the vetor of dered ontrol fore, f = [ f 1, f2,... fn] baed on the meaured trutural repone vetor, y and the meaured ontrol fore vetor, f appled to the truture a follow f = 1 y L K ( L f ) (13) where L {} the Laplae tranform. he optmal ontroller K () obtaned from H 2 /LQG method. he th ommand gnal v for MR damper eleted aordng to the followng ontrol law

4 160 v V max H ({ f C f } f ) = (14) In th applaton, the meaurement typally avalable for ontrol fore determnaton nlude the aeleraton of eleted pont on the truture, the dplaement of the MR damper and the meaurement of the ontrol fore provded by the MR damper. In general, the ontrol algorthm for the damper may requre that the damper perform work on the truture uh that the energy wthn the trutural ytem nreaed. In developng the ontrol law, the ommand voltage retrted to the range V 0, V ], and for a [ max fxed et of tate, the magntude of the appled fore, f nreae when V nreae, and dereae when V dereae. 5. NUMERICAL SUDY o evaluate the performane of MR damper under varaton of the ommand voltage a numeral example ondered. he properte of a fve-tory buldng buldng are a follow: () the ma of eah floor dental m = kg for = 1, 2,, 5; () he tffne k (= 1, 2,, 5) of fve tory unt are 6.84x10 8, 6.84x10 8, 6.84x10 8, 6.84x10 8, 5.16x10 8 kn/m repetvely, and () Dampng rato for eah mode of 5%. he em repone of the truture tuded for four dfferent trong earthquake ground moton: () El Centro SE (1940, PGA= 0.348g; () Kobe NE (1995, PGA= 0.834g); () Loma Preta NE (1989, PGA= 0.57g); and (v) Northrdge NE (1994, PGA= 0.843g). he damper parameter are a follow, 0a = 4.40 N-e/m, 0b = N-e/m/V, α a = e5N/m, α b = e5N/m/V, γ = 3 m -1, β = 3 m -1, A= 1.2, n= 1, η = 50 e -1. he damper parameter ued n th tudy are from Yohda and Dyke (2004), the maxmum MR deve apaty of 1,000 kn wth maxmum ommand voltage of 10V. o nvetgate the effet of varaton n ommand voltage n the range 0 to 10 V, a parametr tudy performed ung the dfferent ontrol algorthm. he effet of parametral tude are evaluated by omparng dynam tme-htory analy reult. he everal poble trutural ontrol onfguraton wth dfferent damper deployment are ondered for evaluaton of the optmum ommand voltage parameter. Here the plang equene adopted one em-atve MR damper between the ground and the frt floor and gradually nreang the damper to all the floor of fve-tory truture. he varou reult of voltage are plotted wth peak dplaement, abolute aeleraton, bae hear and peak ontrol fore agant varaton of voltage n the range of 0 to 10V a hown n Fgure 2 to 10 under dfferent earthquake ground moton ung three dfferent ontrol algorthm. Fgure 2. Effet of voltage on peak dplaement, aeleraton, bae hear and ontrol fore when MR damper plaed at frt floor of fve-tory buldng ubjeted to dfferent ground moton for Bang-Bang ontrol algorthm. Fgure 3. Effet of voltage on peak dplaement, aeleraton, bae hear and ontrol fore when MR damper plaed at bottom three floor of fve-tory buldng ubjeted to dfferent ground moton for Bang-Bang ontrol algorthm. Fgure 4. Effet of voltage on peak dplaement, aeleraton, bae hear and ontrol fore when MR damper plaed at all the floor of fve-tory buldng ubjeted to dfferent ground moton for Bang-Bang ontrol algorthm.

5 161 Fgure 5. Effet of voltage on peak dplaement, aeleraton, bae hear and ontrol fore when MR damper plaed at frt floor of fve-tory buldng ubjeted to dfferent ground moton for Lyapunov ontrol algorthm. Fgure 8. Effet of voltage on peak dplaement, aeleraton, bae hear and ontrol fore when MR damper plaed at frt floor of fve-tory buldng ubjeted to dfferent ground moton for Clpped-optmal ontrol algorthm. Fgure 6. Effet of voltage on peak dplaement, aeleraton, bae hear and ontrol fore when MR damper plaed at bottom three floor of fvetory buldng ubjeted to dfferent ground moton for Lyapunov ontrol algorthm. Fgure 9. Effet of voltage on peak dplaement, aeleraton, bae hear and ontrol fore when MR damper plaed at bottom three floor of fvetory buldng ubjeted to dfferent ground moton for Clpped-optmal ontrol algorthm. Fgure 7. Effet of voltage on peak dplaement, aeleraton, bae hear and ontrol fore when MR damper plaed at all the floor of fve-tory buldng ubjeted to dfferent ground moton for Lyapunov ontrol algorthm. Fgure 10. Effet of voltage on peak dplaement, aeleraton, bae hear and ontrol fore when MR damper plaed at all the floor of fve-tory buldng ubjeted to dfferent ground moton for Clpped-optmal ontrol algorthm.

6 162 able 1. Comparon of 5-tory peak trutural repone of MR damper ung Bang-bang ontrol algorthm under dfferent ground moton. Control ype Damper Plaed at Voltage Input (Vmax) Imperal Dplaement (m) Aeleraton (m/²) Preta Northrdge Imperal Preta Northrdge Unontrolled Pave-OFF 1F ,2F ,2,3F ,2,3,4F , 2,3,4,5F Pave-ON 1F 10V ,2F 10V ,2,3F 10V ,2,3,4F 10V , 2,3,4,5F 10V Sem-atve 1F 4V (8.88) (8.35) (10.64) (10.49) (6.41) (2.98) (4.28) (6.82) 1,2F 6V (39.12) (38.64) (45.51) (37.17) (7.46) (24.78) (20.52) (25.48) 1,2,3F 5V (56.81) (59.14) (52.21) (54.15) (17.41) (41.62) (25.94) (32.73) 1,2,3,4F 5V (75.28) (68.43) (59.41) (73.23) (21.08) (46.58) (20.74) (52.87) 1, 2,3,4,5F 5V 0.33 (80.58) 1.03 (74.69) 0.55 (81.67) 0.68 (83.04) 5.80 (32.96) (48.38) 9.78 (28.97) 9.04 (53.61) Number n parenthee denote the % reduton n repone wth the Pave-OFF ontrol ytem

7 163 able 2. Comparon of 5-tory peak trutural repone of MR damper ung Lyapunov ontrol algorthm under dfferent ground moton. Control ype Damper Plaed at Voltage Input (Vmax) Imperal Dplaement (m) Aeleraton (m/²) Preta Northrdge Imperal Preta Northrdge Unontrolled Pave-OFF 1F ,2F ,2,3F ,2,3,4F , 2,3,4,5F Pave-ON 1F 10V ,2F 10V ,2,3F 10V ,2,3,4F 10V , 2,3,4,5F 10V Sem-atve 1F 7V 1.61 (10.55) 3.62 (16.01) 2.73 (17.02) 3.40 (20.74) 8.78 (1.12) (9.06) (11.84) (14.31) 1,2F 6V 1.23 (30.89) 2.61 (38.87) 2.01 (37.77) 2.84 (33.17) 7.84 (9.98) (31.01) (28.40) (26.55) 1,2,3F 6V 0.78 (55.69) 1.51 (64.13) 1.53 (50.32) 2.15 (48.68) 6.45 (25.17) (48.58) (30.09) (34.24) 1,2,3,4F 5V 0.69 (60.34) 1.49 (64.09) 1.44 (53.24) 1.75 (57.42) 6.46 (25.14) 9.85 (51.28) (22.97) (43.94) 1, 2,3,4,5F 5V 0.47 (72.35) 1.19 (70.76) 0.92 (69.33) 1.16 (71.07) 6.06 (29.94) 9.67 (51.16) (27.16) (49.92) Number n parenthee denote the % reduton n repone wth the Pave-OFF ontrol ytem

8 164 able 3. Comparon of 5-tory peak trutural repone of MR damper ung lpped -optmal ontrol algorthm under dfferent ground moton. Control ype Damper Plaed at Voltage Input (Vmax) Imperal Dplaement (m) Aeleraton (m/²) Preta Northrdge Imperal Preta Northrdge Unontrolled Pave-OFF 1F ,2F ,2,3F ,2,3,4F , 2,3,4,5F Pave-ON 1F 10V ,2F 10V ,2,3F 10V ,2,3,4F 10V , 2,3,4,5F 10V Sem-atve F 2V (1.66) (1.85) (5.16) (1.63) (3.82) (1.10) (1.76) (1.25) ,2F 5V (15.73) (14.52) (17.02) (16.23) (7.46) (6.42) (6.57) (2.90) ,2,3F 4V (36.93) (18.76) (32.91) (31.34) (9.74) (12.60) (26.87) (8.85) ,2,3,4F 4V (58.04) (32.53) (48.37) (40.63) (20.16) (16.42) (35.39) (24.43) , 2,3,4,5F 6V (65.88) (61.67) (57.67) (70.05) (40.97) (48.83) (34.50) (39.25) Number n parenthee denote the % reduton n repone wth the Pave-OFF ontrol ytem

9 165 It oberved from the Fgure 2 to 10 that, the ommand voltage play an mportant role n the repone of the buldng and alo t vare wth dfferent onfguraton of damper plaement. From Fgure 2, an optmum value of the ommand voltage an be found a 4V when the damper plaed at frt floor of a fve-tory buldng, for the all the repone under the dfferent earthquake ground moton. Smlarly, from Fgure 3 to 10, the optmum parameter of voltage an be oberved for the Bang-bang, Lyapunov and Clpped-optmal when the damper are plaed at bottom floor to all the floor of a fve-tory buldng. able 1 to 3 how the peak repone quantte for the dentfed optmum nput ommand voltage to MR damper under the four real earthquake ground moton. he overall reult ndate that the MR damper wth Bang-Bang, Lyapunov and Clpped- Optmal theory ontrol algorthm under dfferent ground moton aheve a reaonable level of performane a ompared to pave ON and OFF deve. he reult from able 1 for the Bang-bang ontrol algorthm wth dentfed optmum ommand voltage under dfferent ground moton how maxmum tory dplaement reduton rangng from 74 to 83%, whle the maxmum tory abolute aeleraton reduton ranged from 28 to 53%. Smlarly, the reult from able 2 for the Lyapunov ontrol algorthm wth dentfed optmum ommand voltage under dfferent ground moton how maxmum tory dplaement reduton rangng from 69 to 72%, whle maxmum abolute aeleraton reduton ranged from 27 to 51%. And the reult from able 3 for the Clpped-optmal ontrol algorthm wth dentfed optmum ommand voltage parameter under dfferent ground moton how the maxmum tory dplaement reduton rangng from 57 to 70%, whle the maxmum tory abolute aeleraton reduton ranged from 34 to 48%. hu for gven onfguraton, t alo mportant to note that nreang the number of em-atve damper from the eonom pont of vew not derable. Hene, by omparng reult from the able 1 to 3, wth the mnmum number of three MR damper more effetve to ontrol the trutural repone n a fve-tory buldng. Fgure 11. me-varaton of top floor dplaement of Unontrolled, Pave and Sem-atve MR damper ontrol ytem under El Centro (1940) ground moton. Fgure 12. me-varaton of top floor aeleraton of Unontrolled, Pave and Sem-atve MR damper ontrol ytem under El Centro (1940) ground moton. Fgure 11 and 12 ompare the tme varaton of the top tory dplaement, and the abolute top tory aeleraton for the unontrolled buldng and the buldng wth all the floor wth pave damper/ em-atve damper under the El Centro (1940) real ground moton. From Fgure 11 and 12 t an be een that the em-atve MR damper for all ontrol ytem are the mot effetve n redung the dplaement and the aeleraton ompared to the pave damper. 6. CONCLUSIONS For buldng ubjeted to dfferent type of real earthquake, the effetvene and performane of varou ontrol algorthm for em-atve MR damper have been nvetgated and preented. he parametr tudy onduted on a fve-tory buldng to oberve the nfluene of varaton of the nput ommand voltage n the range 0 to 10V wth dfferent onfguraton of the MR damper deployment poton n buldng, wth and wthout ontrol deve. Comparatve performane of dfferent MR ontrol algorthm wth the optmum nput ommand voltage parameter determned under real earthquake ground moton. All ontrol algorthm wth ung an optmum nput ommand voltage parameter demontrated t effetvene n redung the trutural repone. From the numeral nvetgaton of the buldng wth MR damper ued a a protetve ontrollng ytem, the followng onluon may be drawn: 1) It hown from the numeral tudy that the ematve MR damper are qute effetve n redung both the peak dplaement and the peak aeleraton under dfferent type of real earthquake ground moton. 2) From the parametr tudy, the peak dplaement and trutural aeleraton are redued wth an nreae n the nput ommand voltage of the MR damper. However there ext an optmum value of the voltage nput dependng upon the damper loaton. 3) he ontrol algorthm ondered for the MR damper, namely, the Bang-bang, the Lyapunov, and the Clppedoptmal mpart reduton n repone for the truture. But omparatvely the Bang-bang ontrol algorthm preformed better for the optmum nput ommand voltage. 4) he reult how that the buldng wth multple MR damper wth optmum ommandng voltage how mproved em repone when ompared wth the pave-on damper.

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