A COMPARATIVE STUDY OF SISO AND MIMO CONTROL STRATEGIES FOR FLOOR VIBRATION DAMPING

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1 6th ECCOMAS Conference on Smrt Structure nd Mteril SMART2013 Politecnico di Torino, June 2013 E. Crrer, F. Miglioretti nd M. Petrolo (Editor) A COMPARATIVE STUDY OF SISO AND MIMO CONTROL STRATEGIES FOR FLOOR VIBRATION DAMPING Iván M. Díz *, Emilino Pereir, Crlo Znuy *, Critin Alén * Univeridd Politécnic de Mdrid, Deprtment of Continuum Mechnic nd Theory of Structure E.T.S. Ingeniero de Cmino, Cnle y Puerto, 28040, Mdrid, Spin e-mil: ivn.munoz@upm.e, cz@cmino.upm.e, web pge: Univeridd de Alclá de Henre, Deprtment of Signl Theory nd Communiction Ecuel Politécnic Superior, 28805, Alclá de Henre (Mdrid), Spin e-mil: emilino.pereir@uh.e, criti.len@uh.e Key word: Active vibrtion control, Inertil ctutor, MIMO control, Humn-induced vibrtion, Floor vibrtion. Summry. Civil engineering tructure uch floor ytem with open-pln lyout or lightweight footbridge re uceptible to exceive level of vibrtion cued by humn loding. Active vibrtion control (AVC) vi inertil m ctutor h been hown to be vible technique to mitigte vibrtion, llowing tructure to tify vibrtion ervicebility limit. Mot of the AVC ppliction involve the ue of SISO (ingle-input ingle-output) trtegie bed on collocted control. However, in the ce of floor tructure, in which mot of the vibrtion mode re loclly ptilly ditributed, SISO or multi-siso trtegie re quite inefficient. In thi pper, MIMO (multi-input multi-output) control in decentrlied nd centrlied configurtion i deigned. The deign proce imultneouly find the plcement of multiple ctutor nd enor nd the output feedbck gin. Additionlly, ctutor dynmic, ctutor nonlineritie nd frequency nd time weighting re conidered into the deign proce. Reult with SISO nd decentrlied nd centrlied MIMO control (for given number of ctutor nd enor) re compred, howing the dvntge of MIMO control for floor vibrtion control. 1 INTRODUCTION Improvement in deign method hve led to light nd lender floor tructure with openpln lyout. Thee floor tify ultimte limit tte criteri but hve the potentil of ttrcting complint coming from exceive humn-induced vibrtion [1]. Active vibrtion control (AVC) vi inertil m ctutor h been hown to ignificntly reduce the level of repone, llowing tructure to tify vibrtion ervicebility limit. Up to now, ppliction

2 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. minly involve the ue of SISO (ingle-input ingle-output) trtegie bed on collocted control (i.e., the pir ctutor/enor (A/S) re phyiclly plced t the me point) rther thn MIMO (multiple-input multiple-output) trtegie. Thi i due to the fct tht SISO control trtegie re eier to be deigned nd, unconditionl tbility nd good vibrtion reduction performnce cn be chieved under the bence of ctutor nd enor dynmic [2]. Although the incluion of ctutor nd enor dynmic mke the tbility conditionl nd degrde the vibrtion reduction performnce, there exit SISO control trtegie tht mitigte thee problem (ee for exmple [3] nd [4]). Floor tructure exhibit vibrtion mode which re uully loclly ptilly ditributed with cloely pced nturl frequencie. Thi men tht there i no ingle loction tht cn be ued to control ll the ignificnt mode. Under thee circumtnce, everl pir of A/S hould be ued. The deign hould tke into ccount the ction of ll the A/S pir. However, uch ction cn be conidered in two different configurtion: (i) if thee pir ct independently of ech other, thi trtegy i known decentrlied control, nd (ii) if the ctutor output tke into ccount not only it enor prtner but lo ll the other, thi trtegy i referred to centrlied control, or "full MIMO trtegy". The min drwbck ocited to the ue of decentrlied control i tht one cn ure the control of one point but cnnot ure the control t other point [5]. Generlly peking, MIMO control h the potentil to chieve better trdeoff between energy conumption nd vibrtion reduction performnce in the ce of multiple vibrtion mode with nturl frequencie cloely pced ditributed. Thi ttement w hown in [6], where n optiml plcement of ctutor nd enor for MIMO control of floor vibrtion w preented. A two-tge lgorithm, which combine performnce index (PI) nd time weighting function to conider the level nd the durtion of the vibrtion, w ued to imultneouly find n optiml loction of predefined number of A/S pir nd the feedbck gin of direct velocity feedbck (DVF) control. The min concluion i tht MIMO trtegy control my be more pproprite thn SISO nd decentrlied MIMO control. In ddition, the lgorithm propoed in [6] conider the force/troke turtion of the ctutor nd higher unmodelled mode of the floor, howing tht MIMO control i robut to thi turtion nd unmodelled floor dynmic. Thi work build on the ide of MIMO vibrtion control of floor tructure, propoing n extenion of the lgorithm preented in [6]. The control trtegy propoed i lo bed on DVC control, conidering not only force/troke turtion of the ctutor nd time weighting function into the PI, but lo the ctutor dynmic, which ffect ignificntly the tbility of the overll control ytem. Then, PI repreenttive of the diiption energy nd obtined from n initil diturbnce i minimied. Additionlly, the humn perception of vibrtion depend on the mgnitude, frequency content nd durtion of the vibrtion nd the orienttion of the body. Thu, the deign of control trtegy hould conider thee fctor. In thi pper, the control trtegy lo include frequency weighting function which tke into ccount the dependency of the perception of vibrtion on the frequency [7]. The propoed deign proce i run uming, firtly, SISO control, econdly, decentrlied MIMO control, nd, thirdly, centrlied MIMO control, in order to crry out comprtive tudy between them. The tudy i undertken for n ll-ide imply upported rectngulr 2

3 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. plte which model floor tructure. The deign proce need, input, the tructurl modl model, which my be obtined nlyticlly, if poible, by finite element model or, experimentlly, by n experimentl modl teting. Finlly, the dvntge nd didvntge of ech trtegy re highlighted. 2 COMPONENTS OF THE CONTROL SCHEME The generl control trtegy nd the min element of the control cheme re decribed below. 2.1 Generl control trtegy Figure 1 how block digrm of MIMO output feedbck control in which the objective r t = ). When the gin i to chieve zero vibrtion (reference commnd i et to zero ( ) 0 mtrix K i digonl, the control i decentrlied nd when it i clr number, the control i SISO. The floor nd the ctution ytem hve been repreented uing tte-pce model [8]. The control cheme i completed by turtion nonlinerity which limit the control voltge in order to void force nd troke turtion [9]. U e Structure model B e r = 0 + U B X ɺ X C Y A Y T X X ɺ + T T C T + B T U T turtion K Gin mtrix A T Actution ytem model Figure 1: Control trtegy uing output feedbck. 3

4 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. 2.2 Stte-pce model of the floor A ditributed prmeter ytem (like floor tructure) cn be dicretied (uing the finite element method) uch tht m, dmping nd tiffne propertie re lumped t n degree of freedom. The dynmic behviour i repreented by n-coupled econd-order differentil eqution tht cn be expreed in mtrix form ( ) + ( ) + ( ) = ( ) Muɺɺ t Duɺ t Ku t F t, (1) T where ( ) = [,,, ] i the diplcement vector, ( ) [,,, ] u t u1 u2 u n F t F1 F2 F n = i the force n n vector nd M, D nd K R re the m, dmping nd tiffne mtrice. Uing the modl nlyi nd the mode uperpoition method (or eprtion of vrible), the diplcement vector i expreed liner combintion of generlied coordinte (uully known norml or modl coordinte) ( ) [,, T η t = η1 ηm ], m being the number of vibrtion mode conidered into the nlyi. Tht i, ( ) η ( t) u t = Φ, (2) n m where Φ R i the modl trnformtion mtrix which contin the modl hpe in column, Φ = φ1 φ m, with n 1 φ i R nd i 1,, = m. (3) Thu, φ i re the be vector nd ηi re the coordinte of the modl model. The ubtitution of T (2) into (1) nd pre-multiplying by Φ yield et of m-decoupled econd-order differentil eqution. It mtrix repreenttion conidering m-normlied mode hpe i follow T ( ) + Σ ( ) + Λ ( ) = Φ ( ) Iɺɺ η t ɺ η t η t F t, (4) where I i the identity mtrix, ( ζ ω ζ ω ) re de modl prticiption fctor, nd ζ i nd Σ = dig 2 1 1,,2 m m, dig ( ω 2 2 1,, ωm ) Λ =, Φ T F ( t) ω i re the dmping rtio nd nturl frequency ocited to the i-vibrtion mode. Conider tte-pce repreenttion of (4) in which ubcript nd e indicte tructure nd excittion, repectively, ( ) = ( ) + ( ) + ( ); ( ) = ( ) Xɺ t A X t B U t BU t Y t C X t, (5) e e in which the tte vector i X = [ η,, η, ɺ η,, ɺ η ] 1 m 1 m T, the ytem mtrix T A 0 m m I m m = Λ Σ, (6) 4

5 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. the control input,, T U = FF 1 F Fp for p ctutor, the input mtrix where B m p Φ R nd i, Fj 0 m p Φ, with = Φ = φ φ φ φ 1, F1 1, Fp m, F1 m, Fp, (7) φ i the vlue of the modl hpe i t the poition of the ctutor j. The output vector i,, T Y = uɺ S1 uɺ Sq, in which i umed tht the velocity i the quntity meured t q point. The output mtrix i follow where Finlly, m q Φ R nd i, Sj e C 0 q m Φ, with = Φ = φ φ φ φ 1, S1 m, S1 1, Sq m, Sq, (8) φ i the vlue of the modl hpe i t the poition of the enor j. B i the ytem noie input mtrix nd U ( ) e t i the ytem noie. From the tte-pce repreenttion (5), the chrcteritic eqution i given by [8] λ being the open-loop pole of the tructure (or eigenvlue of 2.3 Actutor dynmic behviour λ I A = 0, (9) The ctutor conidered i n inertil ctutor tht generte force through ccelertion of n inertil m to the tructure on which it i plced. The ctutor conit of n inertil (or moving) m m ttched to current-crrying coil moving in mgnetic field creted by n rry of permnent mgnet. The inertil m i connected to the frme by upenion ytem. The mechnicl prt i modelled by pring tiffne k nd vicou dmping c. The electricl prt i modelled by the reitnce R, the inductnce of the coil L nd the voice coil contnt C e, which relte the coil velocity nd the bck electromotive force (Figure 2) [10]. Combining the mechnicl nd the electricl prt, the liner behviour of the ctutor cn be cloely decribed third-order dynmic model. A w hown in [11], the trnfer function between the inertil force nd the control voltge cn be plit into two prt: econd-order model ( m-pring dmper model) nd low-p element (which repreent the electricl prt) G ( ) ( ) ( ) A ). F g, (10) 2 1 = 2 2 V + 2ζ ω + ω + ε 5

6 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. where = jω, ω being the ngulr frequency, g > 0, nd ζ nd ω re, repectively, the dmping rtio nd nturl frequency. The pole t ε provide the low-p property. From Eqution (10), the following tte-pce model cn be obtined in which the tte vector i X [ x, x, x ] A ( ) = ( ) + ( ); ( ) = ( ) Xɺ t A X t B U t Y t C X t, (11) = 1 0 ω + 2 repectively. The control input T =, the ytem, input nd output mtrice re 0 0 εω ζ ω ε, B 0 1 ε + 2ζ ω U 0 = 0 g nd [ 0 0 1] C =, (12) = V R i the control voltge for the ctutor nd the output i the trnmitted force to the tructure Y = F R. The tte-pce model (11) for one ctutor cn be generlied for p ctutor quite trightforwrdly. Thu, the tte-pce model for the totl number of ctutor i follow (it w referred the ctution ytem in Figure 1) in which the model mtrice re A T ( ) = ( ) + ( ); ( ) = ( ) Xɺ t A X t B U t Y t C X t, (13) A A 2 0 =, Ap T T T T T T T T nd, C T 3 p 3 p A T R, B T C C2 0 =, Cp B B 2 0 =, Bp B T R 3 p p p 3 p C T R. (14) 6

7 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. Figure 2: Inertil ctutor. ) Sketch of n electrodynmic ctutor (fter [10]). b) APS Electro-Sei Dynmic Shker Frequency weighting The vibrtion tht cn be perceived by humn depend on the direction of incidence to the humn body nd the frequency content of the vibrtion (for given mplitude), mong other fctor. A uch, the vrition of enitivity of frequency for body poition cn be tken into ccount by ttenuting or enhncing the ytem repone for frequencie where perception i le or higher enitive, repectively. The degree to which the repone i ttenuted or enhnced i referred to frequency weighting. Thu, frequency weighting function re pplied in order to ccount for the different cceptbility of vibrtion for different direction nd body poition. ISO 2631 [7] nd BS 6841 [12] provide detil for frequency nd direction weighting function tht cn be pplied which re ll bed on the bricentric coordinte ytem hown in Figure 3. Thee hve been included in current floor deign guideline uch the SCI guidnce [13]. According to ISO 2631, for z-xi vibrtion nd tnding nd eting, the frequency weighting function i W k. Thi curve nd it ymptotic definition re grphed in Figure 4. Thu, the frequency weighted tte vector i obtined follow in frequency domin in which W ( ) k ( ) ( ) ( ) X = X W, (15), w k i the trnfer function (or Fourier trnform) of the frequency weighting function. Eqution (15) cn lo be expreed in time domin ( ) ( ) ( ) X t = X t w t, (16), w k where ( ) denote the convolution proce nd wk ( ) W ( ). k t i the impule repone function of 7

8 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. Figure 3: Direction for vibrtion ccording to ISO 2631 [7] nd BS 6841 [12] (fter [13]). Figure 4: W k frequency weightingg function (thicker curve) nd it ymptotic definitionn (thinner curve) [7]. 8

9 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. 2.5 Time weighting A it h been mentioned before, the humn comfort to vibrtion i directly relted to the durtion of utined vibrtion. Thu, peritent vibrtion hould be penlied in the control deign, giving more importnce to trnient vibrtion of long-durtion thn thoe of hortdurtion. A it w commented before, the control deign propoed in thi work conit of minimizing PI tht depend on the energy of the ytem fter n initil condition. Therefore, exponentil time weighting will be uitble for thi ppliction. The time weighted tte X ˆ i computed from the tte vector X follow αt ( ) ( ) Xˆ t = e X t. (17) with α 0. Note tht the exponentil time weighting dd contrint in the reltive tbility of the controlled ytem. Note lo tht peritent tte re more penlied α i increed. Finlly, if the tte vector i time weighted by (17) nd frequency weighted by (16), the time nd frequency weighted tte i follow 3 CONTROL DESIGN ( ) ˆ ( ) ( ), w k Xˆ t = X t w t. (18) The purpoe of thi ection i to provide procedure to find n optiml loction of given number of A/S pir nd the gin mtrix when DVF of Figure 1 i conidered. 3.1 Cloed-loop ytem Conider the floor model given by (5) in which i umed the me number of ctutor nd enor ( p = q in Eqution (5)) locted t the me point (in pir). Tht i, p A/S pir re conidered. On the one hnd, the control force ( U ( t ) in Figure 1 nd Eqution (5)), which i the input to the tructure nd the output of the ctution ytem, cn be expreed follow ( ) ( ) ( ) U t = Y t = C X t. (19) T T T Note tht the turtion nonlinerity i omitted t thi point. Subtituting (19) into (5), it i obtined ( ) = ( ) + ( ) + ( ) Xɺ t A X t B C X B U t. (20) T T e e On the other hnd, the control voltge, which i the input to the ctution ytem, i Subtituting (21) into (11) ( ) ( ) ( ) U t = KY t = KC X t. (21) T 9

10 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. ( ) = ( ) + ( ) Xɺ t A X t B KC X t. (22) T T T T Hence, the tte-pce model of the cloed-loop ytem cn be written uing (20) nd (22) follow ( t) ( t) ( ) ( ) Xɺ A BCT X t Be = + U Xɺ B T T KC A T X T t 0 e ( t), Y ( t) [ C 0] X ( t) ( t) = X T (23) with the cloed-loop ytem mtrix being A A B C. (24) T c = BT KC A T The chrcteritic eqution of the cloed-loop ytem i then [8] λ c being the cloed-loop pole (or eigenvlue of ymptoticlly tble if the rel prt of the (2m+3p) eigenvlue of 3.2 Deign proce λ I A = 0, (25) c c ( λ c, i ) <, i = 1,,( 2m + 3p) Re 0 A c ). The cloed-loop ytem will be A c i negtive. (26) The deign proce i bed on the minimition of PI relted to the diiption energy of the whole tructure due to the AVC ction for given excittion. The PI i clculted uing the time nd frequency weighted tructure tte follow (ee Eqution (18) nd Figure 5) 1 (, ) t f ˆ T J K Z =, ( ) ˆ, ( ) 2 X 0 w t QX w t, (27) 2m 2m p in which the weighting mtrix Q R i poitive define mtrix, Z R i the poition of the A/S pir (obviouly, Z mut be included into the ptil domin of the tructure) nd t f i the finl time ued to compute the PI. Thi time hould be ufficiently long uch tht the ytem energy i totlly diipted due to the control ction. The weighting mtrix i tken [6] 10

11 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. 2 2 ω1 φ1,mx ωmφm,mx Q = 2, (28) φ1,mx φm,mx in which φ i,mx i the mximum vlue of the i-th eigenvector φ i. Note tht the diplcement tte re weighted by the nturl frequencie, mking thu the diplcement tte comprble to the velocity tte. Figure 5 how block digrm which drft the computtion of the time nd frequency weighted tte ued to obtin the PI (27). Note tht the turtion nonlinerity i tken into ccount to compute the PI. X Structure tte t e α X ˆ Xˆ, W w k Actutor Structure Y Sturtion nonlinerity Gin mtrix Figure 5: Block digrm of the computtion of the PI. The deign proce propoed for the A/S pir loction nd the gin mtrix cn be divided into the following tep: Step 1: Obtin model of the tructure conidering m vibrtion mode defined t n point ptilly ditributed long the tructure. Step 2: Obtin the eigenvlue of open-loop tructure (Eqution (9)), chooe prmeter α ( λ, i ) chooe the finl time ued to compute the PI α min Re, i = 1,,2m, (29) i 11

12 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. t f 10 α, (30) decide the frequency weighting function to be ued [7], the number of A/S pir, p, nd the excittion. Typiclly n initil condition for the tructure tte will be conidered perturbtion. Step 3: For ech poible combintion of poition of the p A/S pir, find the optiml gin mtrix K by minimiing the PI (27) ubjected to the tbility condition for the cloedloop ytem hown in (26), but updted for exponentilly weighted tte. Mthemticlly, the problem my be etblihed ( ) min J ( K, Z ) J Z =,.t. Re( λc, i ) K < α, i = 1,,2m. (31) Step 4: When the optiml mtrix gin for ech poible combintion of A/S pir poition i obtined, the combintion of poition Z, together with it correponding gin mtrix, tht provide the minimum PI i the olution erched 4 EXAMPLE ( ) J = min J Z. (32) Z The tudy i undertken for n ll-ide imply upported rectngulr iotropic plte of dimenion 10 6 m nd depth of 0.20 m. The mteril propertie conidered re: modulu of elticity E = N m, Poion' rtio ν = 0.15 nd denity ρ = 3000 kg m. The denity h been increed from kg m (the chrcteritic vlue for reinforced or 3 pretreed concrete) to 3000 kg m in order to include portion of the impoed lod nd the totl ded lod [13]. Figure 6 how the ptil grid conidered nd the obtined nturl frequencie nd mode hpe. The dmping rtio for ll the mode h been tken Thi vlue i repreenttive of prtilly fully fitted out floor. Note tht the tructure model cn be obtined experimentlly, through experimentl modl nlyi, or numericlly, through the finite element method. Current experimentl modl identifiction procedure ue ttepce relition, uch [14]. For the prticulr exmple conidered here, the tructure h nlyticl olution, which i not vilble for mot rel-life tructure. 12

13 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. Figure 6: Grid nd Mode hpe. An APS Dynmic Model 400 electrodynmic hker [15] operted in inertil mode with n inertil m of 30.4 kg i conidered here the ctutor (Figure (Fi 2). The trnfer function (10) w identified uing voltge-driven voltge mode G ( ) = , (33) in which ω = 13.2 rd (2.1 Hz), ζ = 0.5 nd ε = The tructure h been modelled conidering the firt four vibrtion mode ( m = 4 ). The condition for α i obtined from (29): α A vlue of α = 1.1 w finlly choen. Uing α, it i obtined the minimum time conidered to compute the PI (Eqution (30)): t f 10 α = A vlue of t f = 10 w decided to be ued. An impulive input modelled vi n initil condition of velocity tructure tte w ued to diturbnce the tructure X ( 0) X ( 0) T, with X ( 0 ) = [η1 = 0,,ηm = 0,ηɺ1 = 1,,ηɺm = 1]. = X T ( 0 ) 0 (34) Once ll the needed prmeter re elected, Step 3 nd 4 cn be undertken. Thu, the lgorithm h been run for three ce: (1) only one A/S i conidered ( p = q = 1 ), (2) two A/S pir ( p = q = 2 ) in decentrlied configurtion (the gin mtrix i digonl), nd (3) 13

14 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. two A/S pir ( p = q = 2 ) in centrlied configurtion (the gin mtrix i full mtrix). For ech ce, the effect of the incluion of the ctutor i tudied nd the effect of frequency weighting i lo tudied. Tble 1 how the PI obtined for the three ce conidering two ce for ech one: (i) the ctutor behve contnt (it dynmic nd the turtion nonlinerity re not included), nd (ii) the ctutor dynmic nd the turtion nonlinerity re included into the control cheme. Tble 1 h been crried out conidering time weighted tte only. For the ce of n idel ctutor, the trnfer function of the ctutor (10) i implified G g ε =. (35) ( ) 241 N V Tble 1 how the PI vlue, the optiml poition nd the gin mtrix component. For the idel ce, the PI re much mller thn thoe obtined for the non-idel ce. The gin vlue re drticlly reduced nd the PI re ubtntilly increed for the non-idel ce minly due to tbility reon. Tble 2 how the PI obtined for the three ce conidering two ce for ech one: (i) time weighted tte, nd (ii) time nd frequency weighted tte. Tble 2 h been crried out conidering the ctutor dynmic nd the turtion nonlinerity. From both tble, it i oberved tht MIMO control lwy provide mller PI thn SISO control nd tht centrlied MIMO lwy improve the performnce of decentrlied MIMO, lthough uch improvement my not be very ignificnt in thi exmple. Idel Actutor Non-idel Actutor 1 A/S 2 dec. A/S 2 cen. A/S 1 A/S 2 dec. A/S 2 cen. A/S PI Poition (x,y) (3.0,1.8) (4.0,2.4) (3.0,1.8) (3.0,1.8) (1.0,0.6) (7.0,3.6) (6.0,4,2) (7.0,1.8) (6.0,4.2) (7.0,1.8) K K K Tble 1: PI including non-idel ctutor. 14

15 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. Without Weighting With Weighting 1 A/S 2 dec. A/S 2 cen. A/S 1 A/S 2 dec. A/S 2 cen. A/S PI Poition (7.0,3.6) (6.0,4.2) (7.0,1.8) (6.0,4.2) (7.0,1.8) (5.0,2.4) (4.0,1.8) (6.0,3.6) (6.0,1.8) (5.0,4.8) K K K CONCLUSIONS Tble 2: PI including the frequency weighting function. Thi pper preent the deign of MIMO trtegy for controlling humn-induced vibrtion on floor tructure. The deign proce conit of determining the poition of A/S pir nd the control gin within velocity feedbck cheme. The deign proce conider: (i) time nd frequency weighting for the tte, which re ued to compute the PI, (ii) PI, which i repreenttive of the diiption energy, i minimied, nd (iii) the ctutor dynmic behviour i included. The incluion of the ctutor dynmic led to more relitic reult thn thoe obtined in [6]. Additionlly, the tudy crried out h hown the influence of frequency weighting into the deign proce. It h been demontrted through the PI tht MIMO control improve reult with repect to SISO control nd tht centrlied MIMO behve better thn decentrlied MIMO. Tble 3 gther the pro nd con of the ue of centrlied control with repect to decentrlied control. Thi tudy will contribute to motivte future reerch on MIMO control for floor vibrtion. Intereting topic uceptible to be explored re: optiml plcement of inertil ctutor within MIMO control, more efficient (uully more complicted) control lw thn the DVF control ued here, environmentl nd economic ement of the AVC nd experimentl implementtion on in-ervice floor, mong other. Advntge Ech ctutor conider the vibrtion of the whole ytem Non-trnference of energy Alwy improve reult Didvntge More complicted to be deign Le intuitive deign Tble 3: Advntge nd didvntge of centrlied veru dicentrlied control. REFERENCES [1] A. Ebrhimpour nd R. L. Sck. A review of vibrtion ervicebility criteri for floor tructure. Computer nd Structure 83, ,

16 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. [2] M. J. Hudon nd P. Reynold. Implementtion conidertion for ctive vibrtion control in the deign of floor tructure. Engineering Structure 44, , [3] I. M. Díz, E. Pereir nd P. Reynold. Integrl reonnt control cheme for cncelling humn-induced vibrtion in light-weight pedetrin tructure. Structurl Control nd Helth Monitoring 19, 55 69, [4] I. M. Díz, E. Pereir, M. J. Hudon nd P. Reynold. Enhncing ctive vibrtion control of pedetrin tructure uing inertil ctutor with locl feedbck control. Engineering Structure 41, , [5] M. J. Hudon, P. Reynold nd D. Nywko. Efficient deign of floor tructure uing ctive vibrtion control. ASCE Structure Congre 401 (35), [6] L. M. Hngn, E. C. Kulekere, K. S. Wlgm nd K. Premrtne. Optiml plcement of ctutor nd enor for floor vibrtion control. Journl of Structurl Engineering 126(12), , [7] ISO Mechnicl vibrtion nd hock evlution of humn expoure to wholebody vibrtion. Prt 1. Generl requirement. Interntionl Orgniztion for Stndrdiztion, [8] R. S. Burn. Advnced Control Engineering. Butterworth-Heinemnn, [9] I. M. Díz nd P. Reynold. On-off nonliner ctive control of floor vibrtion. Mechnicl Sytem nd Signl Proceing 24, , [10] A. Preumont. Vibrtion Control of Active Structure: An Introuduction. Kluwer Acdemic Publiher, [11] I. M. Díz nd P. Reynold. Accelertion feedbck control of humn-induced floor vibrtion. Engineering Structure 32(1), , [12] BS Guide to meurement nd evlution of humn expoure to whole-body mechnicl vibrtion nd repeted hock. Britih Stndrd Intitute, [13] A. L. Smith, S. J. Hick, nd P. J. Devine. Deign of floor for vibrtion: A new pproch ( P354). The Steel Contruction Intitute, [14] F. J. Cr, J. Cpio, J. Jun nd E. Alrcón. An pproch to opertionl modl nlyi uing the expecttion mximiztion lgorithm. Mechnicl Sytem nd Signl Proceing 31, ,

17 Iván M. Díz, Emilino Pereir, Crlo Znuy nd Critin Alén. [15] APS Mnul 400. Intruction Mnul Electro-Sei Model 400 Shker. APS Dynmic, INC.,