MICROVIBRATION isolation has become a growing research

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1 462 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 11, NO. 4, AUGUST 2006 Dvlopmnt of a Thr-Axis Activ Vibration Isolator Using Zro-Powr Control Md. Emdadul Hoqu, Studnt Mmbr, IEEE, Masaya Takasaki, Associat Mmbr, IEEE, Yuji Ishino, and Takshi Miuno, Mmbr, IEEE Abstract This papr prsnts th dvlopmnt of an activ 3-dgr-of-frdom (DoF) vibration isolation systm using ropowr magntic suspnsion. Th dvlopd systm is capabl to supprss dirct disturbancs and isolat ground vibrations of th 3-DoF motions, associatd with vrtical translational and rotational mods. Two catgoris of control stratgy for th actuators ar proposd, i.., local control and mod control. Th lattr mthod allows to ovrcom limitations of th poor prformancs for rotational mods xhibitd by th formr. A mathmatical modl of th systm is drivd and ach DoF motion is tratd sparatly for th control systm. It is dmonstratd analytically that th infinit stiffnss to static dirct disturbancs can b gnratd and th rsonanc pak du to floor vibration can ffctivly b supprssd for th systm. Morovr, th xprimnts hav bn carrid out to masur th static and dynamic rsponss of th isolation tabl to dirct disturbancs, and transmissibility charactristic of th isolator from th floor. Th rsults indicat good vibration isolation and attnuation prformancs, and show th fficacy of th dvlopd isolator for industrialiation. Indx Trms Activ control, local control, mod control, vibration isolation, ro-powr control. I. INTRODUCTION MICROVIBRATION isolation has bcom a growing rsarch fild du to th dmand of high-prformanc systms, and th advnt of micro- and nanotchnology in various scintific and industrial filds such as smiconductor manufacturing, biomdical nginring, arospac quipmnts, and high-prcision masurmnts. Ths hi-tch rsarch arnas nd sophisticatd systms that ar isolatd from microvibrations. For vibration isolation systms, it is invitabl to isolat ground vibrations in addition to th ffct of dirct disturbancs. Dirct disturbancs to th systm du to th chang of load, us of lctric motors and rotating dvics on th tabl, and ground vibrations causd by othr prim movrs, and arthquak and movmnt of vhicls can, howvr, b th sourc of dtrimntal vibrations that may influnc th ffctivnss and accuracy of oprations, and objctiv prformancs. Gnrally, th vibration-control rsarch can b dividd into two catgoris, i.., activ and passiv control. For th formr, xtrnal nrgy is ncssary. On th othr hand, no xtrnal nrgy Manuscript rcivd Novmbr 22, 2004; rvisd Dcmbr 20, Rcommndd by Tchnical Editor R. Rajamani. This work was supportd in part by a Grant-in-Aid for th Dvlopmnt of Innovativ Tchnology from th Ministry of Education, Cultur, Sports, Scinc, and Tchnology of Japan. Th authors ar with th Dpartmnt of Mchanical Enginring, Saitama Univrsity, Saitama , Japan (-mail: mhoqu@mch.saitama-u.ac.jp; masaya@mch.saitama-u.ac.jp; ishino@mch.saitama-u.ac.jp; miar@mch. saitama-u.ac.jp). Digital Objct Idntifir /TMECH is ndd for th lattr tchniqu, and th vibration supprssion is stabl if th dynamic charactristic of th primary systm ar unchangd [1]. Suspnsion with highr stiffnss can b usd for supprssing th ffct of dirct disturbancs whil that of lowr stiffnss is suitabl for isolating ground vibrations in cas of convntional passiv-typ vibration isolation systm [2]. So a tradoff btwn th suspnsions is ncssary, which is th major drawback of this control tchniqu. Activ control can ovrcom this stback and has bn applid to svral vibration isolation dvics rcntly [3] [7]. Howvr, this tchniqu rquirs xtrnal nrgy, in on hand, and highprformanc snsors, such as srvo-typ acclromtrs, on th othr, and maks th systm rathr xpnsiv. To ovrcom ths difficultis, th authors hav proposd an activ vibration-control tchniqu using ro-powr magntic suspnsion [8]. This tchniqu usually rquirs only ddycurrnt rlativ-displacmnt snsors that cost far lss than srvo-typ acclromtrs. Morovr, thr is no stady powr consumption in th systm during stabl opration [9], [10]. Sinc a ro-powr systm bhavs as if it has a ngativ stiffnss, infinit stiffnss against disturbancs on th isolation tabl can b achivd by combining it with a normal spring in sris. It nabls th systm to hav good charactristics both in rducing vibration transmittd from th ground and in supprssing dirct disturbing forc. It can b notd that ngativ stiffnss can b ralid by ithr passiv or activ tchniqus. Platus [11], [12] prsntd a passiv-typ vibration isolator by conncting a ngativ stiffnss in paralll with a normal spring, and th isolator stiffnss was mad to approach ro for ground vibration isolation only. Howvr, th ffct of dirct disturbanc was not addrssd in th rsarch. Trumpr and Sato [7] dvlopd an isolator by conncting an activ ngativ stiffnss spring in paralll with a positiv spring that achivd good vibration isolation prformanc and platform rlvling by position and vlocity control of th platform. Whras, in that cas, xcssiv hat was gnratd in th actuator causd by driv currnts and powr was consumd by th systm. Thrfor, th motivation of this papr is to dvlop a vibration isolator with low cost and to downsi th powr consumption abruptly. A singl-axis apparatus was manufacturd for basic xprimntal study [13]. Th xprimnts that wr carrid out with th apparatus hav dmonstratd th ffctivnss of th mthod for gnrating infinit (high) stiffnss against static dirct disturbanc. Th control systms of raliing infinit stiffnss can also b gnralid by using a linar actuator, instad of a hybrid magnt [14]. This papr is concrnd with th dvlopmnt of a thrdgr-of-frdom (3-DoF) vibration isolation apparatus aiming /$ IEEE

2 HOQUE t al.: DEVELOPMENT OF A THREE-AXIS ACTIVE VIBRATION ISOLATOR USING ZERO-POWER CONTROL 463 Fig. 1. Basic modl of ro-powr magntic suspnsion systm. at industrialiation, and dsign of controllrs basd on a thortical modl. 3-DoF motions of th isolation tabl in th vrtical and rotational motions ar succssfully controlld by th proposd systm. This papr is organid as follows. First, th concpt of vibration isolation systm using ngativ stiffnss is brifly dscribd. Scond, a basic modl of th dvlopd systm is analyd and control stratgis ar discussd. Finally, xprimntal procdurs and rsults ar prsntd to dmonstrat th fficacy of th proposd systm. II. CONCEPT OF VIBRATION ISOLATION SYSTEM A. Basic Principl Virtually infinit (high) stiffnss of a spring can b gnratd by conncting a normal softr spring in sris with a spring that has ngativ stiffnss and qual magnitud [8], [14]. Ngativ stiffnss is ralid by using ro-powr magntic suspnsion, which is discussd in Sction II-B. Whn two springs with spring constants of k 1 and k 2 ar connctd in sris, th total stiffnss k c is givn by k c = k 1k 2. (1) k 1 + k 2 This quation shows that th total stiffnss bcoms lowr than that of ach spring whn normal springs ar connctd. Howvr, if th absolut valus of th springs ar qual and on of th springs has ngativ stiffnss that satisfis th rsultant stiffnss bcoms infinit, i.., k 1 = k 2, (2) k c =. (3) This rsarch applis this principl of gnrating high stiffnss against dirct disturbanc to vibration isolation systms. Morovr, if th stiffnss of ach spring is low nough, th systm is capabl to isolat ground vibrations as wll. B. Zro-Powr Magntic Suspnsion 1) Basic Modl: A singl-dof-of-motion modl for dscribing ro-powr magntic suspnsion is shown is Fig. 1. Th suspndd objct with mass of m is assumd to mov only in th vrtical translational dirction. Th quation of motion is givn by mẍ = k s x + k i i + f d, (4) whr x is th displacmnt of th suspndd objct; k s is th gap-forc cofficint of th magnt; k i is th currnt-forc cofficint of th magnt; i is th control currnt; and f d is th disturbanc acting on th suspndd objct. Th transfr function rprsntation of th dynamics dscribd by (4) bcoms 1 X(s) = s 2 [a 23 I(s)+d 0 F d (s)], (5) a 21 whr ach Laplac-transformd variabl is dnotd by its capital, and a 21 = k s m, a 23 = k i m, d 0 = 1 m. 2) Dsign of Control Systm: Th ro-powr control oprats to accomplish lim i(t) =0, (6) t for stpwis disturbancs. Th minimal ordr compnsator achiving ro-powr control and assigning th closd-loop pols arbitrarily can b rprsntd as [15], [16] I(s) = s( h 2 s + h 1 ) s 2 X(s), (7) + g 1 s + g 0 and th charactristic polynomial of th closd-loop systm is obtaind as =s 4 + g 1 s 3 +( a 0 + g 0 + b 0 h2 )s 2 +( a 0 g 1 + b 0 h1 )s a 0 g 0. (8) Assuming that th charactristic polynomial spcifying th dsird location of th roots is t d (s) =(s 2 +2ζ 1 ω 1 s + ω1)(s ζ 2 ω 2 s + ω2). 2 (9) th cofficints of g i s and h i s of th controllr of (7) ar dtrmind uniquly by comparing th cofficints in (8) and (9). 3) Ngativ Stiffnss: Whn a constant forc F 0 is applid to th suspndd objct, th suspndd objct is maintaind at a position satisfying 0=k s x( )+k i i( )+F 0, (10) in th stady stats. In th ro-powr control systm, th coil currnt convrgs to ro, i.., i( ) =0. (11) Thrfor, x( ) = F 0. (12) k s Th ngativ sign apparing in th right-hand sid vrifis that th nw quilibrium position is in th dirction opposit to th applid forc. It indicats that th ro-powr control systm bhavs as if it has ngativ stiffnss.

3 464 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 11, NO. 4, AUGUST 2006 and that of th middl tabl can b writtn as [ M] θx = f m x + f p m p θy m x, (14) y m p y whr [M] =diag(m, J x,j y ), (15) [ M] =diag( m, J x, J y ), (16) Fig. 2. Vibration isolation systm using ro-powr magntic suspnsion. C. Configuration of Vibration Isolation Systm A schmatic drawing of th proposd vibration isolation systm is shown in Fig. 2 [13]. A middl tabl m 1 is connctd to th bas through a spring k 1 and a dampr c 1 that work as a convntional vibration isolator. An lctromagnt for ro-powr magntic suspnsion is fixd to th middl tabl. Th part of an isolation tabl m 2 facing th lctromagnt is mad of soft iron matrial. This systm can rduc vibration transmittd from ground by stting k 1 small and, at th sam tim, gnrat infinit stiffnss against dirct disturbanc by stting th amplitud of th ngativ stiffnss qual to k 1. III. DEVELOPED 3-DOF VIBRATION ISOLATOR A. Modl A 3-DoF vibration isolator has bn dvlopd so as to supprss dirct disturbancs, as wll as ground vibrations. Th schmatic diagram of th manufacturd vibration isolator for xprimntal study is shown in Fig. 3. It has a circular isolation tabl, a middl tabl, and a bas. Th ngativ stiffnss is gnratd by thr hybrid magnts, which ar fixd to th middl tabl and suspnd th isolation tabl. Th middl tabl is suspndd by thr pairs of springs and damprs from th bas. Thy ar locatd at th vrtics of an quilatral triangl. Each hybrid magnt is alignd with a pair of spring and dampr vrtically. Hnc, th isolation tabl is suspndd by thr pairs of normal and ngativ springs so that th thr mods (3-DoF motions) of th tabl can b controlld by th proposd mchanism. Thy ar: on translational motion in th vrtical dirction (Z) and two rotational motions, roll (Θ x ) and pitch Θ y. Th coordinat systm is shown in Fig. 3(b). It is assumd that th roll and pitch angls ar so small that cosθ x = 1, sinθx = θx, cosθ y = 1, and sinθy = θy, whr θ x,θ y ar th roll and pitch angls of th isolation tabl. Th quations of motion of th isolation tabl can b writtn as [M] θx = f m x + f d m d θ y m x, (13) y m d y m J x J y f m x m y f d m d x m d y f p m p x m p y is th mass of th isolation tabl; is th inrtial momntum of th isolation tabl about x-axis; is th inrtial momntum of th isolation tabl about y-axis; is th displacmnt of th cntr of th isolation tabl; is th -dirction total forc by th hybrid magnts; is th total momnt about x- axis by th hybrid magnts; is th total momnt about y- axis by th hybrid magnts; is th -dirction dirct disturbanc; is th dirct disturbanc about th x-axis; is th dirct disturbanc about th y-axis; is th -dirction total forc by th springs and damprs; is th total momnt about x-axis by th springs and damprs; and is th total momnt about y-axis by th springs and damprs. Th corrsponding rprsntation of th middl tabl is dnotd by th ovrbar notations. Whn th hybrid magnts ar locatd as shown by Fig. 3(c), th total forc and torqus ar rlatd with th forcs gnratd by th thr hybrid magnts as and f m x m y = R a f 1 f2 f3 R a = r, (17) 2 3r 2 r r 2 r 2, (18) whr fk is th attractiv forc of th hybrid magnt k(k = 1, 2, 3) and r is th distanc of th hybrid magnts from th cntr. Th forc of ach magnt is approximatly givn by f k = k s g k + k i i k (k =1, 2, 3), (19) whr g k is th dviation of th gap btwn th lctromagnt and th targt on th isolation tabl and i k is th control currnt. Th gaps ar rlatd with th displacmnts as g 1 g 2 = R b θx θ x, (20) g 3 θ y θ y

4 HOQUE t al.: DEVELOPMENT OF A THREE-AXIS ACTIVE VIBRATION ISOLATOR USING ZERO-POWER CONTROL 465 Fig. 3. Schmatic diagram of th dvlopd vibration isolator. and 1 0 r R b = r 1 2, (21) 3r 2 1 3r 2 It is to b notd that th lctromagnts on th middl tabl ar abov th targts on th isolation tabl at th gaps. Th total forc and torqus by th springs and damprs ar givn by f p m p x m p y = R a f p 1 f p 2, f p 3 ( ) d = R a k p + c p dt ẑ1 ẑ 2 ẑ 3 r 2 R b θx θ y, (22) whr ẑ k is th displacmnt of th bas at th position k; k p is th stiffnss of th spring; and c p is th damping constant of th dampr. It is found from (13) to (22) that th dynamics of th thr mods can b tratd sparatly and, in addition, ach is rprsntd in a similar form such as m ξ ξ = k ξ s (ξ ξ)+k ξ i iξ + w ξ, (23) and m ξ ξ = k ξ s (ξ ξ) k ξ i iξ (kp ξ + c ξ d p dt )( ξ ˆξ). (24) Th variabls and cofficints for ach mod ar dfind as shown in Tabl I. B. Control Stratgy Th dvlopd vibration isolation systm is a thr-channl multipl-input multipl output systm. Sinc th numbr of actuators for th ro-powr control and th numbr of mods ar qual, two control stratgis ar possibl. Thy ar local con- TABLE I VARIABLES AND COEFFICIENTS OF EACH MODE trol [15] and mod control [16]. In th formr, th coil currnt of ach magnt is controlld on th basis of local information at th corrsponding position as shown in Fig. 4(a). In th lattr, a controllr is dsignd for ach of th mods (Z, Θ x, and Θ y ) as shown in Fig. 4(b). Snsors 1, 2, and 3 ar th displacmnt signals of th tabl masurd from th corrsponding hybrid magnts, rspctivly. In th cas of mod-basd control, th displacmnt signal of thr mods (X,X θx, and X θy ) ar calculatd from th snsor signals. Again th control currnts (i 1,i 2,i 3 ) for thr hybrid magnts ar calculatd from

5 466 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 11, NO. 4, AUGUST 2006 Fig. 4. Block diagram of th proposd controllrs. (a) Local control. (b) Mod control. th outputs (i,i θx, and i θy ) of th ro-powr controllrs. Th ro-powr controllr of ach channl is dsignd to hav such dynamics as (7) I ξ (s) = s( h 2 s + h 1 ) s 2 ξ(s) = sc ξ 2 (s)ξ(s). (25) + g 1 s + g 0 C. Rspons to Dirct Disturbanc It is assumd for simplicity that th initial valus ar ro. Equations(23) (25) yild Ξ(s) = (cξ ps + kp)(k ξ ξ i cξ 2 (s)s kξ s ) ˆΞ(s) + t 1(s)+k ξ i cξ 2 (s)s kξ s Ξ(s) = (cξ ps + kp)t ξ 2 (s) ˆΞ(s) W ξ (s), (26) + kξ i cξ 2 (s)s kξ s W ξ (s), (27) t 1 (s) = m ξ s 2 + c ξ ps + kp, ξ (28) t 2 (s) =m ξ s 2 + k ξ i cξ 2 (s)s kξ s, (29) =t 1 (s)t 2 (s)+m ξ s 2 (k ξ i cξ 2 (s)s kξ s ). (30) To stimat th stiffnss for dirct disturbanc, th dirct disturbanc W ξ is assumd to b stpwis, i.., W ξ = F 0 (F 0 : const). (31) s Whn th vibration of th floor is nglctd, th stady-stat displacmnt of th tabl is obtaind as ξ( ) F 0 = lim s 0 m ξ s 2 +(c ξ p + k ξ i cξ 2 (s))s + kξ p k ξ s = 1 k ξ p 1 k ξ s (32) =0 (whn k ξ p = k ξ s ). (33) Fig. 5. Analytical displacmnt transfr function (transmissibility) of th isolator from floor. Sinc k ξ p = k ξ s is satisfid in thr mods, thrfor, th suspnsion systm btwn th isolation tabl and th floor has infinit stiffnss. D. Rspons to Floor Vibrations Whn th dirct disturbancs ar assumd to b nglctd, th transmissibility of th isolator from th floor during floor xcitation along vrtical translation mod (Z), can b writtn from (26) as Ξ(s) ˆΞ(s) = (3c ps +3k p )(k i c 2(s)s 3k s ). (34) Th paramtrs of (34) ar chosn as, k i =57.2 N/A, 3k p = 3k s =59.5 N/mm and, th closd-loop pols for c 2 ar slctd by putting ω(= ω 1 = ω 2 )=2π 4 [1/s] and ζ(= ζ 1 = ζ 2 )=1.0in (9). Fig. 5 shows th analytical displacmnt transfr function (transmissibility) of th isolator. It is found that a suitabl damping (c p ) btwn bas to middl tabl could supprss th amplitud of rsonanc ffctivly and th vibration isolation prformanc is not worsnd during floor vibrations. IV. EXPERIMENT A. Exprimntal Stup Th photograph of th dvlopd vibration isolation systm is shown in Fig. 6. Each hybrid magnt for ro-powr

6 HOQUE t al.: DEVELOPMENT OF A THREE-AXIS ACTIVE VIBRATION ISOLATOR USING ZERO-POWER CONTROL 467 Fig. 6. Photograph of th dvlopd isolator. magntic suspnsion consistd of a disk-shapd prmannt magnt (30 mm 10 mm) and a 2500-turn lctromagnt. Th prmannt magnt was mad of NdFB matrials. Th stiffnss of ach normal spring was 20 N/mm. As a dampr paralll with th normal spring, an activly controlld lctromagnt was usd. It nabld th stiffnss and damping charactristics of th normal springs to b adjustd flxibly. Th hight, diamtr, and mass of th apparatus wr 400 mm, 440 mm, and 150 kg, rspctivly. Th isolation and middl tabls wighd 22 kg and 23 kg, rspctivly. Th radial motions of th isolation tabl wr confind by th othr thr lctromagnts whil thos of th middl tabl wr constraind by th thr springs for positiv stiffnss. Th rlativ displacmnts of th middl tabl to th bas and thos of th isolation tabl to th middl tabl wr dtctd by six ddy-currnt gap snsors providd by Baumr lctric. Th radial displacmnts of th isolation tabl wr masurd by anothr thr gap snsors, and th radial motions of th tabl wr activly controlld. Dsignd control algorithms wr implmntd with a digital controllr DS1103 supplid by dspace. Th sampling rat was 10 kh. B. Exprimntal Rsults Th xprimnt was carrid out with th controllrs basd on local control and mod control. Furthrmor, th systm prformancs wr valuatd by masuring th static and dynamic rspons of th isolation tabl to dirct disturbancs and th transmissibility charactristics of th isolation tabl from th bas during floor xcitations. 1) Rspons to Dirct Disturbancs: First, th static rspons of th isolation tabl to dirct disturbanc using local control and mod control wr masurd for thr mods. Dirct static loads wr addd to th cntr of th tabl for vrtical translational mod and on th y- and x-axs (150-mm apart from cntr) for roll and pitch mods, rspctivly. Fig. 7 shows th rsults using local control. It is found that displacmnt of th Fig. 7. Static rspons of th local control isolator to dirct disturbanc. (a) Translation (Z). (b) Roll. (c) Pitch. isolator along vrtical translational mod and th rotational angl of th isolator along roll and pitch axis wr small compard to that of th middl tabl. Fig. 8 shows th static charactristic of th isolator using mod control. It is obsrvd from diffrnt mods that th tabl was maintaind almost at th sam position, whil th position of th middl tabl changd proportional to th load. It is also found that th stiffnss of th isolator using mod control was 1.4 tims in th vrtical translation mod, 11.8 tims in th roll mod, and 11 tims in th pitch mod, mor than that of using local control. It is obvious that supprssing dirct disturbancs along rotational mods was wakr in th cas of using local control. It can b notd that positiv stiffnss along rolling axis could b adjustd to mak th rolling stiffnss of th isolator strongr. But, in that cas, th othr two stiffnsss would b wakr. Th sam was tru for pitch axis. Nxt, th dynamic rsponss of th isolation tabl wr masurd. In this cas, th tabl was xcitd by two voic coil motors along th -axis. Fig. 9 shows th frquncy rspons of th isolator in th vrtical translational (Z) mod whn local

7 468 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 11, NO. 4, AUGUST 2006 Fig. 9. Frquncy rspons of th local control isolator to dirct disturbancs along Z axis. Fig. 8. Static rspons of th mod control isolator to dirct disturbanc. (a) Translation (Z). (b) Roll. (c) Pitch. control was usd. It is sn from th figur that th displacmnt of th isolation tabl at low frquncy (0.015 H) was much lowr ( 28 db) than that of th middl tabl. Fig. 10 shows th rsults of using mod control. In this xprimnt, th closd-loop pols of th controllr wr assignd by varying th dsign frquncy (ω 1 = ω 2 = ω) from2π 3 [1/s] to 2π 6 [1/s], whil th damping ratio (ζ 1 = ζ 2 = ζ) was fixd to 1.0. It was found from Fig. 10(a) that th displacmnt of th isolation tabl ( 48 db) is much lowr than th middl tabl ( 37 db) at 0.15 H. Fig. 10(b) and (c) shows that th displacmnt of th isolation tabl is furthr rducd ( 69 db at ω =2π 6 [1/s]) by slcting highr closd-loop pols. 2) Rspons to Floor Vibrations: In th scond xprimnt, th absolut transmissibility of th isolator (/ẑ) from th floor was masurd at th cntr of th tabl by xciting th bas of th apparatus vrtically by a pnumatic actuator. Fig. 11 shows th transmissibility charactristics of th isolator using local control. Th xprimnts wr carrid out by changing th damping cofficints (c p ) of th dampr lctromagnt locatd btwn th bas and th middl tabl. Th rsult shows Fig. 10. Frquncy rsponss of th mod control isolator to dirct disturbancs along Z axis. (a) ω =2π 3 [1/s]. (b) ω =2π 4.5 [1/s]. (c) ω =2π 6 [1/s]. Fig. 11. Absolut transmissibility of th local control isolator from th floor during floor xcitation.

8 HOQUE t al.: DEVELOPMENT OF A THREE-AXIS ACTIVE VIBRATION ISOLATOR USING ZERO-POWER CONTROL 469 REFERENCES Fig. 12. Absolut transmissibility of th mod control isolator from th floor during floor xcitation. that incrasing th damping cofficint could improv th vibration isolation prformancs. Th isolation prformanc was furthr improvd whn mod control was usd, as shown in Fig. 12. Th closd-loop pols of th ro-powr controllr for Z-mod wr slctd as ω(= ω 1 = ω 2 )=2π 3 [1/s] and ζ(= ζ 1 = ζ 2 )=1.4. It is obvious that th rsonanc pak was dampd down in cas of highr damping. It agrd with th thortical transmissibility calculatd from th modl (Fig. 5), xcpt that th rsonanc frquncy of th middl tabl and that of th pnumatic vibration tabl affctd th xprimntal rsults. It is rvald that ground vibration isolation prformanc, nonthlss, was not worsnd in th cas of gnrating high stiffnss to supprss th ffct of dirct disturbancs. V. CONCLUSION An activ 3-DoF vibration isolation systm using ro-powr controllr was dvlopd and two control stratgis wr proposd. Th xprimntal rsults rvald that th mod-basd controllr was bttr for multi-dof systm, whil local control could bttr b applicabl for singl-dof and unit-basd systm. Th dvlopd vibration isolator using ddy-currnt gap snsor ralid high stiffnss to static and low-frquncy dirct disturbancs and showd good capability to supprss dirct disturbanc. It is obvious from th transmissibility charactristic that th systm could isolat ground vibration in vrtical dirction ffctivly. Th systm prformancs, both for supprssing th ffct of dirct disturbancs and isolating ground vibrations, could furthr b improvd by assigning th propr closd-loop pol of th ro-powr controllrs and slcting suitabl damping btwn th bas to th middl tabl. It is hopd that th controllr has a possibility to b usd in th wid application rang. Th dvlopd isolator prformd vry wll in th analytical and xprimntal phas and, with furthr dvlopmnt, it could matriali th basis of an industrially and commrcially fasibl, adaptabl, and compliant isolator for hi-tch systms. ACKNOWLEDGMENT Th authors would lik to thank H. Suuki for his contributions to this projct rgarding th dsign and fabrication of th apparatus. [1] S. T. Ho, H. Matsuhisa, and Y. Honda, Passiv vibration supprssion of bam with piolctric lmnts, JSME Int. J., Sr. C, vol. 43, no. 3, pp , [2] E. I. Rivin, Passiv Vibration Isolation. Nw York: ASME, [3] M. Yasuda and M. Ikda, Doubl-activ control of microvibration isolation systms to improv prformancs (application of two-dgr-offrdom control), Trans. Jpn. Soc. Mch. Eng.,vol.59,no.562,pp , [4] H. Yoshioka, Y. Takahashi, K. Katayama, T. Imaawa, and N. Murai, An activ microvibration isolation systm for hi-tch manufacturing facilitis, ASME J. Vib. Acoust., vol. 123, pp , [5] M. Yasuda, T. Osaka, and M. Ikda, Fdforward control of a vibration isolation systm for disturbanc supprssion, in Proc. 35th IEEE Conf. Dcision Contr., Kob, Japan, 1996, pp [6] K. Watanab, S. Hara, Y. Kanmitsu, T. Haga, K. Yano, T. Miuno, and R. Katamura, Combination of H and PI control for an lctromagntically lvitatd vibration isolation systm, in Proc. 35th IEEE Conf. Dcision Contr., Kob, Japan, 1996, pp [7] D. L. Trumpr and T. Sato, A vibration isolation platform, Mchatron., vol. 12, pp , [8] T. Miuno, Proposal of a vibration isolation systm using ro-powr magntic suspnsion, in Proc. Asia-Pac. Vib. Conf.,2001,vol.2,pp [9] A. V. Sabnis, J. B. Dndi, and F. M. Schmitt, A magntically suspndd larg momntum whl, J. Spaccraft, vol. 12, pp , [10] M. Morishita, T. Aukiawa, S. Kanda, N. Tamura, and T. Yokoyama, A nw Maglv systm for magntically lvitatd carrir systm, IEEE Trans. Vh. Tchnol., vol. 38, no. 4, pp , [11] D. L. Platus, Ngativ-stiffnss-mchanism vibration isolation systms, in Proc. SPIE Conf. Vib. Contr. Microlctron Opt. Mtrol., 1991, vol. 1619, pp [12], Ngativ-stiffnss-mchanism vibration isolation systms, in Proc. SPIE Conf. Curr. Dv. Vib. Contr. Optomch. Syst., 1999, vol. 3786, pp [13] T. Miuno, Vibration isolation systm using ro-powr magntic suspnsion, prsntd at th Prprints of th 15th World Congrss IFAC, 2002, Papr 955. [14] T. Miuno, T. Toumiya, and M. Takasaki, Vibration isolation systm using ngativ stiffnss, JSME Int. J., Sr. C,vol.46,no.3,pp , [15] T. Miuno, M. Takasaki, H. Suuki, and Y. Ishino, Dvlopmnt of a thr-axis activ vibration isolation systm using ro-powr magntic suspnsion, in Proc. 42nd IEEE Conf. Dcision Contr., Hawaii, Dc. 2003, pp [16] M. E. Hoqu, M. Takasaki, Y. Ishino, and T. Miuno, Dsign of a modbasd controllr for 3-DoF vibration isolation systm, in Proc IEEE Conf. Robot. Autom. Mchatron., Singapor, pp Md. Emdadul Hoqu (S 06) rcivd th B.Sc. and M.Eng. dgrs in mchanical nginring from Rajshahi Univrsity of Enginring and Tchnology, Rajshahi, Bangladsh, and Nanyang Tchnological Univrsity, Singapor, in 1996 and 2003, rspctivly. Currntly, h is working toward th Ph.D. dgr in th Dpartmnt of Mchanical Enginring, Saitama Univrsity, Saitama, Japan. Sinc 1996, h has bn with Rajshahi Univrsity of Enginring and Tchnology. His currnt rsarch intrsts includ activ control, magntic lvitation, ro-powr control, and vibration isolation. Mr. Hoqu is a mmbr of th Amrican Socity of Mchanical Enginrs, th Socity of Instrumnt and Control Enginrs, Japan, and Institution of Enginrs, Bangladsh.

9 470 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 11, NO. 4, AUGUST 2006 Masaya Takasaki (A 05) rcivd th B.E., M.E., and Ph.D. dgrs from th Univrsity of Tokyo, Tokyo, Japan, in 1996, 1998, and 2001, rspctivly. Sinc 2001, h has bn a Rsarch Associat in th Dpartmnt of Mchanical Enginring at Saitama Univrsity, Saitama, Japan. His currnt rsarch intrsts includ magntic suspnsion, ultrasonic application for mchatronics, surfac acoustic wav utiliation, and tactil display. Dr. Takasaki is a mmbr of th Japan Socity of Mchanical Enginrs, th Socity of Instrumnt and Control Enginrs, th Institut of Elctrical Enginrs of Japan, th Japan Socity for Prcision Enginring, th Japan Socity of Applid Elctromagntics and Mchanics, and th Virtual Rality Socity of Japan. Yuji Ishino graduatd from th Univrsity of Tsukuba, Tsukuba, Japan, in Sinc 1988, h has bn working as a Tchnician with th Dpartmnt of Mchanical Enginring, Saitama Univrsity, Saitama, Japan. His currnt rsarch intrsts includ magntic suspnsion, vibration isolation, and mass masurmnt undr microgravity conditions. Takshi Miuno (M 00) graduatd from th Dpartmnt of Mathmatical Enginring and Instrumntation Physics, Univrsity of Tokyo, Tokyo, Japan, in H rcivd th M.Eng. and Ph.D. dgrs from th Univrsity of Tokyo, in 1980 and 1985, rspctivly. From 1980 to 1985, h was a Rsarch Associat at th Institut of Industrial Scinc, Univrsity of Tokyo. During , h was an Assistant Profssor at th Polytch Univrsity, Japan. From 1988 to 2000, h was an Associat Profssor, and sinc 2000, h has bn a Profssor in th Dpartmnt of Mchanical Enginring, Saitama Univrsity, Saitama, Japan. From 1990 to 1991, h workd at th Swiss Fdral Institut of Tchnology (Eidgnössisch Tchnisch Hochschul Zürich), Zurich, Switrland. His currnt rsrach intrsts includ magntic barings, magntic and lctric suspnsion tchnology, vibration control, mchatronics, and application of dynamic vibration absorbr. Prof. Miuno is a mmbr of th Amrican Socity of Mchanical Enginrs, th Socity of Instrumnt and Control Enginrs, th Japan Socity of Mchanical Enginring, th Institut of Systms, Control, and Information Enginrs, and th Japan Socity for Prcision Enginring. H is th rcipint of numrous awards for papr and rsarch prformancs.