Pneumatic Three-axis Vibration Isolation System Using Negative Stiffness
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1 Proeei of te t IEEE Coferee o Deiio Cotrol, te Europe Cotrol Coferee Seville, Spi, Deeer -, TC6. Peuti Tree-i Virtio Ioltio Syte Ui Netive Stiffe Tei Miuo, Meer, IEEE, Mto Murit, My Ti, Yuji Iio Atrt A tree-i tive virtio ioltio yte wit peuti tutor for eerti etive tiffe w evelope. A otrol eto of relii upeio wit etive tiffe y te tutor w erive. It w ipleete i te evelope yte were e tutor w otrolle lolly. It w eotrte eperietlly tt te equlitio of te plitue of etive poitive tiffe ele te yte to ve ero oplie to iret iture. I. INTRODUCTION or irovirtio ioltio, i perfore i require i upprei te effet of iret iture i itio to ioltio fro rou virtio. I ovetiol pive-type virtio ioltio yte, owever, tre-off etwee te i ievitle eue ier tiffe of upeio i etter for te forer wile lower tiffe i etter for te ltter. Miuo propoe uique ppro to rei trou te tre-off [],[]. Te propoe virtio ioltio yte ue ero-power eti upeio yte. Sie te ero-power yte eve if it etive tiffe, ifiite tiffe it tti iture o te ioltio tle e ieve y oii it wit orl pri. It ele te yte to ve oo rteriti i ot reui virtio tritte fro rou upprei iret virtio. I ero-power eti upeio yte, owever, te itue of etive tiffe i futio of te p etwee te eletroet te upee ojet. We Muript reeive erury 7,. Ti wor w upporte i prt y Grt-i-Ai for Sietifi Reer B fro te Miitry of Eutio, Culture, Sport, Siee Teoloy of Jp, reer rt fro Suui outio. Tei MIZUNO i wit te Deprtet of Meil Eieeri, Sit Uiverity, Sio-Ouo, Sit 8-87 Jp orrepoi utor to provie poe: ; f: ; e-il: ir@e.it-u..jp. Mto MURASHITA w wit Sit Uiverity, Sit 8-87 Jp. He i ow wit Suui Motor Corportio, Jp. My TAKASAKI i wit te Deprtet of Meil Eieeri, Sit Uiverity, Sio-Ouo, Sit 8-87 Jp e-il: y@e.it-u..jp. Yuji ISHINO i wit te Deprtet of Meil Eieeri, Sit Uiverity, Sio-Ouo, Sit 8-87 Jp e-il: yiio@e.it-u..jp. te o te ioltio tle vrie, terefore, te etive tiffe vrie fro te oil vlue o tt te tiffe it iret iture eoe lower []. I ti pper, we propoe to ue peuti tutor ite of eletroet for eerti etive tiffe. It eep te tiffe very i for wier re of opertio t te forer yte. I itio, peuti tutor upport evy tle y irei teir effetive re te o y ir. Ti pper i orie follow. irt, te oept of te propoe virtio ioltio yte i riefly erie. Seo, otrol eto of relii etive tiffe wit peuti tutor i lrifie y trfer futio ppro. Tir, frite tree-i tive virtio ioltio yte ui peuti tutor i erie. ourt, it perfore to iret iture i etite eperietlly. II. CONCEPT O VIBRATION ISOLATION SYSTEM A. Seril Coetio of Two Spri Te i of ti etio i to ow tt ifiite tiffe e relie y oeti orl pri wit pri tt etive tiffe i erie. We two pri wit pri ott of re oete i erie, te totl tiffe i ive y Ti equtio ow tt te totl tiffe eoe lower t tt of e pri we orl pri re oete. However, if oe of te pri etive tiffe tt tifie, te reultt tiffe eoe ifiite, tt i. Ti reer pplie ti priiple of ievi ero oplie to iret iture ti o te virtio ioltio tle //$. IEEE 8
2 B A B. Cofiurtio of Virtio Ioltio Syte i. ow te eerl ofiurtio of te propoe ei []. A ile i oete to te e trou pri per tt wor ovetiol virtio ioltor; uffiiet ioltio fro rou virtio i ieve y etti to e ll. A lier tutor i tte to te ile. Te tutor upe rive ioltio tle. Te lier tutor i otrolle for te upeio yte to ve etive tiffe. I te iitil tey tte ow i i., te ite etwee te tle te e i ept to e L. We te of te tle iree y, te ite iree y L ow i i.. Te ipleet of te tle i i te iretio oppoite to te e fore o tt te tti tiffe of te upeio i ive y L. We te tutor i otrolle i ti wy, te yte ow y i. eve follow. We te ioltio tle i ujet to owwr fore f, te tle woul ove upwr y f / if te ile were fie. Mewile, te ile ove owwr y f / eue of te iree of te upeio fore. We, te iree i te let of te tutor i elle y te owwr ipleet of te ile. Tu te ioltio tle i itie t te e poitio efore o tt te yte ero oplie to iret tti iture. III. REALIZATION O NEGATIVE STINESS A. Moel A peuti ylier of ipr type i frite for te relitio of upeio wit etive tiffe. i. ow it eti rwi. Ti type of ylier i rterie y ort troe ll fritio. i. ow lytil oel for iui te otrol yte ei. Te ylier ove tle, wi i oete to te e trou pri per. Te equtio of otio i ive y f f, were f i te fore eerte y te ylier, f i iret iture ti o te tle. Te fore f i ive y Ioltio tle Atutor Preure eor Mile Top view Dipr i.. Geerl truture of te propoe virtio ioltio yte. Air Mover Cro etio view lo te lie A-B i.. Seti rwi of peuti ylier L L+ L Tle f Cylier iitil tte e f i.. Opertio of te tutor i.. Bi oel 8
3 Ap f, 6 were A i te effetive re of te ylier, te o y ir, p i te preure of te ir. It i ue tt te preure i otrolle wit vlve to tify I T P i, 7 were i i te oil urret of te vlve, i i te preure-urret oeffiiet of te vlve, T i te tie ott epei o te yi rteriti. ro to 7, we et I t X o, 8 were t o, T T T T A i T B. Cotrol Syte Dei Te ipleet of te tle i trete output il ere. Coieri lier output fee otrol, we repreet te otrol iput X I. 9 We te trfer futio of te otroller i proper, te polyoil re repreete,. Sutituti 9 ito 8 le to t X o. Te iture i ue to e tepwie o tt it e oele : ot. It i ue tt te otroller i elete to tilie te loe loop yte. Te tey-tte ipleet i ive y li. or te yte to ve etive tiffe wit itue of, te followi equtio ut e tifie. or ii te loe-loop pole ritrrily, tir- or ier-orer opetor re eery. We tir-orer opetor i ue, te rteriti polyoil of te loe-loop yte eoe 6 t 6 To oti yte wit rteriti equtio of te for, 6 t 7 we t te oeffiiet to oti, 8, 9,,. IV. THREE-AXIS VIBRATION ISOLATION SYSTEM A. Eperietl Apprtu i. ow potorp of te frite ylier. It ipr e of ruer wit tie of. It 86
4 effetive etiol re i pproitely. A potorp of ufture eperietl pprtu wit i ylier i ow y i.6. It eti ir i preete y i.7. Te ieter eit i 6, repetively. It irulr ioltio tle irulr ile tle orrepoi to te ile i i.. Te ioltio ile tle wei 6 7, repetively. Te ile tle i upee y tree ylier for poitive tiffe pi, wi orrepo to i i.. Tey re lote t te vertie of equilterl trile o te e. Te ioltio tle i upee y tree Cylier i.. Potorp of te ylier Dipleet eor y Ioltio tle Mile tle Be ylier for etive tiffe, wi re fie to te ile tle. E ylier for etive tiffe i lie wit ylier for poitive tiffe vertilly. Hee, te tree-eree-of-freeo otio of te ioltio tle e otrolle y te propoe eto. Tey re oe trltiol otio i te vertil iretio two rottiol otio, pit roll. Te ipleet of te ioltio tle re etete y tree ey-urret eor, wi lote t te vertie of equilterl trile o te e. Te ipleet of te ile tle i etete iilrly. Te etete ple re ow i i.8, wi re t te ile etwee te tutio poitio ot ollote. Te ipleet t te poitio of e ylier, te ipleet of e otio re lulte fro tee etete il. B. Struture of Cotroller or ulti-el otrol yte, tere re two pproe to otruti te otroller: - lol otrol eetrlie otrol - oe otrol etrlie otrol. I te firt otroller, e tutor i otrolle e o te lol ifortio, wi i te ipleet t te poitio i ti e []. I te eo otroller, opetor i uilt for e oe []. Ti wor opt te firt ppro. E ylier i otrolle wit tir-orer otroller woe oeffiiet re eterie ori to 8 to. Te otrol lorit i ipleete wit DSP-e iitl otroller. Te otrol perio i. V. EXPERIMENTAL RESULTS A. Syte Ietifitio Te preter of te otrolle ojet re etite o te i of frequey lyi. I te ietifitio, tree ylier for etive tiffe re operte we te ile Preure eor i. 6. Potorp of te eperietl pprtu y Cylier for etive tiffe Dipleet eor Ioltio tle Liitter Seor Cylier Seor Cylier Cylier Seor Mile tle Cylier for poitive tiffe Be i. 7. Seti rwi of te eperietl pprtu i. 8. Lotio of ylier eor. 87
5 tle i lpe ot to ove. It i ue tt te ylier otrol vlve for otrolli te re ietil. Tey re rive iulteouly ori to te e eittio il o to operte ile ylier tt ove te ioltio tle i te -iretio. Preter etitio i rrie out for ti virtul ile ylier. i.9 ow te frequey repoe i wi te output il i te ipleet of te tle, te preure of te ylier wile te iput il i te eittio. Tey re pproite y tir-orer firt-orer trfer futio, wi re eterie y ui urve-fitti pror. Te preter of te otrolle ojet re lulte fro tee trfer futio. B. Relitio of Supeio wit Netive Stiffe Supeio wit prerie etive tiffe i relie y te tree ylier. I ti eperiet, te ile i lpe ot to ove. E ylier i otrolle to ve te plitue of etive tiffe to e [N/], [N/]. Te plitue of tiffe i te -iretio i, terefore, et Gi [B] Gi [B] reqey [H] Dipleet rteriti reqey [H] Preure rteriti -9 Pe [e] Pe [e] i.9. requey repoe of te ylier ie lie: eure reult, Bol lie: pproiti urve to e 7 [N/], [N/]. Te eure fore-ipleet rteriti re ow i i. i wi fore ipleet i te owwr iretio re repreete to e poitive, vie ver. Diture fore i proue y putti weit o te ioltio tle. It ow tt te fore-ipleet reltio i quite lier. Te etite tiffe i ~ ~ 7[N/ ], 6 [N/ ]. Te ifferee etwee te prerie eperietl vlue re witi %. i. ow repoe to tepwie iture i te -iretio. Te pole re elete 8 [/ ],. 8,,, [/ ],. 8,,, [/ ],. 8,,. Te iture w eerte y uperipoi retulr il o otrol il. It eotrte tt te ettli tie e reue y etti to e lre. Dipleet [] [N/] [N/] -. ore [N] i.. Relitio of upeio wit etive tiffe Dipleet [] [/ ] [/ [/ Tie [./iv] ] ] i.. Repoe to tepwie iture 88
6 C. Relitio of Supeio wit Zero Coplie I ti eperiet, te lp of te ile tle i relee. E ylier upei te ile tle fro te e i otrolle to relie prerie poitive tiffe. Ietifitio otrol ei for ti ylier re rrie out i er iilr to tt erie i te previou etio. Te ifferee i tt i reple y. p i. ow te ipleet of te ioltio tle to te e, tt of te ioltio tle to te ile tt of te ile to te e of te tree oe. E ylier i otrolle to ve tti tiffe of [N/]. It i oerve tt te poitio of te ioltio tle i itie t te e poitio wile te poitio of te ile e proportio to iret iture i ll te oe. Te rtio of te totl tiffe to te iiviul tiffe i 68 trltio pit yw Ti reult eotrte tt te equlitio of te plitue of etive poitive tiffe ele te yte to ve virtully ero oplie to iret iture. Ale [ e] Dipleet[ ] Poitive tiffe Netive tiffe Dipleet of tle to e ore [N] Trltio Poitive tiffe Netive tiffe AulrAle ipleet of e of to tle to e VI. CONCLUSION A tree-i tive virtio ioltio yte wit peuti tutor w evelope. A otrol lw for relii upeio wit etive tiffe y ui te peuti tutor w erive. Virtully ero oplie w ieve i te tree oe y equlii te plitue of etive poitive tiffe iiviully. urter tuy o virtio ioltio rteriti to rou virtio i uer wy for te iutrilitio of te propoe virtio ioltio yte. REERENCES [] Miuo, T., Propol of Virtio Ioltio Syte Ui Zero-power Meti Supeio, Pro. Ai-Pifi Virtio Coferee, Vol., pp.-7,. [] Miuo, T., Virtio Ioltio Syte Ui Zero-Power Meti Supeio, Preprit of t Worl Core IAC, 9,. [] Miuo, T., Touiy, T. Ti, M., Virtio Ioltio Syte Ui Netive Stiffe, JSME Itertiol Jourl, Serie C, Vol.6, No., pp.87-8,. [] Miuo, T., Ti, M., Suui, H. Iio, Y., Developet of Tree-Ai Ative Virtio Ioltio Syte Ui Zero-Power Meti Supeio, Pro. IEEE Coferee o Deiio Cotrol, pp.9-98,. [] Hoque, M.E., Ti, M., Iio, Y. Miuo, T., Dei of Moe-Be Cotroller for -DO Virtio Ioltio Syte, Pro. IEEE Coferee o Rooti, Autotio Metroi, pp.78-8,. Ale [ e] Torque [N] pit Poitive tiffe Netive tiffe Aulr ipleet of tle to e 6 Torque [N] roll i.. ore-ipleet rteriti of te ioltio yte 89
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