044501-9 K.A.Strain and B.N.Shapiro Rev.Sci.Instrum.83,044501(2012) for all except the x direction,where the model is not over- Losurdo,J.-M.Mackowski,E.Majorana,C.N.Man.M.Mantovani,F. sensitive to the relevant parameters of the suspension and Marchesoni,F.Marion,J.Marque,F.Martelli,A.Masserot,F.Menzinger, the extra performance provided by the modal method is most L.Milano.Y.Minenkov,C.Moins.J.Moreau.N.Morgado,S.Mosca,B. Mours,I.Neri,F.Nocera,G.Pagliaroli,C.Palomba,F.Paoletti,S.Pardi, beneficial. A.Pasqualetti,R.Passaquieti,D.Passuello,F.Piergiovanni,L.Pinard,R. We have presented the rationale and design method for Poggiani,M.Punturo,P.Puppo,P.Rapagnani,T.Regimbau,A.Remil- active damping of the mirror-suspensions of a gravitational lieux,F.Ricci,L.Ricciardi,A.Rocchi,L.Rolland,R.Romano,P.Ruggi wave detector and shown that a combination of approaches G.Russo,S.Solimeno,A.Spallicci,M.Tarallo,R.Terenzi,A.Toncelli,M. Tonelli,E.Tournefier,F.Travasso,C.Tremola,G.Vajente,J.F.J.van den can be expected to provide the required performance.A par- Brand,S.van der Putten,D.Verkindt,F.Vetrano,A.Vicere,J.-Y.Vinet,H. ticular advantage of our approach is that relatively simple sen- Vocca,and M.Yvert.Class.Quantum Grav.25,114045(2008). sors are adequate to meet even the exceedingly tight noise tol- 4G.M.Harry and the LIGO Scientific Collaboration,Class.Quantum Grav. 27,084006(2010). erances associated with gravitational wave detection 5S.Rowan,J.Hough,and D.R.M.Crooks,Phys.Lett.A 347,25 (2005). 6M.V.Plissi.K.A.Strain,C.I.Torrie,N.A.Robertson,S.Killbourn,S. ACKNOWLEDGMENTS Rowan,S.M.Twyford,H.Ward,K.D.Skeldon,and J.Hough,Rev.Sci. nstrum.6.3055(1998). The authors would like to thank members of the LSC- 7S.Braccini.C.Casciano,F.Cordero.F.Corvace,M.DeSanctis,R.Franco, Virgo collaboration for their interest in this work.We would F.Frasconi,E.Majorana,G.Paparo,R.Passaquieti,P.Rapagnani,F.Ricci, like to thank the NSF in the USA(Award Nos.PHY-05 02641 D.Righetti,A.Solina,and R.Valentini,Meas.Sci.Technol.11,467 and PHY-07 57896).LIGO was constructed by the California (2000). R.Abbott,R.Adhikari,G.Allen,D.Baglino,C.Campbell,D.Coyne,E. Institute of Technology and Massachusetts Institute of Tech- Daw,D.DeBra,J.Faludi.P.Fritschel,A.Ganguli,J.Giaime,M.Ham- nology with funding from the National Science Foundation mond,C.Hardham,G.Harry,W.Hua,L.Jones,J.Kern,B.Lantz,K. and operates under cooperative agreement PHY-0107417.In Lilienkamp,K.Mailand,K.Mason.R.Mittleman,S.Nayfeh.D.Ott- the UK,we are grateful for the financial support provided by away,J.Phinney,W.Rankin,N.Robertson,R.Scheffler,D.H.Shoe- maker,S.Wen,M.Zucker,and L.Zuo,Class.Quantum Grav.21.915 Science and Technology Facilities Council (STFC)and the (2004) University of Glasgow.This paper has LIGO Document No. 9M.V.Plissi,C.I.Torrie,M.Barton,N.A.Robertson,A.Grant,C.A.Cant- LIGO-P1200009.Public internal LIGO documents are found ley,K.A.Strain,P.A.Willems,J.H.Romie,K.D.Skeldon,M.M.Perreur- at https://dcc.ligo.org/cgi-bin/DocDB/DocumentDatabase/. Lloyd,R.A.Jones,and J.Hough,Rev.Sci.Instrum.75,4516(2004). 10M.V.Plissi,C.I.Torrie,M.E.Husman,N.A.Robertson.K.A.Strain,H. Ward,H.Luick,and J.Hough,Rev.Sci.Instrum.71,2539 (2000). 1B.Willke,Class.Quantum Grav.19,1377 (2002). 1N.A.Robertson,G.Cagnoli,D.R.M.Crooks,E.Elliffe,J.E.Faller,P. 2D.Sigg and the LIGO Scientific Collaboration,Class.Quantum Grav.25 Fritschel,S.GoBler,A.Grant,A.Heptonstall,J.Hough,H.Liick,R.Mit- 114041(2008). tleman,M.Perreur-Lloyd,M.V.Plissi,S.Rowan,D.H.Shoemaker,P.H 3F.Acernese,M.Alshourbagy,P.Amico,F.Antonucci,S.Aoudia,P.As- Sneddon.K.A.Strain,C.I.Torrie.H.Ward,and P.Willems,Class.Quan- tone,S.Avino,L.Baggio,G.Ballardin,F.Barone,L.Barsotti,M.Bar- tum Grav..19,4043(2002). suglia,T.S.Bauer,S.Bigotta,S.Birindelli,M.A.Bizouard,C.Boccara 2C.Torrie,"Development of suspensions for the Geo 600 gravitational wave F.Bondu.L.Bosi,S.Braccini,C.Bradaschia.A.Brillet,V.Brisson,D. detector,"Ph.D.dissertation(University of Glasgow,1999). Buskulic,G.Cagnoli,E.Calloni,E.Campagna,F.Carbognani,F.Cavalier, 13M.Barton,Models of the Advanced LIGO Suspensions in MathematicaTM R.Cavalieri,G.Cella,E.Cesarini,E.Chassande-Mottin,A.-C.Clapson,F. Internal Technical Document T020205-02D (LIGO,2006). Cleva.E.Coccia,C.Corda,A.Corsi,F.Cottone,J.-P.Coulon,E.Cuoco, 4B.Shapiro,Fitting the Quad Noise Prototype Model to Measured Data, S.D'Antonio,A.Dari,V.Dattilo,M.Davier,R.De Rosa,M.DelPrete,L Internal Technical Document T1000458 (LIGO,2010). Di Fiore,A.Di Lieto,M.D.P.Emilio,A.Di Virgilio,M.Evans,V.Fafone 5L.Ruet,"Active control and sensor noise filtering duality application to I.Ferrante,F.Fidecaro,I.Fiori,R.Flaminio,J.-D.Fournier,S.Frasca,F. advanced LIGO suspensions,"Ph.D.dissertation (Institut National des Frasconi,L.Gammaitoni,F.Garufi,E.Genin,A.Gennai,A.Giazotto,L. Sciences Appliques de Lyon (INSA Lyon).2007). Giordano,V.Granata,C.Greverie,D.Grosjean,G.Guidi,S.Hamdani, 16B.Shapiro,"Modal control with state estimation for advanced LIGO S.Hebri,H.Heitmann,P.Hello,D.Huet,S.Kreckelbergh,P.La Penna, quadruple suspensions,"Master's thesis (Massachusetts Institute of M.Laval,N.Leroy,N.Letendre,B.Lopez,M.Lorenzini,V.Loriette,G. Technology,2007). Reuse of AlP Publishing content is subject to the terms at:https://publishing.aip.org/authors/rights-and-permissions.Download to IP:183.195.251.6 On:Fri.22 Apr 2016 00:5549044501-9 K. A. Strain and B. N. Shapiro Rev. Sci. Instrum. 83, 044501 (2012) for all except the x direction, where the model is not over￾sensitive to the relevant parameters of the suspension and the extra performance provided by the modal method is most beneficial. We have presented the rationale and design method for active damping of the mirror-suspensions of a gravitational wave detector and shown that a combination of approaches can be expected to provide the required performance. A par￾ticular advantage of our approach is that relatively simple sen￾sors are adequate to meet even the exceedingly tight noise tol￾erances associated with gravitational wave detection. ACKNOWLEDGMENTS The authors would like to thank members of the LSC￾Virgo collaboration for their interest in this work. We would like to thank the NSF in the USA (Award Nos. PHY-05 02641 and PHY-07 57896). LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Tech￾nology with funding from the National Science Foundation and operates under cooperative agreement PHY-0107417. In the UK, we are grateful for the financial support provided by Science and Technology Facilities Council (STFC) and the University of Glasgow. This paper has LIGO Document No. LIGO-P1200009. Public internal LIGO documents are found at https://dcc.ligo.org/cgi-bin/DocDB/DocumentDatabase/. 1B. Willke, Class. Quantum Grav. 19, 1377 (2002). 2D. Sigg and the LIGO Scientific Collaboration, Class. 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Crooks, Phys. Lett. A 347, 25 (2005). 6M. V. Plissi, K. A. Strain, C. I. Torrie, N. A. Robertson, S. Killbourn, S. Rowan, S. M. Twyford, H. Ward, K. D. Skeldon, and J. Hough, Rev. Sci. Instrum. 69, 3055 (1998). 7S. Braccini, C. Casciano, F. Cordero, F. Corvace, M. DeSanctis, R. Franco, F. Frasconi, E. Majorana, G. Paparo, R. Passaquieti, P. Rapagnani, F. Ricci, D. Righetti, A. Solina, and R. Valentini, Meas. Sci. Technol. 11, 467 (2000). 8R. Abbott, R. Adhikari, G. Allen, D. Baglino, C. Campbell, D. Coyne, E. Daw, D. DeBra, J. Faludi, P. Fritschel, A. Ganguli, J. Giaime, M. Ham￾mond, C. Hardham, G. Harry, W. Hua, L. Jones, J. Kern, B. Lantz, K. Lilienkamp, K. Mailand, K. Mason, R. Mittleman, S. Nayfeh, D. Ott￾away, J. Phinney, W. Rankin, N. Robertson, R. Scheffler, D. H. Shoe￾maker, S. Wen, M. Zucker, and L. Zuo, Class. Quantum Grav. 21, 915 (2004). 9M. V. Plissi, C. I. Torrie, M. Barton, N. A. Robertson, A. Grant, C. A. Cant￾ley, K. A. Strain, P. A. Willems, J. H. Romie, K. D. 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Ruet, “Active control and sensor noise filtering duality application to advanced LIGO suspensions,” Ph.D. dissertation (Institut National des Sciences Appliques de Lyon (INSA Lyon), 2007). 16B. Shapiro, “Modal control with state estimation for advanced LIGO quadruple suspensions,” Master’s thesis (Massachusetts Institute of Technology, 2007). Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 183.195.251.6 On: Fri, 22 Apr 2016 00:55:49