VIRTUAL MODEL OF THE UCSD-NEES HIGH PERFORMANCE OUTDOOR SHAKE TABLE

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1 4 th World Confrnc on Structural Control and Monitoring 4WCSCM-85 Abstract VIRTUAL MODEL OF THE UCSD-NEES HIGH PERFORMANCE OUTDOOR SHAKE TABLE O. Ozclik, J. P. Cont, and J. E. Luco Univrsity of California, San Digo, CA 909 USA In this study an arly vrsion of a virtual modl of th UCSD-NEES shak tabl is prsntd. This virtual modl includs th following subsystms: a virtual rplica of th controllr, nonlinar srvo-valv modl, singl-ndd actuator modl with intrnal volum chang, and simplifid modls of th mchanical subsystms, namly a rigid platn, horizontal stiffnss providd by th hold-down struts, and dissipativ/friction forc mchanisms. Comparison of actual tst data and simulation data show that this modl, with th sam controllr gains as thos usd on th ral systm, is abl to rproduc th signal distortion obsrvd in sinusoidal tst data. Improvmnts in th virtual modl ar ndd for rproducing th actual systm rspons to commandd broadband signals such as arthquak rcords. A mor advancd vrsion of this virtual modl will b usd to improv th prformanc of th currnt controllr basd on physical knowldg of th shak tabl systm. Introduction Larg srvo-hydraulic shaking tabl systms ar ssntial tools in xprimntal arthquak nginring. Thy provid ffctiv ways to subjct spcimns of structural componnts, substructurs, or ntir structural systms to dynamic xcitations similar to thos inducd by ral arthquaks. Within th NEES Consortium, major shak tabl facilitis xist at Buffalo, Rno, and San Digo. Th UCSD-NEES Larg High Prformanc Outdoor Shak Tabl (LHPOST) at Camp Elliott nabls landmark sismic xprimnts to b conductd on larg- and full-scal structural and soil-foundation-structur intraction systms. Th spcifications for th LHPOST ar a strok of ±0.75m, a pak horizontal vlocity of.8m/s, a horizontal forc capacity of 6.8MN, an ovrturning momnt capacity of 50MN-m, and a vrtical payload capacity of 0MN. Th frquncy bandwidth is 0-0Hz. Th LHPOST consists of a moving stl platn (7.6m wid by.m long), a rinforcd concrt raction block, two srvo-controlld dynamic actuators with a forc capacity in tnsion/comprssion of.7mn and 4.MN, rspctivly, a platn sliding systm (6 hydrostatic prssur balancd barings ach with a vrtical forc capacity of 9.4MN), an ovrturning momnt rstraint systm consisting of two nitrogn-filld hold-down struts, a yaw rstraint systm (two hydrostatic prssur balancd barings on ach longitudinal sid of th platn), a ral-tim multi-variabl controllr, and a hydraulic powr supply systm. Th complx dynamics of larg shaking tabl systms manat from multipl dynamic intractions and nonlinaritis among various systm componnts. An intraction diagram of th subsystms of th LHPOST is shown in Figur. MECHANICAL Spcimn Du to concrns about prmaturly damaging th spcimn, th tuning of currnt shaking tabl Barings Raction Surrounding Platn controllrs is typically conductd at a scald down Block Soil Actuators vrsion of th targt ground motion or undr bar tabl condition. As a rsult of th complxity of th Controllr Srvovalvs Accumulators Blowdown complt tabl-spcimn systm, controllr tuning Valvs at scald down amplituds lads to significant Command Surg Accumulators Accumulator Pumps rrors whn th full-scal input is commandd as Signal Tank Bank shown by rcnt xprimnts prformd on th ELECTRONIC HYDRAULIC UCSD-NEES tabl. Thus, thr is a crucial nd to Figur. Componnt and intraction diagram improv th controllr basd on physical of shak tabl systm knowldg of th systm. This can b don, as a first stp, by dvloping a comprhnsiv mchanics-basd modl of th systm. This modl will also Ozclik, Cont and Luco

2 play a critical rol in planning and dsigning shak tabl xprimnts, optimizing th location of snsors, intrprting th rsults of xprimnts, and off-lin virtual tuning of th actual controllr using th systm simulation modl. A complt virtual modl of th LHPOST would rquir th following componnts (Figur ) to b modld: raction block and surrounding soil, platn and supporting barings, actuators, srvo-valvs, accumulators, hydraulic pumps, controllr, and tst spcimns. Sinc shak tabl xprimnts ar oftn prformd to invstigat th nonlinar bhavior of structural systms undr strong arthquak xcitation, nonlinar finit lmnt modls of structural spcimns must b incorporatd in th virtual systm modl. In th litratur, w find a limitd numbr of studis focusing on modling and simulation of complt shak tabl systms (Hwang t al., 987; Rinawi and Clough, 99; Clark, 99; Cont and Trombtti, 000; Trombtti and Cont, 00; Twitchll and Symans, 00). In particular, Cont and Trombtti (000) dvlopd a linar analytical modl of a small-to-mdium siz shak tabl systm accounting for srvovalv tim dlay, actuator dynamics, oil lakag through th actuator sals, foundation flxibility, and linar lastic multi-dgr-of-frdom (MDOF) spcimn dynamics. Williams t al. (00) hav dvlopd a ralistic modl of a dynamic structural tsting systm, which includs a dtaild nonlinar modl of th srvovalv actuator systm, th controllr, and th spcimn modld as a linar lastic singl-dgr-of-frdom (SDOF) systm. A comprhnsiv virtual modl of th LHPOST with all th componnts shown in Figur is undr dvlopmnt. In this papr, an arly vrsion of this virtual UCSD-NEES shak tabl modl is prsntd. Th componnts of th LHPOST incorporatd in th currnt modl consist of: th control algorithm (a virtual rplica of th actual controllr), four srvo-valvs, two singl ndd actuators, nitrogn-filld holddown struts, various dissipativ and friction mchanisms xisting in th systm, and th platn. Actual physical quantitis idntifid for this virtual modl through tsts conductd on th systm ar th ffctiv mass of th platn, ffctiv horizontal stiffnss providd by th hold-down struts, and ffctiv dissipativ/friction forcs. Comparisons btwn actual systm rspons and its prdiction obtaind through th currnt virtual modl ar providd for harmonic tsts. Formulation and Implmntation of th Componnts of th Virtual Shak Tabl Modl This sction prsnts som of th mathmatical formulations of th various componnts of th virtual modl of th ovrall shak tabl systm and thir implmntations in th Matlab-Simulink programming nvironmnt. Controllr Th controllr of th LHPOST consists of MTS digital Thr Variabl Controllr (TVC) rfrrd to as Modl 469DU and known in control thory as a stat variabl controllr. It has additional spcial faturs to compnsat for linar and nonlinar systm distortions for both harmonic and broadband command signals (.g., amplitud/phas control, adaptiv harmonic cancllation, adaptiv invrs control, on-lin itration, and notch filtrs). Th thr stat variabls controlld by th TVC ar displacmnt, vlocity, and acclration. Th controllr can b st to run undr displacmnt, vlocity or acclration control mod. Dpnding on th control mod, only on stat variabl bcoms th primary control variabl with th othrs srving only as compnsation (fd-forward and/or fdback) signals to improv damping and stability of th systm. Th transfr functions btwn all th inputs and outputs of th TVC wr providd by MTS Systms Corporation. Dtails rgarding ths transfr functions and thir implmntation in Matlab-Simulink can b found lswhr (Thon, 004). A concptual rprsntation of th controllr is givn in Figur. Th rfrnc gnrator taks th rfrnc signal, which rprsnts th dsird displacmnt, vlocity, or acclration dpnding on th control mod, and crats th rfrnc stats x rf, x rf, x rf, and x rf (jrk), which ar usd as fd- Ozclik, Cont and Luco

3 forward signals in th controllr. Th fdback stats x fbk, x fbk, and x fbk ar gnratd by th fdback gnrator which combins displacmnt and acclration snsors (fdback signals), ach with thir rspctiv bandwidth limitations to crat widband stimats of th fdback stats. Th rfrnc and fdback stats ar wightd by th rfrnc and fdback gains, rspctivly, shown in th figur. It should b notd hr that th displacmnt fdback gain is th only non-zro fdback gain. Thrfor, it can b said that th TVC is simply a displacmnt controllr with sophisticatd rfrnc (fd-forward) gains (Thon, 00). Th high-pass filtr applid on th forc fdback signal (quivalnt to th dltaprssur signal multiplid by th actuator ffctiv piston ara) rmovs static and low frquncy componnts from th forc fdback, prior to input it into th TVC to damp th oil column rsonanc. Fiv notch filtrs ar also incorporatd in th controllr to compnsat for rsonancs and antirsonancs. Each notch filtr frquncy rspons is dfind by thr paramtrs: th cntr frquncy, db bandwidth, and notch dpth (Thon, 004). Rfrnc Signal Displacmnt Fbk Acclration Fbk Rfrnc Gnrator Fdback Gnrator Forc Fbk x rf x rf x rf x rf x fbk - x fbk x fbk k JF k AF k VF k PF k P k V k A k DP Σ Σ Highpass Filtr Rsonanc Compnsation Notchs Controllr Σ Output - to Srvovalvs Notch Filtr Paramtrs f,b W, dpth Figur. Concptual rprsntation of TVC. Not that signals with diffrnt units ar blndd togthr. Blnding of signals with diffrnt units to obtain a hybrid command signal to th srvo-valvs is possibl through normalization of th various signals to thir rspctiv maximum valu (.g., D max, V max, A max, F max ) and convrsion to Volt units (not shown in th figur). Srvo-Valvs Thr ar four four-stag srvo-valvs in th systm, two at ach actuator. Ths srvovalvs ar spcially manufacturd to achiv th high prformanc spcifications of th LHPOST. Th fourth stag flow rating of ach srvo-valv is 0,000 lit/min. Srvo-valvs ar inhrntly nonlinar dvics in which th flow output is proportional to th squar root of th prssur drop across thm. An ovrall schmatic of srvo-valv and actuator combination with four flow paths corrsponding to th xtnt and rtract dirctions of th actuator piston is shown in Figur. Actuator Extnt Dirction Actuator Rtract Dirction x v x v P S P S P R V P R 4 V P A A P P A A P Figur. Four stag srvovalv and singl ndd actuator combination with four flow paths (V and V ar th xtnt and rtract vlocitis of th actuator piston, rspctivly). Th four flows from th srvovalv orifics (labld through 4) into th actuator chambrs can b xprssd using Brnoulli s quation as q = A V = K w x P P q = AV = K vw x sv P PR () v sv S q = A V = K w x P P q 4 = AV = K vw 4x sv PS P () v sv R Ozclik, Cont and Luco

4 whr A and A ar th comprssion and tnsion aras of th actuator piston, rspctivly; K v is a linarizd flow cofficint; xsv is th srvovalv 4 th stag spool displacmnt; w, w, w, w 4 ar th spcially manufacturd valv port window widths; and P S and PR dnot th systm supply prssur and th rturn prssur, rspctivly ( P 0.7 MPa and P 0.5 MPa). S R Du to th singl ndd natur of th actuators, th actuator piston aras on th tnsion and th comprssion sids ar diffrnt; th ratio of tnsion ara ( 0.97 m ) to comprssion ara ( 0.07 m ) is 0.64 for both actuators. A dsign critrion for achiving minimum wavform distortion for singl ndd actuators is to kp th no load (i.., zro forc carrid by th actuator) prssurs within th actuator th sam for ach dirction of travl whil maintaining th sam constant vlocity. With this critrion satisfid, thr is thortically no prssur discontinuity in ach chambr whn th actuator piston changs dirction (Gram, MTS Systms Corporation, prsonal communication, 006). This critrion rducs to th following conditions on th port orific widths: / / w 4 w A w A w A = = 0.8, = = 0.5, =, = = 0.64 w A w A w w A Onc th fourth stag spool displacmnt, x sv, of a srvo-valv is known, th corrsponding port orific aras can b obtaind as th product of x sv and port orific width as givn in () whr w = 5.4 cm. Thn, by using ths port orific aras, th flows from srvo-valvs into actuator chambrs can b found from () and () for givn valus of P and P. Th srvovalv spool displacmnt (innr) control loop within th srvovalv xhibits scond-ordr lowpass dynamics. Ths dynamics can b masurd by xciting th tabl with a random command signal, rcording valv drivr command and valv spool displacmnt fdback, and fitting an Auto Rgrssiv Moving Avrag (ARMA) dynamic modl to th data (Williams t al., 00; Thon and Laplac, 004). Modling of th fourth stag srvo-valv spool dynamics is not includd hrin du to lack of th ndd xprimntal data. Only a simpl convrsion factor is usd to convrt th valv command signal in Volts to th srvo-valv spool displacmnt in mm (9.05/0 mm/v). Onc th ncssary data is availabl, th spool dynamics will b incorporatd in th shak tabl simulation modl. 4th Stag Spool Disp w Prssur to Tnsion w Comprssion to Rturn w4 Prssur to Comprssion w Tnsion to Rturn P P -C- PS -C- PR Ps A_sa q_ Pa Orific Pa A_ar q_ Pr Orific Ps A_sb q_4 Pb Orific 4 Pb A_br q_ Pr Orific Figur 4. Matlab-Simulink implmntation of a four-way srvovalv. q_in/out_ q_in/out_ () Th Matlab-Simulink implmntation of th fourth stag of a four-way srvovalv with th abov mntiond charactristics is givn in Figur 4. Hrin, four-way dfins th numbr of flow paths in and out of th srvovalv. Th orific to 4 sub-blocks contain th implmntation of Brnoulli s quations givn in () and () to comput th flows into th actuator chambrs, whil th w to w 4 subblocks calculat th port orific aras as a function of th fourth stag spool displacmnt, x sv. Sinc th LHPOST has four four-way srvo-valvs, four srvo-valv modls as shown in Figur 4 ar implmntd in th virtual shak tabl modl. Ozclik, Cont and Luco 4

5 Singl Endd Actuators Th srvo-valv modl dvlopd in th prvious sction dtrmins th oil flow into th actuator prssur chambrs. Th load prssur (diffrntial prssur across th actuator piston) that drivs th actuator piston can b drivd from th flow continuity quation. Th actuator modl usd in this study taks into account th chang in volum of th actuator chambrs (Williams t al., 00), a sourc of nonlinarity. Each singl-ndd actuator has two prssur chambrs as shown in Figur 5. By intgrating in tim th quation of flow continuity, th xprssions for th actuator chambr prssurs P and P can b obtaind as P = dy q A β y dt v ( y y ) v ( y y) strok strok dt, P = dy q A β y dt strok strok dt (4) whr A and A ar th piston aras, yt () is th piston displacmnt rlativ to th actuator cylindr (which is qual to th platn total displacmnt assuming that th platn, actuators, raction block and surrounding soil ar all rigid), P and P ar th actuator chambr prssurs, β is th oil bulk modulus ( β = 689.5MPa from th litratur), and v and v ar th initial actuator chambr volums. Onc th actuator chambr prssurs ar known, th actuator driving forc can b obtaind as Fact () t = PA PA. Th Matlab-Simulink implmntation of th singl-ndd actuator modl dfind abov with varying chambr volums is shown in Figur 6. Sinc th LHPOST has two singl-ndd actuators, two actuator modls as shown in Figur 6 ar implmntd in th virtual shak tabl P modl. 4 Piston Vlocity - q_in/out_ A A A Modling and Idntification of Mchanical Subsystms cylindr pr-strssing systm consisting of two nitrogn-filld hold-down struts. Th mchanical componnts of th LHPOST considrd in this papr includ a moving stl platn, a platn sliding systm composd of six hydrostatic prssur balancd barings, a yaw rstraint systm with two hydrostatic prssur balancd barings on ach longitudinal sid of th platn, and an ovrturning momnt rstraint systm providd by a discrt tnsion For idntification purposs, a simplifid mathmatical modl with a small numbr of paramtrs of th abov mntiond mchanical componnts of th LHPOST nds to b dfind. Such a modl is givn in Figur 7, whr Fact () t is th total actuator forc applid to th tabl by th two horizontal actuators, M is th ffctiv mass of th platn, K is th total ffctiv horizontal stiffnss providd by th two holddown struts, C is th ffctiv viscous damping cofficint, and µ is th ffctiv Coulomb friction q_in/out_ Piston Displacmnt P P A -Cy_strok -Cy_strok -Ks Bta * y_strok / Vbar Bta * y_strok / Vbar Actuator Forc Figur 6. Matlab-Simulink implmntation of th singlndd actuator modl. - s P P q y s trok y s trok, v A y(t) A P q, v Figur 5. Singl-ndd actuator with actuator piston at th cntrd position. Ozclik, Cont and Luco 5

6 forc, and ux () t is th horizontal movmnt of th platn along x dirction. Th rational bhind choosing ths paramtrs to modl th mchanical systm can b found lswhr (Ozclik t al., 006). Th quation of motion of th concptual modl givn in Figur 7 can b writtn as follows F () t act K ( α µ ) M u () t K u () t C u () t sign( u ()) t = F () t (5) M C CL x x x x act u () x t Figur 7. Concptual mathmatical modl of th mchanical subsystms of th LHPOST µ K Th unknown paramtrs of th abov modl wr stimatd by using an xtnsiv st of tsts prformd on th systm ranging from simpl harmonic tsts to arthquak and whit nois tsts. Dtails rgarding th stimation procdur can b found in Ozclik t al. (006). Th stimatd modl paramtrs ar M = 44 tons, K =.66 MN/m, C = 0.04MN-s/m, α = 0.5, and µ = (0.58%) F. Th dissipativ V forc trm apparing in (5) is a function of vlocity. In ordr to tak this variation into account, th following viscoplastic friction law is usd (Bondont t al., 997): ( () α dz F = H C ux t µ ) Z, Y = { Z κ ( κ) sign( Zy ) } y (6) dt whr FH is th ffctiv horizontal dissipativ forc, Z is th hystrtic dimnsionlss paramtr which satisfis (6), Y is th quivalnt yild displacmnt, and κ is a dimnsionlss constant. Th valus of Y and κ usd in this study ar 0. mm and 0.5, rspctivly. Th Matlab-Simulink implmntation of th abov dissipativ forc modl is shown in Figur 8. Vl [m/s] u Varying Friction Forc -C- Z Z Kappa -Ks /Y Sign -Kappa Figur 8. Matlab-Simulink implmntation of th viscoplastic friction law. Dissipativ Forc [N] Notic that th Varying Friction Forc block shown in Figur 8 implmnts th dissipativ forc givn in (6). Th Simulink implmntation of th rigid platn and th horizontal stiffnss du to th pr-chargd hold-down struts is not givn hr du to spac limitation. Virtual Modl of Shak Tabl Systm and Comparison of Exprimntal and Simulation Rsults Th Matlab-Simulink implmntation of th complt virtual modl of th LHPOST is shown in Figur 9. Notic th modular implmntation of th various subsystms, which nhancs th undrstanding of th intraction btwn th various componnts and sub-systms. Data obtaind from sinusoidal tsts prformd on th ral systm undr bar tabl conditions (no spcimn attachd to th platn) ar usd to assss th prdiction capability of th virtual modl. Tst data obtaind from two sin tsts both at Hz frquncy and.7g (SP07) and.0g (SP09) targt amplitud wr usd for comparison purposs. Th control gains for ths tsts wr st at: displacmnt gain =.5 (V/V) (th only nonzro fdback gain), displacmnt lad = 0.0 (V/V), vlocity lad = 0.8 (V/V), Z Ozclik, Cont and Luco 6

7 acclration lad = 0.5 (V/V), jrk lad = (V/V), and dynamic forc gain = -.5 (V/V). Ths sam control gain valus ar usd in th virtual modl of th LHPOST. Disp / Vl / Acc Cmd W qwa PWa PWb qwb SV's on th Wst Cmd Disp Fdback Disp Function Gnrator Disp Snsor Controllr Output Acc Snsor Forc Snsor Thr Variabl Controllr (Disp / Vl / Acc) Cmd E qa PEa PEb qb SV's on th East qwa Act Forc qwb PWa qa PWb qb vl PEa disp PEb East and Wst Actuators Disp Act Forc Acc Vl Rigid Platn, Hold-down Stiffnss and Dissipativ Forc Modls Comparison of fdback platn acclrations obtaind from th actual tsts and th simulation modl is givn in Figur 0. It is obsrvd that th actual and simulatd fdback acclration rcords ar in good agrmnt. Th prdiction accuracy of th virtual modl dcrass as th amplitud of th rfrnc incrass. On possibl xplanation for this discrpancy is that th srvo-valv modl usd, Equations () and (), dos not tak into account th nonlinar rlationship btwn srvo-valv spool displacmnt and srvo-valv flow (Zhao t al., 005). Nvrthlss th simulation modl is abl to captur th distortion sn in th actual fdback acclration rcords. It was found that odd harmonics of th fundamntal frquncy caus this distortion in th fdback signal and that th mchanical sourc of this distortion is th nonlinarity in th srvo-valv orific flow. Simulations basd on a linar srvovalv modl for which th flow into th actuator is calculatd simply by multiplying th spool displacmnt with a crtain flow gain (obtaind from th manufacturr) do not captur th odd-harmonic distortion obsrvd in th actual fdback signal. Conclusions Figur 9. Complt virtual modl of th LHPOST (undr bar tabl condition) In this study, an arly vrsion of th virtual modl of th UCSD-NEES larg high-prformanc outdoor shak tabl is prsntd. This modl incorporats a virtual rplica of th actual controllr, nonlinar modls of srvo-valvs with spcially manufacturd port orific widths, singl-ndd actuator modls with variabl intrnal volum chang, and simplifid modls of mchanical sub-systms including rigid platn, horizontal stiffnss providd by th hold-down struts, and dissipativ forc mchanisms modld through a combination of Coulomb friction and viscous damping forcs. Comparison of actual rcordd tst data with simulation data shows that th currnt vrsion of th virtual modl with th sam controllr gains as on th actual systm is abl to captur th main faturs of th actual sinusoidal tst data. It was found that th distortion sn in th actual fdback signals is du to th nonlinarity in th srvo-valv orific flow. Comparisons (not shown hrin) of actual and simulatd data Acclration [g] - Sp07 Acclration [g] - Sp Cmd Signal Fbk from Tst Fbk from Sim Cmd Signal Fbk from Tst Fbk from Sim Tim [sc] Figur 0.Tst-Analysis Comparison. Ozclik, Cont and Luco 7

8 for broadband command signals (whit nois and arthquak rcords) do not show as good an agrmnt as that obsrvd for th sinusoidal tsts. Futur improvd vrsions of th virtual shak tabl modl will incorporat th flxibility of th platn, th raction block and th surrounding soil, dtaild modls of th supporting vrtical and latral barings, th dynamics of th rd and 4 th stag spools of th srvo-valvs, th nonlinar rlationship btwn srvo-valv spool displacmnt and srvo-valv flow, and finally intrnal and xtrnal lakag in th actuators and srvo-valvs. Nonlinar modls of typical tst spcimns will also b dvlopd and intgratd into th shak tabl virtual modl to study th shak tabl - spcimn intraction. This improvd comprhnsiv mchanics basd virtual modl will thn b usd as a starting point to improv th xisting controllr basd on physical knowldg of th systm. Acknowldgmnts Partial support of this rsarch by th Englkirk Cntr Industry Advisory Board and NEESinc through a NEES facility nhancmnt projct is gratfully acknowldgd. Th authors also wish to thank Mr. Bradford K. Thon, Mr. Marty Gram and Mr. Alln Clark from MTS Systms Corporation for providing all th rqustd information rgarding th controllr and srvohydraulic systm componnts and for insightful discussions. Th hlp of Prof. José Rstrpo (U.C. San Digo) in planning th tsts and intrprting th tst rsults and of Mr. Lauranc Brman, Mr. Jams Batti, Mr. Knny Knzl and Mr. Babak Moavni in xcuting th tsts is gratfully acknowldgd. Rfrncs Bondont, G. and A. Filiatrault (997), Frictional Rspons of PTFE Sliding Barings at High Frquncis, Journal of Bridg Enginring, ASCE, (4), Clark, A. (99), Dynamic Charactristics of Larg Multipl Dgr of Frdom Shaking Tabls, Proc. 0th World Conf. on Earthquak Enginring, Madrid, Spain, Cont, J.P. and T.L. Trombtti (000), Linar Dynamic Modling of a Uni-axial Srvo-Hydraulic Shaking Tabl Systm, Earthquak Enginring and Structural Dynamics, 9, Hwang, J. S., K.C. Chang, and G.C. L (987), Th Systm Charactristics and Prformanc of a Shaking Tabl, NCEER Rport No , National Cntr for Earthquak Enginring Rsarch, Stat Univrsity of Nw York at Buffalo, NY, 987. McKnna, F. and G.L. Fnvs (000), An Objct-Orintd Softwar Dsign for Paralll Structural Analysis, Proc. of th SEI/ASCE Structurs Congrss, Philadlphia, PA, 000. Ozclik, O., J.E. Luco, J.P. Cont, and T.L. Trombtti (006), Exprimntal Charactrization, Modling and Idntification of th Mchanical Subsystm of th UCSD-NEES Shak Tabl, in prparation, 006. Rinawi, A. M., and R.W. Clough (99), Shaking Tabl-Structur Intraction, EERC Rport No. 9/, Earthquak Enginring Rsarch Cntr, Univrsity of California at Brkly, CA, 99. Thon, B. K. (00), How to Tun Thr Variabl Controllr (TVC), MTS Corporation, 00. Thon, B. K. (004), TVC Transfr Functions, MTS Corporation, 004. Thon, B. K., and P.N. Laplac (004), Offlin Tuning of Shaking Tabls, Proc. th World Conf. on Earthquak Enginring, Vancouvr, B.C., Canada, Aug. -6, Papr No. 960, 004. Trombtti, T.L. and J.P. Cont (00), Shaking Tabl Dynamics: Rsults from a Tst Analysis Comparison Study, Journal of Earthquak Enginring, 6(4), Twitchll, B. S. and M.D. Symans (00), Analytical Modling, Systm Idntification, and Tracking Prformanc of Uniaxial Sismic Simulators, Journal of Enginring Mchanics, 9(), Williams, D. M., M.S. Williams and A. Blakborough (00), Numrical Modling of a Srvohydraulic Tsting Systm for Structurs, Journal of Enginring Mchanics, 7(8), Zhao, J., C. Shild, C. Frnch and T. Posbrgh (005), Nonlinar Systm Modling and Vlocity Fdback Compnsation for Effctiv Forc Tsting, Journal of Enginring Mchanics, (), Ozclik, Cont and Luco 8