EFFECTIVE FORCE TESTING WITH NONLINEAR VELOCITY FEEDBACK COMPENSATION

Transcription

1 3 th World Conference on Earthquake Engineering Vancouer, B.C., Canada Augut -6, 4 Paper No. 68 EFFECTIVE FORCE TESTING WITH NONLINEAR VELOCITY FEEDBACK COMPENSATION Jian ZHAO, Catherine FRENCH, Carol SHIELD, and Thoma POSBERGH 3 SUMMARY Effectie force teting (EFT) i a tet procedure that can be ued to apply real-time earthquake imulation to large-cale tructure. Sero-ytem nonlinearitie are ignificant for teting tructure with large hydraulic flow demand, which can be caued by large tructure elocitie and/or large effectie force. Thi paper firt reiew the nonlinear ero-ytem modeling and the deign of nonlinear elocity feedback compenation, and then explain a procedure for the lab implementation of the EFT method. The feaibility of EFT with the nonlinear elocity feedback compenation wa ealuated by comparing repone of a ingle-tory teel tructure incorporating two fluid damper teted on a hake table and ubequently teted uing the EFT method. Global repone (e.g., diplacement, elocity, and acceleration) and local repone (e.g., damper force and column hear) were compared. The tet reult indicate that with the nonlinear elocity compenation, dynamic force and real-time eimic imulation can be uccefully applied to the tet tructure. INTRODUCTION Paie or emi-actie damping deice are ued worldwide to mitigate eimic damage to building and bridge. Deign and control algorithm for thee energy diipation deice are typically ealuated uing computer imulation. Howeer, the accuracy of the imulation reult depend on the characterization of the damping deice. Real-time dynamic teting i likely to yield more accurate information regarding the behaior of tructure employing elocity dependent deice under eimic loading. A hake table i often ued to imulate the dynamic effect of earthquake on tructural model. Howeer, tructure teted on hake table typically hae to be caled down due to limited table capacitie. At maller cale, tructural detail uch a connection cannot be repreented realitically, and energy diipation of tructural control deice may not be demontrated accurately. Reearch Aociate, Department of Ciil, Contruction, and Enironmental Engineering, Iowa State Unierity, 384 Town Engineering Building, Ame, IA 5, USA Department of Ciil Engineering, Unierity of Minneota, Minneapoli, Ciil Engineering Building, 5 Pillbury Drie, SE, Minneapoli, MN 55455, USA. 3 Department of Electrical and Computer Engineering, Unierity of Minneota, Minneapoli, 4-74 Electrical Engineering & Computer Science Bldg., Union St., SE, Minneapoli, MN 55455,USA

2 Effectie force teting (EFT) i a dynamic teting procedure to apply real-time earthquake load to large-cale tructure that can be implified a lumped ma ytem. A chematically hown in Figure, the tet tructure in an EFT tet i anchored to a tationary bae, and dynamic force are applied by hydraulic actuator to the center of each tory ma of the tructure. The force to be impoed (effectie force) i the product of the tructural ma and the ground acceleration record, and thu i independent of the tructural propertie uch a tiffne and damping, and their change during the tet. Motion meaured relatie to the ground are equialent to the repone that a tructure can deelop relatie to a moing bae a in a hake table tet or an earthquake eent. Structure ubjected to ground acceleration Global Reference Structure ubjected to Effectie Force Teting xg x t x m x&& t P Actuator eff = mx && g m xx&&, k c k k c k x&& g (&& g + && x) m x mx && g mx&& kx cx& kx (&& g + && ) + & + = m x x cx kx kx Figure Concept of Effectie Force Teting cx& g kx mx && + cx& + kx = mx && = P Early inetigation of the EFT method indicated that in the direct implementation of EFT, the actuator wa not able to apply force accurately near the natural frequency of the tet tructure (Dimig et al. 999), which wa attributed to the natural elocity feedback in the ero-hydraulic ytem (i.e., the interaction between the actuator piton elocity and the actuator control) identified by Dyke et al. (995) in a tudy of actie tructural control. The effect of the natural elocity feedback can be explained a follow: the actuator i controlled by a eroale through hydraulic flow under preure, and the differential preure inide the actuator chamber caue the force applied to the tet tructure. The actuator chamber olume change due to the actuator piton moing with the tructure, reulting in unwanted chamber preure ariation. A tandard Proportional-Integral-Deriatie (PID) controller i unable to compenate for the preure ariation near reonance, thu cauing force-tracking error. The natural elocity feedback need to be compenated to uccefully implement EFT. In the elocity feedback correction propoed by Dimig et al. (999) and erified by Shield et al. (), the effect of the natural elocity feedback wa compenated by modifying the command to the eroale (i.e., a compenation ignal wa added to the eroale command ignal). The compenation ignal wa determined a the product of the meaured piton/tructure elocity and the piton area, and multiplied by the inere of the forward ytem dynamic before being added to the original command ignal. The eff

3 compenation algorithm i independent of the tructural propertie (i.e., damping and tiffne) and their change during a tet. Characterization of the forward ytem dynamic i critical becaue the modified command ignal compenate for the effect of the piton motion after going through the forward dynamic. Nonlinearitie of the ero-ytem can hae ignificant impact on the performance of the elocity feedback compenation (Zhao et al. 3a; Zhao et al. 3b), epecially when a tet inole large effectie force and/or large elocitie compared to the actuator/eroale capacitie. The large force and/or elocitie uually caue large hydraulic flow demand. Hence, nonlinear elocity feedback compenation i neceary to extend the EFT method to fully utilize the equipment. Thi paper firt preent a reiew of nonlinear ero-ytem modeling and nonlinear elocity feedback compenation followed by a procedure for implementing the EFT method. The application of the EFT method with the nonlinear elocity feedback compenation to a imple one-tory teel tructure with icou damper i preented. The tet reult are compared with thoe of a hake table tudy to alidate the EFT method and the nonlinear elocity feedback compenation cheme. NONLINEAR SYSTEM MODELING Figure preent a block diagram for the EFT ytem, which how the relation between ytem component (block with input and output labeled), including the interaction between the actuator piton elocity and the actuator control (natural elocity feedback). During a tet, the eroale controller compare the command ignal to a feedback ignal (both conerted from force to oltage ignal by C F ) and end an amplified error ignal () to the eroale (H ) to drie the ale pool. The pool regulate the hydraulic flow entering the actuator (Q L ), cauing differential preure acro the actuator piton (P L ). The preure difference multiplied by the piton area (A) produce the force (F) applied to the tet tructure. The force meaured by a load cell on the actuator piton i finally fed back to the controller to cloe the control loop. C F Cmd. C F (f) - + Load cell (c) (a) e x Q L P L F Vel. H c H f ( x A, PL ) K a+ C _ l m + c+ k Controller Vale Flow Actuator Structure Forword dynamic ( H fd ) (b) Natural elocity feedback A (e) compenation ignal H fd (d) A Velocity feedback compenation Figure A block diagram model of an EFT ytem The natural elocity feedback i hown by the loop (a)-(b)-(c) from the tructural elocity to the umming point (c), which repreent the law of coneration of ma: the hydraulic flow into the actuator need to counteract the fluid compreibility(k a ), ytem leakage(c l ), and chamber olume change ( A& x ). The effect of the natural elocity feedback loop (a)-(b)-(c) i compenated by a poitie feedback loop (a)-

4 (d)-(e)-(f). In order to cancel the effect of the natural elocity feedback at point (c), the compenation loop need to incorporate the inere of the dynamic between (f) and (c) (forward dynamic H fd ), which repreent the behaior of the eroale and it controller. Therefore, the eroale and it controller need to be characterized in detail. The mathematical model of the ero-ytem hae been deried by Zhao et al. (3) baed on the formulation by Merritt (967). The dynamic of the three-tage eroale (H fd ) contain three major component: () the proportional-integral-deriatie (PID) control with zero I gain, H = G G, () c p + where G p and G d are the proportional and deriatie gain of controller, repectiely; () the econd-order eroale dynamic, d H K = τ A A KK x p p max. () where τ i the equialent time contant of the pilot-tage ale, K p i the pilot-tage ale flow gain, A i the main-tage pool area, K 3 i the enitiity factor of the internal LVDT, and x max i the maximum pool troke; and (3) the nonlinear eroale flow characteritic tated by Q = x PL K x x P (3) L where x i the pool opening of the eroale (- to ), K i the no-load flow gain of the eroale, which i a function of pool opening, P L i the load preure (P L A i approximately the force applied to the tructure, and A i the actuator piton area), and P i the upply preure. The eroale flow relation include two type of nonlinearity: the load preure influence expreed by the quare root term and the nonlinear no-load flow gain (K ) (Zhao 3). The forward dynamic component are hown in detail in Figure 3. In order to implement the elocity feedback compenation, the inere of the component dynamic i needed. NONLINEAR VELOCITY FEEDBACK COMPENSATION To inere the nonlinear eroale flow characteritic, the chamber olume ariation to be L compenated ( A& x ) wa firt multiplied by x P x P to conider the effect of large force applied to the tructure (load preure influence). Thi proce required two more input, the pool opening (x ) and the load preure (P L ). The pool opening wa obtained directly from the eroale controller while the load preure wa approximated by the applied force diided by the piton area. Secondly, the nonlinear no-load flow gain (K ) wa repreented by a piecewie linear cure (eroale flow. pool opening); hence, the inere relation wa imple once the flow cure wa identified: A look-up table baed on the piece-wie linear flow cure wa ued to find the required pool opening to compenate the flow to the actuator.

5 Forward dynamic (H fd ) P L feedback Load preure influence (f) (c) Q e Gd+ G x Q L p Cmd. x ( τ A + A + KK 3 p) xmax x PL x P Controller Seroale dynamic Nonlinear flow gain Seroale flow x P L (e) G p T ld + ( αt + ) K ld x Q x x L P P (d) Ax& Inere dynamic (/H fd ) Figure 3 Nonlinear elocity feedback compenation deign The direct inere of the eroale dynamic reult in a tranfer function with a econd-order term in the numerator, correponding to an inherently untable ytem becaue it can greatly amplify ignal with high frequencie, uch a electrical noie. For the frequency range of interet (i.e., - Hz in thi tudy), the eroale dynamic hown in Eq () wa repreented with reaonable accuracy by a firt-order delay ( K ( Td +), where K i the ale gain) with a time contant (T d ); hence, a firt-order phae-lead network wa ued to inert the ale dynamic. H() = Tld + K αt + and Td Tld =. (4) α ld where the contant α wa taken a. becaue it could proide both good phae-lead performance (the performance would be reduced if α were too large) and acceptable noie amplification (noie would be greatly amplified if α were too mall). PID control with a zero I gain introduce ome phae lead into the DC error ignal if the deriatie gain (controller D gain) i not zero. Becaue the D gain wa uually et ery mall (e.g.,. m) in thi tudy (ytem with large D gain would amplify noie ignal), the controller dynamic were implified a a pure gain, and the related phae lead wa lumped into the dynamic of the eroale: the lead-time (G d /G p ) wa conidered by reducing the eroale repone delay (T d ). Hence, the inere dynamic of the eroale controller wa imply /G p. The inere of the forward dynamic and the deign of the nonlinear elocity feedback compenation are preented in Figure 3. The lab implementation of the EFT method with the nonlinear elocity feedback compenation i dicued in the next ection.

6 LAB IMPLEMENTATION OF EFT In addition to a ero-hydraulic controlled actuator and a data acquiition ytem, the implementation of the EFT method require the following hardware: a elocity tranducer to meaure the piton/tructure elocity ( x& ) and determine the actuator chamber olume ariation ( A& x ), a Digital Signal Proceor (DSP) and a hot computer. Thi ection preent a typical procedure for teting tructure uing the EFT method. Note that the dicuion hown below include ome empirical quantitie obtained in thi tudy. Equipment Capacity Equipment capacity include the load capacity of the actuator and the flow capacity of it eroale. The load capacity of an actuator can be found in it product pecification (e.g., 56 kn (35 kip) for an MTS 44.3 actuator), or etimated by 9% of the upply preure time the actuator piton area, which can be found in the actuator pecification. The eroale flow capacity wa etimated a Qrated.9P P rated, where Q rated i the rated flow of the eroale at a preure drop of P rated acro the eroale (e.g., 34 lpm (9 gpm) for an MTS 56.9 three-tage eroale under 6.9 MPa ( pi)) and P i the upply preure (roughly MPa (3 pi) in thi tudy). The calculated flow capacity wa limited by other factor in the hydraulic ytem, uch a the capacity of the pump and erice manifold, and the diameter of hydraulic upply hoe. Accurate flow capacity of a eroale wa obtained a preented in a later ection. During an EFT tet, the maximum tructural elocity hould be maller than 8% of the eroale flow capacity diided by the actuator piton area, and the maximum effectie force hould be maller than 5% of the actuator load capacity. If the maximum force likely happen at the ame moment a the maximum elocity (i.e., the effectie force input ha ignificant content near the reonant frequency of the tet tructure), the maximum pool opening hould be maller than 6%. Refer to Spink () for an actuator/eroale izing technique. Structural Propertie Identification Static loading tet and free ibration tet were ued for tructure identification. Note that the effectie force command i directly related to the tructure ma, and error in the tructural ma etimation would affect the force applied to the tructure and potentially the nonlinear tructural behaior. In addition, the tability of the tet ytem i related to the tructural damping. Teting of a tructure with a minimum of % critical damping uing EFT can be conducted with reaonable confidence (Zhao 3). The identified tructural propertie were ued to etimate the peak tructural repone for the capacity check of equipment and enor. Seroale Dynamic Identification The inere eroale dynamic hown in Eq. (4) require the ale gain (K ) and the repone delay (T d ), which may be determined uing the econd-order eroale model hown by Eq. (). Howeer, equation () require many ale parameter uch a ale pool area and the maximum pool troke. If the ale parameter are not aailable, a meaured frequency repone can be ued to etimate the parameter for an equialent econd-order model, from which the ale gain and the repone delay can be etimated. H K =. (5) ζ + + ω ω

7 A tet wa conducted to generate a frequency repone plot, in which the actuator wa in diplacement control, the actuator piton wa kept in it neutral poition, and the hydraulic upply to the main-tage ale wa turned off. The proportional gain of the eroale controller wa et to unity and the deriatie gain et to zero, uch that the ale command ignal could be controlled without additional equipment. A ine wae weep (- Hz in econd) with amplitude equialent to % pool opening wa choen a the input ignal. The pool opening wa obtained a an output from the eroale controller. The obtained frequency repone are hown in Figure 4, in which the magnitude repone i the Fourier magnitude ratio of the output to the input ignal, while the phae repone i the phae difference between the two ignal. Magnitude Experimental reult Simulation reult Phae (deg.) Frequency (Hz) Figure 4 Meaured eroale dynamic The amplitude correponding to the aymptotical line of the magnitude repone gae a ale gain (K ) of.. An equialent natural frequency of 57.5 Hz and a damping of 8% fit the phae repone well, from which the repone delay wa found to be 4.4 m for low frequencie. It hould be noted that the eroale dynamic can be affected by ytem nonlinearitie, and the repone delay increae with an increae in the hydraulic demand. To account for thi increae, a repone delay of 5 m wa found to be appropriate for thi tudy through mall amplitude tet a tated in a later ection (Tet with Small Amplitude Sineweep Input). Seroale Flow Property Identification Dynamically meauring the eroale flow uing a flow meter wa deemed inappropriate becaue flow meter typically do not repond quickly. Hence, a flow cure (i.e., the flow controlled by eroale Q L. the main-tage pool opening x ) wa contructed a follow. The actuator wa put into diplacement control with a unity controller P-gain and zero D-gain. Tet were conducted under no load condition (the tructure wa diconnected) uch that the preure difference acro the actuator piton (load preure P L ) wa negligible. The pool opening wa obtained directly by meauring the main-tage pool poition while the correponding flow wa calculated a the piton elocity multiplied by the piton area ( A& x ). The piton elocity wa calculated uing the central difference method from the meaured piton diplacement. Note that the leakage flow wa neglected in the aboe calculation becaue the leakage wa typically mall (le than.5% of ale capacity). Sinuoidal input with a frequency of 3 Hz were ued to control the pool opening. Refer to Zhao (3) for a procedure to determine the input frequency. Tet with 9% (4.5 in.), 8% (4 in.), 6% (3 in.), 4% ( in.), and % ( in.) full troke command were conducted. A piecewie linear cure that connected control point at interal of % of the pool opening wa contructed to repreent the flow

8 property of the eroale. The flow alue at the control point were calculated a the aerage alue of all tet reult. The reulting piecewie linear flow cure i compared to the tet reult with the 9% full troke command in Figure 5. It i noted that the real flow property of the eroale (a hown in grey dot) catter, indicating ome intantaneou oer-or under- compenation for the natural elocity feedback when the compenation i baed on the flow cure. Flow (cm 3 /) Spool opening Figure 5 Seroale no-load flow property Determination of Maximum Controller P Gain Relatiely large P gain hould be ued becaue they uually improe the oerall performance of a table ytem. On the other hand, larger controller P gain may caue intability, and reult in a highfrequency ibration of the actuator. The maximum controller P gain can be obtained through trial and error; howeer, a tability analyi of the tet ytem a hown in Zhao (3) could be ued to proide a guideline. A unity P gain wa ued in thi tudy. Tet with Small Amplitude Sineweep Input Small amplitude tet with ineweep input were conducted before the "real" tet to inetigate if the identified parameter (i.e., the repone delay and flow property of the eroale, and the controller gain) were uitable for ue in "real" tet. The following oberation were made: When the P gain wa too large, a high frequency ibration wa excited een with zero command. When the flow cure underetimated the real flow property of the eroale, a large amplitude pike reulted at the natural frequency of the tet tructure or the ytem became untable with ibration at the reonant frequency of the tructure. On the other hand, tet baed on an underetimated flow cure had a harp amplitude drop at the natural frequency of the tructure. With inufficient delay compenation, a peak before a alley appeared in the FFT of the meaured force while a peak after a alley appeared in the frequency domain when the delay wa oercompenated. Refer to Zhao (3) for detailed analyi and experimental erification of the effect of the ariou parameter on the performance of the EFT ytem. Following thi procedure, the EFT method with the nonlinear elocity feedback compenation wa applied to a one-tory teel tructure, and the reult were compared to a companion hake table tudy.

9 EXPERIMENTAL VALIDATION OF EFT Experimental Program A imple one-tory tructure wa elected for the tudy. The tructure conited of a rigid diaphragm (a rectangular teel frame filled with reinforced concrete) upported on four replaceable teel column at it corner a hown in Figure 6. The hake table tudy wa conducted at the Unierity of Illinoi at Urbana-Champaign. The concrete ma weighed about 44.5kN (. kip) to fit the load capacity of the table, and the column pacing wa.5.83 meter (6 7 inche) to fit the hole-pattern of the bae plate of the table. Four plate with tapped hole were welded on the teel frame of the diaphragm to proide connection for the column. Rigid diaphragm.5m m Wx5 Top plate 3-mm bolt Ground motion Damper.83 m m Figure 6 One-tory tet pecimen Bottom plate The column were made of Wx5 ection (A57 grade 5 teel) with a reported yield tre of 43. MPa (6.5 ki). The column were.83 m (7 inch) high and oriented in weak-axi bending uch that the reonant frequency of the tructure wa low enough to be excited by mot earthquake ground acceleration record. The tructural tiffne in the orthogonal direction wa much ( time) larger than that in the motion direction uch that out-of-plane motion wa preented without additional diagonal brace. In order to minimize the effect of the connection on the comparion of the dynamic repone of the tructure, the column were welded to a 38-mm (.5-inch) plate at the bottom and a 5-mm (-inch) plate at the top. The end plate were bolted to the diaphragm and bae uing four 3-mm (½-inch) diameter A49 bolt. The middle cheron brace connected two Taylor Deice fluid damper to limit the tructural repone uch that tet could be repeated and reult compared. The behaior of the damper wa found to be nonlinear a hown in Figure 7; hence, the tructural behaior wa difficult to predict een when the column were in their linear range of behaior. In the hake table tudy, the column were bolted to a 3-mm (½-inch) thick bae plate, which wa bolted to the diaphragm of the table; while in the EFT tudy, the column were bolted to a 9-mm (¾inch) thick bae plate, which wa anchored to the trong floor. Due the difference in the column boundary condition, the tructural tiffne during the EFT tet wa % greater than that in the hake table tudy. In addition, the tructural ma increaed by % during the EFT tet, which wa in part due to the addition of a thick plate for connecting the actuator. With the aboe tructural propertie, the natural frequency of the tructure in the two tudie changed by approximately % (from.89 Hz in the hake

10 table tudy to.87 Hz in the EFT tudy). In addition, the tructural damping during the EFT tet decreaed by % (from 9.6% in the hake table tudy to 8.% in the EFT tudy), which wa attributed to an unknown change in the damper and a change in tet enironment. With reduced damping, it wa anticipated that the diplacement and elocity of the tructure in the EFT tudy would be lightly greater than thoe in the hake table tudy. Damper force (kn) Velocity (cm/) Figure 7 Force-elocity characteritic of the icou damper The effectie force were applied to the tructure by a 56-kN (35-kip) MTS 44.5 actuator controlled by a 34 lpm (9-gpm) MTS 56.9 eroale, which wa in turn controlled by an MTS 47 analog controller. The elocity feedback compenation cheme were implemented uing a dspace DS DSP controller with a TI TMS3C3 floating-point digital ignal proceor with a khz ampling rate. A tachometer type elocity tranducer by Unimeaure (V erie linear elocity tranducer) wa ued to meaure the tructure/piton elocity. In addition, train gage and load cell were ued to monitor the local tructural repone uch a column bae hear and damper force. Tet Reult With the identified parameter, a erie of tet were conducted uing the EFT method and reult were compared to thoe of the hake table tudy. In the following force comparion, "Shake table tet" repreent the meaured table acceleration time the etimated tructural ma, which i alo the effectie force command for EFT tet, while "EFT tet" repreent the force applied to the tructure meaured by the actuator load cell. Tet reult with a.55 g Northridge earthquake input are preented in Figure 8 and 9. Only econd of repone (from 6 to 6 ec) are hown to make the graph more readable. The force comparion in Figure 8 how that the effectie force command wa followed by the actuator cloely in the EFT tet. The Fourier amplitude of the force applied to the tructure by the actuator wa lightly greater than the force command in the frequency domain, indicating a light oercompenation of the natural elocity feedback due to uncertaintie in the etimation of the eroale flow propertie. Both the global repone (diplacement, elocity, and acceleration) and local repone (column bae hear) of the EFT tet matched well with thoe of the hake table tet a hown in Figure 9. The tructural repone in the EFT tet were lightly greater than thoe obtained in the hake table tet, which wa attributed to the light oercompenation of the natural elocity feedback and the decreae in tructural damping. In addition, the after-hock free ibration, which began at 5 ec, wa accurately captured. After-tet inpection indicated that the column end partially yielded during the tet. The maximum pool opening in the tet wa about 5%, which i beyond the linear range (%) of the eroale

11 performance (refer to Figure 5). Thee oberation indicate that with nonlinear elocity feedback compenation, the EFT method can be ued to tet nonlinear tructure with large hydraulic demand. Force (kn) Florce amplitude Time ().4 Shake table tet.3 EFT tet Frequency (Hz) Figure 8 Comparion of effectie force and the force output of the tet with.55g Northridge earthquake diplacement (cm) elocity (cm/) Shake table tet EFT tet acceleration (g) column hear(kn) Time () Time () Figure 9 Comparion of tructural repone of the tet with.55g Northridge earthquake

12 CONCLUSIONS Effectie Force Teting (EFT) i a real-time earthquake imulation method for teting large-cale lumped ma tructural ytem. The effect of natural elocity feedback mut be compenated in the laboratory implementation of the EFT method. The elocity feedback compenation require an accurate characterization of the eroale and it controller. The high-order eroale dynamic can be accurately repreented by a firt-order delay with a ale gain for the frequency range of interet (- Hz); hence, a firt-order phae-lead network can be ued in the elocity feedback compenation. The eroale behaed nonlinearly when large flow demand were required during teting aociated with large tructural elocity repone (repreented by the nonlinear no-load flow gain) and/or large effectie force (repreented by the load preure influence). To fully utilize the eroale capacity, the nonlinearitie were conidered in the elocity feedback compenation with an experimentally determined eroale flow cure and meaured pool opening and load preure. Detailed procedure were dicued in thi paper to determine the parameter required in the ytem modeling and the laboratory implementation of the EFT method. The feaibility of EFT with the nonlinear elocity feedback compenation wa demontrated by teting a one-tory teel tructure uing a hake table and the EFT method. The comparion of the tet reult with the two tet technique howed that with proper elocity feedback compenation, the EFT method can be ued to apply real-time eimic imulation to a tructure that ha complex damping propertie and hyteretic behaior. A the EFT method become aailable to reearcher, the teting capability of exiting laboratory equipment will expand from tatic teting to real-time dynamic teting. ACKNOWLEDGEMENTS Funding for thi reearch wa partly proided by the National Science Foundation (NSF) under grant number: CMS The Doctoral Diertation Fellowhip proided by the 3M Corporation through the Graduate School at the Unierity of Minneota i acknowledged. Howeer, information contained herein doe not necearily repreent the iew of the ponor. REFERENCES. Dimig, J., Shield, C., French, C., Bailey, F., and Clark, A. (999) Effectie force teting: A method of eimic imulation for tructural teting. Journal of Structural Engineering. 5(9), Dyke, S. J., Spencer, B. F., Quat, P., and Sain, M. K. (995) Role of control-tructure interaction in protectie ytem deign. Journal of Engineering Mechanic, ASCE, (), Merritt, H. E. (967) Hydraulic control ytem. Wiley, New York. 4. Murcek, J. A. (996) Ealuation of the effectie force teting method uing a SDOF model, Mater thei, Ciil Engineering, Unierity of Minneota, Minneapoli. 5. Shield, C., French, C., and Timm, J. () Deelopment and implementation of the Effectie force teting method for eimic imulation of large-cale tructure. Philoophical Tranaction of the Royal Society: Theme Iue on Dynamic Teting of Structure; A 359: Spink, M. () MDOF implementation of effectie force teting: a method of eimic imulation, Mater thei, Unierity of Minneota, Minneapoli.

13 7. Timm, J. (999) Natural elocity feedback correction for effectie force teting. Mater thei, Ciil Engineering, Unierity of Minneota, Minneapoli. 8. Zhao J, French C., Shield C., and Pobergh T. () Deelopment of EFT for nonlinear SDOF ytem. Proc. 7th National Conf. on Earthquake Engineering. Boton, MA 9. Zhao J, French C., Shield C., and Pobergh T. (3a) Nonlinear elocity compenation for Effectie Force Teting. Proc. 3 Structural Congre and Exhibition. Seattle, WA. Zhao J, French C., Shield C., and Pobergh T. (3b) Conideration for the deelopment of realtime dynamic teting uing ero-hydraulic actuation. Earthquake Engineering and Structural Dynamic. Vol. 3, No.. pp Zhao, J. (3) Deelopment of EFT for Nonlinear SDOF Sytem, Ph.D thei, Ciil Engineering, Unierity of Minneota, Minneapoli.