REAL-TIME HYBRID SIMULATION WITH ADAPTIVE ACTUATOR CONTROL FOR STRUCTURAL ENGINEERING RESEARCH ABSTRACT

Transcription

1 REAL-TIME HYBRID SIMULATION WITH ADAPTIVE ACTUATOR CONTROL FOR STRUCTURAL ENGINEERING RESEARCH Cheng Chen 1, James M. Riles 2, Rihard Sause 2, and Theodore L. Karavasilis 2 ABSTRACT Real-time hybrid simulation ombines experimental testing and numerial simulation, and thus provides a viable experiment tehnique for strutural engineering researh. Servo-hydrauli atuators are typially utilized to failitate large- or full-sale real-time hybrid simulation. Time delay introdued in an atuator s response due to servo-hydrauli dynamis an destabilize the simulation if not ompensated properly. This paper disusses an adaptive ompensation method for real-time hybrid simulation to minimize atuator delay. An evolutionary variable is introdued to adapt the ompensation parameter based on an atuator traking indiator. Laboratory tests involving large-sale real-time hybrid simulations of a two-story-four-bay moment resisting frame with Magneto-Rheologial (MR) dampers are onduted to experimentally demonstrate the effetiveness of the proposed adaptive ompensation method. The steel moment resisting frame is modelled analytially with the aid of a finite element program and the MR dampers are taken as the experimental substrutures to be physially tested. The atuator traking apability is shown to be greatly improved and reliable experimental results are ahieved, even when a good estimate of atuator delay is not used and variable atuator delay ours during the simulation. INTRODUCTION Experimental testing is an essential tool to evaluate the performane of strutures under extreme events suh as earthquakes. It enables researhers to study the response of strutures to earthquakes, and provides data for developing numerial models and assessing design methodologies for new types of strutural systems. Various testing tehniques have been developed for strutural engineering researh, and inlude quasi-stati yli testing, shake-table testing, pseudodynami testing, and hybrid simulation. Although shake-table testing provides the most realisti means of simulating seismi effets in the laboratory, the test struture is usually a saled-down version of the prototype struture to aommodate the apaity of the shake table. Due to the saling effet, shake-table tests of redued-sale models may not aurately repliate the behaviour of some strutural omponents of the prototype struture suh as ontrol devies. Numerous rate-dependent devies have been reently developed for seismi hazard mitigation [Soong et al. 2002]. The behaviour of these devies varies under different loading frequenies and evaluation of their performane requires that the tests be onduted using a real-time sale so that the true response of the test struture an be obtained during the experiment. Conventional experiment tehniques, suh as quasi-stati yli testing and pseudodynami testing, are not suitable when rate-dependent devies exist in the test struture sine these methods of testing are onduted using an expanded time sale. Two alternatives have been suggested to overome this hallenge to failitate experimental researh involving rate-dependent devies. The first involves 1 Shool of Engineering, San Franiso State University, San Franiso, CA ATLSS Engineering Researh Center, Lehigh University, Bethlehem, PA

2 the use of a large apaity shake tables that enables the seismi response of large-sale strutures to be experimentally [NIED]. Large shake table tests however often lead to a great amount of ost assoiated with test struture onstrution and table operation. Another alternative is to extend the onventional pseudodynami testing and hybrid simulation methods from an expanded time sale to a real-time sale, and is known as real-time pseudodynami testing and real-time hybrid simulation [Nakashima et al. 1999; Blakeborough et al. 2001]. In a real-time hybrid simulation the strutural system is divided into analytial and experimental substrutures, where the analytial substrutures are numerially modelled and the experimental substrutures (i.e., test struture) are physially tested in the laboratory. An integration algorithm is usually used to solve for the strutural response in a real-time hybrid simulation. By numerially modelling parts of the strutural system using the finite element method, real-time hybrid simulation provides a viable alternative to experimentally evaluate the performane of large- or full-sale strutural systems, espeially systems with rate-dependent seismi devies. The interation between the integration algorithm and the substrutures ensures that the dynami performane of the entire strutural system is onsidered throughout the simulation. Unlike onventional experimental tehniques, suh as quasi-stati testing and pseudodynami testing, real-time hybrid simulation requires that the servo-hydrauli atuator(s) impose ommand displaement(s) aurately onto the experimental substruture(s) in a real-time manner. Due to inherent servo-hydrauli dynamis the atuator has an inevitable time delay in response to the displaement ommand. This time delay is usually referred to as atuator delay and will result in a desynhronization between the measured restoring fore(s) from the experimental substruture(s) and the integration algorithm in a real-time hybrid simulation. Studies on the effet of atuator delay [Wallae et al. 2005; Chen and Riles 2008b] show that atuator delay is equivalent to reating negative damping whih an destabilize a real-time hybrid simulation if not ompensated properly. Atuator delay ompensation is often used to minimize atuator delay and ahieve aurate atuator ontrol for real-time hybrid simulation. Horiuhi et al. [1999] and Horiuhi and Konno [2001] proposed two ompensation shemes for atuator delay that are based on polynomial extrapolation and a linear aeleration assumption. Methods originating from ontrol engineering theory have also been used in real-time testing, and inlude derivative feedforward [Jung and Shing 2006]. The above ompensation methods are often utilized for a predefined onstant atuator delay. Chen and Riles [2009] showed that the performane of these ompensation methods an be analyzed through a frequeny response analysis of the equivalent disrete transfer funtion. An aurate estimate of atuator delay is often diffiult to aquire before a real-time test. Moreover, the atuator delay might be variable during a real-time hybrid simulation due to the nonlinearities in the servo-hydrauli system and the experimental substruture(s). Compensation methods for variable atuator delay have also been developed. Darby et al. [2002] proposed an online proedure to estimate and ompensate for atuator delay during a real-time hybrid test using a proportional feedbak system. Bonnet et al. [2007] applied model referene adaptive minimal ontrol synthesis (MCS) to real-time testing. Carrion and Spener [2007] used a feedforward-feedbak ontroller in onjuntion with inverse modelling to ompensate for variable atuator delay when onduting real-time hybrid simulation of substrutures suh as semi-ative MR dampers. Chen and Riles [2008a] developed an adaptive inverse ompensation 2

3 method based on a simplified disrete model of a servo-hydrauli system. In this paper, the appliation of real-time hybrid simulation with adaptive inverse ompensation method is demonstrated by experimentally evaluating the seismi performane of a steel moment resisting frame (MRF) with magneto-rheologial (MR) dampers. ADAPTIVE INVERSE COMPENSATION METHOD FOR ACTUATOR DELAY COMPENSATION The modelling of the servo-hydrauli system an be ompliated due to nonlinearities in the system. To inorporate the atuator delay into a stability analysis of a real-time hybrid simulation Chen and Riles [2008b] proposed a simplified first-order disrete model to model the servohydraulis. The inverse of the simplified model was subsequently applied for atuator delay ompensation in real-time hybrid simulation of a single-degree-of-freedom struture with an elastomeri damper by Chen et al. [2009]. Good performane was observed for atuator traking with the resulting inverse ompensation. The inverse ompensation model is expressed as p X ( z) α z G z es ( αes 1) ( ) = = X ( z) z In Eq. (1a) α es is the estimated atuator delay onstant; z is the omplex variable in the disrete z-domain; X (z) is the disrete z-transform of the displaement ommand di + 1, whih is usually omputed by an integration algorithm in a real-time hybrid simulation; X p (z) is the disrete z- transform of the predited displaement d p i + 1 from the ompensation method to be sent to the servo-hydrauli atuator to ompensate for atuator delay; and G (z) is the disrete transfer funtion for the inverse ompensation method. Applying the inverse disrete z-transform to Eq. (1a) leads to the following equivalent differene equation for the inverse ompensation method: p di+ 1 = α es di+ 1 ( αes 1) di (1b) In Eq. (1b) p di + 1 and d i+ 1 are the predited displaement and ommand displaement for the (i+1) th time step, respetively, and d i the ommand displaement for the i th time step. Eq. (1b) indiates that the inverse ompensation method an be interpreted as an extrapolation using the ommand displaements of the previous time steps. It an also be observed from Eqs. (1a) and (1b) that the performane of the inverse ompensation method is dependent on the auray of the delay onstant α es, whih is often estimated from previous experiene. To minimize the effet of an inaurately estimated or variable atuator delay, Chen and Riles [2008a] developed an adaptive inverse ompensation method based on the inverse ompensation method, whih is formulated as p X ( z) ( αes + Δα ) z ( αes + Δα 1) G ( z) = = (2) X ( z) z In Eq. (2), Δα is an evolutionary variable with an initial value of zero, and is determined using the following adaptive ontrol law t (1a) Δα ( t) = k TI ( t) + k TI ( τ ) dτ (3) p In Eq. (3) k p and k i are proportional and integrative gains for the adaptive ontrol law, respetively; and TI is the traking indiator based on the enlosed area of the hysteresis in the synhronized subspae plot, as shown in Fig. 1, where the atuator ommand displaement d is i 0 3

4 plotted against the atuator measured response d m. The alulation of TI for eah time step an be formulated as [Meran 2007] TI.5( A TA ) (4a) where i+ 1 = 0 i+ 1 i+ 1 m i 1 = Ai dai + 1 = Ai ( di+ 1 + di )( di+ 1 m m i 1 = TAi + dtai = TAi + 0.5( di+ 1 + di )( di+ 1 m A + di ) (4b) TA + di ) (4) m i+ is the measured displaement of the servo-hydrauli atuator at the (i+1) th time step. d 1 d d i+1 d i dta i da i d i m m d i+1 d m Fig. 1. Definition of traking indiator It an be observed that the adaptive inverse ompensation method redues to the inverse ompensation method when both the gain k p and k i are set equal to zero. When α es, k p, and k i are set equal to zero, no atuator delay ompensation ours during the real-time hybrid simulation. Generally, a larger value of k p results in a faster response and a larger osillation in the evolutionary variable, while inreasing the integrative gain k i redues the osillation and leads to a smaller steady state error. In this paper, the integrative gain k i is seleted to be one tenth of the proportional gain k p based on studies involving numerial simulations, where k i = 0.1k p was found to produe good adaptation with a small error. EXPERIMENTAL EVALUATION OF THE SEISMIC PERFORMANCE OF A STEEL MRF WITH MR DAMPERS USING REAL-TIME HYBRID SIMULATION Real-time hybrid simulation is onduted on a steel MRF with MR dampers in passive mode to demonstrate the performane of the adaptive inverse ompensation method. MR dampers are ontrol devies proposed for vibration ontrol of engineering strutures. Experimental studies involving predefined displaements have been reported that led to the development of phenomenologial models for MR dampers [Dyke et al. 1996; Yang et al. 2002; Bass and Christenson 2007]. Shake table tests of strutures with small-sale MR dampers also have also been onduted by researhers [Jansen and Dyke 2008]. These experiments provide valuable insight into the behaviour of MR dampers. However, the real-time tests with predefined displaements do not aount for the struture-damper interation during the earthquake, and the saled shake table tests may not realistially represent the nonlinear behaviour of large-sale MR dampers that exist in the prototype struture. Large-sale real-time hybrid simulation provides a viable tehnique to investigate the performane of large-sale MR dampers for seismi hazard mitigation with struture-damper interation onsidered. 4

5 Prototype Steel MRF Struture A 2-story, 6-bay by 6-bay prototype offie building is seleted as the prototype struture for the experimental study presented in this paper. The building is assumed to be loated on a stiff soil site near Los Angeles and has four idential perimeter steel MRFs to resist lateral fores. Fig. 2 shows the plan view and the perimeter frame of the prototype struture. The experimental study presented in this paper fouses on one typial perimeter MRF, whih is designed with MR dampers as shown in Fig. 2(b). The yield strength of the material for the MRF is assumed to be equal to 345 MPa. The gravity loads desribed in the International Building Code [ICC 2006] are onsidered in the design. A smooth design response spetrum with parameters S DS =1.0, S D1 =0.6, T 0 =0.12 se. and T s =0.6 se. represents the design basis earthquake (DBE) [BSSC 2003]. The omputer program SAP2000 [2008] is utilized for seleting the frame member sizes in aordane with the AISC-LRFD provisions [AISC 2005]. The same olumn ross setion and various beam ross-setions are used for the two-story MRF. (a) (b) dampers dampers dampers dampers 4.6m 3.8m 9.1m = 36.4m Fig. 2. Prototype building (a) plan view; (b) perimeter MRF with dampers and braes A simplified design proedure developed by Lee et al. [2007] is utilized to design the MRF with MR dampers, where the properties of the resulting MRF are tabulated in Table 1, inluding olumn and beam ross-setions, fundamental period of vibration and story stiffness. The MR dampers are assumed to be in passive mode with the maximum urrent input of 2.5 Amps. A total of six and four MR dampers are determined by the simplified design proedure for the first and seond stories, respetively. To utilize the MR dampers, the perimeter MRF is re-designed with a design base shear equal to 50% of that of the onventional SMRF. Table 1. Properties of MRF with MR Dampers Column Beams Fundamental Story stiffness (kn/m) 1 st story 2 nd story period (se) 1 st story 2 nd story W14x120 W24x55 W18x Experimental Setup The real-time hybrid simulation was performed using the NEES Real-Time Multi-Diretional (RTMD) Faility at Lehigh University. Fig. 3 shows the experimental setup for the real-time hybrid simulation, whih onsists of two experimental substrutures (two MR dampers), two servo-hydrauli atuators with supports and roller bearings; reation frames, and beams seuring the MR dampers to the strong floor. The large-sale MR dampers used in this study are 5

6 manufatured by Lord Corporation and have a nominal apaity of 200 kn at the maximum urrent input of 2.5 Amps [Bass and Christenson 2007]. The MR fluid damper has an available stroke of 584 mm and an aumulator to aommodate a temperature hange in the fluid up to 44.4 ºC. An Advaned Motion Control PWM servo-amplifier is utilized to provide an eletrial urrent ommand signal that ontrols the eletromagneti field for the damper. Sine the dampers at a story level of the prototype struture are plaed in parallel in the MRF, they are assumed to be subjeted to the same veloity and displaement, and hene eah of the MR dampers test setups in the laboratory represents all of the dampers in one story. The measured restoring fore from eah MR damper setup is multiplied by the number of dampers to obtain the total restoring fore of all the dampers at a story level in the MRF. The MRF is analytially modeled using a nonlinear finite element program with a total 122 degrees of freedom and 71 elements [Karavasilis et al. 2009]. The highest natural frequeny of the MRF is around 20k Hz. The two atuators eah have a 500 mm stroke and different maximum fore apaity of 1700 kn and 2300 kn, respetively. Two servo-valves, eah with a flow apaity of 2500 liters/min, are mounted on eah atuator to enable them to ahieve a maximum veloity of 760 mm/se and 560 mm/se, respetively. The servo-ontroller for the atuator used in the real-time tests onsisted of a digital PID ontroller with the proportional gain of 20, integral time onstant of 5.0 resulting in an integral gain of 4.0, differential gain of 0 and a roll-off frequeny of 39.8 Hz [Lehigh RTMD 2009]. Reation frames Atuator Atuator MR dampers Tie-down beam Roller bearing Fig. 3. Experimental setup for real-time hybrid simulation Real-Time Hybrid Simulation Results The unonditionally stable expliit CR integration algorithm [Chen and Riles 2008] is used for the real-time hybrid simulation. The strutural response alulated by the CR algorithm is translated into the displaement for the DOFs of the experimental substrutures, whih is then imposed to the MR dampers by the servo-hydrauli atuators. The integration time step Δt used for the present study is equal to 10/1024 se. To ensure a smooth and ontinuous atuator response, a ramp generator is used to interpolate the ommand displaement at the servo ontroller sampling rate, whih is 1/1024 se. The TCU105-E omponent of the 1999 Chi-Chi earthquake reorded at the TCU105 station was used as the ground motion for the real-time hybrid simulation. The ground motion is saled to the design basis earthquake (DBE) by employing the saling proedure of Somerville [1997]). 6

7 The estimates of the atuator delay onstant for the adaptive inverse ompensation are α 1es =30 and α 2es =45 based on previous experiments. The adaptive gains are set to be k p =0.4 and k i =0.04 for both atuators. Real-time hybrid simulation results are presented in Figs. 4 and 5. The floor displaement and damper deformation time histories are presented in Fig. 4. The MRF is observed to have a maximum lateral displaement magnitude of 35.2 mm and 62.6 mm for the first and seond floors, respetively. The resulting maximum story drifts are about 0.8% and 0.7% story drift and muh less than the design drift of 1.6%. The experimental substrutures, i.e., the MR dampers, developed a maximum deformation magnitude of 35.8 mm and 29.3 mm for the first and seond floors, respetively. Fig. 4. Real-time hybrid simulation results of MRF subjeted to DBE earthquake: (a) floor displaements; (b) damper deformations The atuator traking for the real-time hybrid simulation is shown in Fig. 5. The omparisons between the ommand and measured displaements are presented in Fig. 5(a) and 5(b) for the atuators attahed to the first and seond story dampers, respetively. Good agreement an be observed in the omparison, indiating that good atuators ontrol is ahieved. The time history of the TI is presented in Fig. 6(a) and 6(b) for the two atuators, where small values of the TI an be observed and indiates good atuator ontrol during the real-time hybrid simulation. The time histories for the evolutionary variable Δα are presented in Fig. 7(a) and 7(b) for the atuators. Spikes of small amplitude an be observed for the evolutionary variable Δα for both atuators, where the adaptive ompensation tried to aommodate a sudden inrease in the atuator delay due to the inreased deformation in the MR dampers and the assoiated larger fores and veloities developed by the atuators. It an also be observed that the evolutionary variable Δα for the two atuators have different trends, where the atuator attahed to the first story damper is observed to have a osillation around zero while the atuator attahed to the seond story damper has a negative value of Δα between zero and -10. This means that the auray of the estimated atuator delay for the two atuators is different. The atuator attahed to the seond story damper appears to have a slight over-ompensation indued by the value used 7

8 for the initial estimate α es. The different trends in Δα an be attributed to the different power urve apaities of the two atuators resulting in different delay when applying a similar fore and veloity, where the smaller 1700 kn atuator used for the 1 st story damper has a faster maximum veloity than the 2300 kn atuator used for the 2 nd story, as desribed previously. Fig. 5. Comparison of ommand and measured atuator displaements Fig. 6. Time history for traking indiator Fig. 7. Time history for evolutionary variable Δα SUMMARY AND CONCLUSIONS An adaptive inverse ompensation method is disussed in this paper to minimize atuator delay in order to ahieve reliable and aurate real-time hybrid simulation results. The adaptive ompensation method employs an initial estimate for the atuator delay and utilizes an evolutionary variable to aommodate inaurately estimated and variable delay during a realtime hybrid simulation. The adaptive ontrol law for the evolutionary variable is based on a traking indiator. The adaptive inverse ompensation is experimentally demonstrated through a 8

9 real-time hybrid simulation of a steel MRF with MR dampers in passive mode. The MRF with MR dampers is designed using a simplified design proedure to ahieve a presribed performane objetive under earthquake loading. One ground motion reord is seleted and saled to the DBE level for the simulation. Aurate atuator ontrol is shown to be ahieved through the adaptive inverse ompensation method in terms of atuator ontrol error as well as traking indiator, thus enabling a suessful real-time hybrid simulation to be performed. The experimental results also show that the MRF designed by the simplified proedure employed in this paper satisfies the performane objetive. The results from this paper demonstrate the potential of real-time hybrid simulation with adaptive inverse ompensation for assessing the performane of strutures with rate-dependent devies. ACKNOWLEDGEMENTS This paper is based upon work supported by grants from the Pennsylvania Department of Community and Eonomi Development through the Pennsylvania Infrastruture Tehnology Alliane, and by the National Siene Foundation under Grant No. CMS within the George E. Brown, Jr. Network for Earthquake Engineering Simulation Consortium Operation. Any opinions, findings, and onlusions expressed in this paper are those of the authors and do not neessarily reflet the views of the sponsors. The MR fluid dampers used for the study in this paper were provided by Dr. Rihard Christenson of University of Connetiut. The authors appreiate his support. REFERENCES AISC Load and Resistane Fator Design Speifiation for Strutural Steel Buildings. Amerian Institute of Steel Constrution, Chiago, Illinois. Bass, B.J. and Christenson, R System identifiation of a 200kN Magneto-Rheologial fluid damper for strutural ontrol in large-sale smart strutures. Proeedings, 2007 Amerian Control Conferene, New York City. Blakeborough, A., et al The development of real-time substruture testing. Philosophial Transations of the Royal Soiety of London A 359: Bonnet, P.A., et al Real-time hybrid experiments with Newmark integration, MCSmd outer-loop ontrol and multi-tasking strategies. Earthquake Engineering and Strutural Dynamis 36(1): Building Seismi Safety Counil (BSSC) NEHRP reommended provisions for seismi regulations for new buildings and other strutures. Report FEMA 450, Federal Emergeny Management Ageny, Washington, D.C. Carrion, J.E. and Spener, B.F., Jr Model-based strategies for real-time hybrid testing. NSEL Report No. NSEL-006, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign. Chen, C., and Riles, J.M. 2008a. Traking error-based servo-hydrauli atuator adaptive ompensation for real-time hybrid simulation. Journal of Strutural Engineering, submitted for publiation. Chen, C. and Riles, J.M. 2008b. Stability analysis of SDOF real-time hybrid testing systems with expliit integration algorithms and atuator delay. Earthquake Engineering and Strutural Dynamis 37(4): Chen, C. and Riles, J.M Development of diret integration algorithms for strutural dynamis using disrete ontrol theory. Journal of Engineering Mehanis 134(8):

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