Real‐time control of shake tables for nonlinear hysteretic systems

Summary Shake table testing is an important tool to challenge integrity of structural and non-structural specimens by imposing excitations at their base. When shake tables are loaded with specimens, the interaction between the tables and specimens influences the system dynamics that may result in undesired performance. In order to compensate the effects of the interaction, open loop feedforward compensation methods have been widely used successfully in current practice of table controls, assuming that the specimens remain linear. On the contrary, unsatisfactory signal performances during shake table testing were observed when flexible and heavy specimens experience nonlinear behavior. While lack of high fidelity might be acceptable for the purpose of exploration research of specimens subjected to random excitations, a high fidelity of signal reproduction is necessary for shake table qualification testing where specific target motion is required to challenge the specimens. In this study, a nonlinear tracking control scheme based on the feedback linearization method is proposed for the control of shake tables to simulate target motions at specific locations of test structures, having nonlinear hysteretic behavior. Additionally, a real-time estimator using the extended Kalman filter is adopted and combined with the controller in order to account for the changes and uncertainties in system models due to nonlinearities and yielding caused by extreme excitations. The proposed adaptive tracking control method has been applied to a realistic shake table–structure test setup by means of numerical simulations, and the results show good tracking and estimation performance. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  Kang Li,et al.  Development of high‐performance shake tables using the hierarchical control strategy and nonlinear control techniques , 2015 .

[2]  Chia-Ming Chang,et al.  Real‐time hybrid testing with equivalent force control method incorporating Kalman filter , 2011 .

[3]  T. T. Soong,et al.  Experimental Study of Active Control for MDOF Seismic Structures , 1989 .

[4]  Shirley J. Dyke,et al.  Real-Time Dynamic Model Updating of a Hysteretic Structural System , 2014 .

[5]  Narutoshi Nakata,et al.  Acceleration trajectory tracking control for earthquake simulators , 2010 .

[6]  Jann N. Yang,et al.  On-line identification of non-linear hysteretic structures using an adaptive tracking technique , 2004 .

[7]  Zexiang Li,et al.  Control of sliding-isolated buildings using dynamic linearization , 1994 .

[8]  Andrew W. Smyth,et al.  On-Line Parametric Identification of MDOF Nonlinear Hysteretic Systems , 1999 .

[9]  Andrei M. Reinhorn,et al.  Simulation of floor response spectra in shake table experiments , 2011 .

[10]  Gilberto Mosqueda,et al.  Implementation of online model updating in hybrid simulation , 2014 .

[11]  Michael C. Constantinou,et al.  Seismic testing of a building structure with a semi-active fluid damper control system , 1997 .

[12]  Ralph E. Hudson,et al.  Parametric Identification of Nondegrading Hysteresis in a Laterally and Torsionally Coupled Building Using an Unscented Kalman Filter , 2013 .

[13]  Chung Bang Yun,et al.  Identification of Linear Structural Dynamic Systems , 1982 .

[14]  Ki Pung Ryu.  Modeling and seismic evaluation of nonstructural components: Testing frame for experimental evaluation of suspended ceiling systems , 2010 .

[15]  Bin Wu,et al.  Model updating with constrained unscented Kalman filter for hybrid testing , 2014 .

[16]  R. Bouc.  Forced Vibration of Mechanical Systems with Hysteresis , 1967 .

[17]  Marcial Blondet,et al.  ANALYSIS OF SHAKING TABLE-STRUCTURE INTERACTION EFFECTS DURING SEISMIC SIMULATION TESTS , 1988 .

[18]  D. P. Stoten,et al.  Adaptive control of shaking tables using the minimal control synthesis algorithm , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[19]  Joel P. Conte,et al.  SHAKING TABLE DYNAMICS: RESULTS FROM A TEST-ANALYSIS COMPARISON STUDY , 2002 .

[20]  Joel P. Conte,et al.  Acceleration Tracking Performance of the UCSD-NEES Shake Table , 2010 .

[21]  M. V. Sivaselvan,et al.  Hysteretic models for deteriorating inelastic structures , 2000 .

[22]  Adam Mueller,et al.  Real-Time Hybrid Simulation with Online Model Updating: Methodology and Implementation , 2016 .

[23]  R. V. Jategaonkar,et al.  Aerodynamic Parameter Estimation from Flight Data Applying Extended and Unscented Kalman Filter , 2010 .

[24]  Shirley J. Dyke,et al.  Role of Control-Structure Interaction in Protective System Design , 1995 .

[25]  J. Luco,et al.  Experimental characterization, modeling and identification of the NEES‐UCSD shake table mechanical system , 2008 .

[26]  Ping Lu,et al.  Optimal predictive control of continuous nonlinear systems , 1995 .

[27]  Y. Wen.  Method for Random Vibration of Hysteretic Systems , 1976 .

[28]  Joel P. Conte,et al.  Linear dynamic modeling of a uni‐axial servo‐hydraulic shaking table system , 2000 .

[29]  Andrew W. Smyth,et al.  Application of the unscented Kalman filter for real‐time nonlinear structural system identification , 2007 .