ADVANCES IN SHAKE TABLE CONTROL AND SUBSTRUCTURE SHAKE TABLE TESTING by Matthew Joseph James Stehman A dissertation submitted to The Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy. Baltimore, Maryland June, 2014 c Matthew Joseph James Stehman 2014 All rights reserved Abstract Shake table tests provide a true representation of seismic phenomena including a fully dynamic environment with base excitation of the test structure. For this rea- son shake tables have become a staple in many earthquake engineering laboratories. While shake tables are widely used for research and commercial applications, further developments in shake table techniques will allow researchers to use shake tables in a broader range of studies. This dissertation presents recent advances in the use of shake tables for the seismic performance evaluation of civil engineering structures. Develop- ments include theoretical and experimental investigations of substructure shake table testing, a technique where the entire test structure is separated into computational and experimental substructures. Challenges in meeting the boundary conditions be- tween the substructures have limited the number of implementations of substructure shake table testing to date; thus in this dissertation, appropriate methods of address- ing the boundary conditions between experimental and computational substructures are presented and evaluated. Also, a novel strategy for acceleration control of shake tables is presented to enhance the acceleration tracking performance of shake tables ii ABSTRACT to be used in substructure shake table testing. Results are presented that show the promise in using the developed techniques over traditional shake table testing meth- ods. Primary Reader: Narutoshi Nakata Secondary Readers: Benjamin Schafer and Judith Mitrani-Reiser iii Acknowledgments I would like to sincerely thank my advisor, Professor Narutoshi Nakata, for all of his helpful advice and mentoring during my time at Johns Hopkins. I would also like to thank my colleagues John Hinchcliffe and Richard Erb, for helping me design and build the test setups necessary for the experimental part of my research. I would like to extend a special thanks to Nick Logvinovsky for always helping me find the right tool for the job. Finally, I would like to acknowledge the National Science Foundation for their financial support. The research presented in this dissertation was fully supported by the grant entitled \CAREER: Advanced Acceleration Control Methods and Sub- structure Techniques for Shaking Table Tests (grant no. CMMI- 0954958)". iv Dedication To my family, for all the support and encouragement they have given me. v Contents Abstract ii Acknowledgments iv List of Tables xi List of Figures xii 1 Introduction 1 1.1 Literature Review . 2 1.1.1 Shake Table Testing . 3 1.1.2 Real-Time Hybrid Simulation . 7 1.1.3 Substructure Shake Table Testing . 10 1.2 Overview of Dissertation . 13 2 Shake Table Dynamics 15 2.1 Dynamics of Shake Tables with Hydraulic Actuators . 16 vi CONTENTS 2.2 Acceleration Relationships . 21 2.3 Summary and Discussion . 23 3 Substructure Shake Table Testing of Upper Stories in Tall Buildings 24 3.1 Formulation . 25 3.1.1 Equations of Motion . 25 3.1.2 Compatibility Requirements . 27 3.1.3 Concept of Substructure Shake Table Testing . 29 3.2 Experimental Setup and Modeling . 30 3.2.1 Uni-Axial Shake Table . 30 3.2.2 Control and Data Acquisition System . 31 3.2.3 Experimental Substructure . 32 3.2.4 Computational Substructure . 33 3.2.5 Measurement of Base Shear . 34 3.3 Acceleration Control Performance . 35 3.3.1 Issues of Acceleration Control and Control-Structure-Interaction 35 3.3.2 Propagation of Input Acceleration Errors . 38 3.4 Substructure Shake Table Test System with Error Compensation . 39 3.4.1 Numerical Integration for the Computational Substructure . 40 3.4.2 State Observer and Kalman Filter . 42 3.4.3 Model-Based Actuator Delay Compensation . 44 vii CONTENTS 3.4.4 Corrector for Errors in Base Shear Induced by Input Accelera- tion Errors . 46 3.5 Experimental Results . 47 3.5.1 Harmonic Ground Excitation Inputs . 48 3.5.2 Earthquake Ground Excitation Input . 54 3.6 Advanced Model-Based Shake Table Compensation Techniques . 58 3.6.1 Feedforward Compensation using Derivatives of Reference Signal 58 3.6.2 IIR Compensation Technique for Significant Control-Structure- Interaction . 60 3.6.3 Experimental Investigation of Model-Based Delay Compensa- tion Techniques . 62 3.7 Summary and Discussion . 69 4 Substructure Shake Table Testing of Lower Stories in Tall Buildings 71 4.1 Interface Compatibility using a Controlled Mass . 72 4.1.1 Simulation Models . 78 4.1.2 Numerical Investigation . 81 4.2 Interface Compatibility using a Force Controlled Actuator . 91 4.2.1 Actuator Control Scheme . 91 4.2.2 Numerical Case Study . 95 4.3 Summary and Discussion . 101 viii CONTENTS 5 Acceleration Feedback Control of Shake Tables 102 5.1 Acceleration Feedback Control with Force Stabilization . 103 5.1.1 Control Architecture . 103 5.1.2 Hardware Requirements . 105 5.2 Experimental Setup . 107 5.3 Experimental Investigation of the Proposed Acceleration Control Strat- egy . 108 5.3.1 Experimental Modeling of the Shake Table System . 110 5.3.2 Design of the Feedback Controllers and Pre-Gains . 112 5.3.3 Experimental Validation of the Proposed Acceleration Control Strategy . 116 5.4 Impact of Input Acceleration Errors in Shake Table Tests on Structural Response . 120 5.5 Summary and Discussion . 123 6 Conclusions and Future Work 125 6.1 Conclusions . 125 6.2 Future Work . 127 6.2.1 Near Term . 127 6.2.2 Long Term . 129 Appendix A 131 ix CONTENTS References 133 Vita 142 x List of Tables 3.1 Dynamic properties of the entire 10-story RTHS structure . 34 3.2 Summary of shake table performance from substructure shake table testing using 3 different compensation techniques. 66 4.1 Properties and dynamic characteristics of the 5-story structure. 79 4.2 RMS differences for simulation responses under different earthquake simulations. 86 5.1 Dynamic characteristics of three story test structure. 108 5.2 Analytical representations of the open loop shake table dynamics. 112 5.3 Errors between measured and reference shake table accelerations. 120 5.4 Errors between measured and reference top floor structural accelerations.123 xi List of Figures 1.1 Schematic of a early stage hand powered shake table, CREDIT: Severn (2011). 4 1.2 Schematic of the E-Defense shake table system, CREDIT: Ogawa et al. (2001). 4 1.3 Early implementation of pseudo-dynamic testing, CREDIT: Nakashima et al. (1992). 9 1.4 Implementation of RTHS where the experimental substructure is a single damper, CREDIT: Carrion et al. (2009). 9 1.5 Concept of substructure shake table testing including a tuned mass damper, CREDIT: Igarashi et al. (2000). 11 2.1 Schematic of a uni-axial shake table with linear structure. 16 2.2 Block diagram of shake table system including hydraulic actuator, test structure and feedback controller. 19 3.1 Schematics of substructure shake table testing in comparison with the entire simulation. 26 3.2 A block diagram for the concept of substructure shake table testing. 30 3.3 A three-story steel frame structure on the uni-axial shake table at Johns Hopkins University. 31 3.4 Frequency response curves of the three-story steel experimental sub- structure. 33 3.5 Frequency response curves of closed-loop (reference to measured) dis- placement and acceleration: (a) displacement magnitude; (b) acceler- ation magnitude; (c) displacement phase; and (d) acceleration phase. 37 3.6 Frequency response curve and coherence from the table acceleration to measured base shear. 39 3.7 A block diagram of the substructure shake table test system with com- pensation techniques for experimental errors. 40 xii LIST OF FIGURES 3.8 Acceleration and base shear time histories under 2.0 Hz harmonic ground excitation: (a) the entire acceleration time histories; (b) a zoomed section of the acceleration time histories; (c) the entire base shear time histories; and (d) a zoomed section of the base shear time histories. 48 3.9 Structural responses under 2.0 Hz harmonic ground excitation: (a), (d), and (g), relative floor displacement at the 10th, 6th and 2nd floor, respectively; (b), (e), and (h), absolute floor displacement at the 10th, 6th and 2nd floor, respectively; and (c), (f), and (i), absolute floor acceleration at the 10th, 6th and 2nd floor, respectively. 51 3.10 Acceleration and base shear time histories under 6.0 Hz harmonic ground excitation: (a) the entire acceleration time histories; (b) a zoomed section of the acceleration time histories; (c) the entire base shear time histories; and (d) a zoomed section of the base shear time histories. 52 3.11 Structural responses under 6.0 Hz harmonic ground excitation: (a), (d), and (g), relative floor displacement at the 10th, 6th and 2nd floor, respectively; (b), (e), and (h), absolute floor displacement at the 10th, 6th and 2nd floor, respectively; and (c), (f), and (i), absolute floor acceleration at the 10th, 6th and 2nd floor, respectively. 54 3.12 Acceleration and base shear time histories under the 1995 Kobe earth- quake excitation: (a) the entire acceleration time histories; (b) a zoomed section of the acceleration time histories; (c) the entire base shear time histories; and (d) a zoomed section of the base shear time histories. 55 3.13 Structural responses under the 1995 Kobe earthquake excitation: (a), (d), (g), (j), and (m), relative displacement at the even floors from top to bottom (10th to 2nd); (b), (e), (h), (k), and (n), absolute displace- ment at the even floors from top to bottom (10th to 2nd); and (c), (f), (i), (l), and (o), absolute displacement at the even floors from top to bottom (10th to 2nd)...........................