Earthquake Engineering and Engineering Vibration

, Volume 16, Issue 4, pp 671–691 | Cite as

Model-based framework for multi-axial real-time hybrid simulation testing

  • Gaston A. Fermandois
  • Billie F. SpencerJr.
Special Section: State-of-the-Art of Hybrid Testing Method


Real-time hybrid simulation is an efficient and cost-effective dynamic testing technique for performance evaluation of structural systems subjected to earthquake loading with rate-dependent behavior. A loading assembly with multiple actuators is required to impose realistic boundary conditions on physical specimens. However, such a testing system is expected to exhibit significant dynamic coupling of the actuators and suffer from time lags that are associated with the dynamics of the servo-hydraulic system, as well as control-structure interaction (CSI). One approach to reducing experimental errors considers a multi-input, multi-output (MIMO) controller design, yielding accurate reference tracking and noise rejection. In this paper, a framework for multi-axial real-time hybrid simulation (maRTHS) testing is presented. The methodology employs a real-time feedback-feedforward controller for multiple actuators commanded in Cartesian coordinates. Kinematic transformations between actuator space and Cartesian space are derived for all six-degrees-offreedom of the moving platform. Then, a frequency domain identification technique is used to develop an accurate MIMO transfer function of the system. Further, a Cartesian-domain model-based feedforward-feedback controller is implemented for time lag compensation and to increase the robustness of the reference tracking for given model uncertainty. The framework is implemented using the 1/5th-scale Load and Boundary Condition Box (LBCB) located at the University of Illinois at Urbana- Champaign. To demonstrate the efficacy of the proposed methodology, a single-story frame subjected to earthquake loading is tested. One of the columns in the frame is represented physically in the laboratory as a cantilevered steel column. For realtime execution, the numerical substructure, kinematic transformations, and controllers are implemented on a digital signal processor. Results show excellent performance of the maRTHS framework when six-degrees-of-freedom are controlled at the interface between substructures.


real-time hybrid simulation multiple actuators dynamic coupling kinematic transformations model-based compensation 


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The first author gratefully acknowledges the financial support for his Doctorate Studies from CONICYTChile through Becas Chile Scholarship No. 72140204, and Universidad Tecnica Federico Santa Maria (Chile) through Faculty Development Scholarship No. 208-13.


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Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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