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Robust stability analysis of real-time hybrid simulation considering system uncertainty and delay compensation

  • Chen, Pei-Ching (Department of Civil and Construction Engineering, National Taiwan University of Science and Technology) ;
  • Chen, Po-Chang (Department of Civil and Construction Engineering, National Taiwan University of Science and Technology)
  • Received : 2019.09.24
  • Accepted : 2020.03.05
  • Published : 2020.06.25

Abstract

Real-time hybrid simulation (RTHS) which combines physical experiment with numerical simulation is an advanced method to investigate dynamic responses of structures subjected to earthquake excitation. The desired displacement computed from the numerical substructure is applied to the experimental substructure by a servo-hydraulic actuator in real time. However, the magnitude decay and phase delay resulted from the dynamics of the servo-hydraulic system affect the accuracy and stability of a RTHS. In this study, a robust stability analysis procedure for a general single-degree-of-freedom structure is proposed which considers the uncertainty of servo-hydraulic system dynamics. For discussion purposes, the experimental substructure is a portion of the entire structure in terms of a ratio of stiffness, mass, and damping, respectively. The dynamics of the servo-hydraulic system is represented by a multiplicative uncertainty model which is based on a nominal system and a weight function. The nominal system can be obtained by conducting system identification prior to the RTHS. A first-order weight function formulation is proposed which needs to cover the worst possible uncertainty envelope over the frequency range of interest. Then, the Nyquist plot of the perturbed system is adopted to determine the robust stability margin of the RTHS. In addition, three common delay compensation methods are applied to the RTHS loop to investigate the effect of delay compensation on the robust stability. Numerical simulation and experimental validation results indicate that the proposed procedure is able to obtain a robust stability margin in terms of mass, damping, and stiffness ratio which provides a simple and conservative approach to assess the stability of a RTHS before it is conducted.

References

  1. Carrion, J.E. and Spencer, B.F. (2007), "Model-based strategies for real-time hybrid testing", No. 6; Newmark Structural Engineering Laboratory Report Series, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
  2. Chae, Y., Kazemibidokhti, K. and Ricles, J.M. (2013), "Adaptive time series compensator for delay compensation of servohydraulic actuator systems for real-time hybrid simulation", Earthq. Eng. Struct. Dyn., 42(11), 1697-1715. https://doi.org/10.1002/eqe.2294
  3. Chen, C. (2007), "Development and numerical simulation of hybrid effective testing method.", Ph.D. Dissertation; Lehigh University, Bethlehem, PA, USA.
  4. Chen, C. and Ricles, J.M. (2008), "Stability analysis of SDOF real-time hybrid testing systems with explicit integration algorithms and actuator delay", Earthq. Eng. Struct. Dyn., 37(4), 597-613. https://doi.org/10.1002/eqe.775
  5. Chen, C. and Ricles, J.M. (2009), "Analysis of actuator delay compensation methods for real-time testing", Eng. Struct., 31(11), 2643-2655. https://doi.org/10.1016/j.engstruct.2009.06.012 https://doi.org/10.1016/j.engstruct.2009.06.012
  6. Chen, P.C. and Tsai, K.C. (2013), "Dual compensation strategy for real-time hybrid testing", Earthq. Eng. Struct. Dyn., 42(1), 1-23. https://doi.org/10.1002/eqe.2189
  7. Chen, C., Ricles, J.M., Marullo, T.M. and Mercan, O. (2009), "Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm.", Earthq. Eng. Struct. Dyn., 38(1), 23-44. https://doi.org/10.1002/eqe.838
  8. Chen, P.C., Tsai, K.C. and Lin, P.Y. (2014), "Real-time hybrid testing of a smart base isolation system", Earthq. Eng. Struct. Dyn., 43(1), 139-158. https://doi.org/10.1002/eqe.2341
  9. Doyle, J., Francis, B. and Tannenbaum, A. (1992), Feedback Control Theory, Macmillan, New York, NY, USA.
  10. Gonzalez-Buelga, A., Wagg, D.J. and Neild, S.A. (2007), "Parametric variation of a coupled pendulum-oscillator system using real-time dynamic substructuring", Struct. Control Health Monitor., 14(7), 991-1012. https://doi.org/10.1002/stc.189 https://doi.org/10.1002/stc.189
  11. Hayati, S. and Song, W. (2017), "An optimal discrete-time feedforward compensator for real-time hybrid simulation", Smart Struct. Syst., Int. J., 20(4), 483-498. https://doi.org/10.12989/sss.2017.20.4.483
  12. Horiuchi, T. and Konno, T. (2001), "A new method for compensating actuator delay in real-time hybrid experiments", Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, 359, 1786-1893. https://doi.org/10.1098/rsta.2001.0878
  13. Horiuchi, T., Inoue, M., Konno, T. and Namita, Y. (1999), "Real-time hybrid experimental system with actuator delay compensation and its application to a piping system with energy absorber", Earthq. Eng. Struct. Dyn., 28(10), 1121-1141. https://doi.org/10.1002/(SICI)1096-9845(199910)28:10<1121::AID-EQE858>3.0.CO;2-O https://doi.org/10.1002/(SICI)1096-9845(199910)28:10<1121::AID-EQE858>3.0.CO;2-O
  14. Huang, L., Chen, C., Guo, T. and Chen, M. (2019), "Stability analysis of real-time hybrid simulation for time-varying actuator delay using the Lyapunov-Krasovskii functional approach", J. Eng. Mech., 145(1), 04018124. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001550 https://doi.org/10.1061/(asce)em.1943-7889.0001550
  15. Jung, R.Y., Shing, P.B., Stauffer, E. and Bradford, T. (2007), "Performance of a real-time pseudodynamic test system considering nonlinear structural response", Earthq. Eng. Struct. Dyn., 36(12), 1785-1809. https://doi.org/10.1002/eqe.722
  16. Maghareh, A., Dyke, S.J., Rabieniaharatbar, S. and Prakash, A. (2017), "Predictive stability indicator: a novel approach to configuring a real-time hybrid simulation", Earthq. Eng. Struct. Dyn., 46(1), 95-116. https://doi.org/10.1002/eqe.2775
  17. Mercan, O. and Ricles, J.M. (2007), "Stability and accuracy analysis of outer loop dynamics in real-time pseudodynamic testing of SDOF systems", Earthq. Eng. Struct. Dyn., 36(11), 1523-1543. https://doi.org/10.1002/eqe.701
  18. Merritt, H.E. (1967), Hydraulic Control Systems, Wiley, New York, USA.
  19. Oppenheim, A.V., Schafer, R.W. and Buck, J.R. (1999), Discrete-Time Signal Processing, Prentice Hall, NJ, USA.
  20. Phillips, B.M., Takada, S., Spencer, B.F. and Yozo, F. (2014), "Feedforward actuator controller development using the backward-difference method for real-time hybrid simulation", Smart Struct. Syst., Int. J., 14(6), 1081-1103. https://doi.org/10.12989/sss.2014.14.6.1081
  21. Rekasius, Z.V. (1980), "A stability test for systems with delay", Proceedings, Joint Automatic Control Conference, San Francisco, CA, USA, Paper no. TP9-A.
  22. Tang, Z., Dietz, M. and Li, Z. (2018), "Substructuring stability analysis in light of comprehensive transfer system dynamics", Bull. Earthq. Eng., 16(1), 129-154. https://doi.org/10.1007/s10518-017-0192-9
  23. Wallace, M.I., Sieber, J., Nield, S.A., Wagg, D.J. and Krauskopf, B. (2005), "Stability analysis of real-time dynamic substructuring using delay differential equations", Earthq. Eng. Struct. Dyn., 34(15), 1817-1832. https://doi.org/10.1002/eqe.513
  24. Zhou, K. and Doyle, J. (1998), Essentials of Robust Control, Prentice Hall, New Jersey, USA.
  25. Zhu, F., Wang, J.T., Jin, F., Chi, F.D. and Gui, Y. (2015), "Stability analysis of MDOF real-time dynamic hybrid testing systems using the discrete-time root locus technique", Earthq. Eng. Struct. Dyn., 44(2), 221-241. https://doi.org/10.1002/eqe.2467