An adaptive delay compensation method based on a discrete system model for real-time hybrid simulation

  • Wang, Zhen (School of Civil Engineering and Architecture, Wuhan University of Technology) ;
  • Xu, Guoshan (Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology) ;
  • Li, Qiang (Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology) ;
  • Wu, Bin (School of Civil Engineering and Architecture, Wuhan University of Technology)
  • Received : 2019.07.19
  • Accepted : 2019.12.17
  • Published : 2020.05.25


The identification of delays and delay compensation are critical problems in real-time hybrid simulations (RTHS). Conventional delay compensation methods are mostly based on the assumption of a constant delay. However, the system delay may vary during tests owing to the nonlinearity of the loading system and/or the behavioral variations of the specimen. To address this issue, this study presents an adaptive delay compensation method based on a discrete model of the loading system. In particular, the parameters of this discrete model are identified and updated online with the least-squares method to represent a servo hydraulic loading system. Furthermore, based on this model, the system delays are compensated for by generating system commands using the desired displacements, achieved displacements, and previous displacement commands. This method is more general than the existing compensation methods because it can predict commands based on multiple displacement categories. Moreover, this method is straightforward and suitable for implementation on digital signal processing boards because it relies solely on the displacements rather than on velocity and/or acceleration data. The virtual and real RTHS results show that the studied method exhibits satisfactory estimation smoothness and compensation accuracy. Furthermore, considering the measurement noise, the low-order parameter models of this method are more favorable than that the high-order parameter models.


  1. Ahmadizadeh, M., Mosqueda, G. and Reinhorn, A.M. (2008), "Compensation of actuator delay and dynamics for real-time hybrid structural simulation", Earthq. Eng. Struct., 37(1), 21-42.
  2. Bonnet, P., Lim, C., Williams, M., Blakeborough, A., Neild, S., Stoten, D. and Taylor, C. (2007), "Real-time hybrid experiments with newmark integration, MCSmd outer-loop control and multitasking strategies", Earthq. Eng. Struct. Dyn., 36(1), 119-141.
  3. 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.
  4. Chae, Y., Ricles, J.M. and Sause, R. (2014), "Large-scale real-time hybrid simulation of a three-story steel frame building with magneto-rheological dampers", Earthq. Eng. Struct. Dyn., 43(13), 1915-1933.
  5. Chae, Y., Park, M., Kim, C.Y. and Park, Y.S. (2017), "Experimental study on the rate-dependency of reinforced concrete structures using slow and real-time hybrid simulations", Eng. Struct., 132, 648-658.
  6. Chen, C. and Ricles, J. (2009), "Improving the inverse compensation method for real-time hybrid simulation through a dual compensation scheme", Earthq. Eng. Struct. Dyn., 38(10), 1237-1255.
  7. Chen, C., Ricles, J.M. and Guo, T. (2012), "Improved adaptive inverse compensation technique for real-time hybrid simulation", J. Eng. Mech., 138(12), 1432-1446.
  8. Chen, P.C., Hsu, S.C., Zhong, Y.J. and Wang, S.J. (2019), "Realtime hybrid simulation of smart base-isolated raised floor systems for high-tech industry", Smart Struct. Syst., Int. J., 23(1), 91-106.
  9. Christenson, R. and Lin, Y. (2008), "Real-time hybrid simulation of a seismically excited structure with large-scale magnetorheological fluid dampers", In: Hybrid Simulation: Theory, Implementation and Applications, (V. Saouma and M. Sivaselvan eds.), Taylor & Francis, pp. 169-180.
  10. Darby, A.P., Williams, M.S. and Blakeborough, A. (2002), "Stability and delay compensation for real-time substructure testing", J. Eng. Mech., 128(12), 1276-1284. https://doi:10.1061/(ASCE)0733-9399(2002)128:12(1276)
  11. Eem, S.H., Koo, J.H. and Jung, H.J. (2018), "Feasibility study of an adaptive mount system based on magnetorheological elastomer using real-time hybrid simulation", J. Intell. Mater. Syst. Struct., 1045389X1875434.
  12. Gao, X., Castaneda, N. and Dyke, S.J. (2013), "Real time hybrid simulation: from dynamic system, motion control to experimental error", Earthq. Eng. Struct. Dyn., 42(6), 815-832.
  13. 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.
  14. Horiuchi, T. and Konno, T. (2001), "A new method for compensating actuator delay in realtime hybrid experiments", Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 359(1786), 1893-1909.
  15. Horiuchi, T., Inoue, M., Konno, T. and Namita, Y. (1999), "Realtime 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.<1121::AID-EQE858>3.0.CO;2-O<1121::AID-EQE858>3.0.CO;2-O
  16. 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.
  17. Jung, R. and Shing, P. (2006), "Performance evaluation of a realtime pseudo dynamic test system", Earthq. Eng. Struct. Dyn., 35(7), 789-810.
  18. Levine, W.S. (1999), Control System Fundamentals, CRC Press, Boca Raton, FL, USA.
  19. Lu, L., Fermandois, G.A., Lu, X., Spencer, B.F. Jr., Duan, Y.F. and Zhou, Y. (2019), "Experimental evaluation of an inertial mass damper and its analytical model for cable vibration mitigation", Smart Struct. Syst., Int. J., 23(6), 589-613.
  20. Nakashima, M. and Masaoka, N. (1999), "Real-time on-line test for MDOF systems", Earthq. Eng. Struct. Dyn., 28(4), 393-420.<393::AID-EQE823>3.0.CO;2-C<393::AID-EQE823>3.0.CO;2-C
  21. Nakashima, M., Kato, H. and Takaoka, E. (1992), "Development of real-time pseudo dynamic testing", Earthq. Eng. Struct. Dyn., 21(1), 79-92.
  22. Ning, X., Wang, Z., Zhou, H., Wu, B., Ding, Y. and Bin, X. (2019), "Robust actuator dynamics compensation method for real-time hybrid simulation", Mech. Syst. Signal Process., 133(15), 49-70.
  23. Ou, G., Ozdagli, A.I., Dyke, S.J. and Wu, B. (2015), "Robust integrated actuator control: experimental verification and realtime hybrid-simulation implementation", Earthq. Eng. Struct. Dyn., 44(3), 441-460.
  24. Phillips, B.M. and Spencer, B.F. (2013), "Model-based feedforward-feedback actuator control for real-time hybrid simulation", J. Struct. Eng., 139(7), 1205-1214.
  25. Shao, X., van de Lindt, J., Bahmani, P., Pang, W., Ziaei, E., Symans, M., Tian, J. and Dao, T. (2014), "Real-time hybrid simulation of a multi-story wood shear wall with first-story experimental substructure incorporating a rate-dependent seismic energy dissipation device", Smart Struct. Syst., Int. J., 14(6), 1031-1054.
  26. Soderstrom, T. and Stoica, P. (1989), System Identification, Prentice Hall.
  27. Strano, S. and Terzo, M. (2016), "Actuator dynamics compensation for real-time hybrid simulation: an adaptive approach by means of a nonlinear estimator", Nonlinear Dyn., 85(4), 2353-2368. http://doi:10.1007/s11071-016-2831-0
  28. Wallace, M., Sieber, J., Neild, S., Wagg, D. and Krauskopf, B. (2005a), "Stability analysis of realtime dynamic substructuring using delay differential equation models", Earthq. Eng. Struct. Dyn., 34(15), 1817-1832.
  29. Wallace, M., Wagg, D. and Neild, S. (2005b), "An adaptive polynomial based forward prediction algorithm for multiactuator real-time dynamic substructuring", Proc. R. Soc., 461(2064), 3807-3826.
  30. Wang, Z., Wu, B., Bursi, O.S., Xu, G. and Ding, Y. (2014), "An effective online delay estimation method based on a simplified physical system model for real-time hybrid simulation", Smart Struct. Syst., Int. J., 14(6), 1247-1267. http://doi:10.12989/sss.2014.14.6.1247
  31. Wang, J.T., Gui, Y., Zhu, F., Jin, F. and Zhou, M.X. (2016), "Realtime hybrid simulation of multi-story structures installed with tuned liquid damper", Struct. Control Heal. Monit., 23(7), 1015-1031.
  32. Wang, Z., Li, Q. and Wu, B. (2018), "Adaptive delay compensation method for real-time hybrid testing", Eng. Mech., 35(9), 37-43. [In Chinese]
  33. Wu, B. and Zhou, H. (2014), "Sliding mode for equivalent force control in real-time substructure testing", Struct. Control Heal. Monit., 21(10), 1284-1303.
  34. Wu, B., Shi, P., Wang, Q., Guan, X. and Ou, J. (2011), "Performance of an offshore platform with MR dampers subjected to ice and earthquake", Struct. Control Heal. Monit., 18(6), 682-697.
  35. Wu, B., Wang, Z. and Bursi, O.S. (2013), "Actuator dynamics compensation based on upper bound delay for real-time hybrid simulation", Earthq. Eng. Struct. Dyn., 42(12), 1749-1765.
  36. Zhang, Z., Basu, B. and Nielsen, S.R.K. (2019), "Real-time hybrid aeroelastic simulation of wind turbines with various types of full-scale tuned liquid dampers", Wind Energy., 22(2), 239-256.
  37. Zhao, J., French, C., Shield, C. and Posbergh, T. (2003), "Considerations for the development of real-time dynamic testing using servo-hydraulic actuation", Earthq. Eng. Struct. Dyn., 32(11), 1773-1794.
  38. Zhou, H., Wagg, D.J. and Li, M. (2017), "Equivalent force control combined with adaptive polynomial-based forward prediction for real-time hybrid simulation", Struct. Control Heal. Monit., 24(11), e2018.