An optimal discrete-time feedforward compensator for real-time hybrid simulation

  • Hayati, Saeid (Department of Civil, Construction and Environmental Engineering, The University of Alabama) ;
  • Song, Wei (Department of Civil, Construction and Environmental Engineering, The University of Alabama)
  • Received : 2017.03.18
  • Accepted : 2017.05.29
  • Published : 2017.10.25


Real-Time Hybrid Simulation (RTHS) is a powerful and cost-effective dynamic experimental technique. To implement a stable and accurate RTHS, time delay present in the experiment loop needs to be compensated. This delay is mostly introduced by servo-hydraulic actuator dynamics and can be reduced by applying appropriate compensators. Existing compensators have demonstrated effective performance in achieving good tracking performance. Most of them have been focused on their application in cases where the structure under investigation is subjected to inputs with relatively low frequency bandwidth such as earthquake excitations. To advance RTHS as an attractive technique for other engineering applications with broader excitation frequency, a discrete-time feedforward compensator is developed herein via various optimization techniques to enhance the performance of RTHS. The proposed compensator is unique as a discrete-time, model-based feedforward compensator. The feedforward control is chosen because it can substantially improve the reference tracking performance and speed when the plant dynamics is well-understood and modeled. The discrete-time formulation enables the use of inherently stable digital filters for compensator development, and avoids the error induced by continuous-time to discrete-time conversion during the compensator implementation in digital computer. This paper discusses the technical challenges in designing a discrete-time compensator, and proposes several optimal solutions to resolve these challenges. The effectiveness of compensators obtained via these optimal solutions is demonstrated through both numerical and experimental studies. Then, the proposed compensators have been successfully applied to RTHS tests. By comparing these results to results obtained using several existing feedforward compensators, the proposed compensator demonstrates superior performance in both time delay and Root-Mean-Square (RMS) error.


  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. D., 37(1), 21-42.
  2. Astrom, K.J., Hagander, P. and Sternby, J. (1984), "Zeros of sampled systems", Automatica, 20(1), 31-38.
  3. Butterworth, J.A., Pao, L.Y. and Abramovitch, D.Y. (2008), "The effect of nonminimum-phase zero locations on the performance of feedforward model-inverse control techniques in discrete-time systems", Proceedings of the 2008 American Control Conference, Westin Seatle Hotel, Seatle, Washington, USA.
  4. Carrion, J.E. and Spencer, Jr., B.F. (2007), "Model-based strategies for real-time hybrid testing", NSEL-006, University of Illinois at Urbana-Champaign, Champaign-Urbana, IL, USA.
  5. Carrion, J.E., Spencer, Jr., B.F. and Phillips, B.M. (2009), "Realtime hybrid simulation for structural control performance assessment", Earthq. Eng. Eng. Vib.. 8(4), 481-492.
  6. 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. D., 42(11), 1697-1715.
  7. Chen, C. (2007), "Development and numerical simulation of hybrid effective force testing method", Ph.D. Dissertation, Lehigh University, Bethlehem, PA.
  8. Chen, C. and Ricles, J.M. (2009a), "Analysis of actuator delay compensation methods for real-time testing", Eng. Struct., 31(11), 2643-2655.
  9. Chen, C. and Ricles, J.M. (2009b), "Improving the inverse compensation method for real-time hybrid simulation through a dual compensation scheme", Earthq. Eng. Struct. D., 38(10), 1237-1255.
  10. Chen, C. and Ricles, J.M. (2010), "Tracking error-based servohydraulic actuator adaptive compensation for real-time hybrid simulation", J. Struct. Eng. - ASCE, 136(4), 432-440.
  11. Chonhenchob, V., Singh, S.P., Singh, J.J., Stallings, J. and Grewal, G. (2012), "Measurement and analysis of vehicle vibration for delivering packages in small-sized and mediumsized trucks and automobiles", Packaging Technol. Sci., 25(1), 31-38.
  12. Darby, A.P., Blakeborough, A. and Williams, M.S. (1999), "Realtime substructure tests using hydraulic actuator", J. Eng. Mech., 125(10), 1133-1139.
  13. Darby, A.P., Blakeborough, A. and Williams, M.S. (2001), "Improved control algorithm for real-time substructure testing", Earthq. Eng. Struct. D., 30(3), 431-448.
  14. 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.
  15. Dyke, S.J., Spencer, Jr., B.F. Quast, P. and Sain, M.K. (1995), "Role of control-structure interaction in protective system design", J. Eng. Mech., 121(2), 322-338.
  16. Fu, Y. and Dumont, G.A. (1989), "Choice of sampling to ensure minimum-phase behaviour", IEEE T. Autom. Contr., 34(5), 560-563.
  17. Gao, X., Castaneda, N. and Dyke, S.J. (2013), "Real time hybrid simulation: from dynamic system, motion control to experimental error", Earthq. Eng. Struct. D., 42(6), 815-832.
  18. Gillespie, T.D. and Sayers, M. (1981), "Role of road roughness in vehicle ride", Proceedings of the 60th Annual Meeting of the Transportation Research Board, Washington District of Columbia, United States.
  19. Gomez, D., Dyke, S.J. and Maghareh, A. (2015), "Enabling role of hybrid simulation across NEES in advancing earthquake engineering", Smart Struct. Syst., 15(3), 913-929.
  20. Goodwin, G.C., Graebe, S.F. and Salgado, M.E. (2001), Control System Design, Prentice Hall.
  21. Gross, E., Tomizuka, M. and Messner, W. (1994), "Cancellation of discrete time unstable zeros by feedforward control", J. Dyn.. Syst. Meas. Control, 116(1), 33-38.
  22. Hagiwara, T. (1996), "Analytic study on the intrinsic zeros of sampled-data systems", IEEE T. Autom.Contr., 41(2), 261-263.
  23. Horiuchi, T., Nakagawa, M., Sugano, M. and Konno, T. (1996), "DEVELOPMENT OF A REAL-TIME HYBRID EXPERIMENTAL SYSTEM WITH ACTUATOR DELAY COMPENSATION", Proceedings of the 11th World Conference on Earthquake Engineering, Acapulco, Mexico.
  24. 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. D., 28(10), 1121-1141.<1121::AID-EQE858>3.0.CO;2-O
  25. Jung, R.Y. and Shing, P.B. (2006), "Performance evaluation of a real-time pseudodynamic test system", Earthq. Eng. Struct. D., 35(7), 789-810.
  26. Kailath, T., Sayed, A.H. and Hassibi, B. (2000), Linear Estimation, Prentice Hall.
  27. Marlin, T.E. (2000), Process control: designing processes and control systems for dynamic performance, McGraw-Hill.
  28. MATLAB (Version R2014a), The MathWorks, Inc., Natick, Massachusetts, USA.
  29. Nakashima, M. and Masaoka, N. (1999), "Real-time on-line test for MDOF systems", Earthq. Eng. Struct. D., 28(4), 393-420.<393::AID-EQE823>3.0.CO;2-C
  30. Oppenheim, A.V. and Schafer, R.W. (2010), Discrete-time Signal Processing, Pearson.
  31. 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. D., 44(3), 441-460.
  32. Phillips, B.M. and Spencer, Jr., B.F. (2011), "Model-based feedforward-feedback tracking control for real-time hybrid simulation", NSEL-028, University of Illinois at Urbana-Champaign, Champaign-Urbana, IL, USA.
  33. Phillips, B.M. and Spencer, Jr., B.F. (2013), "Model-based feedforward-feedback actuator control for real-time hybrid simulation", J. Struct. Eng. - ASCE, 139(7), 1205-1214.
  34. Phillips, B.M., Takada, S., Spencer, Jr., B.F. and Fujino, Y. (2014), "Feedforward actuator controller development using the backward-difference method for real-time hybrid simulation", Smart Struct. Syst., 14(6), 1081-1103.
  35. Schneider, A.M., Kaneshige, J.T. and Groutage, F.D. (1991), "Higher order s-to-z mapping functions and their application in digitizing continuous-time filters", Proceedings of the IEEE. 79(11), 1661-1674.
  36. Smith, J.O. (2008), Introduction to Digital Filters: With Audio Applications, W3K.
  37. Tomizuka, M. (1987), "Zero Phase Error Tracking Algorithm for Digital Control", J. Dyn. Syst. Meas. Control, 109.
  38. Tyan, F. and Tu, S.H. (2015), "A Lyapunov based multi-level controller for semi-active suspension system with an MRF damper", Asian J. Control., 17(2), 615-625.
  39. Wen, J.T. and Potsaid, B. (2004), "An experimental study of a high performance motion control system", Proceedings of the American Control Conference, Boston, MA, USA.