Stability Analysis of Real-Time Hybrid Simulation for Time-Varying Actuator Delay Using the Lyapunov-Krasovskii Functional Approach
Publication: Journal of Engineering Mechanics
Volume 145, Issue 1
Abstract
In a real-time hybrid simulation (RTHS), the actuator delay in experimental results might deviate from actual structural responses and even destabilize the real-time test. Although the assumption of a constant actuator delay helps simplify the stability analysis of RTHS, experimental results often show that the actuator delay varies throughout the test. However, research on the effect of time-varying delay on RTHS system stability is very limited. In this study, the Lyapunov-Krasovskii functional is introduced for the stability analysis of RTHS system. Two stability criteria are proposed for a linear system with a single constant delay and a time-varying delay. It is demonstrated that (1) the stable region of a time-varying delay system shrinks with the increase of the first derivative of time-varying delay; and (2) the stable region of the time-varying delay system is smaller than that of constant-time-delay system. Computational simulations were conducted for RTHS systems with a single degree of freedom to evaluate the proposed criteria. When the experimental specimen is an ideal elastic spring, the stability region of RTHS system with time-varying delay is shown to depend on the stiffness partition, structural natural period, and damping ratio. Significant differences in stability regions indicate that the time-varying characteristics of actuator delay should be considered for stability analysis of RTHS systems.
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Acknowledgments
The research described in this paper was financially supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions, No. 1105007002.
References
Bajaj, C. 1986. “Limitations to algorithm solvability: Galois methods and models of computation.” In Proc., 5th Association for Computing Machinery Symp. on Symbolic and Algebraic Computation, 71–76. New York: Association for Computing Machinery.
Botelho, R. M., and R. E. Christenson. 2015. “Robust stability and performance analysis for multi-actuator real-time hybrid substructuring.” In Vol. 4 of Dynamics of coupled structures, 1–7. New York: Springer.
Botelho, R. M., J. A. Franco, and R. E. Christenson. 2015. “System-level vibration testing of physical hardware components using real-time hybrid substructuring.” In Proc., ASME 2015 Noise Control and Acoustics Division Conf. at InterNoise 2015. New York: ASME.
Boyd, S., L. El Ghaoui, E. Feron, and V. Balakrishnan. 1994. Linear matrix inequalities in system and control theory. Philadelphia: Society for Industrial and Applied Mathematics.
Carrion, J. E., and B. F. Spencer, Jr. 2007. Model-based strategies for real-time hybrid testing. Champaign, IL: Univ. of Illinois at Urbana-Champaign.
Chae, Y., K. Kazemibidokhti, and J. M. Ricles. 2013. “Adaptive time series compensator for delay compensation of servo-hydraulic actuator systems for real-time hybrid simulation.” Earthquake Eng. Struct. Dyn. 42 (11): 1697–1715. https://doi.org/10.1002/eqe.2294.
Chen, C., and J. M. Ricles. 2008. “Stability analysis of SDOF real-time hybrid testing systems with explicit integration algorithms and actuator delay.” Earthquake Eng. Struct. Dyn. 37 (4): 597–613. https://doi.org/10.1002/eqe.775.
Chen, C., and J. M. Ricles. 2010. “Tracking error-based servohydraulic actuator adaptive compensation for real-time hybrid simulation.” J. Struct. Eng. 136 (4): 432–440. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000124.
Chen, C., J. M. Ricles, and T. Guo. 2012. “Improved adaptive inverse compensation technique for real-time hybrid simulation.” J. Eng. Mech. 138 (12): 1432–1446. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000450.
Chen, C., J. M. Ricles, R. Sause, and R. Christenson. 2010. “Experimental evaluation of an adaptive inverse compensation technique for real-time simulation of a large-scale magneto-rheological fluid damper.” Smart Mater. Struct. 19 (2): 025017. https://doi.org/10.1088/0964-1726/19/2/025017.
Chen, P. C., and K. C. Tsai. 2013. “Dual compensation strategy for real-time hybrid testing.” Earthquake Eng. Struct. Dyn. 42 (1): 1–23. https://doi.org/10.1002/eqe.2189.
Combescure, D., and P. Pegon. 1997. “α-operator splitting time integration technique for pseudodynamic testing error propagation analysis.” Soil Dyn. Earthquake Eng. 16 (7): 427–443. https://doi.org/10.1016/S0267-7261(97)00017-1.
Gu, K. 2000. “An integral inequality in the stability problem of time-delay systems.” In Vol. 3 of Proc., 39th IEEE Conf. on Decision and Control, 2805–2810. Piscataway, NJ: IEEE.
Gu, K., J. Chen, and V. L. Kharitonov. 2003. Stability of time-delay systems. New York: Springer.
Guo, T., C. Chen, W. J. Xu, and F. Sanchez. 2014. “A frequency response analysis approach for quantitative assessment of actuator tracking for real-time hybrid simulation.” Smart Mater. Struct. 23 (4): 045042. https://doi.org/10.1088/0964-1726/23/4/045042.
Han, Q. L. 2005. “Absolute stability of time-delay systems with sector-bounded nonlinearity.” Automatica 41 (12): 2171–2176. https://doi.org/10.1016/j.automatica.2005.08.005.
Hessabi, R. M., A. Ashasi-Sorkhabi, and O. Mercan. 2016. “A new tracking error-based adaptive controller for servo-hydraulic actuator control.” J. Vib. Control 22 (12): 2824–2840. https://doi.org/10.1177/1077546314548205.
Hessabi, R. M., and O. Mercan. 2012. “Phase and amplitude error indices for error quantification in pseudodynamic testing.” Earthquake Eng. Struct. Dyn. 41 (10): 1347–1364. https://doi.org/10.1002/eqe.1186.
Horiuchi, T., M. Inoue, T. Konno, and Y. Namita. 1999. “Real-time hybrid experimental system with actuator delay compensation and its application to a piping system with energy absorber.” Earthquake Eng. Struct. Dyn. 28 (10): 1121–1141. https://doi.org/10.1002/(SICI)1096-9845(199910)28:10%3C1121::AID-EQE858%3E3.0.CO;2-O.
Horiuchi, T., and T. Konno. 2001. “A new method for compensating actuator delay in real–time hybrid experiments.” Philos. Trans. R. Soc. London, Ser. A 359 (1786): 1893–1909. https://doi.org/10.1098/rsta.2001.0878.
Huang, L., T. Guo, C. Chen, and M. H. Chen. 2018. “Restoring force correction based on online discrete tangent stiffness estimation method for real time hybrid simulation.” Earthquake Eng. Eng. Vib. 17 (4): 805–820.
Huang, L., T. Guo, and W. J. Xu. 2016. “Theoretical analysis and experimental verification of errors in real-time hybrid simulation.” [In Chinese.] J. Southeast Univ. (Natural Science Edition) 46 (5): 1045–1050.
Huang, W. 1989. “Generalization of Liapunov’s theorem in a linear delay system.” J. Math. Anal. Appl. 142 (1): 83–94. https://doi.org/10.1016/0022-247X(89)90166-2.
Maghareh, A., S. Dyke, S. Rabieniaharatbar, and A. Prakash. 2017. “Predictive stability indicator: A novel approach to configuring a real-time hybrid simulation.” Earthquake Eng. Struct. Dyn. 46 (1): 95–116. https://doi.org/10.1002/eqe.2775.
Maghareh, A., S. J. Dyke, A. Prakash, and J. F. Rhoads. 2014. “Establishing a stability switch criterion for effective implementation of real-time hybrid simulation.” Smart Struct. Syst. 14 (6): 1221–1245. https://doi.org/10.12989/sss.2014.14.6.1221.
Maghareh, A., C. E. Silva, and S. J. Dyke. 2018. “Servo-hydraulic actuator in controllable canonical form: Identification and experimental validation.” Mech. Syst. Sig. Proc. 100: 398–414. https://doi.org/10.1016/j.ymssp.2017.07.022.
Mahin, S. A., and P. S. B. Shing. 1985. “Pseudodynamic method for seismic testing.” J. Struct. Eng. 111 (7): 1482–1503. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:7(1482).
Meng, H. F. 2013. Study on several stability problems of linear retarded systems. Shanghai, China: Univ. of Science and Technology of China.
Mercan, O., and J. M. Ricles. 2007. “Stability and accuracy analysis of outer loop dynamics in real-time pseudodynamic testing of SDOF systems.” Earthquake Eng. Struct. Dyn. 36 (11): 1523–1543. https://doi.org/10.1002/eqe.701.
Mercan, O., and J. M. Ricles. 2008. “Stability analysis for real-time pseudodynamic and hybrid pseudodynamic testing with multiple sources of delay.” Earthquake Eng. Struct. Dyn. 37 (10): 1269–1293. https://doi.org/10.1002/eqe.814.
Mosqueda, G., B. Stojadinovic, and S. A. Mahin. 2007. “Real-time error monitoring for hybrid simulation. Part I: Methodology and experimental verification.” J. Struct. Eng. 133 (8): 1100–1108. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:8(1100).
Nakashima, M., T. Kaminosomo, and M. Ishida, and K. Ando. 1990. “Integration techniques for substructure pseudo dynamic test.” In Vol. 2 of Proc., 4th U.S. National Conf. on Earthquake Engineering, 515–524. Palm Springs, CA: Earthquake Engineering Research Institute.
Nakashima, M., H. Kato, and E. Takaoka. 1992. “Development of real-time pseudodynamic testing.” Earthquake Eng. Struct. Dyn. 21 (1): 79–92. https://doi.org/10.1002/eqe.4290210106.
Olgac, N., and R. Sipahi. 2002. “An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems.” IEEE Trans. Autom. Control 47 (5): 793–797. https://doi.org/10.1109/TAC.2002.1000275.
Phillips, B. M. 2012. “Model-based feedforward-feedback control for real-time hybrid simulation of large-scale structures.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Illinois at Urbana–Champaign.
Rekasius, Z. V. 1980. “A stability test for systems with delay.” In Proc., Joint Automatic Control Conf. New York: ASME.
Thewalt, C., and M. Roman. 1994. “Performance parameters for pseudodynamic tests.” J. Struct. Eng. 120 (9): 2768–2781. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:9(2768).
Wallace, M. I., J. Sieber, S. A. Neild, D. J. Wagg, and B. Krauskopf. 2005. “Stability analysis of real-time dynamic substructuring using delay differential equation models.” Earthquake Eng. Struct. Dyn. 34 (15): 1817–1832. https://doi.org/10.1002/eqe.513.
Wang, Z., B. Wu, O. S. Bursi, G. S. Xu, and Y. Ding. 2014. “An effective online delay estimation method based on a simplified physical system model for real-time hybrid simulation.” Smart Struct. Syst. 14 (6): 1247–1267. https://doi.org/10.12989/sss.2014.14.6.1247.
Xu, W. J., T. Guo, and C. Chen. 2017. “Localized evaluation of actuator tracking for real-time hybrid simulation using frequency-domain indices.” Struct. Eng. Mech. 62 (5): 631–642. https://doi.org/10.12989/sem.2017.62.5.631.
Zhu, F., J. T. Wang, F. Jin, D. C. Fu, and G. Yao. 2015. “Stability analysis of MDOF real-time dynamic hybrid testing systems using the discrete-time root locus technique.” Earthquake Eng. Struct. Dyn. 44 (2): 221–241. https://doi.org/10.1002/eqe.2467.
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©2018 American Society of Civil Engineers.
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Received: Jan 23, 2018
Accepted: Jun 28, 2018
Published online: Oct 30, 2018
Published in print: Jan 1, 2019
Discussion open until: Mar 30, 2019
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