Stability Anaysis of Real-time Hybrid Simulation for a Multi-story Structure Considering Time-delay of Hydrolic Actuator

Document Type : Research Article


Golpayegan university


Real-Time Hybrid Simulation (RTHS) is a kind of simulation in which an experiment part of a structure tested within the real-time simulation of its other parts. In this article, a building with multi-story structure divided into numerical and experimental substructures and the vibration behavior of experiment story studied among the numerical simulation of other stories. To apply the effect of static and inertial forces produced by the other stories to the experimental story, an electrohydraulic actuator is used. The dynamic of the electrohydraulic actuator can be estimated by pure time-delay and this delay in the loop of simulation can reduce accuracy and cause the system instability. Therefore, Delayed Differential Equation (DDE) used to determine the critical time-delay depending on the system parameters. The results of simulation show the effect of non-dimensional parameters and time-delay in stability margin of hybrid simulation.


Main Subjects

[1] Saouma V, Sivaselvan M. Hybrid simulation: Theory, im- plementation and applications: CRC Press; 2014.
[2]  Wallace M, Wagg D, Neild S. An adaptive polynomial based forward prediction algorithm for multi-actuator real- time dynamic substructuring. Proceedings of the Royal So- ciety A: Mathematical, Physical and Engineering Sciences. 2005;461(2064):3807-26.
[3]  Tu J-Y, Hsiao W-D, Chen C-Y. Modelling and control is- sues of dynamically substructured systems: adaptive forward prediction taken as an example. Proceedings of the Royal So- ciety A: Mathematical, Physical and Engineering Sciences. 2014;470(2168):20130773.
[4]  Zhou H, Wagg DJ, Li M. Equivalent force control com- bined with adaptive polynomial‐based forward prediction for real‐time hybrid simulation. Structural Control and Health Monitoring. 2017;24(11):e2018.
[5] Reinhorn A, Sivaselvan M, Weinreber S, Shao X. Real-time dynamic hybrid testing of structural systems. 2004.
[6]  Gawthrop P, Virden D, Neild S, Wagg D. Emulator-based control for actuator-based hardware-in-the-loop testing. Con- trol Engineering Practice. 2008;16(8):897-908.
[7]  Horiuchi T, Konno T. A new  method  for  compensat- ing actuator delay in real–time hybrid experiments. Philo- sophical Transactions of the Royal Society of London Se-ries A: Mathematical, Physical and Engineering Sciences. 2001;359(1786):1893-909.
[8]  Jung RY, Benson Shing P. Performance evaluation of a real‐time pseudodynamic test system. Earthquake engineering & structural dynamics. 2006;35(7):789-810.
[9]  Chen C, Ricles JM. Improving the inverse compensation method for real‐time hybrid simulation through a dual com- pensation scheme. Earthquake Engineering & Structural Dy- namics. 2009;38(10):1237-55.
[10]  Carrion JE, Spencer Jr BF. Model-based strategies for re- al-time hybrid testing. Newmark Structural Engineering Labo- ratory. University of Illinois at Urbana …; 2007. Report No.: 1940-9826.
[11]  Chen C, Ricles JM. Tracking error-based servohydraulic actuator adaptive compensation for real-time hybrid simula- tion. Journal of Structural Engineering. 2010;136(4):432-40.
[12]  Gao X, Castaneda N, Dyke SJ. Real time hybrid simu- lation: from dynamic system, motion control to experimen- tal error. Earthquake Engineering & Structural Dynamics. 2013;42(6):815-32.
[13]  Ou G, Ozdagli AI, Dyke SJ, Wu B. Robust integrated ac- tuator control: experimental verification and real‐time hybrid‐ simulation implementation. Earthquake Engineering & Struc- tural Dynamics. 2015;44(3):441-60.
[14]  Phillips BM, Takada S, Spencer Jr B, Fujino Y. Feedfor- ward actuator controller development using the backward-dif- ference method for real-time hybrid simulation. Smart Struc- tures and Systems. 2014;14(6):1081-103.
[15]  Newmark NM, editor A method of computation for struc- tural dynamics1959: American Society of Civil Engineers.
[16]  Wu B, Xu G, Wang Q, Williams MS. Operator‐splitting method for real‐time substructure testing. Earthquake Engi- neering & Structural Dynamics. 2006;35(3):293-314.
[17]  Combescure D, Pegon P. α-Operator splitting time inte- gration technique for pseudodynamic testing error propaga- tion analysis. Soil Dynamics and Earthquake Engineering. 1997;16(7-8):427-43.
[18]    Chang S-Y. Explicit pseudodynamic algorithm with unconditional stability. Journal of Engineering Mechanics. 2002;128(9):935-47.
[19]  Wu B, Wang Q, Benson Shing P, Ou J. Equivalent force control method for generalized real‐time substructure testing with implicit integration. Earthquake engineering & structural dynamics. 2007;36(9):1127-49.
[20]  Chen C, Ricles JM. Development of direct integration al- gorithms for structural dynamics using discrete control theory. Journal of Engineering Mechanics. 2008;134(8):676-83.
[21]   Gui Y, Wang J-T, Jin F, Chen C, Zhou M-X. Develop- ment of a family of explicit algorithms for structural dy- namics with unconditional stability. Nonlinear Dynamics. 2014;77(4):1157-70.
[22]   Chung J, Hulbert G. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. 1993.
[23]  Kolay C, Ricles JM, Marullo TM, Mahvashmohammadi 
A, Sause R. Implementation and application of the uncondi- tionally stable explicit parametrically dissipative KR‐α method for real‐time hybrid simulation. Earthquake Engineering & Structural Dynamics. 2015;44(5):735-55.
[24]  Ahmadizadeh M, Mosqueda G, Reinhorn A. Compensa- tion of actuator delay and dynamics for real‐time hybrid struc- tural simulation. Earthquake Engineering & Structural Dynam- ics. 2008;37(1):21-42.
[25]  Darby A, Williams M, Blakeborough A. Stability and de- lay compensation for real-time substructure testing. Journal of Engineering Mechanics. 2002;128(12):1276-84.
[26]  Wu B, Wang Z, Bursi OS. Actuator dynamics compen- sation based on upper bound delay for real‐time hybrid sim- ulation. Earthquake Engineering & Structural Dynamics. 2013;42(12):1749-65.
[27]   Shi P, Wu B, Spencer Jr BF, Phillips BM, Chang CM. Real‐time hybrid testing with equivalent force control meth- od incorporating Kalman filter. Structural Control and Health Monitoring. 2016;23(4):735-48.
[28] Horiuchi T, Inoue M, Konno T, Namita Y. Real‐time hybrid experimental system with actuator delay compensation and its application to a piping system with energy absorber. Earth- quake Engineering & Structural Dynamics. 1999;28(10):1121- 41.
[29]  Wallace M, Sieber J, Neild SA, Wagg DJ, Krauskopf B. Stability analysis of real‐time dynamic substructuring using delay differential equation models. Earthquake engineering & structural dynamics. 2005;34(15):1817-32.
[30]   Kyrychko Y, Blyuss K, Gonzalez-Buelga A, Hogan S, Wagg D. Real-time dynamic substructuring in a coupled os- cillator–pendulum system. Proceedings of the Royal Soci-  ety A: Mathematical, Physical and Engineering Sciences. 2006;462(2068):1271-94.
[31]   Mercan O, Ricles JM. Stability analysis for real‐time pseudodynamic and hybrid pseudodynamic testing with mul- tiple sources of delay. Earthquake Engineering & Structural Dynamics. 2008;37(10):1269-93.
[32]  Chi F, Wang J, Jin F. Delay-dependent stability and added damping of SDOF real-time dynamic hybrid testing. Earth- quake Engineering and engineering vibration. 2010;9(3):425- 38.
[33]  Botelho RM, Christenson RE. Robust stability and per- formance analysis for multi-actuator real-time hybrid substruc- turing. Dynamics of Coupled Structures, Volume 4: Springer; 2015. p. 1-7.
[34]  Chen C, Ricles JM. Stability analysis of SDOF real‐time 
hybrid testing systems with explicit integration algorithms and actuator delay. Earthquake Engineering & Structural Dynam- ics. 2008;37(4):597-613.
[35]  Zhu F, Wang JT, Jin F, Chi FD, Gui Y. Stability analysis of MDOF real‐time dynamic hybrid testing systems using the discrete‐time root locus technique. Earthquake Engineering & Structural Dynamics. 2015;44(2):221-41.
[36] Maghareh A, Dyke SJ, Prakash A, Bunting GB. Estab 
lishing a predictive performance indicator for real‐time hybrid simulation. Earthquake Engineering & Structural Dynamics. 2014;43(15):2299-318.
[37] Maghareh A, Dyke S, Rabieniaharatbar S, Prakash A. Pre- dictive stability indicator: a novel approach to configuring a real‐time hybrid simulation. Earthquake Engineering & Struc- tural Dynamics. 2017;46(1):95-116.