Performance and Application of Equivalent Force Control Method for Real-Time Substructure Testing
Publication: Journal of Engineering Mechanics
Volume 138, Issue 11
Abstract
The equivalent force control (EFC) method has been developed for real-time substructure testing with implicit integration to replace the numerical iterative process with feedback control. This paper addresses two issues concerning the performance of this method. One is the determination of the force-displacement conversion factor (a key component of EFC) for nonlinear specimens. The analysis conducted here shows that the force-displacement conversion factor is largely governed by the properties of the numerical substructure and the numerical scheme when a small integration time interval is used. Otherwise, the factor has to be determined with the secant stiffness of the specimen and of the numerical substructure if a proportional-derivative controller is used for EFC. The other issue is the overshooting problem, which may arise for multidegree-of-freedom structures because of the relatively quick response feedback from the numerical substructure in the closed-loop EFC. This problem can be resolved by reducing either the EFC gains or the increment size of the equivalent force command. The analytical studies on these two issues are verified by numerical simulations and for real-time substructure tests conducted on structural models with buckling restrained braces. Furthermore, a real-time substructure test was conducted on an offshore platform with magnetorheological dampers in order to serve as an example of a practical application of the method.
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Acknowledgments
This work was supported by Grant Nos. 51161120360, 90715036, and 50578047 from the National Science Foundation of China, and the Fundamental Research Funds for the Central Universities (Grant No. HIT.BRET2.2010009, HIT.ICRST2010016, HIT.NSRIF.2010018). Mr. Y. Ma of the Mechanical and Structural Testing Center, Harbin Institute of Technology, is gratefully acknowledged for his assistance with the operation of the MTS testing system.
References
Ahmadizadeh, M., Mosqueda, G., and Reinhorn, A. M. (2008). “Compensation of actuator delay and dynamics for real-time hybrid structural simulation”. Earthquake Eng. Struct. Dyn., 37(1), 21–42.
Bayer, V., Dorka, U. E., Füllekrug, U., and Gschwilm, J. (2005). “On real-time pseudo-dynamic sub-structure testing: Algorithm, numerical and experimental results”. Aerosp. Sci. Technol., 9(3), 223–232.
Bonnet, P. A., et al. (2007). “Real-time hybrid experiments with Newmark integration, MCSmd outer-loop control and multi-tasking strategies”. Earthquake Eng. Struct. Dyn., 36(1), 119–141.
Bonnet, P. A., Williams, M. S., and Blakeborough, A. (2008). “Evaluation of numerical time-integration schemes for real-time hybrid testing”. Earthquake Eng. Struct. Dyn., 37(13), 1467–1490.
Bursi, O. S., Gonzalez-Buelga, A., Vulcan, L., Neild, S. A., and Wagg, D. J. (2008). “Novel coupling Rosenbrock-based algorithms for real-time dynamic substructure testing”. Earthquake Eng. Struct. Dyn., 37(3), 339–360.
Chang, S. Y. (2002). “Explicit pseudodynamic algorithm with unconditional stability”. J. Eng. Mech., 128(9), 935–947.
Chen, C., and Ricles, J. M. (2008). “Development of direct integration algorithms using discrete control theory”. J. Eng. Mech., 134(8), 676–683.
Chen, C., and Ricles, J. M. (2010). “Tracking error-based servohydraulic actuator adaptive compensation for real-time hybrid simulation”. J. Struct. Eng., 136(4), 432–440.
Chen, C., Ricles, J. M., Marullo, T. M., and Mercan, O. (2009). “Real-time hybrid testing using the unconditionally stable explicit CR integration algorithm”. Earthquake Eng. Struct. Dyn., 38(1), 23–44.
Christenson, R., Lin, Y. Z., Emmons, A., and Bass, B. (2008). “Large-scale experimental verification of semiactive control through real-time hybrid simulation”. J. Struct. Eng., 134(4), 522–534.
Combescure, D., and Pegon, P. (1997). “α-operator splitting time integration technique for pseudodynamic testing error propagation analysis”. Soil. Dyn. Earthquake Eng., 16(7–8), 427–443.
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.
Gawthrop, P. J., Wallace, M. I., Neild, S. A., and Wagg, D. J. (2007). “Robust real-time substructuring techniques for under-damped systems”. Struct. Contr. Health Monit., 14(4), 591–608.
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. Contr. Health Monit., 14(7), 991–1012.
Guyan, R. J. (1965). “Reduction of stiffness and mass matrices”. AIAA J., 3(2), 380.
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”. Earthquake Eng. Struct. Dyn., 28(10), 1121–1141.
Jung, R. Y., and Shing, P. B. (2006). “Performance evaluation of a real-time pseudodynamic test system”. Earthquake Eng. Struct. Dyn., 35(7), 789–810.
Jung, R. Y., Shing, P. B., Stauffer, E., and Thoen, B. (2007). “Performance of a real-time pseudo dynamic test system considering nonlinear structural response”. Earthquake Eng. Struct. Dyn., 36(12), 1785–1809.
Lambert, G. D. (1973). Computational methods in ordinary differential equations, Wiley, London.
Leng, D. (2005). “Semi-active control of isolated JZ20-2NW offshore platform with MR damper.” M.S. thesis, Harbin Institute of Technology, Harbin, China (in Chinese).
Li, Y. (2007). “Seismic performance of buckling-restrained braces and substructure testing methods.” Ph.D. thesis, Harbin Institute of Technology, Harbin, China (in Chinese).
Lim, C. N., Neild, S. A., Stoten, D. P., Drury, D., and Taylor, C. A. (2007). “Adaptive control strategy for dynamic substructuring tests”. J. Eng. Mech., 133(8), 864–873.
Mercan, O., and Ricles, J. M. (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.
Mosqueda, G., and Ahmadizadeh, M. (2007). “Combined implicit or explicit integration steps for hybrid simulation”. Earthquake Eng. Struct. Dyn., 36(15), 2325–2343.
Mosqueda, G., Stojadinovic, B., and Mahin, S. A. (2007a). “Real-time error monitoring for hybrid simulations. Part I: Methodology and experimental verification”. J. Struct. Eng., 133(8), 1100–1108.
Mosqueda, G., Stojadinovic, B., and Mahin, S. A. (2007b). “Real-time error monitoring for hybrid simulations. Part II: Structural response modification due to errors”. J. Struct. Eng., 133(8), 1109–1117.
MTS. (2001). Model 793.10 multipurpose test software: User information and software reference, MTS System Corporation, Eden Prairie, MN.
Nakashima, M., Kato, H., and Takaoka, E. (1992). “Development of real-time pseudo dynamic testing”. Earthquake Eng. Struct. Dyn., 21(1), 79–92.
Sajeeb, R., Roy, D., and Manohar, C. S. (2007). “Numerical aspects of a real-time sub-structuring technique in structural dynamics”. Int. J. Numer. Methods Eng., 72(11), 1261–1313.
Shao, X., and Reinhorn, A. M. (2006). “Force controlled actuators in hybrid testing.” Proc., 4th World Conf. Struct. Control Monitor., Univ. of California, San Diego.
Spencer, B. F., and Carrion, J. E. (2007). “Real-time hybrid testing of semi-actively controlled structure with MR damper.” Proc., 2nd Int. Conf. Adv. Exp. Struct. Eng., Tongji Univ., Shanghai, China, 49–64.
Wagg, D. J., and Stoten, D. P. (2001). “Substructuring of dynamical systems via the adaptive minimal control synthesis algorithm”. Earthquake Eng. Struct. Dyn., 30(6), 865–877.
Wallace, M. I., Sieber, J., Neild, S. A., Wagg, D. J., and Krauskopf, B. (2005). “Stability analysis of real-time dynamic substructuring using delay differential equation models”. Earthquake Eng. Struct. Dyn., 34(15), 1817–1832.
Wallace, M. I., Wagg, D. J., Neild, S. A., Bunniss, P., Lieven, N. A. J., and Crewe, A. J. (2007). “Testing coupled rotor blade–lag damper vibration using real-time dynamic substructuring”. J. Sound Vibrat., 307(3–5), 737–754.
Wang, Q. (2007). “Real-time substructure testing method and its application.” Ph.D. thesis, Harbin Institute of Technology, Harbin, China (in Chinese).
Wu, B., Bao, H., Ou, J., and Tian, S. (2005). “Stability and accuracy analysis of central difference method for real-time substructure testing”. Earthquake Eng. Struct. Dyn., 34(7), 705–718.
Wu, B., Wang, Q., and Ou, J. (2006a). “Stability analysis of operator-splitting method for real-time substructure testing with actuator delay and compensation.” Proc., 8th U.S. National Conf. Earthquake Eng., San Francisco.
Wu, B., Wang, Q., Shi, P., Ou, J., and Guan, X. (2006b). “Real-time substructure test of JZ20-2NW offshore platform with semi-active MR dampers.” Proc., 4th Int. Conf. Earthquake Eng., Taipei, Taiwan.
Wu, B., Wang, Q. Y., Shing, P. B., and Ou, J. P. (2007). “Equivalent force control method for generalized real-time substructure testing with implicit integration”. Earthquake Eng. Struct. Dyn., 36(9), 1127–1149.
Wu, B., Xu, G., and Shing, P. B. (2011). “Equivalent force control method for real-time testing of nonlinear structures”. J. Earthquake Eng., 15(1), 143–164.
Wu, B., Xu, G., Wang, Q., and Williams, M. (2006c). “Operator-splitting method for real-time substructure testing”. Earthquake Eng. Struct. Dyn., 35(3), 293–314.
Zhang, Y., Sause, R., Ricles, J., and Naito, C. (2005). “Modified predictor–corrector numerical scheme for real-time pseudo dynamic tests using state-space formulation”. Earthquake Eng. Struct. Dyn., 34(3), 271–288.
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Published In
Journal of Engineering Mechanics
Volume 138 • Issue 11 • November 2012
Pages: 1303 - 1316
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Jun 4, 2008
Accepted: Mar 29, 2012
Published online: Mar 31, 2012
Published in print: Nov 1, 2012
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