Acta Mechanica Sinica

, Volume 20, Issue 6, pp 661–667 | Cite as

Construction of polynomial matrix using block coefficient matrix representation auto-regressive moving average model for actively controlled structures

  • Li Chunxiang
  • Zhou Dai


The polynomial matrix using the block coefficient matrix representation auto-regressive moving average (referred to as the PM-ARMA) model is constructed in this paper for actively controlled multi-degree-of-freedom (MDOF) structures with time-delay through equivalently transforming the preliminary state space realization into the new state space realization. The PM-ARMA model is a more general formulation with respect to the polynomial using the coefficient representation auto-regressive moving average (ARMA) model due to its capability to cope with actively controlled structures with any given structural degrees of freedom and any chosen number of sensors and actuators. (The sensors and actuators are required to maintain the identical number.) under any dimensional stationary stochastic excitation.

Key Words

actively controlled MDOF structures stationary stochastic processes polynomial matrix auto-regressive moving average 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Housner GW, Bergman LA, Caughey TK, et al. Structural control: past, present, and future.J Engl Mech, 1997, 123(9): 897–971CrossRefGoogle Scholar
  2. 2.
    Spenser BF, Sain MK. Controlling buildings: a new frontier in feedback.IEEE Control. Syst Mag, 1997, 17: 19–35CrossRefGoogle Scholar
  3. 3.
    Åström KJ. Introduction to Stochastic Control Theory. New York: Academic Press, 1970MATHGoogle Scholar
  4. 4.
    Åström KJ. Theory and applications of self tuning regulators.Automatica, 1977, 13: 457–476MATHCrossRefGoogle Scholar
  5. 5.
    Gawthrop PJ. Some interpretations of self tuning controller.Proceedings of the IEEE, 1977, 124: 889–894Google Scholar
  6. 6.
    Clarke DW. Introduction to self tuning controller. In: Nichelson H, Swanick BH, eds. IEEE, Control Engineering Series 15, Self Tuning and Adaptive Control: Theory and Applications, London: Peter Pereginus, 1981Google Scholar
  7. 7.
    Clarke DW. Self tuning control of non-minimum phase systems.Automatica, 1984, 20: 501–517MATHCrossRefGoogle Scholar
  8. 8.
    Athans M. The role and the use of the stochastic linear-quadratic-Gaussian problem in control system design.IEEE Trans Automat Contr, 1971, AC-16: 529–552MathSciNetCrossRefGoogle Scholar
  9. 9.
    Yong LP, Mickleborough NC. Model identification of vibrating structures using ARMA model.J Eng Mech, 1989, 115(10): 2232–2250Google Scholar
  10. 10.
    Safak E. Adaptive modelling, identification, and control of dynamics systems. I: Theory.J Eng Mech, 1989, 115(11): 2386–2405Google Scholar
  11. 11.
    Loh CH, Lin HM. Application of off-line and on-line identification techniques to buildings seismic response data.Earthquake Eng Struct Dyn, 1996, 25: 269–290CrossRefGoogle Scholar
  12. 12.
    Spanos PD, Zeldin BA. Efficient iterative ARMA approximation of multivariate random processes for structural dynamics applications.Earthquake Eng Struct Dyn, 1996, 25: 497–507CrossRefGoogle Scholar
  13. 13.
    Enrique LJ. A simple model for structural control including soil-structure interaction effects.Earthquake Eng Struct Dyn, 1998, 27: 225–242CrossRefGoogle Scholar
  14. 14.
    Hoshiya M, Saito Y. Prediction control of SDOF system.J Eng Mech, 1995, 121 (10): 1049–1055CrossRefGoogle Scholar
  15. 15.
    Yamada K, Kobori T. Control algorithm for estimating future responses of active variable stiffness structure.Earthquake Eng Struct Dyn, 1995, 24: 1085–1099Google Scholar
  16. 16.
    Keyhani A, Allam MM. Closed loop predictive optimal control algorithm using ARMA models.J Eng Mech, 2000, 126(6): 620–625CrossRefGoogle Scholar
  17. 17.
    Guenfal L, Djebiri M, Boucherit MS, et al. Generalized minimum variance control for buildings under seismic ground motion.Earthquake Eng Struct Dyn, 2001, 30: 945–960CrossRefGoogle Scholar
  18. 18.
    Samaras E, Shinozuka M, Tsurui A. ARMA representation of random processes.J Eng Mech, 1985, 111(3): 449–461CrossRefGoogle Scholar
  19. 19.
    Spanos PD, Mignolet MC. Z-transformation modeling of P-M spectrum.J Eng Mech 1986, 112(8): 745–759CrossRefGoogle Scholar
  20. 20.
    Li Y, Kareem, A. ARMA modeling of random wind and wave fields. In: Eng Mech-6th Conf, Abstracts, ASCE, New York, NY, 1987Google Scholar
  21. 21.
    Li Y, Kareem A. Recursive modeling of dynamics systems.J Eng Mech, 1990, 116(3): 660–679Google Scholar
  22. 22.
    Owen JS, Eccles BJ, Choo BS, et al. The application of auto-regressive time series modelling for the time-frequency analysis of civil engineering structures.Eng Struct, 2001, 23: 521–536CrossRefGoogle Scholar
  23. 23.
    Neild SA, Mcfadden PD, Williams MS. A review of time-frequency methods for structural vibration analysis.Eng Struct, 2003, 25: 713–728CrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2004

Authors and Affiliations

  • Li Chunxiang
    • 1
  • Zhou Dai
    • 1
  1. 1.Department of Civil EngineeringShanghai Jiaotong UniversityShanghaiChina

Personalised recommendations