Parameter Identification of Vibrating MIMO Mass-Spring-Damper Mechanical Systems with Coulomb Friction

Year : 2025 | Volume : 03 | Issue : 01 | Page : 20 34
    By

    KangSok Wi,

  • KonKi Ri,

  • KwangIl Ri,

  • YongIl Ri,

  1. Associate Professor, Department of Dynamics, Kim Il Sung University, Pyongyang, DPR, Korea
  2. Associate Professor, Department of Dynamics, Kim Il Sung University, Pyongyang, DPR, Korea
  3. Associate Professor, Department of Dynamics, Kim Il Sung University, Pyongyang, DPR, Korea
  4. Associate Professor, Department of Aerospace Electronics, University of Science, Pyongyang, DPR, Korea

Abstract

This study presents a time-domain method for identifying parameters in multi-degree-of-freedom (DOF) linear mass-spring-damper systems that include Coulomb friction, where the friction coefficient varies within a limited range, using measurements of position and control force. For mass identification in single-degree-of-freedom (DOF) vibrating mechanical systems with stiffness and no damping but Coulomb friction, the friction term is eliminated by first derivative processing. In addition, the identification of the coefficient of friction is not considered, and friction is treated as measurement noise by reference trajectory search control. A method of implementing online algebraic parameter identification by measuring position and control force in the time domain for MIMO (Multiple-Input, Multiple-Output) mass-spring-damper systems with limited Coulomb friction is proposed. The results of the mathematical model and study of the differential flatness of an n-DOF mass-spring-damper system with friction were obtained. An output feedback control scheme for trajectory tracking tasks considering Coulomb friction was obtained. The friction coefficient and parameters of mass, stiffness, and damping coefficient have been algebraically estimated from real-time position and input control force measurements to extend the application range of the online algebraic parameter identification method. By determining the velocity sign in two short time intervals when Coulomb friction exists and by processing the friction term in the manner of linearizing the sign function, in the case of an integral near a singular point, the reference trajectory tracking problem is realized. Based on this, a six-DOF mechanical system, for example, mass, stiffness, and damping factor without friction, was identified in real-time, and mass, stiffness, damping factor, and Coulomb friction coefficient in the presence of friction were identified. When friction exists and does not, parameter identification of a six-DOF vibrating mechanical system and reference trajectory tracking have been realized correctly. The method is of great help in realizing the static motion control of multi-DOF MIMO mechanical systems, including robot manipulators, medical devices, and precision tracking mechanisms. As a result, control costs are reduced.

Keywords: Coulomb friction, vibrating mechanical systems, parameter identification, control force measurements, vibration control

[This article belongs to International Journal of Mechanical Dynamics and Systems Analysis ]

How to cite this article:
KangSok Wi, KonKi Ri, KwangIl Ri, YongIl Ri. Parameter Identification of Vibrating MIMO Mass-Spring-Damper Mechanical Systems with Coulomb Friction. International Journal of Mechanical Dynamics and Systems Analysis. 2025; 03(01):20-34.
How to cite this URL:
KangSok Wi, KonKi Ri, KwangIl Ri, YongIl Ri. Parameter Identification of Vibrating MIMO Mass-Spring-Damper Mechanical Systems with Coulomb Friction. International Journal of Mechanical Dynamics and Systems Analysis. 2025; 03(01):20-34. Available from: https://journals.stmjournals.com/ijmdsa/article=2025/view=216770


References

  1. Heylen W, Lammens S, Sas P. Modal Analysis, Theory and Testing. Leuven (BE): Katholieke Universiteit Leuven; 2003.
  2. Le TP, Paultre P. Modal identification based on the time–frequency domain decomposition of unknown-input dynamic tests. Int J Mech Sci. 2013;71:41–50. doi:10.1016/j.ijmecsci.2013.03.005.
  3. Lardies J, Gouttebroze S. Identification of modal parameters using the wavelet transform. Int J Mech Sci. 2002;44:2263–83. doi:10.1016/S0020-7403(02)00175-3.
  4. Lin RM. Development of a new and effective modal identification method – Mathematical formulations and numerical simulations. J Vib Control. 2011;17:741–58. doi:10.1177/107754631
  5. Vu VH, Thomas M, Laheurte F, Marcouiller L. Towards an automatic spectral and modal identification from operational modal analysis. J Sound Vib. 2013;332:213–27. doi:10.1016/j.jsv.2
    08.019.
  6. Yang Y, Nagarajaiah S. Output-only modal identification with limited sensors using sparse component analysis. J Sound Vib. 2013;332:4741–65. doi:10.1016/j.jsv.2013.04.004.
  7. Liao Y, Wells V. Modal parameter identification using the log decrement method and band-pass filters. J Sound Vib. 2011;330:5014–23. doi:10.1016/j.jsv.2011.05.017.
  8. Chakraborty A, Basu B, Mitra M. Identification of modal parameters of a MDOF system by modified L–P wavelet packets. J Sound Vib. 2006;295:827–37. doi:10.1016/j.jsv.2006.01.037.
  9. Hung CF, Ko WJ, Peng YT. Identification of modal parameters from measured input and output data using a vector backward auto-regressive with exogeneous model. J Sound Vib. 2004;276:1043–63. doi:10.1016/j.jsv.2003.08.020.
  10. Isermann R, Münchhof M. Identification of Dynamic Systems. Berlin (DE): Springer-Verlag; 2011. doi:10.1007/978-3-540-78879-9.
  11. Ljung L. Systems Identification: Theory for the User. Upper Saddle River (NJ): Prentice Hall; 1987.
  12. Söderström T, Stoica P. System identification. New York (NY): Prentice Hall; 1989.
  13. Fliess M, Sira-Ramírez H. An algebraic framework for linear identification. ESAIM Control Optim Calc Var. 2003;9:151–68. doi:10.1051/cocv:2003008.
  14. Fliess M, Mboup M, Mounier H, Sira-Ramirez H. Questioning some paradigms of signal processing via concrete examples. In: Sira-Ramirez H, Silva-Navarro G, editors. Algebraic Methods in Flatness, Signal Processing and State Estimation. Mexico: Lagares; 2003. p. 1–21.
  15. Fliess M. Analyse non standard du bruit. Acad Sci Paris Ser I. 2006;342:797–802.
  16. Fliess M, Join C. Model-free control. Int J Control. 2013;86:2228–52. doi:10.1080/00207179.2013.
  17. Sira-Ramírez H, Silva-Navarro G, Beltran-Carbajal F. On the GPI balancing control of an uncertain Jeffcott rotor model. Proc 4th Int Conf Electr Electron Eng. ICEEE; 2007. p. 306–9.
  18. Mboup M, Join C, Fliess M. A revised look at numerical differentiation with an application to nonlinear feedback control. 2007 Mediterranean Conference on Control & Automation, Athens, Greece. 2007. p. 1–6. doi:10.1109/MED.2007.4433728.
  19. Mboup M, Join C, Fliess M. Numerical differentiation with annihilators in noisy environment. Numer Algorithms. 2009;50:439–67. doi:10.1007/s11075-008-9236-1.
  20. Mikusiński J. Operational Calculus. 2nd ed. Oxford: PWN & Pergamon; 1983. Vol. 1.
  21. Glaetske HJ, Prudnikov AP, Skrnik KA. Operational Calculus and Related Topics. London (GB): Chapman & Hall; 2006.
  22. Beltrán-Carbajal F, Silva-Navarro G. Adaptive-like vibration control in mechanical systems with unknown parameters and signals. Asian J Control. 2013;15:1526–1613.
  23. Beltrán-Carbajal F, Silva-Navarro G, Arias-Montiel M. Active unbalance control of rotor systems using on-line algebraic identification methods. Asian J Control. 2013;15:1627–37. doi:10.1002/asjc.
  24. Beltrán-Carbajal F, Silva-Navarro G, Trujillo-Franco LG. Evaluation of on-line algebraic modal parameter identification methods. In: Allemang R, editor. Topics in Modal Analysis II, Volume 8. Conference Proceedings of the Society for Experimental Mechanics Series. Cham: Springer; 2014. p. 145–52. doi:10.1007/978-3-319-04774-4_14.
  25. Korenev BG, Reznikov LM. Dynamic Vibration Absorbers: Theory and Technical Applications. Hoboken (NJ): John Wiley & Sons; 1993.
  26. Asmari Saadabad NA, Moradi H, Vossoughi G. Semi-active control of forced oscillations in power transmission lines via optimum tuneable vibration absorbers: With review on linear dynamic aspects. Int J Mech Sci. 2014;87:163–78. doi:10.1016/j.ijmecsci.2014.06.006.
  27. Preumont A. Vibration Control of Active Structures: An Introduction. Berlin (DE): Springer-Verlag; 2011.
  28. Vance J, Zeidan F, Murphy B. Machinery vibration and rotordynamics. Hoboken (NJ): John Wiley & Sons; 2010. doi:10.1002/9780470903704.
  29. Yao B, Chen Q, Xiang HY, Gao X. Experimental and theoretical investigation on dynamic properties of tuned particle damper. Int J Mech Sci. 2014;80:122–30. doi:10.1016/j.ijmecsci.2014.
    009.
  30. Sheng CY, Lan YM, Li W, Su CC. New parameter identification method for calibrating stiffness of AFM probes. Int J Mech Sci. 2014;79:25–30. doi:10.1016/j.ijmecsci.2013.11.020.
  31. Fliess M, Lévine J, Martin P, Rouchon P. Flatness and defect of non-linear systems: Introductory theory and examples. Int J Control. 1995;61:1327–61. doi:10.1080/00207179508921959.
  32. Fliess M, Marquez R, Delaleau E, Sira-Ramirez H. Correcteurs proportionnels-intégraux généralisés. ESAIM Control Optim Calc Var. 2002;7:23–41.
  33. Sira-Ramírez H, Beltran-Carbajal F, Blanco-Ortega A. A generalized proportional integral output feedback controller for the robust perturbation rejection in a mechanical system. SciTechnol Autom. 2008;5:24–32.
  34. Inman DJ. Vibration with Control. Hoboken (NJ): John Wiley & Sons; 2006. doi:10.1002/0470010
  35. Beltrán-Carbajal F, Silva-Navarro G. On the algebraic parameter identification of vibrating mechanical systems. Int J Mech Sci. 2015;92:178–86. doi:10.1016/j.ijmecsci.2014.12.006.
  36. Sira-Ramírez H, García-Rodríguez C, Cortés-Romero J, Luviano-Juárez A. Algebraic identification and estimation methods in feedback control systems. Hoboken (NJ): Wiley and Sons Ltd; 2014. doi:10.1002/9781118730591.
  37. Gerry JP, Shinskey FG. (2004 May). PID controller specification. [Online]. White paper. Available from: http://www.expertune.com/PIDspec.htm.
Regular Issue Subscription Case Study
Volume 03
Issue 01
Received 26/03/2025
Accepted 12/06/2025
Published 23/06/2025
Publication Time 89 Days
116

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