Algebraic identifiers for an inerter-based passive suspension system
DOI:
https://doi.org/10.20983/culcyt.2025.1.2.7Keywords:
inerter device, algebraic identification, physical parameters, passive suspensionAbstract
In this work, the focus is on the analysis and formulation of identifiers for the physical properties of a quarter-vehicle suspension, such as suspended mass, spring stiffness, damping, and inertance, using a mechanical network based on an inerter. The methodology employed to obtain these identifiers is known as algebraic identification. To develop the algebraic estimators, the mathematical model of a passive suspension was utilized by implementing the C4 mechanical network (TID), considering the effects of translational inertia. The proposed algebraic identifiers allow for the calculation of the physical parameter values of the system in two distinct situations: under a constant harmonic force and with a random signal that simulates road dynamics. The numerical analysis of the identifiers shows that it is feasible to obtain the values of mass, damping, stiffness, and inertance parameters of the passive suspension within a very short time interval, not exceeding 2 seconds.
Downloads
References
L. Cheung, W. O. Wong y L. Cheng, “Optimization of a hybrid vibration absorber for vibration control of structures under random force excitation”, JSV, vol. 332, n.º 3, pp. 494-509, 2013, doi: 10.1016/j.jsv.2012.09.014.
F. Scheibe y M. C Smith, “Analytical solutions for optimal ride comfort and tyre grip for passive vehicle suspensions”, Veh. Syst. Dyn., vol. 47, n.º 10, pp. 1229-1252, 2009, doi: 10.1080/00423110802588323.
Y. Hu, M. Z. Q. Chen y Z. Shu, “Passive vehicle suspensions employing inerters with multiple performance requirements”, JSV, vol. 333, n.º 8, pp. 2212-2225, 2014, doi: 10.1016/j.jsv.2013.12.016.
M. C. Smith, “Synthesis of mechanical networks: the inerter”, en IEEE Transactions on Automatic Control, vol. 47, n.º 10, pp. 1648-1662, oct. 2002, doi: 10.1109/TAC.2002.803532.
M. Z. Q. Chen, C. Papageorgiou, F. Scheibe, F.-c. Wang y M. C. Smith, “The missing mechanical circuit element”, en IEEE Circuits and Systems Magazine, vol. 9, n.º 1, pp. 10-26, First Quarter 2009, doi: 10.1109/MCAS.2008.931738.
S. Evangelou, D. J. N. Limebeer, R. S. Sharp and M. C. Smith, “Steering compensation for high-performance motorcycles”, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No. 04CH37601), Nassau, Bahamas, 2004, pp. 749-754, vol. 1, doi: 10.1109/CDC.2004.1428746.
L. Ljung, System Identification: Theory for the User. Englewood Cliffs, Nueva Jersey: Prentice-Hall, 1987.
S. Sagara, Z. Y. Zhao, “Numerical integration approach to on-line identification of continuous-time systems”, Automatica, vol. 26, n.º 1, pp. 63-74, en., 1990, doi: 10.1016/0005-1098(90)90158-E.
M. Fliess y H. Sira-Ramírez, “An algebraic framework for linear identification”, ESAIM: COCV, vol. 9, pp. 151-168, feb., 2003, doi: 10.1051/cocv:2003008.
L. A. Baltazar-Tadeo, J. Colín-Ocampo, A. Abúndez-Pliego, J. G. Mendoza-Larios, E. Martínez-Rayón, A. García-Villalobos, “Balancing of Asymmetric Rotor‑Bearing Systems Using Modal Masses Array Calculated by Algebraic Identification of Modal Unbalance”, J. Vib. Eng. Technol., vol. 12, pp. 4765-4788, sept., 2023, doi: 10.1007/s42417-023-01151-9.
J. G. Mendoza-Larios et al., “An Algebraic Approach for Identification of Rotordynamic Parameters in Bearings with Linearized Force Coefficients”, Mathematics, vol. 9, n.º 21, pp. 27-47, oct, 2021, doi: 10.3390/math9212747.
L. A. Baltazar-Tadeo et al., “An Integrated Balancing Method for Asymmetric Rotor-Bearing Systems: Algebraic Identification, Modal Balancing, and Active Balancing Disks”, J. Vib. Eng. Technol., vol. 11, n.º 2, pp. 619-645, jul., 2022, doi: 10.1007/s42417-022-00598-6.
H. Sira-Ramirez y M. Fliess, “On discrete-time uncertain visual based control of planar manipulators: an online algebraic identification approach”, Proceedings of the 41st IEEE Conference on Decision and Control, 2002, Las Vegas, NV, EUA, 2002, pp. 4509-4514, vol. 4, doi: 10.1109/CDC.2002.1185084.
S. Fuchshumer, “Algebraic linear identification, modelling, and applications of flatness-based control”, disertación doctoral, Johannes Kepler Universität Linz, Linz, 2005.
M. Fliess, S. Fuchshumer, K. Schlacher y H. Sira-Ramirez, “Discrete-time linear parametric identification: An algebraic approach”, presentado en 2èmes Journées Identification et Modélisation Expérimentale-JIME'2006, 2006.
E. Chávez, R. Castillo y J. M. Pablo, “Identificación algebraica en línea de los coeficientes de amortiguamiento y rigidez de una suspensión pasiva de un cuarto de automóvil”, Repositorio Nacional CONACYT, 2017.
D. Hernandez-Alcantara, R. Morales-Menendez, L. Amezquita-Brooks, O. Sename y L. Dugard, “Fault estimation methods for semi-active suspension systems”, 2015 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC), Ixtapa, México, 2015, pp. 1-5, doi: 10.1109/ROPEC.2015.7395138.
J. Colín-Ocampo, J. G. Mendoza-Larios, A. Blanco-Ortega, A. Abúndez-Pliego, E. S. Gutiérrez-Wing, “Determinación del Desbalance en Sistemas Rotor-cojinete a velocidad constante: Método de Identificación Algebraica”, Ingenier. mecáni. tecnolog. desarroll., vol. 5, n.º 4, pp. 385-394, 2016.
J. G. Mendoza-Larios, J. Colín-Ocampo, A. Blanco-Ortega, A. Abúndez-Pliego, E. S. Gutiérrez-Wing, “Balanceo Automático de un Sistema Rotor-Cojinete: Identificador Algebraico en Línea del Desbalance Para un Sistema Rotodinámico”, Rev. Iberoam. Autom. Inform. Ind., vol. 13, n.º 3, pp. 281-292, 2016, doi: 10.1016/j.riai.2016.03.004.
S. J. Landa-Damas et al., “A simplified Model for the On-Line Identification of Bearing Direct-Dynamic Parameters Based on Algebraic Identification (AI)”, Mathematics, vol. 11, n.º 14 pp. 01-26, jul., 2023, doi: 10.3390/math11143131.
E. Barredo, J. G. Mendoza, L. A. Baltazar, y S. J. Landa, “Identificación algebraica de los parámetros físicos de un sistema rotor-cojinete simplificado de dos grados de libertad”, Cult. Científ. y Tecnol., vol. 21, n.º 1, pp. 4-12, feb. 2024, doi: 10.20983/culcyt.2024.1.2.1.
G. E. Zheng, W. Weirui, L. I. Guangping y R. Daogong. “Design, parameter optimisation, and performance analysis of active tuned inerter damper (TID) suspension for vehicle”, JSV, vol. 525, n.º 116750, 2022, doi: 10.1016/j.jsv.2022.116750.
F. A. E. Pirani, “Mathematical methods of classical mechanics (graduate texts in mathematics, 60)”, Bulletin of The London Mathematical Society, vol. 14, pp. 65-66, 1982.
B. Huang, C.-Y. Hsieh, F. Golnaraghi y M. Moallem, “Development and optimization of an energy-regenerative suspension system under stochastic road excitation”, JSV, vol. 357, pp. 16-34, nov. 2015.
E. Barredo. (2020). “Cuantificación de la capacidad de regeneración de energía en vehículos sujetos a vibración estocástica”, tesis de doctorado, TecNM/CENIDET, Cuernavaca, Morelos, México, 2020.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Edrei Yael Santos García, Eduardo Barredo Hernández, José Gabriel Mendoza Larios, Jesús Francisco Canseco Díaz

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Todos los contenidos de CULCYT se distribuyen bajo una licencia de uso y distribución “Creative Commons Reconocimiento-No Comercial 4.0 Internacional” (CC-BY-NC). Puede consultar desde aquí la versión informativa de la licencia.
Los autores/as que soliciten publicar en esta revista, aceptan los términos siguientes: a) los/las autores/as conservarán sus derechos de autor y garantizarán a la revista el derecho de primera publicación de su obra; y b) se permite y recomienda a los/las autores/as agregar enlaces de sus artículos en CULCYT en la página web de su institución o en la personal, debido a que ello puede generar intercambios interesantes y aumentar las citas de su obra publicada.