Experimental Identification of a Car Dynamic Model Using the Numerical Algorithms for Subspace State-Space System Identification

Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


In this paper, a system identification numerical procedure is used to perform an experimental work based on the System Identification Toolbox available in MATLAB. This work aims to show the possibility of identifying a mathematical model of a car using low-cost sensors. The instrumentation used to reach this goal is composed of an Arduino Mega2560, a GPS receiver module, and an inertial measurement unit. The Arduino is used to handle the sensors and to save the measured data. The inertial platform is used to get the linear acceleration and angular rates of the system, while the GPS is used to get the trajectory of the car. By employing the N4SID algorithm, a discrete state-space model of the system can be identified and used to predict the behavior of the car system. It is also possible to obtain a continuous model from the discrete one and to identify the natural frequencies and the system damping factors. The results show the possibility to easily identify a mathematical model of a complex system using a limited set of experimental data.


Applied system identification Car dynamics State-space representation Numerical Algorithms for Subspace State-Space System Identification (N4SID) 


  1. 1.
    Villecco, F.: On the evaluation of errors in the virtual design of mechanical systems. Machines 6(3), 36 (2018)CrossRefGoogle Scholar
  2. 2.
    Zhang, Y., Li, Z., Gao, J., Hong, J., Villecco, F., Li, Y.: A method for designing assembly tolerance networks of mechanical assemblies. Math. Probl. Eng. 2012, 26 (2012)Google Scholar
  3. 3.
    Villecco, F., Pellegrino, A.: Evaluation of uncertainties in the design process of complex mechanical systems. Entropy 19(9), 475 (2017)CrossRefGoogle Scholar
  4. 4.
    De Simone, M.C., Guida, D.: Modal coupling in presence of dry friction. Machines 6(1), 8 (2018)CrossRefGoogle Scholar
  5. 5.
    De Simone, M.C., Rivera, Z.B., Guida, D.: Finite element analysis on squeal-noise in railway applications. FME Trans. 46(1), 93–100 (2018)CrossRefGoogle Scholar
  6. 6.
    Formato, A., Ianniello, D., Romano, R., Pellegrino, A., Villecco, F.: Design and development of a new press for grape marc. Machines 7(3), 51 (2019)CrossRefGoogle Scholar
  7. 7.
    Formato, G., Romano, R., Formato, A., Sorvari, J., Koiranen, T., Pellegrino, A., Villecco, F.: Fluid-structure interaction modeling applied to peristaltic pump flow simulations. Machines 7(3), 50 (2019)CrossRefGoogle Scholar
  8. 8.
    Formato, A., Ianniello, D., Pellegrino, A., Villecco, F.: Vibration-based experimental identification of the elastic moduli using plate specimens of the olive tree. Machines 7(2), 46 (2019)CrossRefGoogle Scholar
  9. 9.
    Naviglio, D., Formato, A., Scaglione, G., Montesano, D., Pellegrino, A., Villecco, F., Gallo, M.: Study of the grape cryo-maceration process at different temperatures. Foods 7(7), 107 (2018)CrossRefGoogle Scholar
  10. 10.
    Ghomshei, M., Villecco, F.: Energy metrics and Sustainability. In: International Conference on Computational Science and Its Applications, vol. 5592, pp. 693–698. Springer, Berlin, Heidelberg (2009)Google Scholar
  11. 11.
    Cattani, C., Mercorelli, P., Villecco, F., Harbusch, K.: A theoretical multiscale analysis of electrical field for fuel cells stack structures. In: International Conference on Computational Science and Its Applications, vol. 3980, pp. 857–864. Springer, Berlin, Heidelberg (2006)Google Scholar
  12. 12.
    Sena, P., Attianese, P., Carbone, F., Pellegrino, A., Pinto, A., Villecco, F.: A fuzzy model to interpret data of drive performances from patients with sleep deprivation. Comput. Math. Methods Med. 2012, 868410 (2012)CrossRefGoogle Scholar
  13. 13.
    Shabana, A.A.: Dynamics of Multibody Systems, 4th edn. Cambridge University Press, Cambridge (2013)zbMATHCrossRefGoogle Scholar
  14. 14.
    Nikravesh, P.E.: Computer-Aided Analysis Of Mechanical Systems. Prentice-Hall Inc, Upper Saddle River (1988)Google Scholar
  15. 15.
    Concilio, A., De Simone, M.C., Rivera, Z.B., Guida, D.: A new semi-active suspension system for racing vehicles. FME Trans. 45(4), 578–584 (2017)CrossRefGoogle Scholar
  16. 16.
    Rivera, Z.B., De Simone, M.C., Guida, D.: Unmanned ground vehicle modelling in Gazebo/ROS-based environments. Machines 7(2), 42 (2019)CrossRefGoogle Scholar
  17. 17.
    Guida, R., De Simone, M.C., Dašić, P., Guida, D.: Modeling techniques for kinematic analysis of a six-axis robotic arm. IOP Conf. Ser.: Mater. Sci. Eng. 568(1), 12115 (2019)CrossRefGoogle Scholar
  18. 18.
    Pappalardo, C.M., Patel, M.D., Tinsley, B., Shabana, A.A.: Contact force control in multibody pantograph/catenary systems. Proc. Inst. Mech. Eng. Part K: J. Multi-Body Dyn. 230(4), 307–328 (2016)Google Scholar
  19. 19.
    Pappalardo, C.M., Patel, M., Tinsley, B., Shabana, A.A.: Pantograph/catenary contact force control. In: ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers Digital Collection (2015)Google Scholar
  20. 20.
    Kulkarni, S., Pappalardo, C.M., Shabana, A.A.: Pantograph/catenary contact formulations. J. Vib. Acoust. 139(1), 011010 (2017)CrossRefGoogle Scholar
  21. 21.
    Patel, M.D., Pappalardo, C.M., Wang, G., Shabana, A.A.: Integration of geometry and small and large deformation analysis for vehicle modelling: chassis, and airless and pneumatic tyre flexibility. Int. J. Veh. Perform. 5(1), 90–127 (2019)CrossRefGoogle Scholar
  22. 22.
    Pappalardo, C.M.: A natural absolute coordinate formulation for the kinematic and dynamic analysis of rigid multibody systems. Nonlinear Dyn. 81(4), 1841–1869 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Cossalter, V., Lot, R., Massaro, M.: An advanced multibody code for handling and stability analysis of motorcycles. Meccanica 46(5), 943–958 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Pappalardo, C.M., Zhang, Z., Shabana, A.A.: Use of independent volume parameters in the development of new large displacement ANCF triangular plate/shell elements. Nonlinear Dyn. 91(4), 2171–2202 (2018)CrossRefGoogle Scholar
  25. 25.
    Pappalardo, C.M., Wang, T., Shabana, A.A.: Development of ANCF tetrahedral finite elements for the nonlinear dynamics of flexible structures. Nonlinear Dyn. 89(4), 2905–2932 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Pappalardo, C.M., Wang, T., Shabana, A.A.: On the formulation of the planar ANCF triangular finite elements. Nonlinear Dyn. 89(2), 1019–1045 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Pappalardo, C.M., Wallin, M., Shabana, A.A.: A new ANCF/CRBF fully parameterized plate finite element. J. Comput. Nonlinear Dyn. 12(3), 031008 (2017)CrossRefGoogle Scholar
  28. 28.
    Pappalardo, C.M., Yu, Z., Zhang, X., Shabana, A.A.: Rational ANCF thin plate finite element. J. Comput. Nonlinear Dyn. 11(5), 051009 (2016)CrossRefGoogle Scholar
  29. 29.
    Ljung, L.: System Identification Theory for the user, 2nd edn. PTR Prentice Hall, Upper Saddle River (1999)zbMATHGoogle Scholar
  30. 30.
    Juang, J., Phan, M.: Identification and Control of Mechanical Systems. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  31. 31.
    Van Overschee, P., De Moor, B.: Subspace Identification for Linear Systems: Theory—Implementation—Applications. Springer, Berlin (2012)zbMATHGoogle Scholar
  32. 32.
    Katayama, T.: Subspace Methods for System Identification – A Realization Approach. Springer, Berlin (2006)Google Scholar
  33. 33.
    Chu, J., Yuan, L., Hu, Y., Pan, C., Pan, L.: Comparative analysis of identification methods for mechanical dynamics of large-scale wind turbine. Energies 12(18), 3429 (2019)CrossRefGoogle Scholar
  34. 34.
    Favoreel, W., De Moor, B., Van Overschee, P.: Subspace state space system identification for industrial processes. J. Process Control 10(2–3), 149–155 (2000)CrossRefGoogle Scholar
  35. 35.
    Van Overschee, P., De Moor, B.: N4SID: subspace algorithms for the stochastic systems. Automatica 30(1), 75–93 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Astroza, R., Hernandez, F., Dìaz, P., Gutierrez, G.: System identification of a five-story building using seismic strong-motion data. In: Dynamics of Civil Structures, vol. 2, pp. 181–189. Springer (2020)Google Scholar
  37. 37.
    García-Illescas, M.Á., Murià-Vila, D., Alvarez-Icaza, L.: Monitoring and identification of vibration frequencies on a portion of México City Metro Line 12. Adv. Civil Eng. 2019, 4128320 (2019)CrossRefGoogle Scholar
  38. 38.
    Nord, T.S., Petersen, Ø.W., Hendrikse, H.: Stochastic subspace identification of modal parameters during ice–structure interaction. Philos. Trans. R. Soc. A 377(2155), 20190030 (2019)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Colucci, F., De Simone, M.C., Guida, D.: TLD design and development for vibration mitigation in structures. In: Karabegović, I. (ed.) New Technologies, Development and Application II. NT 2019. LNNS, vol 76, pp. 59–72. Springer, Cham (2019)Google Scholar
  40. 40.
    De Simone, M.C., Guida, D.: Identification and control of an unmanned ground vehicle by using Arduino. UPB Sci. Bull. Ser. D. 80, 141–154 (2018)Google Scholar
  41. 41.
    Sharifzadeh, M., Pisaturo, M., Senatore, A.: Real-time identification of dry-clutch frictional torque in automated transmissions at launch condition. Proc. Inst. Mech. Eng. Part D: J. Automob. Eng. (2019).
  42. 42.
    De Simone, M.C., Guida, D.: Control design for an under-actuated UAV model. FME Trans. 46(4), 443–452 (2018)CrossRefGoogle Scholar
  43. 43.
    De Simone, M.C., Rivera, Z., Guida, D.: Obstacle avoidance system for unmanned ground vehicles by using ultrasonic sensors. Machines 6(2), 18 (2018)CrossRefGoogle Scholar
  44. 44.
    Quatrano, A., De, S., Rivera, Z.B., Guida, D.: Development and implementation of a control system for a retrofitted CNC machine by using Arduino. FME Trans. 45(4), 565–571 (2017)CrossRefGoogle Scholar
  45. 45.
    Jiang, Y., Xue, N., Lu, S., Song, X.: Vibration suppression of a cantilevered piezoelectric laminated composite plate subjected to hygrothermal loads. IOP Conf. Ser.: Mater. Sci. Eng. 531(1), 012035 (2019)CrossRefGoogle Scholar
  46. 46.
    Hu, Y.C., Chen, P.J., Chang, P.Z.: Thermal-feature system identification for a machine tool spindle. Sensors 19(5), 1209 (2019)CrossRefGoogle Scholar
  47. 47.
    Costa, A.G., Maldonado, J.L.B., Romero, F.A., Sanmartín, J.C., Valarezo, M., Castillo, H.: N4SID method applied to obtain a discrete-time linear state space system as a mathematical model of a jaw crusher prototype. In: 2017 CHILEAN Conference on Electrical, Electronics Engineering, Information and Communication Technologies (CHILECON), pp. 1–6 (2017)Google Scholar
  48. 48.
    Ni, Z., Liu, J., Wu, Z., Shen, X.: Identification of the state-space model and payload mass parameter of a flexible space manipulator using a recursive subspace tracking method. Chin. J. Aeronaut. 32(2), 513–530 (2019)CrossRefGoogle Scholar
  49. 49.
    Liu, X., Yang, X., Zhu, P., Xiong, W.: Robust identification of nonlinear time-delay system in state-space form. J. Franklin Inst. 356(16), 9953–9971 (2019)MathSciNetzbMATHCrossRefGoogle Scholar
  50. 50.
    Holcomb, C., De Callafon, R.: Subspace identification for disturbance rejection control design in gas turbines. In: 2015 European Control Conference ECC, pp. 842–847. IEEE, Linz (2015)Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.MEID4 Academic Spin-Off of the University of SalernoFiscianoItaly
  2. 2.University of SalernoFiscianoItaly

Personalised recommendations