# A Quarter Car ARX Model Identification Based on Real Car Test Data

## Authors

• Dirman Hanafi Advanced Mechatronic Research Group (AdMiRe), Faculty of Electrical and Electronic Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor, Malaysia.
• Mohammad Saiful Huq Advanced Mechatronic Research Group (AdMiRe), Faculty of Electrical and Electronic Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor, Malaysia.
• Mohd Syafiq Suid Advanced Mechatronic Research Group (AdMiRe), Faculty of Electrical and Electronic Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor, Malaysia.
• Mohd Fua’ad Rahmat Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia.

## Keywords:

Quarter Car Passive Suspension System Dynamics, Speed, Running Test, Artificial Road Surface, ARX Model,

## Abstract

This paper presents a system identification of a quarter car passive suspension system dynamic model based on real-time running test car data. The input-output data of a car were recorded by test-driving the car on a road surface. The input variable is the vertical acceleration of the car shaft, while the output variable is the vertical acceleration of the body of the car. Two acceleration sensors were installed on the front right corner of the car: One on top of the suspension and another on the car shaft at the bottom of the suspension. The acquired data were used to identify the mathematical model of a quarter car passive suspension system dynamics. A quarter car passive suspension system was assumed to have an ARX model structure, hence qualifies to be a candidate model for system identification. The system identification algorithm used in this work was based on linear least-square estimation. The results showed that the best ARX model of the car passive suspension system model is produced with the best fit of 90.65%, Akaike’s FPE is 5.315x10-6. The output order of the model was found to be four, the input order is two and the time delay was one. The fit rate greater than 90% and along with a very small value for the FPE means that the system identification requirements are fulfilled and the identified model is acceptable.

## References

P. Sathishkumar, J. Jancirani, D. John, D. Manikandan. Mathematical modeling and simulation quarter car vehicle suspension. International Journal of Innovative Research in Science, Engineering and Technology, 3(1) (2014) 1280-1283.

Z. Zhang, N. C. Cheung, K. W. E. Cheng. Application of Linear Switched Reluctance Motor for Active Suspension System in Electric Vehicle. World Electric Vehicle Journal, 4(1) (2011) 14-21.

H. Moghadam-Fard, F. Samadi. Active Suspension System Control Using Adaptive Neuro-Fuzzy (ANFIS) Controller. International Journal Engineering Transaction C: Aspects, 28(3) (2015) 396-401.

Reza N. Jazar. Vehicle Dynamics: Theory and Application. Second Edition, Springer, (2014).

A. Podzorov, V. Prytkov. The vehicle ride comfort increase at the expense of semiactive suspension system. Journal of KONES Powertrain and Transport, 18(1) (2011) 463-470.

A. Agharkakli, U.S. Chavan, S. Phvithran. Simulation And Analysis Of Passive And Active Suspension System Using Quarter Car Model For Non Uniform Road Profile. International Journal of Engineering Research and Applications, 2(5) (2012) 900-906.

Yan Cui, Thomas Kurfess, Michael Messman. A Methodology to Integrate a Nonlinear Shock Absorber Dynamics into a Vehicle Model for System Identification. SAE International Journal of Materials and Manufacturing, 4(1) (2011) 527-534.

Moritz Allmaras, Wolfgang Bangerth, Jean Marie Linhart, Javier Polanco, Fang Wang, Kainan Wang, Jennifer Webster, Sarah Zedler. Estimating Parameters in Physical Models through Bayesian Inversion: A Complete Example. SIAM Rev., 55(1) (2013) 149–167.

R. Razaghi, R. N. Amanifard, N. Narimanzadeh. Modeling And MultiObjective Optimization of Stall Control on NACA0015 Airfoil with Synthetic Jet Using GMDH TYPE Neural Networks and Genetic Algorithms. International Journal Engineering Transaction A: Basics, 22(1) (2009) 69-88.

Piotr Fryzlewicz, Theofanis Sapatinas, Suhasini Subba Rao. Normalized Least Squares Estimation in Time-Varying ARCH Models. The Annals of Statistics, 36(2) (2008) 742–786.

Dirman Hanafi, Mohd. Fua’ad Rahmat. Neural Network Based System Identification of an Axis of Car Suspension System. Jurnal Teknik Elektro, 8(1) (2008) 1-7.

R. Diversi, R. Guidorzi, U. Soverini. Identification of ARX models with noisy input and output. Proceeding of the 18th IFAC World Congress, Milano, Italy, (2011) 13121-13126.

Karel J. Keesman. System Identification: An Introduction. Springer, (2011).

G. Koch, E. Pellegrini, S. Spirk, B. Lohmann. Design and Modeling of a Quarter Vehicle Test Rig for Active Suspension Control. Technical Reports on Automatic Control, TRAC-5, (2010).

S. D. García, D. Patino. Estimation based on acceleration measures of an active suspension plant. Proceeding of IEEE 2nd Colombian Conference on Automatic Control (CCAC), Manizales, (2015) 1-6.

L. Ljung. System Identification. Devision of Automatic Control, Linköping University 2016.

Dirman Hanafi. Neural Network System Identification: Experimental Approach of a Quarter Car Modelling. UTHM Publisher, (2012).

G. D. Nusantoro, G. Priyandoko. PID State Feedback Controller of a Quarter Car Active Suspension System. Journal of Basic and Applied Scientific Research, 1(11) (2011) 2304-2309.

2017-06-01

## How to Cite

Hanafi, D., Huq, M. S., Suid, M. S., & Rahmat, M. F. (2017). A Quarter Car ARX Model Identification Based on Real Car Test Data. Journal of Telecommunication, Electronic and Computer Engineering (JTEC), 9(2-5), 135–138. Retrieved from https://jtec.utem.edu.my/jtec/article/view/2413

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