Identification of vehicle parameters and estimation of vertical forces

Abstract

The aim of the present work is to estimate the vertical forces and to identify the unknown dynamic parameters of a vehicle using the sliding mode observers approach. The estimation of vertical forces needs a good knowledge of dynamic parameters such as damping coefficient, spring stiffness and unsprung masses, etc.

In this paper, suspension stiffness and unsprung masses have been identified by the Least Square Method.

Real-time tests have been carried out on an instrumented static vehicle, excited vertically by hydraulic jacks. The vehicle is equipped with different sensors in order to measure its dynamics. The measurements coming from these sensors have been considered as unknown inputs of the system. However, only the roll angle and the suspension deflection measurements have been used in order to perform the observer. Experimental results are presented and discussed to show the quality of the proposed approach.

Keywords:

• vehicle modelling
• vertical forces
• sliding mode observers
• estimation
• identification

Acknowledgements

This work was developed by the French IFSTTAR laboratory (ex LCPC: Laboratoire Central des Ponts et Chausséees) in collaboration with French industrial partners, Renault Trucks, Michelin and Sodit in the framework of French project VIF (Véhicule Lourd Interactif du Future). This work was supported by the French Ministry of Industry and the Lyon Urban Trucks&Bus competitiveness cluster; the authors gratefully acknowledge their contributions. The authors gratefully acknowledge the contributions of Dynamic Testing team of CERAM.

Nomenclature

Symbol	=	Physical meaning
θ	=	roll angle (rad)
q1, q2	=	left and right front suspension deflection (m)
z	=	centre height of gravity (m)
zr1,zr2	=	vertical displacement of the left and right wheel (m)
$\dot{\theta }$	=	roll rate (rad/s)
${\dot{q}}_1$,${\dot{q}}_2$	=	left and right front suspension velocity (m/s)
$\ddot{\theta }$	=	roll acceleration (rad/s2)
${\ddot{q}}_1$,${\ddot{q}}_2$	=	left and right front suspension acceleration (m/s2)
${\ddot{z}}_{r1}$,${\ddot{z}}_{r2}$	=	vertical acceleration of left and right wheel (m/ s2)
Fz1, Fz2	=	left and right vertical force (N)
u1, u2	=	left and right road profile input (m)
k1, k2	=	left and right suspension stiffness (N/m)
k3, k4	=	left and right tyre stiffness (N/m)
B1, B2	=	left and right suspension damping (Ns/m)
B3, B4	=	left and right tyre damping (Ns/m)
T	=	vehicle track width (m)
m	=	sprung mass (kg)
m1, m2	=	left and right unsprung mass (kg)

Notes

1. More information about CERAM (Centre d’Essais et de Recherche Automobile de Mortefontaine) can be found on the following web site: http://www.ceram-mortefontaine.fr

Additional information

Funding

The work of L. Fridman was supported by CONACyT (Consejo Nacional de Ciencia y Tecnología) [grant number 132125]; and by Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica (PAPIIT) [UNAM grant number 117211].

Notes on contributors

H. Imine

Dr Hocine Imine received his Master's Degree and his PhD in robotics and automation from Versailles University, France, in 2000 and 2003, respectively. Recently, he received the Accreditation to Supervise Research (Habilitation à Diriger des Recherches – HDR) on March 2012 from the University of Valenciennes et du Hainaut Cambrésis, France. From 2003 to 2004 he was a researcher at the Robotic Laboratory of Versailles (LRV in French), and an assistant professor at Versailles University. In 2005, he joined IFSTTAR (French Institute of Science and Technology for Transport, Development and Networks), where he is currently a senior researcher. He is involved in different projects such as véhicule Interactif du Futur (VIF) and Heavyroute (Intelligent Route Guidance for Heavy Traffic). He is also responsible for the research project PLInfra on heavy vehicle safety, assessment of their impacts on pavement and bridges. He was a member of the organising committee of the International Conference on Heavy Vehicles (HVParis’ 2008, merging HVTT10 and ICWIM5 in May 2008). He is the guest editor of the International Journal of Vehicle Design, Special Issue on: ‘Variable Structure Systems in Automotive Applications.’ He is a member of IFAC Technical Committee on Transportation systems (TC 7.4) and a member of GTAA (Working Group on Automatic and Automobile) in France. His research interests include intelligent transportation systems, heavy vehicle modelling and stability, diagnosis, non-linear observation and non-linear control. He has published two books, over 60 technical papers, and several industrial technical reports.

L. Fridman

Leonid M. Fridman received the MS degree in mathematics from Kuibyshev (Samara) State University, Samara, Russia, in 1976, the PhD degree in applied mathematics from the Institute of Control Science, Moscow, Russia, in 1988, and the Dr Sc degree in control science from Moscow State University of Mathematics and Electronics, Moscow, Russia, in 1998.From 1976 to 1999, he was with the Department of Mathematics, Samara State Architecture and Civil Engineering University. From 2000 to 2002, he was with the Department of Postgraduate Study and Investigations at the Chihuahua Institute of Technology, Chihuahua, Mexico. In 2002, he joined the Department of Control Engineering and Robotics, Division of Electrical Engineering of Engineering Faculty at National Autonomous University of Mexico (UNAM), México.His main research interests are variable structure systems.He is the author and editor of five books and a guest editor of 12 special issues on sliding mode control. He is the author of more than 350 technical papers. Prof. Fridman is the associate editor of the Journal of Franklin Institute, Nonlinear Analysis: Hybrid Systems and the Conference Editorial Board of IEEE Control Systems Society, Member of TC on Variable Structure Systems and Sliding Mode Control of IEEE Control Systems Society and TC on Discrete Events and Hybrid Systems of IFAC.He received the Scopus prize for the best cited Mexican Scientists in Mathematics and Engineering 2010. He was working as an invited professor in 17 universities and research centres of Australia, France, Germany, Italy, Israel and Spain.

T. Madani

Dr Tarek Madani received the engineering and Magister degrees in automatic control for electrical engineering from the Ecole Nationale Polytechnique, Algiers, Algeria, in 1997 and 2000, respectively, and the PhD in automatic control and robotics from Versailles University in 2005. He joined the Laboratoire d’Ingénierie des systèmes de Versailles. His main research interests include non-linear control.