Open Journal of Applied Sciences, 2013, 3, 41-46

doi:10.4236/ojapps.2013.32B008 Published Online June 2013 (http://www.scirp.org/journal/ojapps)

Estimation of Longitudinal Tire Force Using

Nonlinearity Observer

Suwat Kuntanapreeda

Department of Mechanical and Aerospace Engineering, Faculty of Engineering,

King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

Email: suwat@kmutnb.ac.th

Received 2013

ABSTRACT

Tire forces are the major forces propelling the road vehicles. They significantly affect the dynamic behavior of the ve-

hicles. Estimation of the tire forces is essential in vehicle dynamics and control. This paper presents an observer-based

scheme for estimation of the longitudinal tire force of electric vehicles in real time. The observer is based on a

nonlinearity observer method. The pole-placement technique is used for determination of the observer gains. Simulation

results demonstrate that the observer is able to estimate the tire force successfully. The experiments are implemented on

a single-wheel electric vehicle test rig. The test rig comprises an electric motor driven wheel and a free-rolling drum

simulating vehicle-on-road situations. Experimental results confirm the effectiveness of the present scheme.

Keywords: Estimation; Nonlinearity Observer; Tire Force; Traction Control; Electric Vehicles

1. Introduction

Electric vehicles (EVs) have become very attractive for

replacing conventional internal combustion engine vehi-

cles because of environmental and energy problems [1].

The research and development of EVs and hybrid EVs

have been investigated on various topics such as, for

example, propulsion systems [2], power converters [3],

and motion control [4].

Traction control plays an important role in vehicle mo-

tion control because it increases drive efficiency, safety,

and stability. Tire forces are essential in traction control.

They are the vehicular propulsive forces produced by

friction between the rolling wheel and the road surface.

The characteristic of the friction between the wheel and

the road surface is very nonlinear. It mainly depends on

the wheel slip and the tire/road surface condition. In [5],

an approach to estimate the tire-road friction during

normal drive is presented. The approach is based on a

Kalman filter to give estimates of the slip-slope. In [6],

an on-line least-squares method is used to estimate the

parameters concerned with a friction force margin. The

effect of the estimation is evaluated by applying the

method to the breaking control. A slip-based method to

estimate the maximum available tire-road friction during

breaking is developed in [7]. The method is based on the

hypothesis that the slope of the slip curve at the low-slip

region during normal driving can indicate the maximum

friction coefficient. In [8], vehicle-dynamics-based

methods for tire-road friction coefficients estimation are

reviewed. The methods include slip-slope-based, lateral-

ehicle-dynamics-based, and an EKF-based estimation

methods. In [9], three different observers are developed

for the estimation of slip ratios and longitudinal tire

forces. The observers include one that utilizes engine

torque, break torque, and GPS measurements, one that

utilizes torque measurements and an accelerometer, and

one that utilizes GPS measurements and an accelerome-

ter.

This paper presents an observer-based scheme for es-

timation of the longitudinal tire force of EVs using a

nonlinearity observer. Simulation and experimental stud-

ies are used to illustrate the effectiveness of the present

scheme. A single-wheel test rig is used as an experimen-

tal test bench.

2. Nonlinearity Observer

The nonlinearity observer developed in [10,11] is re-

viewed in this section. Consider the following nonlinear

system

()()( (),)()

() ()

tt tt

tt

t

xAxNfx Bu

yCx

(1)

where , , and are, respectively, the state vector,

the control vector, and the output vector, respectively.

, , and are, respectively, the system ma-

trix, the control input matrix, the output matrix, and the

xu

C

y

NA B

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