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TECHNICAL PAPERS

# Dynamic-Deflection Tire Modeling for Low-Speed Vehicle Lateral Dynamics

[+] Author and Article Information
Shiang-Lung Koo

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720-1720slk@berkeley.edu

Han-Shue Tan

California PATH, University of California at Berkeley, Institute of Transportation Studies, Richmond, CA 94804-4698hstan@path.berkeley.edu

Since the velocity of the material point at A with respect to the ground is zero $v¯wheelcenter=v¯A$.

The identification procedure of the snowblower parameter will be discussed in Sec. 5.

The bicycle model has almost null gains when the speed is extremely small.

J. Dyn. Sys., Meas., Control 129(4), 393-403 (Jan 10, 2007) (11 pages) doi:10.1115/1.2745847 History: Received June 23, 2005; Revised January 10, 2007

## Abstract

Vehicle lateral dynamics depends heavily on the tire characteristics. Accordingly, a number of tire models were developed to capture the tire behaviors. Among them, the empirical tire models, generally obtained through lab tests, are commonly used in vehicle dynamics and control analyses. However, the empirical models often do not reflect the actual dynamic interactions between tire and vehicle under real operational environments, especially at low vehicle speeds. This paper proposes a dynamic-deflection tire model, which can be incorporated with any conventional vehicle model to accurately predict the resonant mode in the vehicle yaw motion as well as steering lag behavior at low speeds. A snowblower was tested as an example and the data gathered verified the predictions from the improved vehicle lateral model. The simulation results show that these often-ignored characteristics can significantly impact the steering control designs for vehicle lane-keeping maneuvers at low speeds.

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## Figures

Figure 1

Top view of (a) contact patch for tire lateral deflection, (b) contact patch for tire yaw deflection

Figure 10

Step response of the closed-loop system C1P2∕(1+C1P2)

Figure 2

Frequency response from steering angle to yaw rate at (a)V=0.5m∕s and (b) V=20m∕s

Figure 3

Frequency response from steering angle to lateral acceleration at (a)0.5m∕s and (b) 20m∕s

Figure 4

(a) Trajectories of the front and rear wheels and the associated slip angles at steady state; frequency response from steering angle to yaw rate. (b) Under various yaw relaxation length, V=0.4m∕s. (c) Under various lateral relaxation length, V=0.4m∕s. (d) Under different tire damping constants, V=0.4m∕s.

Figure 5

Comparison among various models-frequency response from steering angle to yaw rate (a) at zero speed, (b) at 0.45 and 1.6m∕s, (c) at 0.45m∕s and 1.6m∕s

Figure 6

Lateral displacement versus time for (a)V=0.9m∕s, frequency varying from 0.3 to 0.6Hz; (b)V=1.2m∕s, frequency=0.2Hz; (c)V=1.5m∕s, frequency=0.6Hz; (d)V=1.6m∕s, frequency=0.7Hz; (e)V=2.5m∕s, frequency=0.5Hz

Figure 7

(a) The controlled plant with weighting functions; (b) the closed-loop interconnection using μ-synthesis framework; (c) the weighting functions for controller design

Figure 8

Controller bode plot from head position error to steering angle

Figure 9

Step response of the nominal closed-loop systems (a)C1P1∕(1+P1C1); (b)C2P2∕(1+P2C2)

## Errata

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