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Research Papers

Quantification of Road Vehicle Handling Quality Using a Compensatory Steering Controller

[+] Author and Article Information
Giovanni Braghieri, Alexander Haslam, Michalis Sideris, Julian Timings

Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK

David Cole

Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK
e-mail: djc13@cam.ac.uk

1Present address: Imperial College, Exhibition Road, London SW7 2AZ, UK.

2Present address: McLaren Racing Ltd, Chertsey Road, Woking, Surrey GU21 4YH, UK.

3Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 15, 2015; final manuscript received October 12, 2016; published online January 23, 2017. Assoc. Editor: Azim Eskandarian.

J. Dyn. Sys., Meas., Control 139(3), 031010 (Jan 23, 2017) (9 pages) Paper No: DS-15-1382; doi: 10.1115/1.4035009 History: Received August 15, 2015; Revised October 12, 2016

Criteria for stability and controllability of road vehicles are briefly reviewed, and it is argued that there is a need for criteria that might better relate to subjective ratings by drivers. The variance of a driver's closed-loop control action against random disturbances acting on the vehicle is proposed as a realistic criterion that might relate to a driver's assessment of the vehicle. A nonlinear vehicle model with five degrees-of-freedom, negotiating a 90-deg bend in minimum time, is the basis for the theoretical study. The vehicle model is run with the center of mass in two different positions. It is found that the variance of the driver's compensatory steering control varies significantly through the maneuver, reaching a peak at about midcorner. The corresponding variance in the lateral path error of the vehicle also peaks at about the same position in the maneuver. Comparison of these variances to existing stability and controllability criteria shows that the variance of the compensatory control might reveal aspects of the handling behavior that the existing criteria do not. Recommendations for further work are given and include a program of driving simulator experiments or track tests to correlate the new criteria against subjective ratings by human drivers.

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References

Figures

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Fig. 1

Vehicle model with associated forces and dimensions

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Fig. 2

Lateral tire force for one axle. The curves show four different levels of longitudinal slip κ. The vertical axle force Fzj is 6000 N.

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Fig. 3

The road boundaries and the optimal paths of the US and OS vehicles

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Fig. 4

Optimal torque (T) through the maneuver for the US and OS vehicles. The torque is positive (accelerating) if the line is above road level and negative (braking) when the line is below road level. Both vehicles accelerate in the first part of the maneuver, then brake at corner entry and accelerate at the exit. The vertical lines correspond to data at time intervals of 0.4 s. The triangles and circles plotted at road level correspond to the three phases of the maneuver: braking on entry, transition from braking to accelerating at midcorner, and maximum drive torque at exit.

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Fig. 5

Optimal hand wheel angle (δsw) through the maneuver for the US and OS vehicles. The steering angle for the US vehicle is positive through most of the corner while it is positive at the beginning of the corner for the OS vehicle and negative (countersteering) toward the exit.

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Fig. 6

Relationship between maneuver time and CoM position. The optimal value to minimize maneuver time is 0.42.

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Fig. 7

Vehicle in the nominal and perturbed state. The lateral path error e is shown together with nominal and perturbed longitudinal velocity u, lateral velocity v, and yaw angle ψ.

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Fig. 8

Standard deviation of the lateral path deviation and heading angle for the US vehicle, calculated using Eq. (38) and an ensemble of 1000 time-domain responses

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Fig. 9

Standard deviation of the compensatory hand wheel rate calculated using Eq. (38) and drive/brake torque for the US vehicle calculated using Eq. (40) and an ensemble of 1000 time-domain responses

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Fig. 10

Standard deviation of lateral path error through the maneuver

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Fig. 11

Standard deviation of heading error through the maneuver

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Fig. 12

Standard deviation of compensatory hand wheel angle through the maneuver

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Fig. 13

Surface plot showing how the standard deviation of the compensatory hand wheel angle varies with CoM position and time through the maneuver. The US and OS vehicles correspond to the boundaries of the surface.

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Fig. 14

Directional stability derivative for the OS and US vehicles through the maneuver

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Fig. 15

Yaw damping derivative for the OS and US vehicles through the maneuver

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Fig. 16

Control moment derivative for the US and OS vehicles through the maneuver

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Fig. 17

Eigenvalues for the US vehicle going through the maneuver described in Sec. 3. The circles plotted on the time axis correspond to the three phases of the maneuver: braking on entry, transition from braking to accelerating at midcorner, and maximum drive torque at exit. Positive real parts indicate instability; nonzero imaginary parts indicate oscillation.

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Fig. 18

Eigenvalues for the OS vehicle going through the maneuver described in Sec. 3

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