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4 Sensitivity Analysis
0.5 1
0
0.1
0.2
0.3
0.4
0.5
µmax 0.5 1
0
1
2
3
µmax 0.5 1
-15
-10
-5
0
µmax 0.5 1
-20
-15
-10
-5
0
µmax 0.5 1
-6
-5
-4
-3
-2
-1
0
µmax 0.5 1
0
0.5
1
1.5
µmax 0.5 1
0
0.5
1
1.5
µmax
b
a
x
=2.3,
b
a
y
=2
b
a
x
=2,
b
a
y
=3
x10-3
Figure 4.8.: Relation between non-normalised sensitivity of state variables and the fric-
tion potentialµmax for two combined longitudinal and lateral accelerations.
Theunits of the shownsensitivities are the sameas for their respective state
variable.
vary. The sensitivity of the lateral velocity ∂vy/∂µ shows a comparable tendency to
that of the longitudinal velocity vx, but one order of magnitude higher, despite the
fact that the absolute value of vy during cornering is generally far lower than that for
vx. Even without normalisation, this already indicates that considering vy to estimate
µmax will contribute much more than considering vx during a manoeuvre that includes
cornering. In comparison, the sensitivity∂bωz/∂µ is several orders of magnitude smaller
and has a different sign. The yaw rate changes little with changingµmax due to the high
vehicle’s yaw moment of inertia, see Figure 4.9. In comparison, vy changes significantly
withµmax , as can also be seen in Figure 4.9.
4.5.1. Resulting normalised sensitivities at different driving states
Figure4.10 showsall simulatedaccelerations (black lines) andthedifferent regions (gray
areas) that have been analysed. The investigated area corresponds approximately to
the area that is typically traversed by a non-professional driver within the maximum
physicallypossible area, [Weg09, p.70-71]. Theblackdots showall analyseddatapoints,
and the dark gray asterisks show all selected data points that are further shown and
discussed in this section. It has to be mentioned that the resulting absolute values
of the sensitivities depend on the initial longitudinal speed, see Section 4.3.2. Within
one region, the initial longitudinal speed vx,0 is the same. The absolute values of the
sensitivities can be directly compared within one region, but not across regions.
78
Maximum Tire-Road Friction Coefficient Estimation
- Titel
- Maximum Tire-Road Friction Coefficient Estimation
- Autor
- Cornelia Lex
- Verlag
- Verlag der Technischen Universität Graz
- Ort
- Graz
- Datum
- 2015
- Sprache
- englisch
- Lizenz
- CC BY-NC-ND 3.0
- ISBN
- 978-3-85125-423-5
- Abmessungen
- 21.0 x 29.7 cm
- Seiten
- 189
- Kategorie
- Technik