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4 Sensitivity Analysis
ities with the minimum turning circleRmin such that
ω¯z = Rmin
vmaxx · bωz and (4.21)
∂ω¯z
∂µ = Rmin
vmaxx · ∂bωz
∂µ . (4.22)
Accordingly, the values of the four wheel angular speeds ωi are normalised by the ref-
erence effective tire radius re,i. For zero longitudinal slip at the wheel, the longitudinal
velocity of the wheel hub is proportional to the effective tire radius and the wheel’s
angular speed. Thus, the normalised ω¯i is physically equivalent to vx, and its sensitivity
reads
ω¯i = ωi ·rr,i
vmaxx and (4.23)
∂ω¯i
∂µ = rr,i
vmaxx · ∂ωi
∂µ . (4.24)
Thereferenceeffective tire radiusrr,i is calculated for static tire loadsbasedonEquation
3.23. Finally, the normalised state variables and their normalised sensitivities read
z¯ = N ·z and (4.25)
∂z¯
∂µ = N · ∂z
∂µ , (4.26)
where thenormalisationmatrixN is adiagonalmatrixwhoseprincipaldiagonal consists
of the elements 1vmaxx · [
1 1(
lr
Rmin +∆βmax ) Rmin rr,fl rr,fr rr,rl rr,rr].
4.5. Results and discussion of sensitivity analysis
As discussed in Section 4.1.1, the sensitivity p shows the relation between the change
of the state variable z with respect to the change of the investigated parameter in the
investigated case µmax. This means that the sign of the resulting sensitivity takes into
account the relation of the changes in both z andµmax for the investigated data point.
Figure 4.7 shows how the non-normalised sensitivities of all state variables change
with µmax for two different longitudinal accelerations during a manoeuvre with pure
longitudinal acceleration. With increasing longitudinal acceleration, the absolute value
ofthesensitivity increases. This is true forallof thestatevariableszandforall simulated
76
Maximum Tire-Road Friction Coefficient Estimation
- Title
- Maximum Tire-Road Friction Coefficient Estimation
- Author
- Cornelia Lex
- Publisher
- Verlag der Technischen Universität Graz
- Location
- Graz
- Date
- 2015
- Language
- English
- License
- CC BY-NC-ND 3.0
- ISBN
- 978-3-85125-423-5
- Size
- 21.0 x 29.7 cm
- Pages
- 189
- Category
- Technik