Page - 99 - in Maximum Tire-Road Friction Coefficient Estimation

5 Tire/road friction estimator 0 2 4 6 8 10 0 1000 2000 3000 4000 µmax=0.5 0 2 4 6 8 10 -500 0 500 1000 s x in % 0.2 0.4 0.6 0.8 1 1.2 0 1000 2000 3000 4000 µmax s x =0.5% s x =6% 0.2 0.4 0.6 0.8 1 1.2 0 2000 4000 6000 s x in % µmax µmax=1 ∆s x ∆F x,i ∆µmax ∆F x,i Figure 5.2.: Non-linear behaviour of longitudinal tire characteristics forFz,i= 3000 N in dependenceof longitudinal slipsx for twoµ max (top left)anddependingon µmax for two sx (bottom left). The right side shows the partial derivatives ∆Fx,i/∆sx versus sx (top right) and ∆Fx,i/∆µ max versus µmax (bottom right). The graphic representation is based on Boßdorf-Zimmer, [BZ07, p.85]. 5.4. Observer structure Figure 5.3 provides a general overview of the non-linear observer used in this work. The inputs u(k) to both the real vehicle and the parallel observer are the inputs from the driver, including the steering wheel angle δS, the choice of gear and the activation of the accelerator and braking pedal. The wheel torqueMD,i(k) accounts for the driver’s inputs in the longitudinal direction. In the observer, a simplified model is used to incorporate the expected vehicle reaction to the inputs. The real vehicle is also exposed to disturbances d(k) (e.g. wind forces or road unevenness), which are not considered by theobserver. Thevehicle’s state bz(k) ismeasuredand forwarded to theobserver. It is a functionof the internal statex(k), which isnotdirectlymeasured, and themeasurement noisev(k). Ithas tobementioned thatFigure5.3also showsanoutput bz˙(k). Although there is no direct relation such as an ODE considered for bz˙(k) within the model, its components bax and bay are necessary for the observer, e.g. to calculate the tire load variation (cf. Equation 3.22). Finally, an estimate xˆ(k) is calculated in the observer using a model of the observed variable. The observer itself is shown in more detail in Figure 5.4. The main component is the particle filter, where the most probableµmax is 99