Page - 109 - in Maximum Tire-Road Friction Coefficient Estimation

6 Results and conclusion to model simplifications. As bax reacts with a time delay to longitudinal forces built up on the wheel, the estimate of µmax deviates in these transient areas with changing acceleration, see the example in Figure 6.1 around second 5. Nevertheless, this specific behaviourofaparticlefilterwithout the resampling step, whichusesonlyfixedparticles, enables fast detection of changes in the observed variable. Figure 6.2 shows the course of bax for a driving manoeuvre on dry road starting around second 5 with a maximum acceleration bax≈4.5 m/s2, which corresponds to the maximum achievable acceleration of the test vehicle at an initial speed of about 20 kph. 5 5.5 6 6.5 7 0 1 2 3 4 5 Time in s Figure 6.2.: Longitudinal acceleration bax during acceleration manoeuvre as shown in Figure 6.3 performed on dry road with a maximum acceleration bax ≈ 4.5 m/s2. The manoeuvre was started at vx = 20 km/h and ended at 50 km/h. Figure 6.3 shows the estimate of µmax using a particle filter with fixed particles for the manoeuvre shown in Figure 6.2. The reference value for the friction potential was determined using measurements at the longitudinal and lateral physical limits with the vehicle and the investigated tires and by comparing these results to tire characteristics measured on a tire test-bench. The reference values for the the tires show a slight variation, which is due to the degressive influence of the vertical tire load (cf. Section 2.1.3). Due to the steeper slopes of Fx(particles) compared to Fx(MD,i), as shown in Figure6.1,µmax showsahigherdeviationbetweentheestimateofµmax andthereference value in Figure 6.3 shortly before second 5 and until about second 5.5. A similar effect can also be observed at around second 6.2. Although bax is still constant, sx already decreases. 109