Page - 104 - in Maximum Tire-Road Friction Coefficient Estimation

5 Tire/road friction estimator B.3 in the horizontal tire data shown in Table D.3 measured on a tire test bench can be excluded, since this effect does not have a linear dependence with sx,i. 5.5.1. Estimation of the longitudinal slip To use the definition of sx,i presented in Equation 2.3 in Section 2.1.2, the wheel’s rota- tional speedωi, the vehicle’s longitudinal velocity vx and the effective tire radius re,i are required. For the wheel’s rotational speedωi, the series-application ABS sensors of the vehicle were used. The signals were not taken from the CAN bus directly to avoid time delays, a low sample rate and dealing with an unknown filter used in the control unit. Instead, an analogue signal of the ABS sensors was used directly and then filtered using a one-dimensional median filter with order 10, meaning that the median values of the measurements of the last 10 time steps are used to calculate the output for the current time step. Anaccuratemonitoringof thevehicle’s longitudinalvelocityvx ismoredifficult. There aredifferentapproachestocalculatevxusingdifferentsensorcombinations, seeAppendix E.Withinthiswork, thereferencevelocityvxwasmeasuredusingacombinationofGNSS and inertial measurement, as discussed in Section 5.5.1. It has to be mentioned that the inertial measurement platform was not a low-cost sensor, but an advanced laboratory measurement system, [Gmb14]. For automotive series-application, these signals have to be replaced. The velocity estimation methods mentioned in Appendix E also discuss promising solutions for automotive series-application regarding costs. A model for the effective tire radius re,i is shown in Equation 3.23 in Section 3.2.3. The measurements showed that for real driving states, these influences seem to play a minor role compared to other factors. For this reason, re,i was regularly reset for each wheel using free rolling manoeuvres. As proposed by Miller et al., vx calculated based on global navigation satellite system (GNSS) velocity and inertial measurements was used to calculate re,i during free rolling, [MYM +01]. Using the constant values of these calibrated re,i showed better results than additionally considering Equation 3.23. The calculated value of sx was filtered again with a one-dimensional median filter with an order of 50. 104