Page - 105 - in Maximum Tire-Road Friction Coefficient Estimation

5 Tire/road friction estimator 5.5.2. Estimation of the slip angles Several approaches for estimating the side slip angle or the horizontal velocities in the vehicle’s COG have been published. In this work, a non-linear observer developed by Kollienz, [Kol13, p.34-42], which is based on Zhao et al., [ZLC11], was used. With measurements of bax, bay and zωz, the velocities vx and vy in the vehicle’s COG are estimated based on a two-track vehicle model for a given wheel torqueMD,i and the steering wheel angle δS. As mentionend in the case of vx for the estimation of sx, the lateral velocity component vy or the side slip angleβ in the vehicle’s COG also need to be transformed from the vehicle’s COG to the i-th wheel-fixed coordinate system. 5.5.3. Wheel’s torque In the case of propulsion (no braking), the wheel’s torque can be calculated based on the engine torque, which is available on the vehicle’s CAN bus. Thus, the wheel’s torque is calculated based on gear ratios within the powertrain, also considering the current gear and the mechanical efficiency. Unfortunately, for the majority of measurements the demanded engine torque was measured instead of the delivered engine torque. As the signal course of the demanded engine torque is clearly linked to accelerator pedal activation, butnotdirectly linked to thevehicle’s reaction, it couldnotbeused. Using it to directly calculateMD,i resulted in a non-negligible time delay between wheel’s torque and wheel’s longitudinal slip sx in the range of tenths of a second. With a first order element, thisbehaviour couldbe reproduced formanyconditions, butproblemswith the amplitude compared to the course of bax still remained. Overall, the approach described belowwasmoreapplicable. However, thisdoesnotautomatically imply that theoriginal proposal would perform worse. Instead, the wheel torque was calculated using the vehicle’s body longitudinal acceler- ation bax, which is comparable to the approaches of Ray, [Ray97], Rajamani, [RPLG06], etc. This approach has also been used to calculate the wheel’s torques in the case of braking. Interventions of systems like ABS, TC or ESC were not considered and those systems were also deactivated during the driving tests. For future applications, effects of these systems will have to be investigated. Excluding additional wind forcesFW,x and road slope βr in the applied forces given by Equation 3.9, the total of longitudinal applied forces acting on the vehicle reads b ∑ Fx = ∑ i bFx,i−FA. Using this relation in the first row of Equation 3.6, which 105