Page - 102 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

B. Vehicle Dynamics B.3. Combined Lateral and Longitudinal Vehicle Dynamics Combining eqs. (2.16) and (B.1) leads to      cfω˙y crω˙y vv˙x vv˙y vω˙z       ︸ ︷︷ ︸ x˙ =       0 0 vωz vvy −vωz vvx 0       +        1 If (cfTy− cfTy,ro−wfFxrf) 1 Ir (crTy− crTy,ro−wrFxrr) 1 m (2wfFx+2wrFx−Fa) 2 m (wfFy+wrFy) 2 vIzz (wfFy lf+wrFy lr)        ︸ ︷︷ ︸ f(x,δ,ud,ub) (B.17) with five Degrees of Freedom (DOFs), the rotational speed of the front and rear wheels, cfωy, crωy, the longitudinal and lateral vehicle speed, vvx, vvy and the yaw rate vωz. The tyre forceswfFx,wrFx,wfFy andwrFx are calculated using eqs. (B.3) to (B.6) and the tyre model described in appendix B.2. The wheel torque cfTy and cfTy consists of the drive torque for the front and rear wheels cfTd, crTd and the brake torque on each axle cfTb, crTb, described in eqs. (2.19) and (2.21). The air drag is given in eq. (2.14). The input for the model is the steering angle δ, the gas pedal positionud and the brake actuationub. 102