Page - 26 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

2. Adaptive Cruise Control engine at its speedωe. The relation between engine and vehicle speed is given byωe= ifj igv vx rj . The brake torque at one wheel equals Tbj= rbj c ∗ j pj(ub) Abj, (2.21) where rbj is the effective brake radius, and c ∗ j describs the quotient of the clamping force and the friction force at the brake [GOR07]. The brake pressure pj is a function of the actuationub of the driver, andAbj is the brake piston area. 2.4.2. Lower Level Controller Thelower levelcontrollerconvertstheerror inthevehicleaccelerationea=ades−vax into thethrottlepositionofthecombustionengineudorthebrakeactuationub. Asmentioned above, Isermann showed in [Ise02] that the dynamics of the combustion engine can be approximated by a first-order lag element with non-constant parameters, see eq. (2.20). This leads to problems in the parametrization of a Proportional-Integral Controller (PI) (kPd and kId) or Proportional-Integral-Derivative Controller (PID) (kPd, kId and kDd). If the controller is optimized for high loads, the closed loop may become unstable at low loads, due to the high gain kPd of the controller. On the other hand, if the controller is optimized for low loads, the settling time will be very high, due to the low gain. There is a trade-off between these two extreme examples. In [Ise02], Isermann proposed using a loadof30 to40%inorder togainanacceptableperformanceof theclosed loop. Ga¨chter showed in [Ga¨c12] that a sufficient performance can be reached with a PI controller. He addedananti-windupfunctionality (kAWd) to limit theoutputof the integral termof the controller. This is important when the vehicle cannot meet the desired acceleration (e.g. at very high speeds). Another possible way to achieve a better controller performance is to use a method called gain scheduling, [Ise02]. One possibility is shown in [XZ12]. There, a fuzzy system is used to adjust thekId and kPd components of a PID controller. The component kDd is constant. It is important to limit the parameters to the stable range of the closed loop. In [XZ12], the verification stability method of Ziegler-Nichols is used. Additionally, the acceleration controller has to control the gear box because it scales the drive torque, see parameter ig in eq. (2.19). The combination of a PID controller with gain scheduling and an anti-windup functionality will deliver effective acceleration control, see fig. 2.17. If the deceleration using the drag torque of the engine is not enough, the lower level con- troller actuates the brake to meet the desired deceleration. Using eqs. (2.18) and (2.21), therequiredbakepressurepdesandthereforetherequiredactuationub canbedetermined. The only problem is that the parameter c∗, which describes the friction at the brake, is not precisely known. Wallner and Tonchev showed in their investigations [Wal12] and [Ton08] that the friction strongly depends on the temperature, the brake pressure and the velocity. They discovered that with organic brake pads the friction coefficient varies in the range of 0.25 to 0.6, and for sintered pads between 0.4 and 0.8. To compensate for 26