Among the most important characteristics of autonomous vehicles are the safety and robustness in various traffic situations and road conditions. In this paper, we focus on the development and analysis of the extended version of the canonical proportional-derivative PD controllers that are known to provide a good quality of steering on non-slippery (dry) roads. However, on slippery roads, due to the poor yaw controllability of the vehicle (suffering from understeering and oversteering), the quality of control of such controllers deteriorates. The proposed predicted PD controller (PPD controller) overcomes the main drawback of PD controllers, namely, the reactiveness of their steering behavior. The latter implies that steering output is a direct result of the currently perceived lateral- and angular deviation of the vehicle from its intended, ideal trajectory, which is the center of the lane. This reactiveness, combined with the tardiness of the yaw control of the vehicle on slippery roads, results in a significant lag in the control loop that could not be compensated completely by the predictive (derivative) component of these controllers. In our approach, keeping the controller efforts at the same level as in PD controllers by avoiding (i) complex computations and (ii) adding additional variables, the PPD controller shows better quality of steering than that of the evolved (via genetic programming) models.