The benefits of automated driving can only be fully realized if the occupants are protected from motion sickness. Active suspensions hold the potential to raise the comfort level in automated passenger vehicles by enabling new functionalities in chassis control. One example is to actively lean the vehicle body toward the center of the corner to counteract the inertial lateral acceleration. Commonly known as curve tilting, the concept is deemed effective in reducing postural disturbance on the occupants and the visual-vestibular conflict when the occupants do not have an external view. We present in this article a nonlinear model predictive control (NMPC) method for the curve tilting functionality. The controller incorporates the nonlinear suspension forces in the prediction model to help achieve high tracking accuracy near the physical limit of the suspension system. The optimization process is accelerated with an explicit initialization method that is based on piecewise-affine (PWA) modeling and offline solution to an alternative optimal control problem (OCP). The controller is able to operate at 20 Hz in a hardware-in-the-loop (HIL) setup. Given sufficient computational resources, we observe a significant reduction in the lateral acceleration sensed by the passenger over a vehicle with passive suspensions, namely, by 46.5%, 25.4%, and 25.4% in the highway, rural, and urban driving scenarios, respectively. The NMPC also outperforms the baseline proportional-integral-derivative (PID) controller by achieving lower tracking error, namely, by 12.9%, 16.4%, and 38.0% in the aforementioned scenarios.@en