Recent advances in autonomous vehicles and vehicular communications are envisioned to enable novel approaches to managing and controlling traffic intersections. In particular, with intersection controller units (ICUs), passing vehicles can be instructed to cross the intersection safely without traffic signals. Previous efforts on autonomous intersection control mainly focused on guaranteeing the safe passage of vehicles and improving intersection throughput, without considering the quality of the travel experience from the passengers' perspective. In this paper, we aim to design an enhanced autonomous intersection control mechanism, which not only ensures vehicle safety and enhances traffic efficiency but also cares about the travel experience of passengers. In particular, we design the metric of smoothness to quantitatively capture the quality of experience. In addition, we consider the travel time of individual vehicles when passing the intersection in scheduling to avoid a long delay of some vehicles, which not only helps with improving intersection throughput but also enhances the system's fairness. With the above considerations, we formulate the intersection control model and transform it into a convex optimization problem. On this basis, we propose a new algorithm to achieve an optimal solution with low overhead. Finally, we build the simulation model and implement the algorithm for performance evaluation. Comprehensive simulation results demonstrate the superiority of the proposed algorithm.