Real-time control solutions for unmanned aerial vehicles (UAVs) have attracted great interest in recent years. Most existing control methods use Wi-Fi technology. While Wi-Fi is inexpensive and easy-to-use, it has only a limited transmission range. Thus, 4G/5G cellular networks have been proposed as an alternative enabling technology. This study focuses on the problem of improving the appropriateness of the control commands sent by the ground control station (GCS) to the UAV over the control and non-payload communication (CNPC) link of the UAV through the cellular network. To satisfy the low-latency requirement of the CNPC link, multi-access edge computing (MEC) technology is leveraged to collocate the GCS and base station. The effectiveness of the proposed edge-based approach is demonstrated by conducting experiments on two LTE platforms with different MEC deployment methods. An edge-enabled UAV control solution is proposed in which each end-to-end control delay in the UAV-GCS system is estimated based on the preceding delay such that the location of the UAV at the moment it receives the control command from the GCS can be predicted in advance and taken into consideration by the GCS when formulating an appropriate control decision. To this end, an analytical modeling method is proposed for estimating the expected error range of each control delay based on a bimodal distribution approximation of the empirical control delays observed at the UAV. Finally, an event-driven simulator is developed to confirm the accuracy of the analytical predictions of the control delay based on the expected error between consecutive delays.