Arrival management is a promising solution to the issue of delays and inefficiencies surrounding inbound flights at a congested airport such as Tokyo International Airport. In our previous work, we proposed a method for sequencing and arrival time assignment; it forms a key part of an arrival management system. This study focuses on controlling the arrival time, which is another critical part of the time-based arrival management system. We devised a strategy to accurately control the required time of arrival at a meter fix located on the terminal area's boundary by utilizing a currently operational flight management system's required time of arrival function. Experiments using flight management system simulators showed robust control logic and performance against wind error disturbances.