The research study that has been presented in this paper depicts automatic control of downwhole pressure by topside choking in managed-pressure-drilling (MPD) that is an example of automated drilling and also elaborates automatic control needs for drilling operations. For a set of normal operations, MPD operations require a specified accuracy, including rate changes and set point ramping during connections, swab and surge, as well as certain failure operations namely; gas kicks, blocked choke and power loss. In the future, adaptive control solutions for drilling are anticipated to be extensively used. Furthermore, in this research study, two methods have been implemented for adaptive control for Automatic Managed Pressure Drilling System that are the Massachusetts Institute of Technology (MIT) rule and Lyapunov, and later-on comparison was also conducted between the two. In the end, few viewpoints for the future of intelligent-drilling operations with growing adaptation were also included.