Stick–Slip Vibration Characteristics Study of the Drill String Based on PID Controller

In order to address the issue of drill string stick–slip vibration, which leads to drill bit wear and reduces the drilling velocity, we conducted a study on the characteristics of stick–slip vibration using a proportional-integral-derivative (PID) controller. By applying the principles of rigid body mechanics, we established a two-degree-of-freedom torsional dynamics equation and derived the first-order differential dynamics equation for the drill string. Subsequently, we designed a PID controller and obtained an equation for the control of stick–slip vibration. The research findings indicate that variations in the difference between the static and dynamic friction coefficients directly impact the nature of the limit cycles in the phase plane. As this difference decreases, the limit cycle narrows and the stick–slip vibrations weaken progressively. When the static and dynamic friction coefficients are equalized, no stick–slip vibrations occur within the drill string. The implementation of PID control effectively manages stick–slip vibrations in the drill string, with greater efficiency observed in controlling the turntable velocity compared to the drill bit velocity. This research provides valuable insights for the development of control strategies aimed at mitigating stick–slip vibrations in drilling engineering applications, thereby facilitating the efficient and safe extraction of oil and gas resources.