Abstract
The role of time delay in the control processes aimed at mitigating stick-slip vibration in drill-strings, is of paramount importance. Its influence on the controlled system's settling time cannot be understated; indeed, it can lead to significant consequences such as controller instability. In this study, a numerical analysis was conducted, initially a sliding mode control was employed to suppress stick-slip vibration in drill-string. Then we explore a spectrum of time delay values alongside varying reference angular velocities. The results of this investigation suggest a critical finding: the controller's susceptibility to limit cycles is notably heightened in the presence of time delay and its experiences a decline when faced with fluctuating reference angular velocities. Despite this degradation, it is noteworthy that the system does not always reach a state of complete instability. These insights are invaluable, offering essential considerations for the development of robust control strategies. Addressing the challenges posed by time delay-induced issues in suppressing stick-slip vibration during drilling operations requires a nuanced approach, taking into account the intricacies highlighted in this study.
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