ABSTRACT Systems containing ambiguous components demonstrate intricate behaviours crucial for designing control systems. Handling twist oscillations and stick‐slip fluctuations in a drill‐string system presents a significant engineering challenge in oil drilling, due to their detrimental and expensive effects. This control system regulates the rotational speeds of drill‐string components to achieve predetermined targets. In this study, we utilise a lumped‐parameter model to analyse the twisting dynamics of the drill‐string with four degrees of freedom. To alleviate stick–slip oscillations, reduce bit sticking in vertical oil‐well drill strings and diminish saturation effects on control performance, a composite nonlinear feedback is used with a supertwist integral sliding mode control technique, including an anti‐windup mechanism. By identifying a suitable Lyapunov function, mathematical calculations derive a condition based on actuator saturation areas for exponential stabilisation, expressed as an LMI. Additionally, such oscillatory phenomena are not confined to vertical oil‐well drill strings; analogous dynamic instabilities are observed in both offshore and onshore derrick systems, emphasising the broader applicability of the proposed control strategy. The efficacy of the approach is confirmed by simulation results.
Amiri et al. (Thu,) studied this question.