Despite a significant research effort to understand and mitigate stick-slip in drill-strings, this problem yet to be solved. In this work, a comprehensive parametric robustness analysis of the sliding mode controller has hitherto been performed. First, a model verification and extensive parametric analysis of the open-loop model is presented. This is followed by a detailed parametric analysis of the sliding-mode controller based closed-loop system for two cases, (i) an ideal actuator with no delay or constraint and (ii) a realistic actuator with delay or/and constraint. It is shown that though the proposed controller works robustly across a wide range of parameters, in the absence of delay, it fails in the presence of a delay, thereby limiting its practical application. Experimental results are included to support these claims. This work underlines the importance of including the inherent system characteristics during the control design process. Furthermore, the parametric analysis presented here is aimed to act as a blue-print for testing the efficacy of relevant control schemes to be proposed in the future.
Bifurcations are an interesting class of dynamic behavior exhibited by many nonlinear systems. Drill string typically employed in underground oil exploration are highly nonlinear systems whose dynamic behavior has generated huge research interest. Though it is well-known that typical drill-strings behave like piecewise smooth systems and the severity of bifurcations they exhibit has not been studied in depth. In this work, a two degree of freedom (2-DOF) model of the drill-string is constructed and its dynamic behavior. In-depth analysis of the effect of parameter variation on the severity of bifurcations is conducted. This can potentially deliver key insights in the design of control strategies aimed at suppressing problematic stick-slip oscillation.
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