Dealing with torsional vibrations and stick–slip oscillations of a drill string system is a challenging engineering task in the oil drilling process because of the harmful and costly consequences of such vibrations. In this article, the drill string system is modeled using a lumped-parameter model with four degrees of freedom, and the bit–rock contact is represented by a nonlinear function of a bit velocity. Also, tracking the desired velocity of a drill string system with known constant input delay is addressed in the presence of external disturbance and parameter uncertainties by applying the Smith predictor–based sliding mode control method. The performance of the smith predictor–based sliding mode control with input delay and disturbance in tracking the desired velocity and controlling the stick–slip oscillations is compared with the sliding mode control with/without input delay. The system output’s sensitivity to the delay parameter is also investigated, indicating how the bit velocity changes concerning the delay parameter. The proper choice of adaptation gain is determinative in the performance of the controller, and its impact is investigated. Moreover, the robustness of the smith predictor–based sliding mode control is shown by changing the weight on the bit parameter. Simulation results demonstrate the effectiveness of the proposed method.

在石油钻井过程中，应对钻柱系统的扭转振动和粘滑振动是一项艰巨的工程任务，因为这种振动会产生有害且代价高昂的后果。在本文中，使用具有四个自由度的集总参数模型对钻柱系统进行建模，并且钻头与岩石的接触由钻头速度的非线性函数表示。另外，在存在外部干扰和参数不确定性的情况下，通过应用基于Smith预估器的滑模控制方法，可以解决在已知的恒定输入延迟下跟踪钻柱系统的理想速度的问题。将具有输入延迟和干扰的基于史密斯预测器的滑模控制在跟踪所需速度和控制粘滑运动中的性能与有/无输入延迟的滑模控制进行了比较。还研究了系统输出对延迟参数的敏感性，表明位速度如何与延迟参数有关。自适应增益的正确选择取决于控制器的性能，并研究其影响。此外，通过更改位参数的权重，可以显示基于史密斯预测变量的滑模控制的鲁棒性。仿真结果证明了该方法的有效性。指示有关延迟参数的位速度如何变化。自适应增益的正确选择取决于控制器的性能，并研究其影响。此外，通过更改位参数的权重，可以显示基于史密斯预测变量的滑模控制的鲁棒性。仿真结果证明了该方法的有效性。指示有关延迟参数的位速度如何变化。自适应增益的正确选择取决于控制器的性能，并研究其影响。此外，通过更改位参数的权重，可以显示基于史密斯预测变量的滑模控制的鲁棒性。仿真结果证明了该方法的有效性。