Practical Stability Analysis of a Drilling Pipe Under Friction With a PI-Controller
Practical Stability Analysis of a Drilling Pipe Under Friction With a PI-Controller
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使用 PI 控制器对摩擦下钻杆进行实际稳定性分析
DOI：
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发表时间：
2019
影响因子：
4.8
通讯作者：
A. Seuret
中科院分区：
文献类型：
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作者：
Matthieu Barreau;F. Gouaisbaut;A. Seuret
本文对采用PI控制器控制的钻杆进行了稳定性分析。该模型是一个耦合的常微分方程/偏微分方程（PDE），因此是无限维的。利用时滞系统的最新进展，我们推导出一个新的李雅普诺夫功能的基础上，由投影的黎曼坐标的状态扩展。首先，我们将提供一个指数稳定性的结果表示使用线性矩阵不等式（LMI）的框架。该结果专用于扭转动力学的线性版本。另一方面，通过一个新的稳定性定理，分析了非线性摩擦力的影响，这可能会产生众所周知的粘滑现象。数值仿真结果表明了该方法的有效性，并表明使用PI控制器不能削弱粘滑振荡。
This article deals with the stability analysis of a drilling pipe controlled by a PI controller. The model is a coupled ordinary differential equation/partial differential equation (PDE) and is consequently of infinite dimension. Using recent advances in time-delay systems, we derive a new Lyapunov functional based on a state extension made up of projections of the Riemann coordinates. First, we will provide an exponential stability result expressed using the linear matrix inequality (LMI) framework. This result is dedicated to a linear version of the torsional dynamic. On the other hand, the influence of the nonlinear friction force, which may generate the well-known stick-slip phenomenon, is analyzed through a new stability theorem. Numerical simulations show the effectiveness of the method and that the stick-slip oscillations cannot be weakened using a PI controller.