Design of a sliding mode controller for suppressing coupled axial & torsional vibrations in horizontal drill strings using Extended Kalman Filter

Abstract

Nowadays, drill string technologies are among the leading fields in the industries of oil and gas extraction and are widely used in the construction of subway tunnels. Due to their significant applications, horizontal drill strings have attracted the attention of researchers. Various vibrations that occur during the drilling process are also sources of system uncertainty. To solve the mentioned problems, in this paper, a coupled axial-torsional model is considered for a horizontal drill string, and all the forces and torques that are involved in the drilling process, are modeled. All the primary modes of the axial and torsional vibrations are calculated using a numerical solution. For solving the PDE equations of motion, the mode summation method is used, and in order to determine the minimum necessary modes, mode convergence analysis has been accomplished for this coupled axial-torsional plant for the first time. In the next step, a novel nonlinear sliding mode controller (SMC) is designed for this plant to eliminate the coupled axial and torsional vibrations, using only two control inputs. As the proposed controller requires the state variables, and the sensors are incapable of recording all the state variables, an Extended Kalman Filter (EKF) is designed to estimate all the 12 state variables, which is one of the novelties of this research. Eventually, a comparison analysis with a conventional SMC and a Pole-Placement controller is provided to ensure the performance of the proposed controller. Moreover, unmodelled dynamics and parametric uncertainties are considered to ensure the robustness of the proposed controller.