Design and simulation of a classic controller to reduce undesired coupling axial and torsional vibrations in a horizontal drill string

Drilling technologies are widely used in the gas and oil extraction. Nowadays for further extraction, horizontal drillings are more popular than vertical drillings. One of the main problems in the drilling process is the destructive vibrations. If these vibrations are not controlled, they can destroy the drilling components, reduce the drilling efficiency and minimize the penetration rate. In this paper, by considering all forces and torques, the nonlinear coupled axial and torsional dynamics of the horizontal drill string are studied. Then eight modes for axial and torsional vibrations are obtained. Coupled PDE equations are converted in to ODE equations, using the mode summation method. After simulating the system and considering the vibrations, an active controller is designed to eliminate the undesired axial and torsional vibrations. It must be mentioned that the proposed controller used only two control inputs, one for axial movement and the other one for rotation of the system, which is the novelty of the designed controller.