Coupling analysis and control of axial and torsional vibrations in a horizontal drill string

Vertical drilling methods have been often used for oil and gas extraction so far. In some places, for further extraction and access to the locations that cannot be obtained by the vertical drilling (due to its restrictions); horizontal drilling has become more popular. In horizontal drilling, a variety of longitudinal, torsional and lateral vibrations occur. These vibrations, if left uncontrolled, can damage the drilling rig and equipment, as well as reduce the efficiency of the drilling process and increase the processing time. The purpose of this research is to obtain the coupled axial and torsional vibration equations by analysing the vibrational modes in the horizontal section of the horizontal drilling. The obtained equations, which are in the form of continuous vibrations, are discretized by the mode summation method, and then the stability of the horizontal drilling string is investigated, and the controller is designed to stabilize the unstable process. In this research, the friction coefficient has been modeled randomly to be closer to the actual conditions. The controller was initially designed with four inputs, and then its inputs were reduced to the two inputs. First, the feedback linearization approach plus the pole placement method have been used to design the controller. To show the efficiency of the controller performance, uncertainties in the parameters of the forces are considered.