Multivariable control of the undesirable axial vibrations of the horizontal drill string

Although new technologies in energy area such as the wind turbines, solar systems and etcetera are introduced as some alternatives for the oil and gas energy sources, the latter ones are still the most important sources of energy in the world. So, researches have been continued to investigate in these fields to optimize all the steps from the extraction to producing the new products. After our previous article about the horizontal drilling dynamics, modeling the system with mode summation method, modes' convergence analysis, evaluation of the stability situation of the system with changing the parameters and identifying the instability; in this article designing an effective controller for that system is on agenda. Preventing the instability condition can lead to the increasing of the extraction and life time of the components. For the fourth mode in which the instability is observed, the controller is designed and this controller is examined in the case of five modes. It is shown that the controller performs efficiently in suppression of the undesirable axial vibrations of the horizontal drilling process. In addition, through a parametric study of the dynamic system, the number of inputs is decreased and the magnitude of them is reduced to have a more suitable design for using in the realistic applications.