Bifurcation and chaos from drilling system driven by IFOCIM

Abstract

In this paper, the dynamics of the nonlinear drilling system has been investigated. The used drilling system is a two Degree of Freedom (DoF) drilling string actuated by an AC drive system, the indirect field oriented controlled induction motor (IFOCIM) has been used as a controller for the AC drive system. The drilling system model is derived by combining a geared induction motor, IFOCIM controller, and the drilling string, the obtained model involves eleven nonlinear first order differential equations. The mathematical and numerical analyzes have been used to find the equilibrium points of the drilling system model. The nonlinear dynamics of the induction motor drive-based drilling system has been investigated numerically under the changes in the system parameters. The results are characterized by bifurcation diagrams, Lyapunov exponents spectrum, basins of attractions, phase portraits, and time series plots, the different nonlinear dynamics oscillations such as periodic, chaotic, and fixed point attractors have been shown. Furthermore, the system displays coexistence attractors.