<p>In this paper, the dynamics of an induction motor drive-based oil drilling system with a top drive is considered. The system model, consisting of an eleventh-order set of differential equations, is first derived. Then, its nonlinear dynamics are numerically investigated under variations of parameter values. Using this nonlinear model, the bifurcation diagram and the corresponding Lyapunov exponent spectrum are calculated, revealing undesired subharmonic periodic regimes and chaotic behavior for certain parameter values. The fixed-time synergetic control technique (FTSCT) is employed to stabilize the system toward a desired equilibrium point. The control strategy uses a macro-variable, defined as a linear combination of the speed error and the flux error of the induction motor. The results show that the FTSCT is effective in suppressing undesired oscillations.</p>