Controlling Torsional Vibrations Through Proper Orthogonal Decomposition

Abstract

Nonlinear excitations cause angular vibrations in torsional strings. As an example for long torsional strings, we consider a drill string for drilling deep holes for the exploration and production of oil and gas. Due to the nonlinear torque at the bit, self-excited oscillations can occur by means of a supercritical Hopf bifurcation. Such vibrations are highly unwelcome, and in severe cases they could damage the string. In order to minimize these vibrations, we present an active damping system by employing the drive via feedback of the system state. The feedback law is formulated by a projection of the infinite-dimensional system state onto a real input variable. The basis of the projection will be determined by proper orthogonal decomposition (POD). The design of a POD-based controller and the determination of the controller parameters by optimization will be presented. The improvement of the dynamics will be verified by simulations.