Control of longitudinal or torsional vibration in a drill pipe/BHA using infinite dimensional techniques

The goal of this paper is to investigate how the vibration characteristics within a drill pipe can be modulated using (i) active control laws, or (ii) appropriate choices of impedance properties within the continuum. It is assumed in the paper that the continuum could have multiple sources of inputs, some acting as disturbance and some as control. The continuum was assumed to have generalized impedance at the two boundaries. In the paper, the structure of the transfer function is derived. Then, control laws are developed using the infinite dimensional models to actively modulate vibration characteristics within the continuum. Multi-sensor implementation of these control laws is then investigated which would provide these sought performances without requiring knowledge of the boundary impedance. Additionally, the role of boundary impedance on the performance of the control law is investigated. The concepts proposed in this paper are illustrated by simulations.