Modeling and Control of Drill-String System With Stick-Slip Vibrations Using LPV Technique

Abstract

In this article, a systematic linear parameter-varying (LPV) model and a gain-scheduled control methodology for drill-string systems are proposed to analyze drill-string dynamics and suppress stick-slip vibrations, finally achieving efficient drilling. First, the changing length of drill string over the entire drilling process is emphasized and the corresponding LPV model is presented by combining the existing multi-degree-of-freedom (DOF) drill-string model, so as to capture length-varying effect. Then, we construct a generalized gain-scheduled control structure based on the $\mathcal {H}_\infty $ framework and gain-scheduling technique. Procedures for obtaining original and reduced gain-scheduled controllers are designed. Using the measured top drive speed and drill-string length in real time, the gains of the proposed controllers are automatically scheduled, enforcing satisfactory tracking and disturbance rejection performances. Finally, simulations and comparisons between our model and finite-element method-based model and our control method and existing active damping controller are carried out. The simulation results illustrate the effectiveness of the proposal.