Practical Stability Analysis of a Drilling Pipe Under Friction With a PI-Controller

This article deals with the stability analysis of a drilling pipe controlled by PI controller. The model is coupled ordinary differential equation/partial equation (PDE) and consequently infinite dimension. Using recent advances in time-delay systems, we derive new Lyapunov functional based on state extension made up projections Riemann coordinates. First, will provide an exponential result expressed using linear matrix inequality (LMI) framework. dedicated to version torsional dynamic. On other hand, influence nonlinear friction force, which may generate well-known stick-slip phenomenon, analyzed through theorem. Numerical simulations show effectiveness method that oscillations cannot be weakened