Exponential Lyapunov Stability Analysis of a Drilling Mechanism

TL;DR

This paper develops a Lyapunov-based stability analysis for a coupled drilling system modeled by differential equations, proposing a boundary measurement controller to enhance stability and performance.

Contribution

It introduces a linear matrix inequality condition for exponential stability and designs a finite-dimensional dynamic controller based on boundary measurements.

Findings

Derived a stability condition via LMIs for the drilling system.

Designed a boundary measurement controller to accelerate system dynamics.

Validated improvements through simulations.

Abstract

This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The aim is to derive a linear matrix inequality ensuring the exponential stability with a guaranteed decay-rate of this interconnected system. A strictly proper dynamic controller based on boundary measurements is proposed to accelerate the system dynamics and its effects are investigated through the stability theorem and simulations. It results in an efficient finite dimension controller which subsequently improves the system performances.