Islam Boussaada

Analysis of drilling vibrations: A time-delay system approach

The main purpose of this study is the description of the qualitative dynamical response of a rotary drilling system with a drag bit, using a model that takes into consideration the axial and the torsional vibration modes of the bit. The studied model, based on the interface bit-rock, contains a couple of wave equations with boundary conditions consisting of the angular speed and the axial speed at the top additionally to the angular and axial acceleration at the bit whose contain a realistic frictional torque. Our analysis is based on the center manifold Theorem and Normal forms theory whose allow us to simplify the model.

Control of Drilling Vibrations: A Time-Delay System-Based Approach

Abstract The main purpose of this study is the control of both axial and torsional vibrations occurring along a rotary oilwell drilling system. This work completes a previous authors paper (Boussaada et al. [2012a]) which presents the description of the qualitative dynamical response of a rotary drilling system with a drag bit, using a model that takes into consideration the axial and the torsional vibration modes of the bit. The studied model, based on the interface bit-rock, contains a couple of wave equations with boundary conditions consisting of the angular speed and the axial speed at the top additionally to the angular and axial acceleration at the bit whose contain a realistic frictional torque. Our analysis is based on the center manifold theorem and normal forms theory whose allow us to simplify the model. By this way we design two control laws allowing to suppress the undesired vibrations guaranteeing a regular drilling process.

Isochronicity conditions for some planar polynomial systems II

Abstract We study the isochronicity of centers at O ∈ R 2 for systems x ˙ = − y + A ( x , y ) , y ˙ = x + B ( x , y ) , where A , B ∈ R [ x , y ] , which can be reduced to the Lienard type equation. Using the so-called C-algorithm we have found 27 new multiparameter isochronous centers.

Inverted pendulum stabilization: Characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains

The paper considers the problem of stabilization of systems possessing a multiple zero eigenvalue at the origin. The controller that we propose, uses multiple delayed measurements instead of derivative terms. Doing so, we increase the performances of the closed loop in presence of system uncertainties and/or noisy measurements. The problem formulation and the analysis is presented through a classical engineering problem which is the stabilization of an inverted pendulum on a cart moving horizontally. On one hand, we perform a nonlinear analysis of the center dynamics described by a three dimensional system of ordinary differential equations with a codimension-three triple zero bifurcation. On the other hand, we present the complementary stability analysis of the corresponding linear time invariant system with two delays describing the behavior around the equilibrium. The aim of this analysis is to characterize the possible local bifurcations. Finally, the proposed control scheme is numerically illustrated and discussed.

Analysis and Control of Oilwell Drilling Vibrations

-Develops a comprehensive model of coupled torsional-axial vibrations to show the practicing engineer how to reduce the most damaging forms of drillstring vibration. -Uses partial differential equations to show the researcher how a distributed-parameter model can be transformed into a neutral-type time-delay system or simplified analysis and simulation. -Various methods of modeling and control analysed comparatively so that the reader can choose the most appropriate Self-contained treatment introduces the student to mathematical background and existing models before developing novel techniques and results. This book reports the results of exhaustive research work on modeling and control of vertical oilwell drilling systems. It is focused on the analysis of the system-dynamic response and the elimination of the most damaging drillstring vibration modes affecting overall perforation performance: stick-slip (torsional vibration) and bit-bounce (axial vibration). The text is organized in three parts. The first part, Modeling, presents lumped- and distributed-parameter models that allow the dynamic behavior of the drillstring to be characterized; a comprehensive mathematical model taking into account mechanical and electric components of the overall drilling system is also provided. The distributed nature of the system is accommodated by considering a system of wave equations subject to nonlinear boundary conditions; this model is transformed into a pair of neutral-type time-delay equations which can overcome the complexity involved in the analysis and simulation of the partial differential equation model. The second part, Analysis, is devoted to the study of the response of the system described by the time-delay model; important properties useful for analyzing system stability are investigated and frequency- and time-domain techniques are reviewed. Part III, Control, concerns the design of stabilizing control laws aimed at eliminating undesirable drilling vibrations; diverse control techniques based on infinite--dimensional system representations are designed and evaluated. The control proposals are shown to be effective in suppressing stick-slip and bit-bounce so that a considerable improvement of the overall drilling performance can be achieved. This self-contained book provides operational guidelines to avoid drilling vibrations. Furthermore, since the modeling and control techniques presented here can be generalized to treat diverse engineering problems, it constitutes a useful resource to researchers working on control and its engineering application in oilwell drilling.

Computing the Codimension of the Singularity at the Origin for Delay Systems: The Missing Link with Birkhoff Incidence Matrices

A standard framework in analyzing Time-delay systems consists first, in identifying the associated crossing roots and secondly, then, in characterizing the local bifurcations of such roots with respect to small variations of the system parameters. Moreover, the dynamics of such spectral values are strongly related to their multiplicities (algebraic/geometric). This paper focuses on an interesting type of such singularities; that is when the zero spectral value is multiple. The simplest case,whichisquitecommoninapplications,ischaracterizedby an algebraic multiplicity two and a geometric multiplicity one known as Bogdanov-Takens singularity. Unlike finite dimen- sional systems, the algebraic multiplicity of the zero spectral value may exceed the dimension of the delay-free system of differential equations. To the best of the authors’ knowledge, the bound of such a multiplicity for Time-delay systems was not deeply investigated in the literature. Our contribution is two fold. First, we emphasize the link between the multiplicity characterization and Birkhoff matrices. Secondly, we elaborate a constructive bound for the zero spectral value in the regular case; i.e. when the delay polynomials of a given quasipolynomial are complete, as well as in the singular case; i.e. when such polynomials are sparse. In the last case, the established bound is sharper than Polya-Szego generic bound.

An Overview on the Modeling of Oilwell Drilling Vibrations

Abstract In drilling operations, the drillstring interaction with the borehole gives rise to a wide variety of undesired oscillations. The main types of drilling vibrations are torsional (stick- slip), axial (bit-bounce) and lateral (whirling). The analysis and modeling of rotary drilling vibrations is a topic whose economical interest has been renewed by recent oilfields discoveries leading to a growing literature. This paper summarizes the most popular modeling strategies allowing the oscillatory behavior analysis of the physical system.

Tracking the Algebraic Multiplicity of Crossing Imaginary Roots for Generic Quasipolynomials: A Vandermonde-Based Approach

A standard approach in analyzing dynamical systems consists in identifying and understanding the eigenvalues bifurcations when crossing the imaginary axis. Efficient methods for crossing imaginary roots identification exist. However, to the best of the authors knowledge, the multiplicity of such roots was not deeply investigated. In recent papers by the authors [1], [2], it is emphasized that the multiplicity of the zero spectral value can exceed the number of the coupled scalar delay-differential equations and a constructive approach Vandermonde-based allowing to an adaptive bound for such a multiplicity is provided. Namely, it is shown that the zero spectral value multiplicity depends on the system structure (number of delays and number of non zero coefficients of the associated quasipolynomial) rather than the degree of the associated quasipolynomial [3]. This technical note extends the constructive approach in investigating the multiplicity of crossing imaginary roots jω where ω ≠ 0 and establishes a link with a new class of functional confluent Vandermonde matrices. A symbolic algorithm for computing the LU-factorization for such matrices is provided. As a byproduct of the proposed approach, a bound sharper than the Polya-Szegö generic bound arising from the principle argument is established.

A control oriented guided tour in oilwell drilling vibration modeling

In drilling operations, the interaction of the drillstring with the borehole leads to vibrations affecting the performance and increasing the drilling cost. The development of controllers to get a faster and efficient drilling operation is based on a mathematical modeling allowing a proper system characterization and the identification of the vibration sources to avoid them or mitigate their influence. This paper presents an overview of the modeling of axial and torsional self-excited drilling vibrations.

Flatness-Based Control for a Non-Linear Spatially Distributed Model of a Drilling System

The main purpose of this study is the control of both axial and torsional vibrations occurring along a rotary oil well drilling system. The considered model consists of a system of wave equations with non-linear coupled boundary conditions. We propose a flatness-based control approach for suppressing harmful dynamics. Moreover, numerical simulations illustrate the efficiency of the established control laws.