Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor

Леонов, Г. А.; Kuznetsov, Nikolay V.; Kiseleva, M.A.; Solovyeva, E.P.; Zaretskiy, A.M.

doi:10.1007/s11071-014-1292-6

Cited by 239 publications

(86 citation statements)

References 47 publications

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“…It is worth noting that systems with stable equilibria are systems with 'hidden attractors' [26][27][28][29]. Hidden attractors have received considerable attention recently because of their roles in theoretical and practical problems [30][31][32][33][34][35][36][37][38]. Different definitions and main properties of fractional calculus have been reported in the literature [47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

A fractional-order form of a system with stable equilibria and its synchronization

et al. 2018

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There has been an increasing interest in studying fractional-order chaotic systems and their synchronization. In this paper, the fractional-order form of a system with stable equilibrium is introduced. It is interesting that such a three-dimensional fractional system can exhibit chaotic attractors. Full-state hybrid projective synchronization scheme and inverse full-state hybrid projective synchronization scheme have been designed to synchronize the three-dimensional fractional system with different four-dimensional fractional systems. Numerical examples have verified the proposed synchronization schemes.

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Section: Introductionmentioning

confidence: 99%

A fractional-order form of a system with stable equilibria and its synchronization

et al. 2018

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“…The case of an electro-vibro-impact system was considered in [10], where the authors studied a broad range of dynamical scenarios with coexisting periodic and chaotic solutions. More recently, hidden coexisting oscillations were investigated in a drilling system [3], which were identified as a possible cause of harmful vibrations in the drill strings.…”

Section: Introductionmentioning

confidence: 99%

Controlling multistability in a vibro-impact capsule system

Liu

Chávez

2017

Nonlinear Dyn

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This work concerns the control of multistability in a vibro-impact capsule system driven by a harmonic excitation. The capsule is able to move forward and backward in a rectilinear direction, and the main objective of this work is to control such motion in the presence of multiple coexisting periodic solutions. A position feedback controller is employed in this study, and our numerical investigation demonstrates that the proposed control method gives rise to a dynamical scenario with two coexisting solutions, corresponding to forward and backward progression. Therefore, the motion direction of the system can be controlled by suitably perturbing its initial conditions, without altering the system parameters. To study the robustness of this control method, we apply numerical continuation methods in order to identify a region in the parameter space in which the proposed controller can be applied. For this purpose, we employ the MATLAB-based numerical platform COCO, which

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“…In the present work, we will consider the lumped-parameter model shown in Fig. 2, which has been studied in the past by various authors; see, e.g., [10][11][12][13]. The generalized lumped-parameter model can be written in a single-input and multi-output form as follows Fig.…”

Section: Introductionmentioning

confidence: 99%

Numerical and experimental studies of stick–slip oscillations in drill-strings

Liu

Chávez

et al. 2017

Nonlinear Dyn

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The cyclic nature of the stick-slip phenomenon may cause catastrophic failures in drillstrings or at the very least could lead to the wear of expensive equipment. Therefore, it is important to study the drilling parameters which can lead to stickslip, in order to develop appropriate control methods for suppression. This paper studies the stick-slip oscillations encountered in drill-strings from both numerical and experimental points of view. The numerical part is carried out based on path-following methods for nonsmooth dynamical systems, with a special focus on the multistability in drill-strings. Our analysis shows that, under a certain parameter window, the multistability can be used to steer the response of the drill-strings from a sticking equilibrium or stick-slip oscillation to an equilibrium with constant drill-bit rotation. In addition, a small-scale downhole drilling rig was implemented to conduct a parametric study of the stick-slip phenomenon. The parametric study involves the use of two flexible shafts with varying mechanical properties to observe the effects that would have on stick-slip during operation. Our experimental results demonstrate that varying some of the mechanical properties of the drill-string could in fact control the nature of stick-slip oscillations.

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Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor

Cited by 239 publications

References 47 publications

A fractional-order form of a system with stable equilibria and its synchronization

A fractional-order form of a system with stable equilibria and its synchronization

Controlling multistability in a vibro-impact capsule system

Numerical and experimental studies of stick–slip oscillations in drill-strings

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