Regulation of Inhomogeneous Drilling Model With a P-I Controller

Terrand-Jeanne, Alexandre; Andrieu, Vincent; Tayakout‐Fayolle, Mélaz; Martins, Valérie Dos Santos

doi:10.1109/tac.2019.2907792

Cited by 21 publications

(21 citation statements)

References 22 publications

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“…It is quite natural to note that the larger k i is, the slower the system is, while increasing the proportional gain leads to a faster system. As a conclusion, for small values of k p and k i , the system is stable and that was the conclusion of the two papers [44], [45] using a different Lyapunov functional. Note that with the previous papers, it was not possible to quantify the notion of "small enough gains k p and k i " while it is possible to give an estimation with the method of this paper.…”

Section: A On the Linear Modelmentioning

confidence: 64%

“…Since the existence and uniqueness of a solution to the previous problem is not the main contribution of this paper, it is assumed in the sequel. This problem has been widely studied (see [10], [12], [37], [39], [44] among many others) and the solution belongs to the following space if the initial conditions (φ 0 , φ 1 , ψ 0 , ψ 1 ) satisfies the boundary conditions (see [9] for more details): for θ = 0 because of the sign function. Nevertheless, since the nonlinearity acts directly on the variable z, it follows that there exists a unique solution to the ODE system in the sense of Filipov [19].…”

Section: Problem Statementmentioning

confidence: 99%

“…It is more restrictive and taking k p = 0 practically leads to a decrease of the robustness (even if some other performances might be enhanced). This phenomenon has been studied in many articles [22], [29], [44]. Hence, to be robust to delays in the loop, one then needs to ensure the following:…”

Section: Strong Stability Against Small Delay In the Controlmentioning

confidence: 99%

“…Lyapunov theory to some classes of Partial Differential Equations (PDE) [9], [16], [33]. These advances have given rise to the stability analysis of the linearized infinite-dimensional drilling pipe with a PI controller [44], [45]. Since this kind of controller provides only two degree of freedom, to better enhance the performances, slightly different controllers arose.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Barreau

Gouaisbaut

Seuret

2021

IEEE Trans. Contr. Syst. Technol.

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

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Section: A On the Linear Modelmentioning

confidence: 64%

Section: Problem Statementmentioning

confidence: 99%

Section: Strong Stability Against Small Delay In the Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Barreau

Gouaisbaut

Seuret

2021

IEEE Trans. Contr. Syst. Technol.

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“…On another hand, taking the the value of a and b given by (17) and (18), one can rewritten them with 0 < β < 1 and…”

Section: Discussion On the Resultsmentioning

confidence: 99%

Adding Integral Action for Open-Loop Exponentially Stable Semigroups and Application to Boundary Control of PDE Systems

Terrand-Jeanne

Andrieu

Martins

et al. 2020

IEEE Trans. Automat. Contr.

Self Cite

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The paper deals with output feedback stabilization of exponentially stable systems by an integral controller. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop system. An example of parabolic PDE (partial differential equation) systems and an example of hyperbolic systems are worked out to show how exponentially stabilizing integral controllers are designed. The proof is based on a novel Lyapunov functional construction which employs the forwarding techniques.All authors are with LAGEP-

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Uniform exponential stability approximations of semi‐discretization schemes for two hybrid systems

Zhang,

Zheng,

Wang

et al. 2024

Math Methods in App Sciences

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The uniform exponential stabilities (UESs) of two hybrid control systems comprised of a wave equation and a second‐order ordinary differential equation are investigated in this study. Linear feedback law and local viscosity are considered, as are nonlinear feedback law and internal anti‐damping. The hybrid system is first reduced to a first‐order port‐Hamiltonian system with dynamical boundary conditions, and the resulting system is discretized using the average central‐difference scheme. Second, the UES of the discrete system is obtained without prior knowledge of the exponential stability of the continuous system. The frequency domain characterization of UES for a family of contractive semigroups and the discrete multiplier approach are used to validate the main conclusions. Finally, the Trotter–Kato theorem is used to perform a convergence study on the numerical approximation approach. Most notably, the exponential stability of the continuous system is derived by the convergence of energy and UES, which is a novel approach to studying the exponential stability of some complex systems. Numerical simulation is used to validate the effectiveness of the numerical approximating strategy.

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Regulation of Inhomogeneous Drilling Model With a P-I Controller

Cited by 21 publications

References 22 publications

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

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

Adding Integral Action for Open-Loop Exponentially Stable Semigroups and Application to Boundary Control of PDE Systems

Uniform exponential stability approximations of semi‐discretization schemes for two hybrid systems

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