Axial-torsional dynamics of a drilling bit with non-uniform blade arrangement

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Suppression of axial-torsional vibrations of a distributed drilling system by the eigenvector contradiction method

This article proposes an active control strategy to suppress self-excited coupled axial-torsional vibrations of a distributed drill-string system while the coupling takes place through the bit-rock interaction. The drill-string model is expressed as Neutral-type Delay Differential Equations (NDDEs) with constant and state-dependent state delays and constant input delays. As a first step in the novel controller design, an implementable input transformation is introduced, resulting in the elimination of the neutral terms from the equations of motion. This supports a simplified next step of stabilizing controller design. In the second step, a new analytic method named the “Eigenvector Contradiction Method” is proposed to provide sufficient conditions to ensure that all eigenvalues have real parts less than a prescribed value. Based on this criterion, an automated parametric feedback control law is designed. A case study simulation is presented to illustrate the effectiveness of the proposed control strategy.</p

Multiple robust controllers design for linear uncertain systems

This thesis presents two design methods for multiple robust controllers (MRC) and a design method for switched robust controllers that can be used for linear systems with parametric uncertainty. These methods are helpful in enhancing the performance of feedback control systems beyond the performance limitations associated with conventional design methods for uncertain linear systems. MRC have been introduced to overcome the performance limitations imposed by the requirements for robustness. The design of MRC involves dividing the uncertainty set of a linear system into a number of subsets, as well as synthesizing of a robust controller for each subset. We propose two methods for the design of the uncertainty set divisions and controllers. The first method determines each controller and each subset in subsequent steps, and can deal with only time-invariant parametric uncertainties. In the second method, we find both each controller and each subset simultaneously. This method can handle both time-invariant and time-varying uncertainties. Switched robust controllers, on the other hand, have the potential to advance the existing performance limitations of a single linear time-invariant robust controller by switching among a set of linear time-invariant controllers. We introduce a new concept, robust finite-time tracking, that is a property of closed-loop uncertain systems. Robust finite-time tracking focuses on the transient response, as opposed to the steady-state response (as in Lyapunov-based techniques). We formulate an optimization problem for the design of switched robust finite-time tracking controllers. The controller design methods that discussed above include nonsmooth non-convex optimization problems. In order to find a local optimum to the problems, nonsmooth optimization techniques are utilized. We compare the performance of developed methods to existing methods in the literature through several numerical examples, such as inverted pendulum and mass-spring-damper systems. Moreover, to demonstrate the advantages of our method for MRC over traditional robust controllers in a practical example, we design multiple robust track-following controllers for hard disk drive servo-systems.Applied Science, Faculty ofMechanical Engineering, Department ofGraduat

Control of Axial-Torsional Dynamics of a Distributed Drilling System

Self-excited vibrations in drill-string systems are one of the main causes of failure and efficiency reduction in drilling operations. To suppress these vibrations, an active control strategy is proposed in this article based on a distributed drill-string model. Herein, the coupled axial-torsional dynamics of the drill string are taken into account. This coupling takes place through the bit-rock interaction, consisting of the cutting and the frictional components. The drill-string model is expressed as a neutral-type delay differential equation (NDDE) with constant and state-dependent state delays and constant input delays. As a first step in the novel controller design, a compensator is designed to mitigate the reflective waves at the top side of the string, which, in turn, results in the elimination of the neutral terms and some of the constant time delays in the delay system model. This supports a simplified next step of stabilizing controller design. Second, a new method is proposed to provide sufficient conditions for exponential stability with a prescribed minimal transient decay rate. Based on these conditions, a parametric feedback control law is designed. Finally, to make the controller causal, a predictor is designed which predicts the future state by only employing top-side measurements, available in practice. A simulation-based case study reflecting real-life scenarios is presented to illustrate the effectiveness of the proposed controller. It is also illustrated that the controller is robust against parametric uncertainties and measurement noise.</p