Backstepping boundary observer based-control for hyperbolic PDE in rotary drilling system

International audienceIt is well known that torsional vibrations in oil well system affect the drilling directions and may be inherent for drilling systems. The drill pipe model is described by second order hyperbolic Partial Differential Equation (PDE) with mixed boundary conditions in which a sliding velocity is considered at the top end. In this paper, we consider the problem of boundary observer design for one-dimensional PDE with the usually neglected damping term. The main purpose is the construction of a control law which stabilizes the damped wave PDE, using only boundary measurements. From the Lyapunov theory, we show an exponentially vibration stability of the partially equipped oil well drilling system. The observer-based control law is found using the backstepping approach for second-order hyperbolic PDE. The numerical simulations confirm the effectiveness of the proposed PDE observer based controller

Delay-Adaptive Control of First-order Hyperbolic PIDEs

We develop a delay-adaptive controller for a class of first-order hyperbolic partial integro-differential equations (PIDEs) with an unknown input delay. By employing a transport PDE to represent delayed actuator states, the system is transformed into a transport partial differential equation (PDE) with unknown propagation speed cascaded with a PIDE. A parameter update law is designed using a Lyapunov argument and the infinite-dimensional backstepping technique to establish global stability results. Furthermore, the well-posedness of the closed-loop system is analyzed. Finally, the effectiveness of the proposed method was validated through numerical simulation

Adaptive prescribed performance control for wave equations with dynamic boundary and multiple parametric uncertainties

In modern engineering, the dynamics of many practical problems can be described by hyperbolic distributed parameter systems. This paper is devoted to the adaptive prescribed performance control for a class of typical uncertain hyperbolic distributed parameter systems, since uncertainties are inevitable in practice. The systems in question simultaneously have unknown in-domain spatially varying damping coefficient and unknown boundary constant damping coefficient. Moreover, dynamic boundary condition is considered in the present paper. These characteristics make the control problem in the paper essentially different from those in the related works. To solve the problem, using adaptive technique based projection operator, backstepping method developed for ODEs and Lyapunov stability theories, a powerful adaptive prescribed performance control scheme is proposed to successfully guarantee that all states of the resulting closed-loop system are bounded, furthermore, the original system state converges to an arbitrary prescribed small neighborhood of the origin. Compared with the existing results, the developed control schemes can not only effectively handle the serious uncertainties, but also overcome the technical difficulties in the infinite-dimensional backstepping control design method caused by the dynamic boundary condition and guarantee prescribed performance

Stability analysis of coupled ordinary differential systems with a string equation: application to a drilling mechanism

Cette thèse porte sur l'analyse de stabilité de couplage entre deux systèmes, l'un de dimension finie et l'autre infinie. Ce type de systèmes apparait en physique car il est intimement lié aux modèles de structures. L'analyse générique de tels systèmes est complexe à cause des natures très différentes de chacun des sous-systèmes. Ici, l'analyse est conduite en utilisant deux méthodologies. Tout d'abord, la séparation quadratique est utilisée pour traiter le côté fréquentiel de ce système couplé. L'autre méthode est basée sur la théorie de Lyapunov pour prouver la stabilité asymptotique de l'interconnexion. Tous ces résultats sont obtenus en utilisant la méthode de projection de l'état de dimension infinie sur une base polynomiale. Il est alors possible de prendre en compte le couplage entre les deux systèmes et ainsi d'obtenir des tests numériques fiables, rapides et peu conservatifs. De plus, une hiérarchie de conditions est établie dans le cas de Lyapunov. L'application au cas concret du forage pétrolier est proposée pour illustrer l'efficacité de la méthode et les nouvelles perspectives qu'elle offre. Par exemple, en utilisant la notion de stabilité pratique, nous avons montré qu'une tige de forage controlée à l'aide d'un PI est sujette à un cycle limite et qu'il est possible d'estimer son amplitude.This thesis is about the stability analysis of a coupled finite dimensional system and an infinite dimensional one. This kind of systems emerges in the physics since it is related to the modeling of structures for instance. The generic analysis of such systems is complex, mainly because of their different nature. Here, the analysis is conducted using different methodologies. First, the recent Quadratic Separation framework is used to deal with the frequency aspect of such systems. Then, a second result is derived using a Lyapunov-based argument. All the results are obtained considering the projections of the infinite dimensional state on a basis of polynomials. It is then possible to take into account the coupling between the two systems. That results in tractable and reliable numerical tests with a moderate conservatism. Moreover, a hierarchy on the stability conditions is shown in the Lyapunov case. The real application to a drilling mechanism is proposed to illustrate the efficiency of the method and it opens new perspectives. For instance, using the notion of practical stability, we show that a PI-controlled drillstring is subject to a limit cycle and that it is possible to estimate its amplitude

Nonlinear Adaptive Control of Drilling Processes

This work deals with the modeling and control of automated drilling operations. Advances in drilling automation are of substantial importance because improvements in drilling control algorithms will result in more efficient drilling, which is beneficial from both economic and environmental points of view. While the primary application of the results is extraction of natural resources, potentially there exists a wide range of applications, including offshore exploration, archaeological research, and automated extraterrestrial mining, where implementation of new methods and control algorithms for drilling processes can bring substantial benefits. The main contribution of the thesis is development of new methods and algorithms for control of drilling processes in industrial drilling systems, ensuring stability and high performance characteristics. The problems of regulation of vertical penetration rate and drilling power in rotary drilling systems are solved; as a result, stability and vibration mitigation is ensured. A number of challenges is addressed, such as complexity and nonlinearity of the drilling model, lack of information about environment and parameters of the drilling system itself, and poor communication between downhole sensors and ground-level equipment. Several cases are considered, depending on the amount of information that is available in advance or in real time. Two mathematical models of the drilling system are investigated: one is finite-dimensional, and another is a distributed parameter model. Several solutions are proposed for both of them, using methods of adaptive, robust, and sliding mode control, and comparisons are made. Feasibility and efficiency of the proposed control algorithms are confirmed by simulations in MATLAB/Simulink

Modeling and Control of Marine Flexible Systems

Ph.DDOCTOR OF PHILOSOPH

Modeling, Optimization, and Control of Down-Hole Drilling System

This dissertation investigates dynamics modeling, optimization, and control methodologies of the down-hole drilling system, which can enable a more accurate and reliable automated tracking of drilling trajectory, mitigating drilling vibration, improving the drilling rate, etc. Unlike many existing works, which only consider drilling control in the torsional dimension, the proposed research aims to address the drilling dynamics modeling and control considering both coupled axial and torsional drill string dynamics. The dissertation will first address optimization and control for vertical drilling, and then resolve critical modeling and control challenges for the directional drilling process. In Chapter 2, a customized Dynamic Programming (DP) method is proposed to enable a computationally efficient optimization for the vertical down-hole drilling process. The method is enabled by a new customized DP searching scheme based on a partial inversion of the dynamics model. Through extensive simulation, the method is proved to be effective in searching for an optimal drilling control solution. This method can generate an open-loop optimal control solution, which can be used as a guide for drilling control or in a driller-assist system. In Chapter 3, to enable a closed-loop control solution for the vertical drilling, a neutral- delay differential equations (NDDEs) model based control approach is proposed, specifically to address an axial-torsional coupled vertical drilling dynamics capturing more transient dynamics behaviors through the NDDE. An equivalent input disturbance (EID) approach is used to control the NDDEs model by constructing the Lyapunov-Krasovskii functional (LKF) and formulating them into a linear matrix inequality (LMI). The control gains can be obtained to effectively mitigate the undesired vibrations and maintain accurate trajectory tracking performance under different control references. The works on Chapter 2 and Chapter 3 are mostly for vertical drilling, and the remaining of the dissertation will focus on modeling and control for directional drilling. Chapter 4 proposes a dual heuristic programming (DHP) approach for automated directional drilling control. By approximating the derivative of the cost-to-go function using a neural network (NN), the DHP approach solves the “curse of dimensionality” associated with the traditional DP. The result shows that the proposed controller is robust, computationally efficient, and effective for the directional drilling system. To validate the DHP based control method using a high-fidelity directional drilling model, a hybrid drilling dynamics model is proposed in Chapter 5. The philosophy of the proposed modeling approach is to use the finite element method (FEM) to describe curved sections in the drill string and use the transfer matrix method (TMM) to model straight sections in the drill string. By integrating different methods, we can achieve both modeling accuracy and computational efficiency for a geometrically complex structure. Compared to existing directional drilling models used for off-line analysis, this model can be used for real-time testbeds such as software-in-the-loop (SIL) system and hardware-in-the-loop (HIL) system. Finally, a software-in-the-loop real-time simulation testbed is built to test the designed DHP based controller in Chapter 6. A higher-order hybrid model of directional drilling is implemented in the SIL. The SIL results demonstrate that the designed DHP based controller can effectively mitigate harmful vibrations and accurately track the desired references

Modeling and control of managed pressure drilling operations

The upstream oil and gas industry has witnessed a marked increase in the number of wells drilled in areas with elevated subsurface formation pressures and narrow drilling margins. Managed Pressure Drilling (MPD) techniques have been developed to deal with the challenge of narrow margin wells, offering great promise for improved rig safety and reduced non-productive time. Automation of MPD operations can ensure improved control over wellbore pressure profiles, and there are several commercial solutions currently available. However, these automation efforts seldom take into account the uncertainty and complex dynamics inherent in subsurface environments, and usually assume ideally functioning sensors and actuators, which is rarely the case in real-world drilling operations. This dissertation describes a set of tools and methods that can form the basis for an automation framework for MPD systems, with specific focus on the surface back-pressure technique of MPD. Model-based control algorithms with robust reference tracking, as well as methods for detecting system faults and handling modeling uncertainty, are integrated with a novel multi-phase hydraulics model. The control system and event detection modules are designed using physics-based representations of the drilling processes, as well as models relating uncertain variables in a probabilistic fashion. Validation on high-fidelity simulation models is conducted in order to ascertain the effectiveness of the developed methods.Mechanical Engineerin

14th Conference on Dynamical Systems Theory and Applications DSTA 2017 ABSTRACTS

From Preface: This is the fourteen time when the conference “Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 250 persons from 38 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 375 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference proceedings [...]