Nonlinear Estimation with Applications to Drilling

This thesis addresses the topic of nonlinear estimation and its applications. Particular emphasis is given to downhole pressure estimation for Managed Pressure Drilling (MPD), but due to the mathematical similarities of the two problems, velocity estimation for mechanical systems is also considered. The thesis consists of the following three parts:Part I of this thesis addresses the problem of pressure estimation for MPD systems. Over the last decade MPD has emerged as a tool for drilling offshore wells with tight pressure margins. Several technologies for MPD have been developed and this thesis focuses on the so called constant bottomhole pressure variation. This version of MPD aims at keeping the pressure at one location in the annulus section of a well constant by applying back-pressure through the use of a choke manifold at the rig. As the pressure profile in the well is not measured, a key element of any control system (manual or automatic) is some sort of estimation scheme for the pressure in the well. To aid in control design for MPD systems, and to solve the pressure estimation problem, a fit for purpose low order model has been developed. Using data from offshore wells, and dedicated experiments onshore, it is demonstrated that the model captures the dominant pressure dynamics. It is also demonstrated that a newly developed adaptive observer, combined with a recursive least squares parameter identification scheme, is able to predict the downhole pressure in the presence of significant parametric uncertainties. Part II of this thesis addresses the problem of adaptive observer design for a class of nonlinear systems including the drilling model. To estimate unmeasured states, in dynamical systems with parametric uncertainties, one can use adaptive observers. Furthermore, if the system is sufficiently (persistently) excited, adaptive observers can be used to identify uncertain parameters. The current state of the art in adaptive observer design does not cover the class of systems to which the drilling model belongs. Motivated by this, a method for adaptive observer design for this class of systems is developed. The method guarantees stability and convergence of the state estimate without requiring persistent excitation. Another weakness with the current state of the art is that existing Lyapunov based adaptive laws have poor parameter identification properties, and can be very hard to tune, when estimating more than one parameter. This motivated the developement of an adaptive observer design that uses multiple delayed observers to improve the convergence rate of the estimation scheme, at the cost of an increased computational burden. In particular, explicit lower bounds on the convergence rate of the state and parameter estimation error are given, and, if the original non-adaptive observer has tunable convergence rate, the redesigned adaptive observer will have tunable convergence rate as well. Part III of this thesis addresses the topic of observer-based output feedback control of general Euler-Lagrange systems. The design of a globally stabilizing output (position) feedback tracking controller for general Euler-Lagrange systems has been an active field of research for at least two decades. Still, it was not until recently that a globally convergent velocity observer was developed. In part III of this thesis a significant obstacle in the development of a constructive observer design is removed yielding a constructive speed observer design with global performance guarantees. In addition, a separation principle is proven, guaranteeing global stability and convergence when the observer is used in conjunction with certain types of certainty equivalence controllers. To the best of the authors knowledge this represents the first observer-based output feedback tracking control solution that guarantees a global region of attraction for general Euler-Lagrange systems.