Øyvind Nistad Stamnes

Switched Control for Pressure Regulation and Kick Attenuation in a Managed Pressure Drilling System

This paper presents a switched control scheme for regulation of the annular pressure in a well during drilling. The main feature is automatic kick attenuation while drilling reservoir sections. A simple mathematical model is presented that captures the dominant phenomena of the drilling system and forms the basis for observer and control design. A switched pressure control algorithm for feedback control of the choke valve opening and the back-pressure pump is proposed, and asymptotic stability properties are established. Kick attenuation is guaranteed for a set of reservoir models, including the most common ones. As part of the control scheme, novel observers for estimation of the flow rate through the bit and kick detection are developed. Simulation results obtained with a high fidelity drilling simulator are presented to demonstrate the effectiveness of the proposed switched control scheme.

Adaptive observer design for the bottomhole pressure of a managed pressure drilling system

In this paper a reduced order observer that adapts to unknown friction and density, and estimates the bottomhole pressure in a well during drilling, is presented. The design is based on a newly developed third order nonlinear model with a nonlinear output equation containing a product between an unknown parameter and unmeasured state. Based on a Lyapunov approach the pressure estimate is shown to converge to the true pressure under reasonable conditions. Application of the observer to real data from a North Sea oil well demonstrates promising behaviour.

Adaptive Redesign of Nonlinear Observers

To estimate unmeasured states in dynamical systems with parametric uncertainties one can use adaptive observers. In this technical note a new method for adaptive redesign of reduced order observers for nonlinear systems is presented. The redesign makes the observer robust as it guarantees that the state estimation error converges to zero in the presence of parametric uncertainties. To enable parameter adaption, a new type of update law is derived using Lyapunov analysis and a nonlinear coordinate transformation. The uniqueness of the approach is that it allows terms containing both uncertainty and nonlinearity in the unmeasured states to appear in the dynamics of the unmeasured states, and still achieves convergence of the state estimate without requiring persistent excitation. Two examples are presented that demonstrate these properties.

Brief paper: Redesign of adaptive observers for improved parameter identification in nonlinear systems

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.

Pressure regulation with kick attenuation in a managed pressure drilling system

This paper presents a switched control scheme for regulation of the annular pressure in a well during drilling. The main feature is automatic kick attenuation while drilling reservoir sections. A simple mathematical model is presented that captures the dominant phenomena of the drilling system and forms the basis for observer and control design. A switched pressure control algorithm for feedback control of the choke valve opening and the back-pressure pump is proposed, and asymptotic stability properties are established. Kick attenuation is guaranteed for a set of reservoir models, including the most common ones. As part of the control scheme, novel observers for estimation of the flow rate through the bit and kick/loss detection are developed. Simulation results obtained with a high fidelity drilling simulator are presented to demonstrate the effectiveness of the proposed switched control scheme.

Adaptive output feedback control of a managed pressure drilling system

This paper presents a nonlinear observer-based control scheme to stabilize the annular pressure profile throughout the well bore continuously while drilling. A simple mechanistic model is presented that captures the dominant phenomena of the drilling system and forms the basis for model-based observer and control design. A new nonlinear adaptive observer is developed for state estimations. A new adaptive controller is designed to stabilize the annular pressure and achieve asymptotic tracking by applying feedback control of the choke valve opening and the main pumps.

A constructive speed observer design for general Euler-Lagrange systems

Astolfi, Ortega, and Venkatraman (2010) recently proved the existence of a globally exponentially convergent speed observer for general Euler-Lagrange systems. Key to their result, is a function defined by certain integrals which cannot be solved a priori, and may not have explicit analytic solutions. In this paper, this obstacle to a constructive design is removed and equations that solve the speed observer problem are given in closed form. The design is further simplified by removing up to one third of the observer states used in Astolfi et al. (2010). With the significant reduction in complexity, the new observer is easily applied to estimate the angular velocities in a Furuta pendulum example.

Global Output Feedback Tracking Control of Euler-Lagrange Systems

Abstract We solve the problem of global output feedback tracking control of general Euler-Lagrange systems without velocity measurement. The output feedback scheme consists of a novel nonlinear observer and any certainty equivalence tracking controller satisfying certain assumptions. Using theory for cascaded systems we guarantee uniform stability and convergence of the certainty equivalence output feedback scheme. Simulation results are included to illustrate the performance of the popular Slotine and Li controller together with our proposed observer.

Adaptive observer design for nonlinear systems with parametric uncertainties in unmeasured state dynamics

This paper presents an adaptive observer design for nonlinear systems that have parametric uncertainties in the unmeasured state dynamics. Without persistency of excitation (PE) the convergence of the state estimation error to zero is proved. Under PE conditions, uniform global asymptotic stability of the origin of the state and parameter error is shown. Furthermore, if the regressor is sufficiently smooth, uniform local asymptotic stability of the origin is proved. Two simulation examples are shown to illustrate the results.

Adaptive estimation of downhole pressure for Managed Pressure Drilling operations

The objective of Managed Pressure Drilling (MPD) is to enable precise control of the downhole pressure during drilling and completion operations. An essential part of an automated MPD control system is the downhole pressure estimator, usually referred to as the hydraulic model, which in most cases is the limiting factor for achievable accuracy of the system. In this paper we present a new design of an adaptive observer for online estimation of the downhole pressure in the well. Unlike conventional hydraulic models, which are based on complex partial differential equations, the adaptive observer is based on a simplified lumped model of ordinary differential equations, combined with online adaptation that tunes uncertain model parameters utilizing topside measurements. We demonstrate that the novell adaptive observer design captures the important hydraulics of MPD operations with high accuracy, and fundamentally improves the convergence rate of the parameter estimaties by using delayed observers. The results are demonstrated on field data from an offshore MPD operation.