Recursive dynamics interconnection framework applied to angular velocity control of drilling systems

Abstract

In this paper, we apply a recursive dynamics interconnection framework to achieve reliable angular velocity control of a multi-sectional drilling device with the bit offbottom. The proposed model describing the torsional motion of the drill string takes into account the Coulomb friction between the drill string and the borehole. It has been field validated. Compensating the effects of these Coulomb side forces is necessary to avoid stick-slip oscillations. More precisely, the torsional motion of each section of the drilling pipe is modeled by a wave equation (with some non-linear terms corresponding to the Coulomb friction), while the dynamics of the top-drive and Bottom Hole Assembly are modeled by ordinary differential equations. The reference trajectory tracking problem for the drill string is solved by considering each section independently. The Coulomb side forces are seen as disturbances acting on each section of the drill string. These disturbances do not depend on time, providing there is enough energy in the system (i.e., that we have overcome the static friction). We propose here a switching-mode controller: using first a classical PI controller (with poor performance), we break the static friction. Then, the disturbance terms that correspond to the Coulomb friction terms can be estimated and compensated. The trajectory tracking is guaranteed using a recursive control procedure. The performances of the controller are illustrated through simulations using various field scenarios.

Output regulation and tracking for linear ODE-hyperbolic PDE–ODE systems

“…We assume that we have access to a measurement of the proximal ODE state, such that ( ) = mes ( ) ∈ R ×1 . This structure is chosen since, in many applications [41,42,34], a measurement is available at the actuated end. However, the observer design would follow the same procedure if the measurements were available at the opposite end, only flipping the spatial variable and adapting the matrices used in the assumptions.…”

“…In the mentioned applications, the distal ODE state (i.e., the unactuated ODE) can model the Bottom Hole Assembly (BHA) at the end of a drilling pipe [9], currents in an inductor/voltage across a capacitor, or the dynamics of a suspended object for Unmanned Aerial Vehicles (UAV) [24]. More specifically, the ODE-PDE-ODE structure naturally arises when considering linear systems of balance laws with finite-dimensional actuator and load dynamics, as for the UAV-cable-payload structure [41], mining cable elevators [42] or the top drive electrical motor-drill pipes-BHA structure [34].…”

“…In addition, output regulation and output tracking problems have been solved for interconnected systems. It is necessary for applications such as drilling [34] since the objective here is to impose a specific trajectory to the unactuated device at the end of the chain in the presence of disturbances. Some results have been obtained for cascaded networks of hyperbolic systems using PI controllers [38].…”