Minimum time control of heterodirectional linear coupled hyperbolic PDEs

We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and m leftward convecting transport PDEs. Using the backstepping approach yields solutions to stabilization in minimal time and observer based output feedback

Two sided boundary stabilization of two linear hyperbolic PDEs in minimum time

International audience— We solve the problem of stabilizing two coupled linear hyperbolic PDEs using actuation at both boundary of the spatial domain in minimum time. We design a novel Fredholm transformation similarly to backstepping approaches. This yields an explicit full-state feedback law that achieves the theoretical lower bound for convergence time to zero

Minimum time control of heterodirectional linear coupled hyperbolic PDEs with controls in both sides

Minimum time control of heterodirectional linear coupled hyperbolic PDEs with controls in both side

Control of Homodirectional and General Heterodirectional Linear Coupled Hyperbolic PDEs

Research on stabilization of coupled hyperbolic PDEs has been dominated by the focus on pairs of counter-convecting ("heterodirectional") transport PDEs with distributed local coupling and with controls at one or both boundaries. A recent extension allows stabilization using only one control for a system containing an arbitrary number of coupled transport PDEs that convect at different speeds against the direction of the PDE whose boundary is actuated. In this paper we present a solution to the fully general case, in which the number of PDEs in either direction is arbitrary, and where actuation is applied on only one boundary (to all the PDEs that convect downstream from that boundary). To solve this general problem, we solve, as a special case, the problem of control of coupled "homodirectional" hyperbolic linear PDEs, where multiple transport PDEs convect in the same direction with arbitrary local coupling. Our approach is based on PDE backstepping and yields solutions to stabilization, by both full-state and observer-based output feedback, trajectory planning, and trajectory tracking problems

Prediction-based control of linear input-delay system subject to state-dependent state delay – Application to suppression of mechanical vibrations in drilling

International audienceIn this paper, we consider linear dynamics subject to a distributed state-dependent delay and a pointwise input-delay. We propose a prediction-based controller which exponentially stabilizes the plant. The controller design is based on a backstepping approach where delays are reformulated as hyperbolic transport PDEs. Infinity-norm stability analysis of the corresponding closed-loop system is addressed. We show that this result is of interest to suppress mechanical vibrations arising in drilling facilities, which have been attributed recently to a coupling between torsional and vertical displacement involving an implicit state delay equation. Numerical simulations illustrate the merits of our controller in this context

A first principle model for multiphase slugging flow in vertical risers

International audienceIn this paper, we propose a simple model to represent the slugging flow regime appearing in vertical risers. We consider a one dimensional two-phase flow composed of a liquid phase and a gaseous compressible phase. The presented model can be applied to a wide class of systems, ranging from pure vertical risers to more complex geometries such as those found on actual sub sea petroleum facilities. Following ideas from the literature, we introduce a virtual valve located at the bottom of the riser. This allows us to reproduce observed periodic regimes. It also brings insight into the physics of the slugging phenomenon. Most importantly, this model reveals relatively easy to tune and seems suitable for control design. A tuning methodology is proposed along with a proof of the existence of a limit cycle under simplifying assumptions

Reproducing slugging oscillations of a real oil well

International audienceThis paper addresses the problem of reproducing oscillations generated by the well-known slugging phenomenon in multiphase flow. Reported investigations show how to determine the parameters of a recently proposed ordinary differential equations system, so that it captures the charac- teristics of actually observed slugging oscillations. A tuning procedure based on the mathematical properties of the model is presented. It is then applied to a test case consisting of a real oil well located in the North Sea. An observer using only topside measurements allows asymptotic reconstruction of critical variables such as the downhole pressure

Backstepping stabilization of an underactuated 3 × 3 linear hyperbolic system of fluid flow equations

We investigate the boundary stabilization of a particular subset of 3×3 linear hyperbolic systems with varying coefficients on a bounded domain. The system is underactuated since only one of the three hyperbolic PDEs is actuated at the boundary. The setup considered in the paper occurs in control of multiphase flows on oil production systems. We use a backstepping approach to design a full-state feedback law yielding exponential stability of the origin