Sabine Mondié

Assessing the exact stability region of the single-delay scalar equation via its Lyapunov function

It is well known that one can determine the stability of a delay-free linear system either by verifying that all the roots of its characteristic polynomial are in the left half plane or by checking if the solution of the Lyapunov equation is positive definite. For linear systems with delays, many extensions of the first approach are reported in the literature. On the contrary, there exist no publications on extending the second approach to delay systems. In this note, it is shown that the second approach is possible for one of the simplest linear delay systems: stability conditions in terms of the Lyapunov function for the scalar delay equation, that match the frequency domain well-known result, are presented.

Suppressing Stick-Slip Oscillations in Oilwell Drillstrings

In drilling operations, the drillstring interaction with the borehole gives rise to a wide variety of non-desired oscillations. The main types of drilling vibrations are torsional (stick-slip), axial (bit-bounce) and lateral (whirling). The analysis and modeling of rotary drilling vibrations is a topic whose economical interest has been renewed by recent oil fields discoveries leading to a growing literature. This contribution addresses the problem of modeling and control of the most critical vibration mode: the stick-slip phenomenon. The wave equation subject to mixed boundary conditions is used to reproduce torsional oscillations of the drillstring. By means of a direct transformation we derive an input-output model described by a neutral-type time-delay equation which clearly simplifies the system simulation. A dissipativity analysis of the wave equation model leads to the design of a stabilizing controller guaranteeing a non-growth of energy during the drilling process. Furthermore, by means of a polytopic representation of the neutral-type time-delay model, stability and stabilization conditions in terms of Linear Matrix Inequalities (LMIs) are given. The performance of the proposed approaches is highlighted through simulations showing an effective suppression of the stick-slip phenomenon.

Depth control using artifitial vision with time-delay of an AUV

The purpose of this paper is to present the analysis of the dynamics immersion of an Autonomous Underwater Vehicle considering the time-delay produced by implementing artificial vision algorithm. The parameter tuning of the PD controller is based on the analysis of the stability region taking into account the vision delay. The PD controller goal is to keep the vehicle in a region close to the landmark, and the performance is shown in simulation and real-time experimental results.

Stability analysis and estimate of the region of attraction of a human respiratory model

In this paper, we complete the stability analysis of the human respiratory nonlinear time delay model introduced by (B. Vielle et al., 1998). More precisely, we present a detailed mathematical analysis of the stability of the trivial equilibrium of the nonlinear model, an estimate of its region of attraction and exponential estimates of the solutions starting in this region for two distinct control strategies: linear and Hill controllers, respectively. The proposed approach is constructive and it is based on the use of Lyapunov-Krasovskii functionals of complete type for timedelay systems with a cross term in the derivative.

Cascade proportional integral retarded control of servodrives

The goal of this work is to propose a new time-delay control law called the cascade proportional integral retarded controller, which is aimed at position control of DC servodrives. The proposed controller has a cascade inner loop-outer loop structure. The inner loop is endowed with an integral retarded algorithm, and regulates the servodrive angular velocity. A proportional controller closes the outer loop whose goal is to regulate the servodrive angular position. The tuning of the cascade proportional integral retarded controller is accomplished into two steps. In the first step, the velocity of the inner loop is tuned by assigning a triple dominant root. The second step tunes the outer position loop. It is also possible to modify the cascade proportional integral retarded controller to avoid velocity measurements without adding extra filters. Moreover, the cascade topology of the cascade proportional integral retarded controller makes it easy to introduce a nonlinear saturated gain in the outer loop. This controller termed as the cascade nonlinear proportional integral retarded controller prevents overshoots for large values of the set point, avoids excessive control effort, and maintains a prescribed value of the angular velocity. Experiments in real-time using a laboratory prototype allow assessing the performance of the proposed controllers.

Connected cruise control of a car platoon: A time-domain stability analysis

A compact representation of a vehicle platoon following model considering the headway, velocity, and vehicle-to-vehicle communication delay is presented. Then, a connectivity structure is selected, which includes vehicles equipped with connected cruise control and a conventional vehicle as the leader. The platoon exponential stability and its robust stability with respect to time-varying matrix perturbations are studied. The analysis is carried out in the time domain, via Lyapunov–Krasovskii functionals depending on the delay Lyapunov matrix. The stability results are illustrated by stability charts of the plane of control gain parameters. A total of three platoon illustrative vehicle scenarios show the interest of the approach.

Stability analysis of a car platoon with communication delays and headway compensation

A compact representation of a car following model considering the headway and vehicle-to-vehicle (V2V) communication delay is presented. The platoon exponential stability and its robust stability with respect to time-varying matrix perturbations are studied. The analysis is carried out in the time domain, via Lyapunov-Krasovskii functionals depending on the delay Lyapunov matrix. Platoon illustrative examples with three, four and five vehicles show the interest of the approach.

Stability and Stabilization for Continuous-Time Difference Equations with Distributed Delay

Motivated by linear hyperbolic conservation laws , we investigate in this chapter new conditions for stability and stabilization for linear continuous-time difference equations with distributed delay . For this, we propose first a state-space realization of networks of linear hyperbolic conservation laws via continuous-time difference equations. Then, based on some recent works, we propose sufficient conditions for exponential stability , which appear also to be necessary and sufficient in some particular cases. Then, the stabilization problem as well as the closed-loop performances are analyzed with constructive methods for state feedback synthesis.