Emmanuel Witrant

A control-oriented model of the current profile in Tokamak plasma

This paper proposes a control-oriented approach to the tokamak plasma current profile dynamics. It is established based on a consistent set of simplified relationships, in particular for the microwave current drive sources, rather than exact physical modelling. Assuming that a proper model for advanced control schemes can be established using the so-called cylindrical approximation and neglecting the diamagnetic effects, we propose a model that focuses on the flux diffusion (from which the current profile is inferred). Its inputs are some real-time measurements available on modern tokamaks and the effects of some major actuators, such as the magnetic coils, lower hybrid (LHCD), electron and ion cyclotron frequency (ECCD and ICRH) systems, are particularly taken into account. More precisely, the non-inductive current profile sources are modelled as 3-parameters functions of the control inputs derived either from approximate theoretical formulae for the ECCD and bootstrap terms or from experimental scaling laws specifically developed from hard x-ray Tore Supra data for the LHCD influence. The use of scaling laws in this model reflects the fact that the operation of future reactors will certainly depend upon a great number of scaling laws and specific engineering parameters. The discretization issues are also specifically addressed, to ensure robustness with respect to discretisation errors and the efficiency (in terms of computation time) of the associated algorithm. This model is compared with experimental results and the CRONOS solver for tore supra tokamak.

Remote Stabilization Via Communication Networks With a Distributed Control Law

In this note, we investigate the problem of remote stabilization via communication networks involving some time-varying delays of known average dynamics. This problem arises when the control law is remotely implemented and leads to the problem of stabilizing an open-loop unstable system with time-varying delay. We use a time-varying horizon predictor to design a stabilizing control law that sets the poles of the closed-loop system. The computation of the horizon of the predictor is investigated and the proposed control law explicitly takes into account an estimation of the average delay dynamics. The resulting closed loop system robustness with respect to some uncertainties on the delay estimation is also considered. Simulation results are finally presented.

Natural and anthropogenic variations in methane sources during the past two millennia

Methane is an important greenhouse gas that is emitted from multiple natural and anthropogenic sources. Atmospheric methane concentrations have varied on a number of timescales in the past, but what has caused these variations is not always well understood. The different sources and sinks of methane have specific isotopic signatures, and the isotopic composition of methane can therefore help to identify the environmental drivers of variations in atmospheric methane concentrations. Here we present high-resolution carbon isotope data (δ13C content) for methane from two ice cores from Greenland for the past two millennia. We find that the δ13C content underwent pronounced centennial-scale variations between 100 bc and ad 1600. With the help of two-box model calculations, we show that the centennial-scale variations in isotope ratios can be attributed to changes in pyrogenic and biogenic sources. We find correlations between these source changes and both natural climate variability—such as the Medieval Climate Anomaly and the Little Ice Age—and changes in human population and land use, such as the decline of the Roman empire and the Han dynasty, and the population expansion during the medieval period.

A Strict Control Lyapunov Function for a Diffusion Equation With Time-Varying Distributed Coefficients

In this paper, a strict Lyapunov function is developed in order to show the exponential stability and input-to-state stability (ISS) properties of a diffusion equation for nonhomogeneous media. Such media can involve rapidly time-varying distributed diffusivity coefficients. Based on this Lyapunov function, a control law is derived to preserve the ISS properties of the system and improve its performance. A robustness analysis with respect to disturbances and estimation errors in the distributed parameters is performed on the system, precisely showing the impact of the controller on the rate of convergence and ISS gains. This is important in light of a possible implementation of the control since, in most cases, diffusion coefficient estimates involve a high degree of uncertainty. An application to the safety factor profile control for the Tore Supra tokamak illustrates and motivates the theoretical results. A constrained control law (incorporating nonlinear shape constraints in the actuation profiles) is designed to behave as close as possible to the unconstrained version, albeit with the equivalent of a variable gain. Finally, the proposed control laws are tested under simulation, first in the nominal case and then using a model of Tore Supra dynamics, where they show adequate performance and robustness with respect to disturbances.

Boundary observers for linear and quasi-linear hyperbolic systems with application to flow control

In this paper we consider the problem of boundary observer design for one-dimensional first order linear and quasi-linear strict hyperbolic systems with n rightward convecting transport PDEs. By means of Lyapunov based techniques, we derive some sufficient conditions for exponential boundary observer design using only the information from the boundary control and the boundary conditions. We consider static as well as dynamic boundary controls for the boundary observer design. The main results are illustrated on the model of an inviscid incompressible flow.

Predictive control over wireless multi-hop networks

Remote control over wireless multi-hop networks is considered. Time-varying delays for the transmission of sensor and control data over the wireless network are caused by a randomized multi-hop routing protocol. The characterstics of the routing protocol together with lower-layer network mechanisms give rise to a delay process with high variance and stepwise changing mean. A new predictive control scheme with a delay estimator is proposed in the paper. The estimator is based on a Kalman filter with a change detection algorithm. It is able to track the delay mean changes but efficiently attenuate the high frequency jitter. The control scheme is analyzed and its implementation detailed. Network data from an experimental setup are used to illustrate the efficiency of the approach.

Remote output stabilization under two channels time-varying delays

Abstract In this paper we investigate the problem of remote output stabilization via two channels with time-varying delays. This problem arises when the control law is remotely implemented. The exchange of data between the controller and the system is done via two different transmission channels introducing time-varying delays with known dynamics. Assuming a known model for each of the time-delay dynamics, the work in (Witrant et al ., 2003) is extended to the case of two different delays appearing: (1) in the output measurement channel and, (2) in the transmission of the control law. This result is extended to output stabilisation by introducing a state observer built upon the delayed output of the plant. Simulation results are also presented.

Lyapunov-based distributed control of the safety-factor profile in a tokamak plasma

A real-time model-based controller is developed for the tracking of the distributed safety-factor profile in a tokamak plasma. Using relevant physical models and simplifying assumptions, theoretical stability and robustness guarantees were obtained using a Lyapunov function. This approach considers the couplings between the poloidal flux diffusion equation, the time-varying temperature profiles and an independent total plasma current control. The actuator chosen for the safety-factor profile tracking is the lower hybrid current drive, although the results presented can be easily extended to any non-inductive current source. The performance and robustness of the proposed control law is evaluated with a physics-oriented simulation code on Tore Supra experimental test cases.

Simultaneous Air Fraction and Low-Pressure EGR Mass Flow Rate Estimation for Diesel Engines

Abstract This paper describes a low-pressure exhaust gas recirculation (LP-EGR) mass flow rate estimation method and a robust air mass fraction observer for a Diesel engine with dual-loop EGR system. Both observers operate simultaneously eliminating the need for pressure measurement upstream the LP-EGR valve. A sliding mode observer is designed to estimate the LP-EGR mass flow rate using the standard sensors available in commercial Diesel engines. A robust linear parameter varying Kalman filter is designed for the air mass fraction estimation. The convergence and robustness of the observers are ensured by means of Lyapunov stability and a linear matrix inequality (LMI) framework for the sliding mode observer and robust Kalman filter, respectively. The observers are evaluated with a Motor Vehicle Emission Group (NMVEG) cycle using an engine model validated on an experimental benchmark as a reference.

Remote stabilization via time-varying communication network delays: application to TCP networks

We investigate the problem of remote stabilization via communication networks. This problem arises when the control law is remotely implemented. The exchange of data between the controller and the system is done via a data communication network described by a deterministic model. This leads to the problem of stabilizing an open-loop unstable system with time-varying delay. Assuming a known general model for the time-delay dynamics, we develop a time-varying horizon predictor, which is used as a basis to build a stabilizing control law that includes explicitly the delay dynamics. This control law is then applied to the case of TCP networks. The experimental results are presented.