Rémy Nouailletas

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.

Sliding mode stabilization of the current profile in Tokamak plasmas

This paper deals with the robust stabilization of the spatial distribution of tokamak plasmas current profile using a sliding mode feedback control approach. The control design is based on the 1D resistive diffusion equation of the magnetic flux that governs the plasma current profile evolution. The feedback control law is derived in the infinite dimensional setting without spatial discretisation. Numerical simulations are provided and the tuning of the controller parameters that would reject uncertain perturbations is discussed.

LMI design of a switched observer with model uncertainty: Application to a hysteresis mechanical system

In this paper, a linear matrix inequality (LMI) technique for observer based state estimation of discrete time linear switched systems with uncertainties is developed. Sufficient conditions of global convergence of the observer are proposed. The proposed observer design method is applied to estimate the states of a real continuous non-linear system with hysteresis. First, the non-linearities are divided in linear sub-models, second the system is discretized to give finally a discrete time linear switched model on which the proposed observer is applied. Simulation results are given to show the effectiveness of the proposed observer.

Geometric discretization for a plasma control model

Abstract we define a family of geometric discretization methods for the reduction of a 1D distributed parameters systems of conservation laws and apply these methods to the reduction of plasma control model written in Port-Controlled Hamiltonian (PCH) form. In these discrete schemes, variables are projected into appropriate bases in order to perform exact spatial differentiation. We show that some spectral and energetical properties are therefore preserved. A geometric (symplectic) collocation scheme using Lagrange polynomials is investigated. Numerical results show oscillations in the transient response in case of non homogeneous boundary conditions or sharp distributed control. A second symplectic spectral scheme using Bessel conjugated bases is then derived which allows a more accurate approximation of eigenfunctions and reduces the unwanted numerical oscillations. Finally, the proposed numerical integration of the control model is validated against experimental data from the tokamak Tore Supra.

An IDA-PBC approach for the control of 1D plasma profile in tokamaks

In this paper, a PCH model obtained from the spatial reduction of a thermo-magneto-hydrodynamics model for plasma dynamics in tokamaks is used to design an optimal IDA-PBC (Interconnection and Damping Assignment - Passivity Based Control) controller of the magnetic field profile. Due to the actuator constraints which imply to have a finite dimensional base of physically feasible current profile deposits, the controller inputs/outputs are reduced to be compatible with the system limitations. The loop voltage at the plasma boundary and the total external heating source power are considered as controller outputs. Reference on the total plasma current and the central safety factor value is given to compute the magnetic field profile reference. Bootstrap current and non-linearity of plasma resistivity or external current deposit scaling laws are taken into account. Simulation results based on Tore Supra WEST tokamak (a project of Tore Supra upgrade) are provided to illustrate the effectiveness of the method.

IDA-PBC control for the coupled plasma poloidal magnetic flux and heat radial diffusion equations in tokamaks

The IDA-PBC control of plasma dynamics in a tokamak is investigated. It is based on a model made of the two coupled PDEs of resistive diffusion for the magnetic poloidal flux and of radial thermal diffusion. The used Thermal-Magneto-Hydro-Dynamics (TMHD) couplings are the Lorentz forces (with non-uniform resistivity) and the bootstrap current. The control model is obtained with the coupling of the two finite dimensional approximations obtained from the two diffusion models, using two geometric reduction schemes. A feedforward control is used to ensure the compatibility with the actuator physical ability. Then, an IDA-PBC (Interconnection and Damping Assignment - Passivity Based Control) controller is proposed for the coupled model to improve the system stabilization and convergence speed. The obtained numerical results are validated against the simulation data obtained from the RAPTOR (RApid Plasma Transport simulatOR) code for the TCV (Tokamak of Configuration Variable at CRPP, EPFL, Lausanne, Switzerland) tokamak real-time control system.

Plasma Discharge Management for Long-Pulse Tokamak Operation

Abstract Achieving high-performance long-duration plasma discharges in tokamaks is one of the most important challenges to be addressed in the perspective of the development of a power plant. For this purpose, real-time handling of off-normal events has to be performed through a dedicated plasma discharge management system. In this paper, we describe the main requirements and features of such a system. A generic architecture, based on the principle of subsidiarity, is proposed. A full set of actions is covered, starting from the local subsystems up to the tokamak as a whole, with different levels of mitigation strategies. A simulation of a relevant test case, based on the Tore Supra tokamak, showing the basic principles of the study, is also presented.

New hybrid model and switched PI observer for dry friction systems

In this paper, a polytopic approach is used to derive a new hybrid model of systems submitted to dry friction. The principal characteristics of the proposed approach are that it is easily comprehensible, has few parameters, allows the adjustment of the model complexity to the treated case, models the stick-slip phenomena, and has low simulation time. The proposed new dry friction model is applied to the modeling of a real experimental mechanical system. The model parameters are obtained using an adequate position control which is based on a controller with very low bandwidth. To estimate the states of such system, a polytopic PI observer is proposed using a H1 formulation. Its performance and robustness against model uncertainty are shown in simulation.

Robust Vertical Plasma Stabilization of the future tungsten divertor configuration of Tore Supra

Abstract The paper presents the first results of a robust plasma vertical stabilization of TS-WEST: Firstly, a linear MIMO model is identified around an equilibrium point using the free boundary CEDRES++ tokamak equilibrium code. Secondly, from a bode-diagram analysis, the best coil is chosen to feedback control the vertical position of the plasma. Then a H infinity formulation of the problem is used to obtain a robust PI controller. In simulation, supply limitations are taken into account. The controller is validated on CEDRES evolution with 3 tests: stabilization of the plasma position from an offset of 4cm, tracking of the position and robustness to edge localized mode and to transitions between low and high plasma confinement mode.

Distributed and backstepping boundary controls for port-Hamiltonian systems with symmetries

ABSTRACT A geometric spatial reduction for the port-Hamiltonian models is presented in this paper. It is based on the projection which makes use of the symmetries and on the preservation of the ‘natural’ power pairing for the considered system. Thanks to this reduction, an Interconnection and Damping Assignment Passivity Based Control (IDA-PBC-like) synthesis for infinite dimensional port-Hamiltonian systems is investigated. As for the finite dimensional case, a feedback control transforms the original model into a closed-loop target Hamiltonian model. Both distributed control and boundary control are used. The finite rank distributed control is determined to solve an average IDA-PBC matching equation. A backstepping boundary control is used to stabilize the matching error. The control model chosen to illustrate the approach is the so-called resistive diffusion equation for the radial diffusion of the poloidal magnetic flux.