Robust stabilization of the current profile in tokamak plasmas using sliding mode approach in infinite dimension

Abstract

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. Closed loop simulations performed on realistic test cases using a physics based tokamak integrated simulator confirm the relevance of the proposed control algorithm in view of practical implementation.

Control of the tokamak safety factor profile with time-varying constraints using MPC

“…• Linearized state space models: (4)- (5) • Nominal state and controlled variable (reference) trajectories: (x o k , y o k ) Choose prediction horizon N Choose controller weights in (10): Q, R U and W ε Choose a future input sequence parametrization in (12): P map Compute the prediction matrices at each time instance in 7: (6) and 7Provide actuator command u k+1 from U k,N to actuators Provide to supervisory controller (or user):…”

“…In the literature, a large number of first principle model based feedback control approaches to control the q-profile are proposed of which we mention here the most recent [12][13][14][15][16][17][18][19][20][21][22]. Most of these contributions take fixed actuator constraints passively into account, meaning that they are not included in the controller design, but a posteriori imposed by the use of e.g.…”

Multi-experiment state-space identification of coupled magnetic and kinetic parameters in tokamak plasmas

“…The dynamics of the poloidal magnetic flux profile can be represented by a resistive diffusion, a parabolic equation with spatially distributed rapidly time-varying coefficients. Model-based methods for feedback control of the safety factor profile (also called the q-profile) using Multiple-Input and Multiple-Output (MIMO) finite dimensional systems are developed in [2,3,4,5], and using control algorithms based on infinite dimensional control theory are developed in [6,7,8,9]. The poloidal magnetic flux and the electron temperature are known to be highly coupled [1].…”

Data-driven robust control of the plasma rotational transform profile and normalized beta dynamics for advanced tokamak scenarios in DIII-D

“…First-principles-driven controloriented models have been recently used to determine optimal open-loop (feedforward) actuator trajectories that achieve and sustain a desired q profile [10,11,12], and to design complementing closed-loop (feedback) control laws that add robustness against disturbances and model uncertainties. Several approaches have been recently proposed for first-principles-driven current profile feedback control [13,14,15,16,17,18,19] and some of them have been experimentally tested in DIII-D [20,21,22]. Data-driven modeling techniques such as linear system identification [23] emerge as an alternative to first-principles-driven modeling and have the potential to obtain low-complexity dynamic models.…”