Multivariable Robust Control of the Plasma Rotational Transform Profile for Advanced Tokamak Scenarios in DIII-D

W. Shi, W. Wehner, J. Barton, M.D. Boyer, E. Schuster, D. Moreau, T.C. Luce, J.R. Ferron, M.L. Walker, D.A. Humphreys, B.G. Penaflor and R.D. Johnson

American Control Conference

Montreal, Canada, June 27-29, 2012

Abstract

The tokamak is a high order, distributed parameter, nonlinear system with a large number of instabilities. Therefore, accurate theoretical plasma models are difficult to develop. However, linear plasma response models around a particular equilibrium can be developed by using data-driven modeling techniques. This paper introduces a linear model of the rotational transform iota profile evolution based on experimental data from the DIII-D tokamak. The model represents the response of the iota profile to the electric field due to induction as well as to heating and current drive (H&CD) systems. The control goal is to use both induction and H&CD systems to regulate the plasma iota profile around a particular target profile. A singular value decomposition (SVD) of the plasma model at steady state is carried out to decouple the system and identify the most relevant control channels. A mixed sensitivity H_inf control design problem is formulated to synthesize a stabilizing feedback controller without input constraint that minimizes the reference tracking error and rejects external disturbances with minimal control energy. The feedback controller is then augmented with an anti-windup compensator, which keeps the given profile controller well-behaved in the presence of magnitude constraints in the actuators and leaves the nominal closed-loop unmodified when no saturation is present. Finally, computer simulations and experimental results illustrate the performance of the model-based profile controller.