Optimization of Robust LMI-Control Systems for Unstable Vertical Plasma Position in D-Shaped Tokamak

Yuri Mitrishkin, Evgeniia Pavlova () and Mikhail Khlebnikov
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Yuri Mitrishkin: Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Evgeniia Pavlova: V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 117997 Moscow, Russia
Mikhail Khlebnikov: V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 117997 Moscow, Russia

Mathematics, 2022, vol. 10, issue 23, 1-37

Abstract: The paper is devoted to the synthesis, comparison, and optimization of robust LMI-control systems for the vertical plasma position in a D-shaped tokamak, specifically the T-15MD tokamak (Kurchatov Institute, Moscow, Russia). The novelty of this work is to find out the possibilities of LMI robust control systems, according to the criteria of the robust stability radius and control power peak at the rejection of a minor disruption type disturbance and a reference step signal using a unique unstable first-order plasma model. The plant under control consists of the connected in series plasma model with additive disturbance containing plant uncertainties, horizontal field coil (HFC), and actuator model as a multiphase rectifier. A set of robust controllers was designed by Linear Matrix Inequalities (LMI) method with pole placement in the LMI regions, state H 2 / H ∞ performance, and output signal performance. The LMI theorems of the paper are directed to design the robust controllers and study the systems with the aim of eliminating the gap between theory and practice. The main achievement of this work consists in the optimization of robust control systems of the unstable plant with uncertain disturbance on the set of LMI synthesis approaches. The control systems have original quality criteria, such as control power and robust stability radius. The best control system on the basis of two criteria, namely, D α , r , ϑ control system provides stabilization of the vertical plasma position on the real-time digital control testbed.

Keywords: tokamak; plasma vertical instability; plasma linear model; LMI design; feedback stabilization; H 2 / H ? control; disturbance ellipsoid estimation; robust stability radius; control power assessment; realtime target machine; Speedgoat (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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