This paper highlights the most important results achieved at the spherical tokamak Globus-M2 with a high magnetic field. This paper also covers the most important topics of fusion research: thermal energy confinement in regimes with neutral beam injection, toroidal Alfvén eigenmode and correspondent fast ions confinement issues, L-H transition, turbulence suppression and edge-localized modes' behavior, experimental and theoretical study of regimes with nitrogen seeding that allow to significantly reduce thermal loads on the divertor plates, and experiments and simulations of lower hybrid current drive. The research results provide the basis for the next step toward a fusion neutron source—the development of the Globus-3 spherical tokamak.

The paper deals with the identification of plasma equilibrium reconstruction in D-shaped tokamaks on the base of plasma external magnetic measurements. The methods of such identification are directed to increase their speed of response when plasma discharges are relatively short, like in the spherical Globus-M2 tokamak (Ioffe Inst., St. Petersburg, Russia). The new approach is first to apply to the plasma discharges data the off-line equilibrium reconstruction algorithm based on the Picard iterations, and obtain the gaps between the plasma boundary and the first wall, and the second is to apply new identification methods to the gap values, producing plasma shape models operating in real time. The inputs for on-line robust identification algorithms are the measurements of magnetic fluxes on magnetic loops, plasma current, and currents in the poloidal field coils measured by the Rogowski loops. The novel on-line high-performance identification algorithms are designed on the base of (i) full-order observer synthesized by linear matrix inequality (LMI) methodology, (ii) static matrix obtained by the least square technique, and (iii) deep neural network. The robust observer is constructed on the base of the LPV plant models which have the novelty that the state vector contains the gaps which are estimated by the observer, using input and output signals. The results of the simulation of the identification systems on the base of experimental data of the Globus-M2 tokamak are presented.

This paper presents a methodology for synthesizing discrete MIMO PID controllers through iterative solutions of LMIs. It justifies the necessity of direct synthesis of discrete controllers in digital control systems. The proposed methodology allows for synthesizing an LTI controller for an LTV plant model, ensuring the robust stability of the synthesized system. Robustness is further ensured by the small-gain theorem and a novel approach to loop shaping, enabling the use of arbitrary shape functions. As a result, this methodology provides a broad statement of the problem with performance criteria necessary for practical application in control systems. Numerical examples are used to illustrate the methodology, which is implemented using the MATLAB toolbox, freely available for use.

Ensuring the stability of the vertical position of plasma is a paramount task of magnetic control for modern D-shaped tokamaks. The introduction of an additional horizontal field coil located near the vacuum vessel provides more than an order of magnitude larger vertical controllability domain than the use of a pair of P6&P12 poloidal field coils in the IGNITOR tokamak project. Two robust systems for controlling the vertical position of plasma are synthesized by the \( H_\infty \)-optimization theory method and by tuning PID controllers in a cascade system by the method of linear matrix inequalities. The results of mathematical modeling of control systems show that the modernization of the poloidal system of the IGNITOR tokamak project leads to an increase in the stability margin of the plasma vertical position control system, the quality of control when rejecting disturbances, and the reliability of the tokamak.