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 suggests and develops a new methodology of estimation for a multivariable reachability region of a plasma separatrix shape on the divertor phase of a plasma discharge in D-shaped tokamaks. The methodology is applied to a spherical Globus-M/M2 tokamak, including the estimation of a controllability region of a vertical unstable plasma position on the basis of the experimental data. An assessment of the controllability region and the reachability region of the plasma is important for the design of tokamak poloidal field coils and the synthesis of a plasma magnetic control system. When designing a D-shaped tokamak, it is necessary to avoid the small controllability region of the vertically unstable plasma, because such cases occur in practice at a restricted voltage on a horizon field coil. To make the estimations mentioned above robust, PID-controllers for vertical and horizontal plasma position control were designed using the Quantitative Feedback Theory approach, which stabilizes the system and provides satisfactory control indexes (stability margins, setting time, overshoot) during plasma discharges. The controllers were tested on a series of plasma models and nonlinear models of current inverters in auto-oscillation mode as actuators for plasma position control. The estimations were made on these models, taking into account limitations on control actions, i.e., voltages on poloidal field coils. This research is the first step in the design of the plasma shape feedback control system for the operation of the Globus-M2 spherical tokamak. The developed methodology may be used in the design of poloidal field coil systems in tokamak projects in order to avoid weak achievability and controllability regions in magnetic plasma control. It was found that there is a strong cross-influence from the PF-coils currents and the CC current on the plasma shape; hence, these coils should be used to control the plasma shape simultaneously.

On 22 January 2024, at the age of 78, Yuri Vladimirovich Mitrishkin (Figure 1), an outstanding scientist and remarkable educator with half a century of experience, passed away unexpectedly

Artificial neural networks with different structures are used for identification of complex dynamic plant with distributed parameters. The plant is a high-temperature plasma in the spherical Globus-M2 tokamak. Experimental data from it were processed by plasma reconstruction code based on Picard iterations, namely, the Flux-Current Distribution Identification (FCDI) code. This represents smart technology employed to obtain distributed plasma parameters by minimizing the difference between measured and reconstructed signals. An artificial neural network was then applied to identify the data obtained by the FCDI code on the hardware as a real-time testbed realized on a Speedgoat computer. The aim of this repeated identification is to increase the operational response speed in real time in the closed-loop control system of the plasma shape.