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.