**Hierarchical Cascade Control Systems for Time-Dependent Dynamical Plants as Applied to Magnetic Plasma Control in** *D***-Shaped Tokamaks †**

**Yuri V. Mitrishkin 1,2**


**Abstract:** The systems of poloidal field coils in D-shaped Tokamaks such as ITER, EAST, JET, ASDEX Upgrade, TCV, GLOBUS-M2, DIII-D, SPARC, IGNITOR, JT-60SA, DEMO-9.1, DEMO-1.6, T-15MD, and TRT are analyzed for their efficiency in the application of plasma position, current, and shape control systems in these Tokamaks. The problem of magnetic plasma control in Tokamaks is presented. A methodology for designing hierarchical cascade systems of magnetic plasma control in D-shaped Tokamaks has been developed on the basis of generalizations of existing plasma magnetic control systems. The hierarchical levels are as follows: multivariable robust cascade control level, adaptation level, artificial intelligence level, and decision-making level. To implement these systems in the practice of physical experimentation, it is proposed to use digital twins, the basis of which is a realtime digital testbed created by Lomonosov Moscow State University and the Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences.

**Keywords:** Tokamaks; poloidal field coils; plasma magnetic control; hierarchical control systems; cascade control; digital twins; digital testbed
