Safety Factor Profile Control in a Tokamak

Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, time-dependent, partial differential equations (PDEs). Robustness considerations are ubiquitous in the treatment of analysis and control design because the task of controlling such a system is rendered still more difficult by the fact that direct measurements on the states of the tokamak are often impossible or uncertain. §The brief begins with a presentation of the reference dynamical model of the system under consideration, and continues by developing a Lyapunov function for the discretized system (in a polytopic linear-parameter-variable formulation) and discussing its limitations. The limitations of the finite-dimensional approach motivate the developments in the infinite-dimensional setting. The text then tackles the construction of an input-to-state-stability-Lyapunov function for the infinite-dimensional system that provides a common base for the development of robustness results, and is used as a control-Lyapunov function when dealing with the constraints in the control action. §Finally, the Brief addresses important application- and implementation-specific concerns. In particular, the coupling of the PDE and the finite-dimensional subsystem representing the evolution of the boundary condition and the introduction of profile-reconstruction delays in the control loop (including nonlinear shape constraints imposed on the control input) is analyzed and tested in simulation using advanced physical models (METIS). §Control of the Safety Factor Profile in a Tokamak will be of interest to both academic and industrially-based researchers interested in nuclear energy and plasma-containment control systems, and graduate students in nuclear engineering.§