Adaptive nonlinear burn control in tokamak fusion reactors

There are many challenging control problems critical to the success of burning fusion plasma experiments like ITER. Among them, the most fundamental problem is the control of plasma density and temperature, referred to as the burn condition. While passively stable burn conditions exist, economic and technological constraints may require future commercial fusion reactors to operate at unstable burn conditions. The instability is due to the fact that at low temperatures, the rate of thermonuclear reaction increases as the plasma temperature rises. To stabilize such operating points, it will be essential to have active control of the system. Most existing burn control efforts use control techniques based on linearized models. Such models break down for large perturbations and must be designed around a particular operating point. In this work, we utilize a spatially averaged (zero-dimensional) nonlinear transport model to synthesize a nonlinear feedback controller that can stabilize the burn condition of a fusion reactor. The nonlinear controller guarantees stability of the plasma density and temperature for a much larger range of perturbations than linear designs and is augmented with an adaptive law that guarantees stability despite uncertainty in particle confinement time parameters. A zero-dimensional transport simulation study is presented to show the ability of the controller to bring the system back to the desired equilibrium from a given set of initial perturbations even when there is significant uncertainty in the confinement parameters.