Nonlinear Adaptive Burn Control and Optimal Control Allocation of Over-Actuated Two-Temperature Plasmas

Tokamaks are reactors that produce energy from the fusion, or merging, of atomic particles. A suitable reaction rate is achieved by heating a gas of charged particles (free ions and electrons), or plasma, to extreme temperatures. From the fusion of deuterium and tritium ions, a burning plasma produces alpha particles that contribute to the heating of the plasma. Burning plasmas are highly nonlinear systems that require careful regulation of temperature and density, or burn control, to reach desirable operating points. Once constructed, ITER will be the first tokamak designed for burning plasmas. In this work, a Lyapunov-based burn controller is developed using a full zero-dimensional nonlinear model. An adaptive estimator manages the presence of uncertain model parameters. The control objective is to stabilize equilibria despite model nonlinearity and uncertainty. Density is regulated through the injection of fuel pellets. For ITER, the temperature of the ions may differ significantly from that of the electrons in the plasma core. Therefore, the proposed controller considers separate response models for ion and electron energies. For energy control, the controller commands two virtual control efforts: the external ion heating and the external electron heating. To satisfy these two virtual control efforts, ITER will have access to ion cyclotron heating, electron cyclotron heating and two neutral beam injectors. With more actuators than virtual control efforts, the two-temperature plasma system is over-actuated. Actuator redundancy is resolved by constructing an optimal control allocator that considers actuator saturation and rate limits. A simulation study demonstrates the capability of the adaptive control and control allocation algorithms.