Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

Abstract

ITER will be the first tokamak to sustain a fusion-producing, or burning, plasma. If the plasma temperature were to inadvertently rise in this burning regime, the positive correlation between temperature and the fusion reaction rate would establish a destabilizing positive feedback loop. Careful regulation of the plasma’s temperature and density, or burn control, is required to prevent these potentially reactor-damaging thermal excursions, neutralize disturbances and improve performance. In this work, a Lyapunov-based burn controller is designed using a full zero-dimensional nonlinear model. An adaptive estimator manages destabilizing uncertainties in the plasma confinement properties and the particle recycling conditions (caused by plasma-wall interactions). The controller regulates the plasma density with requests for deuterium and tritium particle injections. In ITER-like plasmas, the fusion-born alpha particles will primarily heat the plasma electrons, resulting in different electron and ion temperatures in the core. By considering separate response models for the electron and ion energies, the proposed controller can independently regulate the electron and ion temperatures by requesting that different amounts of auxiliary power be delivered to the electrons and ions. These two commands for a specific control effort (electron and ion heating) are sent to an actuator allocation module that optimally maps them to the heating actuators available to ITER: an electron cyclotron heating system (20 MW), an ion cyclotron heating system (20 MW), and two neutral beam injectors (16.5 MW each). Two different actuator allocators are presented in this work. The first actuator allocator finds the optimal mapping by solving a convex quadratic program that includes actuator saturation and rate limits. It is nonadaptive and assumes that the mapping between the commanded control efforts and the allocated actuators (i.e., the effector model) contains no uncertainties. The second actuator allocation module has an adaptive estimator to handle uncertainties in the effector model. This uncertainty includes actuator efficiencies, the fractions of neutral beam heating that are deposited into the plasma electrons and ions, and the tritium concentration of the fueling pellets. Furthermore, the adaptive allocator considers actuator dynamics (actuation lag) that contain uncertainty. This adaptive allocation algorithm is more computationally efficient than the aforementioned nonadaptive allocator because it is computed using dynamic update laws so that finding the solution to a static optimization problem is not required at every time step. A simulation study assesses the performance of the proposed adaptive burn controller augmented with each of the actuator allocation modules.

Divertor-safe nonlinear burn control based on a SOLPS parameterized core-edge model for ITER

“…The mapping between the power-producing actuators and the heating control laws P aux,i and P aux,e can be resolved using actuator allocation (also known as control allocation-see [40] for a survey). The actuator allocation problem for burn control has been investigated in prior work with a variety of different actuator allocator designs [8][9][10]. All of the actuator allocators presented in [8][9][10] were designed independently from the burn controller such that any of these actuator allocators can work immediately with the burn control scheme proposed in this work.…”

“…( 55) and ( 56)) was solved by posing the actuator allocation problem as a strictly convex quadratic program with a unique optimal solution. In [9], this actuator allocator design was compared to an adaptive design based on dynamic update laws, removing the requirement of solving an optimization problem at every time step. This adaptive actuator allocator was designed to overcome the existence of uncertain actuator dynamics.…”

“…This adaptive actuator allocator was designed to overcome the existence of uncertain actuator dynamics. The particular actuator dynamics consider in [9] were first-order lags with uncertain time constants. This can be represented by…”

“…The actuator allocation problem for burn control has been investigated in prior work with a variety of different actuator allocator designs [8][9][10]. All of the actuator allocators presented in [8][9][10] were designed independently from the burn controller such that any of these actuator allocators can work immediately with the burn control scheme proposed in this work. Because the design of these actuator allocators would not change when applied to this work, actuator allocation is not included this work for brevity (and to avoid the repetition of prior work).…”

“…The peak heat load on ITER's tungsten (W) divertor should remain below 10 MW m −2 to avoid catastrophic melting [6]. While prior work used Lyapunov techniques [7] to design nonlinear burn controllers [8][9][10] from models of the core-plasma region, the burn condition can also be stabilized using artificial neutral networks that are developed using similar models [11].…”