Optimal Real-time Profile Regulation on EAST using Self-triggered Model Predictive Control

L. Yang, Z. Wang, S.T. Paruchuri, X. Song, E. Schuster

11th ITER International School on “ITER Plasma Scenarios and Control”

San Diego, California, USA, July 25-29, 2022

Actively controlling the safety factor profile, or just the q profile, in tokamaks may provide MHD-stable plasma conditions and facilitate steady-state operation. The term profile refers to the dependence of the plasma property, in this case the safety factor, on the spatial coordinate on the poloidal cross section from the magnetic axis to the plasma boundary. The q profile, which provides a measurement of the pitch of the magnetic field confining the plasma in tokamaks, is a function of the gradient of the magnetic poloidal flux profile (Ψ-profile). Several control approaches have been studied in the last decade to regulate and shape the q profile. The problem is high dimensional due to the dependence of the controlled variable on space. Moreover, the dynamics of the q profile is nonlinearly coupled with the kinetic plasma conditions (temperature and density of the plasma). Due to this complexity, an effective solution demands a model-based control approach. A Model Predictive Control (MPC) strategy based on the magnetic diffusion equation, which governs the dynamics of the poloidal magnetic flux profile, is proposed in this work for the EAST tokamak. The finite-time optimal control problem (FHOCP) is formulated by minimizing the tracking error between actual and desired gradients of the poloidal magnetic flux subject to both actuator and dynamic constraints. The solution of this optimization problem in real time demands a simplified model based on a linearized and spatially discretized version of the original model. As a novelty with respect to previous MPC solutions, a state observer is developed in this work to estimate the error between the original and simplified models and to correct the predictions by the simplified model within the MPC scheme. In addition, a self-triggered mechanism is implemented within the FHOCP to prevent unnecessary computations arising in fixed sampling-time MPC schemes.

*Supported by the US DOE under DE-SC0010537.