Model predictive control of resistive wall mode for ITER

Abstract

Active feedback stabilization of the dominant resistive wall mode (RWM) for an ITER H-mode scenario at high plasma pressure using infinite-horizon model predictive control (MPC) is presented. The MPC approach is closely-related to linear-quadratic-Gaussian (LQG) control, improving the performance in the vicinity of constraints. The control-oriented model for MPC is obtained with model reduction from a high-dimensional model produced by CarMa code. Due to the limited time for on-line optimization, a suitable MPC formulation considering only input (coil voltage) constraints is chosen, and the primal fast gradient method is used for solving the associated quadratic programming problem. The performance is evaluated in simulation in comparison to LQG control. Sensitivity to noise, robustness to changes of unstable RWM dynamics, and size of the domain of attraction of the initial conditions of the unstable modes are examined.

Finite-word-length FPGA implementation of model predictive control for ITER resistive wall mode control

“…The maximum values are notably higher that the average ones because these latencies are relatively short and the server was not optimized for lowlatency operation. In addition to the three variants of the kernel, previous results obtained using a standard CPU using double-and single-precision floating-point arithmetic [26] are included for reference (the double-precision result serves as the reference solution). The numerical accuracy is considered sufficient both for the FWL and the single-precision floating-point implementation.…”

“…The control problem setup [26] is based on that of Ariola and Pironti [16]. In Figure 1, the resistive in-vessel non-axisymmetric ELM correction coils that are used as actuators for RWM suppression are drawn with light blue colour.…”

“…MPC design comprises building the control-oriented model, specifying the infinite-horizon MPC cost function and constraints, and designing the Kalman filter (KF). Certain design choices are motivated by the requirement for very fast implementation with the primal FGM QP solver [26].…”

“…FGM belongs to the family of first-order proximal optimization methods, designed for problems of the minimization of a sum of two functions with specific properties. In our MPC case [26], we are solving the problem…”

“…RWM control with MPC is challenging because very fast dynamics are combined with high system dimensions (27 actuators, 6 sensors, 50 dynamic states). Therefore, a pre-computed (multiparametric) MPC approach [25] is not applicable, and the dual Fast Gradient Method (FGM) solver [20,21] exceeds the allowed computation time, which should be less than 0.1 ms. Our recent work [26] shows that an infinite-horizon MPC considering only actuator constraints using a solver such as the primal FGM is viable. The MPC RWM controller is related to the LQG RWM scheme for ITER of Ariola and Pironti [16], based on the CarMa model [12], however without control vector dimension reduction.…”