Optimal feedback control of the poloidal magnetic flux profile in the DIII-D tokamak based on identified plasma response models

First-principles predictive models based on flux-averaged transport equations often yield complex expressions not suitable for real-time control implementations. It is however always possible to reduce these models to forms suitable for control design while preserving the dominant physics of the system. If further model simplification is desired at the expense of less model accuracy and controller capability, data-driven modeling emerges as an alternative to first-principles modeling. System identification techniques have the potential of producing low-complexity, linear models that can capture the system dynamics around an equilibrium point. This paper focuses on the control of the poloidal magnetic flux profile evolution in response to the heating and current drive (H&CD) systems and the total plasma current. Open-loop data for model identification is collected during the plasma current flattop in a high-confinement scenario (H-mode). Using this data a linear state-space plasma response model for the poloidal magnetic flux profile dynamics around a reference profile is identified. The control goal is to use the H&CD systems and the plasma current to regulate the magnetic profile around a desired target profile in the presence of disturbances. The target profile is defined close enough to the reference profile used for system identification in order to stay within the range of validity of the identified model. An optimal state feedback controller with integral action is designed for this purpose. Experimental results showing the performance of the proposed controller implemented in the DIII-D tokamak are presented.