First-principles-driven model-based current profile control for the DIII-D tokamak via LQI optimal control

Abstract

In tokamak fusion plasmas, control of the spatial distribution profile of the toroidal plasma current plays an important role in realizing certain advanced operating scenarios. These scenarios, characterized by improved confinement, magnetohydrodynamic stability, and a high fraction of non-inductively driven plasma current, could enable steady-state reactor operation with high fusion gain. Current profile control experiments at the DIII-D tokamak focus on using a combination of feedforward and feedback control to achieve a targeted current profile during the ramp-up and early flat-top phases of the shot and then to actively maintain this profile during the rest of the discharge. The dynamic evolution of the current profile is nonlinearly coupled with several plasma parameters, motivating the design of model-based control algorithms that can exploit knowledge of the system to achieve desired performance. In this work, we use a first-principles-driven, control-oriented model of the current profile evolution in low confinement mode (L-mode) discharges in DIII-D to design a feedback control law for regulating the profile around a desired trajectory. The model combines the magnetic diffusion equations with empirical correlations for the electron temperature, resistivity, and non-inductive current drive. To improve tracking performance of the system, a nonlinear input transformation is combined with a linear-quadratic-integral (LQI) optimal controller designed to minimize a weighted combination of the tracking error and controller effort. The resulting control law utilizes the total plasma current, total external heating power, and line averaged plasma density as actuators. A simulation study was used to test the controller's performance and ensure correct implementation in the DIII-D plasma control system prior to experimental testing. Experimental results are presented that show the first-principles-driven model-based control scheme's successful rejection of input disturbances and perturbed initial conditions, as well as target trajectory tracking.

Profile control simulations and experiments on TCV: a controller test environment and results using a model-based predictive controller

“…The controller requires the present plasma profile state x k as defined in (8). This state can be retrieved from the T e and ψ profiles and their gradients that are provided by RAPTOR-observer.…”

Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

“…In order to achieve an optimal current evolution in the plasma discharges of the ramp-up phase, various dynamic optimization techniques are applied to obtain numerical solutions in an open loop fashion, such as [7], [8], [19], [28]. For online implementations of optimized actuation commands, feedback strategies (e.g., [5,6,20,29]) are necessary to attenuate external perturbations and system uncertainties. However, many challenging research problems still remain open.…”

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Dynamic optimization of trajectory for ramp‐up current profile in tokamak plasma

“…In [8] and [20], using the Galerkin method, a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE is obtained, then the optimization of open-loop actuator trajectories for the tokamak plasma profile control is solved by the nonlinear optimization algorithm. There are also several advanced control and optimization approaches being investigated (e.g., [3,4,6,9,22,23]) due to advances in internal diagnostics and plasma actuation.…”