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There are many challenging control problems critical to the success of burning fusion plasma experiments like ITER. Among them, the most fundamental problem is the control of plasma density and temperature, referred to as the burn condition. While passively stable burn conditions exist, economic and technological constraints may require future commercial fusion reactors to operate at unstable burn conditions. The instability is due to the fact that at low temperatures, the rate of thermonuclear reaction increases as the plasma temperature rises. To stabilize such operating points, it will be essential to have active control of the system. Most existing burn control efforts use control techniques based on linearized models. Such models break down for large perturbations and must be designed around a particular operating point. In this work, we utilize a spatially averaged (zero-dimensional) nonlinear transport model to synthesize a nonlinear feedback controller that can stabilize the burn condition of a fusion reactor. The nonlinear controller guarantees stability of the plasma density and temperature for a much larger range of perturbations than linear designs and is augmented with an adaptive law that guarantees stability despite uncertainty in particle confinement time parameters. A zero-dimensional transport simulation study is presented to show the ability of the controller to bring the system back to the desired equilibrium from a given set of initial perturbations even when there is significant uncertainty in the confinement parameters.

The tokamak is a high order, distributed parameter, nonlinear system with a large number of instabilities. Therefore, accurate theoretical plasma models are difficult to develop. However, linear plasma response models around a particular equilibrium can be developed by using data-driven modeling techniques. This paper introduces a linear model of the rotational transform ι profile evolution based on experimental data from the DIII-D tokamak. The model represents the response of the ι profile to the electric field due to induction as well as to heating and current drive (H&CD) systems. The control goal is to use both induction and H&CD systems to regulate the plasma ι profile around a particular target profile. A singular value decomposition (SVD) of the plasma model at steady state is carried out to decouple the system and identify the most relevant control channels. A mixed sensitivity H ∞ control design problem is formulated to synthesize a stabilizing feedback controller without input constraint that minimizes the reference tracking error and rejects external disturbances with minimal control energy. The feedback controller is then augmented with an anti-windup compensator, which keeps the given profile controller well-behaved in the presence of magnitude constraints in the actuators and leaves the nominal closed-loop unmodified when no saturation is present. Finally, computer simulations and experimental results illustrate the performance of the model-based profile controller.

Setting up a suitable toroidal current profile in a fusion tokamak reactor is vital to the eventual realization of a commercial nuclear fusion power plant. Creating the desired current profile during the ramp-up and early flat-top phases of the plasma discharge and then actively maintaining this target profile for the remainder of the discharge is the goal at the DIII-D tokamak. The evolution of the toroidal current profile in toka-maks is related to the evolution of the poloidal magnetic flux profile, which is modeled by the magnetic diffusion equation. A simplified first-principles-driven, nonlinear, dynamic, control-oriented, partial differential equation model of the poloidal flux profile evolution is obtained by combining the magnetic diffusion equation with empirical correlations obtained from experimental data at DIII-D and is used to synthesize a robust H ∞ feedback controller to track a desired reference trajectory of the poloidal magnetic flux gradient profile. We employ a singular value decomposition of the static gain matrix of the plant model to identify the most relevant channels which we control with the feedback controller. A framework for real-time feedforward + feedback control was implemented in the DIII-D Plasma Control System and experimental results in the DIII-D tokamak are presented to illustrate the capabilities of the feedback controller. These experiments mark the first time ever a first-principles-driven model-based magnetic profile controller was successfully implemented and tested in a tokamak device.

Control of the spatial profile of plasma current in tokamak plasmas has been demonstrated to be a key condition for achieving advanced scenarios with improved confinement and possible steady-state operation. The dynamics of the current profile are nonlinear and coupled with several other plasma parameters, motivating the design of model-based controllers that can account for these complexities. In this work, we consider a control-oriented model of the current profile evolution in DIII-D and the problem of regulating the current profile around a desired feed-forward trajectory. In open-loop, the response of the system to disturbances and perturbed initial conditions may be undesirable. To improve the performance of the system, the PDE model is discretized in space using a finite difference method and a backstepping design is applied to obtain a discrete transformation from the original system into an asymptotically stable target system with desirable properties. Through a nonlinear transformation, the resulting boundary control law utilizes the total plasma current, total power, and line averaged density as actuators. A Simserver simulation study is done to test the controller's performance and its implementation in the DIII-D plasma control system. Finally, experimental results showing the ability of the controller to reject input disturbances and perturbations in initial conditions are presented.

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.