## Theses and Dissertations

8-1-2019

Dissertation

#### Degree

Doctor of Philosophy

#### Department

Mechanical Engineering

Eugenio Schuster

#### Abstract

As worldwide energy consumption increases, the world is facing the possibility of an energy shortage problem. While several approaches have been proposed to slow down this process, which include the improvement of the combustion efficiency of fossil fuels and the introduction of nuclear energy and renewable energy, such as solar, wind, and geothermal energy, a replacement for fossil fuels will eventually be needed. The energy that comes from a nuclear reaction, which includes nuclear fission and nuclear fusion, has a high energy production density (rate of energy produced divided by the area of the land needed to produce it) and produces no air pollution or greenhouse gases, which makes it a strong and attractive candidate. Compared with nuclear fission, the radioactive waste from nuclear fusion can be more easily disposed, the reactants in a nuclear fusion reaction are abundantly available in nature, and nuclear fusion poses no risk of a nuclear accident. For all these reasons, nuclear fusion is a potential solution for the energy shortage problem.

However, there are many challenges that need to be conquered to achieve nuclear fusion. The primary challenge is to confine the hot reactants, whose temperatures are about one hundred million degrees Kelvin. At these temperatures, the reactants are in the plasma state and have enough kinetic energy to overcome the repelling electrostatic forces and fuse. One of the most promising approaches to confine the fusion plasma is magnetic confinement, where magnetic fields are used to confine the plasma through the Lorentz force. The tokamak is one of the fusion devices that exploit magnetic confinement. To demonstrate the viability of a nuclear fusion power plant, the International Thermonuclear Experimental Reactor (ITER) tokamak project is aimed at producing 500 megawatts power with 50 megawatts of input power, which will make it the first tokamak with net energy output.

To be able to obtain the desired fusion gain, the ITER tokamak will need to operate at a temperature and a pressure so high that the plasma has a good chance of becoming unstable and difficult to confine. To address this issue, extensive research has been conducted on different fusion tokamaks around the world to find high performance operating scenarios characterized by a high fusion gain, good plasma confinement, plasma stability, and a dominant self-generated plasma current with the goal of developing candidate scenarios for ITER. The shape of the toroidal current density profile, or the safety factor profile ($q$-profile), impacts steady-state operation, magnetohydrodynamic (MHD) stability, and plasma performance. The plasma $\beta$, which is the ratio of the kinetic pressure of the plasma to the magnetic pressure (pressure exerted on plasma by the magnetic field), acts as an important economic factor in fusion power generation. Therefore, active control of the toroidal current density profile and plasma $\beta$ is one path towards advanced scenarios.

This dissertation focuses on developing control solutions for regulating the current density profile, and to some extent the normalized plasma $\beta$ (denoted as $\beta_N$), on the Experimental Advanced Superconducting Tokamak (EAST) located at the Institute of Plasma Physics, Chinese Academy of Sciences (ASIPP), in Hefei, China. Towards this goal, a control-oriented, physics-based model has been developed for the current density profile evolution in EAST in response to available heating and current-drive (H\&CD) systems. The feasibility of reconstructing the internal plasma states, which may be crucial for feedback control, from measurements at the magnetic axis and at the plasma edge has been studied by using experimental data and exploiting the response model. Target scenarios (characterized by desired $q$-profile and $\beta_N$) have been developed by following a model-based finite-time optimization approach. Feedback controllers ranging from simpler Proportional-Integral-Derivative (PID) controllers to more complex model-based optimal controllers, derived from Linear-Quadratic-Regulator (LQR), $H_\infty$, and Model Predictive Control (MPC) theories, have been synthesized to counteract deviations from the desired target scenario. The overall control solution has been implemented in the Plasma Control System (PCS) and closed-loop $q$-profile regulation has been demonstrated for the first time ever in EAST in disturbance rejection and target tracking experiments.

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