Modeling, observer design and robust control of the particle density profile in tokamak plasmas

A new approach to real-time estimation and feedback control of the particle density profile in tokamak plasmas is presented, based on ideas from Kalman filtering and H∞ robust control synthesis. Traditionally, the density profile is reconstructed in real-time by solving an inversion problem using a measurement from a single time instant. Such an approach is sensitive to sensor errors and does not account for the dynamical evolution and spatial continuity of the density. The observer-based approach we presented here includes the system dynamics, which is realized by careful modeling of the particle density behaviour using a 1D PDE with a nonlinear source term and two ODEs, which are discretized in space and time to yield a finite-dimensional nonlinear model. The influence of other plasma quantities and operational modes on the transport dynamics are included in the control-oriented model as time-varying parameters. An extended Kalman filter estimates the density, additive random-walk state disturbances as well as fringe jumps (a specific type of sensor error) from measurements, for which special measures are needed. Offline reconstruction using tokamak measurements show accurate estimation of the density profile and show the quality of fringe jump detection. Moreover, a robust state feedback controller with anti-windup is designed based on the model to track a reference signal for the average density, with the estimate obtained from the observer. Closed-loop simulations show that the controller is able to track representative reference signals, with the performance mostly limited by the nonnegativity constraint of the control input.