Systematic design of a multi-input multi-output controller by model-based decoupling:a demonstration on TCV using multi-species gas injection

In this paper, we present the first results of a systematically designed multi-input multi-output gas-injection controller on Tokamak á Configuration Variable (TCV). We demonstrate the simultaneous real-time control of the NII emission front position and line-integrated electron density using nitrogen and deuterium gas injection. Injection of nitrogen and/or deuterium affects both the NII emission front position and line-integrated electron density. This interplay between control loops is termed interaction and, when strongly present, makes designing a controller a significantly more complex problem. Interaction between the control loops can be reduced to an acceptable level by redefining inputs, decoupling the multi-input multi-output control problem to separated single-input single-output problems. We demonstrate how to achieve this by defining virtual control inputs from linear combinations of the actuators available. For the demonstration on TCV, linear combinations of deuterium and nitrogen gas injection are computed from transfer-function models to obtain these virtual inputs. The virtual inputs reduce the interaction in the control-relevant frequency range to a point where control of the NII emission front position and line-integrated electron density can be considered decoupled, allowing for the much simpler design of single-input single-output controllers for each loop. Implementing the controllers with the virtual inputs gives the multi-input multi-output gas-injection controller. This approach is well established in the control community, and is presented here as a demonstration to drive developments of multi-input multi-output control strategies. In particular, the envisioned control of particle- and heat fluxes impacting the divertor targets by injection of multiple gas species

Improved flux-surface parameterization through constrained nonlinear optimization

Parameterization of magnetic flux-surfaces is often used for magnetohydrodynamic stability analysis and microturbulence modeling in tokamaks. Shape parameters for such local parameterization of a (numerical) equilibrium are traditionally computed analytically using geometrically derived quantities. However, often the shape is approximated by the average of values for different sections of the flux-surface contour or a truncated series, which does not guarantee an optimal fit. Here, instead nonlinear least squares optimization is used to compute these parameters, with a weighted sum of squared error cost function that is robust to outliers. This method results in a lower total absolute error for both the parameterization of the flux-surface contour and the poloidal magnetic field density than current methods for several parameterizations based on the well-known "Miller geometry."Furthermore, rapid convergence of shape parameters is achieved, no approximate geometric measurements of the contour are needed, and the method is applicable to any analytical shape parameterization. Validation with local, linear gyrokinetic simulations using these optimized shape parameters showed reduced root mean square errors in both the growth rate and frequency spectra when compared with simulations based on numerical equilibria. In particular, the popular Turnbull-Miller parameterization benefits from this approach, extending its usability closer toward the last-closed flux-surface for cases with minor up-down asymmetry.</p