Application of model order reduction methods to RFX- mod plasma response model: hints for prospective use in the design of RFX-mod2 control system

The refurbishment of RFX-mod, now named RFX-mod2, will require the design of new control systems of plasma magnetic equilibrium configuration. In particular, for RFX-mod2 operation as a non-circular Tokamak, the control of both plasma vertical position and shape is needed. Linearized plasma response models of RFX- mod operating as a Tokamak had been developed in the framework of a scientific collaboration with CREATE since the very beginning of that experimental program. An order reduction method was applied by means of a Matlab function and used to design the control system of the plasma vertical position and shape. The resulting compensator was then implemented in the real-time control system and different values of its parameters were tested to optimize its performances. The control system operated successfully in Tokamak discharges until the shut-down of the experiment in 2015. In this technical note different reduction methods such as balanced truncation, balanced residualization and minimum degree approximation without balancing have been applied to RFX-mod plasma response model. The comparison of the corresponding reduced order models with the full order one has been carried out with the aim of assessing alternative solutions and providing some hints on their prospective use in RFX-mod2. The analysis of models developed for RFX-mod should not prevent from drawing general conclusions for RFX-mod2, too, because the modifications of the device are not expected to affect substantially the equilibrium dynamics, mainly dependent on the presence of the highly conducting shell, now even closer to the plasma boundary. The eigenvalues of the state matrices of the models provided information on their dynamic response. Nyquist contour plots and singular values plots were also used to characterize the frequency response of the SISO (plasma vertical position control) and MIMO (plasma shape control) models, respectively. The direct comparison of the time responses to step variations of input signals complemented the assessment of the reduced order model performances and their reliability for the design of the control system. All the reduced models exhibited satisfactory accuracy in reproducing the full order system characteristics and responses. Thus several options appear to be available with comparable accuracy for a prospective use in the design of the RFX-mod2 plasma shape and vertical position control systems.