Gray-box modeling of resistive wall modes with vacuum-plasma separation and optimal control design for EXTRAP T2R

Experimental characterization and modelling of the resistive wall mode response in a reversed field pinch

“…The aliasing that arises at the spatial sampling of the magnetic field distribution with a discrete sensor array can affect the experimental estimation of the plasma response. The enhanced sensor array has meant an increase in the spectrum of modes −32 ⩽ n < 32 that can be resolved, and the effects from aliasing observed in previous studies [43,44] is mitigated in this study. The decreasing influence of aliasing with increasing array size was clearly demonstrated for the vacuum case in a comparison of array sizes N s = 32 and N s = 64 [36].…”

“…A more realistic finite element model of the shell in EXTRAP T2R has been developed using the CARIDDI code. The model includes the effects of the toroidal geometry and asymmetries as the horizontal and vertical gaps in the shell [46]. In practice, the choice of complexity in a model-based control algorithm will be a compromise between a realistic description of the RWM plasma response and the requirement that the implementation of the algorithm must be compatible with the computing capabilities of the control hardware.…”

Model predictive control of resistive wall mode for ITER

“…Extensive research of RWMs was carried out in reversed-field pinch (RFP) and tokamak experiments in RFX-mod [11,12,13,14,15], EXTRAP T2R [16,17,18,19,20], HBT-EP [21], DIII-D [4,22,23,8,24,15,25,26,27], NSTX [28,29,30], and JT-60 [6]. Modelling codes, such as VALEN [31,26,27], CarMa [32,33,34,35,36], CarMa0NL [37,38] are generally based on coupling MHD equations for the plasma with the equations describing the currents induced in the conductive wall.…”

“…Both EFC and active RWM feedback act on correction coils positioned perpendicularly along the reactor wall, either internally or externally to the vacuum vessel. They may be implemented using separate coil sets [22,15] or the same coil set [4,24,8,29,17,20,18,19], in some cases even within the same controller [17,20,18,19]. The main distinction is in dynamics -EFC acts on the static field and the slow time-variation of the plasma response to it, while active RWM feedback takes care of dynamics in the range of τW and must be able to stabilize the open-loopunstable RWM.…”

“…The advantage of LQG over PD control was also shown by Dalessio et al [52,53] where control design was further upgraded with the H∞ control approach maximizing robustness to model uncertainty expressed as a single structured uncertainty parameter addressing the variable RWM growth rate. Setiadi et al [20] presented a LQG controller for EXTRAP T2R with a gray-box modelling approach combining a finite-element model for the conductive shell and black-box modelling (model identification) for the plasma. The volume of experimental results of LQG with high-βN H-mode tokamak plasmas is relatively limited in comparison to the conventional PD-control-based approaches, but it was demonstrated that LQG may facilitate longer pulse duration in H-mode high βN conditions in NSTX [30] and DIII-D [26,27].…”