Experiments on feedback control of multiple resistive wall modes comparing different active coil arrays and sensor types

Experiments have been carried out on the EXTRAP T2R reversed-field pinch device to study several important issues related to feedback control of resistive wall modes (RWMs). The feedback system includes a sensor coil array, a feedback controller implementing a feedback law and an active coil array. The issues include 1) effects of sideband harmonics produced by the feedback system, 2) the form of the controller and the feedback law, 3) feedback system stability, 4) selection of the sensor coil configuration and 5) effects of field errors on the feedback system. Side band harmonics are produced by the feedback system because the active saddle coil array consists of discrete coils. The presence of side bands can couple modes thus preventing simultaneous stabilisation of the coupled modes. The side band effect sets requirements for the minimum number of active coils in the array in both the poloidal and toroidal directions. Recent experiments using the intelligent shell concept with proportional-integral-derivative controller action have achieved complete simultaneous stabilisation of all RWMs modes when the requirements are satisfied. In addition to the intelligent shell concept, preliminary experiments have been performed to test the fake rotating shell concept. For this concept, the sensor coil array is shifted in phase relative to the active coil array thus a detected harmonic is induced to rotate by the active coil-produced control field. Under the condition that the phase shift is less than a quarter-wave length of the mode, mode suppression can be achieved. Feedback using a controller incorporating individual mode control has also been tested. This has enabled the first feedback experiments using a sensor array measuring the toroidal field component to be carried out. For this concept, an array consisting of localised toroidal field sensor coils is used. Mode suppression has been successfully accomplished. However pick-up of high order field error harmonics due to the small size of the sensor coils introduces an adverse signal to background ratio as compared to the case with the radial field sensor coil array. Optimal suppression is achieved at the predicted complex feedback gain phase. Mode rotation is induced at other complex gain phases, in agreement with modelling. In other experiments, linear models have been used to evaluate the effect of resonant field errors on mode growth. The thin-wall model is satisfactory for describing the response of the plasma and resistive-shell system and resonant field error amplification is observed.