Due to their discrete nature, a grid of active coils for the feedback control of plasma instabilities produces an infinite sequence of sideband harmonics in the magnetic field. If the magnetic sensors have the same periodicity as the coils, as in the intelligent shell scheme (Bishop 1989 Plasma Phys. Control. Fusion31 1179), the aliasing of the sidebands determines a systematic error on the Fourier analysis of the measurements. Since the intelligent shell scheme relies on raw measurements, it does not recognize the aliasing effect. This is a drawback for error field compensation and for the control of those perturbations that cannot be suppressed by the feedback, but only reduced in their saturation level, such as the non-linear tearing modes (TMs) involved in the dynamo process of reversed field pinch machines. We have derived analytical formulae, valid in cylindrical geometry, for the subtraction of the sideband effect, and we implemented them in a real-time correction algorithm of the Fourier analysis of the magnetic measurements. The Fourier harmonics so obtained are used as the feedback variable of a new control scheme named clean-mode-control (CMC). The first tests of CMC in RFX-mod have given some interesting results in the control of the saturated TMs: besides a reduction of the radial field at the edge and the consequent plasma surface distortion, a systematic rotation of these perturbations with frequencies of up to 100 Hz is seen for the first time. This brings a mitigation of the phase-locking and wall-locking phenomena giving the possibility of operating safely at high currents.
Model-based design of multi-mode feedback control in the RFX-mod experiment