Aspects of Electromagnetic Modelling for Multiple-Input-Multiple-Output Control of MHD Modes in RFX-mod

The research activity object of the present dissertation has been carried out at the Industrial Engeneering Doctoral School (Course of Electric Engeneering) of the University of Padova. The study concerned the electromagnetic systems modelling with regard on active control system analysis for the stabilization of plasma MHD modes in the RFX-mod experiment. Three are the main results of the research activity. The first one is the inclusion of the specific problem in the frame of the Unified Signal Theory, important in order to build a solid theoretical background from which starting developing new control models and techniques. The second one is the production of a mathematical model of the plant based exclusively on experimental measures. This allow the system's structure analysis, the simulation of its dynamic behaviour and the development of innovative control schemes. The third one is the actual production of a new algorithm based on the developed model. The system cosidered in the present study is made up by 192 units, each one including an active coil, its power amplifier, three field sensors (respectively radial, toroidal and poloidal). The active coils and the radial sensors are laid down in a regular manner and in this way they cover exactly the toroidal surfaces they intersects. Both of them form a grid made of 48 poloidal arrays, each one consisting of 4 elements. Metallic structures of different thickness are present in between the active coils and the magnetic field sensors, which are interested by dissipative effects due to the induced currents by the active control system and by the plasma. During a first phase of the research, experimental campaigns have been made in order to measure quantitatively the mutual couplings between saddle coils and the effect of their currents on the magnetic field measured by the radial sensors. Data collected during these campaigns allowed for the mathematical form of the active coils inductance matrix and the mutual inductance between active coils and sensors to be discovered. Due to the presence of the passive structures these matrices are not constant, but variable in the frequency domain. For this reason the campaigns have been carried out studying the behaviour of the couplings at different frequencies. A model of the couplings has then been derived and used in the construction of a bigger model comprehensive of the active coils and power amplifier dynamics. The task has been completed by writing convenient procedures in the Matlabr language, which allowed for an automated processing of the experimental data under some simplifying hypothesis about the number of significative couplings. Later the model has been intensively validated. Tests have been carried out both in open loop and closed loop. The open loop tests have been made by comparing the real and simulated outputs corresponding to the applied voltages and currents. The model was able to reproduce the output quantities with a 5% accuracy, to mimic the real closed loop stability range and has been used with success as a tool to gain insight into marginally stable phenomena. The model analysis evidenced a couple of important facts. The first is that the coupling between active coil and sensor is not so local as expected; this required a great number of couplings to be considered. The second is that the uniformity of the couplings is less than expected. The presence of features, like the inner equatorial gap, ruining the uniformity of the passive structures acts as a limit of the obtainable performance in the present configuration. On the basis of the model a new control algorithm has been designed using the singular value decomposition. Simulation results confirm that this control algorithm is able to compensate the effects of the local features of the passive structures till a limit frequency. Above that frequency the power required for the compensation would exceed the capacity of the amplifiers. Part of the research activity has been carried out in the frame of a collaboration between the Consorzio RFX and the EFDA-JET laboratory of Culham (UK) about the upgrade of the power amplifier of the plasma vertical instability. Here the research has focused on the realisation of part of the software control system of the new resonant amplifier.