In this chapter some results related to Shunt Active Filters (SAFs) andobtained by the authors and some coauthors are reported. SAFs are complex powerelectronics equipments adopted to compensate for cur-rent harmonic pollution inelectric mains, due to nonlinear loads. By using a proper "floating" capacitoras energy reservoir, the SAF purpose is to inject in the line grid currentscanceling the polluting har-monics. Control algorithms play a key role for suchdevices and, in general, in many power electronics applications. Moreover,systems theory is crucial, since it is the mathematical tool that enables adeep understanding of the involved dynamics of such systems, allowing a correctdimensioning, beside an effective control. As a matter of facts, currentinjection objective can be straightforwardly formulated as an output trackingcontrol problem. In this fashion, the structural and insidiousmarginally-stable internal/zero dynamics of SAFs can be immediately highlightedand characterized in terms of sizing and control issues. For what concerns thecontrol design strictly, time-scale separation among output and internaldynamics can be effectively exploited to split the control design in differentstages that can be later aggregated, by using singular perturbation analysis.In addition, for robust asymptotic output tracking the Internal Model Principleis adopted.
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