Equivalence Relation Analysis and Design of Repetitive Controllers and Multiple Quasi-Resonant Controllers for Single-Phase Inverters

Repetitive controllers (RCs) and multiple quasi-resonant controllers (MQ-RSCs), both based on the internal model principle, are widely used in ac voltage/current control of single-phase inverters due to their high tracking accuracy for sinusoid reference and superior harmonic suppression capabilities. However, both controllers have their respective strengths and weaknesses regarding parameter design complexity, convergence rate, or stability margin. In this article, the mathematical equivalence between various types of RCs and MQ-RSCs is established comprehensively, which offers a new perspective for analyzing and designing these two types of controllers. The equivalent relations reveal the connection between the internal model coefficients of RCs and the equivalent resonant bandwidths of MQ-RSCs. Based on these equivalent relations, a novel design way of RCs is proposed to enhance the frequency robustness. Furthermore, a new MQ-RSC design method is also put forward to simplify the design process. Experimental results on a 1.5-kW single-phase grid-tied inverter validate the accuracy of the equivalence relations and showcase their valuable roles in the design of RCs and MQ-RSCs.