## 1 Introduction
Within the isolated topologies, flyback, push-pull, dual active bridge [14], and resonant converters with two inductors and one capacitor (LLC), as well as other particular topologies, can be used to implement microinverters; however, a flyback converter is the most widely used due to its simple structure, low number of components, and simple control compared to the other topologies [4]. In the literature, there are several control structures for flyback-based microinverters. Such a control structure can be divided into two main parts: the MPPT strategy and the inner control of the PV module voltage or current. Regarding the MPPT techniques, the most widely used are perturb and observe (P&O) [7; 13; 15; 16; 17; 18] and incremental conductance (IC) [19; 20; 21; 22]; nonetheless, it is also possible to find MPPT algorithms based on artificial neural networks [22]. Some of those MPPT techniques generate a reference for the PV module voltage [7; 13], while others regenerate a reference for the PV module current [16; 19]. However, it is preferable to generate a voltage reference instead of a current reference since the PV module voltage at the MPP is less sensitive to fast variations in the irradiance, while the current at the MPP may change as fast as the irradiance and produce significant drops in the power production [2]. Other MPPT techniques directly generate the duty cycle of the flyback converter [15; 17; 21; 22], which eliminates the necessity of a controller of the PV module voltage or current. The main drawback of these strategies is that the lack of such a controller produces 100 Hz or 120 Hz oscillations in the PV module voltage and current, which come from the connection with the inverter. Those oscillations are translated into oscillations and reductions in power production [13]. From the analyzed papers, only four implement controllers for the PV module's current or voltage to improve the performance of a flyback-based microinverter. In [19] and [16], the authors propose controllers for the PV module's current to track the reference generated by IC [19] and P&O [16] algorithms, respectively. The controller proposed in [16]is a PI, while the one proposed in [19] is based on the model predictive control theory. Other authors propose linear controllers to track the voltage reference generated by a P&O algorithm [7; 13]. The controller implemented in [7] is a PI, whereas the authors of [13] propose a cascade controller where the outer loop is a PI to track the voltage reference and the inner loop tracks the current reference with a Peak Current Controller (PCC). Among the PV module current and voltage controllers previously described, only the one proposed in [19] is nonlinear and poses an optimization problem to determine the state of the switch to track the reference. However, the performance of this controller depends on the model parameters, and the authors do not consider the transformer leakage inductance in the model. Moreover, the paper does not include the stability analysis of the system, and the load considered is a resistor and not a grid-connected inverter. The other controllers described above are linear; as consequence, they are designed for a particular operating point of the dc/dc converter and particular irradiance and temperature conditions of the PV module. Therefore, those controllers cannot guarantee system stability for any irradiance and temperature conditions due to the nonlinearities of both the dc/dc converter and the PV module. Moreover, the analyzed papers do not include a detailed design procedure of the proposed controllers, which makes it difficult to apply those controllers for a particular flyback-based inverter. Regarding the stability of the controlled systems, only the authors of [13] analyze the stability through the frequency response and quantify the rejection of the 100 Hz voltage oscillations produced by the inverter.