Designing and modelling of the asymptotic perturbed extremum seeking control scheme for tracking the global extreme

This paper presents the designing and modeling of the Asymptotic Perturbed Extremum Seeking Control (aPESC) scheme that is capable to locate and track the Global Extremes on the multimodal patterns. The multimodal patterns may appear on power generated by a photovoltaic (PV) array under Partial Shading Conditions (PSCs), but also on net power generated by a Fuel Cell (FC) system. The proposed aPESC scheme uses a scanning technique to determine the GMPP on different multimodal patterns based on two components of the searching signal: (1) the scanning signal locates the LMPP by sweeping the PV pattern based on a asymptotic dither modulated by the first harmonic of the PV power and controlled by the dither gain (k₂); (2) the tracking signal finds and tracks accurately the GMPP based on similar loop used in PESC schemes proposed in the literature that is controlled by the loop gain (k₁). These tuning parameters are designed based on the averaged model of this aPESC scheme. Also, the averaged scheme and local averaged loop of the aPESCH1 scheme are used to estimate the searching gradient and analyze the closed ESC loop stability. The design methodology is tested on generic multimodal patterns and then is validated considering a PV system and a FC system.