This paper addresses the problem of controlling a single phase shunt active power filter (SAPF) in presence of nonlinear loads. The considered SAPF is based on a Dual Buck Half Bridge converter (DBHB), which has the ability to eliminate the shoot-through problem arising in the conventional inverter circuit. The aim is to design a controller that is able to achieve the following three control objectives: (i) simple and indirect estimation of harmonic components, (ii) compensating for the harmonic and reactive currents generated by the nonlinear load for assuring a satisfactory power factor correction (PFC) in the grid side, (iii) regulating the DC capacitor voltage of the DBHB converter. In order to meet these control objectives, a new controller based on multi-loop structure is proposed. In the inner loop, a hybrid automaton representation of the DBHB-SAPF is used for the purpose of designing an appropriate control law so that to ensure a unity power factor. In the outer loop, a fuzzy logic controller is developed to guarantee a tight regulation of the converter DC voltage to a desired value. The effectiveness of the proposed controller is verified and validated by numerical simulation using MATLAB/Simulink environment. From the obtained results, the designed controller shows significant performance in terms of robustness and tracking compared to the standard strategy based on PI regulator.