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This paper proposes improvements to the control method based on the complete dynamical model published by Kömürcügil and Kükrer, which is very simple by operation in the stationary reference frame and lacks ac-line-current sensors. Nevertheless, the basic control method is very sensitive to variations of the line inductances, which provide difficulties in many industry applications. The modifications proposed in this paper overcome this disadvantage using a fuzzy logic controller to tune parameters and do more robust the basic control in view of line inductance parameters variations. Unfortunately, the new tuning method needs information about the reactive line current; therefore, ac-line-current reconstruction algorithm based on the dc-link current measurement has been included to keep the same number of sensors as the basic solution. Simulation and experimental results have proved the correct system operation at wide variations of the line inductance.