This paper presents the development of improved synergetic current control for the injected current of an inverter in the grid-connected microgrid and the distributed generation system (DGS). This paper introduces new formulas of the macro-variable functions for integral synergetic control (SC) and integral fast terminal SC, which both have an integral term to guarantee zero steady-state error. The proposed integral SC and integral fast terminal SC achieve a seamless performance such as the fast convergence, minimal overshoot, zero steady-state error, and chattering-free operation. To demonstrate the meritorious performance of the proposed scheme for injected current control, it is compared with the performance of a proportional-integral (PI) controller and advanced exponential sliding mode control (SMC). Finally, the practicality of the proposed scheme is justified by experimental results obtained through rapid control prototyping (RCP) using the dSPACE-SCALEXIO platform.Index Terms--Integral synergetic control (SC), current control, integral fast terminal SC, advanced exponential sliding mode control (SMC), proportional-integral (PI) control, microgrid, distributed generation system (DGS).