The term Virtual Synchronous Machine (VSM) commonly refers to the emulation of synchronous machines operation by using power electronics converters. However, a wider application of this control technique is still pending on further refinement of its design aspects and digital implementation. In this paper, a systematic approach to design the VSM parameters is introduced. First, a simplified third-order small-signal model of a VSM based on the conventional model of synchronous generators is developed. Unlike the existing works published in literature, the proposed model takes into account the effects of inductive and resistive weak grids. The model is then used to design the controller parameters by appropriately placing the poles of the closed-loop system. VSM robustness is studied for weak grids dominated by either inductance or resistance, and the aspects of digital control implementation are addressed. All the control system features and improvements were tested on a 15kW prototype of a battery-supported VSM connected to a weak grid.