This paper investigates the controllability of two time-scale systems using both the time-scale separation model and the slow-fast order reduction model. This work considers the effect of a singular per-turbation parameter on the model transformations to improve the criterion precision. The Maclaurin expan-sion method and homotopy arithmetic are introduced to obtain t-dependent controllability criteria. Examples indicate that the ε-dependent controllability criteria are more accurate and that the controllability of two time-scale systems does not change dudng model transformations with these more accurate forms.