This article further considers the abstraction problem of affine control systems proposed in the paper "Consistent abstractions of affine control systems" by Pappas et al. We present a general solution for the problem. Then, constructions in the abovementioned paper are treated as a special case of our results. We also clarify the statement given in the abovementioned paper, claiming that the canonical construction on M gives the desired affine distribution on N, which solves the abstraction problem of smooth affine control systems. Additional assumptions are added to make the statement hold.