Summary: We study nonlinear control systems in the plane, affine with respect to control. We introduce two sets of feedback equivariants forming a phase portrait \(\mathcal{PP}\) and a parameterized phase portrait \(\mathcal{PPP}\) of the system. The phase portrait \(\mathcal{PP}\) consists of an equilibrium set \(E\), a critical set \(C\) (parameterized, for \(\mathcal{PPP}\)), an optimality index, a canonical foliation and a drift direction. We show that under weak generic assumptions the phase portraits determine, locally, the feedback and orbital feedback equivalence class of a system. The basic role is played by the critical set \(C\) and the critical vector field on \(C\). We also study local classification problems for systems and their families.