As I recall the model of a dc motor, it has two time constants ne is mechanical (J/B), and one is electrical (L/R). Motor current flowing into the armature can be driven by a current amp effectively eliminating the electrical time constant. When the output voltage of the current amp rises within range of the supply rails it no longer looks like a current amp, but rather a voltage amp. So, as long as the speed corrections stay within a range to prevent saturation of the current amp, a PI controller and the mechanical time constant will demonstrate a second order system, the root locus of which will approach the imaginary axis as loop gain is increased to a very large value.