So -- what happens if you feed it a pulse, wait five seconds and
then feed it another pulse? Are you saying that it is going to
*predict* exactly when that second pulse will come, and will move at a
steady speed just right so when the second pulse comes it will be in
the right place? If so, it must have some rather impressive CPU power
built into it -- and I see no provisions for that.

Just about any motion control scheme should cause a jump in linear
postion based on a single step. I see where you are trying to go with
this so I'll save you the trouble. It is the **frequency** of the step
input that excites resonance in a stepper motor. The DC motor is
isolated from the **frequency** of the step input. The only
**frequency** the DC motor sees is the frequency of the PWM signal
applied to the controlling H-bridge. It is constant and bears no
relationship whatsoever to the step input **frequency**.

It is the duty cycle of the PWM signal that is varied in order to
provide a moving equilibrium between step input and encoder counts in
response to changes in step input **frequency**. The tuning of the DC
servo system will determine the behaviour of the movement mentioned. If
the **frequency** of the step input suddenly changes then the P & D
settings (aka gain and damping) are supposed to critically damp the
movement in a properly tuned system. An improperly tuned system can
break out into violent oscillations similar to a stepper in resonance.
Perhaps this is what you've seen and confused it with resonance.