What is the main reason for using speed feedback in a motor positioning control system?
Feeding back speed is the same as feeding back the rate of change of distance against time so your question really boils down to why you might use a proportional feedback signal as well as a differential signal.

Simple answer is that when used properly, the speed signal fed back can reduce the rate at which the system homes in on the target position and somewhat reduces the effect of overshoot and hunting. In other words, it’s a stabilising factor in the presence of system inertia.

Maybe do some research on three term controllers or PID controllers. P stands for proportional, I for integral and D for differential. Differential is the same effect as a speed signal in a position control system.




  why waste the expense of a speed sensor, extra circuitry when you can
  just increase the P gain in the position loop PID controller to
  accomplish the same


Try this out: -



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