Shown below is the system contra schematic for a, d, c. armature-controlled motor.
a. Deduce the output speed characteristic corresponding to an input signal of 24 volts as a step function.
(Note: this function may be written in 3 different ways, each defining the required function as = Our S, where S is the system transfer function. The transfer function S may be written In terms of either the armature current, the rotational velocity of the load or the inverse of the back emf constant i.e.:
S α i , or S α (dω/dt), or S α (1/kf)
You are requested to deduce any TWO characteristic speed equations (i.e. any two equations that define the output signal.
b. A voltage of 24v dc is switched on at time t = 0. Assuming that at this stage of operation, there is no error produced by the back emf from induction, show that the current supplied to the armature is given by i=24[1-e-Rt/L]