3. The voltage equation of a dc motor is written as
where ea(t) is the applied voltage: ia(t). the armature current; Ra. the armature resistance; La, the armature
inductance; Kb, the back-emf constant; ωm(/), the motor velocit ity; and ωr/(t), the reference input voltage.
Taking the Laplace transformn on both sides of the voltage equation, with zero initial conditions and solving
for Ω2m(s).we get
which shows that the velocity infornation can be generated by feeding back the armature voltage and current.
The block diagram in Fig, C shows a dc-motor system. with voltage and current feedbacks. for speed control.
(1) Find the transfer functions,respectively.【計分:6分】