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; K_b, 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 Ω2_m(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.