A dc servo motor can be described in the following way. Its magnetic field, B, is constant, supplied either by a constant field current or by permanent magnets. The input voltage to the armature of the motor,Vin , connects to a circuit containing the armature impedance, R and L in series, and a dependent voltage source called the motor back emf. This back emf (electromotive force) is a generator type action of the motor and is a voltage which opposes the applied voltage. It is proportional the electromagnetic field and the rotational speed of the motor. Since the electromagnetic field is assumed constant, B may be absorbed into the constant of proportionality yielding for the back emf in V emf back= K V (teta)
The torque produced at the motor shaft is proportional to the electromagnetic field and the armature current. Again, since the magnetic field is constant, B may be absorbed into the constant of proportionality yielding for the torque
T=(K T )(iA)
It is desired to model the behavior of the dc servomotor for a particular mechanical load. Assume that the load is purely inertial such that the equation between motor torque and the load obeys the equation
J (teta")= T
Draw a diagram of the model containing the electrical input on the left side and the mechanical output on the right side.
(A) Analyze the system and obtain the transfer function relating to teta (S) to Vin (S)
(B) Repeat for the case where there is linear friction in the mechanical and the equation describing the angular acceleration of the load becomes J (Teta") = T - f (teta')