Page 76 - Servo Motors and Industrial Control Theory -

4.4 DC Servo Motors in Open and Closed Loop Velocity Control 69

Fig. 4.6 Speed torque char- speed
acteristic of DC servo motors

Rated Torque
Torque

where K is the torque constant of the motor given by the manufacturers. The torque
t
accelerates the motor inertia and assuming a viscous friction the equation becomes,
T: = Js + C ω m ω m

Eliminating T and I from the above equations and with some algebraic manipula-
tion, the relationship between the speed and input voltage becomes

A
:=
ω
T + 1
m
s
Where,
(K )
A := t
RC+C m R
K t
And,
J
T :=
C+C K t
m R
It can be seen that the dynamic characteristic of the motor is a first order transfer
function (Fig. 4.7). This kind of transfer function was studied in previous chapters.
The time constant increases when the inertia of motor is increased. The readers
are encouraged to do the algebraic manipulation to find that the obtained transfer
function is correct. When the external torque is applied, the speed drops according
to the speed torque characteristic of the motor with a dynamic response according
the transfer function given above. When it is required to have a constant speed, the
external velocity feedback must be used. If a steady state error can be tolerated,
a proportional controller may be used. For application where zero steady state is
required, an integrator must be used.
To illustrate the procedure for studying such application, a velocity feedback
with an integrator will be studied.
It can be seen that there is an internal velocity feedback. This helps to increase
the damping of the system. A sensor such as a dc tacho may be used to measure the