Page 150 - Servo Motors and Industrial Control Theory -

9.2 Theory and Performance Criteria 145

assumed to have only load inertia and there is no speed reduction mechanism. This
for reason of comparison and load mechanism depends on particular applications.
In any control system employing servo motors, two important dynamic character-
istics must be considered:
a. The effect of command signal which may be large displacement or small varia-
tions from the operating point. In this chapter, both small and large command
displacement characteristics will be investigated.
b. The effect of external disturbance such as an external torque and friction.
In order to investigate the complete dynamic behavior, an impulse input response
of the system would be an ideal test, since it excites all the modes of the system.
However, because of its impracticality, this test is not normally used for the servo
motor drive system. A step input can be more easily applied either as a command
signal to determine the speed of response, overshoot, damping, and settling time,
or as an external torque to determine the steady state and dynamic accuracy in the
presence of a disturbance. In making the comparison, it is assumed that all the high
performance servo motors incorporate a local velocity feedback to give improved
damping and motor stiffness, that a feed-forward integrator is used to give a zero
steady state error to a ramp input and that the amplifier contains a lead lag network
for dynamic compensation.
In order to obtain the best performance, the parameters of the controller such as
gain, time constants of the compensation network, and the gains of the feedback
must be optimized to give a fast speed of response and low dynamic error caused
by an external torque and input response. It was shown in previous chapters that a
damping ratio of 0.6–0.7 in velocity control gives the best performance in poison
control and also that this damping must be achieved at maximum value of gain in
order to obtain the maximum speed of response and accuracy.
In order to facilitate the dynamic analysis and optimization of the system, the
author developed a computer package to predict the stability and transient response.
This was several years ago and in present day there are several commercial com-
puter programs such as MathCad that the reader may use for particular application.
The optimization procedure is as follows:
1. The gain of the system is first increased. This results in an increase in the speed
of response and a reduction in the damping ratio of the system and a reduction in
steady state error due to external torque.
2. In order to compensate the reduction in damping, a lead-lag network is intro-
duced. The usual effect of the lag network is to introduce damping in the fun-
damental mode of the system but has the opposite effect on the higher mode.
The effect of the lead network is to increase the damping in the higher mode of
vibration.
3. The improvement achieved by a lead-lag network alone is limited, since at high
gain the contribution of higher modes of vibration of the systems becomes sig-
nificant. Acceleration feedback together with a lead-lag network, improves the
dynamic performance of the system by not only introducing damping in the