Page 48 - Servo Motors and Industrial Control Theory -

40 2 Feedback Control Theory Continued

Fig. 2.21 A simple two gear
system

T 1 θ 1
T 2 θ 2

As was discussed in Chap. 1, the response characteristic is completely described
by ω , ζ and the system always remains stable but could be overdamped or under-
n
damped.
Example 5 Gears.
When two gears are in contact, usually the input θ is considered as input and the
1
output is θ (Fig. 2.21). If the diameter of input gear is d and the diameter of output
1
2
gear is d , then the following relations about speed ratio n and torque can be written.
2

n = d 2
d 1
θ (2.28)
θ = 1
2
n
T = nT
2 1
Figure 2.21 shows the correct direction of the parameters defined in Eq. (2.26).
Example 6 Electronics devices for achieving proportional, derivative, integral,
and lead-lag action.
There are electronics devices that can be used to achieve proportional, integral, and
derivative action. These devices are known as Operational Amplifiers or in short
OP-AMP. The purpose of this book is not to describe the circuit designs but to give
brief description of their behavior when included in a control system. An OP-AMP
is shown as a triangle, which shows the direction of flow of signal (Fig. 2.21).
Figure 2.22 shows an amplifier and a proportional control with OP-AMP. There
are two inputs one positive and negative. The negative pin is used for input signal.
The other + and − signs shown on the side of OP-AMP are the power supply pins.
The exact construction of the circuit diagram is usually shown in the manufacturer
data book.
For an amplifier, the output voltage is obtained by multiplying the input signal
by a factor K. That is,
V =− KV 1
o
R (2.29)
K = 2
R 1