Page 268 - Modern Control Systems

242 Chapter 4 Feedback Control System Characteristics

-K„
VJs) O—*- V 0(s) VJs) ^O 1+KJfi+l) -• W

(a) (b)
FIGURE 4.5 Block diagram model of feedback amplifier assuming R p » R 0 of the amplifier.

and
(4.21)

The closed-loop transfer function of the feedback amplifier is

(4.22)
1 + K a(3'
The sensitivity of the closed-loop feedback amplifier is

SK. ~ S GS Ktt ~ x + K ^ (4.23)

If K a is large, the sensitivity is low. For example, if

= 10 4
K a
and
]8 = 0.1, (4.24)
we have

S T 1 (4.25)
K 3
" 1 + 10 '
or the magnitude is one-thousandth of the magnitude of the open-loop amplifier.
We shall return to the concept of sensitivity in subsequent chapters. These chap-
ters will emphasize the importance of sensitivity in the design and analysis of con-
trol systems. •

4.4 DISTURBANCE SIGNALS IN A FEEDBACK CONTROL SYSTEM

An important effect of feedback in a control system is the control and partial elimi-
nation of the effect of disturbance signals. A disturbance signal is an unwanted input
signal that affects the output signal. Many control systems are subject to extraneous
disturbance signals that cause the system to provide an inaccurate output. Electronic
amplifiers have inherent noise generated within the integrated circuits or transistors;