Page 143 - MATLAB an introduction with applications

128 ——— MATLAB: An Introduction with Applications

3.8 ANALYSIS OF FEEDBACK

The most important features, the presence of feedback impacts to a system are the following:
(a) Increased accuracy: its ability to reproduce the input accurately
(b) Reduced sensitivity of the ratio of output to input for variations in system characteristics and
other parameters
(c) Reduced effects of non-linearities and distortion
(d) Increased bandwidth (bandwidth of a system that ranges frequencies (input) over which the
system will respond satisfactorily)
(e) Tendency towards oscillation or instability
(f ) Reduced effects of external disturbances or noise.
A system is said to be unstable, if its output is out of control. Feedback control systems may be classified
in a number of ways, depending upon the purpose of classification. For instance, according to the method
of analysis and design, control systems are classified as linear or non-linear, time-varying or time-variant
systems. According to the types of signals used in the system, they may be: continuous data and discrete-
data system or modulated and unmodulated systems.
Consider the simple feedback configuration shown in Fig. 3.12, where R is the input signal, C is the output
signal, E is error and B is feedback signal.
The parameters G and H are constant-gains. By simple algebraic manipulations, it can be shown that the
input-output relation of the system is given by
C G
M = =
R 1 GH
+
The general effect of feedback is that it may increase or decrease the gain G. In practical control systems,
G and H are functions of frequency, so the magnitude of (1 + GH) is greater than 1 in one frequency range,
but less than 1 in another. Thus, feedback affects the gain G of a non-feedback system by a factor (1 + GH).
+
+ +
R E G C
– B –
+ –

H

Fig. 3.12 Feedback system

If GH = –1, the output of the system is infinite for any finite input, such a state is called unstable system-
state. Alternatively, feedback stabilizes an unstable system and the sensitivity of a gain of the overall system
M to the variation in G is defined as:

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