Feedback Characteristics of Control Systems
Unit1
• Introduction to control system
• Mathematical models of physical systems
• Block diagram, Signal flow graph,
• Feedback Control system characteristics, reduction of
parameter variations, control over system dynamics and
disturbance signals
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Introduction
• A non feed back system
• No provision within the system for supervision of output
• No mechanism for correcting the system behavior
– For any lack of proper performance of system components
– Changing environment
– Ignorance of the exact value of process parameters
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Feed back system( closed loop)
• Input signal
• Feedback signal derived from the output of the system
• Feedback signal acts as self correcting mechanism
• High loop gain
• Improves the speed of the response
• Disadvantages
– Greater system complexity
– System instability
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Reduction of parameter variations
by the use of feedback
• Feedback in control system reduces the sensitivity of the
system to parameter variations
• Parameter of the system may vary
– With age
– Changing environment
• Sensitivity is a measure of the effectiveness of feedback in
reducing the influence of these variations on system
performance.
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Parameter variations effect on open loop and closed
loop system
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Parameter variations effect on open loop and closed
loop system
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Parameter variations effect on open loop and closed
loop system
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Sensitivity
• Sensitivity is used to describe the relative variation in the
overall transfer function
• T(s)= C(s)/R(s)
%changeinT ( s )
Sensitivity
%changeinG( s)
• A small incremental variation in G(s) the sensitivity is written
in quantitative form T T / T LnT
SG
G / G LnG
T
• Where S G denotes the sensitivity of T with respect to G
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Sensitivity
• Sensitivity is used to describe the relative variation in the
overall transfer function
• T(s)= C(s)/R(s)
%changeinT ( s )
Sensitivity
%changeinG( s)
• A small incremental variation in G(s) the sensitivity is written
in quantitative form T T / T LnT
SG
G / G LnG
T
• Where S G denotes the sensitivity of T with respect to G
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Sensitivity of open loop system
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Sensitivity of closed loop system
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Sensitivity of closed loop system
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Effect of feedback on time constant of a control
system
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Effect of feedback on time
constant of a control system
• For open loop system the response is an exponent decay with
a time constant of T= 1/α
• For positive values of k the effect of feedback is to shift the
pole negatively to s= -(α+k)
• So system dynamics becomes faster
• The speed of response of closed loop is faster compared to
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open loop
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Effect of feedback on time
constant of a control system
• The time constant of the closed loop system is less than the
open loop system
• Less the time constant faster is the response.
• The feedback improves the response of the system
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Effect of feedback on overall gain
• Open loop system with overall transfer function G(s) or overall
gain of the system is G(s)
• If feed back with transfer function H(s) is introduced then
overall gain becomes G (s)
1 G (s) H (s)
• For negative feedback the gain is reduced by a factor
1
1 G (s) H (s) 21
• The overall gain of the system reduces with negative feedback
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Effect of feedback on bandwidth
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Effect of feedback on bandwidth
• A large bandwidth means the system responds accurately to
higher frequencies
• More bandwidth means increased speed of response
• Closed loop system bandwidth is 1+K times the bandwidth of
open loop system
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Effect of feedback on stability
• Feedback reduces the time constant and makes the system
response more fast
• Transient response decays more quickly
• For open loop system overall transfer function is G(s)=k/s+α
• Pole is s=-α
• With negative feed back G(s)= k/s+α+k
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• Pole is s=-(α+ k)
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Effect of feedback on stability
• The stability depends on the location of the pole on ‘s’ plane
• Feedback affects the stability of the system
• It may improve the stability or may be harmful to the system
in stability point of view.
• The stability of the system can be controlled by proper design
and application of the feedback
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Linearzing effect of feedback
• Let a forward block gain function is nonlinear expression
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Linearzing effect of feedback
• The input –output relation is approximately linear over a
much wider range for the closed loop system compared to
open loop behavior
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Regenerative feedback
• Regenerative feedback means feedback with positive sign
• Negative feedback is degenerative feedback
C (s) G(s)
R( s) 1 G ( s) H ( s)
• The possibility of denominator equal to zero
• Which results in an ∞ output
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• For finite input this is a condition of instability
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Regenerative feedback
Regenerative feedback is sometimes used for increasing the
loop gain of feedback systems
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Regenerative feedback
• The high loop gain provided by the inner regenerative
feedback loop the closed loop transfer function becomes
insensitive to G(s)
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Effect of feed back on disturbance
• Every control system has some non linearity's present in it which affects the output
of the system adversely
– Friction
– Dead zone
– Saturation etc
– Some external disturbance signal also make the system output inaccurate
• High frequency noise in electronic application
• Thermal noise in amplifier tubes
• Wind guests on antenna of radar systems etc
– The disturbance can be in
• Forward path 31
• Feedback path
• Output of a system
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Disturbance in forward path
• Assume a disturbance in the forward path of the control
system due to surrounding conditions
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Disturbance in forward path
• Assume a disturbance in the forward path of the control
system due to surrounding conditions
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Disturbance in forward path
• Assume a disturbance in the forward path of the control
system due to surrounding conditions
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Disturbance in forward path
Td
c( s )
G1 H
To make the effect of disturbance on the output as small as
possible G1(s) should be selected as large as possible
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Disturbance on feedback path
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Disturbance on feedback path
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Disturbance in output
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Disturbance in feedback path
Designing proper feedback element H1(s) the effect of
disturbance in feedback path on output can be reduced
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Disturbance in output
If disturbance is affecting the output directly then by
changing the values of G,H or both the effect of disturbance
can be minimized.
Feedback minimizes the effect of disturbance signals in the control system
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Consider a feedback control system given below. Evaluvate
the sensitivity of the transfer function T(s)= c(s)/r(s) to the
variations in parameter K
Take the values for ω= 5, K= 1
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