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Preface and acknowledgements xiii
One of the fundamental aims in preparing the text has been to work from basic
principles and to present control theory in a way that is e
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3
Time domain analysis
3.1 Introduction
The manner in which a dynamic system responds to an input, expressed as a function
of time, is called the time response. The theoretical
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System modelling 23
R
v1(t)
i(t)
v2(t)
C
Fig. 2.11 RC network.
or
C
dv2
i(t)
dt
(2:31)
substituting (2.31) into (2.30)
v1 (t) v2 (t) RC
d v2
dt
(2:32)
Equation (2.32) can be ex
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Introduction to control engineering 11
START
Define System
Performance
Specification
Identify System
Components
Model Behaviour
of Plant and
System
Components
Select
Alternative
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Time domain analysis 47
3.5.5
Ramp response of first-order systems
Example 3.6
Find an expression for the response of a first-order system to a ramp function of
slope Q.
Solutio
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Time domain analysis 59
Note that the second-order term in equation (3.76) has had the `square' completed
since its roots are complex (b2 < 4ac). Equate equations (3.75) and (3.
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Closed-loop control systems 107
Amplifier
i(s)
Actuator
2
5
s(1 + 0.5s)
+
o(t)
Sensor
3
Fig. 4.43 Block diagram of a servomechanism.
xv (t)
b
a
xi (t)
xo (t)
ab
ab
If the fo
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Closed-loop control systems 95
5. Tachogenerator
Gain H2 (V s/rad)
Feedback signal B2 (s) H2 so (s)
(4:108)
or, from equation (4.105)
B2 (s)
H2
sXo (s)
p
(4:109)
6. Position t
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Closed-loop control systems 83
When r2 (t) is a unit step, and r1 (t) is zero, the final value theorem (equation (3.10)
gives the steady-state response
K
c( t )
as t 3 I:
1 K1