Chap 2 of control system engineering .ppt

In Chapter 1 we discussed the analysis and design sequence that included obtaining the
system’s schematic and demonstrated this step for a position control system. To obtain a
schematic, the control systems engineer must often make many simplifying assumptions in
order to keep the ensuing model manageable and still approximate physical reality.
The next step is to develop mathematical models from schematics of physical
systems. We will discuss two methods: (1) transfer functions in the frequency domain
and (2) state equations in the time domain. These topics are covered in this chapter and in
Chapter 3,

1. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
3/e
Chapter 2: Modeling in the Frequency Domain
1
Figure 2.1
a. Block diagram
representation of a
system;
b. block diagram
representation
of an
interconnection
of subsystems

2. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
2
Table 2.1
Laplace transform
table

3. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
3
Table 2.2
Laplace
transform
theorems

4. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
4
Figure 2.2
Block diagram of
a transfer function

5. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
5
Table 2.3
Voltage-current, voltage-charge, and
impedance relationships for capacitors,
resistors, and inductors

6. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
6
Figure 2.3
RLC network

7. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
7
Figure 2.4
Block diagram
of series RLC
electrical network

8. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
8
Figure 2.5
Laplace-
transformed
network

9. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
9
Figure 2.6
a. Two-loop electrical
network;
b. transformed
two-loop
electrical
network;
c. block diagram

10. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
10
Figure 2.7
Block diagram of
the network of
Figure 2.6

11. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
11
Figure 2.8
Transformed
network ready
for nodal analysis

12. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
12
Figure 2.9
Three-loop
electrical network

13. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
13
c. inverting
operational amplifier
configured for transfer
function realization.
Typically, the amplifier
gain, A, is omitted.
Figure 2.10
a. Operational
amplifier;
b. schematic for an
inverting operational
amplifier;

14. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
14
Figure 2.11
Inverting
operational
amplifier circuit
for Example 2.14

15. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
15
Figure 2.12
General
noninverting
operational
amplifier
circuit

16. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
16
Figure 2.13
Noninverting
operational
amplifier
circuit for
Example 2.15

17. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
17
Figure 2.14
Electric circuit for
Skill-Assessment
Exercise 2.6

18. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
18
Table 2.4
Force-velocity,
force-
displacement, and
impedance
translational
relationships
for springs,
viscous dampers,
and mass

19. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
19
Figure 2.15
a. Mass, spring, and
damper system;
b. block diagram

20. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
20
Figure 2.16
a. Free-body diagram of mass,
spring, and damper system;
b. transformed free-body diagram

21. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
21
Figure 2.17
a. Two-degrees-of-
freedom translational
mechanical
system
8
;
b. block diagram

22. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
22
Figure 2.18
a. Forces on M
1 due
only to motion of M
1
b. forces on M
1
due
only to motion of M
2
c. all forces on M
1

23. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
23
Figure 2.19
a. Forces on M
2

due only to motion
of M
2
;
b. forces on M
2 due
only to motion
of M
1;
c. all forces on M
2

24. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
24
Figure 2.20
Three-degrees-of-freedom
translational
mechanical system

25. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
25
Figure 2.21
Translational
mechanical system
for Skill-Assessment
Exercise 2.8

26. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
26
Table 2.5
Torque-angular
velocity, torque-
angular
displacement,
and impedance
rotational
relationships for
springs, viscous
dampers, and
inertia

27. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
27
Figure 2.22
a. Physical system;
b. schematic; c. block diagram

28. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
28
Figure 2.23
a. Torques on J
1
due only to the
motion of J
1
b. torques on J
1
due only to the
motion of J
2
c. final free-body
diagram for J
1

29. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
29
Figure 2.24
a. Torques on J
2
due only to the
motion of J
2;
b. torques on J
2
due only to the
motion of J
1
c. final free-body
diagram for J
2

30. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
30
Figure 2.25
Three-degrees-of-
freedom rotational
system

31. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
31
Figure 2.26
Rotational mechanical
system for Skill-Assessment
Exercise 2.9

32. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
32
Figure 2.27
A gear system

33. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
33
Figure 2.28
Transfer functions for a. angular
displacement in lossless gears
and b. torque in lossless gears

34. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
34
Figure 2.29
a. Rotational
system driven
by gears;
b. equivalent
system at the
output after
reflection of input
torque;
c. equivalent
system at the input
after reflection of
impedances

35. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
35
Figure 2.30
a. Rotational mechanical system with gears;
b. system after reflection of torques and
impedances to the output shaft;
c. block diagram

36. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
36
Figure 2.31
Gear train

37. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
37
Figure 2.32
a. System using a gear train;
b. equivalent system at the input;
c. block diagram

38. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
3/e
Chapter 2: Modeling in the Frequency Domain
38
Figure 2.33
Rotational mechanical system
with gears for Skill-Assessment
Exercise 2.10

39. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
39
Figure 2.34
NASA flight
simulator
robot arm with
electromechanical
control system
components
© Debra Lex.

40. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
40
Figure 2.35
DC motor:
a. schematic
12
;
b. block diagram

41. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
41
Figure 2.36
Typical equivalent
mechanical loading
on a motor

42. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
42
Figure 2.37
DC motor driving a rotational
mechanical load

43. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
43
Figure 2.38
Torque-speed
curves with an
armature
voltage, e
a,
as a parameter

44. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
44
Figure 2.39
a. DC motor and
load;
b. torque-speed
curve;
c. block diagram

45. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
45
Figure 2.40
Electromechanical system for
Skill-Assessment Exercise 2.11

46. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
46
Figure 2.41
Development of
series analog:
a. mechanical
system;
b. desired electrical
representation;
c. series analog;
d. parameters for
series analog

47. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
47
Figure 2.42
Series analog of mechanical
system of Figure 2.17(a)

48. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
48
Figure 2.43
Development of
parallel analog:
a. mechanical
system;
b. desired
electrical
representation;
c. parallel analog;
d. parameters for
parallel analog

49. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
49
Figure 2.44
Parallel analog of
mechanical
system
of Figure 2.17(a)

50. ©2000, John Wiley & Sons, Inc.
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Chapter 2: Modeling in the Frequency Domain
50
Figure 2.45
a. Linear system;
b. nonlinear system

51. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
51
Figure 2.46
Some physical
nonlinearities

52. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
52
Figure 2.47
Linearization
about a point A

53. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
53
Figure 2.48
Linearization
of 5 cos x about
x = /2

54. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
54
Figure 2.49
Nonlinear
electrical
network

55. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
55
Figure 2.50
Nonlinear electric circuit for
Skill-Assessment Exercise 2.13

56. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
56
Table 2.6
Subsystems of the antenna azimuth
position control system

57. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
57
Figure 2.51
Cylinder model
of a
human leg
© 1996 McGraw-Hill, Inc.

58. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
58
Figure 2.52
Free-body
diagram of
leg model

59. ©2000, John Wiley & Sons, Inc.
Nise/Control Systems Engineering,
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Chapter 2: Modeling in the Frequency Domain
59
Figure 2.53
Nonlinear electric
circuit