Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 5, Problem 24P
a.
To determine
The signal flow graph of the given system and represent the system in state space in phase variable form.
b.
To determine
The signal flow graph of the given system and represent the system in state space in cascade form.
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Example-1:
l
D
A uniform rotor of length 0.6 m and diameter 0.4 m is made of steel (density 7810 kg/m³)
is supported by identical short bearings of stiffness 1 MN/m in the horizontal and vertical
directions. If the distance between the bearings is 0.7 m, determine the natural frequencies
and plot whirl speed map.
Solution:
B
find the laplace transform for the
flowing function
2(1-e)
Ans. F(s)=-
S
12)
k
0
Ans. F(s)=
k
s(1+e)
0 a
2a 3a 4a
13)
2+
Ans. F(s)=
1
s(1+e")
3
14) f(t)=1, 0
Find the solution of the following Differential Equations
Using Laplace Transforms
1) 4y+2y=0.
y(0)=2.
y'(0)=0.
2) y+w²y=0,
(0)=A,
y'(0)=B.
3) +2y-8y 0.
y(0)=1.
y'(0)-8.
4)-2-3y=0,
y(0)=1.
y'(0)=7.
5) y-ky'=0,
y(0)=2,
y'(0)=k.
6) y+ky'-2k²y=0,
y(0)=2,
y'(0) = 2k.
7) '+4y=0,
y(0)=2.8
8) y+y=17 sin(21),
y(0)=-1.
9) y-y-6y=0,
y(0)=6,
y'(0)=13.
10) y=0.
y(0)=4,
y' (0)=0.
11) -4y+4y-0,
y(0)=2.1.
y'(0)=3.9
12) y+2y'+2y=0,
y(0)=1,
y'(0)=-3.
13) +7y+12y=21e".
y(0)=3.5.
y'(0)=-10.
14) "+9y=10e".
y(0)=0,
y'(0)=0.
15) +3y+2.25y=91' +64.
y(0)=1.
y'(0) = 31.5
16)
-6y+5y-29 cos(2t).
y(0)=3.2,
y'(0)=6.2
17) y+2y+2y=0,
y(0)=0.
y'(0)=1.
18) y+2y+17y=0,
y(0)=0.
y'(0)=12.
19) y"-4y+5y=0,
y(0)=1,
y'(0)=2.
20) 9y-6y+y=0,
(0)-3,
y'(0)=1.
21) -2y+10y=0,
y(0)=3,
y'(0)=3.
22) 4y-4y+37y=0,
y(0)=3.
y'(0)=1.5
23) 4y-8y+5y=0,
y(0)=0,
y'(0)=1.
24)
++1.25y-0,
y(0)=1,
y'(0)=-0.5
25) y 2 cos(r).
y(0)=2.
y'(0) = 0.
26)
-4y+3y-0,
y(0)=3,
y(0) 7.
27) y+2y+y=e
y(0)=0.
y'(0)=0.
28) y+2y-3y=10sinh(27),
y(0)=0.
y'(0)=4.
29)…
Chapter 5 Solutions
Control Systems Engineering
Ch. 5 - Prob. 1RQCh. 5 - Name three basic forms for interconnecting...Ch. 5 - For each of the forms in Question 2, state...Ch. 5 - Besides knowing the basic forms as discussed in...Ch. 5 - For a simple, second-order feedback control system...Ch. 5 - Prob. 6RQCh. 5 - Prob. 7RQCh. 5 - How are summing junctions shown on a signal-flow...Ch. 5 - If a forward path touched all closed loops, what...Ch. 5 - Name five representations of systems in state...
Ch. 5 - Prob. 11RQCh. 5 - Which form of the state-space representation leads...Ch. 5 - When the system matrix is diagonal, what...Ch. 5 - What terms lie along the diagonal for a system...Ch. 5 - Prob. 15RQCh. 5 - Prob. 16RQCh. 5 - For what kind of system would you use the observer...Ch. 5 - Describe state-vector transformations from the...Ch. 5 - Prob. 19RQCh. 5 - Prob. 20RQCh. 5 - Prob. 21RQCh. 5 - Find the closed-loop transfer function, T(s) =...Ch. 5 - Find the equivalent transfer function, T(s) =...Ch. 5 - Reduce the system shown in Figure P5.4 to a single...Ch. 5 - Reduce the block diagram shown in Figure P5.6 to a...Ch. 5 - Find the unity feedback system that is equivalent...Ch. 5 - 8. Given the block diagram of a system shown in...Ch. 5 - 9. Reduce the block diagram shown in Figure P5.9...Ch. 5 - Reduce the block diagram shown in Figure P5.10 to...Ch. 5 - 11. For the system shown in Figure P5.11, find the...Ch. 5 - 12. For the system shown in Figure P5.12, find the...Ch. 5 - Prob. 13PCh. 5 - For the system of Figure P5.14, find the value of...Ch. 5 - 15. For the system shown in Figure P5.15, find K...Ch. 5 - For the system of Figure P5.16, find the values of...Ch. 5 - Find the following for the system shown in Figure...Ch. 5 - 18. For the system shown in Figure P5.18, find ,...Ch. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - Find the transfer function G(s) = Eo(s)/T(s) for...Ch. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - State Space SS
24. Given the system below, draw a...Ch. 5 - Prob. 25PCh. 5 - Using Mason’s rule, find the transfer function,...Ch. 5 - Using Mason’s rule, find the transfer function,...Ch. 5 - Prob. 28PCh. 5 - Use block diagram reduction to find the transfer...Ch. 5 - State Space SS 30. Represent the following systems...Ch. 5 - Prob. 31PCh. 5 - State Space SS 32. Repeat Problem 31 and represent...Ch. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Repeat Problem 34 for the system shown in Figure...Ch. 5 - Prob. 37PCh. 5 - State Space SS 38. Consider the rotational...Ch. 5 - Prob. 40PCh. 5 - Prob. 41PCh. 5 - State Space SS
42. Consider the subsystems shown...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - State Space SS
45. Diagonalize the following...Ch. 5 - Prob. 46PCh. 5 - Prob. 48PCh. 5 - Prob. 51PCh. 5 - Figure P5.33 shows a noninverting operational...Ch. 5 - Figure P5.34 shows the diagram of au inverting...Ch. 5 - Prob. 54PCh. 5 - A car active suspension system adds an active...Ch. 5 - Prob. 58PCh. 5 - Prob. 60PCh. 5 - Some medical procedures require the insertion of a...Ch. 5 - Prob. 62PCh. 5 - Prob. 64PCh. 5 - Prob. 65PCh. 5 - The purpose of an Automatic Voltage Regulator is...Ch. 5 - 68. Integrated circuits are manufactured through a...Ch. 5 - Prob. 69PCh. 5 - Prob. 72PCh. 5 - Prob. 73PCh. 5 - Assume ideal operational amplifiers in the circuit...Ch. 5 - Parabolic trough collector. Effective controller...
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