Modern Control Engineering

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250 Chapter 5 / Transient and Steady-State Response Analyses

A–5–16. Consider the system subjected to the initial condition as given below.

(There is no input or forcing function in this system.) Obtain the response y(t) versus t to the

given initial condition by use of Equations (5–58) and (5–60).

y=[1 0 0]C

x 1

x 2

x 3

S

C

x

1

x

2

x

3

S = C

0 1 0

0 0 1

- 10 - 17 - 8

SC

x 1

x 2

x 3

S, C

x 1 ( 0 )

x 2 ( 0 )

x 3 ( 0 )

S = C

2

1

0.5

S

(a)

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2 4 6 8 10 12

Outputs

t Sec

= 0= 0

0 0.2. 2

0 0.4. 4

0 0.6. 6

0 0.8. 8

1 1.0. 0

Unit-Step Response Curves

Three-Dimensional Plot of Unit-Step Response Curves using Command “mesh(y)”

800

60

40

20

0 1 2

3

4

5

6

0.5

1

1.5

2

Outputs

Computation Time Points n, where n = 1, 2, 3, 4, 5, 6

(b)

(^06)
5
4
3
2
1 0 10
20 30
40 50
60 70
0.5
1
1.5
2
Outputs
Three-Dimensional Plot of Unit-Step Response Curves using Command “mesh(y transpose)”
n, where n = 1, 2, 3, 4, 5, 6 Computation Time Points
(c)
Figure 5–64
(a) Two-dimensional
plot of unit-step
response curves;
(b) three-dimensional
plot of unit-step
response curves
using command
“mesh(y)”;
(c) three-dimensional
plot of unit-step
response curves
using command
“mesh(y¿)”.
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