Modern Control Engineering

852 Chapter 10 / Control Systems Design in State Space

x^1

0246810

t (sec)

0246810

t (sec)

0246810

t (sec)

0246810

t (sec)

0246810

t (sec)

−0.02

0

0.02

0.04

x^5

0

1

2

3

x^2

−0.05

0.05

0

0.1

0.15

x^3

−0.5

0.5

0

1

1.5

x^4

−0.2

0.2

0

0.4

0.6

Figure 10–55

Response curves to a

unit-step input.

Cart Position x 3 versus t

Cart Position

x^3

t (sec)

012345678910

1.2

1

0.8

0.6

0.4

0.2

0

Figure 10–56 −0.2

Cart position versus t

curve.

A–10–18. Consider the stability of a system with unstructured additive uncertainty as shown in Figure

10–57(a). Define

true plant dynamics

G=model of plant dynamics

¢a=unstructured additive uncertainty

G=

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