자동제어 8판 솔루션 (Automatic Control Systems , Wiley , 8e)

Chapter 2 MATHEMATICAL FOUNDATION
2-1 (a)
Poles: s = 0, 0, Zeros: s =

?1, ?10;

(b)

Poles: s =

?2, ?2; ?1 cancel each other.

?2, ∞, ∞, ∞.

Zeros: s = 0. The pole and zero at s =

(c)

Poles: s = 0,

?1 + j, ?1 ? j; ?2.

(d)

Poles: s = 0,

?1, ?2, ∞.

Zeros: s =

2-2 (a) G (s) = (d)
G ( s)

(b) 5

(c) G ( s) = (e)

( s + 5)
1 s
2

2

(s
=

4s
2

+4
∞

)

+

1 s+ 2

G (s)

=

4 s
2

+ 4s +8

=

+4

G (s)

∑e
k =0

kT ( s + 5 )

=
1

1

?e

?T ( s+5 )

2-3 (a)
g ( t ) = u s ( t ) ? 2u s (t ? 1) + 2 u s( t ? 2) ? 2 u s ( t ? 3) + L G (s ) = 1 s

(1 ? 2e ? s + 2e?2 s ? 2e ?3s + L ) =
1 s

s 1+ e

(

1?e

?s ?s

)

gT (t ) = u s (t ) ? 2us ( ? 1) + us (t ? 2) t GT (s ) =

0≤ t ≤ 2
2

(1 ? 2e ? s + e ?2s ) = ( 1 ? e ? s )
1 s

1

g(t )

=

∑
k =0

∞

g

T

(t

? 2k )us (t ? 2k )

G (s)

=

∑s
k =0

∞

1 (1

?e

?s

) e

2

?2 ks