PDF《《自动控制原理》 自动控制原理》部分习题解答》

5 s

1 s

1 s

2 j s

6 5

4 ,

3 2 ,

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5 j s

2 ,

1 ± ± ± ± = = = = 系统不稳 系统不稳 系统不稳 系统不稳 定定定定. . . . 3-13

7 .

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3-14

0 0 ≠ ≠ ≠ ≠ τ τ τ τ >

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τ τ τ τ 3-15 (1) ∞ ∞ ∞ ∞ = = = = ∞ ∞ ∞ ∞ = = = = = = = = ss ss e e

20 k (2) ∞ ∞ ∞ ∞ = = = = = = = = = = = = ss ss e

2 .

0 e

10 k (3)

20 e

0 e

1 .

0 k ss ss = = = = = = = = = = = = 3-16 (1) (3) (2)

0 k

0 k

50 k a v p = = = = = = = = = = = =

0 k

200 k k k a v p = = = = = = = = ∞ ∞ ∞ ∞ = = = =

1 k k k a v p = = = = ∞ ∞ ∞ ∞ = = = = ∞ ∞ ∞ ∞ = = = = 3-18 (1) (2) (3)

0 essr = = = =

0 e

1 ssn = = = =

0 e

2 ssn = = = = 3-20 k1 )

1 s T ( s k

1 2 + + + +

1 s T

1 2 + + + + R u B C E(s)=R(s)-C(s) 由题意 由题意 由题意 由题意 得得得得: : : :

2 1

2 2

1 1

2 o

2 T T k T T k ) T ( k

1 + + + + <

<

<

<

≤ ≤ ≤ ≤ + + + + ε ε ε ε ( ( ( (4-4题题题题~4-5 题题题题) ) ) ) -0.88

10 j

7 = k -0.293 -1.707 -0.9 -4.236 o p

135 ± = θ θ θ θ o p

0 = θ θ θ θ ( ( ( (4-20题题题题~4-21题题题题) ) ) ) 主导极点离虚轴太 主导极点离虚轴太 主导极点离虚轴太 主导极点离虚轴太 近近近近! ! ! ! 主导极点离虚轴太 主导极点离虚轴太 主导极点离虚轴太 主导极点离虚轴太 近近近近! ! ! ! ]

6 )

24 .

3 )[(

3 .

23 ( )

20 (

10 ) (

2 2

1 + + + + + + + + + + + + + + + + = = = = ′ ′ ′ ′ s s s s k s G t ]

6 )

24 .

3 )[(

3 .

23 ( )

20 (

10 ) (

2 2

2 2 + + + + + + + + + + + + + + + + = = = = ′ ′ ′ ′ s s s s k s G t ]

6 )

24 .

3 )[(

3 .

23 (

10 ) (

2 2

2 3 + + + + + + + + + + + + = = = = ′ ′ ′ ′ s s s k s G t

2 = = = = ω ω ω ω

1 k= = = =

0 >

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>

τ τ τ τ τ τ τ τ >

>

>

>

T 5-6

0 j

0 j

0 j

0 j

0 j

0 j

1 = = = = v

2 = = = = v

3 = = = = v

4 = = = = v 5-7 )

1 s

20 ( s )

1 s

05 .

0 (

10 ) s ( G + + + + + + + + ? ? ? ? = = = = 5-8 o

4 .

153 9 .

17 )

5 .

0 j ( G ? ? ? ? ∠ ∠ ∠ ∠ = = = = o

53 .

327 383 .

0 )

2 j ( G ? ? ? ? ∠ ∠ ∠ ∠ = = = =

6 1 ? ? ? ? ( ( ( (5-9题题题题~5-13 题题题题) ) ) ) j -10 ? ? ? ? = = = = ω ω ω ω

2 + + + + = = = = ω ω ω ω

2 0 o

90 )

0 j ( G ? ? ? ? ∞∠ ∞∠ ∞∠ ∞∠ = = = = + + + + o

4 .

153 )

2 j ( G ? ? ? ? ∞∠ ∞∠ ∞∠ ∞∠ = = = = ? ? ? ? o

4 .

333 )

2 j ( G ? ? ? ? ∞∠ ∞∠ ∞∠ ∞∠ = = = = + + + + o

360 0 ) j ( G ? ? ? ? ∠ ∠ ∠ ∠ = = = = ∞ ∞ ∞ ∞ 5-9 -10 ? ? ? ? = = = = ω ω ω ω

2 + + + + = = = = ω ω ω ω

2 0 -10 ? ? ? ? = = = = ω ω ω ω

2 + + + + = = = = ω ω ω ω

2 0 o

90 )

0 j ( G ? ? ? ? ∞∠ ∞∠ ∞∠ ∞∠ = = = = + + + + o

4 .

153 )

2 j ( G ? ? ? ? ∞∠ ∞∠ ∞∠ ∞∠ = = = = ? ? ? ? o

4 .

333 )

2 j ( G ? ? ? ? ∞∠ ∞∠ ∞∠ ∞∠ = = = = + + + + o

360 0 ) j ( G ? ? ? ? ∠ ∠ ∠ ∠ = = = = ∞ ∞ ∞ ∞ 5-9 5-11 (1)

02 .