PDF《《自动控制原理》 自动控制原理》部分习题解答》

1 ) eg

1 )( bc a ( ade bcde ) s ( R ) s ( C

1 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + = = = = adeh cefg bcdeh eg cf

1 leha lehbc ) cf

1 ( le ) s ( R ) s ( C

2 + + + + + + + + + + + + + + + + + + + + ? ? ? ? ? ? ? ? + + + + = = = = (f) fg deg f

1 ) ci cfdej cfdh ( ) i deg b bdej bdh ( ] aegi aej ) fg

1 ( ah [ ) s ( R ) s ( C

1 ? ? ? ? ? ? ? ? + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ? ? ? ? = = = = fg deg f

1 fj i fdej fdh ) s ( R ) s ( C

2 ? ? ? ? ? ? ? ? + + + + + + + + + + + + = = = = fg deg f

1 egi ej ) fg

1 ( h ) s ( R ) s ( C

3 ? ? ? ? ? ? ? ? + + + + + + + + ? ? ? ? = = = = ( ( ( (3-1题题题题~3-9题题题题) ) ) ) 3-1 T t e

1 ) t ( h T T ? ? ? ? τ τ τ τ ? ? ? ? ? ? ? ? = = = = 3-2 (1)

10 ) t ( k = = = = t

10 ) t ( h = = = = 3-2 (2) t

4 sin e

4 25 ) t ( k t

3 ? ? ? ? = = = = )

13 .

53 t

4 sin( e

4 5

1 ) t ( h o t

3 + + + + ? ? ? ? = = = = ? ? ? ? 3-3 (1)

25 .

1 s

0125 .

0 ) s ( + + + + = = = = Φ Φ Φ Φ (2)

16 s )

4 s (

50 s

5 ) s (

2 2 + + + + + + + + + + + + = = = = Φ Φ Φ Φ (3) )

1 s

3 ( s

1 .

0 ) s ( + + + + = = = = Φ Φ Φ Φ 3-4 s

917 .

2 t s

96 .

1 t %

478 .

9 %

2 6 .

0 s p n = = = = = = = = = = = = = = = = = = = = σ σ σ σ ω ω ω ω ξ ξ ξ ξ 3-5

686 .

1 5 .

2 z

5 .

0 1

0066 .

1 r

2 d n ? ? ? ? = = = = = = = = = = = = = = = = = = = = = = = = ψ ψ ψ ψ β β β β ξ ξ ξ ξ ω ω ω ω π π π π %

99 .

17 % s

0133 .

6 t s

156 .

3 t s

45 .

1 t s p r = = = = = = = = = = = = = = = = σ σ σ σ 3-6

5 .

24 43 .

1 n = = = = = = = = ω ω ω ω ξ ξ ξ ξ 3-7

311 .

0 k

44 .

1 k

2 1 = = = = = = = = 3-8 (a)

1 0 n = = = = = = = = ω ω ω ω ξ ξ ξ ξ 系统临界稳定 系统临界稳定 系统临界稳定 系统临界稳定 (b) s

51 .

7 t %

8 .

29 %

1 5 .

0 1 s s

1 s ) s ( s n

2 = = = = = = = = = = = = = = = = + + + + + + + + + + + + = = = = σ σ σ σ ω ω ω ω ξ ξ ξ ξ Φ Φ Φ Φ (c) s

08 .

8 t %

3 .

16 %

1 5 .

0 1 s s

1 ) s ( s n

2 = = = = = = = = = = = = = = = = + + + + + + + + = = = = σ σ σ σ ω ω ω ω ξ ξ ξ ξ Φ Φ Φ Φ (b)比比比比(c)多一个零点 多一个零点 多一个零点 多一个零点,附加零点有削弱阻尼的作 附加零点有削弱阻尼的作 附加零点有削弱阻尼的作 附加零点有削弱阻尼的作 用用用用. . . . 3-9 (1)

2 .

0 e s

5 .

3 t %

09 .

35 %

10 10

1 5 k )

1 s

5 .

0 ( s

5 ) s ( G ss s n = = = = = = = = = = = = = = = = = = = = = = = = + + + + = = = = σ σ σ σ ω ω ω ω ξ ξ ξ ξ (2)

249 .

1 1 r

10 z

10 10

1 10 k )

1 s ( s )

1 s

1 .

0 (

10 ) s ( G d n = = = = = = = = = = = = = = = = = = = = = = = = + + + + + + + + = = = = β β β β ω ω ω ω ξ ξ ξ ξ

1 .

0 e s

3 t %

06 .

37 %

2 ss s = = = = = = = = = = = = ? ? ? ? = = = = σ σ σ σ π π π π ψ ψ ψ ψ ( ( ( (3-11题题题题~3-20题题题题) ) ) ) 3-11 劳斯表变号两次 劳斯表变号两次 劳斯表变号两次 劳斯表变号两次, , , ,有两个特征根在 有两个特征根在 有两个特征根在 有两个特征根在s右半平面 右半平面 右半平面 右半平面,系统不稳定 系统不稳定 系统不稳定 系统不稳定. . . . 3-12 (1) 有一对纯虚 有一对纯虚 有一对纯虚 有一对纯虚 根根根根: : : :

2 j s

2 ,

1 ± ± ± ± = = = = 系统不稳 系统不稳 系统不稳 系统不稳 定定定定. . . . (2)