现代控制理论第五章答案

第五章 习题答案

y(t)0.83sin(t25.26) 5-2 解: (1)

y(t)0.83sin(t4.76)1.64sin(2t35.54) (2)

39.295-3 解: ， kg20.82dB

5-4 解: 系统地传递函数为

100s210s100

G(s)5-5 解: (a)

6(s300)(s5)(s10) ， 91.35

G(s) (b)

0.1s0.02s1 ， 258.7

G(s) (c)

32s(0.5s1) ， 14.04

G(s) (d)

G(s)25s(100s1)(0.1s1)， 1.71

(e)

G(s)0.5(2s1)s2(0.5s1) ， 36.86

(f)

G(s)31.620.01s20.116s1 ， 5-6 解: (1) k=1 (2) k=25

5-7解: (a).N=1，Z=0 稳定 (c).N=1，Z=0 稳定 (e).N=0，P=0， Z=0 稳定 (g).N=-2，P=0，Z=2 不稳定 (i).N= -2， P=1 ，Z=3 不稳定

(b).N=-1， Z=1 不稳定

， P=0， Z=0 稳定

(f).N= -1 ，P=1 ，Z=2 不稳定

(h).N=0 ，P=0， Z=0 稳定

(d).N=0

5-8 解: 0k10,25k10000时，系统稳定

10k25,k10000时，系统不稳定

21114k225-9 解:（1）

114k2(114kcos(（2） w=2.1642 ，k=5.156

5-10解: (1) 39.29 ， kg20.82dB

(2) k=1.69

(3) k=12.1

5-11解: 0.1

5-12解: (1)

(s)14125s210340s10000

(2)

Mp15% ts0.058~0.077s

5-13解: (1)k=0.74 (2)k=1.1 (3)k=0.511

2k)

5-14 解: 当K>1时，奈氏图如图所示，P=1，N=1，Z=0系统稳定

5-15 解: (1)

(2)

Nyquist Diagram10.80.60.4six0.2A yra0nigam-0.2I-0.4-0.6-0.8-1-3-2.5-2-1.5-1-0.500.5Real Axis

Nyquist Diagram201510s5ixA yar0ginamI-5-10-15-20-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10Real Axis

Nyquist Diagram5432six1A yra0nigam-1I-2-3-4-5-2-1.5-1-0.500.511.52Real AxisBode DiagramGm = -5.34 dB (at 1.44 rad/sec) , Pm = 28.6 deg (at 1.84 rad/sec)100B)d( e-10duting-20aM-30-40270)ge180d( esahP90010-1100101102Frequency (rad/sec)

5-16

5-17

Bode Diagram20 Magnitude (dB)Phase (deg)0-20-40-60 0-45-90-135-18010-110010Frequency (rad/sec)1102

5-18

(1)

Nyquist Diagram0.80.60.40.20-0.2-0.4-0.6-0.8-1Imaginary Axis-0.8-0.6-0.4-0.20Real Axis0.20.40.60.81

Bode Diagram0Magnitude (dB)Phase (deg)-50-100-1500-90-180-27010-210-1100101102103Frequency (rad/sec)

(2) 幅值裕量G =19.8168，相角裕量P = Inf，相位穿越频率wg =5.6578，开环剪切频率wc = NaN

5-19当K=10.428时，相角裕量P = 300

Bode DiagramGm = 3.86 dB (at 3.17 rad/sec) , Pm = 30 deg (at 2.87 rad/sec)50Magnitude (dB)Phase (deg)0-50-1000-90-180-27010-110010Frequency (rad/sec)1102

5-20（1）当K=5时，bode图如图所示

Bode DiagramGm = 11 dB (at 0.834 rad/sec) , Pm = 64.9 deg (at 0.211 rad/sec)50Magnitude (dB)Phase (deg)0-50-100-150270180900-9010-210-1100101102Frequency (rad/sec)