自動控制原理考試試題第五章習題及答案-2

1、.第五章 線性系統(tǒng)的頻域分析與校正練習題及答案2 ( )、和G s G (s) G (s)312G (s)G (s)2G s ( )11G (s)G (s)423L ( ) 20lg1K 1K 1801G s K( )11KsG s ( )22s(8K2120lgK / 20lg0 , K 122L 3KK( ) 20lg020lg331K 9 , G (s) K s 9s0.111333GG1G (s) 21G G42318將G G G, , 代入得：G (s)s(0.125s4123. 解 題號備注P000NK123202123K12KG(s) s2(Ts.400012122K567G(s

2、)000200G(s)12G(s)056s(TsTsTsTs1234K8911100121KKG(s) s(Ts KG(s) ；(K,T ss2KT K10T , K T2KK T) jT )解 G(j )X( ) Y( ) T)2 2j j jT )21令 ) 0 Y X( )TKT1X() 11TT1或TK 132；2110；9 , K T 10(s22sG(s) (s2)(s.解 ( )G jG(j0)50180G(j)100G(j )210(5 j2 )G(j )(2 j )(0.5 j )222210 )3 j (5.53.5 )222 ) ) 令 ( )G j 0 / 0Re G(

3、j ) 4.03701Z P2N 12()22 1s3G s ( ), H(s)ss)2(s2s2解 G s G s H s ( )( ) ( )(s40.G(j 00G(j0 ) 01800G(j) 01800大致畫出G j( )G (j )00Z P N 20 2 0 0000P Z 00 Z P2N Z 2 02( 2N1 10G(s)s(0.2s 0.8s2解 210100.8 j0.2 )G(j ) 22j j0.2 j ) 0.04 )G(j )G(j 270G(j) G(j0 )limRe ( ) 8G j0 ( )T 0.2G j1T 1 ( )21Z P2N 12() 22.

4、 G(s) s2s(s 4G(j )0解 的G(j0) 0 90G(j0 )G(j2 ) 153.4 333.4G(j2 )G(j) ( )G jZ P2N 02( 2 .100G s ( )s(0.2s50G s ( )(0.2ss2)(s10G s ( )s(s25ss100( 2G(s)sss(s 10 20100100解 G s ( )s(0.2sss( 5 5 Cg180 G(j ) 180 90 tg 2 12.600010C1hG( )g 5050G s ( )(0.2ss2)(sss( ( 2s52. 6由Bode圖得：c50G(j )16.3 cc5 2cc1110G(j )

5、 2 3.7gg52gggC5C2001110 G(j )180 tgtgtg 2 29.4C( ) 1 ( ) 1 (2 ) 1g2g22152gh0.391G( )50g 1025s10G s ( )sss(ss( ( 104 410 6.325 410 6.325 00Cg1h. s100( 2sss(s 1020cg 180 ( ) 24.8ch 0.343 9.3(dB) as1G(s) s2 1(a )2G(j )( a )解1021a22( )A1c2ca2142cc. 0( ) 0c 180 45 180 1350( ) tg a100cca 1c a 0.84。，c 10G

6、s ( ) , H(s) 1 K ss(sh。Kh解 K s)G(s)H(s) hs(s10(K j hG(j )H(j ) j (j ) 90 180 tg tg K 18000110cchc1 90tgtg K10chc K cch 1 Kchc10K 2hc.1K h2c c 0.1KhK j ) G(j )H(j ) ) )hu j (j 2 K )10(Ku( ) ; v( ) hh ( 2(20令 v( ), 則10(K 01 K22hh1Kh K )u() 1h ( 21K ) (Khh10K 9 10K2hh9 1K K ,K 110hhh 10故當K 110hKes G s

7、( )s1K解G j ( )ej1 KG j ( )121 ( ) 0.8tg ( )ej11 K即G j ( )112 tg1( ) ( ) . G j 0 8. tg1 tg(tg ) tg( . ) tg .08 081 tgK :11(0.8)2 K 1tg(0.8 ) sec0.82 2.45 , K 2.65c s5s e2G(s) (s4 2解 令G(j ) 1 )2 2180 G(j ) 18004tg1800 1 52 618,0.61812 180360 4tg10 （3）10G(s) ss(0.1. ( ) 90arctanarctan0.120 0.1 1c 180 )

8、 2.85c100G(s)ss(s(200 101c 180 ) 2.85 111=o 0.160.4(1)osin1ooKKt 0.1t00s1c1 3， 0.7 nc度 。解 322ns1)n4.2 )L 2.143c 180 ( ) 63c t 3s解 。s2G(s) nn. oe2 ooot 3 3.5 sn 0.517有 2.257n2s(s22.257)G(s) ss(1) )L 2.1824c 180 ( ) 46.9c 16.7sG s ( )(0.8s25s0625s解 111 , 1625 ,40.82506251230.01 0.05 0.1 0.3 0.6-15 -2

9、13 19 24 1588 85 83 70 54 -23 -94 -127 -143 -151 -156 -160 -163 -164 -166-15 -4.5 -2 -.75 -0.6 -0.5 1.8 4.3 2.3 -3.4 -7.5 -11 -16 -20310 20 30 40 50 60 70 80 100472-3 -7 -10 -13 -16 -200M (db)0 ( )6948 30 125-1 -11 -28 -53 -110 -140 -152 -158 -162 -1650. s)4.8s12s )20 。ts c圖5-83 某控制系統(tǒng)結構圖 rcs)解 G(s)

10、G (sG (s) s12s8s )2020lg 33.6 201 80.125 ,1 ,123 650 6,c6.6 得 % 21%, t 秒SC ,MrC當 ( 1M 1.103, (r 65 ),sinrCr.6.8 得 % 21%, t秒SC 123543506789 0 令0M 1M 173 或10M 1.05(dB)0rr3ff f f a,2224b6afM( )a41N M0f M7 1.13 1F f Mar6041Ln()17%2.16F 0.40.6秒t Sfa 2sint rt)c (t) 4sin(t 45) , 。sn解 2(s) n s 22s2nn42( 22令

11、n 2( ) 422 22nn ( n12n1.244， 0.22。n t 0.05 ss ,oo.解 1 0.160.4(1)osinoKt s0c11K 2 2sinsin0110.16)11.5o0.4o K 3.3750K0 (rad/s)tcs ， 212.1。c 解 1ss 5(s(s)1.256.250.5G(s) 1(s) s(s2.825)(ssss(2.8254.425。K11 ( ) 1112.825 4.425有tg601.732112.521 4.186 12.5 0211 2.02 K11 K K 2.02 0.5 。1. KG(s) s(0.2s0.5s2(r/m

12、in) 2o0.4s1G (s) 08s1c解 C 2e 20 的K, , h:0MaxCK K 6eVss6G(s) s(0.2ss2 6 c 2 5 8oocc 3.2g20lgh dB)6(0.4sG (s)G(s) s(0.08s0.2s0.5sc6 2.562， c2c 4 2 08 5 22.5oocccc. 2.371 20lg 7.5h dBh 7.3,，。g KG(s)s(se 115；ss c 1KssvK c 180( ) 180 90 arctanG j000cc90 arctan3.87314.4800定7.5cb48dB (AB 5dB) 5, 2DDC CE Es

13、12G (s) cs128.125 7.5mcs12G (s)G(s) s( s sc111e K ssv.7.5(rad/)c ( ( GG0cccc180 90 arctg 67.732 450arctgarctg00c02c KG(s) s(s25s vK解G(s)ss(s 4取K K 5v 5 c ( ) 5.12180c 5 c取 0.8(0.8) 40.03(0.8) 1取 0.5 56.3(0.5) 1802取 0.6(0.6) (0.6) 50.573取 0.6c 3 c過D 0.10.06)0.6作DDc (E Ess11sG (s) Dsc11Es0.06 G (s)G(s

14、) csss(s 40.0072. 180G (j ) ( ) 45.56 45G jccc 40G(s) s(0.2s0625s4040解G s ( )sss(0.2s0625ss( ( 165 ,5 14.14cc1690 arctg arctg 00c5 ( ) 00000m 14.1416cc . 5 00 2.4 (2.4)830 取 2.4c G ) c 2.4在 2.4 =0.2420/c24到E： 015E16s10.24s G (s)c10.015 s s s sG (s)G(s) cs 5 2.42.452.4162.490 arctanarctanarctanarctan

15、00.240.015 8 0.0000008.6g 4035.88.61.991.29573.33h 20lgGG 20lg18.9dB30dBcggh減40dB( 處的920lgG( 40cgc. 4040L 20clg40lg lg1 c , 0.4 2 cc0.450.4(0.4) 90 arctanarctan8400160.7 28 340 c 000以20 / 0.0028dB decEs128G (s) sc10.40.4 34.5900.28c在0.4142.86 scL 20lgG lgc 38.27c4010.28G (sG(s) cs s s0.0028s 516驗算：

16、6g40738.6995h 20lgG G( ) 70.4cg0.40.450.4180 G G(0.4) 180 90 arctanarctanarctanarctan0000.28160.0028c 4.57 6 000000 s1s128G (s) ss 1c1 KG(s) s(s25s. vc 2解 在 2，K K 5cv24 G(j ) 180 arctan2 arctan90 0 180 c 5 4505 50m 8， 10lg aa c過 2作 、C GDE、F 252 2.5*c22 0.1 0.1 2 0.2 Ec0.67 0.22.5 DFE* 3 6Gcss10.2 0.

17、67有G (s)c ss 10.0536 6 ss10.2 0.67G (sG(s) cs ss s(s 11 14 0.0536 6 180G (j) ( )G jccc.22226arctan 48.87 45arctanarctanarctan0.20.670.0536 c0 和 LL0C ( )G sC解 20G (s) s0s( 10 10 c014.14 180 ( ) 18090arctan35.261000c0s1G (s)c(a)10s1.20(sG(s) G (s)G (s) ssc(a)0s( ( 100.11有， 2ca0.1ca 180 ( ) 55aa 35.2655 ooa0 214.14c0高頻段被壓低 s110sG (s) c(b)1100s1202010sG