西安科技大学自动控制原理教学同步教程-第五章课件

1、主要内容：（1）介绍频率特性的基本概念和开环频率特性曲线的绘制方法。（2）研究频率域稳定判据、频率性能指标的估算、频率特性与稳态响应及暂态响应之间的关系。)()()()()()(21npspspssNsDsNsG)(sNtRtrsin)()()(22jsjsRsRsR)()()()()(21jsjsRpspspssNsCnnjjjpsAjsAjsAsC1)(tpnjjtjtjjeAeAAetc1)()(tc)(sC)(sR)(tcss)(sG)(tcjpttjtjeAAetc)(jRjGjsjsjsRsGAjs2)()()()(jRjGjsjsjsRsGAjs2)()()()(tjtjejRj

2、GejRjGtc2)(2)()()(sGs)(jG)(jG )(jG)()()(jeGjG)()(jGG)()(jGj)(jG )()()(jeGjG)(sin)(2)()()()(tCjeeRGtctjtjRGC)()(joRe)()(jeCtRtrsin)()(sin)()(tCtcjojjeCeGjGRe)()()()()()(sGsjnnnmmmjsajajabjbjbsGjG110110)()()()()()()(jGjs )(jGnnnmmmajajabjbjbjRjCjG110110)()()()()()()(d)()(21d)(21)(tjtjejRjGejctc)(jG)(j

3、G)(jR)(tc)(jG)(tc)(jC)(jRjs)(jG)()()()()(jVUeGjGj)()(jGG)()(22VU)()(arctan)()(UVjG)(cos)()(Re)(GjGU)(sin)()(Im)(GjGV)(G)(U)()(V)(jG)(jG)(G)()(jG)(lg20G)(o)(lg20G)(oCiuou图5-2 RC滤波网络R11)()()(TssRsCsG22)arctan(2)(1)(111)(111)(TTjTeTTjjGTj100jVUa )极坐标图T01. 0T1T10020020400450900b)rad/s(对数坐标图20lgG() (dB)(

4、)40040018000180）（c)20lgG() (dB)对数幅相图 从图中可以直观的看出该电路传递不同频率正弦信号的能力，这就是频率特性图的优越性。对于复杂系统，这一优越性尤其明显。在以上三种频率特性图中，幅相频率特性图和对数坐标图是应用最广泛的。)(GKsG)(0)(jKKejGjoKG)(o0)()0,(jKKGlg20)(lg20Klg20o0)(ssG1)(11)(90jejGoj1)(Go90)()(G)()(Glg20)(lg20G0)(lg20GdecdB20o90)(090)(G)(Glg20)(lg20G0)(lg20GssG)(jejGoj90)()(Go90)()(

5、decdB20o90)(o9011)(TssG22)arctan(2)(1)(111)(111)(TTjTeTTjjGTj)(G)(01)(Go0)(0)(Go90)()(G)()(jG)(G2)(1lg20)(lg20TGTarctan)()dB( 3)lg20(1)(lg20)(lg2012TTTG1)(TssGTjeTTjjGarctan21)(1)()(G2)(1lg20)(lg20TG222222121)(nnnssTssTsG10nT/1nnjjG2)1 (1)(222222)2()1 (1)(nnG2212arctan)(nn0n1)(Go0)(1n21)(Go90)(n0)(G

6、o180)()(G)(G0d)(dG0)1 (2422222nnn221nr220220r)(G2121rM220), 0(r)(G)(G)(G),(r122)(G2222)2()1 (lg20)(lg20nnGnnn2212arctan)(nn0o0)(no90)(o180)()(nno90nn22222212)(nnnssTssTsG10nnjjG2)1 ()(222222)2()1 ()(nnG2212arctan)(nn0n1)(Go0)(1nn2)(Go90)()(Go180)()(G2222)2()1 (lg20)(lg20nnGTsesG)(TjejG)(1)(GT)(T1)(G

7、dB)(01lg20)(lg20G)(niinjGjGjGjGjG121)()()()()(nijijniieGeGjG1)()(1)()()(niiGG1)(lg20)(lg20nii1)()()(lg20iG)(i)(lg20G)()164)(1()2(20)()(2ssssssHsG 14)4()1() 15 . 0(10)()(2jjjjjHjG2)4/(14/arctanarctan5 . 0arctan90)(o112243)(i)(0901802703601 . 001. 01101002图 5-14 例5-2 系统开环频率特性对数坐标图40200204060604rad/s)(

8、w)20lgG(w) (dB)1)()()()(1)()()( 1)()()()(2)1 () 1()(1110111011101122jajajajjbjbjbKjajajajjjKjGnnnmmmnnniibibibiai0211121101101)()()(1( 1)()(1)()(nnmmmnnmajabjbaKjajjbKjGmnmnnmjaKbjajKbjG11)()()(0000mn )(mn mn 0,00jaKbmn )(G)()(o180)()(G0 ; ) 1)(1()(2121, TK , TsTsTKsG)(sGjs )arctanarctan(222121211)(

9、1)() 1)(1()(TTjeTTKTjTjKjG0KG)(o0)(0)(Go180)()(G)()(jGoTT90arctanarctan)(21211TT1)(1)()(2221TTKG2121)(TTTTKG2121TTTTjKUjV00K图 5-17 例5-3系统开环频率特性极坐标图2121, 0TTTTjK0 ; ) 1)(1()(2121, TK , TsTsTsKsG)(sGjs 0)(Go90)(0)(Go270)()(G)()(jGooTT180arctanarctan90)(21211TTx1)(1)()(2221TTKG2121)(TTTKTG2121TTTTKUjV2

10、121TTTKT0图 5-18 例5-4系统开环频率特性极坐标图)(21TTK0 )()(21TTKU0 ; ) 1)(1() 1()(2121, , T K , TsTsTssKsG)(sGjs )arctanarctan90(arctan2221221211)(1)(1)() 1)(1() 1()(TTjoeTTKTjTjjjKjG0)(Go90)(0)(Go180)()(GooTT90arctanarctanarctan90)(212121TTTT21TT 21TT )()(G212121211)(1)(1)()(22212TTTTTTTTTTKG212121)(TTTTTTKG2121

11、21TTTTTTKj )()(21TTKUooTT180arctanarctanarctan90)(21)(12121TTTTx2121TTTT2121TTTT)(x)(G)(12221221211)(1)(1)()(TTTTxTTKG212121)()(TTTTTTKGx212121)(TTTTTTK )()(21TTKU212121TTTTTT0 ; ) 1() 1()( K , T, TsssKsG)arctanarctan90(221)(1)() 1() 1()(TjoeTKTjjjKjG0)(Go90)(0)(Go270)()()(G)(jGooT180arctanarctan90)

12、(Tx1TxTKG1221)(1)()(KG)(K0 ; 1)( K , T, TsKesGs)()(1)(1)(21arctan2jGjGeeTKTjKejGjTjj)(1jGTsssG11)(1TsssG11)(2T0)(2sG)(2sG)arctantan(2211)(1)()(TaicjeTjG)arctantan(2221)(1)()(TaicjeTjG)(2jGdec/dB)(20mn omn90)( dec/dB20dec/dB4021dec/dB402dec/dB20) 12)(1 ()(121222sssKssGK及,212lg20K0lg2012K1155511205/10

13、026lg20rM2rM214424355. 0) 1571. 05)(201 ()(22sssssGnjjjjGeMjM1)()()()(1)()()(1)()()( 2)1 () 1(2)1 () 1()(1110111011221122jajajajbjbjbKTjTTjjjKjMnnnmmmjjbjbjbjajiibibibiairrMrMb2/ )0(M)0(lg20M)()()()()(2121nmrpspspszszszsKsFPZNnjjmiirpszsKsF11)()()()()()(11njjmiipszssF0)()()()()(1)()(1)(sAsBsAsAsBsHs

14、GsFFGHFGH)0, 1(jjsReR009090FFGH)0, 1(jGH) 1() 1()(11101110sasasassbsbsbKsGnnnmmmjRsRelim）9090: （ ) 1() 1()(o)(00Relim11101110RelimonmjmnsnnnmmmseRaKbsasasassbsbsbKsGjRjR)0()0(jHjG)0()0(jHjG)()(jHjG)0, 1(j)()(jHjG)0, 1(j)()(jHjG0)(21PZN)()(jHjG)0, 1(jnjs) 1)(1(1)()(321sTsTsTKsHsG）（000ZNP，) 1)(1(1)()(

15、321sTsTsTKsHsG）（220ZNP，) 1(1()()(21sTsTsKsHsG）000ZNP，) 1(1()()(21sTsTsKsHsG）220ZNP，）1()()(2TssKsHsG220ZNP，3) 1s()()(sKsHsG220ZNP，) 1)(1)(1(1() 1)(1()()(432121sTsTsTsTsssKsHsG）000ZNP，1)()(TSKsHsG101ZNP，01-1ZNP，1)()(TSKsHsG1, 0,30PK321,)()(1jGjKjG)(1jG1)0(1G2)(1jG5 . 1)(2jG5 . 0)(3jG1)(ijG151K202K603K

16、10KK 21KKK32KKK3KK 12)()(sesHsGs0)0, 1(j)(, 1)()(HG)(, 1)()(HGarctan)(, 112)()(2HG3x)(332)()(jHjG)0, 1(j)()(jHjG), 1(N), 1(N)(2NNNPZNNN)(2)0, 1(jo1800)()(lg20HGo1800)()(lg20HG)(o180PZNN)(2PNN)(2o90)0()0(0)()(lg20HG)(o180hc1)()(ccHG)(180cohx)1,0,( ) 12()(kkx)()(1xxHGhhhh)()(lg20 xxHGhh2) 1()()(ssKsHs

17、G)arctan290(220) 1() 1()()(jeKjjKjHjGx1x2/1)(xG2h68. 0co6 .212)(xG2/1h38. 1co1 .181h01h0) 11 . 0)(1()()(sssKsHsG)1 . 0arctanarctan90(221)1 . 0(1) 11 . 0)(1()()(ojeKjjjKjHjGx10 x11/5)(xG2 . 2hc5co4 .1111/20)(xG55. 0h2lg20)()(lg20KHGc20co5 .11o302h5 . 0)()(xxHGdB6hcc0dsin121)( 1)(tttr lim)( 1)(0tettr)

18、( 1 t22000limdlim)(jteejRtjtttsind)()()(jeMjMo0)0(0d)(sin)(12)0()(tMMtc)(111)()(jeMjM)(11)(2212)()()()(kjjekMjkMeMjM01111d)(sin)(12)0()(tMMtc)(d)(sin)(12)0( d)(sin)(12)0()(1011102222ktckkktkkkMMtMMtc 2)1 () 1()(2)1 () 1()(11221122jjbjbjbjajiibibibiaiTjTTjjjjKjG 2)1 () 1(2)1 () 1()()(11221122jjbjbjbjajiibibibiaipTjTTjjjKjHjG0pKjHjG)()(pKHGlg20)()(lg20pKlg20图5-35 2)1 () 1(2)1 () 1()()(11221122jjbjbjbjajiibibibiaivTjTTjjjjKjHjG0jKjHjGv/)()(lg20lg20)()(lg20vKHG1)()(lg20HGvKvK图5-36 2)1 () 1()(2)1 () 1()()(112221122jjbjbjbjajiibibibiaiaTjTTjjjjKjHjG02)/()()(jKjHjGa2lg20lg20)()(lg20aKHG1)()(lg20HGaK