1、1111)()()(RCsCsRCssUsUsGioR RC CiuouiuouiurcAAA tAtrr sin)()sin()(tAtcc crACAR,o0tAtrr sin)()sin()(tAtcc rcrcAAAARCjGo0)()()(jG|)(|)(jGAAArc )()()()()(jQPAjG )(Re)(jGP)(jG)(Im)(jGQ)(cos)()(AP)(sin)()(AQ)()()(22 QPA )()()(1 PQtg 1111)()()(RCsCsRCssUsUsGioR RC Ciuou jssGjG|)()(1111)(RCjCjRCjUUjGrc j j
2、s dtds dtdj jssGjG|)()(0)(jG DecDecDecDec1 2 012.lg01.001.0110100 lg )(lg20)(AL)(lg20 A)lg(20幅值增益 KP)(0)(QKsG)(KjG)(KA)(0)(dBL/)()(180 180KA)(0)(111000lg20)(KKKKL常数常数 Klg201 K1 KKlg201 KKlg20 0)(1)(TsKsG1)(TjKjG TtgTKA122)(,1)(22221)(,1)(TKTQTKP 0)0()0(0)0()0(0 QKPKA,时:时:2)1(2)1(45)1(2)1(1KTQKTPTKTA
3、T ,时:时:0)(0)(90)(0)(QPA,时:时:0 0 T1 221)(TKA 1)(TsKsG1)(jTKjG221lg20lg20)(lg20)(TKAL 1 TKLlg20)(1 T TKLlg20lg20)(Ttg1)(TKKlg20lg20lg20 T1o o 2211lg20 T o TTlg201lg20222 To1 )(31lg202o2maxdBT Ttg1)(。时,时,当当时,时,当当时,时,当当ooo90)(;45)1(1;0)0(0 TT2)(eKKjjKjG2)(KA)(KQ )(0)(P0 sKsG)(lg20lg20lg20)(lg20)(KKAL2)(
4、KA)(1 KdBL/)()(902040204011010011010010 K0)(lg20)(1 LKKL时,时,当当时,时,当当2)(12)(1)()(22 TssTsGTssGssG TjTjGjTjGjjG 21)(1)()(22 jjG)(2)(,)(A )(,0)(QPReReImIm02)(lg20)()(LA jjG)(TQP )(,1)(TtgTA122)(,1)(0 jTjG 1)(2)(,;4)(,1;0)(,0 T2 0)(lg201)(1 AAT,时时,当当 TLTATlg20)()(1 ,时时,当当22221lg20)(,1)(TLTA Ttg1)(T1 222
5、222222222224)1(2)(,4)1(1)(TTTQTTTP 222222)2()1(1)()()(TTQPA 221112)()()(TTtgPQtg 222222121)(nnnssTssTsG 10 TjTjG 2)1(1)(22 221 nm谐谐振振频频率率2121)(mmAA谐振峰值谐振峰值1 2.0 0 1.0 1.0 3.0 4.0 5.0 6.0 7.0 8.0 2 时时707.0 10 2222)2()1(1)(TTA 22112)(TTtg 2222)2()1(lg20)(lg20)(TTAL 0)(1 LT时时,TTLTlg40)(lg20)(1222 时时,To
6、1 22112)(TTtg 。)(,;2)(,1;0)(,0T3.0,1,10 TKTo1 DecdB/4016.010)(2 ssjG 222)2()(1 lg20)(nnL 2222)lg(20)2()(1 lg20)(nnnL n n 221222212)(,)2()1()(TTtgTTA 12)(22 TssTsG 0)(1 LT时时,TTTLTlog40)2()1(lg20)(12222 时时,To1 )(,;2)(,1;0)(0T时,时,当当2222)2()1(lg20)(TTL 0 0 sesG )(jejG )(1)(A(deg)3.57)()(radsesG )(jejG )
7、(1)(A(deg)3.57)()(rad100-10 1 101 51 21 5 10 2-540-450-360-270-180-900)(dBL)()()(jQP)()(jeA)(),(QP)(),(A)1)(1()(21 jTjTKjG 5,1,121 TTK)()()1)(1()()1)(1()1()1)(1()1)(1()(2222212122222122122222121 jQPTTTTKjTTTTKTTjTjTKjG 5,1,121 TTK)251)(1(6)(,)251)(1(51)(22222 QP ,0 )(P)(Q 5165 5)(11 tgtg)(51)51)(1(1
8、)(sssG 5,1,121TTk5,1,121TTk0)51)(1(1)(ssssG 5,1,1021TTk0)51)(1(10)(ssssG njjmiijTjjKjG11)1()1()()(njjmiiTtgtg11112)(0 ,2)0(,2)(2)(22)(mnnm 00|)(|)(jKjG)(,0|)(mnjG 若若 00pKKG|)0(|,0)0(0 型型:0 ,2)0(00|)(|)(jKjG|)0(|,2)0(G 型:型:|)0(|,)0(G 0pKK ,2)(2)(22)(mnnm )(,0|)(mnjG 若若 2)(1 时,时,mn23)(3 时,时,mn )(2时时,m
9、n)()()()(21 jGjGjGjGn 设设开开环环频频率率特特性性)()()()(lg20)(lg20)(lg20)()()(lg20)(lg20)(212121 nnnLLLjGjGjGjGjGjGjGL )()()()(21 n 2121,)1)(1()(TTsTsTsKsG 20406011T21T2040608011T21T4590135180)(270,KjjiiT11 ,lg20lg20)(KL)/(20decdB )(j)14.025.0)(125.0(10)(2 ssssGk5.0,25.0,10,021 TTK dBKTT20lg20,21,412211 decdB/0
10、1012420)(L4060244060)05.01)(125.01)(101()1001(10)(223ssssssG 2005.01,8125.01,1.0101,01.01001;2;1043213 KdecdB/40 1 )(6010lg20lg203dBK )60,1(21231211 s171 s)121()171(6.5)(ssssG)(L0)()(1 sHsG)()(1sHsG)()(jHjG niinjjpszsKsF111)()()(设设 niinjjpszssF11)()()(sC 1z j平平面面s2z 2p 1p FC平平面面)(sFeRmI0 niinjjpszss
11、F11)()()(sC 1z j平平面面s2z 2p 1p FC平平面面)(sFeRmI0)()()()()(sNsMKsHsGsGgk )()()()()(1)()(1)(sNsMKsNsNsMKsHsGsFgg )()()()()(sNsMKsHsGsGgk )()()()(1)()(sFsGsHsGsGs )()(1)(sHsGsF 闭环系统右半极点数开环系统右半极点数 右半零点数右半零点数右半极点数右半极点数|)(|)(sFsFN)(jGK 0 22,从从ReRsj0 je 0 j常常数数 )()(1 lim)(limsHsGsFss j)(1)()(1)(jGjHjGjFk j j
12、j j j1)()(jFjGk)(jGk)01(j,)(jF)(jGk)(jGk)(jF)01(j,)(jGk)(0 NPZ)01(j,)(jGk)(jGk)(0 NPZ)(jGk 0从从 0 从从 2PN )01(j,)(jGk)1)(1()(21 sTsTKsGk)52)(1(52)(2 ssssGk21j 0 P1 2)2(0 NPZ1 sK)(sR)(sC2/K)0,2/(K 1 sK)(sR)(sC1 P njjmiiksTssKsG11)1()1()(0 22,ReRsj 0 22,0,jes jejeR 0 0 jejeR 0 0 jjesniimjieskeeKsTssKsGj
13、j )lim()1()1()(0lim11lim00 jes0lim 2 )(sGk2 2 2 jejeR 0 0 2 2 2 0 0 eRmI jejeR 0 0 0 0 eRmI 01 00 P1 0 00 P2)2(0 NPZ0ReIm)()(L o00o180 dBL0)(若系统开环传递函数有若系统开环传递函数有P P个位于个位于s s右半右半平面的特征根,则系统闭环稳定的充要条平面的特征根,则系统闭环稳定的充要条件是:在件是:在L()0 的所有频率范围内,相频的所有频率范围内,相频特性曲线特性曲线()与与-180线的正负穿越次数线的正负穿越次数之差等于之差等于P/2。)14.025.
14、0)(125.0(10)(2 ssssGk)05.01)(125.01)(101()1001(10)(223ssssssG )(jGkBA两点。两点。、交与交与实轴实轴曲线分别与单位圆和负曲线分别与单位圆和负设系统的开环频率特性设系统的开环频率特性BAjGk)(称为相角穿越频率称为相角穿越频率点处的频率点处的频率也称剪切频率也称剪切频率称为幅值穿越频率称为幅值穿越频率点处的频率点处的频率gcBA ,表示。表示。用用裕度,裕度,的幅值的倒数称为幅值的幅值的倒数称为幅值处处在相角穿越频率在相角穿越频率gkgKjG)()(1ggAK 即即ReIm)(180co 两点。两点。、交与交与实轴实轴曲线分别
15、与单位圆和负曲线分别与单位圆和负设系统的开环频率特性设系统的开环频率特性BAjGk)(BAReIm称为相角穿越频率称为相角穿越频率点处的频率点处的频率也称剪切频率也称剪切频率称为幅值穿越频率称为幅值穿越频率点处的频率点处的频率gcBA ,0ReImc g c g 0 0 gK/1 gL)()(L o00o180)(180c 0 gL0 0 gL0 )(lg20)(1lg20lg20ggggAAKL )()(L o00o180 c g 0ReIm)()(L o00o180 c g 0ReIm)()(L o00o180 c g 0ReImc g c g c g)5()1(sssK)(sR)(sC
16、c g 104.0112)(22 ccccA c 112)(2 cccA o114.1552.090)(ccctgtg )(180c )12.0()1(2)(jjjjGsradc/25.1 解得:解得:ooo6.2438.155180 c o111802.090)(gggtgtg sradg/24.2 33216.004.0112)(22 ggggA )(6.9)(lg20dBALgg g)12.0()1(2)(jjjjGK=10K=1001c c g c 1.00cc 101.0c 10 的值。的值。,并且要尽可能提高,并且要尽可能提高附近的斜率为附近的斜率为在在曲线曲线望望稳定性能和快速性
17、,希稳定性能和快速性,希为了使系统具有较好的为了使系统具有较好的ccdecdBL /20)()2()(2nnksssG )2()(2nnkjjjG 22224)(nnA nntgtg2180290)(1010 c 14)(2222 nccncA 由由24214 nc得得cnst 24214)43(43 调整时间调整时间。越大,系统快速性越好越大,系统快速性越好反映了系统的快速性。反映了系统的快速性。幅值穿越频率幅值穿越频率cc cntg 2)(18010 2412142 tg越越大大。越越大大,有有关关,只只和和阻阻尼尼比比相相角角裕裕度度 性越好。性越好。最大超调量越小,稳定最大超调量越小,
18、稳定越大,越大,相角裕量相角裕量反映了系统的稳定性,反映了系统的稳定性,相角裕度相角裕度 21%e2412142 tg%cst 24214)43(stc 2222)(nnnsss 222)(2)()(nnnjjj 22222)2()()(nnnM )(M:谐谐振振峰峰值值rM带宽频率带宽频率:截止频率:截止频率b:谐谐振振频频率率r 得得由由0)(ddM)707.00(212 nr谐谐振振频频率率)707.00(1212 rM谐振峰值谐振峰值。越大,系统快速性越好越大,系统快速性越好反映了系统的快速性。反映了系统的快速性。谐振频率谐振频率rr rM性越差。性越差。最大超调量越大,稳定最大超调量
19、越大,稳定越大,越大,谐振峰值谐振峰值反映了系统的稳定性,反映了系统的稳定性,谐振峰值谐振峰值rrMM)(M)0(22M,0b b 42244221 nb由由定定义义求求得得。越大,系统快速性越好越大,系统快速性越好反映了系统的快速性。反映了系统的快速性。带宽频率带宽频率bb 21)(MdBM3)(lg20 b )(M12)(1)()(22 TssTsGTssGssG TjTjGjTjGjjG 21)(1)()(22 )()(jQP)()(jeA)(),(QP)(),(A)(1)()(1)(jGjHjGjFk j j j j j)5()1(sssK)(sR)(sC c g o111802.090)(gggtgtg sradg/24.2 33216.004.0112)(22 ggggA )(6.9)(lg20dBALgg g)12.0()1(2)(jjjjG)(M)0(22M,0b b 42244221 nb由由定定义义求求得得。越大,系统快速性越好越大,系统快速性越好反映了系统的快速性。反映了系统的快速性。带宽频率带宽频率bb