車輛工程-大三自動控制原理課件ch55bode criterion stability margin

3.BodeStabilityA(c)G(jc)H(c) c)20lg c)cCutofffrequency截止頻率j

0

(0)A() 00()(2k1),k CH5 3.BodeStability存在積分環(huán)

1（v0），0，向上補畫v90s存在振蕩環(huán)

n(s22n

0),

,向下補畫v1正穿越次數NL(1由下向上穿越(2k1)線次數負穿越次數NL(由上向下穿越(2k1)線次數 CH5 3.BodeStability對數頻率穩(wěn)定判據P正實部開環(huán)極點的個數和L()0dB時對數相頻特性曲穿越 1)線的次NN滿足：ZP2N CH5 3.BodeStabilityEx5- (dB)cj0 (0)NN

PZP2N CH5 3.BodeStabilityEx5- v3,P12

3,

N2ZP2NSystemis CH5 5-5StabilityStabilityMargin穩(wěn)定裕度)：deviationfromunstable (相角裕度Gain (幅值裕度)is CH5 jh

L()0h h1,r

(0 Cutofffrequency(截止頻率G( c)H( c)1 Phasemargin:1800G(j)H(j

h1,r

G(j)H(j

20lgG( x)H( x) CH5 (1)TypicalEx：2-ndorderFre G(j) j(j2n

2G(s) s(s2n

900n2 n2c: 1n 2n CH5 2.c 4

212arctg2narctg2ncCH592.（2）High-order試x量hThecondition0,h0cannotDegreeofstabilityisnotonlydeterminedbyeitherorIngeneralK，，ess CH5 -loopFrequencyPerformanceIndicesthisControlSystemTime-Scale&Frequency-GraphicalMethodforCLPerformanceIndicesforFre vs CH5 ControlSystemBandwidthfrequency(帶寬頻率b

20(0,b

( b

20

(j0)1-storder

(

3(s)

0 0bT—bandwidthinverseprop.time CH5 ControlSystem2-nd

(s) s22s(s)

1

2

22 22 (j0)1 (1 )242 2n (122)

n(122)2d( bn∵n

bandwidthisinverse CH5 h(t)L1[1(s)],h(t)L1[1(s)] If(s)(s L[f

t)]aF(as) a 111

h2(t) [h1(tThat

2 )] (s)]sh1(t)h2(tTime-scaleisinverselyproportionaltofrequency- CH5 GraphicalMethodforCLFrequencyG(j)A()ej( )M

)ej(A()ej(1A()ej() CH5 PerformanceIndicesforFrequencyvs CLfre indicesb,MrvsOLindicescMr～

)1800 r， )haslessdeviationwithr CH5 4.PerformanceIndicesforFrequencyvs G(j)A()ej[1800()]A()[cos()jsinM()

G( 1G(

1[

cos()]2sin2whenA()

cos

，M() uthatMrMr(r)

sin(r with，crwhen0，cThusfor ，Mr

hashighestimationFordesig：b,Mr c, CH5 4.PerformanceIndicesforFrequencyvs indicesVs 22-ndsystem：G(s) s(s2n 41 arctg 4412

300c n

CH5 4.PerformanceIndi