西安石油大学电子工程学院：《自动控制理论 Modern Control System》精品课程教学资源（英文PPT课件）Frequency-Domain Analysis of Control System

The phase angle can also therefore be approximated by tangents. One tangent for low frequencies where the angle is approx. 00, one for high frequencies where the angle is approx 900 and a third tangent linking these other two. The lines can be summarised as follows 0≤0≤-m→p≈0 57 5 ≤O≤0→≈-90 T The Bode diagram consequently is drawn as shown below 2022-2-3

2022-2-3 11 The phase angle can also therefore be approximated by tangents. One tangent for low frequencies where the angle is approx. 0 0 , one for high frequencies where the angle is approx. -900 and a third tangent linking these other two. The lines can be summarised as follows: 0 1 5T 5 T        w  w  0 90 o o The Bode diagram consequently is drawn as shown below:

号 1/10T d/ ①0元 丌 2022-2 Frequency (rad/sec)

2022-2-3 12

Example Consider N noninterac ting first order systems in series and open loop G(S)=G(S)G2(S).GN(s) K K K 1Ts+1 Gain dB 20 log G(jo ) =20l0gG(jo)*|G2(1o)*…*G(j) 20 log G, (jo)+20 log G2(jo)+.+20 log G(jo ) K but 71j K K TjO+1 Ki-jKITI TJO+1 TiJO+I-TijO+l K2(+T2o2) K O 1+r +T, K ->caIn dB 20 log K K 20 lo +.+20lo: +to φ=∠G(jo)=φ1+p2+…+p 2022-2-3 p=-tan oTi-tan oT2 - tanot 13

2022-2-3 13 Example       N N N N dB N N dB N N N T T T G j T K T K K Gain T K T K T G j T K jK T T j T j T j K T j K T j K G j G j G j G j G j G j G j Gain G j T s K T s K T s K G s G s G s G s N  w w w  w    w w  w w w w w w w w w w w w w w w w w w w w 1 2 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 2 2 1 1 2 2 2 1 2 2 1 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 1 1 1 2 tan tan ... tan ( ) ... 1 ... 20 log 1 20 log 1 20 log 1 1 1 ( ) 1 1 1 1 1 , but 1 ( ) 20 log ( ) 20 log ( ) ... 20 log ( ) 20 log ( ) * ( ) * ... * ( ) 20 log ( ) 1 ... 1 1 ( ) ( ) ( )... ( ) systems in series and open loop Consider noninterac ting first order                                                                    

In general the ar and phase angle can be determined for a system represented as a transfer function as follows k(1+T1s)(1+12s).( GOPENLOOP (S)= s(1+Ts(1+hs).(1+ T,S) GoPENLooPLR =20logl K]+201og 1+ jo 201og 1+ jo T:++201og l+joT 20log101-200g1+1o|-20lg1+1o 201og 1+joT, ∠ G(o)=∠K+∠(1+1o)+∠1+1o2)+ +∠1+joTn ∠o)-∠1+1o)-∠1+1o)--∠(1+1or ZGoPEnLooP J@)=0+tan"(oT)+tan"(af)+ +tan(oT 90°-tan(o)-tan(OT)-…-tan-(oTn) 2022-2-3 14

2022-2-3 14 In general the AR and phase angle can be determined for a system represented as a transfer function as follows:           G s K T s T s T s s T s T s T s G K j T j T j T j j T j T j T G j K j T j T j T j j T OPENLOOP m a b n OPENLOOP dB m a b n OPENLOOP m a ( ) ( )( )...( ) ( )( )...( ) log log log ... log log log log ... log ( ) ...                                          1 1 1 1 1 1 20 20 1 20 1 20 1 20 20 1 20 1 20 1 1 1 1 1 1 1 2 1 2 1 2 w w w w w w w w w w w w w                        j T j T G j T T T T T T b n OPENLOOP m o a b n w w w w w w w w w ... ( ) tan ( ) tan ( ) ... tan ( ) tan ( ) tan ( ) ... tan ( ) 1 0 90 1 1 1 2 1 1 1 1