제어이론복습 강의보조자료. 박상혁

Transcription

1 제어이론복습 강의보조자료 박상혁

2 u inut t t utut : y t t u Linear System with zer C Linear System with zer C Linear System with zer C N k utut g t d g t : utut by imulse inut u gt u k g t k u g nvlutin t t k N k k 2 fr t k ut u k Linear System with zer C Linear System with zer C Linear System with zer C Linear System with zer C Linear System with zer C Linear System with zer C Linear System with zer C k yt t u k g t k + t k +

3 Bde Plt Technique ntrductin dea: feedback ntrl 이므로 l 을이루는요소들이중요 L Transimssin L Gain: L s K s G serv s G s H s magine frequency resnse f the l transmissin, i.e. L L : crssver frequency Tyically fr hysical system.

4 Mtivatin f Bde Plt Technique Perfrmance Tracking : Gd L L H r y : e Reectin Disturbanc L G d y d : Reectin Nise L L H n y frequencies higher at L frequencies lwer at L high sufficiently ω : We want L Transmissin 의주파수응답으로 Clsed L 시스템의성능을판별할수있음! s H s G s G s K s L serv

5 Mtivatin f Bde Plt Technique Stability nte : L s K s s 2 L. K 4 :unstable L -9-8 K 2:neutral K.5 :stable Fr stability: L 8-27

6 Bde Plt Technique 정리 Ks 를잘설계하여 L 가다음과같이되도록한다. L / GM. L -9 Tyically -8 PM - Phase Margin > 45 - Gain Margin > 2 =6dB 8-27

7 P Cmensatr K K s K s K s s K 주목적 : 저주파에서 L Gain을크게하기위해쓰임 Tracking 성능향상 K 5 45 Tyically, arund here 9

8 Cntrller Design with Bde Plt 예제 # /3 2 G Gain [rad/s] Nte 8 At 3rad/s, rad/s Phase f hase lead is nt used Phase [deg] - -2 chse 3rad/s -3-2 [rad/s] 3rad/s

9 Cntrller Design with Bde Plt 예제 # 2/3 Prrtinal Cntrl Chse K fr L K G K.6 2 G KG ω 3 rad/s, PM 83, ω8. 6rad/s, GM 5. Gain [rad/s] Phase [deg] - -2 G KG -3-2 [rad/s] Steady Errr Need t add ntegral ntrller

10 Cntrller Design with Bde Plt 예제 # 3/3 P Cmensatr Chse / sufficently lwer than 3/ K.6. s ω 3rad/s, PM 63, ω8 rad/s, GM 4. 4 Gain 2-2 G KG -4-2 [rad/s] Phase [deg] - -2 G KG -3-2 [rad/s]

11 PD Cmensatr K K s K s D Phase 를끌어올리기위해. K D y 와 dy/dt를직접측정할수있는경우가아니면미분으로인한노이즈특성에주의. K K D 9 45 Tyically, arund here

12 PD Cmensatr K K s K Ds K D s s D s, with K K D 9 Tyically, arund here 9

13 Cntrller Design 예제 Unstable Ple #2 /3 Unstable le at + Gain 2-2 Befre l shaing Ntice the hase is nt zer when the gain sle is zer due t unstable system [rad/s] We need hase increase Let s try PD ntrller Phase [deg] [rad/s] Fr an unstable real le at, shuld be chsen higher than in rder t make it stable. Tyically, > 2

14 Cntrller Design 예제 Unstable Ple #2 2/3 Fr real unstable le at, we need >2. Here, = +, s let s try =4. Chse / D sufficiently lwer than D =5/ Chse K such that D K G = PD Cmensatr Gain 2-2 PD ntrller design G KG [rad/s] Phase [deg] [rad/s] G KG Steady Errr Need t add ntegral ntrller

15 Cntrller Design 예제 Unstable Ple #2 3/3 PD Cmensatr Chse / sufficiently lwer than / D =5 D Gain 2-2 PD ntrller design G KG Phase [deg] [rad/s] [rad/s] G KG

16 Lead Cmensatr s K s K s Phase 를끌어올리기위해. K K PD 와유사하나 PD 의단점을어느정도극복 K K K 9 sin ex Chse this frequency fr

17 Cntrller Design 예제 #3 /2 2 G Gain -2 Phase [deg] [rad/s] At 5 rad/s, Phase = We need hase increase by 33 Let s try Lead mensatr -3-2 [rad/s] 5rad/s

18 Cntrller Design 예제 #3 2/2 sin required sin Chse such that Lead Cmensatr Chse K such that K G 2 Lead Cntrller Design G KG Gain [rad/s] Phase [deg] - -2 G KG -3-2 [rad/s] 5rad/s

19 P+Lead Lead-Lag Cmensatr K K s K s s s s K K 9 sin Chse this frequency fr 9

20 Cntrller Design 예제 #4 Nn-minimum Phase Zer /2 Nn-minimum hase zer at s=+5 2 G Gain [rad/s] Ntice the additinal hase decrease due t the nn-minimum hase zer A nn-minimum hase zer at z Phase [deg] [rad/s] imses a severe restrictin n. Tyically, < z/2 Als, need t bst lw frequency gain Let s try P ntrller with small enugh

21 Cntrller Design 예제 #4 Nn-minimum Phase Zer 2/2 Fr a nn-minimum hase zer at z, we need < z/2 Here, z = +5, s let s try =2. P Cmensatr Chse K fr K G Chse / sufficently lwer than 3/ 2 Lead Cntrller Design G KG Gain [rad/s].2 Clsed L Ste Resnse fr y Tracking Phase [deg] G KG y [rad/s] t [sec]