Chapter #3 EEE Subsea Control and Communication Systems

Transcription

1 EEE 87 Chter #3 EEE 87 Sube Cotrol d Commuictio Sytem Cloed loo ytem Stedy tte error PID cotrol Other cotroller Chter 3 /3

2 EEE 87 Itroductio The geerl form for CL ytem: C R ', where ' c ' H or Oe Loo (OL) TF:, c TF of cotroller, TF of lt R - Cotroller E c U Sytem C Feedbck H Feedbck TF Our Tk: DESIN c d H (if licble). OLFT: Oe loo reoe (deired outut): Chter 3 /3

3 EEE 87 Ste Reoe.8 Amlitude Time (ec) CLTF: C CL C R Cloed loo reoe (k): Chter 3 3/3

4 EEE 87 Ste Reoe.8 Amlitude Time (ec) : Ste Reoe.8 Amlitude Time (ec) Chter 3 4/3

5 EEE 87 Higher order ytem Util ow we hve ee oly t order ytem with feedbck. I thee ytem, the feedbck d the cotroller ifluece the tedy tte d the time cott. The decree of the time cott me tht we moved the ole further ito miu ifiity re. Hece we chged the -le of the ytem. Wht i it goig to he if we ue d order ytem i feedbck ytem? ( )( ).4 Ste Reoe. Amlitude Time (ec) So rt from fter ytem d mller tedy tte error we hve ocilltio! k k CL ( )( ) k 3 k Chter 3 5/3

6 EEE 87 CE: 3 k but the geerl from: ζ o ζ 3 d k d for k hece ζ ζ : d So the feedbck d the cotroller c comletely chge the loctio of the ole i the -le. Exmle: ( )( )( 3) The oe loo reoe for vriou gi i: 9 Ste Reoe Amlitude Time (ec) The oe loo ytem will be tble for ll vlue of ice they do ot ifluece the ole of the ytem. The reoe of cloed loo ytem for,, i: Chter 3 6/3

7 EEE 87 5 Ste Reoe 4 3 Amlitude Time (ec) Hece the feedbck my itroduce itbility. To udertd why we hve thee chge olve the CE. Proertie of feedbck ytem:. Miimie tedy tte error.. Fter ytem. 3. Le eitive to ytem ucertitie. 4. Itroduce itbility (eve for egtive feedbck). 5. Exeive (we eed to feedbck the igl, i.e. ue eor). Chter 3 7/3

8 EEE 87 PID cotrol Coider the ytem: () for : ( )( )( 3).9 error.8.7 outut To icree the tye of the OLTF (which i C x) we dd itegrtor: c ( ) i > OL ( ) i ( )( )( 3) (Thi i the o-clled PI cotroller). Chter 3 8/3

9 EEE 87 Itegrtor i Ste 36 6 Trfer Fc Scoe i i i Further icree of, i: Chter 3 9/3

10 EEE , i 6, i Check the derivtive of error, i.e. the rte of chge of e: De e Chter 3 /3

11 EEE 87 Mximum vlue of De jut before e. So De c cotrol the ocilltio: ( ) i d > c OL ( ) d i ( )( )( 3) Ste Itegrtor i 36 6 Trfer Fc Scoe du/dt Derivtive d Chter 3 /3

12 EEE d d 5 d Sice I hve o ocilltio I c icree little bit more to mke the ytem fter: Chter 3 /3

13 EEE P outut Outut Chter 3 3/3

14 EEE 87.5 D outut Outut I Outut Outut Chter 3 4/3

15 EEE 87 Aother wy to write the PID cotroller: CL CL i i d ( ) d ( ) Td Ti Tuig of PID cotroller. Tril d error.. Ziegler Nichol I 3. Ziegler Nichol II 4. Root locu 5. Frequecy reoe 6. Other dvced cotrol method Tril d error: P: Fter ytem, i ome ce reduce the error (c cue itbility). I: Reduce the tedy tte error, icree the umber of ocilltio. D: Reduce the ocilltio. Chter 3 5/3

16 EEE 87 Ziegler Nichol I Aume ytem with o dely (we do ot tudy thee ytem) d with o-comlex cojugte ole. It oe loo te reoe my look like (obtied exerimetlly of from imultio): Thi c be modelled : C( ) U ( ) L e T Bed o tht we hve the followig tble: Chter 3 6/3

17 EEE 87 Tye of cotroller P PI PID T i T d T L.9T L L.3.T L L.5L Ziegler Nichol II Iitilly ume i d. Icree util the ytem i mrgilly tble. Record the cr d the frequecy of ocilltio: P cr c(t) t, Chter 3 7/3

18 EEE 87 Tye of cotroller P PI PID Ti Td.5 cr.45 cr..6 cr.5pcr P cr.5pcr Thee method im t chievig overhoot of 5%. Root locu method With the RL we ecificlly trget ole loctio t the -le, i.e. we trget dmig fctor, turl d dmed frequecie. Exmle: The OLTF i ( ) ue PI cotroller. 34 OL ( ) i 34 ( 34) i CL ( ) ( 34) i i Thi i 3 rd order ytem d order x t order: Chter 3 8/3

19 EEE 87 CE: ( ) ( )( ) 34 i ζ ( ) ( ) ( ) i ζ ζ 34 i ζ ζ Aume tht the deig ec re:.5 6 ζ So: i i Homework: Fid the PID gi : the CLTF of 6 6 ) ( h.5 6 ζ d rel ole t -5. Solutio: 5, i 8, d 5. Frequecy reoe Advced method We will ot tudy thee. Chter 3 9/3

20 EEE 87 Other cotroller By uig the reviou (root locu) method we c deig more geerl cotroller. Exmle: R() ( ) ( b) C() C() b?? 6 θ 6 o 6 ζ co ( ) o 6 6 ζ.5 () ( ) b C R () () ( ) ( b) ( ) CE : CE 3 b ( )( ζ ) 3 : b Chter 3 /3

21 EEE 87 ( )( ) 3 : b CE ζ ( ) ( ) 3 3 : b CE ζ ζ b ζ ζ b Exmle: () ( )( ).5 OL, Uity feedbck d iut: r(t)5t ) If.5, fid the tedy tte error b) The ytem mut hve tedy tte error, E<. fid the vlue of C() C() ( )( ).5 5 () R () () ( )( ) R C.5 () ( )( ) C.5 5 Chter 3 /3

22 EEE 87 E ( ) R( ) C( ) E() 5 ( )(.5 ) E () 5 ( )(.5 ) ( )(.5 ) E ( )(.5 ) ( )( ).5 5 lim 5 E 5 ) E E <. > 5 b) <. Exmle: OL () (. )(. ) ) Fid the vlue of uch the ytem i mrgilly tble b) Fid the frequecy of ocilltio t tht oit Chter 3 /3

23 EEE 87 C R () () (. )(. ) (. )(. ) CE : For mrgilly tble ytem: j (. j )(. j ) CE : j 3 (.. ) (.. ) j CE : j rd / d 5 Chter 3 3/3