Exercises Unit 5. Simulink

Transcription

1 Erciss Uit 5. imli Worig priod: Ws 9 d 0 D dt: 5 My 03 bmit o il my_m_e5.pd cotiig () imli modls d sbmodls tht solv th proposd rciss d () th rsltig plots. Ercis my ot b icldd i th soltios il. I yo dcid to solv y o th optiol rciss th yo mst icld ll th grtd ils (*.mdl *.m ) i *.zip or *.rr il.. imli. Bsic rciss Ercis. Itrodctio to imli. ) loo to th blocs tht c b od i th imli (sb)librris. loo to th vilbl optios i th modl widow m d toolbr. ) Loo or blocs md PID Cotrollr (corrspodig to proportiol-itgrl-drivtiv cotrollr). 3) Ect th dmo il sldmo_hosht.mdl. (or sldmo_hosht.sl i v8). o op it typ >> sldmo_hosht i th Mtlb commd widow. Chg th dirt prmtrs d s wht hpps. Ercis. No lir dirc qtio: Dymics o popltio. ) Bild th modl corrspodig to th discrt systm did s r ( ). Hit: ) Plot its bhvior or th css r = 0. d r =.7. iitil coditio 0.5 smplig priod 0.8s d il tim or th simltio 40s. 3) Prmtriz th cop bloc so tht it psss th rslt to th MALAB worspc r th modl rom th commd widow (ctio sim) d plot () with stirs. MERI. MALAB. Fdmtls d/or Applictios. Cors /3b

2 Erciss Uit 5. imli Ercis 3. Dirtil qtio. h t igr shows th stt l digrm corrspodig to th dirtil qtio ( t) ( t) ( t). h ipt to th l digrm is d th otpt is th stt y=. Not tht or implmttio rsos w prr to s itgrtors (/ rthr th drivtios (.. /s y - ) Bild th qivlt imli modl (blocs: Itgrtor m Gi cop). Choos th pproprit bloc i th orcs librry to grt sqr sigl (t) o mplitd d rqcy rd/s. ) Plot i th sm cop th two sigls (t) d (t). o do so pt mltiplor bloc (M) bor th cop.. imli. Applictio rciss Ercis 4. Robot rm. Op loop bhvior. Cosidr th two dgrs o rdom mipltor i th igr (). h lod is modld s mss m tht vris with tim btw 0. d 5g s show i th igr (b). m t () (b) With o cotrol (op loop) th positioig lmt (plt) prsts th ollowig trsr ctio 40 P (. ms 0s 0 W wt to stdy th tim voltio o th otpt y(t) wh th ipt r(t) is sqr sigl o mplitd d rqcy 0.05Hz. o do so ollow th stps listd blow: ) Loo or th tmplt il md csc.m (cotios tim systms or s i ctio. Copy it to th worig dirctory <wor> d chg its m (cll it robot.m or istc). Modiy it with th dt corrspodig to th cosidrd plt P( (try to drstd th cod blow): ctio [sys0strts] = robot(tlg) m=; MERI. MALAB. Fdmtls d/or Applictios. Cors /3b

3 Erciss Uit 5. imli i t>=0;m=5;d i t>=40;m=0.;d A=[0 ;-0/m -0/m];B=[0;40/m];C=[ 0];D=0; switch lg cs 0 [sys0strts]=mdliitilizizs(abcd); cs sys=mdldrivtivs(tabcd); cs 3 sys=mdlotpts(tabcd); cs { 4 9 } sys = []; othrwis rror(['uhdld lg = 'mstr(lg)]); d ctio [sys0strts]=mdliitilizizs(abcd) sizs = simsizs; sizs.nmcottts = ; % cot tim stt vrs (=[;]) sizs.nmdisctts = 0; sizs.nmotpts = ; %oly o otpt (y) sizs.nmipts = ; %oly o ipt (r) sizs.dirfdthrogh = ; sizs.nmmplims = ; sys = simsizs(siz; 0 = zros(sizs.nmcottt; %zro iitil coditios str = []; ts = [0 0]; ctio sys=mdldrivtivs(tabcd) sys = A* + B*; ctio sys=mdlotpts(tabcd) sys = C* + D*; Not tht th mricl simltio o dymic systms is lwys prormd by ms o th stt qtios (or this rso mtrics A B C D hv pprd). Not lso tht ctios r bl to simlt olir d/or tim-vryig systms. ) Bild th ollowig imli modl (spciy th il robot.m i th -ctio bloc). R th simltio p to 60s. igl Grtor robot plt M lzo birto Ercis 5. Robot rm. PID cotrol. ic w do ot li th robot rm bhvior i op loop w r goig to try dirt closd loop cotrol coigrtios i ordr to improv th systm prormc. W wold li cotrolld (closd loop) bhvior corrspodig to th ollowig trsr 4 ctio M (. s 4 Nt bloc digrm shows th cotrol coigrtio tht hs to b trsltd ito imli modl. h cotrollr C( is PID sic it provids proportiol itgrtiv d drivtiv ctios. MERI. MALAB. Fdmtls d/or Applictios. Cors /3b 3

4 Erciss Uit 5. imli R + U 40 Y C( c ds P ( i s ms 0s 0 ) Cclltio PID: Plot i sm cop th otpt y(t) d th ipt r(t) (sqr sigl) or th ollowig slctio o th PID cotrollr prmtrs: C( s c d whr c = i = 0.5 d = 0. i s (Not : Us th imli bloc tht implmts th idl PID (imli Etrs dditiol Lir) bt b crl with th prmtrs: Yo do ot hv to tr c i d bt th prmtrs P I D istd. th diitio o sch prmtrs i th PID bloc) (Not : o drstd th trm cclltio ot tht th cotrollr mrtor is th plt domitor or m=: d s s / i s 0s 0 C( c 0. s s s 0s Hc th loop trsr ctio is L( 0. d th s s 0s 0 s L( 4 closd loop trsr ctio is th dsird o (. W c dsig L( s 4 cclltio PIDs or th css m=5 d m=0. s wll). ) PID with chorig zros d distt pol (robst cotrollr): Rpt th rcis or th s s 70 cotrollr giv by C(. Compr d commt th obtid rslts. s 50s Ercis 6. Robot rm. Modl rrc dptiv cotrol (MRAC). Now implmt i 4 imli modl th ollowig cotrol coigrtio. h rrc modl is M ( th s 4 40 plt is th robot rm P ( d th loop gi A mst b lrg ogh (try ms 0s 0 dirt vls d commt th obtid rslt. Modl M( R + U + Plt P( - - Y m Y A Y MERI. MALAB. Fdmtls d/or Applictios. Cors /3b 4

5 Erciss Uit 5. imli Ercis 7. Robot rm. Gi schdlig. ic th tim voltio o prmtr m is priori ow it is possibl to dsig thr cclltio PIDs ch o or ch vl o prmtr m d bl th corrspodig cotrollr dpdig o th prticlr tim istt. Implmt i imli this cotrol strtgy. I igl Grtor m I4 I3 Ot robot plt gi_sch cotroldors Hit: Us sbsystms d bl blocs. Us cloc bloc to ow th tim istt d implmt th cssry Bool comprisos i ordr to ctivt o or othr cotrollr. Ercis 8. O-li prmtr idtiictio. Cosidr procss tht c b modld s scod ordr low pss iltr G(. W ow tht its trl rqcy is s s = 3 bt w do ot ow th ct vl or its gi d dmpig coicit. I this rcis w r goig to implmt o-li prmtr idtiictio schm i ordr to idtiy d. Assm tht = 0.3 d = 9 r th ow vls w r srchig or. h schm to b implmtd is th MI rl show i t igr: (t) Rl procss to b idtiid G( Adptiv modl or th rl procss G( ^ Rl stt + rror Q Estimtd stt Prmtr vctor s sitivity modl MI rl: ic th rror dpds o th stimtd prmtrs ( t ) w will vry til =0 (th rror will b zro wh ). Cosidr th positiv diit Lypov ctio o rror V ( ) Q whr Q is positiv diit symmtric mtri. ic V() is positiv diit i th grdit V is gtiv MERI. MALAB. Fdmtls d/or Applictios. Cors /3b 5

6 Erciss Uit 5. imli MERI. MALAB. Fdmtls d/or Applictios. Cors /3b 6 will td symptoticlly to zro (its miimm vl). hror wht w d is tht vry s th grdit o V V >0. his c b prssd s Q whr is th ssitivity mtri. Prmtr cts th covrgc proprtis. Not: h grdit is V V whr i th mtri Q is sqr d symmtric w hv V Q Q Q Q Q Q. Hr w hv sd th vctor drivtio prssios: c c ) ( y A A ) (. Ad th ssitivity mtri is ) (. ) Rl procss: Implmt i imli sbsystm th rl procss stt qtios ) ( whr is th stt vctor is th procss ipt sigl d is th prmtr vctor: (Not tht w r ot goig to s rsr Fctio blocs. W r goig to dirctly implmt th systm stt qtios sig th blocs: Itgrtor m Gi) h two otpts o th sbsystm mst b d. h ipt mst b it mplitd sisoid o rqcy rd/s.

7 Erciss Uit 5. imli MERI. MALAB. Fdmtls d/or Applictios. Cors /3b 7 ) Adptiv modl: o stimt prmtrs d w r goig to bild dptiv modl with th sm strctr th th rl procss ) ( bt hr d â r stimts o d. ) ( ) ( I ordr to vry th prmtrs d isrt two dditiol ipts: d. Fi th dditiol ipts to th ow rl vls = 0.3 y = 9 (s blocs Costt or tp) d cit th sbmodl with th sm s bor. Chc tht th otpt is th sm th th rl procss. 3) Us blocs m to obti th rror sigl btw th two sbmodls (rl plt d dptiv modl). Lt th cittio sigl b sisoid (t) o it mplitd d rqcy = rd/s. 4) sitivity modl: h ssitivity modl or th dptiv modl is comptd blow: (Not tht th ssitivity modl cosists o 4 stt qtios o or ch o its 4 stt vribls ij ). Bild IMULINK sbsystm to implmt th ssitivity modl (Blocs: Itgrtor m Gi). Not tht th modl cosists o 4 dirtil qtios. bsystm ipts r prmtr stimts d cittio d stt stimt. Otpts r ssitivitis d. 5) o obti th prmtr vctor rom d implmt sbsystm to prorm th ollowig prodct: Q (t Q = I d = ). h pt two itgrtor blocs to

8 Erciss Uit 5. imli obti rom. Iitil vls or d mst b icldd isid th two itgrtor blocs. Coct ll th sbsystms d pt cop blocs. Nt igr shows possibl soltio. It is sggstd to s mss d dirt bloc ormts. 6) Plot th tim voltio o d (t il simltio tim 50s d iitil coditios =5). o which vls do th stimts covrg? 7) Plot th tim voltio o th stt vctor d its stimt. 8) tdy th ct o i th covrgc o prmtr stimts y. imlt with = 0.7 d =. Ercis 9. ttlow (optiol). Propos d solv simpl ttlow mpl (or istc som pplictio o sqtil cotrol smphor ). th mpl i th Uit 5. Ercis 0. Aimtio (optiol). Implmt imtio ct by sig -ctio bloc d GUI tools (or istc pdlm movmt crt-sprig-dmpr systm ). th mpl i th Uit 5. MERI. MALAB. Fdmtls d/or Applictios. Cors /3b 8