3 Simulation exercise 3

Transcription

1 3 Smulato xrc 3 3. Dcrpto of a lctrc drv ytm I th cod hom agmt a modl of a lctrc mach wa gv ad th ma focu wa o how to xpr a dyamc ytm ad to tudy a rpo of th ytm. Sc that, th tudy ad dvlopmt of th automatd cotrol ytm hav b movg toward cacadd cotrol of a lctrc drv ytm. h a mot commo way to cotrol a lctrc drv. Prvouly, th outr loop, whch th pd cotrol, ha b aalyd ad a cotrollr paramtr drvd. h torqu cotrol of th r loop ha o far ot b tudd dtal. It aumd that th rpo of th r loop could b dcrbd a a frt ordr low pa fltr wth cut-off frqucy at /c. hrfor, th ma targt of th hom agmt to focu o th torqu cotrol of a lctrcal mach. A th torqu proportoal to th currt ad th currt aly maurabl, th currt cotrol ud ordr to trac th torqu. h tructural bloc dagram of th cacadd cotrol of th lctrc drv ytm how Fgur 3.. h lctrcal mach togthr wth th load dcrbd udr a ubytm Machoad. h ubytm corrpod to th ytm that wa drvd th prvou homwor cto.4. h mach fd from a powr amplfr (whch wll b dcud cto 3.3) that ralz th dco mad a currt cotrollr. wo dffrt currt cotrollr wll b focud o: a drct currt cotrol (DCC) (cto 3.4) ad a ampld currt cotrol (SCC) wth a PIE rgulator ad a modulator (cto 3.5). h ma trt of th tudy focu o th r loop, but oc th wll udrtood ad tud th outr pd cotrol loop ca b addd ( accordac wth th prvou hom cto.6). Bacally th whol drv ytm d to b bult Smul (mlar but ot carly dtcal to th ytm Fgur 3.) ad d to b aalyd. It rcommdd to ta advatag of M-fl ordr to lav th mootoou wor to th computr (cto 3.6) ad focu o th cratv wor! Fgur 3. Cacadd cotrol of th lctrc drv ytm wth two altratv currt cotrol loop Am of th homwor to gt om practcal xprc through buldg th mulato modl ad carryg out th aaly. h agmt covr a fw topc ad om of th trt ar Cotrollr carr out tracg but t alo th afty lmtato {Automaatjuhtmütmd üt pt 4} Sytm may gt aturatd.. th output bcom olar rpct to th put dffrt way {Mttlaard lüld pt 5} Nowaday th cotrol oft carrd out μ-computr by ug dcrt cotrol {Drtd ütmd pt 6}

2 frc to cour ltratur Automatc Cotrol by aul Naadl ar gv th parth {Et l} (v th tm th rfrc ar rathr gral d). Each tp of olvg a agmt corrpod to crta amout of crdt gv bract (0). U ad mprov th m- fl (Ch 3.6) to carry out your wor. 3. Itgrator at-wdup For ay cotrol ytm th ral world, th actuator that prform th cotrol acto hav crta dyamc rag. Du to th lmt of th dyamc rag, th output of th ral actuator ca aturat f th output byod th rag. Such aturato xt th ytm a olarty. Wthout carful tratmt, t wll dgrad ytm prformac. A a mattr of fact, th ca, th cotrol gal to th proc do ot hav fluc upo th actuator output a th fdbac codrd to b op. hrfor, th tr ytm bcom op loop, wth th rror gal a th put. It ow that a PI cotrollr ca accomplh a good prformac a gal tracg ad zro tady-tat rror. I ca of actuator aturato th actuator top chagg ad du to rror th tgrator p growg ad th ow a tgrator wd-up. h tgrator wd-up dtrorat th trat rpo of th ytm. h pobl actuator aturato that mght cau tgrator wdup At pd cotrol th cotrollr rqur hghr mchacal output tha actuator abl to gv. For xampl th thrmal lmt of th currt durg th log prod of acclrato, At currt cotrol th cotrollr rqur fatr lctromagtc rpo tha actuator abl to gv. For xampl th voltag lmt from a powr amplfr wh bac mf th am z a th output voltag of th amplfr, Fgur 3. how how to olv th problm by cacllg out th aturato olarty wth tgrator at-wdup mcham. Oc thr appar dffrc btw th xpctd output ad th protctd or th lmtd output t uppr th tgral acto. I th ca, th fdbac ga, Kaw, hould b cho larg ough ordr to rduc th o-zro ytm rror gal (t) ad to p th put gal to th tgrator mall. Fgur 3. h PI pd cotrollr wth at-wdup chm. h followg ta you ar ad to prform. h frt ta to aaly a pd cotrolld lctrcal drv, whr th torqu rpo modlld a a frt ordr fltr. h at to prform th ta to u th ytm modl that you bult prvou hom wor cto.6 at xrc (th ytm loo l fgur.4 but t uppo to hav clod pd loop) (0). a. Chag th bloc dagram a way that th rfrc pd com from Matlab worpac ad th output of th trt wll b avalabl Matlab worpac (mlar to Fgur 3.). b. plac th pd cotrollr l t how Fgur 3.. St th torqu lmtato far abov th omal torqu max4 th torqu lmtato bloc ad

3 tgrator aturato lmt m4. (Notc that tgrator aturato lmt oprat alo a a tgrator at wdup). c. Slct PI cotrollr paramtr accordg to c0.00 c, a3 ad th mach momtum of rta J oly. St Kaw0. d. Itroduc pd rfrc a a quar wav of Ωm0.9/60p ad.5hz, whr a omal pd. Choo th mulato tm pa ovr a coupl of prod. Pla fd th dfto from th m-fl Scto Evaluat th pd rpo {rdprot avltatv hdam 3.}. U o Worpac ad From Worpac bloc ordr facltat mulato ad vualzato rout (loo at Fgur 3. ad Matlab Scrpt Scto 3.6).. Itroduc a dffcult tartg codto o that th mach currt at lat doubl a much a th omal currt I>I. By dog that cra th momtum of rta of th haft JJ ad rpat th mulato ad aaly mad prvou cto. (6). 3. pat th aaly ad mulato mad th prvou ta. Now troduc torqu lmtato (that alo lmt th currt) o that max ad tudy th rpo of th ytm (6). 4. pat th aaly ad mulato mad th prvou ta 3. Now troduc atwdup acto o that Kaw0 ad tudy th rpo of th ytm (6). What ca you obrv? Pla ma commt o th ffct of th at-wdup chm. 3.3 Powr amplfr h powr lctroc rgy covrtr oprat a a powr amplfr a lctrcal cotrol ytm. h purpo of th powr amplfr to cotrol th voltag fd to a load, whch th ca th dc-mach. A powr flow ca b thr drcto for a four quadrat (4Q) covrtr. h ma that th output voltag ca b thr potv or gatv ad th load ca b coumg or dlvrg th lctrc powr. A wtchg mod allow a vry hgh powr ffccy of th covrtr, whr th powr wtch ar thr op-crcutd or hort-crcutd (Fgur 3.3). Swtch tat th brach a df whch trator opd ad whch clod that tur dtrm th output pottal va for th brach. dc U dc U dc a va u vb b U dc Fgur 3.3 Powr lctroc crcutry of th 4Q covrtr (H-brdg) wth dc-mach a a load. h wtch tat of th brach df th pottal dffrc ad th voltag acro th load: uva-vb, whch ca b Udc, -Udc or 0. h load modl cot of a rally coupld rtac (), ductac () ad bac mf (), (E-crcut). Hr a coupl of warmg up quto:

4 5. Ca th wtch b clod th am arm at th am tm ad why? (4) 6. What happd wth dc-l voltag f >Udc ad why? (4) 7. Ca th 4Q covrtr output b altratg voltag or t ca oprat oly a dc-dc covrtr ad why? (4) hr ar may dffrt way of troducg th fuctoalty of powr covrtr Smul. O pobl vro how Fgur 3.4. Fgur 3.4 A pobl mplmtato of powr amplfr Smul. h crcutry clud coutr that dtct th umbr of commutato a brach of th covrtr. h coutr fucto ca b mad a followg: Fgur 3.5 A pobl mplmtato of a coutr. Slct Ihrt Sampl m th mmory bloc. h ma purpo of th powr amplfr to dlvr a crta amout of voltag durg a prod, whch t by rfrc voltag ad rgulatd by th chagg of th wtch tat. h cotrol of th voltag tm ara uually carrd out by voltag modulato comparo wth a rfrc. h targt to df th approprat wtch tat o that th powr covrtr dlvr th avrag voltag that t by rfrc voltag ovr o wtchg prod. h rfrc voltag dtrmd by a paratly tadg currt cotrollr. hr ar alo mthod whr voltag modulato ad currt cotrol caot b paratd. h typ of cotrol oft calld tolrac bad of cotrol of currt (or om othr phycal quatty) or drct currt cotrol. 3.4 Drct Currt Cotrol DCC I th ta you ar ad to dg a Drct Currt Cotrollr (DCC), whch purpo to cotrol th currt of a dc-mach. A four quadrat covrtr uppl voltag acro a E crcut of th mach accordg to a rlvat wtch tat, whch lctd agrmt wth th tataou valu of th currt rror. By tartg from th pobl wtch tat ad th corrpodg currt drvatv (abl 3.) th cotrol acto of th drct currt cotrollr ca b udrtood. {Hütrga a-put 5.. ja olm-put 5..4 rgulaator}

5 abl 3. Swtch tat of a four quadrat covrtr, th chmatc prtato of th wtch tag th H-brdg ad load ad th xpro for th currt drvatv. Not that wtch tat ar dotd [,0] a logc hgh ad low, ad [,-], whch uful a a mplmtato mplfcato Smul. Stat of wtch [a,b] Schmatc prtato Currt drvatv d/dt [0 0] or [-, -] U dc E d dt E [0 ] or [-, ] U dc E d U dc E dt [ 0] or [, -] U dc E d U E dc dt [ ] or [, ] U dc E d dt E h cotrol acto of th drct currt cotrollr to p th tataou valu of th currt rror wth a bad or a rag Δ, whr Δ th allowd currt rppl th load currt. wo actv tag ca b ud ordr to carry out th cotrol acto: ( a, b) f f f Δ < th Δ > th Δ Δ < < th [, ] [, ] h prvouly dcrbd wtch fucto ca b mplmtd by ug a hytr cotrollr (a lay bloc Smul). Fgur 3.6 how th graphcal rprtato of th hytr cycl btw th actv tat, whch tr to p th actual currt clo th rfrc currt. h accptd dffrc btw th rfrc ad th actual currt t by th tolrac bad Δ. (3.)

6 (a,b) ON: cra actual currt ad t to [,-] OFF: dcra actual currt ad t to [-,] - Fgur quadrat DCC hytr by ug oly th actv tat Δ h mplt form of DCC u oly th two actv tat ([,-] ad [-,]) by applyg th dc-l voltag acro th load (Udc ad Udc, rpctvly). h drawbac wth that oluto that both wtch ar opratd at th am tm ad th hgh valu of (b-drctoal) currt drvatv, whch du to th u of actv tat oly, may grat ucary hgh wtchg frqucy. A good DCC for a 4-quadrat covrtr mut alo u th two pobl pav wtch tat ([-,-] ad [,]), whr a zro voltag appld to a load. h d of wtchg tratgy wll rduc th umbr of commutato. O oluto of pcfyg thr output voltag [Udc, 0, -Udc] to u two tolrac bad to th currt rppl, o lghtly wdr tha th othr. Four actv tag ca b ud ordr to carry out th cotrol acto: ( a, b) f f f f Δ < th Δ > th Δ Δ < or > Δ Δ < < th [, ] [, ] th [, ] or [, ] h prvouly dcrbd wtch fucto ca b mplmtd by ug two hytr cotrollr (a lay bloc Smul). Fgur 3.7 how th graphcal rprtato of th hytr cycl wth th tolrac bad Δ wth two wdth Δ ad Δ. A actv tat alway cho at vry hgh currt rror. Wh th currt rror dcra t ht th r tolrac bad ad a pav tat lctd. (3.) ON & OFF: mf drv or frwhlg actual currt t to [-,-] or [,] OFF: dcra actual currt ad t to [-,] (a,b) ON: cra actual currt ad t to [,-] - Fgur quadrat DCC hytr cludg th pav tat Δ Δ

7 Sc thr ar two pav tat, a rul mut b mad o whch of th two tat that hould b ud at a gv tm. It favourabl to dvd th commutato (lo) vly btw th wtch. h followg ta you ar ad to prform 8. Study oly th r loop.. th currt cotrol ad xclud th pd cotrol. 9. Implmt th DCC wth th actv wtch tat oly. Iclud th 4-quadrat powr covrtr th drv ytm (Scto 3.3). U th mach modl togthr wth tc that you drvd cto.4 AutP_.pdf (0). a. a th dc-l voltag Udc5V, u th orgal mach momt of rta ad df tolrac bad Δ 0.I b. U o Worpac ad From Worpac bloc ordr facltat mulato ad vualzato rout (loo at Fgur 3. ad Matlab Scrpt Scto 3.6). c. Itroduc a quar wav of th currt rfrc that magtud about 0.5I ad prod m (you wll fd th dfto wth th l th m-crpt). 0. Iclud th poblty to hav DCC wth th actv ad th pav wtch tat (0). a. h tal codto rma th am a.a,.b ad.c ul th tolrac bad dvdd btw th r bad Δ 0.I ad th outr bad Δ.30.I, whch ta.3 tm wdr.. Compar th two dffrt drct currt cotrollr (0). a. Commt th currt rppl ad th umbr of commutato durg th mulato. b. St th tal pd to 0.9/60p th tgrator bloc that put rotatoal acclrato ad th output th rotatoal pd. Commt aga th currt rppl ad th umbr of commutato durg th mulato.. Optoal ta: Iclud cotrol algorthm that ma that both pav tat ([-,-] ad [,]) ar ud vry othr tm a pav tat calld by DCC (5). 3.5 Modulator ad PIE currt cotrollr Practcally t ot too dffcult to u aalog-lctroc ordr to mplmt a dual-bad hytr cotrollr by ug two comparator. Nowaday, t ot alway practcal to carry out cotrol dco wth aalog crcut cotuou tm fram rathr tha wth μ-computr dcrt tm fram {Drtd ütmd pt 6}. Nxt, a ampld currt cotrol for a E-load wll b drvd. h d of dcrt cotrol carrd out by computr. h cotrol acto ta plac dcrt tm fram wth a fxd amplg trval ad t ba o th formato ta th bgg of th amplg trval. Idally, a fat computr abl to provd a output rfrc voltag for th am amplg trval, whr th maurmt wr ta. O cotrary, a low computr gv th output rfrc voltag, whch wa bad o th maurmt ta th bgg of th prvou amplg trval. A vral prdcto mthod ca b ud ordr to hadl th dlay du to th procg pd a raltc low computr. I th comg aaly that ba o mmdat fat computr acto a fw aumpto hav b mad: h cotrollr acto ba o formato achvd th amplg tac : () dcat th actual currt ad () th rfrc currt.

8 h am of th cotrollr to lmat th currt rror ()- () durg th amplg trval (, ). h voltag dd durg th trval, whch drag th ral currt () to th rfrc valu (), ca b drvd from th voltag quato: dt dt d dt u (3.3) h tgrato of th tataou voltag xpro ovr amplg trval gv th avrag voltag quato: ( ),,, u (3.4) I ordr to carry out a currt cotrol algorthm th followg aumpto ha b mad. h rfrc voltag, u u th avrag valu of th voltag that ha to cau th drd currt chag by th d of th amplg trval, Accordg to th aumpto of dad bat currt cotrol th ral currt ha to hav th am valu th d of th ampl a th rfrc valu, h avrag valu of th currt durg th ampl aumd to b ( ) ( ) 0.5, (larzato!) A th amplg frqucy uually vral ordr of magtud fatr tha th dyamc of th load mf,. I coquc of th dad bat aumpto th currt at amplg tac th um of all chag of currt utl th lat chag at tac - ( ) ( ) 0. I accordac wth all th aumpto a currt cotrollr ca b drvd from th avrag voltag xpro (3.4). ( ) ( ) ( ) ( ) { Fdforward Itgral oportoal u Pr 0 (3.5) Not that a PIE currt cotrollr ha b drvd, wth both ga ad tgrator tm cotat drctly rlatd to th crcut paramtr, ad fd forward trm drctly rlatd to mf of th load.

9 h proprt ar uful c t ow pobl to dtrm th cotrollr tvty to chag of a partcular paramtr.g. aturato dpdt ductac ad tmpratur dpdt rtac. h currt cotrollr a for a rfrc voltag ordr to achv th cotrol acto.. lmat th currt rror ()- (). h wtch tat o th powr wtch ha to b chagd th way that th powr amplfr dlvr xactly th avrag voltag that currt cotrollr a. I th ca a modulator ud to dtrm th wtchg tac ordr to dlvr th cary avrag voltag out of th maxmum voltag (Udc) avalabl. h commutato tm tac dtrmd wh a carrr wav u m ad th rfrc valu u ar qual. A tragl wav ud a th carrr wav. h ha advatag of havg rg ad dclg fla, whch ud to dtrm commutato tac or Pul Wdth Modulatd (PWM) cotrol gal for th powr amplfr. h cotrol acto ummard abl 3. ad vuald Fgur 3.0. Each brach (a ad b) of th four quadrat covrtr cotrolld dpdtly h tragular carrr wav var u m btw ±0.5Udc ad hav prod of (.. cotrol acto carrd out twc durg th tragular carrr prod!) h rfrc valu u dvdd btw two brach o that uuvavb h rfrc valu for th brach a ad b ar u a 0.5u ub 0.5u h wtch tat, whch ar dtrmd by modulator, ca b dcrbd a abl 3. abl 3. Codto ad wtch tat Codto u m >u a u m >u b u m >u a u m <u b u m <u a u m >u b u m <u a u m <u b Swtch tat [, ] (pav, u0) [, -] (actv, uudc) [-, ] (actv, uudc) [-, -] (pav, u0) hr ca b a fw dffrt way dfg a modulator ad o how Fgur 3.8. h carrr ampltud [ - ]0.5Udc ad th corrpodg tm vctor [0 ]. Fgur 3.8 A pobl mplmtato of a modulator Smul. h bloc dagram for th PIE currt cotrollr how Fgur 3.9. h voltag lmt ca b mad mplr a th dc l voltag pt uchagabl durg th mulato. Ad t ca b v xcludd a th at-wdup crcut ca b xcludd.

10 Fgur 3.9 A pobl mplmtato of a PIE cotrollr Smul. Notc that Zro-Ordr Hold ma th cotrollr to bhav a a ampld dcrt cotrollr that ha amplg tm. Fgur 3.0 ad 3. how th cotrol acto ad th modulato. Notc that th rfrc voltag, whch how Fgur 3., dvdd to two rfrc Fgur 3.0 btw two covrtr brach a ua ad ub. h output voltag u from covrtr that appld acro th dc mach how Fgur 3.. h voltag u cau currt that cotrollr hould ta car ormalzd quatt u(t)/udc u m -0.4 u a u b tm, t [c] x 0-3 Fgur 3.0 h carrr tragl wav ad th PWM modulatg rfrc ormalzd quatt u(t)/udc ad (t)/i U -0.6 U I -0.8 I Ω tm, t [c] x 0-3 Fgur 3. h currt rfrc, th voltag rfrc from th currt cotrollr ad th output voltag from a powr amplfr ad th armatur currt of th dc-mach ad th pd of th mchacal ytm.

11 h followg ta you ar ad to prform 3. Implmt th SCC wth th modulator (0). a. a th dc-l voltag Udc5V, u th orgal mach momt of rta ad df amplg tm 0. m b. h dfto ad calculato of th cotrollr paramtr you wll fd from th m-fl how cto 3.6. U th prvou fuctoalty ordr to facltat mulato ad vualzato rout. c. Itroduc a quar wav of th currt rfrc that magtud about 0.5I ad prod m (you wll fd th dfto wth th l th m-crpt). Ma th mulato wth th currt rfrc that dfd th m-fl. What you ca obrv? Pla ma commt o th cotrol acto. 4. Compar th ampld currt cotrol wth th two dffrt drct currt cotrollr (0). a. Commt th currt rppl ad th umbr of commutato durg th mulato. b. St th tal pd to 0.9/60p th tgrator bloc that put rotatoal acclrato ad th output th rotatoal pd. Commt aga th currt rppl ad th umbr of commutato durg th mulato. 5. Implmt th SCC wth th modulator (0) ad tudy th rpo wh th cotrol acto a a low. a. Itroduc a quar wav of th currt rfrc that magtud about 0.5I ad prod m that dfd a currt rfrc m-fl ad ru mulato ovr a coupl of prod. What you ca obrv? Pla ma commt o th cotrol acto. 6. Optoal ta: how do you ca obta th lctroc commutato of a gl-pha ac mach accordg to th currt cotrollr that you hav b xprmtg o far? Motvat? (5). 7. Optoal ta: Iclud th pd cotrol ad u th am ttg a you hav b ug th ta 4 ad mulat th ytm rpo (0). Notc that th mulato ca b (vry) tm coumg. 8. Optoal ta: Aaly how th tm cotat c (mplfd torqu rpo modl) rlatd to th amplg tm. I t pobl to ma pd cotrol fatr? What you ca obrv? Pla ma commt o th cotrol acto (5).

12 3.6 M-fl h th m-fl that you hould u your hom agmt ordr to gt th tal data for a lctrcal mach. a a advatag of th crpt to carry out ffctly all th agmt! % Hom agmt 3 o CAD of Automatc Cotrol Sytm % mach dcrpto % th prmat magt mach aumd to hav rotor damtr of D, % tator damtr of D ad mach lgth l. Magtc gap D/4, wdg % hght D/4 ad fll factor ovr th crcular cro-cto 0.5. % upply voltag V, gap flux dty aumd 0.8 ad allowd currt % dty 3A/mm wth th thrmal lmt. Ma dty of th mach % 7000 g/m3 Krjuta a oma martl umbr jätt umbrt vahl tühud % paramtrato [ ]; % tudt dtfcato umbr mu0 4p-7; % magtc prmablty vacuum D ((6) 0)-3; % rotor damtr [m] l ((5) 40)-3; % lgth of mach [m] U ; % upply voltag [V] 4000; % omal pd [rpm] Ph 0.5pDl 0.8; % maxmum magtc Bgap0.8 [V] N 0.5((D-D/4)^-(D/)^)p 0.536; % magtomotv Jm36A/m [Atur] dph Ph/(p/); % dph/dhta [V/(rad/)] NdPh; % lctromagtc torqu [Nm] P /60p; % lctromagtc powr [W] N cl(u/(dph/60p)); % umbr of tur [tur] I N/N; % ratd currt [A] Km dphn; % mach cotat [Nm/AV/rad] M pd^l 7000; % ma of th mach [g].4-8(l.6d)/(0.5((d-d/4)^-(d/)^)p)n^; % rtac [Ohm] /(/mu0d/4/(0.5pdl))n^; % armatur ductac [H] J /47000lp(D/)^((D/)^); % rotor momtum of rta [gm^] Dm J/0.0; % mchacal dampg 0 0.9/60p0; % tal pd (df to acclrato tgrator) Udc 5; % dc-l voltag -4; % amplg tm trval %JJ; c0.00; % torqu rpo tm, c % PI pd cotrollr paramtr a3; % optmum cotrol wa^c; % tgral tm cotat

13 KpwJa/w; Kw/w; Kaw0; max 4; m 4; % proportoal ga % tgral ga % at-wdup ga % Hytr currt cotrollr dt / 0.I; % tolrac bad.. allowd currt rppl dt dt; % r tolrac bad dt dt.3; % outr tolrac bad % PIE tator currt cotrollr paramtr Kp //; % Ga //; % Itgral tm cotat K / ; % gral ga Ka 0 ; % at-wdup ga Umax Udc; Um U; % th hght tgrator voltag allowd wor a at-wdup! ta3; wtch ta ca % currt rfrc m4-3; tm0:-5:0.004; wavg((tm/max(tm)4p))0.5i; ca % currt rfrc m4-3; tm[ ]/4m; wav[ ]0.5I; ca 3 % pd rfrc m0.; tm[ ]/4m; wav[ ]0.9/60p; othrw d rf[tm; wav]'; % Smulato % op('autp_3a_mdl.mdl') % moptmt('maxstp',-4); % m('autp_3a_mdl',[0 m],mopt);

14 % wtch ta % ca {,} % fgur(); clf; hold o; grd o % htar(dt,ua/udc); t(h, 'Color',[ ]0.9, 'Wdth',.0) % plot(t,ua/udc, '-', 'Color',[ ]0.9, 'Wdth',.0) % plot(tm,wav/i, '--', 'Color',[ ]0.9, 'Wdth',.5) % plot(t,ia/i, '-.', 'Color',[ ]0.9, 'Wdth',.0) % plot(t,wa/(/60p), ':', 'Color',[ ]., 'Wdth',.0) % hlgd('u','u','i','i','\omga',4); t(h,'fotsz',) % xlabl('tm, t [c]','fotsz',); % ylabl('ormalzd quatt u(t)/udc ad (t)/i','fotsz',); % ca 3 % fgur(3); clf; hold o; grd o % plot(tm,wav/(/60p), '--', 'Color',[ ]0.9, 'Wdth',.5) % plot(t,ia/i, '-.', 'Color',[ ]0.9, 'Wdth',.0) % plot(t,wa/(/60p), ':', 'Color',[ ]., 'Wdth',.0) % hlgd('\omga','i','\omga',4); t(h,'fotsz',) % xlabl('tm, t [c]','fotsz',); % ylabl('ormalzd quatt u(t)/udc % ad (t)/i','fotsz',); % othrw %d