Verification of adaptive PID and PIDD 2 control algorithm by hybrid simulation

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1 XXVI A ' mn, Instmnts nd Contol, Ostv, Al 6 7, P Vfcton of dtv PI nd PI contol lgothm y hyd smlton ALEXÍ, Mláš & ALEXÍ, ml Pof, Ing, Ph, Unvsty of Žln, Vľý dl, FI, 6 Žln, lx@ftftcs, smo@ftftcs Astct: hs dscs l tm hyd modllng nd smlton of IO contol loo th clsscl nd dtv contol lgothms nd PI nd PI lgothms synthss fo thd od lnt y nvs dynmc mthod Fo xmntl vlton of th contol lgothm n l tm th hyd smlton, hch lcs l lnt th ts nlog modl, th A/ nd /A convts nd PC s contoll, s sd Hyd smlton ncss motvton of stdnts dng lotoy vfcton of contol lgothms t lssons nd lso ncss lty of vfcton lgothms dvlod y sch ocss yods: Hyd smlton, smlton xmnt, nlog modl, dntfcton, PI Intodcton Modllng nd smlton of contol loos s th otn mthod n th ocss of vlton of contol lgothms, sclly dtv lgothms Mnly t s ld dsct o PC smlton hn th hol contol loo s lsd y sngl comt ogm By tho onon hyd smlton s th st y fo vlton of contol lgothms In Fg th s loc schm of dtv contol smlton s n xml of sng of hyd smlton fo contol lgothm vfcton Fo xmntl vlton of th contol lgothm n l tm th hyd smlton, hch lcs l lnt th ts nlog modl nd th A/ nd /A convts, s sd Hyd smlton ncss motvton of stdnts nd sch os dng dsgnng o lotoy vfcton of contol lgothms h s ognsd s follos In cton th s dscd nlog modl of th contolld lnt sd fo hyd smlton cton s synthss of PI lgothm In cton th dscd l tm smlton xmnts ccodng to th loc schm dctd n Fg h nds th conclson nd otloo n cton ynthss Cton Modl of Contolld Loo Bhvo Contoll ynthss Comt s mlton Modl o Pocss Contoll Contoll Pmts Plnt Pmts ystm Idntfcton A/ Modl of Plnt Bhvo W E U Contoll /A Plnt l ystm o ts mlton Modl Fg Hyd smlton of dtv contol loo th onln dntfcton Y

2 Anlog modl of th contolld ocss Fo vlton of contol lgothms, th hyd smlton n comson th th dgtl on s mo stl In o cs t s th contnos ocss modlld th th contnos modl ong n l tm h tchncl dsgn of th contnos modl nls s to modl th ootonl ln systm of th fst to th sxth od nd lso to chng th mts nd th stct of th contolld systm, hch s stl fo th vlton of ostnss of th contol lgothm Fg shos nd dscs th modl h dynmcs of th ocss lsd th th modl nd Fg s dscd th tnsf fnctons of th scond nd fst od ng th tnsnt stt, t s ossl to chng th ltv dmng fo th scond od systm o tm constnt of th scond o fst od nd th totl gn o od of th systm fom th fst to sxth ods It s lso ossl to connct modl s th MIMO systm th nts nd otts Potnc fo dstnc mgntd t chng of dstnc m of sgnls U Modl of th ystm 8 gtl Vmt Y U, Y,, U Y t chng of gn Int U Y Ott U, Y,, Contn chng of gn tch fo tm constnt cond od ystm th vl dmng cond od ystm th vl tm constnt tch comnton of systms Fst od systm th vl, tm constnt, Fst od ystm Fg Modl of th contolld systm h ndvdl modls cn connctd to th nt of th gn loc, hch s md s "U" n Fg nd thn t s ossl to chng th systm gn dng th tnsnt stt n contnos o st mnn h stch nls to comn ndvdl tnsf fnctons n sch y tht th "Y" ott hs dynmc chctstcs of th ootonl systm tll th sxth od hs nd of modl of th contolld lnt nls s to chng ndvdl tm constnts, gns nd stct of th contolld systm n contnos o st y st mnn Eo of A/ convt ld fo hyd smlton th st A/ s shon n Fg 6 t[s] mlng Intvl Qntton o of A/ convt 6 t [V] Fg Qntton o of A/ convt ld fo hyd smlton

3 nsnt sonss of scond nd ffth od systm msd fom vos dscd nlog modl of th contolld lnt shon n Fg l tm smlton xmnts o hyd smlton dscd n nxt cton mnly lsd th ffth od modl, hch sons s dctd s "" n Fg nd dtv PI o PI contol lgothm y[t] ystm,c ystm,,, ystm,,,, ystm, 9 ^ ^ ^ ^ , 7 t[s] Fg nsnt sonss of th scond nd ffth od systms ynthss of PI nd PI lgothms h m of th synthss of fdc s to oos stct nd mts of th contoll Pol lcmnt contol consst n ssgnng y fndng sch th contoll tht stsfs th scd fdc contol dynmcs Consd th stscd dynmcs of fdc h hvo of th fdc nd consdton s dscd y tnsnt sons dctd n Fg Bcs ll contolld lnts dynmcs t s mossl consd dl sons n Fg, only sonss to fo scd dynmcs of fdc h st l dynmcs of fdc s dct s sons "" n Fg, hch s dscd s th fst t yt t g dl sons I od sons II od odcty od II od th ovshoot t g ln/δ fo sons t g,9 fo δ, t g,6 fo δ, t g sttlng tm tm const of I od dm ndd sons, m ts of II od dm ndd sons δ 6 t[s] Fg nsnt sonss of fdc scd dynmcs

4 od tnsf fncton Consd III od contolld lnt dscd y ton h l ols o on l ol nd comlx ols dsc lnt dynmcs If comlx ols: If l dffnt ols thn : / < < λ ω λ If consd scd dynmcs of fdc s th scond od tnsf fncton cs n Fg, thn th contol dsgn cn cd ot ccodng to th follong tons Y F W Fo dgtl contol If h xmls of tnsnt sonss th dgtl PI lgothm tht hs n dvd ov, fo tnsf fncton nd scd dynmcs dctd n Fg 6 Also f smlng ntvl chngng th tnsnt sons lty s sonsl to scd dynmcs of fdc fo 6 Y 77 s scd : W / Anlytcl sons of scd dynmcs thot mnltd vl constnt yt,,,, sonss of PI contol tht mnltd vl constnd mlng, s,,σ%, t g 966 mlng, s,,97 σ8%, t g 9 s mlng s,,8 σ %, t g 9 s mlng, s,,68 σ %, t g 8 s mnltd vls x dcsd t [s] Fg 6 nsnt sonss of fdc th PI lgothm

5 Unfotntly dscd PI lgothm s mo fo lnts th comlx ols hn l ol s mch clos mgny xs s l t of comlx ols m constnt hch ffcts sttlng tm s too g nd PI lgothm fl comnst ts In ths cs s th st to dsgn PI contol lgothm An xml fo tnsf fncton 6 s dctd n Fg 6 [ ] [ ] 6 ω λ t[s] y nsnt sons of contolld lnt Fdc sons th PI lgothm Fdc sons th PI lgothm / mlng ntvl [m s] Fg 6 nsnt sonss of fdc th PI nd PI lgothms In nxt t of ths s dscd dsgn of contnos nd dsct PI contol lgothm fs tm dvd y tho Algothm PI cn dvd th sm dvnc s n to f consd fst od sons of fdc sons n Fg h dvncmnt gnst PI s osslty choos th sttlng tm of fdc sons y sttng tm constnt " " ynthss dvnc fo contnos lgothm s cl fom ton 7 to 9 slt of ths dvnc s stct nd mts of contol lgothm 9 d d PI F In ths contnos cs th nflnc of tm constnt to th sttlng tm s dscd n Fg f mnltd vl s thot constnt In th cs of constnt of mnltd vl AntWndU lgothm ll dscd fo dsct domn Fo dv of dsct PI lgothm ssm thd od lnt th l ols slts ll vld

6 6 lso fo lnt th on l nd comlx ol Fo convson of III od tnsf fncton fom contnos to dsct domn lton's vld / x : P očt o sojtého do dstného tv ltí h fst od scd dynmcs of fdc n dsct domn cn dscd s Fom dvd ton of contoll fomlly cn ttn Z tnsf fncton of contoll n fom If com th tm fom of Z tnsf fncton of dsct PI lgothm thn otnd lgothm mts n fom 6, hch mts of contolld lnts n dsct domn [ ] [ ] [ ] lm Wh th xndng constnts : lm lm nto fom : cn xndd Eton nd, da da / 6 B B F F F d d da da da da h xssons fo ootonl gn of contoll n ton hv to lgnd If consd th stdy stt of fdc thn ootonl gn of contoll cn dscd y ton 8 m constnts of lgothm y consd 6 otnd n fom 9 nd dnd on lnt mts nd smlng ntvl only Pootonl gn of contol lgothm s dndng on lnt mts nd tm constnt " " of fdc dmndd sttlng tm m constnt sttng ncssty consttts th mn nss of ths dsgn

7 ndlty of sttlng tm cosondnt to smlng ntvl mnltd vl constnt nd contolld lnt dynmcs ll hv to xlnng n noth lm B lm lm d d [ ] B B lm lm lm lm If t ncssy to comt mts of dsct PI lgothm fom mts of contnos tnsf fncton of contolld lnt nd smlng ntvl, t cn ld Pd oxmton fo cston of oxmt solton d d / s 7 y / s 6s t g 7s s s t g s > s s s tg 78 oxm ton of lgothm m ts s s t g s s d 8s d 6s t[s ] Fg 7 nsnt sonss of fdc th PI lgothms y constnts of 7

8 8 Fo comtng tn contnos nd dsct vson of PI contol lgothm ton nd vld Esclly ton vy sml nd n th fom s t of Bn lgothm [ ] [ ] [ ] / lm / / / I I I d d h AntWndU lgothm xndd fo PI fom s dvd y tho nd s dscd y nsnt sonss th ths lgothm dctd n Fg 7 nd lso n th nxt t of ths mlton xmnts mlton xmnts th contol lgothms, dscd n ths scton, dtv contol xmnts th contnos dntfcton In ncl, th onln mthmtcl modl of contolld lnt nd onln synthss of contol lgothm fo dmndd lty of contol ocss sggstd hs dvnc s clld lfnng Contol C o ndct dtv contol cs th mts of th contol systms djstd ft th clclton of lnt mts ynthss of dtv contol lgothm fom dt clcltd y contnos dntfcton dscd n Alx, 997, Bol t l, nd o, 99 Exml of l tm smlton xmnt s shon n Fg 8 Advntg of hyd smlton s lso l tm jm chng of lnt mts Contol loo sons nd dntfd mts' tnng y jm chng of lnt mts s dctd n Fg 9 t yt tm [s] 8 6 Fs s 7s s s s 9 mlng ntvl: [s] Anlog modl of th lnt Modl fo contol fom contnos dntfcton Ms s s Idntfd mts n tm t 8 [s] 98, 79, vlomnt of dntfd mt " " vlomnt of dntfd mt "" Mnltd vl x dcd t [V] Fg 8 Adtv onln contol sd on contnos dntfcton

9 [V] t yt mlng ntvl o [ms] m nstnd of ystm chng fom, to, mt "" mt "" mt "^",c >>, m [s] Fg 9 Hyd smlton of mts tnng y th jm chng of lnt mts Comson of comt smlton nd hyd smlton of dtv PI contol, ncldng dntfd mt tnng y hyd smlton, s shon n Fg Contolld lnt s fom Fg nd contoll synthss s lsd fo thd od dntfd modl ynthss of contnos nd dsct PI lgothm fom dntfd dt, dvd y tho s dscd n Alx, Eton,, nd dsc contol lgothm ncldng AntWndU t yt tnng of dntfd mts n fst 8 sts t[v] t[v] m m m m hyd smlton PC smlton mlng [s] 6 mx [V] Idtfd modl of th lnt mn [V] F t[v] tm [s] Fg Comson of dgtl nd hyd smlton of dtv PI contol Also nxt to Fgs sho smlton xmnts th dtv PI lgothm In th Fg hyd smlton th ffth od lnt fo th dffnt smlng ntvls s shon Fom Fg s ll s fom Fg s vdnt, tht contol lgothm dscd y ton to nls good lty of contolld loo hvo fo svl 9

10 smlng ntvl nd hgh ods of contolld lnt s ssmd fo contoll synthss Contol lgothm synthss s ndndnt fom smlng ntvl, s s vdnt fom to Hov, to olms mst solvd comltly: contnos dntfcton lgothm, lcl fo d scl of smlng ntvl nd fo dntfcton of vl tnsot dly nd convnnt contnos clclton of tm constnt "" Alxí, hch dfn dmndd lty of contol loo sons On osslty fo good synthss of contol lgothms s dscd n Vtčová, 998 Ffth od lnt dntfd s thd od lnt nd dsct PI dtv contol lgothm t yt t [V] Anlog modl of th lnt 9 Fs s 7s s s s, [s] mlng ntvl: [s] [s], t [V] Mnltd vl x dcd Idntfd modl fo contol lgothm F 6 9 tm [s] Fg On ln dtv contol of th ffth od nlog modl PC A/&/A h nxt smlton xmnt shon t Fg s dgtl not hyd smlton of dtv contol of lnt th nonmnml hs fo fo dffnt smlng ntvls o contol sch ty of lnt s vy dffclt, t fom Fg s vdnt, tht dscd PI dtv lgothm ovds vy good lty clos to tmotml hv contolld loo sons h stt of dtton ocss tm ntvl [s] s th ont of ll dtv contol lgothms yt mlng ntvl [s] [s] [s] [s] 6 9 tm [s] s Fs 6s s 6s Fg gtl smlton dtv contol of lnt th nonmnml hs

11 h nxt smlton xmnt shon t Fg nd s lso comson of dgtl th hyd smlton of dtv PI contol of scond nd ffth od lnt As cn sn fom oth fg lgothms PI t cn ld lso fo scond od systm nd tnsnt sons lty n th oth smltons xmnts dgtl nd hyd vy sml Hov th s th olm th contnos clclton of tm constnt "", hch s not stsfy solv nd ll hv to xln n noth sscton yt mlng ntvl [s] 6 tm [s] 9 scond od lnt,c ffth od lnt, ffth od lnt, Fg gtl smlton dtv PI contol of scond nd ffth od lnt cfc olms lso th stt of dtton In th fst svn to svl tnth sts t dnds fom o of dntfcton, hch s comtd, P lgothm th vyng gns s ld In ths cs s th olm th dtv comtng of gns nd dntfcton o dnd on smlng ntvl nd dntfd mt of lnt At ths tm ths olm s not stsfy solv nd coffcnt of vyng gns nd n o of dntfcton hn dtton ocss s sttd hv to tn hd of stt of smlton xmnt yt mlng ntvl [s] 6 tm [s] 9 scond od lnt,c ffth od lnt, ffth od lnt, Fg Hyd smlton dtv PI contol of scond nd ffth od lnt

12 mlton xmnt th constnt gns nd constnt dntfcton o fo stt dtton n ll th sons dctd n Fg, h hyd smlton xmnts th th sm nlog modl of lnts s n Fg t th dffnt smlng ntvl Mntond olm th comtng of vyng gns nd o of dntfcton fo sttng dtton ll solvd n noth yt mlng ntvl [s] stt of dtton 6 tm [s] 9 scond od lnt,c ffth od lnt, ffth od lnt, Fg Hyd smlton dtv PI contol of scond nd ffth od lnt Conclson nd otloo Bsd on snt xnc, th lotoy vfcton nd tchng of contol lgothms on dscd hyd smlton ovds good slts hs y, th vfd clsscl nd dtv PI, PI, Bn, Bn lgothms, stt lgothms, sldng mod lgothms nd slftnng PI lgothm In ths, th s dscd s xml n dtv PI lgothm th contnos dntfcton, nd nlog modl of contolld systm sd fo hyd smlton mlton xmnts th dgtl modls of contolld systms nd l tm smlton hyd smlton lsd n ogm nvonmnt of AAPLAB, dvlod nd lsd y tho It s stl fo dvlong nd vfcton of clsscl s ll s dtv contol lgothms fo IO nd MIMO contol loos h ogm cn sd n to sc mods: mlton nd Msmnt h smlton mod os th contnos tnsf fncton st y oto In th msmnt mod th ott nt fom modl of th lnt dscd n cton s msd th A/ /A convt th smlng ntvl contolld y l tm cloc o ntt fom A/ convt A t of dscd nvonmnt s sccssflly sd n lotoy ctclly n sjcts "gtl Contol", "Comt Contol" nd "mlton of th ystms" t th Unvsty of Žln h nvonmnt lso hls dvlong nd vfcton of n dtv contol lgothms s dtv PI lgothm mntond ov U to no xnc of tho shod, tht hyd smlton s mo ot s dgtl smlton oth fo vfcton nd tchng In ft, th tho ll focs on sch of slftnng lgothms, stt of dtton olm nd vl tnsot dly dntfcton Acnoldgmnts hs contton s d nd th ojct VEGA /68/999 "Adtv lgothm fo tomtc contol"

13 6 fncs ALEXÍ, M 998 Adtv lfnng PI Algothm Bsd on Contnos ynthss In N nds n sgn of Contol ystms molnc, lov lc, 7 tm 997 Plshd fo IFAC y Pgmon n Imt of Elsv cnc, 998, 886 ALEXÍ, M Anlytcl synthss of PI lgothm fo thd od systm A&P Jonl 9/, lov chnologcl Unvsty, Btslv, 66 IN 7 In lov BOBÁL V t l lf nng PI Contolls Bsd on ynmcs Invson Mthod In: Pocdngs fom IFAC Wosho, gtl ContolPst, Psnt nd Ft of PI Contol Unvsty of Ctlny, ss, n,, 888 OZÁ, Š 99 Nonln lftnng Contoll Bsd on Lg s sntton In N nds n sgn of Contol ystms tm 99, molnc, 8 VÍEČOVÁ, M 998 říní číslcových nlógových gláto o glovné sostvy s dovným sožděním Atomtc, č, 998, st 6

3. Anomalous magnetic moment

3. Anomalous magnetic moment 3. Anolos gntc ont 3.1 Mgntc ont of th lcton: Dc qton wth lcton colng to lcto-gntc t fld: D A A D ψ 0 cnoncl ont Anstz fo th solton s fo f tcl: t t Χ Φ Φ Χ 0 A 0 A Χ Φ 0 Χ Φ χ ϕ x x 4 Non-ltvstc lt: E,