Comparison of Digital Control Techniques for Low Cost UPS Applications

Transcription

1 omarison of Digital ontrol chniqus for ow ost UPS Alications assiano ch, Humbrto Pinhiro, Hélio. Hy, Hilton A. Gründling and José. Pinhiro Powr Elctronics and ontrol sarch Grou GEPO Fdral Univrsity of Santa Maria UFSM Santa Maria, S Brazil cassiano@i.org, rns@ctlab.ufsm.br - htt:// Abstract his ar rsnts a comarison among digital control tchniqus with rtitiv intgral action suitabl to unintrrutibl owr sulis. As a rsult of th rtitiv action, ths digital control schms can rduc th stady-stat rror and distortions causd by unknowriodic disturbancs usually rsultd from th inut sourc and outut load. Morovr, ths digital control schms masur only th outut voltag, dcrasing th amount of snsors and, consquntly, th ovrall systm cost. h control laws, stability analysis, common and distinguishing faturs of ths control algorithms ar discussd. Exrimntal rsults from a PWM invrtr ( V MS, kva) controlld by a low cost micro ar rsntd to dmonstrat th control tchniqus rformanc undr diffrnt load conditions, outut filtrs and command stratgy. I. INODUION h widsrad availability of low cost micros and DSP rocssors has mad ossibl th incrasingly us of ths comonnts for ral-tim control of static convrtrs. h ossibility to includ as many of th control functions as ossibl in softwar, thrby incrasing rliability and rducing costs, maks th digital control of unintrrutibl owr suly (UPS) systms commrcially attractiv. Digital control tchniqus should gnrat th uls width modulatd (PWM) signal to roduc th sinusoidal outut voltag of th UPS systm with low total harmonic distortion (HD) for linar and nonlinar loads [], []. Nvrthlss, although ths tchniqus rsnt satisfactory rsults for load transints, th outut voltag wavform normally rsnts high HD for nonlinar cyclic loads, such as ac hascontrolld loads and rctifir loads. titiv control thory rovids an altrnativ to minimiz riodic rrors that can occur in a dynamic systm []. h rtitiv action imrovs th stady-stat rsons of a control systm whn th rfrnc inut signal and disturbancs ar riodic, consisting of harmonic comonnts of a common fundamntal frquncy. Svral rtitiv control schms hav bn dvlod and alid to minimiz th stady-stat rror and riodic distortions that can aar in singl-has PWM invrtrs [4] []. Although many digital control schms hav bn dvlod for UPS alications in th last yars, most of th ublishd work has concntratd on th control law and suosd advantags of th scific control schm, rathr than oroviding an in dth analysis of th ovrall control systm. It is thrfor th aim of this ar to rovid a comarison among digital control tchniqus with rtitiv intgral action alid to low owr (5 VA 5 kva) UPS systms. h digital control tchniqus analyzd ar: rdictiv OSAP (On Samling Ahad Prviw), rdictiv PID (roortional-intgral-drivativ) with a fdforward action, and modl rfrnc. h digital control schms considrd masur only th outut voltag, dcrasing th amount of snsors and, consquntly, th ovrall systm cost. h control laws, stability analysis, and simulation and xrimntal rsults ar rsntd to dmonstrat th main faturs of ths digital control schms. ommon and distinguishing faturs ar idntifid, and systm rformanc analyzd in trms of ths faturs. his ar is organizd as follows. Sction II dscribs th lant modl and analyzs th ffcts of incrasing th PWM invrtr switching frquncy. h rdictiv OSAP with rtitiv intgral action is dscribd in Sction III. Sction IV rsnts th rdictiv PDfdforward control law with rtitiv. h modl rfrnc with rtitiv intgral action is rsntd in Sction V. Sction VI givs th stability analysis of th closd-loo systms with th s of rvious sctions. Sction VII shows a comarison of th simulation rsults, and Sction VIII rsnts xrimntal rsults obtaind for linar and nonlinar loads basd on a micro-controlld systm. II. PAN MODE A tyical singl-has PWM invrtr is shown in Fig., whr th full-bridg invrtr, filtr and rsistiv load ar considrd as th lant to b controlld. A riac connctd in sris with a rsistiv load or a full-bridg rctifir with filtr can b usd to valuat th rformanc of th systm with nonlinar loads. V B S S Drivrs S v in( S 4 v c (k) v c( Micro-basd Fig.. Digitally controlld PWM invrtr.

2 .9 VB (or -VB)... n n ( ) Fig.. PWM attrn. h owr circuit shown in Fig. is modld as a scondordr systm with th stat vctor [ v ] c ( v c (, whr v c ( is th outut voltag and v c ( is th drivativ of v c (. As a rsult, th stat quation and th outut quation ar: x ( = Ax( Bvin ( () y( = x( whr vc ( x ( =, A =, B = v c ( ω ζ ω, ω () = [ ], ω =, ζ = It is wll known that incrasing th switching frquncy of th PWM invrtr it is ossibl to rduc th aramtrs of th outut filtr and ossibly imrov th dynamic rsons of th systm. Howvr, du to th comutation tim of th control law, it is not ossibl to incras th samling frquncy (udating frquncy of th control law) at th sam rat. In this way, th switching frquncy can b incrasd whil th samling frquncy is maintaind th sam, as shown in Fig.. With this PWM attrn, which may b calld of MPWM (Multi-Puls Width Modulation) attrn, th switching dvics ar turnd on and off tims during ach samling intrval so that th invrtr voltag v in ( bcoms ulss of magnitud V B or V B, and width /. hrfor, th samld-data quation of th systm can b obtaind solving () in a samling riod, that is: x( k ) = ( k ) A x( A( τ) ( k ) A( τ) BVBdτ ( n ) BVB dτ... ( n ) ( k )... A( τ) BV dτ In this way, th nonlinar discrt-tim stat quation can b obtaind solving (): n ia k A ( ) A n n x( k ) = x( A I BVB (4) i= A ( onsidring that can b comutd by using aylor sris, it is ossibl to obtain a linar discrt modl from (4) by nglcting trms of highr than, that is: g g h x ( k ) = x( ( (5) g g h B () Normalizd rror of h Normalizd rror of h n = n = n = n = 4 n = ( n = 5 n = 4 n = n = n = ( Fig.. Modling rrors for diffrnt valus of (ω = 55 rad/s, ζ =.4). or, in a comact form: x ( k ) = G x( H ( (6) whr g ij is th corrsonding lmnt of G = A, and n ia n h i is th corrsonding lmnt of H = BVB n. i= Howvr, du to th linarization of th nonlinar discrttim lant modl (4), th aramtrs of th inut matrix H ar diffrnt from th ral ons. Fig. shows th normalizd rrors, whr th rsctiv aramtr of th nonlinar modl is usd as bas valu, btwn th aramtrs of th inut matrix H (h and h ) and rsctiv aramtrs of th nonlinar modl, for diffrnt valus of voltag ulss r samling riod ( ). It can b clarly sn that th modling rrors causd by th linarization ar rducd, incrasing only th switching frquncy of th PWM invrtr [8]. From a linar discrt-tim lant modl, th inut-outut rrsntation of (5) in th z-domain can b obtaind: y( z) = z h ( h g h g ) z ( g g ) ( g g g g ) z ( z) Hnc, th following diffrnc quation can b obtaind: y k ) a y( a y( k ) = b u( b u( k ) (8) ( whr th inut variabl and th gains of th quation ar: a ( u( = V B a = ( g ) g = gg g g (7) b h V B = ( h g h g ) V (9) B = b

3 III. PEDIIVE OSAP ONOE WIH EPEIIVE INEGA AION h OSAP is a dadbat control law that uss only on voltag snsor []. hus, th cost of th ovrall systm and th comutation tim of th ar rducd. h OSAP control law can b obtaind from (8) considring that th outut is qual to th rfrnc signal at th nxt samling instant, thn y(k ) can b substitutd by r(k ). hn, th following control law can b obtaind: u OSAP r( k ) y( y( k ) qu( k ) ( = () q If th OSAP gains,, q and q ar qual to th lant aramtrs a, a, b and b, rsctivly, it bcoms a dadbat control law which forcs th outut voltag to b qual to th rfrnc signal at th nxt samling intrval. Howvr, if th lant aramtrs chang aftr th gains in () hav bn dtrmind, thn th dadbat rsons is no longr obtaind []. Morovr, th uls width dtrmination for k-th samling intrval is startd at t = k with th acquisition of th outut voltag and thn aftr th comutation tim th uls width is dtrmind. onsquntly, th dlay tim causd by th outut voltag analog-to-digital (A/D) convrsion and control law comutation rducs th maximum availabl uls width. o solv this roblm, Nishida and Hanyoshi rsntd a rdictiv OSAP [5]. his control law can b found by using (8) to obtain y(, and substituting in (), thn: r( k ) P y( k ) P y( k ) Qu( k ) Qu( k ) u OSAP ( = () Q whr P, P, Q, Q and Q ar th gains, givn by: P P = ( g gg g g g ) ( g g g g g g g g g ) = g Q = h V B ( h g h g ) VB Q = ( h ( gg g ) h ( gg g g ) VB Q = () Equation () shows that th rquird signals for th dtrmination of th control law ar th outut voltag at th rvious samling instants (y(k ) and y(k )), th valus of th control law at th rvious samling instants (u(k ) and u(k )), and th rfrnc signal at th nxt samling instant (r(k)). Hnc, th uls width comutation can b comltd during th rvious samling riod, and th uls width can b xtndd to th ntir riod. In addition, a rtitiv can b addd to th rdictiv OSAP, as shown in Fig. 4, to rduc th stady-stat rror and distortions causd by riodic disturbancs, such as nonlinar loads [5]. h rtitiv control law with an intgral action can b writtn as: ( k N i n) i= u P ( = c () r Prdictiv u OSAP OSAP titiv u P u Plant Fig. 4. Block diagram of th control systm with OSAP-P. whr ( = r( y( is th outut rror, c is th gain of th rtitiv, N is th tim advanc st siz and n is th numbr of samls in a riod of rfrnc voltag. h choic of th rtitiv gain must nsur a good transint rsons and th stability of ovrall closd-loo systm. Highr rtitiv gain rsults in fast convrgnc of th outut rror, howvr th fdback systm may bcom unstabl for high valus of c. hn, th rsulting control law u( bcoms: u( = u ( u ( (4) OSAP IV. PEDIIVE PD-FEEDFOWAD ONOE WIH EPEIIVE INEGA AION h classic PID has bn usd in many industrial control systms, rincially bcaus of its siml structur that can b asily undrstood and imlmntd in ractic, and its xcllnt flxibility mad ossibl by adjustmnt of th cofficints K P, K I and K D. h quation of th PID in th continuous-tim domain is: d( u PID ( = K P( K I ( dt K D (5) dt For a micro imlmntation, (5) bcoms k K D u PID ( = K P( K I ( n) [ ( ( k ) ] (6) n= According to (6), th control variabl u PID ( dnds uon th rsnt valu and th rvious valus of th outut rror (. If th rquird comutation tim to imlmnt u PID ( is not small, thr may b bnfit irdicting th valu of ( at tim t = (k ), and thn comuting u PID ( from (6). In this way, a siml linar rdiction algorithm can b usd to rdict th outut rror ( [], [], that is: P ( = ( k ) [ ( k ) ( k ) ] (7) Using (7) to rdict ( in (6), th rdictiv PID quation bcoms: u PID ( = [ K K K ] P I ( k ) k [ ] [ ] K P K I K D ( k ) K I n= D ( n) y (8)

4 r Prdictiv PD u PD u titiv u P Plant Fig. 5. Block diagram of th control systm with rdictiv PD-fdforward with rtitiv intgral action. o rduc th outut rror for linar and nonlinar cyclic loads, a fdforward action and a rtitiv ar addd to rdictiv PID [9], as shown in Fig. 5. onsquntly, du to inclusion of th rtitiv with intgral action along with th control law, it is ossibl to liminat th intgral action from th PID. hus, th comutational ffort for th imlmntation is rducd without affcting systm rformanc. By rmoving th intgration from th rdictiv PID, (8) bcoms, u PD ( = K( k ) K ( k ) (9) whr K = KP KD () K = KP KD hn, th control law u( bcoms: u( = upd ( up ( r( () In [9], rdictiv PD-fdforward gains (K and K ) ar dtrmind by allocating th two dominant ols of th closd-loo systm, such that th fdback systm with rtitiv has a good rformanc for any rsistiv load. V. MODE EFEENE ONOE WIH EPEIIVE INEGA AION onsidr a singl-inut singl-outut lant as rsntd in Fig. 6. h inut u( and outut y( signals ar usd to gnrat m dimnsional auxiliary vctors, ω and ω rsctivly, whr m is th ordr of th systm to b controlld. Such that, ω ( k ) = F ω( qu( () ω ( k ) = F ω ( q y( whr F is a stabl matrix and (F,q) is a controllabl air. As dfind in [], (F,q) is th stat sac ralization of α ( z) Λ( z), i.., α( z) ( z F) q = () Λ( z) h olynomial Λ(z) is chosn as bing monic, Hurwitz of dgr m and its ols must b matchd with th dynamics of th rfrnc modl as wll as with th dynamics of th knowart (nominal modl) of th lant. In this cas, th control law is givn by: u M o ( = θ ω( c r( (4) y r u y c o Plant θ θ θ ω ω ( z F ) q ( z F ) q Fig. 6. Block diagram of th systm with th modl rfrnc. r u θ ω c M o r titiv u P u Plant Fig. 7. Block diagram of th control systm with th modl rfrnc with rtitiv intgral action. whr θ = [ θ θ θ] is a (m ) dimnsional control aramtrs vctor tund a riori using a robust modl rfrnc adativ (MA), which uss a modifid last-squars adatation algorithm [7], []. Furthrmor, ω ( = [ ω( ω ( y( ] is a vctor containing th auxiliary stats ω ( and ω ( and th outut y(, and c o is a fdforward gain. Again, a rtitiv is addd to modl rfrnc, as shown in Fig. 7, to rduc th stady-stat rror and riodic rrors causd by riodic disturbancs. h control law u( thn bcoms: u( = u M ( u P ( (5) VI. SABIIY ANAYSIS h absolut stability of th fdback systms has bn invstigatd by th localization of th closd-loo ols with th variation of th lant aramtrs (, and ). Fig. 8 shows th stability rgion of th rdictiv OSAP in ω ζ lan. his figur also givs th trajctoris of th lant aramtrs in this lan. For a givn trajctory, on aramtr varis along th trajctory and th othr two aramtrs ar hld constant at thir nominal valus. Fig. 8(a) shows th stability rgion whn th rdictiv OSAP is dsignd with ζ =.5 and ω = 65 rad/s. On th othr hand, if a MPWM attrn is usd, it is ossibl to rduc th outut filtr aramtrs and, consquntly, to dsign th rdictiv OSAP for a highr natural frquncy. By using a MPWM attrn with thr voltag ulss r samling riod, th rdictiv OSAP is dsignd with ζ =.5 and ω = 55 rad/s, and stability rgion is shown in Fig. 8(b). It can b sn that with th aroriat dsign of th rdictiv OSAP th stability margin of th closd-loo systm incrass and, thn, its rformanc can b imrovd. y

5 Fig. 9(a) rsnts th stability rgion of th rdictiv PDfdforward, whn th switching frquncy is qual to th samling frquncy (.8 khz). hus, th natural frquncy of th outut filtr is ω = 65 rad/s. Fig. 9(b) shows th stability rgion of th rdictiv PD-fdforward, whn a MPWM attrn with thr voltag ulss r samling riod is usd for a natural frquncy of th outut filtr qual to ω = 55 rad/s. In th sam way, Fig. shows th stability rgion of th modl rfrnc in ω ζ lan. From Fig. 9 and Fig., it is ossibl to vrify that th rdictiv PD-fdforward and th modl rfrnc ar lss snsitiv to aramtric variations if comard with th rdictiv OSAP. hus, considring that th closd-loo systms without th rtitiv control action ar stabl for a larg rang of lant aramtrs, as can b sn in Fig. 8(b) to Fig., th stability of th systms is dtrmind by th rtitiv. In [8], [9] and [], th stability analysis with rtitiv was carrid out. hrfor, dmonstrating that th control systms shown in Fig. 4, Fig. 5 and Fig. 7 ar stabl..8.6 ζ ω (rad/s) x ζ ω (rad/s) x 4 (b) (a) Fig. 8. Stability rgion of rdictiv OSAP in ω ζ -lan. (a) Nominal valus: = 5 µf, = mh and = Ω. (b) Nominal valus: = 5 µf, =.5 mh and = Ω..8.6 ζ ω (rad/s) x ζ ω (rad/s) x 4 (b) (a) Fig. 9. Stability rgion of rdictiv PD-fdforward in ω ζ - lan. (a) Nominal valus: = 5 µf, = mh and = Ω. (b) Nominal valus: = 5 µf, =.5 mh and = Ω..8.6 ζ ω x 4 (rad/s).8.6 ζ ω x 4 (rad/s) (b) (a) Fig.. Stability rgion of modl rfrnc in ω ζ -lan. (a) Nominal valus: = 5 µf, = mh and = Ω. (b) Nominal valus: = 5 µf, =.5 mh and = Ω. VII. SIMUAION ESUS abl I givs th aramtrs of th singl-has fullbridg PWM invrtr systm usd in digital comutr simulation (with MAAB ) to vrify th rformanc of th digital control schms rsntd in th rvious sctions. h aramtrs of ths s for a PWM attrn with on voltag uls in th bginning of th samling riod and for a MPWM attrn with thr voltag ulss r samling riod ar rsntd in abl II. ABE I PAAMEES OF PWM INVEE Outut filtr I = mh (Switching frquncy =.8 khz) = 5 µf Outut filtr II =.5 mh (Switching frquncy =.4 khz) = 5 µf D inut voltag V B = V frnc voltag r = V MS, f = 6 Hz Nominal rsistiv load = Ω Samling frquncy f S =.8 khz Samling riod = 9.6 µs ABE II PAAMEES OF HE ONOES ONOE PWM PAEN MPWM PAEN P =.64 P =.96 Prdictiv OSAP P =.6 P =.4698 Q =.785 Q =.556 Q =.4 Q =.684 Q = Q =.944 Prdictiv PDfdforward K =. K =.99 K =.5 K =.9 Modl rfrnc θ = [ ] θ = [ ] c o = c o = q =.8 q =.7 F =.744 F =.5979 titiv c =. c =. A. PWM attrn with on voltag uls in th bginning of th samling riod Initially, th rdictiv OSAP with rtitiv control action (OSAP-P) was simulatd using a PWM attrn with on uls in th bginning of th samling riod. Fig. shows th outut voltag v c ( wavform for nominal rsistiv load ( Ω). Voltag (V) v c ( im (ms) Fig.. sons of th OSAP-P for nominal load, using a PWM attrn with on uls in th bginning of th samling intrval.

6 Du to simlifications ralizd to obtain a linar discrttim modl, and considring th dsign mthodology mloyd to dtrmin th outut filtr aramtrs, it can b obsrvd that th rdictiv OSAP with rtitiv intgral action dos not rform wll whn this PWM attrn is usd. With ths outut filtr aramtrs, th control signal rsntd undsird oscillations, causing a dgradation of th outut voltag wavform [8]. In addition, th closd-loo systm bcam unstabl for no-load, as shown in Fig.. onsquntly, only th rdictiv PD-fdforward with rtitiv intgral action (PD-P) and th modl rfrnc with rtitiv intgral action (M-P) wr simulatd undr nonlinar loads with this PWM attrn. Simulation rsults obtaind for ths two s ar similar, as can b sn in Fig. to Fig. 4, bcaus ths s hav bn dsignd from similar scifications. Fig. shows th HD of th outut voltag wavform for nominal load and no-load. On th othr hand, Fig. rsnts a comarison of th simulation rsults obtaind for nominal rsistiv load in sris with a riac, with diffrnt firing angls, to vrify th rformanc of ths s for ac has-controlld loads. Finally, Fig. 4 shows th HD of th outut voltag wavform for a rctifir load (with a currnt crst factor of.5), to dmonstrat th rformanc of ths s for this ty of load. HD (% ) OSAP-P PD-P M-P Nominal load No-load Fig.. HD of th outut voltag for linar loads, using a PWM attrn with on voltag uls in th bginning of th samling intrval. HD (%) PD-P M-P 6º/6º 7º/5º 9º/7º º/º Fig.. HD of th outut voltag for nonlinar loads, using a PWM attrn with on voltag uls in th bginning of th samling intrval. HD (%).4. B. MPWM attrn with thr voltag ulss r samling riod It was dmonstratd in Sction II that th lant modling rrors causd by th linarization of th discrt-tim lant modl bcom smallr as th numbr of voltag ulss r samling riod incrass. hrfor, th switching frquncy was incrasd to.4 khz (maximum frquncy allowd by th usd micro with an 8-bit rsolution) whil th samling frquncy was maintaind th sam. With this, th outut filtr aramtrs could b rducd to imrov th rformanc of th rdictiv OSAP [8]. Fig. 5 shows a comarison of th HD for nominal load and no-load. In addition, to vrify th rformanc of ths s with fixd-oint routins, Fig. 6 rsnts a comarison of th simulation rsults obtaind for nominal load with doubl rcision floating-oint routins (-bit of signal, -bits of xonnt and 5-bits of mantissa) and with fixd-oint routins (8-bits). his figur shows that th modl rfrnc with rtitiv intgral actiorsntd th surior rformanc with fixd-oint routins among ths tchniqus. On th othr hand, Fig. 7 rsnts a comarison for nominal rsistiv load in sris with a riac, with diffrnt firing angls, to vrify th rformanc of ths s for cyclic loads. h rdictiv PD-fdforward and th modl rfrnc, both with th inclusion of th rtitiv control, rsntd a similar rformanc, whil th rdictiv OSAP with rtitiv intgral actiorsntd a highr HD. HD (% ) Nominal load No-load.7.94 OSAP-P PD-P M-P Fig. 5. HD of th outut voltag for linar loads, using a MPWM attrn with thr voltag ulss r samling riod. HD (% ) 4.5 HD (%) OSAP-P PD-P M-P Fig. 6. Floating-oint vrsus fixd-oint Floatingoint Fixd-oint OSAP-P PD-P M-P PD-P M-P Fig. 4. HD of th outut voltag for a rctifir load, using a PWM attrn with on voltag uls in th bginning of th samling intrval. 6º/6º 7º/5º 9º/7º º/º Fig. 7. HD of th outut voltag for nonlinar loads, using a MPWM attrn with thr voltag ulss r samling riod.

7 Fig. 8 shows th influnc of th rtitiv intgral action for inut and outut riodic disturbancs. Fig. 8(a) rsnts th convrgnc of HD for nominal rsistiv load in sris with a riac commuting at 7º/5º (riodic outut disturbanc). Although th HD of th outut voltags ar similar at th first cycl, it can b sn that th HD of th outut voltags by using th rdictiv PD-fdforward or th modl rfrnc, both with rtitiv control, ar lss than by using th rdictiv OSAP with rtitiv control. On th othr hand, Fig. 8(b) rsnts th convrgnc of HD whn th dc bus voltag rsnts Hz ril with amlitud of ±5% of th inut nominal voltag (riodic inut disturbanc), which could b causd by a front-nd rrgulator convrtr connctd to th utility grid. Again, it is ossibl to obsrv that th rtitiv intgral action minimizs th HD of th outut voltag, howvr th outut voltag wavform rsntd a highr HD by using th rdictiv OSAP. onsquntly, th rtitiv gain c should b highr for th rdictiv OSAP with rtitiv action to synthsiz an outut voltag with low HD for inut and outut riodic disturbancs. If th rtitiv gain c is incrasd, th convrgnc of th outut rror will b fastr, howvr th fdback systm may bcom unstabl. In this way, th choic of c is a comromis btwn th rlativ stability of th closd-loo systm and th convrgnc rat of th outut rror [6]. HD (%) HD (%) OSAP-P PD-P M-P Numbr of cycls PD-P OSAP-P (a) M-P Numbr of cycls (b) Fig. 8. Influnc of th rtitiv intgral action for a riodic disturbanc (c =.). (a) Nominal rsistiv load in sris with a riac commuting at 7º/5º (outut disturbanc). (b) D bus voltag containing Hz ril with amlitud of ±5% of th inut nominal voltag (inut disturbanc). VIII. EXPEIMENA ESUS A laboratory rototy of th singl-has PWM invrtr using IGB s has bn built to vrify th ral rformanc of th s analyzd in this ar. h comonnt valus of th invrtr systm and th aramtrs of th s ar th sam as thos usd in th simulation (abls I and II). h s hav bn imlmntd using an ight bits wid data word micro (PI7756 of Microchi chnology Inc.). It has an mbddd -bit A/D convrtr and a PWM signal gnrator. abl III shows th xcution tim of th control algorithms imlmntd with PI7756 micro. h xcution tim (outut voltag A/D convrsion tim and control law comutation) snt by th PI7756 dos not allow to incras th samling frquncy, howvr th PWM signal frquncy can b qual to.4 khz with an 8-bit rsolution. ABE III EXEUION IME OF HE AGOIHMS ONOE EXEUION IME Prdictiv OSAP with rtitiv control action 65 µs Prdictiv PD-fdforward with rtitiv 6 µs control action Modl rfrnc with rtitiv control action 7 µs A. PWM attrn with on voltag uls in th bginning of th samling riod Fig. 9 shows a comarison of th xrimntal rsults obtaind for nominal rsistiv load and no-load. Du to th fact that th rdictiv OSAP with rtitiv intgral action bcam unstabl for no-load in simulations, only th othr two s wr imlmntd undr noload and nonlinar cyclic loads. Fig. rsnts a comarison of th xrimntal rsults obtaind for a rctifir load with a currnt crst factor of.5. Fig. rsnts th rsons of th modl rfrnc with rtitiv intgral action for this rctifir load, which rsntd th surior rformanc for this load. HD (% ) Nominal load No load OSAP PD-P M-P Fig. 9. Exrimntal rsults obtaind for nominal load and no-load, using a PWM attrn with on uls in th bginning of th samling riod. HD (%) PD-P M-P Fig.. Exrimntal rsults obtaind for a rctifir load, using a PWM attrn with on voltag uls in th bginning of th samling intrval..5

8 i ( v c ( Fig.. sons of th modl rfrnc with rtitiv intgral action for a rctifir load, using a PWM attrn with on voltag uls in th bginning of th samling intrval (5 V/div, A/div, ms/div). B. MPWM attrn with thr voltag ulss r samling riod Fig. rsnts a comarison of th xrimntal rsults obtaind for nominal load and no-load with a MPWM attrn with thr voltag ulss r samling riod. Fig. shows th HD of th xrimntal rsults obtaind for a rctifir load. h rdictiv OSAP rsntd a bttr rformanc with th rduction of th outut filtr aramtrs, which has bn mad ossibl with th us of a MPWM attrn. Howvr, as discussd irvious sction, th rtitiv gain c should b highr for th OSAP-P to synthsiz an outut voltag with low HD for cyclic loads. On th othr hand, th rdictiv PDfdforward and th modl rfrnc, both with rtitiv action, rsntd a similar rformanc (in trms of HD) to that obtaind with a PWM attrn. HD (%) OSAP-P PID-P M-P Nominal load No load Fig.. Exrimntal rsults obtaind for nominal load and no-load with a MPWM attrn with thr voltag ulss r samling riod. HD (%) OSAP-P PID-P M-P Fig.. Exrimntal rsults obtaind for a rctifir load with a MPWM attrn with thr voltag ulss r samling riod. IX. ONUSIONS his ar rsnts a comarison among digital control tchniqus with rtitiv intgral action alid to low cost UPS. As a rsult of th rtitiv action, ths digital control schms can rduc th stady-stat rror and distortions causd by riodic disturbancs. In addition, th digital control tchniqus analyzd masur only th outut voltag, dcrasing th amount of snsors and th ovrall systm cost. sults show that th rformanc of th rdictiv OSAP dnds on th accuracy of th discrt-tim lant modl and aramtrs of th outut filtr. Howvr, it was dmonstratd that th incras of th switching frquncy rducs th ffcts of th lant modling rrors causd by linarization of th discrt-tim lant modl. As th switching frquncy is incrasd, th outut filtr aramtrs can b rducd, dcrasing wight, volum and cost of th systm, as wll as imroving normously th rformanc of th closdloo systm with th OSAP-P. In addition, as th samling frquncy is maintaind th sam, it is ossibl to imlmnt this in a low-cost micro or DSP. On th othr hand, th rdictiv PD-fdforward and th modl rfrnc, both with th inclusion of th rtitiv intgral action, ar lss snsitiv to aramtric variations if comard with th rdictiv OSAP, and rsntd a good rformanc for linar and nonlinar loads. Howvr, among th analyzd control tchniqus, th modl rfrnc rsntd a surior rformanc with fixd-oint routins. EFEENES [] A. Kawamura,. Hanyoshi and. G. Hoft, Dadbat controlld PWM invrtr with aramtr stimation using only voltag snsor, IEEE rans. Powr Elctr., v.,. 8-5, Ar [] S.. Jung and Y. Y. zou, Discrt sliding-mod control of a PWM invrtr for sinusoidal outut wavform synthsis with otimal sliding curv, IEEE rans. Powr Elctr., v., , Jul [] S. Hara, Y. Yamamoto,. Omata and M. Nakano, titiv control systm: A nw ty srvo systm for riodic xognous signals, IEEE rans. Autom. ontrol, v., , Jul [4]. Hanyoshi, A. Kawamura and. G. Hoft, Wavform comnsation of PWM invrtr with cyclic fluctuating loads, IEEE rans. Ind. Al., v. 4, , Jul./Aug [5] Y. Nishida and. Hanyoshi, Prdictiv instantanous valu controlld PWM invrtr for UPS, in IEEE Powr Elctr. Sc. onf. c., 99, [6] Y. Y. zou,. S. Ou, S.. Jung and M. Y. hang, High-rformanc rogrammabl A owr sourc with low harmonic distortion using DSP-basd rtitiv control tchniqu, IEEE rans. Powr Elctr., v., , Jul [7] H. A. Gründling, E. G. arati and J.. Pinhiro, A robust modl rfrnc adativ for UPS alications, in IEEE Ind. Elctr. onf. c., 997, [8]. ch, H. Pinhiro, H. A. Gründling, H.. Hy and J.. Pinhiro, Imrovd modifid OSAP for voltag sourc PWM invrtrs, in Brazilian Powr Elctr. onf. Proc.,, [9]. ch, H. Pinhiro, H. A. Gründling, H.. Hy and J.. Pinhiro, Analysis and dsign of a rtitiv rdictiv-pid for PWM invrtrs, in IEEE Powr Elctr. Sc. onf. c.,, []. ch, H. A. Gründling and J.. Pinhiro, A modifid discrt control law for UPS alications, in IEEE Powr Elctr. Sc. onf. c.,, [].. Phillis and J. M. Parr, obust dsign of a digital PID rdictor, IEEE rans. Ind. Elctr., v.,. 8-, Nov [] J. H. Aylor,.. amy and G. ook, Dsign and alication of a microrocssor PID rdictor, IEEE rans. Ind. Elctr. and ontrol Instrum., v. 7,. -7, Aug. 98. [] P. A. Ioannou and J. Sun, obust Adativ ontrol. Ur Saddl ivr, NJ: Prntic-Hall, 996,. -7.