Influence of Covariance-Based ALS Methods in the Performance of Predictive Controllers With Rotor Current Estimation

Depósi o de In es igación de la Uni e sidad de Se illa h ps://idus.us.es/ This is an Accep ed Manusc ip o an a icle published by IEEE: J. Rodas, C. Ma ín, M. R. A ahal, F. Ba e o and R. G ego , "In luence o Co a iance-Based ALS Me hods in he Pe o mance o P edic i e Con olle s Wi h Ro o Cu en Es ima ion," in IEEE T ansac ions on Indus ial Elec onics, ol. 64, no. 4, pp. 2602-2607, Ap il 2017, DOI: 10.1109/TIE.2016.2636205 “© 2017 IEEE. Pe sonal use o his ma e ial is pe mi ed. Pe mission om IEEE mus be ob ained o all o he uses, in any cu en o u u e media, including ep in ing/ epublishing his ma e ial o ad e ising o p omo ional pu poses, c ea ing new collec i e wo ks, o esale o edis ibu ion o se e s o lis s, o euse o any copy igh ed componen o his wo k in o he wo ks.” IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS In luence o Co a iance-Based ALS Me hods in he Pe o mance o P edic i e Con olle s wi h Ro o Cu en Es ima ion Jo ge Rodas, Membe ,IEEE, C is ina Ma ´ ın, Manuel R. A ahal, Membe ,IEEE, Fede ico Ba e o, Senio Membe ,IEEE, and Ra´ ul G ego Abs ac —The use o on-line o o cu en es ima o s wi h p edic i e cu en con olle s has been e y ecen ly s a ed in i e-phase induc ion mo o d i es, whe e he closed-loop pe o mance o he sys em is imp o ed using sub-op imal es ima o s based on Kalman il e s. In his wo k, he in e es o using op imiza ion me hods in he de ini ion o he Kalman il e , like he co a iance echnique, is analyzed. Ob ained sys em pe o mances using op imal and sub-op imal o o cu en es ima o s a e expe imen ally compa ed. Index Te ms—Kalman il e , mul iphase d i es, op imal co a iance es ima ion, p edic i e cu en con ol. I. INTRODUCTION THE in e es in model p edic i e con ol like an al e na i e in powe con e e s and d i es o ield o ien ed o di ec o que con olle s has been g owing up in he las decade [1]. In he mul iphase d i es’ esea ch ield he p edic i e cu en con ol (PCC) echnique ep esen s he mos popula case s udy [2]. PCC uses a s a e-space ep esen a ion o he d i e o op imize he con ol ac ion. The es ima ion o non-measu able s a e componen s, ypically o o cu en s, is a complex p oblem ha has been ecen ly sol ed using di e en me hods o he on-line es ima ion o he o o a iables [3, 4]. These s udies illus a e he bene i s in using o o cu en obse e s like Kalman il e s (KF), al hough sub-op imal echniques we e applied du ing he necessa y uning p ocess o hese obse e s. Manusc ip ecei ed May 5, 2016; e ised Sep embe 1, 2016 and Oc obe 17, 2016; accep ed No embe 15, 2016. This wo k was suppo ed by he Pa aguayan Go e nmen h ough he CONACYT g an 14-INV-101 ( esea ch P ojec ) in he amewo k o he p og am “P og ama Pa aguayo pa a el Desa ollo de la Ciencia y Tecnolog´ ıa,” PROCIENCIA. This wo k was also unded by he Spanish Minis y o Science and Inno a ion unde P ojec DPI2013-44278-R, he Uni e si y o Se ille, Spain (V Resea ch Plan, ac ion II.2). J. Rodas and R. G ego a e wi h he Labo a o y o Powe and Con ol Sys ems, Facul ad de Ingenie ´ ıa, Uni e sidad Nacional de Asunci´ on, 2060 Luque, Pa aguay (e-mail: [email p o ec ed]y; [email p o ec ed]y). C. Ma ´ ın and F. Ba e o a e wi h he Depa men o Elec onic Enginee ing, Uni e si y o Se ille, 41004 Se ille, Spain (e-mail: cma [email p o ec ed]; [email p o ec ed]). M. R. A ahal is wi h he Depa men o Sys ems Enginee ing and Au oma ic Con ol, Uni e si y o Se ille, 41004 Se ille, Spain (e-mail: a [email protected]). In his pape , a o o cu en obse e based on KF is included in he con en ional PCC echnique, being a ema kable con ibu ion o he wo k he op imal design o he KF by means o a obus co a iance es ima ion me hod. In [4] he KF gains a e uned based on ial and e o s a egies, using some p io expe knowledge o hypo hesis abou he noise. The p oposed me hod is based on he es ima ion o ue co a iances in he con ol sys em, which has no been p e iously es ed in he mul iphase elec ical d i es’ ield. A i e-phase induc ion machine (IM) is used as a case example, bu he ob ained esul s can be ex apola ed o di e en elec ical machines. II. PREDICTIVE CURRENT CONTROL WITH OPTIMAL ROTOR CURRENT ESTIMATION A i e-phase IM d i e wi h dis ibu ed windings equally displaced #=2⇡/5and powe ed by a i e-phase wo-le el ol age sou ce in e e (VSI) is used. A block diag am o he con en ional PCC echnique de ailed in [2] is shown in Fig. 1(a) oge he wi h a schema ic ep esen a ion o he i e-phase IM d i e. This PCC con olle u ilizes a disc e e model o he sys em, named p edic i e model, o p edic (a ime k) he u u e alues ( ime k+1) o he machine’s s a o cu en s, bis(k+1|k), o each possible s a o ol age, u(k). Thus, he p edic i e model elies on he knowledge o some a iables such as he measu ed s a o cu en s is(k)and elec ical speed ! (k), as i is shown in he ollowing equa ion: bi(k+1|k)=Ai(k)+Bu(k)(1) whe e i=(i↵s,i s,i xs,i ys,i ↵ ,i  ),u=(u↵s,u s,u xs,u ys), and Aand Ba e ma ices ha depend on he elec ical pa ame e s o he machine and he sampling ime Ts. Ma ix Aalso depends on he ac ual alue o ! (k), and i mus be calcula ed e e y sampling ime. A de ailed explana ion o he machine model is no included he e o he sake o conciseness and can be ound in [3]. I is wo h s a ing ha , acco ding o he well-known ec o space decomposi ion app oach [4], he elec omechanical ene gy con e sion a iables a e mapped in o he ↵subspace, meanwhile he cu en componen s in he xysubspace in he analyzed elec ical machine a e ela ed o ha monic losses. In con en ional PCC he compu a ion o he con ol signal akes a signi ican amoun o ime which is compa able wi h IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS &RVWIXQFWLRQ (T 0LQLPL]HU PLQ-N_N 3UHGLFWLYHPRGHO (TVDQG 7DEOHRISRVVLEOH YROWDJHYHFWRUV )LYHSKDVH,0 96, 3&& (a) &RVWIXQFWLRQ (T 0LQLPL]HU PLQ-N_N 3UHGLFWLYHPRGHO (TVDQG 7DEOHRISRVVLEOH YROWDJHYHFWRUV HVWLPDWRU (T DQG HVWLPDWRUV 4U5Q )LYHSKDVH,0 96, 3&& .) $/6 (b) Fig. 1. Schema ic diag am o he i e-phase IM d i e and blok diag am o (a) he con en ional PCC echnique applied in [2] o he egula ion o i e-phase IM d i es, and (b) he p oposed PCC echnique ha uses a KF-based op imum o o cu en es ima o . Ts, so a second-s ep ahead p edic ion o he s a o cu en s bis(k+2|k)is equi ed [3]. In he exis ing li e a u e his e m is ob ained i e a i ely using he p edic i e model. Rega ding he o o quan i ies ha appea in (1), mos esea ch wo ks ely on agg ega ing all unmeasu able quan i ies in o one e m ha is acked, al hough he use o es ima o s o o o quan i ies has been ecen ly p oposed in [4], a he expense o a ema kable inc emen o he compu a ional cos o he implemen ed con olle (by 36 % o he o al). Once he second-s ep ahead p edic ion is ob ained, an op imiza ion p ocess is applied e e y sampling pe iod, whe e a cos unc ion Jis calcula ed o all 32 (25) possible s a o ol ages o ob ain a desi ed e e ence ajec o y i⇤ s(k). The ol age ec o ha minimizes he cos unc ion is selec ed and applied o he sys em du ing he nex sampling pe iod. The cos unc ion can be de ined in di e en ways, al hough he de ia ion be ween e e ence and p edic ed s a o cu en s is no mally used as ollows: J(k+2|k)=kbe↵ k2+xy kbexy k2(2) being be he second-s ep ahead p edic ed e o compu ed as be=i⇤ s(k+ 2) bis(k+2|k), and xy a uning pa ame e ha allows o pu mo e emphasis on ↵o xysubspaces [1, 5]. A. In luence o Ro o Cu en in P edic ion As commen ed be o e, he p edic i e model gi en by (1) canno be used o p oducing p edic ions i o o cu en s a e no measu able (as i is he no mal case) unless some es ima ion o o o cu en s is p o ided. PCC me hods ha e o e come his p oblem by agg ega ing all non-measu able e ms in one ac o ha is la e acked and upda ed (G). Fo his pu pose, he s a o cu en ec o is di ided in o a measu able pa , is=(i↵s,i s,i xs,i ys), and a non-measu ed pa , i =(i↵ ,i  ), and he p edic i e model akes he ollowing o m: bis(k+1|k)=¯ Ai s(k)+¯ Bu(k)+b G(k|k)(3) wi h app op ia e ¯ Aand ¯ Bma ices ob ained om (1) using elemen al algeb a. The b G(k|k) e m is app oxima ed holding i s p e ious alue b G(k1|k)compu ed a ime k, using pas alues o measu ed a iables: b G(k1|k)=is(k)¯ Ai s(k1) ¯ Bu(k1) (4) B. Ro o Cu en Es ima o Based on Kalman Fil e Ins ead o using he acking and upda ing echnique p oposed in con en ional PCC me hods, a KF is used in [4] as i is shown in Fig. 1(b), whe e he b Q⇢and b R⌫es ima o s block we e no aken in o accoun . The o o cu en s ( bi ) a e es ima ed e e y sampling ime using he measu ed o o speed ! , s a o phase cu en s isand s a o phase ol ages u. Conside ing unco ela ed p ocesses and ze o-mean Gaussian measu emen noises, he machine’s model (1) can be w i en as ollows: bi(k+1|k)=Ai(k)+Bu(k)+H⇢(k) is(k)=Ci(k)+⌫(k)(5) being ⇢(k) he dis u bance ec o (p ocess noise), ⌫(k) he measu emen noise, and H he noise weigh ma ix. Di iding he cu en ec o in wo pa s, i↵s=(i↵s,i s) and i↵ =(i↵ ,i  ), he dynamic o he educed-o de o o cu en es ima o can be de ined in he ollowing way: bi↵ (k+1|k)=(A22 K(k)A12)bi↵ (k) +K(k)bi↵s(k+1|k) +(A21 K(k)A11)i↵s(k) +(B2K(k)B1)u↵(k) (6) IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS whe e K(k) ep esen s he KF gain ma ix and u↵ =(u↵s,u s). This es ima ion o o o cu en s can now be used o p oduce he second-s ep ahead p edic ion o he s a o cu en as: bi↵s(k+2|k)=A11 bi↵s(k+1|k)+A12 bi↵ (k+1|k) +B1u↵(k+ 1) (7) The KF gain ma ix is calcula ed a each sampling ime in a ecu si e manne using an es ima ion o wo co a iance ma ices o he noises called b Q⇢and b R⌫. These co a iances a e de ined as he expec ed alues o he dis u bance and he measu emen noise as Q⇢=co (⇢)=E{⇢·⇢T}and R⌫=co (⌫)=E{⌫·⌫T}, being he KF gain ma ix ob ained using he ollowing s eps: (k)='(k)'(k)·CT(C·'(k)·CT+b R⌫)1·C·'(k)(8) K(k)=(k)·CTb R1 ⌫(9) '(k+ 1) = A(k)·AT+Hb Q⇢·HT(10) This comple es he equi ed ela ions o he s a e es ima ion, whe e he minimum es ima ion e o s depends on K(k)and i is gua an eed i he es ima ed noise co a iances and he ini ial condi ion o he s a e co a iance ('(0)) a e known. No ice ha he in e es o using KF in he con ex o he s a o cu en p edic ion and PCC is p esen ed in [4], whe e he KF was ha dly uned using ini ial alues, bu he ob ained expe imen al esul s encou aged u u e esea ch owa ds es ablishing he KF as a ool o choice o he de ini ion o p edic i e con olle s in elec ical d i es. C. P oposed op imiza ion p ocedu e The KF op imal implemen a ion is di icul due o he lack o in o ma ion abou he noises. The use o an op imal es ima ion using KF equi es he es ima ion o b Q⇢and b R⌫, which can be done h ough Bayesian, maximum likelihood, co a iance ma ching o co ela ion echniques. Bayesian and maximum likelihood a e complex and equi e much da a. Co a iance ma ching uses he esiduals o he s a e es ima ion p oblem, bu i p o ides biased es ima es o he ue co a iances, esul ing in a non op imal KF uning. In [6] he Au oco a iance Leas Squa es me hod (ALS) is p oposed o p o ide unbiased es ima es wi h he lowes a iance, gua an eeing op imal KF uning. The ALS me hod is done o -line based on da a ga he ed om closed-loop ope a ion. The posi i e semi-de ini eness o he co a iance es ima ion is gua an eed by adding cons ain s o he ALS p oblem. No e ha wi hou his me hod, and gi en he cu en le el o sophis ica ion o he p edic i e con ol me hods, he use o KF is incomple e, ollowing he Bellman op imali y p inciple. Fu he mo e, he KF algo i hm compu a ional cos is he same whe eas he sys em pe o mance imp o es. The ini ial es ima ion o dis u bance co a iances ( b Q⇢0and b R⌫0) can be ob ained om he esiduals o he es ima o using (11) and (12), as i is s a ed in [7]. Then, by sol ing he op imiza ion p oblem (13) he es ima ed co a iances ( b Q⇢ and b R⌫) a e ob ained. The i s e m in (13) is he esidues no m, he second e m is he cons ain penaliza ion e m, he <(6 12 ,QLWLDO9DOXHV 5HDG6WRUHG'DWD ,I RU FRQYHUJHV 3HUIRUP1HZWRQ6WHSIRU DQG(VWLPDWH8SGDWH 2EWDLQHGIURP(T 2EWDLQHGIURP(T 8VHU'H¿QHG Fig. 2. ALS low cha conside ing ini ial co a iances (Q⇢0and Rnu0) and numbe o da a poin s (Nd). 3UHGLFWLYH0RGHO(T 3UHGLFWLYH0RGHO(T &RVW)XQFWLRQ(YDOXDWLRQ(T <(6 12 <(6 12 5RWRU&XUUHQW(VWLPDWLRQ (T .)*DLQ0DWUL[ (YDOXDWLRQ (TV Fig. 3. P oposed PCC algo i hm in a low cha diag am. e m |·|deno es he de e minan o he ma ix, Aand bba e de ined in [6] as Eqs. (11) and (12), espec i ely, and µis he ba ie pa ame e o he semi-de ini e cons ain (Q⇢0and R⌫0). By using a New on-based op imiza ion p ocedu e, he co a iances a e ob ained a e a p ede ined numbe o i e a ions (n) o when he esul s con e ge as shown in Fig. 2. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 6SHHG(QFRGHU )LYH3KDVH,0 '&0RWRU'&0RWRU 3RZHU(OHFWURQLF&RQYHUWHU &RPSXWHU '&/LQN Fig. 4. Scheme o he expe imen al es ig. b Q⇢0=co {bi(k+1|k)Abi(k|k1) Bu(k)H⇢(k|k1)}(11) b R⌫0=co {is(k)Ci(k|k1) I⇢(k|k1)}(12) minQ⇢ R⌫A(Q⇢)s (R⌫)sbb 2 2 µlog Q⇢0 0R⌫(13) No e ha b Q⇢and b R⌫a e cons an alues du ing he p oposed PCC algo i hm. To make hings clea e , a low cha o he p oposed PCC con ol algo i hm is p esen ed in Fig. 3. In gene al, uning pa ame e s o he p edic i e con olle s is no easy as many s udies ocusing on his a ea ha e shown [5, 8]. Al hough he use o KF imp o es he modeling o complex elec ical sys ems and consequen ly he be e pe o mance o he PCC con olle , he op imal pa ame e s o he il e was s ill a p oblem o be sol ed, and he p oposed me hod co e s his pa o he p oblem by an op imal es ima ion o b Q⇢and b R⌫. The con ibu ion o his pape analyzes he ob ained imp o emen when his op imal o o cu en es ima o is applied. III. EXPERIMENTAL RESULTS To alida e he p oposed con ol me hod, an expe imen al e alua ion has been conduc ed. A diag am o he es ig is shown in Fig. 4. The p incipal elemen is a h ee pai s o poles i e-phase IM whose nominal pa ame e s ha e been expe imen ally de e mined as Rs= 19.45 ⌦,R =6.77 ⌦, Lls = 100.7mH, Ll = 38.06 mH, M= 656.5mH, !n= 1,000 pm and Pn=1kW. Two 2-le el h ee-phase powe con e e s om Semik on (SKS22F) a e used o d i e he i e-phase IM, whe e he DC-link ol age is se o 300 V using a DC powe supply sys em. The con ol sys em is based on a MSK28335 boa d and a TMS320F28335 DSP, being he o o mechanical measu ed using a GHM510296R/2500 digi al encode and he eQEP pe iphe al o he DSP. A DC mo o is also used o in oduce a a iable load o que in he sys em. Di e en es s we e ca ied ou o alida e he cu en con olle pe o mance using he con en ional PCC me hod (C1), he PCC me hod wi h KF de ailed in [4] (C2) and he PCC wi h he p oposed op imum-KF (C3). A sampling TABLE I EXPERIMENTAL RESULTS AT DIFFERENT OPERATING POINTS ![ pm] Figu es o me i C1 C2 C3 400 MSEi⇤ ↵s0.1068 0.0972 0.0954 MSE b i⇤ ↵s0.1468 0.1390 0.1382 MSEi⇤ xs 0.1217 0.1199 0.1176 THD(%) 14.15 13.29 13.47 500 MSEi⇤ ↵s0.1075 0.0950 0.0907 MSE b i⇤ ↵s0.1411 0.1343 0.1267 MSEi⇤ xs 0.1284 0.1051 0.0963 THD(%) 16.86 15.07 14.07 550 MSEi⇤ ↵s0.1227 0.1044 0.0879 MSE b i⇤ ↵s0.1526 0.1363 0.1247 MSEi⇤ xs 0.1408 0.1354 0.1260 THD(%) 16.08 14.63 13.18 600 MSEi⇤ ↵s0.1177 0.0924 0.0860 MSE b i⇤ ↵s0.1469 0.1318 0.1234 MSEi⇤ xs 0.1435 0.1355 0.1203 THD(%) 16.42 12.50 12.96 700 MSEi⇤ ↵s0.1266 0.0875 0.0835 MSE b i⇤ ↵s0.1579 0.1300 0.1285 MSEi⇤ xs 0.1524 0.1433 0.1430 THD(%) 17.34 14.81 14.70 equency o 15 kHz and hal o he nominal load a e conside ed, as well as he cos unc ion de ined in (2) wi h xy =0.1( he o que and lux p oduc ion a e p omo ed by he con olle o e he ha monic losses). Fou igu es o me i a e used o compa e he e iciency o he di e en o o cu en es ima o s in e ms o con ol pe o mance and p edic ion accu acy. These a e mean squa ed alues o he cu en con ol e o in ↵and xaxis, de ined in (14), he model p edic ion e o in ↵axis (15), and a o al ha monic dis o ion measu emen (THD) o he s a o phase (15). MSEi⇤ (↵,x)s= u u PN j=1 ⇣i(↵,x)s(j)i⇤ (↵,x)s(j)⌘2 N(14) MSEbi↵s= u u PN j=1 ⇣i↵s(j)bi↵s(j)⌘2 N(15) IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 7LPHV &XUUHQW$ (a) 7LPHV &XUUHQW$ (b) 7LPHV &XUUHQW$ (c) Fig. 5. Expe imen al compa ison o ob ained s a o cu en s in ↵and xaxis using (a) C1, (b) C2 and (c) C3 echniques a 550 pm and hal nominal o que load. THDbis=sMSEbi2 ↵s+MSE bi2 xys i↵s peak/2(16) Table I and Fig. 5 summa ize he ob ained esul s in s eady-s a e ope a ion, whe e i is quan i ied he ob ained imp o emen when he p oposed o o cu en es ima o is used. I is obse ed ha all mean squa ed alues a e imp o ed (lowe alues) i he p oposed op imum KF o o cu en es ima o (C3) is used. Fo ins ance, he ob ained MSEi⇤ ↵s alue a 550 pm using C3 is educed in 28.36 % and 15.80 % when i is compa ed wi h hose ob ained using C1 and C2, espec i ely. Simila ly, he ob ained MSEbi↵s alue a 600 pm is also educed in 16.00 % and 6.37 % when C3 is employed ins ead o C1 and C2, espec i ely. No e ha simila esul s a e ob ained a di e en ope a ing poin s. Fig. 5 de ails he pe o mance o he sys em using C1, C2 and C3 a 550 pm, whe e he cu en acking cha ac e is ics in ↵and xaxis a e plo ed, showing ha he closed-loop pe o mance o he sys em using C3 echnique o e s be e acking cha ac e is ics han o he s. Rega ding he ha monic con en o he s a o cu en , he ob ained alue is lowe i he o o cu en es ima o is used, being C3 he bes in mos cases. The dynamic pe o mance using he C3 me hod is inally analyzed, and he ob ained esul s a e shown in Fig. 5. The qs a o cu en e e ence (i⇤ qs) is a ied acco ding o a s ep p o ile, while he ds a o cu en e e ence is se o a cons an alue (i⇤ ds=0.57 A); see Fig. 5 (uppe plo ). The measu ed s a o cu en s in synch onous (dand qaxis, uppe plo o Fig. 5) and s a iona y (↵xyaxis, middle plo o Fig. 5) ames ollow he imp essed e e ences, which con i ms ha he p oposed con olle wo ks well a di e en mechanical speed and du ing ansien s a es. No e ha he ou e speed con olle is no used in he es and he mechanical speed is no egula ed, hence i a ies as i is shown in he lowe plo o Fig. 5. I is also wo h men ioning ha a sampling equency o 15 kHz (sampling ime o abou 67 µs) is used, which s ill enables he implemen a ion o he KF-based o o es ima o in he C2 and C3 con olle s. No e also ha he p oposed ALS me hod does no a ec he compu a ional cos ( he p oposed 7LPHV                    6SHHGUSP DQG&XUUHQWV$ &XUUHQWV$ Fig. 6. T ansien esponse using he C3 con olle . F om op o bo om: dqs a o cu en s ids and iqs, and hei e e ences i⇤ ds and i⇤ qs;↵and xcu en s i↵sand ixs, wi h he imposed e e ence i⇤ ↵s, and mechanical speed !m. op imiza ion p ocedu e is pe o med o -line, p io o s a ing he no mal ope a ion o he mul iphase d i e). IV. CONCLUSION This wo k add esses he applica ion o KF in he design o o o cu en obse e s when PCC me hods a e used in IM d i es. In pa icula , a p ocedu e o he design o an op imal KF is p esen ed. Expe imen al esul s in a i e-phase IM d i e show he in e es o he p oposed p ocedu e, which imp o es s a o cu en p edic ion and acking, compa ing wi h o he con en ional o KF-based PCC me hods. No ice ha all he ob ained conclusions o a pa icula case example based on i e phase IM can be ex ended o di e en mul iphase and con en ional IM. REFERENCES [1] S. Kou o, M.A. Pe ez, J. Rod iguez, A.M. Llo , and H.A. Young, “Model P edic i e Con ol: MPC’s Role in he E olu ion o Powe Elec onics,” IEEE Ind. Elec on. Mag., ol. 9, DOI 10.1109/MIE.2015.2478920, no. 4, pp. 8–21, Dec. 2015. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS [2] F. Ba e o and M.J. Du an, “Recen Ad ances in he Design, Modeling, and Con ol o Mul iphase Machines – Pa I,” IEEE T ans. Ind. Elec on., ol. 63, DOI 10.1109/TIE.2015.2447733, no. 1, pp. 449–458, Jan. 2016. [3] C. Ma in, M.R. A ahal, F. Ba e o, and M.J. Du an, “Mul iphase Ro o Cu en Obse e s o Cu en P edic i e Con ol: a Fi e-Phase Case S udy,” Con ol Eng. P ac ., ol. 49, DOI 10.1016/j.conengp ac.2016.01.011, pp. 101–111, Ap . 2016. [4] J. Rodas, F. Ba e o, M.R. A ahal, C. Ma in, and R. G ego , “On-Line Es ima ion o Ro o Va iables in P edic i e Cu en Con olle s: a Case S udy Using Fi e-Phase Induc ion Machine,” IEEE T ans. Ind. Elec on., ol. 63, DOI 10.1109/TIE.2016.2559420, no. 9, pp. 5348–5356, Sep . 2016. [5] C.S. Lim, E. Le i, M. Jones, N.A. Rahim, and W.P. Hew, “FCS-MPC based Cu en Con ol o a Fi e-Phase Induc ion Mo o and i s Compa ison wi h PI-PWM Con ol,” IEEE T ans. Ind. Elec on., ol. 61, DOI 10.1109/TIE.2013.2248334, no. 1, pp. 149–163, Jan. 2014. [6] B.J. Odelson, M.R. Rajamani, and J.B. Rawlings, “A New Au oco a iance Leas -Squa es Me hod o Es ima ing Noise Co a iances,” Au oma ica, ol. 42, DOI 10.1016/j.au oma ica.2005.09.006, no. 2, pp. 303–308, Feb. 2006. [7] T. Sode s om, M. Mossbe g, and M. Hong, “A Co a iance Ma ching App oach o Iden i ying E o s-in-Va iables Sys ems,” Au oma ica, ol. 45, DOI 10.1016/j.au oma ica.2009.05.010, no. 9, pp. 2018–2031, Sep . 2009. [8] S.A. Da a i, D.A. Khabu i, and R. Kennel, “An Imp o ed FCS–MPC Algo i hm o an Induc ion Mo o Wi h an Imposed Op imized Weigh ing Fac o ,” IEEE T ans. Powe Elec on., ol. 27, DOI 10.1109/TPEL.2011.2162343, no. 3, pp. 1540–1551, Ma . 2012. Jo ge Rodas (S’08–M’12) was bo n in Asuncion, Pa aguay, in 1984. He ecei ed his B.Eng. deg ee in Elec onic Enginee ing om he Na ional Uni e si y o Asuncion, Pa aguay, in 2009. He ecei ed his M.Sc. deg ees om he Uni e si y o Vigo, Spain, in 2012 and om he Uni e si y o Se ille, Spain, in 2013. He ecei ed his Ph.D. deg ees om he Na ional Uni e si y o Asuncion, in 2016 and om he Uni e si y o Se ille, in 2016. In 2011, P o . Rodas joined he Enginee ing Facul y a he Na ional Uni e si y o Asuncion, whe e he is cu en ly a Full P o esso . His main esea ch a eas a e p edic i e con ol, mul iphase d i es, ma ix con e e s and con ol o powe con e e s o enewable ene gy applica ions. C is ina Ma ´ın was bo n in Se ille, Spain, in 1989. She ecei ed he Indus ial Enginee deg ee om he Uni e si y o Malaga, Spain, in 2014. In 2015, she joined he Elec onic Enginee ing Depa men o he Uni e si y o Se ille, whe e she is cu en ly wo king owa d he Ph.D. deg ee. He cu en esea ch in e es s include modeling and con ol o mul iphase d i es, mic op ocesso and DSP de ice sys ems, and elec ical ehicles. Manuel R. A ahal (M’06) was bo n in Se ille, Spain, in 1966. He ecei ed he M.Sc. and Ph.D. deg ees in Indus ial Enginee ing om he Uni e si y o Se ille, Spain, in 1991 and 1996, espec i ely. He is cu en ly a P o esso a he Sys ems Enginee ing and Au oma ion Depa men a he Uni e si y o Se ille. He has been dis inguished wi h he Bes Pape Awa ds om he IEEE T ansac ions on Indus ial Elec onics o 2009, and om he IET Elec ic Powe Applica ions o 2010–2011. Fede ico Ba e o (M’04–SM’05) ecei ed he M.Sc. and Ph.D. deg ees in Elec ical and Elec onic Enginee ing om he Uni e si y o Se ille, Spain, in 1992 and 1998, espec i ely. In 1992, he joined he Elec onic Enginee ing Depa men a he Uni e si y o Se ille, whe e he is cu en ly an Associa e P o esso . He ecei ed he Bes Pape Awa ds om he IEEE T ansac ions on Indus ial Elec onics o 2009 and om he IET Elec ic Powe Applica ions o 2010–2011. Ra´ul G ego was bo n in Asuncion, Pa aguay, in 1979. He ecei ed his B.Eng. deg ee in Elec onic Enginee ing om he Ca holic Uni e si y o Asuncion, Pa aguay, in 2005. He ecei ed he M.Sc. and Ph.D. deg ees in Elec onic, Signal P ocessing and Communica ions om he Highe Technical School o Enginee ing (ETSI), Uni e si y o Se ille, Spain, in 2008 and 2010, espec i ely. Since Ma ch 2010, P o . G ego is Head o he Labo a o y o Powe and Con ol Sys em o he Enginee ing Facul y in he Na ional Uni e si y o Asuncion, Pa aguay. He ecei ed he Bes Pape Awa ds om he IEEE T ansac ions on Indus ial Elec onics o 2009 and om he IET Elec ic Powe Applica ions o 2010–2011. His esea ch in e es s include; mul iphase d i es, ad anced con ol o powe con e e s opologies, quali y o elec ical powe , enewable ene gy, modelling, simula ion, op imiza ion and con ol o powe sys ems, sma me e ing & sma g ids and p edic i e con ol.