Decoupling control for permanent magnet in-wheel motor using internal model control based on back-propagation neural network inverse system

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1 BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES, Vol. 66, No. 6, 8 DOI:.44/bpas DEEP LEARNING: THEORY AND PRACTICE Dcoupling for prmannt magnt inwhl motor using intrnal modl basd on backpropagation nural ntwork invrs systm Y. LI, *, B. ZHANG and X. XU, Automotiv Enginring Rsarch Institut, Jiangsu Univrsity, Zhnjiang, 3, China School of Automotiv and Traffic Enginring, Jiangsu Univrsity, Zhnjiang, 3, China Abstract. Th prmannt magnt inwhl motor (PMIWM) is a nonlinar, multivariabl, strongly coupld and highly complx systm. Th ky to th dvlopmnt and application of th PMIWM consists in th improvmnt of its accuracy and dynamic prformanc. In ordr to ffctivly dcoupl th PMIWM, this papr prsnts a novl intrnal modl (IMC) approach basd on th backpropagation nural ntwork invrs (BPNNI) mthod. First, thortical analysis is conductd to show th xistnc of th PMIWM invrs systm, to b modld mathmatically. Th invrs systm approximatd and idntifid by th backpropagation nural ntwork (BPNN) constituts th backpropagation nural ntwork invrs (BPNNI) systm. Thn, by cascading th BPNNI systm on th lft sid of th original PMIWM systm, a nw dcoupling, psudolinar systm is stablishd. Morovr, th DOF intrnal modl (IMC) mthod is mployd to dsign th xtra closdloop lr that furthr improvs disturbanc rjction and robustnss of th whol systm. Consquntly, th proposd dcoupling approach incorporats th advantags of both th BPNNI and th IMC. Effctivnss of thus proposd approach is vrifid by mans of simulation and raltim hardwarinthloop (HIL) xprimnts. Ky words: lctric vhicl, prmannt magnt inwhl motor, backpropagation nural ntwork, invrs systm, intrnal modl.. Introduction Rcntly, th inwhl motor drivn lctric vhicl (EV) has dvlopd rapidly as a nw nrgy and nvironmntfrindly transportation altrnativ, thanks to its high fficincy, nonpollution, low nois and a varity of othr charactristics. Diffring from th traditional driving mannr, th inwhl motor drivs th whls dirctly. Thus, th inwhl motor drivn EV has uniqu advantags, such as simpl and compact structur, high nrgy fficincy and indpndnt torqu [, ]. Th prmannt magnt synchronous motor (PMSM) has bn widly mployd in such EVs thanks to its faturs (including high powr dnsity, high torqu/wight ratio, high fficincy, high torqu capability and asy maintnanc). It constituts th bst choic for an inwhl motor [3 5]. Th prmannt magnt inwhl motor (PMIWM), installd in a narrow spac, is sriously rstrictd by svral uncrtaintis, such as tmpratur, magntic saturation, skin ffcts, road surfac xcitation, xtra load disturbanc, lctromagntic paramtr variations and friction forc. Each of ths factors could lad to distinct dgradation of PMIWM prformanc [6, 7]. Thrfor, rsarch on th stratgy for th PMIWM within a complx nvironmnt bcoms an important stp towards improvmnt of safty, rliability * mail: liyongthinkpad@outlook.com Manuscript submittd 8, rvisd 835, initially accptd for publication 836, publishd in Dcmbr 8. and practicability of th inwhl motor drivn EVs. Spdtracking accuracy, disturbanc rjction and robustnss of th PMIWM ar th main valuation indics of such EVs prformanc [8, 9]. Th PMIWM, howvr, is a highordr, multivariabl and strongly coupld nonlinar systm. Dcoupling and linarization constitut th kys to ling th complx nonlinar systm. At th sam tim, th accuracy of th lr is sriously influncd by a varity of uncrtaintis and nonlinaritis of th PMIWM, which maks it difficult to achiv strong robustnss and disturbancrjction prformanc. To nhanc th robustnss and dynamic prformanc of th PMIWM systm, many fforts hav bn mad [ 3] by rsarchrs around th world to improv prcision. A varity of advancd tchniqus hav bn dvlopd to improv PMIWM prformanc in th past dcads, including dirct torqu (DTC), vctor, diffrntial gomtry, prdictiv, sliding mod, fuzzy, support vctor machin, modl rfrnc adaptiv, invrs systm, tc. Th DTC is supposd to achiv dynamic dcoupling by using torqu and flux hystrsis. Howvr, it lads to poor lowspd prformanc and larg torqu rippl [4, 5]. Th vctor (VC) schm is an approximat stadystat dcoupling approach. Th dcoupling of torqu and flux could b achivd whn flux is accuratly obsrvd [6, 7]. Th diffrntial gomtry (DG) approach is usd for th of nonlinar coupling systms, but it rquirs an accurat mathmatical modl [8 ]. Manwhil, dynamic dcoupling and linarization ar achivd Bull. Pol. Ac.: Tch. 66(6) 8 96

2 Y. Li, B. Zhang, and X. Xu by using abstract and complx mathmatical tools. Th modl prdictiv (MPC) has th ability to xplicitly handl constraints. As an optimum mthod, th MPC, howvr, involvs a massiv computation load and long procssing tim, mainly suitabl for th linar systm [, ]. Th support vctor machin (SVM) algorithm is also difficult to implmnt for largscal training sampls du to its larg computation [3 6]. Fuzzy logic (FLC), unlik othrs, can obtain bttr spd tracking prformanc. Th dsign of fuzzy logic, howvr, lacks in systmatic mthods [7 9]. Th mmbrship functions and fuzzy ruls ar mainly dtrmind by th xprts xprinc, which is difficult to obtain automatically. Th impact of nonlinar factors on th systm prformanc cannot b fundamntally waknd. Th sliding mod (SMC) mthod is applid to th spd of a brushlss DC motor [3, 3]. SMC improvs robustnss of th spd systm, but its inhrnt highfrquncy jittr is difficult to liminat. Manwhil, th modl rfrnc adaptiv (MRAC) tchniqu is matur and asy to implmnt [33 36]. Adjustmnt of th adaptiv paramtrs is rlatd to th rror and its drivativ. Th tracking prformanc of th spd systm is bttr and mor adaptabl aftr introducing th adaptiv law, but th MRAC dpnds on th fixd paramtrs and th structur of th systm. Th systm will rquir complx calculations whn th systm modl is uncrtain or unknown. Th NNC dos not dpnd on th prcis mathmatical modl of th systm, but it lads to a slow larning spd, long training tim and local minima mrging [37 4]. Rfrnc [6,, 4] mployd th invrs systm mthod to dcoupl a baringlss PMSM. Howvr, th PMIWM cannot b compltly dcoupld by mans of a singl mthod du to th complxity of its systm. To ffctivly dcoupl th PMIWM systm, th hybridization approach nds to b invstigatd. This papr proposs novl intrnal modl (IMC) for spd of th PMIWM, which is basd on th backpropagation nural ntwork invrs (BPNNI) schm. On contribution of this papr is to dcoupl th PMIWM into a psudolinar systm using BPNN and invrs systm thory. Th BPNN is usd to obtain a datadrivn modl of th invrs systm. It dos not rly on th accurat systm modl or prior knowldg of th systm. Th αordr BPNNI systm is asy to implmnt according to th systm rlativ ordrs and basd on corrct training of nural ntworks. Th othr contribution of this papr is to ovrcom unprdictd disturbancs and improv th robustnss and dynamic prformanc of th PMIWM by mans of th IMC schm. Th proposd BPNNIIMC schm combins th advantags of mthods, rsulting in prompt rspons, high accuracy and tangibl dcoupling ffctivnss of th mthod. Th papr is organizd as follows: first, in Sction, PMIWM modling and invrtibility analysis ar sought. In Sction 3, th BPNNI schm is dscribd. Aftr that, th IMC mthod is prsntd in dtail in Sction 4. Simulation and xprimntal works ar prsntd and discussd in Sction 5. Sction 6 is dvotd to th conclusions of th prsnt work as wll as prospcts for futur rsarch.. Invrs systm modling.. Mathmatical modl of th PMIWM. Figur illustrats th crosssctional viw of th outrotor PMIWM. Th concntratd armatur coil is th lmnt wound around ach stator pol. Prmannt magnts ar sandwichd btwn th rotor and th stator to adjust to th airgap flux. Th stator of th motor adopts thrphas winding with fractional slots pr pol pr phas, thus offring th low cogging torqu highly dsirabl for application in vhicls [4]. Fig.. Block diagram of th PMIWM Th mathmatical modl of th PMIWM in th synchronously rotating d q rfrnc fram is xprssd as Eq. (): di d dt di q dt = L (u d R s i d Li q ω) = L (u q R s i q Li d ω ψ f ω) whr i d and i q ar th daxis and qaxis currnts of th stator, rspctivly. u d and u q rprsnt th voltag componnt on th daxis and qaxis, rspctivly. ω dnots th lctrical angular vlocity of th PMIWM rotor. L indicats th inductanc of th daxis and qaxis, rspctivly. R s shows th stator rsistanc and ψ f stands for prmannt magnt flux linkag of th rotor. Th lctromagntic torqu quation of th PMIWM in th d q coordinat is dscribd as Eq. (): () T = 3 p nψ f i q () whr p n is th numbr of pol pairs. Th motion quation of th PMIWM is shown as: J M d dt Rotor Stator Prmannt Magnt Shaft ω p n = T T L B ω p n (3) whr J M dnots th momnt inrtia of th PMIWM. T L is th load torqu and B is th cofficint of motion damping, which is in fact ignord. 96 Bull. Pol. Ac.: Tch. 66(6) 8

3 Dcoupling for prmannt magnt inwhl motor using intrnal modl basd on backpropagation nural ntwork invrs systm Thus, according to Eq. () and Eq. (3), th motion quation could b rwrittn as: dω dt = 3 p n J M ψ f i q T L p n J M. (4).. Invrtibility analysis of th PMIWM. In this papr, rotor flux orintd vctor is applid to th PMIWM. Rotor spd and flux can b dynamically dcouplingld using th invrs systm mthod. Thrfor, rvrsibility of th mathmatical modl of th PMIWM should b discussd first. Th purpos is to dcoupl spd ω, d axis currnt i d, q axis currnt i q and flux ψ f. Thus, i d and ω ar slctd as outputs of th PMIWM, whos variabls ar y = [ y, y ] T = [i d, ω] T. Furthrmor, u d and u q ar slctd as variabls, whr u = [u, u ] T = [u d, u q ] T, whil i d, i q and ω ar stat variabls, whr x = [x, x, x 3 ] T = [i d, i q, ω] T. Consquntly, th corrsponding stat quation of th nonlinar systm can b formulatd as: x = f (x, u) = x x x 3 = L (u R s x Lx x 3 ) L (u R s i Lx x 3 ψ f x 3 ) 3 p n ψ f x J M p nt L J M. (5) According to th invrs systm thory, th Jacobian matrix of th output drivation can b xprssd as: Howvr, as aformntiond, it is difficult to compltly dcoupl th PMIWM, vn if its invrs systm has bn xprssd in th abov sction. Furthrmor, th unprdictabl disturbanc and paramtr prturbation during th opration of th PMIWM could hav a massiv influnc on th motor s prformanc. Thus th BPNNI, is introducd in this sction to improv PMIWM robustnss. 3.. Backpropagation nural ntwork. Although thr ar many nural ntwork modls, th modl mainly usd in th ara of pattrn rcognition or classification is th fdforward/ backpropagation (BP) ntwork [43, 44]. Th BP, originally introducd by Wrbos in 974, ows much of its dvlopmnt to Rumlhart. Th BP nural ntwork (BPNN) consists of fully intrconnctd rows of procssing units calld nods, which ar organizd into groups namd layrs. Intrnal layrs provid th intrconnctions btwn th input and output. Th BPNN is fittd by mans of training th ntwork with known input/output data sts, somtims rfrrd to as facts. Th training paradigm finds a st of wight valus that minimizs th rror across th st of facts. During th training, diffrncs btwn actual outputs and prdictd outputs ar propagatd back through th architctural structur of th ntwork. Th importanc of this procss is that, as th ntwork is traind, th nurons in th intrmdiat layrs organiz thmslvs in such a way that diffrnt nurons larn to rcogniz diffrnt charactristics of th total input spac. Morovr, in ordr to improv th adaptiv ability and paramtr chang rjction of th systm, th TakagiSugno fuzzy infrnc systm is introducd into th BPNN. A(x, u) = y u y u y u y u = L 3 J M L p n ψ f. (6) Input layr x in Mmbr function layr Rul layr output layr y out Flux ψ f of th PMWIM could not b zro if A(x, u) wr to b a nonsingular matrix. Th rlativ ordr of th systm is α = (α, α ) = (, ), and α α = 3. As a rsult of i = α = = 3 n, n is th numbr of th stat variabl, which satisfis th sufficint conditions of th xistnc of th invrs systm [, 3]. Thus, in accordanc with th invrs systm thory, it can b concludd that thr xists th αordr invrs systm of th original systm. Th invrs systm of th PMIWM can b xprssd as: u = (u, u ) = ξ(y, y, y, y, y, [v, v ] T ) (7) whr v and v ar th nw input vctors. 3. RBFNNIbasd dcoupling schm of th PMIWM x in Fig.. BPNN chart Th BPNN shown in Fig. consists of 4 layrs: input layr, mmbrship function layr, rul layr and output layr. Th paramtrs of th BPNN, including layr numbrs, th nuron numbr in ach layr, wight cofficint and larning rat, can b optimizd by trial and rror [45]. As illustratd in Fig., th first layr is th input layr, which contains two nurons. Th input variabl is rprsntd by x and x. Th scond layr is th function layr, which rndrs th output of th first layr fuzzifid. Th third layr is th fuzzy law layr, which will gnrat fuzzy infrnc. Th fourth layr is th output layr, which is rprsntd by y out. Bull. Pol. Ac.: Tch. 66(6) 8 963

4 Y. Li, B. Zhang, and X. Xu Variabls x and x ar supposd to b introducd into th input layr, which contains nurons. Th input and output of th nurons ar xprssd as: nt i (M) = x i (M) y i (M) = f i (nt i (M)) = nt i (M) whr i =, ; M stands for th itrations, x (M) = ω s (M), x (M) = ω(m); and nt is th nural ntwork. Th mmbrship function layr is usd to fuzzify y and y. Th mmbrship function during th fuzzy procss is th Gaussian function. Each nuron in th mmbrship function layr has functional ability. Th input and output of nod j could b xprssd as: nt j (M) = (x j m j ) σ j y j (M) = f j (nt j (M)) = sp(nt j (M)) (8) and j =,, n (9) whr x j is th input of th jth nuron, m j is th avrag valu and standard dviation of th jth mmbrship function, and n is th total numbr of input variabls, qual to th total numbr of nurons in th mmbrship function layr. Th rror quation of th mmbrship function layr is dscribd as: δ j (M) = E I(M) nt j (M) = δ k 3 (M)y 3 k (M). () k Th rul layr is mployd to complt fuzzy infrnc work. Th input and output of th kth nuron ar writtn as: nt k 3 (M) = w3 jk x 3 j (M) j y k 3 (M) = f k3 (nt k 3 (M)) = nt k 3 (M) () whr x j 3 (N) is th input of th kth nuron, and w 3 jk is th corrsponding wight cofficint of x j 3 (N). Th rror in th rul layr should b calculatd during th training procss, and th quations ar writtn as: δ k 3 (M) = E I(M) nt k 3 (M) = δ o 4 (M)x k 4 (M). () Thr is only on nuron Σ in th output layr. Th input and output of Σ ar shown by: whr x k 4 (M) is th input of nuron Σ, w k 4 is th corrsponding wight cofficint of x k 4 (M) and R is th total numbr of fuzzy ruls. To satisfy th actual opration of th PMIWM, th BPNN rquirs continuous onlin training. Training a ntwork bgins by randomly assigning wighting factors for ach nod intrconnction and a bias trm. Th larning rat is an adjustabl factor that s th spd of th larning procss. Gnrally, ntwork larning can b facilitatd by starting at a high larning rat. Spd larning rducs th probability that th ntwork solution will sttl into a nonoptimum and local rror minimum. Th proprty standard function is dfind as: E (M) = (ω(m) ω (M)). (4) According to th BP algorithm, th rror of th output layr could b dscribd as: δ o 4 (M) = E I(M) nt o 4 (M) = δ o 4 (M) = E I(M) i (M) ω r (M)y o 4 (M) i (M) ω r (M)y o 4 (M)nt o 4 (M). (5) 3.. BPNNI systm construction. To tak th advantags of th BPNN mthod and of th invrs approach, two schms ar combind to stablish a novl dcoupling systm. BPNN is mployd to raliz th rvrsibility of th PMIWM systm. By cascading crtain intgrators on th lft sid of th BPNN block, a novl NNI systm is stablishd with th ability of gnralization. It will improv robustnss and faulttolrant prformanc. Th proposd NNI is locatd on th lft sid of th PMIWM shown in Fig. 3, which lads to mrgnc of a psudolinar systm for systm dcoupling. Th NNI approach dos not rquir an accurat mathmatical modl of th PMIWM, yt it improvs robustnss and th ability to rjct disturbancs. v v s s s BPNN Invrs Systm BPNN u u PMIWM Fig. 3. Psudolinar systm y y v v s s Psudo linar systm y y nt o 4 (M) = R w k 4 x k 4 (M) k = y o 4 (M) = f o4 (nt o 4 (M)) = nt o 4 (M) (3) Th simpl driv cycl is usd as th rfrnc spd in th nural ntwork training procss. Thr sts of data, slctd from th driv cycl, ar shown in Tabl in th rapidly changing ara. Th data ar mployd as th training sampl 964 Bull. Pol. Ac.: Tch. 66(6) 8

5 Dcoupling for prmannt magnt inwhl motor using intrnal modl basd on backpropagation nural ntwork invrs systm of th BPNN. Th input sampls that go into th ntwork work priodically during th whol training procss. Th output rror dos not ntr th prmittd rang bfor convrgnc of th nural ntwork. Th larning rat is st at.8 during th training procss. Th BP nural ntwork is supposd to mt th rquirmnt whn th training rror is lss than. aftr 6 pochs of training. Th BPNN is stablishd and rady for th PMIWM systm. Tabl Training sampls of BPNN Numbr Tam Tam Tam BPNNIbasd IMC dsign Th IMC schm was introducd by Garcia and Morari and thn subjctd to intnsiv rsarch during th past dcads. Th IMC is ffctiv at tracking, rjcting disturbanc and nhancing robustnss. Th IMC mthod was originally mployd to procss a systm and thn xtndd to th motor systm, which rlis on th intrnal modl principl, including a modl of th plant [46, 47]. It should b pointd out that th convntional IMC mthod could provid an adquat supprssing ability for th disturbancs addd to th output channl. Howvr, it might not provid a satisfactory load disturbanc rjction proprty for th disturbancs addd to th input channl whn th procss dynamics ar much slowr than th dsird closd loop dynamics [48 5]. Figur 4 shows th structur of th DOF intrnal modl lr of th PMIWM. Ds () Rs () Y() s P s Gs () ( ) Qs () s () G () m s Rfrnc modl whr G(s) is th ld objct, and G m (s) th idal intrnal modl. Q(s) and P(s) ar th intrnal modl lrs. Y(s) is th output of th systm. D(s) stands for xtrnal disturbanc. R(s) is th input of th systm. Th PMIWM output is xprssd as: Y(s) = G m (s)p(s)r(s) ( Q(s)G m (s))d(s). (6) Equation (7) illustrats that tracking prformanc is dtrmind by P(s), and disturbanc rjction rlis on Q(s). To track th input R(s) without any stadystat rror and to improv robustnss, low pass filtrs F (s) and F (s) ar introducd into th intrnal modl lrs G c (s) and G c (s), which could b xprssd as: P(s) = F (s)g m (s) Q(s) = F (s)g m (s). (7) Low pass filtrs F (s) and F (s) ar commonly dscribd as follows: F (s) = F (s) = (λ s ) (λ s ) whr λ and λ ar th tim constants of th filtr. Figur 5 is a structur quivalnt to Fig. 4. R s Gn s Gc s Gm s Fig. 5. Diagram of th DOF intrnal modl lr D s (8) Th output rror quation of th closdloop systm is rprsntd by: E(s) = R(s)G n (s) Y(s) = = [ G c(s)g m (s) G n (s)g c (s)g m (s)]r(s) D(s) G c (s)g m (s). (9) As for th stp signals, if R(s) = R, th stady stat rror s could b givn as: Y s Fig. 4. Control diagram of DOF IMC E() = lim s (λ s ) R s! (λ s ) s =. () Bull. Pol. Ac.: Tch. 66(6) 8 965

6 Y. Li, B. Zhang, and X. Xu As for th sinusoidal signal, and if R(s) = R, th stady s stat rror could b writtn as: d Gn Gn s s E() = lim s (λ s ) R =. () s! (λ s ) s Hnc, th closdloop systm of th PMIWM could track th stp and sinusoidal signal without any obvious stady stat rrors. Th ovrall schm of th PMIWM is shown in Fig. 6. c Gc G s s v v s Fig. 6. Ovrall BPNNIbasd IMC diagram s s BPNN 5. Simulation and xprimntal validation u u PMIWM To validat th ffctivnss and prformanc of th proposd BPNNIbasd IMC schm of th PMIWM, simulation and xprimnts hav bn dvlopd. Comparativ rsults of th BPNNI schm ar masurd. IMC paramtrs λ and λ ar.4 and.8, rspctivly. Th currnt loops bandwidth is dsignd to b 5 tims that of traditional currnt loops. IGBT is usd as th bidirctional convrtr. Th highr th frquncy, th largr th loss. According to th Shannon s sampling thorm, th uppr limit switching frquncy of th convrtr is half of th carrir frquncy. i d = is usd for vctor of th PMIWM. i d 5.. Simulation vrification. Comparativ studis of th PMIWM systm ar carrid out with th us of Matlab/ Simulink softwar. Th systm is modld in Simulink. Th nominal powr of th PMIWM motor is 8 kw. Nominal spd is 6 r/min and nominal torqu is Nm. ) Dcoupling and tracking proprty To tst dcoupling and tracking proprty of th systm, motor spd ω is st to incras from r/min to r/min. Th simulation rsults from th motor with BPNNI and th proposd BPNNIbasd IMC ar illustratd in Fig. 7, from th top to th bottom, rspctivly. Figur 7 illustrats that th BPNNIbasd stratgy visibly rducs th fluctuations as compard with th BPNNI schm. This provs that th proposd BPNNIbasd IMC approach will not only guarant stability of th PMIWM systm, but also ffctivly solv th strong coupling problms. Far mor importantly, it obviously has xcllnt proprtis with only slight ovrshoot and smallr oscillation onc th systm rachs th stady stat. From Fig. 7 it can b sn that th motor spd manifsts ithr small or larg fluctuations at t =. s. Th fluctuations last for a short tim, from t =. s. Aftr that, th spd gos to a stadystat valu, which is r/min. It thus taks lss than. s from th start to stabilizd tim with both schms. Th simulation rror with diffrnt schms is lss than 8 r/min bfor gtting to stabilizd tim. Aftr. s, fluctuations with th BPNNI mthod ar largr than that thos with th proposd approach, which could b sn from th simulation rror spd at th bottom in Fig. 7. To furthr tst dcoupling and tracking prformanc of th PMIWM systm, a simpl driv cycl is slctd as th spd rfrnc. Th rfrnc spd stps up from r/ min to 3 r/min, and thn dcrass to r/min. To compar th prformanc of th two mthods, th output spd rsponss of th PMIWM masurd with th two lrs ar compard and shown in Fig. 8. a b Bull. Pol. Ac.: Tch. 66(6) 8

7 o a a st o n h t tim. Figur 8 (a) dmonstrats that th ovrshoot is.9% at 3s with a.8s sttling tim. And, th ovrshoot is.88% at 6s with a.6s sttling tim. Compard with Figur Dcoupling 8(a), th for spd prmannt tracks magnt th inwhl rfrnc motor vry using intrnal wll in modl basd on backpropagation nural ntwork invrs systm Figur 8(b), and thr is no obvious stadystat rror. And th sttling tim ar.8s and.77s in Figur 8(b), rspctivly. a b Spd (m/min) Spd (m/min) Spd (m/min).56% at.s, rspctivly. Th sttling tim a Figur is.9s from.s and.4s rspctivly. 3 is s l th Spd (m/min) (a).6.8 Tim. (s) Rfrnc(b) 5 Fig. 8. Simulation rsults of dcoupling and tracking Simulation proprty with diffrnt Fig. 8. Simulation schms: a) rsults BPNNI of, dcoupling b) proposd and tracking proprty with diffrnt schms, a) BPNNI, b) It can b obviously sn that th proposd schm. s, which lasts for Proposd. s. Thn th load is dcrasd from (b) rducs th ovrshoot and shortns th transint tim. Figur 8a 6 Nm to 3 Nm at. s. dmonstrats Fig. 8. Simulation that th ovrshoot rsults is of.9% dcoupling at 3 s, with and a tracking ) Disturbanc rjction and robustnss prformanc.8 s From top to bottom, simulation rsults of th spd trajctory, closup.9 at. s and.95 closup at.. s, ar shown.5 in. 5 sttling tim. Thn it is.88% at 6 s, with a.6 s sttling proprty with diffrnt schms, a) BPNNI, In b) ordr to vrify th disturbanc rjction and 5 tim. Compard with Proposd Fig. 8a, th spd tracks th rfrnc Fig., rspctivly. Obviously, Fig. shows that thr ar robustnss prformanc of th proposd schm vry wll in Fig. 8b, and thr is no obvious stadystat rror. som spd fluctuations undr th BPNNI at t =. s 6 ) Disturbanc And th sttling rjction tims ar.8 and s and robustnss.77 s in Fig. prformanc 8b, rspctivly. don with th closups th xrtd illustrat load that th shown spd rspons in Figur has a 9. larg Th ovr motor undr a and suddn t =. s, load whn th impact, loads ar simulation applid. As is sn tsts in hav Fig., bn In ordr to vrify th disturbanc rjction and shoot of.7% at oprats at a constant. spd s and.43% at. r/min. s, rspctivly. A 6 Nm It could load is robustnss ) Disturbanc prformanc rjction of and th robustnss proposd prformanc schm b notd that in Fig. th sttling tim is. s from. s and In ordr to vrify th disturbanc rjction and robustnss addd to. th s from motor 5. at s,.9 rspctivly..s, which.95 lasts. for.s.. Thn, th. undr a suddn load impact, simulation tsts hav bn prformanc of th proposd schm undr a suddn load is dcrasd from 6 Nm to 3 Nm at.s. don with load impact, th xrtd simulation load tsts shown hav bn in Figur prformd 9. with Th th motor 8 Fig.. Simulation rsults of suddn load disturb 3 oprats xrtd at a load constant shown in spd Fig. 9. Th motor r/min. oprats A at 6 a constant Nm load is BPNNI 7 spd of r/min. A 6 Nm load is addd to th motor at 3 addd to th motor at.s, which lasts for.s. Thn, th 6 load is dcrasd from 6 Nm to 3 Nm at.s. Torqu (Nm) Rfrnc Simulation Torqu (Nm) From top to bottom, th simulation rsults of spd trajctory, closup at.s and closup at.s ar shown Fig. 9. Simulation rsults of suddn load disturbanc in Figur, rspctivly. Obviously, Figur shows Fig. 9. Simulation rsults of suddn load disturbanc From top to bottom, th simulation rsults that of spd thr ar som spd fluctuations undr th BPNNI trajctory, closup at.s and closup at.s ar shown at t=.s and t=.s whn th loads ar applid. As Bull. Pol. Ac.: Tch. 66(6) 8 in Figur, rspctivly. Obviously, Figur is sn shows in Figur, th closups illustrat that th spd that thr ar som spd fluctuations undr th rspons BPNNI has 5. a larg Exprimntal ovrshoot of.7% vrification..s Matlab and an at t=.s and t=.s whn th loads ar applid..43% As at.s, softwar rspctivly. provid It a could rapid b prototyping notd that nviro in 5 Rfrnc Simulation Fig. 9. Simulation rsults of suddn load disturbanc Fig.. Simulation rsults of suddn load disturbanc with BPNNI Fig.. Simulation rsults of suddn load disturban proposd schm 967

8 Th spd rsponss from th proposd systm ar shown in Fig., from top to bottom. Simulation rsults of th spd trajctory, closup at. s and closup at. s, ar also rspctivly illustratd. Compard to Fig., no noticabl fluctuations xist at t =. s and t =. s. Th closups of spd trajctory at t =. s and t =. s ar shown in Fig.. Th spd rspons has a small ovrshoot of.47% at. s and.56% at. s, rspctivly. Th sttling tim as shown in Fig. is.9 s from. s and.4 s from. s, rspctivly. xprimnt and tst nvironmnt, which is usd for ralizing th paramtr adjusting, wav obsrving and data rcording. Th Encodr board is usd to convrt th spd signal of th PMIWM. Th PMIWM is installd insid th whl hub. Th dspacebasd HIL tst bnch is shown in Figur. Y. Li, B. Zhang, and X. Xu Inwhl motor 3 5 Load Fig.. Simulation rsults of suddn load disturbanc with th proposd schm 5.. Exprimntal vrification. Matlab and dspace softwar provid a rapid prototyping nvironmnt for tsting and dploying raltim systms. Th schm is stablishd in Simulink, which can crat an xcutabl cod for th host PC. Th xcutabl cod is downloadd to a targt PC, in which th proposd approach is implmntd. Namly, th schm can b tstd in a soft motor lr. A dspacebasd hardwarinthloop (HIL) tst bnch is built in th lab, which consists of a usr PC, dspace hardwar, a box and a consol. Th I/O boards, A/D boards, D/A boards and Encodr boards ar all allowd to b programmd for th aformntiond modls using Simulink blocks. Thn, th xcutabl cod will b cratd and downloadd from th usr PC to th dspace hardwar. Communication among th usr PC, th hardwar boards insid th box and dspace hardwar is ralizd via th RS 3/485 intrfac. Th I/O board convrts signals rad by th physical snsor into th EV modl in th Simulink program. Th A/D board transforms an analog signal into a digital signal, which can b rad by th usr PC. Th dsk softwar is th xprimnt and tst nvironmnt, which is usd for paramtr adjusting, wav obsrving Fig.. Th dspacebasd HIL tst bnch Fig.. dspacebasd HIL tst bnch ) Dcoupling and tracking proprty To and valuat data rcording. th dcoupling Th Encodr board and tracking is usd to proprtis convrt th of th spd proposd signal BPNNIbasd of th PMIWM. Th IMC PMIWM schm, is installd th dcoupling insid and th tracking whl hub. xprimnts Th dspacebasd of th HIL PMIWM tst bnch ar is prsntd carrid out on th in Fig. abovmntiond. HIL tst bnch. Aftr choosing th appropriat incntiv signals, th corrsponding rsponss of th motor spd ω could b obtaind undr various conditions. Th dcoupling ffctivnss of th proposd BPNNIbasd IMC schm could b mulatd by th qaxis currnt i q and th motor spd ω. Th systm of th PMIWM is st to incras from rpm to r/min. Th BPNNI schm is also carrid out for comparison. Th dcoupling and tracking proprtis of th BPNNI and th proposd BPNNIbasd IMC schm ar shown in Figur. 3, in which from top to bottom ar, in ordr, th output spd with th BPNNI schm, BPNNIbasd IMC approach and comparison btwn th output spd, rspctivly. As shown obviously in Figur 3, th fluctuations in th proposd BPNNIbasd IMC ar smallr than that with th BPNNI schm. Morovr, th spd trajctory of th proposd mthod is mor stabl than that of th BPNNI approach. Th actual rsponss illustrat that paramtrs and variabls in th ) Dcoupling and tracking proprty To valuat dcoupling and tracking proprtis of th proposd BPNNIbasd IMC schm, dcoupling and tracking xprimnts of th PMIWM ar carrid out on th abovmntiond HIL tst bnch. Aftr choosing th appropriat incntiv signals, th corrsponding rsponss of motor spd ω could b obtaind undr various conditions. Th dcoupling ffctivnss of th proposd BPNNIbasd IMC schm could b mulatd by qaxis currnt i q and motor spd ω. Th systm of th PMIWM is st to incras from rpm to r/ min. A BPNNI schm is also carrid out for comparison. Dcoupling and tracking proprtis of BPNNI and th proposd BPNNIbasd IMC schm ar shown in Fig. 3, which prsnts, from top to bottom: output spd with th BPNNI schm, th BPNNIbasd IMC approach and comparison btwn th output spds, rspctivly. As shown clarly by Fig. 3, fluctuations in th proposd BPNNIbasd IMC ar smallr than thos within th BPNNI schm. Morovr, th spd trajctory of th proposd mthod is mor stabl than that of th BPNNI approach. Th actual rsponss illustrat that paramtrs and variabls in th spd rgulator dcoupl bttr with th proposd schm than with th BPNNI mthod. It can b sn that th xprimntal rsults actually agr with th simulation rsults. To furthr compar dcoupling and tracking prformanc, xprimnts with two diffrnt schms wr carrid 968 Bull. Pol. Ac.: Tch. 66(6) 8 8

9 Dcoupling for prmannt magnt inwhl motor using intrnal modl basd on backpropagation nural ntwork invrs systm a b Spd Spd (r/min) (r/min) Spd (m/min) Spd (m/min) 8 4 Rfrnc Exprimnt (b) Fig. 3. Exprimntal rsults of dcoupling and tracking proprtis within Fig. diffrnt 3. Exprimntal schms: rsults a) BPNNI of dcoupling, b) proposd and tracking a (a) proprty with diffrnt schms, b a) BPNNI, b) Proposd Rfrnc Exprimnt out on th tst bnch. Th xprimntal rsults, as shown in Fig. 4, comply with th simulation rsults. As shown in Fig. 4a, spd undr th BPNNI lr tracks th rfrnc closly, vn though th actual spd oscillats. Th ovrshoots ar.97% at 3 s and.95% at 6 s undr BPNNI, rspctivly. Th rspons in Fig. 4(b) is much slowr than that in Fig. 4a. Th curv in Fig. 4b shows ovrshoots at.% at 3 s and.% at 6 s undr th proposd schm, rspctivly. Figur 4b illustrats that th proposd Rfrnc lr Exprimnt prforms wll as far as both rspons tim and smooth ovrshoot ar concrnd. Morovr, th spd trajctory undr th proposd schm is mor stabl than for th BPNNI. (b) ) Disturbanc rjction and robustnss prformanc Fig. 4. Exprimntal rsults of dcoupling and tracking In this sction, xprimnts ar carrid out to vrify th prformanc of disturbanc rjction proprty with diffrnt schms. (a) BPNNI. (b) Proposd and robustnss with a suddn load impact on th systm. Th curv of th load disturbanc Disturbanc mployd in rjction th xprimnt and is robustnss shown in Fig. prformanc 5. ) In this sction, xprimnts ar carrid out to vrify th prformanc of disturbanc rjction and robustnss with Bull. Pol. Ac.: Tch. 66(6) 8 a suddn load impact on th systm. Th curv of th load disturbanc mployd in th xprimnt is shown in Figur 5. Spd Spd (m/min) (r/min) 8 4 Th xprimntal rsults of disturbanc rjction with To BPNNI furthr compar and th th dcoupling proposd and tracking ar shown in prformanc, Figur 6 xprimnts and Figur 7, with rspctivly. two diffrnt Th output spd schms trajctory, wr closup carrid at out.s on and th closup tst bnch. at.s ar Th shown xprimntal in Figur rsults 6, from ar top shown to bottom, in Figur rspctivly. 4 agr Obviously, wll with th as simulation sn in Figur rsults. 6, th closups illustrat that th spd rspons has a larg ovrshoot of.9% at.s and As shown in Figur 4(a), th spd undr th BPNNI.46% at.s, rspctivly. Th spd rsponss from th lr tracks th rfrnc wll, and th actual spd proposd systm ar shown in Figur 7, in which, oscillats. th spd Th ovrshoot trajctory, ar closup.97% at at.s 3s and and closup.95% at at.s 6s undr BPNNI, rspctivly. Th rspons in ar illustratd, from top to bottom, rspctivly. From Figur 4(b) is much slowr than that in Figur Rfrnc Figur 7, w can s th spd rspons 4(a). Th Exprimnt has a small curv ovrshoot in Figur 4(b) of.5% shows th at ovrshoot.s and ar.6%.% at at.s, 3s and rspctivly..% at 6s undr th proposd schm, rspctivly. 3 Figur 4(b) Tim illustrats (s) that th proposd lr (b) prforms wll both in rspons tim and smooth ovrshoot. Fig. 4. Morovr, th spd trajctory undr th Exprimntal rsults of dcoupling and tracking proposd proprty with diffrnt schm is schms. mor stabl (a) BPNNI than th. BPNNI (b) Fig (a) Fig. 4. Exprimntal rsults of dcoupling and tracking proprtis within diffrnt schms: a) BPNNI, b) proposd Spd (m/min) 8 Spd (m/min) 6 prformanc 5 of disturbanc rjction and robustnss with 4 5 th load disturbanc mployd in th xprimnt is shown 3 5 in Figur Fig. 6. Exprimntal rsults of suddn load disturbanc with BPNNI Fig. 35. Exprimntal rsults of suddn load disturbanc 5 In this sction, xprimnts ar carrid out to vrify th a suddn load impact on th systm. Th curv of Torqu (Nm) Th BPN Figu traj in F as s rsp.46 prop th ar Figu ovr rsp 8 5. Proposd ) Disturbanc 5 rjction and robustnss prformanc 3 Torqu (Nm) 3 Fig

10 ) th f n ) ) th th of th of of n n 9 proposd systm ar shown in Figur 7, in which, th spd trajctory, closup at.s and closup at.s ar Th illustratd, xprimntal from rsults top to of bottom, disturbanc rspctivly. rjction From with Th xprimntal rsults of disturbanc rjction with Figur BPNNI Th xprimntal 7, w can and rsults s th th proposd of spd disturbanc rspons rjction ar has shown a small with in BPNNI and th proposd ar shown in ovrshoot BPNNI Figur 6 and of Figur.5% and th 7, at proposd rspctivly..s and Th.6% ar output shown at spd.s, in Figur 6 and Figur 7, rspctivly. Th output spd rspctivly. Figur trajctory, 6 closup and Figur at.s 7, rspctivly. and closup Th at.s output ar shown spd trajctory, closup at.s and closup at.s ar shown in trajctory, 3 Figur 6, closup from top at.s to bottom, and closup rspctivly. at.s Obviously, ar shown in Figur 6, from top to bottom, rspctivly. Obviously, as in Figur sn in 6, Figur from 6, top th to closups bottom, rspctivly. illustrat that Obviously, th spd as sn in Figur 6, th closups illustrat that th spd rspons as sn in Figur 6, th closups illustrat that th spd has a larg ovrshoot of.9%.s and rspons has larg ovrshoot of.9% at.s and rspons.46% at.s, has a rspctivly. larg ovrshoot Th spd of.9% rsponss at.s from and th.46% 5 at.s, rspctivly. Th spd rsponss from th.46% proposd at.s, rspctivly. systm ar Th shown spd in Figur rsponss 7, in from which, th proposd proposd systm ar shown in Figur 7, in which, th spd.6.8 trajctory,.systm. closup ar.4shown at.6.s in.8 and Figur closup.7,. in at which,.s.4 th spd trajctory, closup at.s and closup at.s th spd 5 ar 5 illustratd, trajctory, from closup top to bottom, at.s and rspctivly. closup at From.s ar illustratd, from top to bottom, rspctivly. From ar Figur illustratd, 7, w can from s top th to spd bottom, rspons rspctivly. has a From small Figur 7, w can s th spd rspons has small ovrshoot Figur 7, of w can.5% s at th.s spd and rspons.6% has at a small.s, ovrshoot of.5% at.s and.6% at.s, rspctivly. ovrshoot of.5% at.s and.6% at.s, rspctivly. rspctivly Fig. 6. Exprimntal rsults of Tim suddn (s) load disturbanc with BPNNI 3 Fig Exprimntal rsults of suddn load disturbanc with BPNNI Th xprimntal rsults of disturbanc rjction with BPNNI and th proposd ar shown in Fig and.6 Fig. 7,.8 rspctivly... Th.4 output.6 spd.8 trajctoris,.. closup at 5. s and closup at. s, ar shown in Fig. 6, from top to 5 bottom, 5 rspctivly. Obviously, Tim as (s) sn in Fig. 6, th closups Fig. 6. Exprimntal rsults of Tim suddn (s) load disturbanc with Fig. 6. Exprimntal rsults of suddn load disturbanc with Fig. 6. Exprimntal rsults BPNNI of suddn load disturbanc with 3 BPNNI BPNNI proposd Obviously, 5 from Tabl 4 w can s that compard Fig. 7. Exprimntal rsults of suddn load disturbanc with th with th othr two stratgis, th proposd Y. Li, B. Zhang, and X. Xu Fig. 7. Exprimntal rsults of suddn load disturbanc with th Fig. 7. Exprimntal rsults of suddn load disturbanc with th Fig. 7. Exprimntal rsults proposd of suddn load disturbanc with th proposd Fig. 7. Exprimntal rsults proposd of suddn load disturbanc with th Obviously, from Tabl 4 w can s that compard proposd Obviously, from Tabl 4 w can s that compard with Obviously, th othr from two Tabl w stratgis, can s that th compard proposd with th othr two stratgis, th proposd with th othr two stratgis, th proposd illustrat that th spd rspons has a larg ovrshoot of.9% at. s and.46% at. s, rspctivly. Th spd rsponss from th proposd systm ar shown in Fig. 7, in which th spd trajctoris, closup at. s and closup at. s, ar illustratd, from top to bottom, rspctivly. From Fig. 7, w can s that th spd rspons has a small ovrshoot of.5% at. s and.6% at. s, rspctivly. Obviously, from Tabl w can s that compard with th othr two stratgis, th proposd BPNNIbasd IMC schm has prominnt advantags in th form of th dcoupling ffct, trajctory tracking, disturbanc rjction and robustnss. Furthrmor, to compar th proprtis of th diffrnt schms, th comparisons of xprimntal rsults ar givn to vrify th ffctivnss of th proposd schm illustratd quantitativly in Tabl. Tabl. Exprimntal comparisons of tracking, disturbanc rjction and robustnss with diffrnt approachs Control stratgy BPNNI Proposd schm Dcoupling and tracking (simpl driv cycl) Ovr Shoot (%) 6. Conclusions Sttling tim (s) Stp tim (s) Disturbanc rjction (constant rfrnc spd) Ovrshoot (%) Sttling tim (s) Stp tim (s) This papr prsnts a novl BPNNIbasd IMC schm for th PMIWM that guarants tracking prformanc, disturbanc rjction and systm robustnss in cas of paramtr uncrtaintis and load disturbancs. Basd on th backpropagation BPNNI lr, th proposd schm mploys a DOF intrnal modl lr (IMC) that acts as an xtra fdback lr for th nwly dvlopd psudolinar systm. Rsults of comparativ simulation and raltim HIL xprimnts dmonstrat that: first, th PMIWM driv systm could b ffctivly dcoupld with th proposd schm, whr th nonlinar systm was transformd into a psudolinar systm. Thn, by introducing th IMC schm into th psudolinar systm, th whol systm bcoms charactrizd by a solid dynamic, disturbanc rjction and robustnss. Last but not last, th proposd schm is suprior to th BPNNI approach in tracking prcision, robustnss and stability undr various conditions of th PMIWM systm. To rcapitulat, this papr, inspird by th concpt of dp larning, is xpctd to ovrcom th disadvantags of traditional NN for th PMIWM. Howvr, dspit th fforts mad rgarding th NN Bull. Pol. Ac.: Tch. 66(6) 8

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