Int ern at i onal  Journ al of  P ower E le ctr on i cs a n d  Drive  S ystem s   ( IJ PEDS )   Vo l.   1 2 ,  No.   2 ,  Jun   202 1 ,  pp.  1239 ~ 1 25 1   IS S N:  20 88 - 8694 ,  DOI: 10 .11 591/ ij peds . v 1 2 .i 2 . pp 1 239 - 12 5 1           1239       Journ al h om e page :  http: // ij pe ds .i aescore.c om   Torqu e   rippl e   and   nois e   contr ol   of   switc hed   re l uctance   m otor   using   an   adapti ve   fuz zy   PI   contr ol   with   the   aid   of   AR   alg or it hm       Rekha   P .   S . 1 ,   Vij ayak u mar   T . 2   1 Depa rtment   of   El e ct ri ca l   and   E l ec tron ic s   Eng ineeri ng,   SJB   Institute   of   T ec hnolo gy,   Beng al uru - 5 60060,   2 Depa rtment   of   El e ct roni cs   and   Comm unicati on   Engi ne eri ng,   SJB   Instit ut e   of   T e chnol ogy,   Beng a luru - 560060,   Karna ta k a,   and   Affili a te d   to   Vis vesva ray a   T ec hn ologi c al   Univ ersit y,   Belagav i -   59 0018,   Karn at ak a ,   Indi a       Art ic le   In f o     ABSTR A CT   Art ic le   hist or y:   Re cei ved   Ja n   1 7 ,   20 21   Re vised   A pr   3 ,   20 21   Accepte d   Apr   20 ,   20 21       In   rec en t   days   sw it che d   re luc t anc e   mot or   is   widel y   used   fo r   nume rous   industri al   appl i ca t ions   due   to   its   simpl e   str uct ure ,   mi ni mu m   cost   and   ma xim u m   ef fici enc y.   Rega rd le s s   of   nume rous   exc lusiv e   b enefit s   of   th e   sw it che d   re luc t a nce   mo tor   (SRM ),   a cousti c   no ise   of   thi s   mot or   is   high   and   it   is   i mport an t   to   a cc omp li sh   more   ana lysis   on   the   n oise   le ss eni ng ,   which   is   th e   prim ary   go al   of   thi s   pape r .   Th e   ma jor   ca uses   of   ac ousti c   noise   in   a   SR M   are   torque   ripp le   an d   rad ial   magnet i c   forc e .   Sinc e   ra dia l   ma gne ti c   fo rce   is   high ly   infl uentia l   by   th e   d esign   of   motor,   torque   r ippl e   con trol   is   an al y sed   in   thi s   art i cl e   for   ac ous ti c   noise   cont ro l .   To rque   ripple   cont rol   of   SR M   is   proposed   using   opti m izat ion   in   dir ec t   t orque   con trol   ( DTC)   method.   Now ada ys,   opti mi sa ti on   p lays   a   cru c ia l   role   in   mot or   dr ive s   f or   enha n ce d   con trol .   In   thi s   pape r,   a rti f ic i al   r ai ndrop   al gor it h m   is   proposed   in   DTC   of   SR M   to   mi n im ise   torque   r ippl e .   P erf orma n ce   of   p roposed   ARA   base d   DTC   of   fo ur - phase   8/6   SR M   is   analyse d   using   Ma tlab   and   com par ed   with   the   per for mance   of   fu zz y   gai n   sch edul ing   PI   cont rol le r   bas ed   DTC.   Ke yw or d s :   Acousti c   no ise   Ar ti fici al   rain dro p   al gorithm   Direct   to rque   c on t ro l   Fu zz y   gain   sch edu li ng   PI   c ontrolle r   PI D   co ntr oller   Sw it che d   reluc ta nce   m otor   Torq ue   rip ple   This   is   an   open   acc ess   arti cl e   un der   the   CC   BY - SA   l ic ense .     Corres pond in g   Aut h or :   Re kh a   P   S   Re search   Sc hola r   Dep a rtme nt   of   Ele ct ro nics   an d   C om m unic at ion   En gin ee rin g   SJB   I ns ti tute   of   Tec hnolog y,   Be ng al uru - 560060,   Ka r nataka ,   I ndia   Emai l:   rekhas. venkates h@g mail .co m       1.   INTROD U CTION   Simple   a nd   str ong   str uctu re,   maxim um   ef fic ie ncy ,   e xtensi ve   s peed   ra nge,   flexible   co ntr ol   an d   s peed - tor qu e   cha racte risti c   of   switc he d   reluctance   mo to r   make   it   easi er   to   meet   var i ou s   de man ds   [1] .   Be ca use   of   the   exclusi ve   featu res   of   t he   SR M ,   it   has   bee n   co ns i der e d   for   dif fer e nt   a pp li cat ion s   s uc h   as   an   el ect ric   veh ic le   [2 ] - [ 4],   aer osp ace[5 ],   [ 6],   re ne wab le   e ne rgy   [7 ] - [ 9],   w heel chairs   [ 10]   a nd   oth e r   a uto m otive   a pp li cat ion s .   In   this   anal ys is   s witc hed   rel uctance   mo t or   is   pro po se d   f or   el ect ric   ve hicle   a pp li cat io n.   Ne ver t heless,   bec ause   of   its   ro t or   doubly   sal ie nt   str uct ur e   a nd   s witc hi ng   po wer   s ource,   tor que   rip ple   is   en ormo us,   a nd   t he   noise   an d   vibrat ion   are   s el f - evi den t .   E ve ry   one   of   t hes e   imper fecti on s   li mit   the   us e   of   t he   s witc he d   relucta nce   m ot or   for   el ect ric   /hybri d   el ect ric   ve hicle s.   Re duct io n   in   to rque   rip ple   le ads   to   a   re duct ion   in   ac ou sti c   no ise   of   el ect ric   veh ic le   [11 ],   [ 12]   Torq ue   ri pp le   of   S witc he d   R el uctance   M ot or   is   c on tr olle d   us i ng   va rio us   strat egies   like   Indirect   tor qu e   c ontr ol   method,   Dir ect   Torq ue   Con t ro l   M et ho d,   To rque   S ha rin g   F un ct io n,   In te ll igent   C on t rol   Tech niques,   Sl iding   Mod e   C on t ro l,   Op ti mi zat ion   M et hod,   Conve rter   C on t ro l   a nd   so   on   [13 ].   A m ong   t he   numer ous   met hods ,   D TC   is   an   e ff ect ive   m et hod   of   tor qu e   co ntr ol   w hic h   offer s   minim um   t orq ue   ri pple   [14].   Hen ce   in   t his   pa per   DTC   met hod   is   anal ys e d   for   to r qu e   rip ple   co ntr ol   of   8/6   SR M .     Evaluation Warning : The document was created with Spire.PDF for Python.
                          IS S N :   2088 - 8 694   In t J   P ow  Ele c  &  Dr i   S ys t ,   V ol .  12 , N o.   2 ,  J une   202 1   :   1 239   –   125 1   1240   M a ny   researc he rs   anal ys ed   di rect   tor qu e   c on trol   of   SRM   usi ng   c onve ntio nal   PI   an d   P I D   con tr oller.   Com par e d   to   tradit ion al   P I,   P ID   c on t ro ll er   a rtific ia l   in te ll igent   f uzz y   lo gic   c ontr oller   in   DTC   offe red   impro ved   dy na mic   pe rforma nce   of   SR M   presente d   a   co nt ro l   a pproach   dep e nds   on   m od el   predict iv e   flu x   con t ro l   is   a pp li ed   in   t he   direct   tor qu e   co ntr ol   (D TC )   proce dure   f or   t hr ee - phase   12 / 8   SR M   GA   t un e d   PI   in   t he   DTC   re duced   the   tor que   ri pple   eff ect i vely   in   com pa rison   with   DTC   us in g   PI   an d   var i ou s   oth e r   con t ro l   methods .   The   su r ve y   sta te s   that   adv a nce d   co ntr ollers   in   the   a pp li cat ion   of   DTC   r edu ce   t orq ue   rip ple   com par e d   to   a   co nv e ntio nal   con t ro ll er   [ 15 - 18].   He nce   in   this   pap e r   no vel   opti miza ti on   arti fici al   ra indro p   al gorithm   ( A RA)   is   pr opose d   in   DTC   to   re duce   ma ximum   t orqu e   rip ple   to   at ta in   mi nimum   noise .   Perfo rma nce   of   the   pr opos e d   al gorithm   is   co mp a red   with   the   fu zz y   ga in   sc hedulin g   PI   co ntr oller - based   DT C   unde r   va rio us   sp ee ds   an d   loa d.   Sin ce   both   sp ee d   a nd   tor que   pe rformanc e   of   m otor   de ci des   t he   qual it y   of   el ect ric   veh ic l e,   in   this   a rtic le   DTC   ba sed   SRM   dr i ve   al ong   with   no ise   con t ro l   c on ce nt rates   on   ab ov e   sai d   par a mete rs   al s o.       2.   PROP OSE D   METHO DOL OGY     An   as ym m et rical   co nv e rter   is   po pu la rl y   us e d   for   the   SRM   dr i ves   as   it   has   m or e   s witc hing   sta te s   tha n   the   c onve ntio na l   co nverters   [ 19].   In   a   dire ct   to rque   co ntr ol   met hod,   s peed,   a nd   t orqu e   of   SR M   a re   co nt ro ll ed   by   a   c hange   in   the   seq uen ce   of   a   vecto r   of   the   asy mmetric al   conver te r   [20],   [ 21].   Co nv entional   PI   co ntr olle r   in   DTC   res ults   in   rea sona ble   tor qu e   ri pp le   in   SR M .   He nc e   in   this   a rtic le ,   gains   of   PI   co ntro ll er   are   tun e d   us in g   a   f uzzy   log ic   c ontr oller   and   pr opos e d   Ar ti fici al   rain dro p   al gorithm   to   at ta in   pr eci se   tor que   re fer e nc e.           Figure   1.   Sc he mati c   diag ram   of   pro pose d   c ontr oller           Figure   2.   Sc he mati c   diag ram   of   FGS   in   D T C       The   el ect r om e chan ic al   t orqu e   de velo ped   by   t he   SR M   [ 22]   is   giv e n   by     T   ≈   i      ( ,   i)   /      ( )   (1)     wh e re     ( )   a re   the   phase   flu x   li nkage s   as   a   functi on   of   r oto r   posit ion   θ   a nd   sta tor   cu rr e nt   i.     Fu zz y   gain   Sc hedulin g   PI   C on t ro ll er   in   D TC:   The   f uzz y   lo gic   c on t ro ll er   is   an   arti fici al   intel li gen t   con t ro ll er   wor ks   li ke   huma n   thin ki ng,   ca pa ble   of   deali ng   nonlin ear   s yst em   a nd   vagu e   data   [23 - 24].   F uzzy   Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N:  20 88 - 8 694       To r qu e  rip ple  and n oise c on t ro l  of swit ched rel ucta nce  m ot or   us in g an ad ap ti ve fu zzy P I   …  ( Rek ha P. S. )   1241   gain   sc hedulin g   c ontr oller   offer s   onli ne   tu ni ng   of   gain s   of   the   PI   c on t ro l le r   [25 ] - [ 30].   M am da ni   met hod   of   fu zz y   is   pro posed   in   this   a na lysis   with   f ort y - nin e   ru le s   to   tu ne   t he   gai ns   of   a   PI   co nt ro ll er   a nd   is   sh ow n     Figure   2.   Er ror   (E)   in   s pee d   a nd   rate   of   c ha nge   in   er ror   ( Ec )   are   the   two   i nputs   to   F GS   to   pro du ce   t wo   outp uts   of   k p   an d   k i .   B oth   in put   an d   outp ut   va riables   com pr ise   of   s e ven   t rian gu la r   distrib utive   f unct ions.   Neg at i ve   bi g   (N B) ,   ne gative   medi um   ( N M),   ne gative   s m al l   (N S ),   zer o   (ZE),   posit ive   small   (P S ),   po sit ive   medi um   (PM )   and   posit ive   bi g   (P B),   are   the   functi ons   of   in pu t   a nd   ou t pu t   var ia bles.   F uzz y   ru le s   a re   s ho wn   in   Table   2.   Ba sed   on   in pu t   erro r   with   the   help   of   r ules   in   Table   2,   F GS - PI   c ontrolle r   c hanges   k p   a nd   k i ,   w hich   decides   the   refe ren ce   tor que   a nd   res ults   in   the   re du ce d   t orq ue   rip ple.       Table   2 .   Fu zz y   r ules   Co n trol   rules   for   k p   Co n trol   rules   for   k i     Ec   NB   NM   NS   ZE   PS   PM   PB     Ec   NB   NM   NS   ZE   PS   PM   PB   E   Ki   E   Kp   NB   NB   NB   NM   NM   NS   ZE   ZE     B   PB   PB   PM   PM   PS   ZE   ZE   NM   NB   NB   NM   NS   NS   ZE   ZE     NM   PB   PB   PM   PS   PS   ZE   NS   NS   NB   NM   NS   NS   ZE   PS   PS     NS   PM   PM   PM   PS   ZE   NS   NS   ZE   NM   NM   NS   ZE   PS   PM   PM     ZE   PM   PM   PS   ZE   NS   NM   NM   PS   NM   NS   ZE   PS   PS   PM   PB     PS   PS   PS   ZE   NS   NS   NM   NM   PM   ZE   ZE   PS   PS   PM   PB   PB     PM   PS   ZE   NS   NM   NM   NM   NB   PB   ZE   ZE   PS   PM   PM   PB   PB     PB   ZE   ZE   NM   NM   NM   NB   NB       2. 1.   Art ific ial   rain drop   al go ri thm   tuned   PI   c ontr oller   in   DT C   Ar ti fici al   rai ndrop   al gorithm   fo ll ows   t he   va ry i ng   pro ced ure   of   a   rain dro p   [31] .   In   this   proce dure   rain drops   are   a ssu me d   as   obje ct s   and   f un ct io n   of   ob je ct   is   e valuated   by   r el at ing   el evati on .   The   posit ion   of   t he   lowe rm os t   al ti tud e   relat es   to   the   be st   s olut ion .   In   this   a nalysis   mini misat ion   of   IT A E   of   s peed   e r ror   is   consi der e d   as   the   fitnes s   f un ct ion   to   fi nd   opti mu m   va lues   k p   a nd   k i .   T he   entire   rec urring   pr ocedur e   of   this   al gorithm   is   c la ssifie d   i nto   six   ste ps :   rain dro p   generati on,   rai ndrop   de scent,   rain dro p   c olli sion,   ra indro p   flo wing,   RP   up dating   an d   va pour   updatin g.     ARA   init ia te s   with   the   prel imi nary   popula ti on   by   a rb it r aril y   em ployi ng   N   va pours   in   a   hu nting   sp ace,   an d   eac h   vapo ur   has   a   consi ste nt   posi ti on   sta te d   bel ow:      = ( ( 1 ) , . . . , ( ) , . . . ( ) ) , = 1 , 2 , . . .   (2)     In   (2)   siz e   of   popula ti on   is   N,   pr ob le m   dime ns io n   is   D ,   an d   in   the   d th   dim ensio n,   locat io n   of   t he   i th   vapour   is   ( )             Figure   3.   Sc he mati c   diag ram   of   AR A   c on t rol le r .       2.1.1. Ra in drop   gene rat i on   It   is   e xpect ed,   f or   ef f or tl ess ness,   that   the   rain drop   locat i on   is   t he   math emat ic al   fo c us   of   a m bient   water   va pour.   In   this   wa y,   its   locat ion   ca n   be   char act e rized   a s:      = ( 1 ∑ ( 1 ) = 1 , . . . , 1 ∑ ( ) = 1 , . . . 1 ∑ ( ) = 1 )   (3)   Evaluation Warning : The document was created with Spire.PDF for Python.
                          IS S N :   2088 - 8 694   In t J   P ow  Ele c  &  Dr i   S ys t ,   V ol .  12 , N o.   2 ,  J une   202 1   :   1 239   –   125 1   1242   2.1.2. Ra in drop   des cent   At   the   poi nt   w hen   the   im pact   of   outsi de   el e ments   is   disre ga rd e d,   the   RD   fall s   f rom   t he   r ai ncloud   to   the   earth   over   desce nd.   This   su ggest s   t hat   one   pa rt   of   RD   locat ion   is   al te red   a nd   the   RD   tra ns fe rs   to   ano t her   po sit io n   si gn i fied   New   RD .   C on s eq ue ntly,   t he   Ne w   RD   is   e xpresse d   as   in   (4):      ( ) = ( 2 ) + ⋅ ( ( 3 ) − ( 4 ) ) ,  = 1 ;  _ ( ) = ( )   (4)       In   an   ex pr e ssio n   (4)   φ   is   a   ar bi trary   num ber   in   the   bo unda ry   of   ( - 1,   1),   d   =   1,   2,   ·   ·   ·,   D.     2.1.3. Ra in drop   c olli sion   At   the   poi nt   w hen   t he    _    reach es   the   fl oor;   it   is   separ at e d   int o   va rio us   little   RDs   beca us e   of   the   sp ee d   a nd   qu al it y.   At   tha t   po int ,   these   small   rain drops   (  _  ,   i=   1,   2,   ·,   N)   a re   fl ying   in   entire   po s sible   directi on s .   Hence ,    _    can   be   plan ned   be neath:      _ =  _  +  ( − 0 . 5 ) ⋅  ( ) ⋅ (  _  −  )   (5)     wh e re   k   is   ar bitraril y   sel ect ed   ind e x   f rom   the   set   { 1,   2,   ·   ·   ·,   N} ,   α   a nd   β   both   a re   re gu la rly   dis per se d   a rbi trar y   numb e rs   in   the   boun dary   of   ( 0,   1)   a nd   sig n   ()   def ine s   for   si gn   f unct ion.     2.1.4. Ra in drop   fl owing   As   per   the   act i vity   of   gravit y,   these   Small _   RD i   (i=   1,   2,   ·,   N)   pas ses   from   t opmost   he igh t   to   lo w   el evati on   c ours e,   an d   the   maj ori ty   of   them   wi ll   inevita bly   st op   at   the   a reas   with   lo wer   hei gh t   (for   e xam pl e   the   bette r   ar range ments) .   In   the   proce dure   of   a lgorit hm   dev el opment,   t hese   bette r   ar range ments   ca n   gi ve   extra   data   ab out   the   hope fu l   a dv a nc ement   directi on.   T her e fore,   the   rain dro p   pool   (RP)   is   i ntend e d   to   f ollo w   these   lowe r   locat io ns   f ound   up   to   now   th r oughout   t he   purs uit,   an d   the   refreshi ng   of   RP   is   im ple mented   as   fo ll ow s:   1)   RP   is   sta rted   to   be   a ny   at ta ina ble   res ult   of   hu nt   s pace.   2)   The   best   resu lt   of   the   pr e sent   popula ti on   is   a ccum ulate d   to   RP   subse quent ly   eve r y   re petit ion .   3)   On   t he   off   c ha nce   that   t he   si ze   of   RP   s urpa sses   the   li mit   giv e n,   at   th at   po i nt   a   fe w   s ol utions   in   RP   will   be   a rb it ra r il y   erase d   to   re ta in   the   e xtent   of   RP   un c ha nging   a nd   dimini sh   c omp utati on   sum.   Fu rt hermo re,   the   strea min g   di recti on   of   rai ndr op   di   f or   Sm al l_RDi   (i=   1,   2,   ·,   N)   is   bu il t   dep e ndent   on   the   li near   mix   of   dual   vectors   d1 i   a nd   d2 i ,   in   wh ic h   d i ,   d1 i   a nd   d2 i   a re   portr ayed   as:     1 =  ( ( 1 ) − (  _ ) ) ⋅ ( 1 −  _ )   (6)     2 =  ( ( 2 ) − (  _ ) ) ⋅ ( 2 −  _ )   (7)     = 1 ⋅   1 ⋅ 1 + 2 ⋅   2 ⋅ 2   (8)     In   an   e xpressi ons   (11 -   12)   RP k 1   and   RP k 2   are   any   de uce   of   a pp li cant   s ol ution s   in   RP   ( k 1,   k 2   ∈   { 1,   2,   ·   ·   ·,   | RP |} ),   τ 1   a nd   τ 2   a re   two - s te p   par amet e rs   of   S mall _RD i   flo wing,   ra nd 1 i   a nd   ra nd2 i   bo t h   a re   c onsis te ntly   disseminate d   a rb it ra ry   num be rs   within   a   bo unda r y   of   ( 0,   1),   F   ( · )   de note d   f it ness   f unct ion.     Con se quently ,   New   Small _R D i   ( i =   1,   2,   ·   ·   ·,   N )   is   sta te d   as :       _ =  _ +   (9)     Be   that   as   it   may,   the   Sma ll _RD i   not   a ble   to   pass   in   an   act ual   at mosphe re.   It   is   e ssentia l   to   pre sent   a   const raint   m ax   fl ow   num ber   to   regulat e   t he   extreme   qu a ntit y   of   fl ow s .   Subse qu e ntly,   the y   will   re main   in   t he   areas   with   a   m od e ratel y   le sse r   heig ht   or   diss ipate   subse qu e ntly   a   fe w   strea ming.     2.1.5. Vapour   u pd ati ng   Eve ntu al ly,   t he   va pour   disa ppears   in   t he   ai r   by   va nish i ng   a nd   ad diti on al ly   de velo p   the   ne w   rai ndr op.   To   e nh a nce   t he   wor king   reci ta l   and   c onve r gen ce   pro porti on   of   AR A,   in   the   pr ocess   of   va pour   ap pr isi ng,   the   N   finest   res ults   f rom   ne w   s mall   RD   ∪   va pour   a re   nomin at ed   by   mea ns   of   t he   s or ti ng   te c hn i qu e   as   t he   su bse que nt   va pour   popula ti on.   Flo wch a rt   of   ARA   is   sho w n   in   Fig ure   5     Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N:  20 88 - 8 694       To r qu e  rip ple  and n oise c on t ro l  of swit ched rel ucta nce  m ot or   us in g an ad ap ti ve fu zzy P I   …  ( Rek ha P. S. )   1243       Figure   5.   Flo w char t   of   AR A       Fo r   SR M   c on t r ol,   the   mea ns   of   util iz ing   AR A   for   the   ideal   tun in g   of   PI   a r e   as   per   t he   fo l lowing:   Stage   1:   Arbit r aril y   i ntrod uce   the   hu nt   s pace   with   a   po pu la ce   of   ' n'   num be r   of   Vapo ur s .   The   relat in g   posit ion   of   eve ry   Vapour   is   prese nted   in   ( 7).   C hose n   est imat io ns   of   co ntr ol   bounda ries   a re   as   per   the   fo ll owin g   n   =   2,   m os t   extr eme   em phasi s   cycle   =   200,   ven t ur e   bo unda ries   τ _1   =   τ_ 2   =   2,   M a x_ Fl ow_ Numbe r   =   6,   great est   est imat ion   of   coe ff ic ie nt   =   4,   an d   least   es ti mation   of   coe ff ic i ent   =   -   1.   Stage   2:   G over n   the   fitnes s   of   entire   Va pours.   A ssume   gbe st   =   best   Va pour   an d   RP   =   gbest .   Stage   3 :   P rod uc e   RD   as   in dicat ed   by   ( 3)   as   t he   functi on   of   Vapo ur.   Stage   4:   Creat e   Ne w_ R D   as   per   ( 4)   as   the   r ole   of   R D.   Stage   5:   Esti m at e   Small _RD   as   an   el ement   of   Ne w_ R D   a nd   Vapo ur   as   pe r   ( 5).   Stage   6:   Deci de   the   m ovin g   t rack,   d   as   per   (13),   a nd   co m pu te   Ne w_Sm al l_RD   as   pe r   (9)   as   t he   ca pa ci ty   of   Small _RD   an d   d.   Stage   7:   Gove rn   the   apt ness   val ue   of   Ne w_Small _R D   and   S mall _RD.   On   the   off   c han ce   that   the   er ror   aptness   of   t he   pr e vious   is   gre at er   tha n   the   l ast   me ntion e d,   the   strea min g   di recti on   (d)   is   not   ri gh t,   and   the   Ne w _Smal l_RD   is   dis reg a rd e d.   Be   t hat   as   it   may ,   a ll   the   Small _R Ds   a re   permi tt ed   to   strea m   dep e ndent   on   t he   fixing   of   Ma x_Flo w_N umber .   Stage   8:   Ba se d   on   the   fit nes s   sta nd a rds   of   vapo ur   a nd   S mall _RD ,   c hoos e   the   fi nest   'n'   am ount   of   app li can t   reso l utions   as   t he   new   va pour .   A dd it io nally,   apprise   the   gbe st   an d   RP.     Stage   9:   S witc h   to   sta ge   3   till   maxim um   re pe ti ti on s   are   to uc hed.   Stage   10:   A nnounce   t he   gb e s t   as   the   best   s ol ution.       3.   SIMULATI O N   RESU LT S   AND   A NA L Y SIS     Perfo rma nce   of   the   pro po se d   dri ve   is   a na lysed   us i ng   8/ 6   SR M   bu il t - in   matl ab .   Pa r amet ers   of   analyse d   m otor   is   presn et ed   in   Ta ble   3.   T orqu e   ri pp le   of   S RM   is   anal ys e d   unde r   va rio us   s peed s   a nd   va rio us   Evaluation Warning : The document was created with Spire.PDF for Python.
                          IS S N :   2088 - 8 694   In t J   P ow  Ele c  &  Dr i   S ys t ,   V ol .  12 , N o.   2 ,  J une   202 1   :   1 239   –   125 1   1244   loads .   T he   sp e ed   perf or ma nc e   of   SR M   is   a na lyzed   in   t he   a sp ect s   of   pe ak   ov e rs hoot,   Ste ady - sta te   er r or ,   sp ee d   rip ple,   s pee d   dro p   durin g   cha ng e   in   loa d   a nd   resto rati on   ti me   afte r   c hange   in   loa d.   T orq ue   pe rforma nce   of   SRM   is   a nalyz ed   in   t he   a sp e ct s   of   ste a dy - s ta te   error   a nd   t orq ue   rip ple.   S et tl ing   ti me   of   sp e ed   a nd   to r qu e   is   al so   disc us se d.   In   the   a sp ect   of   el ect ric   ve hi cl e   per f orma nc e   of   dri ve   is   analyze d   unde r   va rio us   sp ee ds   a nd   var ia ble   loa d.         Table   3 .   Para m et ers   of   t he   m ot or   a nalyse d   Para m eters   Valu es   Nu m b er   of   stato r   p o les   8   Nu m b er   of   roto r   p o les   6   Stato r   resistan ce   3 .1Ω   Maximu m   cu rr en t   10A   Maximu m   flux   lin k ag e     0 .48 6         Ca se   1 ,   in   thi s   case,   mo t or   sp ee d   is   set   to   1000   RP M   and   sta rts   with   the   no   loa d   then   loa d   is   increase d   to   7Nm   at   2s .   S pee d   a nd   to rque   P erforma nce   of   FG S - PI   based   DTC   of   SRM   unde r   Ca se   1   is   sho wn   in   Fig ure   6.             (a)   (b)       Figure   6.   (a )   S peed   an d   ( b)   T orq ue   perform ance   of   F GS - PI   based   D TC   of   SR M   unde r   c ase   1       Fr om   Fig ur e   6,   it   is   a nalyze d   that   the   F GS   con t ro ll ed   dri ve   set tl es   to   the   sp ee d   of   1000 .74   RP M   at   0.45 s ,   w hich   pro duces   a   ste a dy   sta te   e rro r   of   0.0 74 % .   Osci ll at ion   in   s pee d   is   known   to   be   rip ple   e xists   in   the   range   of   0.0 05%.   At   the   ti me   of   sta rting   pea k   overs hoot   pr oduce d   by   FGS   is   14. 9%.   T he   infl ue nce   of   on li ne   tun in g   of   t orq ue   ref e ren ce   us i ng   FGS   set tl es   tor qu e   a r ound   7.061 Nm   at   0.55 s ,   produces   ste ady   sta te   e rror   as   - 0.87%   with   the   tor que   ri pp le   rati o   of   3.1 4% .   On   t he   ti m e   of   cha nge   in   load ,   s peed   dr op s   to   12. 4%   and   the   resto rati on   ti me   after   c ha ng e   in   loa d   is   0.6 s.   Co mp a re d   to   DTC   with   PI   to rque   rip ple   pro duced   by   FG S   is   reduce d.             (a)   (b)       Figure   7.   (a )   S peed   an d   ( b)   T orq ue   perform ance   of   AR A   ba sed   DTC   of   S RM   unde r   case   1       Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N:  20 88 - 8 694       To r qu e  rip ple  and n oise c on t ro l  of swit ched rel ucta nce  m ot or   us in g an ad ap ti ve fu zzy P I   …  ( Rek ha P. S. )   1245   In   Fi gure   7( a )   performa nce   of   AR A   in   the   a sp ect   of   sp ee d   sh ows   t hat   the   ARA   set tl es   the   sp ee d   of   1000   R PM   at   0.4s,   wh e reas   the   set tl ing   ti me   by   F GS   is   0. 45 s .   It   sho ws   that   FG S   ta kes   more   ti me   for   set tl ing   the   sp ee d   tha n   ARA.   The   ste a dy   sta te   er ror   pro duced   in   AR A   is   0   w hich   is   abso l utely   er r or   fr ee   c ompar ed   to   FG S .   M ore over,   t he   ri pple   rati o   of   t he   s pe ed   by   AR A   is   0.0 04%   wh i ch   is   al s o   reduced   tha n   t he   FGS.   Fu rt hermo re,   t he   pe ak   overs hoot   is   14.83%   wh e reas   t he   F GS   pro du ces   14. 9%.   On   the   ti me   of   cha nge   in   loa d,   sp ee d   dro ps   to   12.38%   w hich   is   0.02 %   le ss   than   the   FGS   a nd   t he   rest or at i on   ti me   a fter   l oad   c ha ng e   is   0.49 s   wh ic h   is   al so   bette r   tha n   F G S.   The   a nal ys is   shows   t he   A RA   has   bette r   performa nce   in   al l   the   co ns i der e d   aspects.   Fr om   Fig ure   7(b ),   it   is   no te d   that   the   tor qu e   set tl es   in   7. 05   Nm   at   0.5s ,   w her eas   t he   FGS   ta kes   0.5 5s   to   set tl e   the   tor que.   T he   st eady   sta te   er r or   pro duced   in   ARA   is   - 0.71%   w hich   is   com pa rati vely   le ss     than   t he   F GS.   ARA   base d   op ti mal   tun in g   of   PI   f or   t orq ue   r efere nce   reduc es   the   rip ple   ra ti o   to   2.54%,   wh ic h   is   al so   le ss   than   the   F GS .   In   this   case,   the   torque   performa nce   of   AR A   is   bette r   th an   F GS   in   al l   the     consi der e d   as pects.   Co m parat ive   perf or ma nce   of   F GS   a nd   AR A   base d   D TC   of   SR M   under   case   1   is   pr ese nted   in   T able   4.         Table   4 .   C omp arati ve   perfor mance   of   F GS   and   AR A   base d   DTC   of   SR M   unde r   case   1   Para m eters   Sp eed   (10 0 0 rpm)   Torq u e   (0   to   7   N M )   FGS   ARA   FGS   ARA   Settlin g   tim e   (s)   0 .45   0 .4   0 .55   0 .5   Rip p le   ratio   (%)   0 .00 5   0 .00 4   3 .14   2 .54   Stead y   state   er ror   ( %)   - 0 .07 4   0   - 0 .87   - 0 .71   Peak   o v ersh o o t   (%)   1 4 .9   1 4 .83   -   -   Res to ration   tim e   af ter   lo ad   ch an g e   (S )   0 .6   0 .49   -   -   Sp eed   d rop   d u ring   ch an g e   in   lo ad   (%)   1 2 .4   1 2 .38   -   -       Fr om   an   a naly sis   of   Ca se   1   both   in   s pee d   a nd   t orqu e ,   the   performa nce   of   ARA   is   bette r   in   al l   the   as pe ct s   su c h   as   set tl in g   ti me ,   rip ple   r at io,   ste a dy   sta te   er ror,   peak   ov e rs hoot,   Re s torati on   ti me   a fter   loa d   c ha ng e   a nd   Sp ee d   dro p   dur ing   c ha ng e   in   load .   Ca se   2 ,   in   ca se   2,   m otor   s pee d   set   to   1000   R PM   a nd   sta rts   with   the   loa d   of   4Nm   the n   raised   t o7Nm   at   2s .   S peed   an d   to r qu e   Per f ormance   of   F GS - PI   base d   DTC   of   SRM   un der   Ca se   2   is   sho w n   in   Fig ure   8.             (a)   (b)       Figure   8.   (a )   S peed   an d   ( b) T orq ue   perf or ma nce   of   F GS   - PI   base d   DTC   of   SRM   unde r   ca se   2       Fr om   Fig ure   8,   it   is   ob ser ved   that   the   sp ee d   and   t orque   are   set tl ed   to   1001 .7   RP M   an d   7.055   Nm   at   0.65 s   a nd   0.6s.   In   t he   as pect   of   s peed,   t he   F GS   pro duces   a   ste ad y   sta te   e r ror   of   - 0.1 7%   and   on   the   as pe ct s   of   the   tor que,   FGS   pro duces   - 0. 78%   ste ad y   sta te   error .   Ri pple   rati o   of   sp ee d   and   tor que   is   r edu ce d   to   0.01%   an d   2.54%   by   FGS .   In   this   ca se,   t he   peak   over shoo t   of   the   s pee d   by   FGS   is   5.95%.   Durin g   c hange   in   loa d,   sp ee d   dro ps   to   3.7%   and   the   resto ra ti on   ti me   afte r   cha nge   in   l oa d   is   0.5 s.   S pee d   a nd   t orq ue   pe rformance   of   ARA   base d   DTC   of   SRM   unde r   ca se   2   is   sho wn   in   Fi gure   9.     In   Fig ure   9( a )   the   performa nc e   of   ARA   in   the   aspect   of   s pe ed   s hows   that   the   ARA   set tl es   the   sp ee d   arou nd   1000   RPM   at   0.5 s.   The   ste ad y   sta te   err or   produ ced   in   ARA   is   abs olu te   zer o   wh ic h   is   er ror   fr ee   in   con t rast   with   FG S .   More ov e r,   t he   rip ple   ra ti o   is   re duced   to   0.004%   by   the   i nf lue nce   of   AR A,   w hich   is   al s o   bette r   the   FGS .   Furthe rm or e ,   the   pea k   over sh oot   of   t he   s peed   is   5.9% ,   wh e reas   t he   F GS   pro du ce d   5.95%.   Sp ee d   dro ps   duri ng   cha nge   in   loa d   is   3.7%   wh ic h   is   simi la r   to   FGS   a nd   t he   resto rati on   ti me   after   loa d   change   is   0. 4s   w hich   is   impro ved   t ha n   F GS .   In   t his   case,   both   FGS   an d   AR A   pe rformed   simi la rly   in   as pect   of   sp ee d   dro p.   Evaluation Warning : The document was created with Spire.PDF for Python.
                          IS S N :   2088 - 8 694   In t J   P ow  Ele c  &  Dr i   S ys t ,   V ol .  12 , N o.   2 ,  J une   202 1   :   1 239   –   125 1   1246   Fr om   Fi gure   9(b),   it   is   note d   t hat   the   t orqu e   s et tl es   in   7.053   Nm   at   0.5s,   w he reas   the   F GS   t akes   0.65s   to   set tl e   the   tor qu e .   It   s how s   that   the   set tl ing   ti me   of   sp ee d   and   tor que   by   ARA   is   s ame.   The   ste a dy   sta te   err or   pro du ce d   in   A RA   is   - 0.76%   wh ic h   is   co mpa rati vely   le ss   t han   t he   F GS.   The   ARA   redu ces   the   ri pp le   r at io   up   to   2.04%,   w hic h   sho ws   i mpro ved   perf or ma nc e   of   opti miza ti on .   In   this   cas e,   t he   t orq ue   pe rformance   of   AR A   is   bette r   than   FG S   in   al l   the   consi der e d   as pe ct s.   Com par at ive   perf or m an ce   of   F GS   a nd   ARA   ba sed   D TC   of   SRM   unde r   ca se   2   is   prese nted   in   Ta ble   5.             (a)   (b)       Figure   9.   (a )   S peed   an d   ( b)   T orq ue   perform ance   of   AR A   ba sed   DTC   of   S RM   unde r   case   2       Table   5 .   C omp arati ve   perfor mance   of   F GS   and   AR A   base d   DTC   of   SR M   unde r   case   2   Para m eters   Sp eed   Torq u e   FGS   ARDA   FGS   ARDA   Settlin g   tim e   (s)   0 .65   0 .5   0 .62   0 .5   Rip p le   ratio   (%)   0 .01   0 .00 4   2 .54   2 .04   Stead y   state   er ror   ( %)   - 0 .17   0   - 0 .78   - 0 .76   Peak   o v ersh o o t   (%)   5 .95   5 .9   -   -   Res to ration   tim e   af ter   lo ad   ch an g e   (S )   0 .5   0 .4   -   -   Sp eed   d rop   d u ring   ch an g e   in   lo ad   (%)   3 .7   3 .7   -   -       The   sp ee d   an d   tor que   pe rformance   of   both   the   co ntr ollers   are   obse rv e d   f or   Ca se   2.   Pe rformance   of   ARA   is   bette r   in   rip ple   rati o,   ste ad y   sta te   er ror   a nd   pe ak   overs hoot.   Both   c ontr ollers   possess   the   same   performa nce   in   set tl ing   the   ti me   f or   s peed   a nd   to rque.   Ca se   3 ,   in   t his   case,   the   m otor   sp ee d   set   to   1300   RP M   an d   sta rts   with   the   l oad   of   4Nm   t he n   raised   to7Nm   at   2s .   S peed   an d   t orq ue   Per forma nce   of   FGS - PI   bas ed   DTC   of   SR M   unde r   Ca se   3   is   s how n   in   F igure   10.   It   is   obse rved   that   t he   s pe ed   a nd   to rque   a re   set tl ed   to   1002.9   RP M   a nd   7.38   Nm   at   0.7 1s   a nd   0.6s.   Stea dy   sta te   error   pro duced   in   t his   cas e   f or   sp ee d   is   - 0.29%   a nd   in   t he   to r qu e   is   - 5.31%.   Ri pple   ra ti o   of   s peed   an d   tor qu e   is   0.0 15 %   an d   2.9 7%.   In   this   case ,   the   pea k   ov e rs hoot   of   t he   s peed   is   4.0 5%   by   F GS .   S peed   drop   durin g   c ha ng e   in   loa d   is   2.9 2%   an d   t he   re storatio n   ti me   a f te r   cha nge   in   load   is   0.4s.             (a)   (b)       Figure   10.   (a)   Sp ee d   a nd   ( b)Torq ue   perfor mance   of   F GS   - PI   bas ed   DTC   of   SR M   unde r   case   3       Sp ee d   a nd   t orqu e   Per f or ma nc e   of   AR A   ba sed   DTC   of   S RM   un der   c as e   3   is   s how n   in   Fig ure   11.   Fr om   Fig ur e   11(a ),   it   is   ob vio us   that   t he   A RA   set tl es   the   sp ee d   in   1300   RP M   at   0.6 6s ,   w her ea s   the   FG S   set tl es   the   sp ee d   at   0.71s.   It   s hows   t hat   set tl ing   ti me   of   sp e ed   is   reduce d   by   pro po se d   AR A   c ompare d   to   FGS.   Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N:  20 88 - 8 694       To r qu e  rip ple  and n oise c on t ro l  of swit ched rel ucta nce  m ot or   us in g an ad ap ti ve fu zzy P I   …  ( Rek ha P. S. )   1247   The   ste a dy   sta te   error   an d   rip ple   rati o   pro du ced   in   AR A   is   abs olu te   zer o   a nd   0.0 092%   w hich   is   bette r   t han   the   FG S .   The   pea k   overs hoot   of   the   s pee d   by   ARA   is   3.9 8%   w he reas   the   F GS   pr oduce d   4.0 5%.   On   the   t ime   of   change   in   l oad,   sp ee d   dr op s   to   2.9 2%   wh ic h   is   simi la r   to   FG S   but   the   re storatio n   ti me   after   loa d   cha nge   is   0.35 s   w hic h   is   bette r   tha n   FGS.   It   sho ws   the   ARA   has   imp r ov e d   pe rforma nce   in   al m os t   a ll   the   aspects .   Fr om   Fig ur e   11( b),   it   is   no te d   that   t he   t orq ue   set tl es   in   7. 368   Nm   at   0.5 5s ,   w her ea s   the   FGS   ta ke s   0.6s   to   set tl e   the   tor qu e .   It   sho ws   that   the   AR A   set tl es   the   spe ed   in   a   qu ic k   man ner.   The   ste ady   sta te   er r or   an d   rip ple   rati o   produce d   by   an   ARA   in   to rque   is   - 5.3 1%   a nd   2.5%.   B oth   a r e   com par at i vely   le ss   tha n   the   FG S   base d   DTC.   In   this   case,   t he   t orq ue   perform ance   of   AR A   is   imp rove d   c ompa red   to   FGS .   Fr om   case   3,   t he   overall   perf ormance   of   F GS   an d   AR A   is   an al ys e d.   Both   in   s pee d   a nd   t orq ue,   the   performa nce   of   ARA   is   bette r   in   al l   the   c on si der e d   as pe ct s   s uch   as   set tl ing   ti me,   rip ple   rati o,   ste a dy   sta te   error   a nd   pea k   overs hoot.   Co mp a red   to   pr e vious   cases   pe ak   ov e rs hoot   in   s peed   is   re duced   in   ca se   3,   w hile   ste ady   sta te   er ror   in   to rque   is   increa sed .   C omparati ve   pe rformance   of   FG S   an d   ARA   base d   DTC   of   SR M   unde r   case   3   is   presente d   in   T able   6.             (a)   (b)       Figure   11.   (a)   Sp ee d   a nd   ( b)   Torq ue   perfor mance   of   ARA   base d   DTC   of   SRM   unde r   ca se   3       Table   6 .   C omp arati ve   perfor mance   of   F GS   and   AR A   base d   DTC   of   SR M   unde r   Ca se   3   Para m eters   Sp eed   Torq u e   FGS   ARDA   FGS   ARDA   Settlin g   tim e   (s)   0 .71   0 .66   0 .6   0 .55   Rip p le   ratio   (%)   0 .01 5   0 .00 9 2   2 .97   2 .5   Stead y   state   er ror   ( %)   - 0 .29   0   - 5 .31   - 5 .26   Peak   o v ersh o o t   (%)   4 .05   3 .98   -   -   Res to ration   tim e   af ter   lo ad   ch an g e   (S )   0 .4   0 .35   -   -   Sp eed   d rop   d u ring   ch an g e   in   lo ad   (%)   2 .92   2 .92   -   -       Ca se   4 ,   in   cas e   4,   mo t or   s pe ed   is   set   to   15 00   RP M   an d   s ta rts   with   the   load   of   4Nm   then   r ai sed   to7Nm   at   2s .   S peed   a nd   to rqu e   pe rformanc e   of   F GS - PI   ba s ed   DTC   of   SR M   unde r   ca se   4   is   sho wn   in   Figure   12.             (a)   (b)       Figure   12.   (a)   Sp ee d   a nd   ( b)Torq ue   perfor mance   of   F GS   - PI   bas ed   DTC   of   SR M   unde r   case   4       Evaluation Warning : The document was created with Spire.PDF for Python.
                          IS S N :   2088 - 8 694   In t J   P ow  Ele c  &  Dr i   S ys t ,   V ol .  12 , N o.   2 ,  J une   202 1   :   1 239   –   125 1   1248   Fr om   Fi gure   12,   t he   set tl ing   value   of   sp ee d   is   1504   RP M   at   0.7s   with   t he   peak   overs hoot   is   3.21 % .   FG S   base d   s ys te m   set tl es   torque   to   7.588 Nm   at   0.65 s .   Stea dy   sta te   error   of   s peed   an d   t orq ue   are   - 0.2 7%   an d   - 8.4%.   F r om   Fi gure   12 (a)   it   is   obser ved   t ha t   the   FG S   reduces   the   rip ple   rati o   of   the   s peed   is   known   to   be   0.033 3%.   Ri pple   rati o   de velo ped   in   tor que   by   usi ng   F GS   is   2.7%,   w hic h   is   sli ghtl y   higher   co mp a re d   to   case   2.   D ur i ng   cha nge   in   loa d,   sp e ed   dro ps   to   2.5 3%   a nd   the   res torati on   ti me   a fter   c hange   in   l oad   is   0.5s   Figure   13(a)   s hows   t hat   the   ARA   set tl es   the   sp ee d   in   1500   RP M   at   0.6 2s,   w hich   is   0.1 2s   le ss   t han   FG S   s pee d   set tl ing   ti me.   It   r eveals   that   AR A   has   offere d   impro ved   perf ormance   in   set tl ing   the   sp ee d.   Th e   ste ady   sta te   er ror   pro du ce d   by   ARA   is   a bsolute   ze r o.   In   al l   the   cases   the   ste a dy   sta te   er ror   of   the   ARA   is   abs olu te   ze ro   wh ic h   is   e rror   fr ee   c ompa red   with   FGS.   Ri pp le   rati o   of   t he   s pee d   by   us ing   AR A   is   0.010 0%   wh ic h   is   c omp arati vely   bette r   than   t he   F GS.   Fu rt hermo re,   t he   peak   over shoo t   of   the   s pee d   is   3.13 % ,   whereas   the   F GS   pro duced   3.2 1% .   S peed   dr op s   du rin g   c hange   in   load   is   2.53%   w hich   is   si mil ar   to   FGS   and   the   resto rati on   ti me   after   l oa d   c ha ng e   is   0.4s   wh i ch   is   im pro ved   than   F GS .   Fr om   Fig ur e   13( b),   it   is   obse r ved   that   the   tor qu e   set tl es   in   7.5 76   Nm   at   0.6 s,   wh e reas   the   FG S   ta kes   0.7s   to   set tl e   the   to r qu e .   It   shows   the   AR A   has   im pro ve d   performa nce   in   set tl ing   the   to r qu e .   T he   ste ad y   sta te   error   produce d   in   AR A   is   - 8. 23%   w hich   is   com par at ivel y   le ss   tha n   t he   F GS .   T orq ue   rip ple   rati o   is   re duced   to   2.32%   by   t he   i nf l uen ce   of   A RA,   wh ic h   is   bette r   tha n   t he   FG S .   In   t his   c ase,   the   t orq ue   perf ormance   of   AR A   sh ows   bette r   in   al mo st   al l   the   consi der e d   a spe ct s.   Com pa rati ve   pe rfo rma nc e   of   F GS   an d   ARA   base d   D TC   of   SRM   unde r   ca se   4   is   prese nted   in   Ta ble   7.             (a)   (b)       Figure   13.   (a)   Sp ee d   a nd   ( b)Torq ue   perfor mance   of   ARA   base d   DTC   of   SRM   unde r   ca se   4       Table   7 .   C omp arati ve   perfor mance   of   F GS   and   AR A   base d   DTC   of   SR M   unde r   case   4   Para m eters   Sp eed   Torq u e   FGS   ARDA   FGS   ARDA   Settlin g   tim e   (s)   0 .7   0 .62   0 .65   0 .6   Rip p le   ratio   (%)   0 .03 3 3   0 .01 0 0   2 .7   2 .32   Stead y   state   er ror   ( %)   - 0 .27   0   - 8 .4   - 8 .23   Peak   o v ersh o o t   (%)   3 .21   3 .13   -   -   Res to ration   tim e   af ter   lo ad   ch an g e   (S )   0 .5   0 .4   -   -   Sp eed   d rop   d u ring   ch an g e   in   lo ad   (%)   2 .53   2 .53   -   -       Fr om   t he   resul ts   of   Ca se   4,   both   in   sp ee d   a nd   to rque ,   the   performa nc e   of   ARA   ha s   imp r ov e d   performa nce   in   al l   as pects   s uc h   as   set tl in g   ti me,   rip ple   rati o,   ste ad y   sta te   error   a nd   peak   ove rsho ot.   From   the   analysis   of   va r iou s   of   cases   of   sp ee d   a nd   lo ad,   it   is   obser ve d   that   ARA   ha s   bette r   performa nce   tha n   F GS   in   sp ee d   in   t he   a s pects   of   set tl in g   ti me ,   rip ple   r at io,   pea k   over sh oot   an d   rest orat ion   ti me   al mo st   un der   al l   cases.   Stea dy   sta te   e r ror   in   s pee d   is   abs olu tl y   el imi nated   with   the   ai d   of   ARA   un der   al l   cases   with   loa d   a nd   wi thout   load.   S peed   dr op   duri ng   ch a ng e   in   l oad   is   al mo st   same   in   bo t h   c on t ro ll ers.   U nd e r   al l   cases   pe rfo rma nce   of   tor qu e   us in g   A RA   is   e nh a nce d   c ompa red   to   FG S   in   t he   a spe ct s   of   set tl ing   ti me,   ri pp le   ra ti o   a nd   ste a dy   sta te   error.   C ompar at ive   performa nce   of   t he   pro po s ed   s ys te m   with   t he   existi ng   s ys te m   in   t he   a sp ect   to rque   rip ple   reducti on   is   presented   in   T abl e   8.     Fr om  Ta ble  8,  it   is  cl ear  that  analyse d  ARA - PI   a nd  F GS - P I  base d  DTC  of  SR M   offe re d  le ss  tor qu e   rip ple  co mp a re d  to  t he  e xisti ng  P I  a nd   G A - P I  ba sed  DTC  of  SR M .  FG S   tun e d  PI   i n  D T C  reduces  69. 32%  of   tor qu e   ri pp le   c ompare d  DTC   with   P I,   w hile  pro pose d  A RA  op ti m ise d  PI   minimi ses   tor que  rip ple  a rou nd  74%. Re du ct io n  in  to rque  rip ple w it h t he  h e lp od AR A bas ed DTC mi nim ise s aco us ti c noise  of   SRM .      Evaluation Warning : The document was created with Spire.PDF for Python.