Journal of Engineering Science and Technology Review 9 (4) (2016) Research Article

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1 Jesr Jornal of Engneerng Scence and echnolog Reew 9 (4) (6) - 9 Research Arcle Enhanced Veloc racng Conrol sng Hgher-Order Model-Free Adape Approach for Permanen Magne Snchronos Moor Feng Qao,, Zhzhen and Jangn Wang School of Elecrcal Engneerng, Shandong Uners, Jnan 56, Chna UFR Scences e echnqes, Unersé d Hare, e Hare 766, France JOURNA OF Engneerng Scence and echnolog Reew Receed 9 Ma 6; Acceped 5 Ags 6 Absrac he eloc of permanen magne snchronos moors (PMSMs) ms be exacl conrolled o promoe he deelopmen of hgh-performance dre ssems. hs wor proposed an enhanced adape conroller o mproe he racng performance of PMSM based on a new hgher-order adape conrol mechansm. Frsl, he conroller adoped a noel hgher-order weghed one-sep-ahead creron fncon o generae he conrol law for an eqalen paral form lnearzaon ssem. hs model-free desgn depended on a psedo paral derae (PPD) ha was dered onlne from he np and op (I/O) nformaon of he conrolled plan. hs approach s especall sefl for nonlnear ssems wh age dnamcs. Secondl, he desgn garaneed he sabl of he bonded np and op and ensred racng error monoonc conergence nder a resrced se of parameers. hrdl, he desgn was smlaed and appled on an acal PMSM ssem o demonsrae he effecs of dfferen conrol parameers. Resls show ha he approach s f for moor conrol and elds sasfacor eloc racng precson and fal olerance along wh he ncreased order. Moreoer, he approach noles lesser calclaon effors for parameer esmaon and smplfes he conroller desgn. hs sd can mee he demand of eloc racng and demonsraes he effece applcaons of hs approach for real nonlnear moor ssems ha are pcall dffcl o model and conrol. Kewords: PMSM, Hgher-order, Model-free, Adape conrol, Veloc racng. Inrodcon Permanen magne snchronos moors (PMSMs) are wdel sed n hgh-performance sero applcaons owng o he hgh effcenc, speror power dens, and large orqe o nera rao []. Howeer, PMSMs are nonlnear mlarable dnamc ssems and s dffcl o conrol her eloc wh hgh precson de o he parameer perrbaons and he non-modeled dnamcs. Adape conrol has been wdel sed for sch nceran ssems [], b hs approach s pcall assmed ha he mahemacal model of he ssem s nown and he parameers are nnown or slow me-arng [3]. For praccal PMSM ssems, he models are ofen complex o bld and he parameers are hard o denf, whch mae he adape conrol qesonable. hs moaes s o sd daa-dren conrol approaches. Daa-dren conrol approaches manl concenrae on he mporance of np and op (I/O) nformaon n sdng ssems behaor and desgn conroller merel sng I/O daa of a plan. Snce hese approaches do no reqre an explc model or he srcral nformaon of he plan, he modelng process and he non-modeled dnamcs all dsappear. Now, seeral daa-dren conrol approaches can be fond, sch as smlaneos perrbaon sochasc approxmaon conrol, ml-leel recrse conrol, model free adape conrol (MFAC), nfalsfed conrol, erae feedbac nng, ral reference feedbac E-mal address: qfeng8@63.com ISSN: Easern Macedona and hrace Inse of echnolog. All rghs resered. nng and laz learnng [4], [5], [6]. Compared wh oher approaches, he MFAC offers low compaonal brden, eas mplemenaon and srong robsness, whch mae sable for man praccal applcaons. B s man problems ha need o be soled are he lzaon amon and he lzaon rao of he hsorcal I/O nformaon. herefore, o sole he menoned problems, hs paper focses on an enhanced adape conrol approach.. Sae of he ar As a noel daa-dren approach, MFAC s based on psedo paral derae (PPD), a new concep of paral derae dered from I/O nformaon [7], [8]. hs approach dffers from proporonal-negral-derae (PID) conrol, fzz conrol, neral newor conrol and exper ssem conrol [9], and does no reqre sppor from he model, rle or pror nowledge. he conergence analss, sabl analss and general procedres of conroller desgn are dreced b farl complee gdelnes []. he recen deelopmens n hs feld hae focsed on mprong he desgns and applcaons of adape conrollers for nonlnear dnamc ssems. For nsance, [] proposed a second-order nersal model adape conroller whch parameers were opmzed b a graden descen algorhm, whls [] desgned a hgher-order model free adape conroller for conrollng a class of sngle-np sngle-op (SISO) nonlnear ssems ha cold oban promsng resls sng onl np nformaon. Howeer, hese desgns do no fll lze he hsorcal I/O daa of he conrolled plan, and

2 Feng Qao, Zhzhen and Jangn Wang./Jornal of Engneerng Scence and echnolog Reew 9 (4) (6) - 9 sng ncomplee or mssng daa resls n he poor robsness, oscllaon and nsabl of hese ssems. Model-free predce conrol [3], [4] and model-free erae learnng conrol [5], [6], [7] hae been deeloped negrang MFAC wh adanced conrol sraeges o mproe her performance. he former offers srong robsness and economc reqremens n an opmzaon creron, b s performance greal depends on he predcon accrac of he model. Howeer, ncorrec model parameers can lead o naccrae predcons. he laer fnds a conrol np ha generaes he desred op oer a fne me neral hrogh ral repeon. Howeer, hs process onl lms he moor conrol. MFAC has been wdel appled o address he heorecal and acal problems n conrol engneerng, power grds and ssems, nellgen ransporaon ssems, elecrcal dres and process ndsr [8]. hs approach can also be sed o conrol nonlnear PMSM ssems. Explong a larger amon of hsorcal I/O nformaon can mproe desgn accrac. Howeer, he approprae amon and he lzaon rao of he I/O nformaon reman nclear. hs paper proposed a hgher-order model-free adape conrol (HMFAC) approach o mproe he racng performance of a PMSM ssem. o desgn he adape conrol law, hs approach adoped a noel weghed one-sep-ahead np creron fncon wh an onlne-dered PPD. he approach exploed a larger amon of hsorcal I/O nformaon n a sldng me wndow and mproed he robsness and sabl of he conrolled ssem. heorecal analss and smlaons were performed o aldae he effeceness of hs approach. he res of hs paper s organzed as follows. Secon 3 descrbes he HMFAC desgn ha emplos he lnearzaon mehod for a SISO nonlnear ssem and presens he conergence and sabl analses. Secon 4 presens a smlaon o llsrae he effeceness and speror performance of HMFAC. Secon 5 concldes he paper. 3. Mehodolog 3. Problem formlaon and dnamc lnearzaon mehod he conrolled ssem s descrbed b he followng SISO nonlnear me-arng eqaon: (+ ) = f( (), ( ),, ( n ), where (), ( ),, ( n )) () () and () are he op and np a me respecel, n and n are he nnown orders and f ( ) s an nnown nonlnear fncon. o gde or dscsson, we mae he followng assmpons: Assmpon : he np and op of ssem () are obserable and conrollable, ha s, for he desred bonded op sgnal ( + ), here exss a bonded feasble np sgnal ha maes he praccal op eqal o he desred op. Assmpon : he paral deraes of f ( ) wh respec o conrol np () are connos. Assmpon 3: Ssem () presens he generalzed pschz condon, ha s, Δ (+ ) b Δ () for an, where Δ () = () ( ), Δ (+ ) = (+ ) (), Δ() and b s a pose consan. heorem : For he nonlnear ssem () ha sasfes assmpons,, and 3, here ms exs PPD ecors φ () and φ() b when Δ(), sch ha ssem () can be ransformed no he followng paral form dnamc lnearzaon descrpon: Δ (+ ) = φ() Δ () () Eqaon () s he nersal model of ssem () ha coners a complex SISO nonlnear ssem no a lnear ssem wh he me-arng parameer φ (). 3. Adape conrol law algorhm he adape conrol law fnds a sable conrol np seqence o achee he desred raecor lm e() lm[ () ()] (), ha s, () = = (3) where e () s he racng error of he op. Unle he conrol law n [5], he noel weghed one-sep-ahead conrol creron fncon of ssem () s defned as follows: ( (),, ) = ( ( + ) ( + )) J ab a + λ b ( ( + ) ( )) = where λ s a pose wegh facor ha resrcs he araon of conrol nps. he frs and second ems n eqaon (4) denoe he weghed op and np errors of he preos or samplng nsances, respecel, whch are defned a samplng nsan. a and b denoe he wegh facors ha drecl deermne he regon and degree of preos nformaon. a = ( a, a,, a ) wh a =, whle b = ( b, b,, b ) wh = b =. Sbsng eqaon () no eqaon (4) defnes J ( (), ab, ) as follows: ( (),, ) = ( ( + ) ( + ) J ab a φ ( + )( ( + ) ( ))) + λ b ( ( + ) ( )) = (4) (5)

3 Feng Qao, Zhzhen and Jangn Wang./Jornal of Engneerng Scence and echnolog Reew 9 (4) (6) - 9 Usng he opmal condon J ( (), ab, ) / () = elds he followng: a φ() a () = ( ) + ( ( (+ ) ()) + aφ() a ( ( ) ( ))) bδ( + ) + aφ() = Remar: he noel conrol creron fncon (5) dffers from he general fncon n [5]. hs fncon conans no onl he conrol nps n a sldng me wndow b also he op error n an sldng me wndow before he crren samplng nsan o achee a hghl accrae conrol. 3.3 PPD esmaon algorhm e ˆ() φ denoes he esmaon of he parameer φ () as descrbed n [5]. he PPD esmaon creron fncon for ssem () s defned as follows: J( ˆ φ()) = [ () ( ) ˆ φ() Δ( )] ˆ ˆ + µφ [ () φ( )] where µ > s he penal facor of he changes n he parameer esmaon. Usng he opmal condon ( ˆ()) / ˆ() J φ φ = elds he followng esmaon algorhms: ˆ ˆ ηδ( ) φ() = φ( ) + [ () µ +Δ ( ) ( ) ˆ φ( ) Δ( )] ˆ φ() = ˆ φ(), f ˆ φ() ε or Δ( ) ε or sgn( ˆ φ()) sgn( ˆ φ()) (6) (7) (8) (9) where < η < s he sep-sze consan seres added n eqaon (8) o generalze he fncon, ε s a small pose consan and ˆ() φ s he nal esmaed ale of ˆ() φ. Eqaon (9) s he rese mechansm ha confrms he condon of Δ() and he racng abl of eqaon (8). he conrol law algorhm (6), he parameer esmaon algorhms (8) and he rese mechansm (9) eld he followng hgher-order adape conrol scheme: ˆ ˆ ηδ( ) φ() = φ( ) + [ () µ +Δ ( ) ( ) ˆ φ( ) Δ( )] ˆ φ() = ˆ φ(), f ˆ φ() ε or Δ( ) ε or sgn( ˆ φ()) sgn( ˆ φ()) a φ() a () = ( ) + ( ( (+ ) ()) + aφ() a ( ( ) ( ))) bδ( + ) + aφ() = () () () Fgre shows he ssem srcre bloc dagram of he proposed conrol scheme. A model-free conroller s desgned sng onl he I/O nformaon of he conrolled plan o eld a praccal op. hs nformaon, along wh he conroller op, s sed b an adape mechansm o esmae drecl he parameer φ () n real me and o force asmpocall he error o zero. When he op racng characersc s nflenced b parameer araons, non-modeled dnamcs or exernal dsrbances, he esmaor correcs he adsable parameer φ () o preen an dfferences n racng. (+ ) Model-free conroller Δ() Conrolled plan () (+ ) Dfferenaor Z Δ( ) φ() Esmaor Z () Fg.. Ssem srcre bloc dagram of he proposed approach 3.4 Conergence and sabl analss Assmpon 4: he sgn of parameer φ () remans consan n an and Δ(), ha s, φ() > ε > or φ() < ε. Onl φ() > ε > s consdered. 3

4 Feng Qao, Zhzhen and Jangn Wang./Jornal of Engneerng Scence and echnolog Reew 9 (4) (6) - 9 emma [9]: e a a a a A =. If M M M M M a <, hen s (A) <, where s (A) s he specral rads of A. heorem : Followng assmpons o 4, when (+ ) = () = cons and he approprae λ s seleced, he HMFAC algorhms () o () ha are appled o ssem () garanee he followng: () lm (+ ) = and () { ()} and { ()} are bonded seqences. he proof s gen n he followng secons Conergence analss Δ φ() = ˆ φ() φ() denoes he esmaon error of PPD. Sbracng φ () n eqaon () elds he followng: ηδ( ) Δ φ() = [ ][ Δφ( ) + φ( )] + µ +Δ( ) ηδ( ) µ +Δ( ) Δ() φ() ηδ( ) = [ ] Δφ( ) + φ( ) φ() µ +Δ( ) (3) e (+ ) = (+ ) (+ ) = (+ ) () φ() Δ() = e() φ() Δ() (7) where Δ () can be obaned from conrol law () as follows: a ˆ() φ Δ () = ( ae () + ae ( + )) + a ˆ() φ (8) b ( ) Δ + + a ˆ() φ = e b b b 3 ˆ ˆ ˆ + a φ() + a φ() + a φ() A() =, M M M M M [ ] Δ U() = Δ(), Δ( ),, Δ( ) +, a ˆ() φ g() = ( ae () + ae ( + )) and φ + a ˆ() [ ],,, C = R. Eqaon (8) can be rewren as follows: Δ U() = A() ΔU( ) + Cg() (9) If φ () and ˆ() φ are bonded, hen λ >. herefore, he followng neqal holds when b.5: ang he absole ale of eqaon (3) elds he followng: ηδ( ) Δ φ() = Δφ( ) + φ( ) φ() µ +Δ( ) (4) b = ˆ ˆ b + a φ() + a φ() ( b) Δ = M = < + a ˆ() φ () η µ Δ ( ) / ( +Δ ( ) ) n eqaon (4) ncreases monoonosl b Δ( ) wh a mnmm ale of ηε /( µ + ε ). herefore, when < <, µ > and φ() b, we oban he followng: η From eqaon () and he emma, here exss ε > sch ha A() s( A()) + ε M + = d < () ε Δ ηδ( ) ηε Δ = d < and (5) µ +Δ( ) µ + ε Δφ() d Δφ( ) + b d Δφ( ) + bd + b d Δ φ() + b( d + d + + ) (6) 3 d φ() b d = d Δ + Eqaon (6) mples he bondedness of herefore, ˆ() φ s bonded wh he bonded φ (). he ssem racng error can be defned as follows: Δ φ(). where A () s he conssen marx norm of A (). Usng Δ U () =, he norm on boh sdes of eqaon (9) elds he followng: Δ U() = A() ΔU( ) + g() < d ΔU( ) + g() < d ΔU( ) + d g( ) + g() < < d g( + ) () Sbsng eqaon (9) no eqaon (7) elds he followng: 4

5 Feng Qao, Zhzhen and Jangn Wang./Jornal of Engneerng Scence and echnolog Reew 9 (4) (6) - 9 e(+ ) = e() φ() C ΔU() e B() = = e() φ()c ( A() ΔU( ) + Cg()) a φ() ˆ φ() = e() ( a e() + + a ˆ() φ a e( + )) φ()c A() ΔU( ) ˆ aφ() ˆ φ()( a + a ) aφ() ˆ φ() a aφ() φ() a 3 a ˆ φ a ˆ φ a ˆ φ + () + () + () M M M M M E(+ ) = e( ) e() e( ) + +. Eqaon (3) can be rewren as follows: (3) and E(+ ) = B() E() φ() C A() ΔU( ) (4) b If λ = mn, hen λ > λ mn. herefore, he followng 4b neqales hold when a+ a.5: aφ() ˆ φ() aφ() ˆ φ() a φ() a ˆ φ() + ˆ b b < = λ b mn ˆ aφ() φ() aφ() ˆ φ() ( a + a) + a ˆ ˆ + aφ() 3 + aφ() aφ() ˆ φ() = + ( ( a + a)) + a ˆ() φ b Δ < + ( ( a+ a)) = M λmnb (5) (6) From eqaon (6) and he emma, here exss ε > sch ha B() s( B()) + ε M + = d < (7) ε Δ 3 where B () s he conssen marx norm of B (). he norm on boh sdes of (4) elds he followng: E(+ ) B() E() + φ() A() ΔU( ) < d E() + φ() d ΔU( ) < < d E() + d ( d φ( ) ΔU( ) ) (8) e 3 3 h(+ ) = d E() + d ( d φ( ) ΔU( ) ). herefore, h(+ ) = d E() + d ( d φ( ) ΔU( ) ) = dh(+ ) + dφ(+ ) ΔU( ) 3 < dh(+ ) + dφ(+ )( d ΔU( ) + g()) 3 < dh(+ ) + dφ(+ )( d ΔU( ) + 3 C () C E B () E () ) φ() E() < dh 3 (+ ) + dφ (+ )( d ΔU( ) + ) φ() h() < dh 3 (+ ) + dφ (+ )( d ΔU( ) + ) φ() d φ(+ ) < + + ( d3 ) h( ) d3φ () (9) If < φ() b, a+ a.5 and b.5, hen λ > λ = b /4b. herefore, he followng neqal holds mn when = = : dφ (+ ) d3+ d3φ () M φ(+ ) = M + + ε M φ () λ ( b ) ( ) ( ( ˆ φ + b a+ a)) aφ () b( ( a+ a)) < ε φ() + ( ) λ φ + < ε 4 a ˆ + () φ()( b λ) φ b φ(+ ) 4b Δ < + ε = d4< 4 ab ( b b ) φ() 4b In hs case, lm h(+ ) < lm d h(+ ) < < lm d h() = lm dd E() = (3) (3) Eqaons (8) and (3) aldae he conclson () of heorem Sabl analss Gen ha () = cons, he conergence of e () mples he bondedness of (). Sbec o conrol np (), 5

6 Feng Qao, Zhzhen and Jangn Wang./Jornal of Engneerng Scence and echnolog Reew 9 (4) (6) - 9 () () ( ) + ( ) () ( ) + ( ) ( ) + ( ) Δ () + Δ( ) + + Δ () + Δ() Δ () < d g( ) = E () < g () < d d φ( ) < ( d )mn φ( ),, < ( d )mn φ( ),, 4 4 E () h () h() < d ( d )( d )mn φ( ),, whch mples he bondedness of conrol np aldaes conclson () of heorem. 4. Resl analss and dscsson (3) () and he PMSM smlaon resls llsrae he asmpoc conergence and racng performance of he proposed hgher-order adape conrol approach. 4. Daa generaor of a praccal PMSM ssem A praccal PMSM sered as an I/O daa generaor o mplemen he proposed approach. No explc model and srcral nformaon of he PMSM were nclded n he conroller desgn. he nonlnear model of PMSM s descrbed as follows []:!θ m = ω m mr!ω m = e frcon rpple where (33) w m and θ m denoe he mechancal anglar eloc and mechancal angle, respecel. e,, frcon and rpple denoe he elecromagnec orqe, load orqe, frcon orqe and rpple orqe, respecel. m denoes he slde wegh and load, and r denoes he oer dameer of he roor. he assmed frcon and rpple orqe were modelled as follows: = + e + rpple = Fsn( ωθ m) δ ( ωm/ ωmd ) frcon ( c ( s c) ωm)sgn( ωm) (34) where c s he mnmm colomb frcon orqe, s s he sac frcon orqe, s he scos frcon orqe, ω md s he desred anglar eloc, ω s he anglar eloc of he rpple orqe, F s he swng of he rpple orqe and δ s an addonal emprcal parameer. Usng a praccal PMSM ssem (whch parameers are lsed n able ) and dscrezng eqaon (33) eld he followng: (+ ) = () + z() z(+ ) = z() + ( () 8 (.6 +.6e z())sgn(z()).6sn(9 ())) (z()/z d ()) (35) where () and z () are he ssem ops denong θ m and w m, respecel, and () s he ssem conrol np e. he op desred raecor n he smlaons was se as follows:, < z (+ ) = 6, < 3 (36) 45, 3 able. PMSM ssem parameers Raed orqe Parameers Smbols Vales Uns N 4 Nm Raed eloc n 6 rpm Slde wegh m 45 g Oer dameer of roor r 6.9 mm Mnmm colomb frcon orqe Sac frcon orqe Vscos frcon orqe c.6 Nm s 3. Nm.6 Nm Addonal parameer δ Swng of he rpple orqe F.6 Nm Anglar eloc of he rpple orqe ω 9 rad / s 4. Smlaon analss Based on algorhms () o () and dscrezaon model (35), a smlaon was performed nder he followng condons. 4.. Inflence of wegh facor λ he frs order of he conrol law was emploed for smplc. Fgre shows he resls, whls able lss he parameers. able. Smlaon parameers λ Ssem nal ales Conroller parameers λ =. or λ = or λ = () =, () =, () =, Δ () =, ˆ() φ = η =.6, µ =, ε =, = =, a = b = (,,, ) 6

7 Feng Qao, Zhzhen and Jangn Wang./Jornal of Engneerng Scence and echnolog Reew 9 (4) (6) - 9 Veloc racng Performance(rad/s) Psedo Paral Deraes () () λ =. () λ = () λ = me(s) λ =. λ = λ = me(s) Fg.. Veloc responses of HMFAC wh dfferen λ ales mes he ales of wegh facor λ srongl nflenced he ssem dnamc properes. he eloc oershoo decreased wh ncreasng λ, whch ndcaed an mproed relae sabl and a redced rapd. Sabl and rapd ms be balanced when selecng he ale of λ n praccal applcaons. Fgre llsraes PPD as a slow me-arng bonded parameer relang o he ssem acon pon or ssem dnamcs. 4.. Inflence of he np and op orders and Fgre 3 shows ha explong addonal hsorcal nformaon can enhance he accrac of he adape conrol. able 3 lss he parameers. he smlaon resls n Fgre 3 show ha he ssem response s hghl precse, has a small oershoo, and s hghl sable when he nrodcon of addonal hsorcal np and op daa ncreases he amon of orders. Howeer, sng excesse hsorcal nformaon wll generae oscllaons a he maon nsan of he desred op. able 3. Smlaon parameers Orders Ssem nal ales Conroller parameers () =, () =, η =.6, µ =, = = () =, Δ () =, ε =, λ =, ˆ() φ = a = b = (,,, ) = = 3 = = 5 () = () = = (4) =, () = () = (3) =, Δ () =Δ () =Δ (3) =, ˆ φ() = ˆ φ() = ˆ φ(3) = () = () = = (6) =, () = () = = (5) =, Δ () =Δ () = =Δ (5) = ˆ φ() = ˆ φ() = = ˆ φ(5) = η =.6, µ =, ε λ =, = a = (.6,.,.,,,) b = (.6,.,.,,,) η =.6, µ =, ε λ =, =, a = (.4,.3,.,.,.,,,) b = (.4,.3,.,.,.,,,) Veloc racng Performance(rad/s) Veloc Error(rad/s) () () = () =3 () = me(s) = =3 = me(s) Fg. 3. Veloc responses wh dfferen and ales 7

8 Feng Qao, Zhzhen and Jangn Wang./Jornal of Engneerng Scence and echnolog Reew 9 (4) (6) Comparson wh radonal PID A second-order conrol law was sed o compare he proposed conrol algorhm wh he radonal PID algorhm. able 4 lss he parameers of hs law. he PID parameers were fne-ned off lne o balance sabl and rapd. Fgre 4 llsraes he speror of he proposed mehod. able 4. Smlaon parameers Conrol scheme Ssem nal ales and parameers 5 Veloc racng Performance(rad/s) Veloc Error(rad/s) HMFAC () =, () = (3) =, () = () =, Δ () =Δ () =, ˆ φ() = ˆ φ() =, η =.6, µ =, ε =, λ =, = =, a = b = (.6,.4,,,) PID K p =., =.5, d = () () HMFAC () PID me(s) HMFAC PID me(s) Fg. 4. Comparson beween HMFAC and PID Smlaons aboe ndcae he followng: () he nonlnear PMSM ssem demonsraes sasfacor adapabl and sabl nder he proposed conrol scheme. () he sabl and rapd of he closed loop PMSM ssem can be balanced b selecng he approprae wegh facors and orders. Hgher ales of λ, and ndcae hgher sabl for he conrolled plan, whls lower ales ndcae faorable rapd. (3) PPD s a slow me-arng bonded parameer ha relaes o he ssem acon pon, he conrol nps or he dnamcs of he ssem. hs parameer can reflec all possble complex behaors of a nonlnear ssem o a ceran exen. 5. Conclsons Usng he dnamc lnearzaon echnqe, a new hgher-order model-free adape conrol approach was proposed o promoe he se of hsorcal np and op nformaon for he PMSM conrol ssem. he proposed conroller effcenl conrolled he eloc and acheed zero-speed racng. he order ncreased along wh accrac, especall when he desred op maon was reached. he followng conclsons were obaned: () Faorable asmpoc conergence and mproed racng performance cold be acheed hrogh proper parameer coordnaon. he desgn dd no se an explc model or he srcral nformaon of he plan, whch wold hae smplfed he conroller desgn as demonsraed n he smlaon. () he wegh facor n he conroller srongl nflenced he dnamc properes. A hgher wegh wold lower he eloc oershoo and negael affec he rapd of he conrolled ssem. Sabl and rapd ms be balanced when mplemenng he proposed approach accordng o dfferen conrol arges. (3) he proposed approach demonsraed hgher precson, smaller oershoo, beer sabl and srong fal olerance along wh ncreasng orders. Howeer, oscllaons were obsered a he maon nsan of he desred op when he amon of orders exceeded a ceran hreshold. (4) he proposed mehod onl had a scalar parameer PPD and demonsraed smlar or beer performance, noled lesser calclaon effors and cold be mplemened mch easer han he radonal PID. he proposed approach can mee he demands of man nonlnear moor ssems ha are dffcl o model and conrol. Howeer, hs paper dd no consder he accrae measremen approaches of he I/O daa, hereb presenng an opporn for fre research. References. ang R Y, Modern Permanen Magne Machnes-heor and desgn. Beng: Chna Mechancal Indsr Press, Chna, 5.. anda I D, ozano R, M'Saad M, Karm A, Adape Conrol: Algorhms, Analss and Applcaons-nd edon. Berln: Sprnger Scence & Bsness Meda, German,. 8

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