Performance comparisons of model-free control strategies for hybrid magnetic levitation system

Transcription

1 Performnce comprisons of model-free control strtegies for hyrid mgnetic levittion system.-j. Wi nd J.-D. Lee Astrct: The study minly focuses on the development of three model-free control strtegies including simple proportionl-integrl-differentil (PID) scheme, fuzzy-neurl-networ (FNN) control nd n dptive control for the ing of hyrid mgnetic levittion (mglev) system. In generl, the lumped-prmeters dynmic model of hyrid mglev system cn e derived from the energy lnce. In prctice, the mthemticl model cn not e estlished precisely ecuse this hyrid mglev system is inherently unstle in the levitted direction, nd the reltionships etween current nd electromgnetic force re highly nonliner. To cope with the unville dynmics, model-free control design is used to hndle the system ehviour. In this study the eperimentl results of PID, FNN nd dptive control schemes for the hyrid mglev system re reported. As cn e seen from performnce comprisons, the dptive control system yields fvorle control performnce superior to tht of PID nd FNN control systems. Moreover, it not only hs lerning ility similr to tht of FNN control ut lso the simple control structure of PID control. 1 Introduction In recent yers, mgnetic levittion (mglev) techniques hve een respected for eliminting friction due to mechnicl contct, decresing mintining cost, nd chieving high-precision ing. They re therefore widely used in vrious fields, such s high-speed trins [1 5], mgnetic erings [6, 7], virtion isoltion systems [8], wind tunnel levittion [9] nd photolithogrphy steppers [10]. In generl, mglev techniques cn e clssified into two ctegories: electrodynmic suspension (EDS) nd electromgnetic suspension (EMS). EDS systems re commonly nown s repulsive levittion, nd the corresponding levittion sources re from superconducting mgnets [11] or permnent mgnets [12]. However, the repulsive mgnetic poles of superconducting mgnets cnnot e ctivted t low speed so tht they re only suitle for long-distnce nd high-speed trin systems. Bsiclly the mgnetic levittion force of EDS is prtilly stle nd llows lrge clernce. Nevertheless, the productive process of mgnetic mterils is more comple nd epensive. On the other hnd, EMS systems re commonly nown s ttrctive levittion, nd the mgnetic levittion force is inherently unstle so tht the control prolem ecomes more difficult. Generlly speing the mnufcturing process nd cost of EMS re lower thn tht of EDS, ut etr electric power is required to mintin levittion height. To merge the merits of these two inds of levittion systems, in this study hyrid mglev system dopted is comined with n electromgnet nd permnent mgnet. The mgnetic force generted y the dditionl permnent r IEE, 2005 IEE Proceedings online no doi: /ip-ep: Pper first received 19th My nd in finl revised form 28th June 2005 The uthors re with Deprtment of Electricl Engineering, Yun Ze University, Chung Li 32026, Tiwn,.O.C. E-mil: rjwi@sturn.yzu.edu.tw mgnet is used to llevite the power consumption for levittion. Becuse the EMS system hs unstle nd nonliner ehviour, it is difficult to uild precise dynmic model. Some reserch hs derived vrious mthemticl models for mny inds of mglev systems in numericl simultion [13, 14], ut there still eist unpredictle uncertinties in prcticl pplictions. In generl, linerised control strtegies sed on Tylor-series epnsion of the ctul nonliner dynmic model nd force distriution t nominl operting points re often employed. Nevertheless, the trcing performnce of the linerised control strtegies [15 18] deteriorte rpidly with incresing devition from nominl operting points. Mny pproches introduced to solve this prolem for ensuring consistent performnces independent of operting points hve een reported in previous literture. Bcstepping methods were reported in [12, 19] due to the systemtic design procedure. Hung et l. [12] ddressed n dptive cstepping controller to chieve desired stiffness for repulsive mglev suspension system. Queiroz nd Dwson [19] utilised nonliner model of n ctive mgnetic ering system for developing nonliner cstepping controller. Unfortuntely some constrining conditions should e stisfied for precision ing. Moreover, the pproch of gin scheduling [20, 21] cn linerise the nonliner reltionships of the mgnetic suspension t vrious operting points with suitle controller designed for ech of these operting points. To chieve etter control performnce over the entire opertionl rnge, it needs to sudivide the operting rnge into pproprite intervls. In this wy fvourle control gins collected in the looup tle will occupy lrge memory to ring out the hevy computtion urden. In ddition, Sinh nd Pechev [22] presented n dptive controller to compenste for pylod vritions nd eternl force disturnce using the criterion of stle mimum descent.overll,the detiled or prtil mthemticl models of complicted modelling processes re usully required to design suitle control lw for 1556 IEE Proc.-Electr. Power Appl., Vol. 152, No. 6, Novemer 2005

2 chieving ing demnd. The im of this study is to introduce model-free control strtegies for hyrid mglev system nd to compre their superiority or defect vi eperimentl results. Conventionl proportionl-integrl-derivtive (PID) controllers hve een widely used in industry due to their simple control structure, ese of design nd inepensive cost. However, this model-free PID-type controller cnnot provide perfect control performnce if the controlled plnt is highly nonliner nd uncertin. On the other hnd, intelligent control techniques (fuzzy control or neurl networ control) hve een dopted in the control field for their powerful lerning ility nd unnecessry prior nowledge of the controlled plnt in the design process [23 28]. Lepetic et l. [25] introduced predictive functionl controller sed on Tgi Sugeno fuzzy model for mgnetic suspension system. Hong nd Lngri [26] represented nonliner mgnetic ering system y Tgi-Sugeno-Kng fuzzy model, where nonliner glol model is pproimted y set of liner locl models. In the ppliction of neurl networs, Cole et l. [27] utilised neurl networ to identify fults ssocited with the system trnsducer mesurements so tht the output from the neurl networ cn e used s the decision tool for reconfigurtion control. Jeng nd Lee [28] proposed Cheyshev-polynomil-sed unified-model (CPBUM) neurl networ with fster lerning speed thn conventionl feedforwrd/recurrent neurl networs for the control of mgnetic ering system. In recent yers the concept of incorporting fuzzy logic into neurl networ hs grown into populr reserch topic [29 31]. Unfortuntely the stility of these control strtegies cnnot e gurnteed, or their control structures re more comple thn tht of the conventionl PID controller. To simplify the control frmewor nd ensure system stility some literture is mentioned [4, 32]. Kloust et l. [4] presented nonliner roust control design for the levittion nd propulsion of mglev system, where recursive controller ws designed vi the nonliner stte trnsformtion nd Lypunov direct method to gurntee glol stility for the nonliner mglev system. Wi [32] developed roust control system sed on hypotheticl dynmic model to chieve high-precision control for liner piezoelectric cermic motor. Due to inherent instility nd high nonlinerity ssocited with the electromechnicl dynmics in the hyrid mglev system, the control prolem is usully quite chllenging to control engineers, especilly in model-free control design. In this study, three model-free control strtegies including PID, FNN nd dptive control systems re implemented for the levittion ing of hyrid mglev system, nd the corresponding eperimentl results re provided to compre individul diversities. 2 Hyrid mglev system The configurtion of hyrid mglev system is depicted in Fig. 1, which consists of hyrid electromgnet, ferrous plte, lod crrier nd gp sensor. Among these, the hyrid electromgnet is composed of permnent mgnet nd n electromgnet. It forms two flu-loops in the E-type hyrid electromgnet, nd the flu psses through permnent mgnet, ferrous plte, n ir gp nd core in ech loop. The mgnetic equivlent circuit cn e represented s Fig. 1. The mgnetomotive force (MMF) of this hyrid electromgnet is the summtion of the permnent mgnet MMF F P nd the electromgnet MMF U (t ) power mplifier permnent mgnet Fe P c Fig. 1 Hyrid mglev system Configurtion Equivlent circuit Φ ferrous plte F(,i ) electromgnet lod crrier N m i,wheren m is the coil turns nd i is the. Moreover, the totl reluctnce of the mgnetic pth is 1 ¼ 1 1 þ ð1þ P þ Fe þ þ c P þ Fe þ þ c where P, Fe, nd c re the reluctnces of the permnent mgnet, ferrous plte, ir gp nd core in the mgnetic pth, respectively. In ddition, the flu F produced ginst the mgnetic reluctnce y this hyrid electromgnetic MMF cn e denoted s F ¼ F P þ N m i ð2þ The energy in this mgnetic field is W f ¼ 1 2 L ti 2 ¼ 1 2 N mðf P þ N m iþ ip gp sensor ð3þ where P ¼ 1/ is the permence of the mgnetic pth; L t is the inductnce of the hyrid electromgnet nd is given y neglecting mgnetic sturtion s L t ¼ l i ¼ N mf ¼ N m F P þ N m i ð4þ i i in which l mens the flu linge. Assume tht there is no loss in energy trnsmission, the power produced y the mgnetic field cn e represented vi the principle of the conservtion of energy s dw f ¼ i dl d F ð5þ dt dt dt where F is the produced mechnicl force, nd is the irgp length. Multiply dt on oth sides of (5), then dw f ¼ idl Fd ð6þ P F P N m i c Fe Φ mg IEE Proc.-Electr. Power Appl., Vol. 152, No. 6, Novemer

3 Since the mgnetic energy is function of l nd, one cn otin dw f ðl; dl d ð7þ To compre (6) with (7), the mechnicl force F ð; iþ cn e epressed vi (3) s F ð; f ðl; ¼ 1 2 N mðf P þ N G f i ð8þ where the term G f is relted to the totl mgnetomotive force, coil turns nd the permence in the mgnetic pth. According to Newton s lw, the dynmic ehviour of the hyrid mglev system is governed y the following eqution: ðtþ ¼ G f m i þ g þ f d m ¼ G f G i m U þ g þ f d m Gð; tþuðtþþmð; tþ ð9þ where m is the mss of totl suspension oject, g is the ccelertion of grvity, f d is the eternl disturnce force, G i represents the trnsfer function of power mplifier, nd U is the control effort. Moreover, Gð; tþ ¼G f G i =m epresses the control gin, nd Mð; tþ ¼g þ f d =m. Due to the nonliner nd time-vrying chrcteristics of the hyrid mglev system, ccurte model dynmics G(, t)nd M(, t) re ssumed to e unnown in this study. Without loss of generlity it is ssumed tht G(, t) is finite nd ounded wy from zero for ll. 3 Control systems design 3.1 PID control system In industril ppliction the PID-type control is usully used due to its simple scheme. The PID control system in this study is depicted in Fig. 2, where s is the Lplce opertor nd the is defined s e ¼ m ð10þ hyrid mglev system in which m represents the reference ir-gp length. The PID control lw cn e represented s Z de U ¼ U P þ U I þ U D ¼ K P e þ K I e þ K D ð11þ dt where U P is proportionl controller; U I is n integrl controller; U D is differentil controller; K P, K I nd K D re the corresponding control gins. Selection of the vlues for the gins in the PID control system hs significnt effect on the control performnce. In generl they re determined ccording to desirle system responses, e.g. rise time, settling time, etc. With proportionl control, corrective force is proportionl to the for the hyrid mglev system, nd the coefficient K P is designed ccording to the mount of initil. Moreover, the integrl controller U I cn llevite the stedy-stte error due to the lod force, nd the gin K I is selected sed on the mount of stedy-stte error. In ddition, the differentil controller U D is good for the fster system response nd the reduction of the tendency to overshoot, nd the prmeter K D is chosen s smll s possile to prevent enlrging the noise effect. 3.2 FNN control system A FNN control system is depicted in Fig. 3, where fourlyer networ structure with the input (i lyer), memership (j lyer), rule ( lyer) nd output (o lyer) lyers is dopted [30, 31]. The memership lyer cts s the memership functions. Moreover, ll the nodes in the rule lyer form fuzzy rule se. The signl propgtion nd the sic function in ech lyer of the FNN re introduced in the following prgrph. For every node i in the input lyer trnsmits the input vriles i ði ¼ 1;...; nþ to the net lyer directly, nd n is the totl numer of the input nodes. Moreover, ech node in the memership lyer performs memership function. In this study the memership lyer represents the input vlues with the following Gussin memership functions: net j ð i Þ¼ ð i m j i Þ2 ðs j ; i Þ2 m j i ðnet jð i ÞÞ ¼ epðnet j ð i ÞÞ ð12þ where m j i nd s j i ði ¼ 1;...; n; j ¼ 1;...; n pi Þ re, respectively, the men nd the stndrd devition of the Gussin hyrid mglev system PID control system FNN control system U I K I s U U e P Σ K P + U D K D s reference model m U = y o y o Σ output lyer o w o φ rule lyer w ji j µ i memership lyer j i input lyer i e e s d dt e + m reference model Fig. 2 Hyrid mglev system with simple PID control Fig. 3 Bloc digrm of FNN controlled hyrid mglev system 1558 IEE Proc.-Electr. Power Appl., Vol. 152, No. 6, Novemer 2005

4 function in the jth term of the ith input vrile i to the node of this lyer, nd n pi is the totl numer of the linguistic vriles with respect to the input nodes. In ddition, ech node in the rule lyer is denoted y P, which multiplies the input signls nd outputs the result of the product. The output of this lyer is given s f ¼ Yn w ji mj i ðnet jð i ÞÞ ð13þ i¼1 where f ð ¼ 1;...; n y Þ represents the th output of the rule lyer; w ji, the weights etween the memership lyer nd the rule lyer, re ssumed to e unity; n y is the totl numer of rules. Furthermore, the node o in the output lyer is lelled with S; ech node y o ðo ¼ 1;...; n o Þ computes the overll output s the summtion of ll input signls, nd n o is the totl numer of output nodes y o ¼ Xn y w o f ð14þ ¼1 where the connecting weight w o is the output ction strength of the oth output ssocited with the th rule. In this study the inputs of the FNN control system re the ( 1 ¼ e) nd its derivtive ( 2 ¼ e s ), nd the single output is the control effort for the hyrid mglev system, i.e. U ¼ y o. The FNN controller is similr to nonliner PD controller s it is sed on e nd e s. To descrie the online lerning lgorithm of this FNN control system vi supervised grdient decent method, first the energy function E is defined s E ¼ð m Þ 2 =2 ¼ e 2 =2 ð15þ In the output lyer the error term to e propgted is given y d o ¼ o o nd the weight is updted y the mount Dw o ¼ o ¼ @y o ¼ Z w d o f ð17þ where Z w is the lerning-rte prmeter of the connecting weights. The weights of the output lyer re updted ccording to the following eqution: w o ðn þ 1Þ ¼wo ðnþþdwo ð18þ where N denotes the numer of itertions. Since the weights in the rule lyer re unified, only the error term to e clculted nd propgted. d ¼ d o w o In the memership lyer, the error term is computed s follows: d j ¼ X d ð20þ j The updte lws of m j i nd s j i cn e denoted s where Z m nd Z s re the lerning-rte prmeters of the men nd the stndrd devition of the Gussin function. The ect clcultion of the jcoin of the ctul o in (16), cnnot e determined due to the unnown system dynmics. Similr to [30, 31], the delt dpttion lw d o De+e s is used for pproimting (16) in this study. Moreover, vried lerning rtes in [31], whichre derived sed on the nlyses of discrete-type Lypunov function, re dopted to gurntee convergence of the. 3.3 Adptive control system To control the ir-gp length of the hyrid mglev system more effectively, n dptive control system shown in Fig. 4 is implemented [32 34], nd the stte vriles re defined s follows: X 1 ¼ ð23þ _X 1 ¼ v ¼ X 2 ð24þ where v represents the derivtive of. ewriting (9) the hyrid mglev system cn e represented in the following stte spce form: " # _X 1 ¼ 0 1 X1 0 0 þ U þ _X X 2 Gð; tþ Mð; tþ ð25þ The eqution cn e epressed s _X P ¼ AX P þ BU D ¼ AX P þðb þ DBÞU ðd þ DDÞ ¼ AX P þ BU D þ L ð26þ where X P ¼½X 1 X 2 Š T ; A ¼ 0 1 ; B ¼½0 Gð; tþš T ; 0 0 D ¼½0 Mð; tþš T ; B nd D re the nominl prmetric mtries of B nd D; DB nd DD denote the uncertinties roust control system d dt U Σ v U s v U d hyrid mglev system stte feedc controller dpttion lw (38) uncertinty controller E C E C control error vector e + m j i ðn þ 1Þ ¼mj i ðnþþdmj i with Dm j i ¼ 2ð i m j i m ¼ Z m d Þ j ðs j i j i ð21þ dpttion lw (39) K E C s j i ðn þ 1Þ ¼sj i ðnþþdsj i with Ds j i ¼ 2ð i m j i s ¼ Z s d Þ2 j ðs j i j i ð22þ Fig. 4 U f feedforwrd controller reference model Adptive control system for hyrid mglev system m IEE Proc.-Electr. Power Appl., Vol. 152, No. 6, Novemer

5 introduced y prmeter vrition nd eternl disturnce; L ¼ DBU DD is the lumped uncertinty. In the dptive control system design the desired ehviour of the hyrid mglev system is epressed through the use of reference model driven y reference input. Typiclly liner model is used. A reference model of the following stte vrile form is selected: _X M ¼ 0 1 A m1 A m2 A M X M þ B M X M þ 0 B m1 ð27þ where X M ¼½ m v m Š T represents the reference ir-gp length nd its derivtive; is reference input; A M nd B M re given constnt mtrices; A M o0 is ssumed to e stle mtri. The control prolem is to find control lw so tht the stte X P cn trc the reference trjectory X M in the presence of the uncertinties. Let the control error vector e E C ¼ X M X P ¼½ m v m v Š T ¼½e e s Š T ð28þ To me the control error vector tend to zero with time, the dptive control lw U is ssumed to te the following form: U ¼ U s þ U f þ U d ¼ HX P þ K þ ð29þ where U s ¼ HX P is stte feedc controller; U f ¼ K is feedforwrd controller; U d ¼ is n uncertinty controller. The control gins H, K nd re djusted ccording to dynmic dpttion lws introduced lter. After some strightforwrd mnipultion the control error eqution governing the closed-loop system cn e otined from (25) through (29) s follows: _E C ¼ A M E C þða M A BHÞX P þðb M BKÞ þðd B LÞ ð30þ If the precise model dynmics nd the uncertinties in prcticl pplictions re ville, there eist idel control gins H *, K * nd * in the following equtions such tht the control error vector tend to zero with time: H ¼ B þ ða M AÞ ð31þ K ¼ B þ B M ð32þ ¼ B þ ðd LÞ ð33þ where B þ is the left penrose pseudo inverse of B, i.e. B þ ¼ðB T BÞ 1 B T. Since the dynmic model nd the uncertinties of the controlled system my e unnown or pertured, the idel control gins shown in (31) (33) cnnot e implemented in prctice. eformulte (30), then _E C ¼ A M E C þ BðE y X P þ E þ E Þ ð34þ in which the control prmeter errors E y, E nd E re defined s E y ¼ H H ð35þ E ¼ K K ð36þ E ¼ ð37þ The idel control gins re oserved y simple dpttion lws nd re ssumed to e constnt during the oservtion. The ssumption is vlid in prcticl digitl processing of the dpttion lws ecuse the smpling periods of the dpttion lws re short enough compred with the vrition of idel control gins. Theorem 1: Consider the hyrid mglev system represented y (25); if the dptive control lw is designed s (29) in which the dpttion lws of the control gins re designed s (38) (40), then the stility of the dptive control system cn e gurnteed _H ¼ g 1 E T CBXP T ð38þ _K ¼ g 2B T E C ð39þ _ ¼ g 3B T E C where g 1, g 2 nd g 3 re positive constnts. ð40þ Proof: The proof of the theorem is similr to [32 34] nd is omitted here. From theorem 1 it follows tht the will tend to zero under the level of slowly vrying uncertinties. However, the control gins will not necessrily converge to their idel vlues in (31) (33); it is shown only tht they re ounded. Moreover, ccording to the unville system prmeters, the nominl vlue of control gin Gð; tþ in the tuning lgorithms is reorgnised s Gð; tþ sgnð Gð; tþþ in prcticl pplictions. Therefore the dpttion lws of the dptive control system shown in (38) (40) cn e reorgnised s follows: _H ¼ 1 e s X T P sgnð Gð; tþþ ð41þ _K ¼ 2 e s sgnðgð; tþþ ð42þ _ ¼ 3 e s sgnðgð; tþþ ð43þ where sgn( )is sign function; the terms g 1 Gð; tþ, g2 Gð; tþ nd g3 Gð; tþ re sored y the tuning gin, 1, 2 nd 3 individully. Consequently only the sign of Gð; tþ is required in the design procedure, nd it cn e esily otined from the physicl chrcteristic of the hyrid mglev system. 4 Eperimentl results The loc digrm of computer-sed control system for the hyrid mglev system is depicted in Fig. 5. In the hyrid mglev system, it cn e divided into two prts: A ferrous frme nd levittion tle. A hyrid electromgnet is fied on the levittion tle, nd the ttrcting levittion force is produced y the mgnetistion of the electromgnetic coil. servo control crd Fig. 5 _ tle A/D converter Pentium U control computer D/A converter memory Computer-sed control system _tle m _ tle digitl oscilloscope 1560 IEE Proc.-Electr. Power Appl., Vol. 152, No. 6, Novemer 2005

6 A servo control crd is instlled in the control computer, which includes multichnnels of D/A, A/D, PIO nd encoder interfce circuits. The moving displcement of the levittion tle _tle is fed c using gp sensor, nd the stte in (10) cn e clculted y ¼ t _tle, where t is the totl ir-gp length. In this study the vlue of t is equl to 12.5 mm. Moreover, the control systems re relised on Pentium PC vi Turo C lnguge to mnipulte the i in the electromgnetic coil y wy of voltge control U pssing through liner power mplifier, nd the smpling time is 6 ms. In ddition, the output of the reference model is designed s step in the following eperimenttion. Furthermore, the men-squre-error (MSE) vlue of the moving displcement is defined s MSE ¼ 1 T X T z¼1 ½ m tleðzþ tleðzþš 2 ð44þ where T is totl smpling instnts. According to (44) the normlised MSE vlue of the moving displcement using per-unit vlues with 1 mm se is used for emining the control performnce in this study. Some eperimentl results re provided here to demonstrte the effectiveness of the PID, FNN nd dptive control systems. In the eperimenttion the initil condition of this hyrid mglev system is loded y two pieces of iron dis with 3.7 g weight. The eperimentl results of the PID control system due to reference tle m _tle re depicted in Fig. 6. In Fig. 6 1 mm-step is set, nd the gins of the PID control system re given vi tril nd error s K P ¼ 32; K I ¼ 10; K D ¼ 0:6 ð45þ One iron disc is unloded t 6 s nd reloded t 12s nd it is ovious tht the drift of the levittion is lmost 1mm when un. Becuse the gins in (45) re selected under the condition these control gins my not eep the levittion height t 1 mm during the un durtion. The normlised MSE vlue is mm. Moreover, the gins of the PID control system for 2 mm-step re designed vi tril nd error s K P ¼ 25; K I ¼ 10; K D ¼ 0:5 ð46þ In Fig. 6 there re similr results s Fig. 6, nd the normlised MSE vlue is mm. As seen from Fig. 6 there re pprent sttic errors fter un. Though this prolem could e improved y incresing the integrl gin K I, it will result in higher inrush control effort. In conclusion, it is time-consuming nd lorious ecuse the control coefficients of the PID control system should e redesigned for vrious demnds to stisfy the desirle dynmic ehviour. For comprison the FNN control system insection 3.2is lso pplied to control the hyrid mglev system. To show the effectiveness of the FNN with smll rule set, the FNN hs two, si, nine nd one neuron t the input, memership, rule nd output lyer, respectively. It cn e regrded tht un tle un tle mm un tle 2.01mm un tle 1 Fig. 6 Eperimentl results of PID control system t lodvrition condition 1 mm-step 2 mm-step 1 Fig. 7 Eperimentl results of FNN control system t lodvrition condition 1 mm-step 2 mm-step IEE Proc.-Electr. Power Appl., Vol. 152, No. 6, Novemer

7 the ssocited fuzzy sets with Gussin function for ech input signl re divided into N (negtive), Z (zero) nd P (positive), nd the numer of rules with complete rule connection is nine. Moreover, some heuristics cn e used to roughly initilise the prmeters of the FNN for prcticl pplictions, e.g. the mens nd the stndrd devitions of the Gussin functions cn e determined ccording to the mimum vrition of e nd e s. The effect due to the inccurte selection of the initilised prmeters cn e constntly djusted y the online lerning methodology. Therefore, for simplicity, the mens of the Gussin functions re set t 1, 0, 1 for the N, Z, P neurons, respectively, nd the stndrd devitions of the Gussin functions re set t one. In ddition, to test the lerning ility of the FNN control system, ll the initil connecting weight etween the output lyer nd the rule lyer re set to zero in the eperimenttion. The responses of the tle, nd using the FNN control system due to 1 nd 2 mm-step s re depicted in Fig. 7 nd 7, where respective normlised MSE vlues re nd mm. From the eperimentl results the overshoot responses t the trnsient stte re cused y the rough initilistion of the networ prmeters. After this, the s reduce to zero quicly even under the lod vritions. Although fvourle trcing performnce cn e otined, this control scheme seems to e too comple in prcticl pplictions. In the end the eperimenttion of the dptive control system is implemented sed on the scheme shown in Fig. 4. The gins of the dptive control system re given s 1 ¼ 1000; 2 ¼ 65; 3 ¼ 65 ð47þ The selection of the positive tuning gins 1, 2 nd 3 is concerned with the trcing speed. The trcing response converges slowly with smll tuning gins, nd the trcing speed increses with lrge tuning gins. Due to the unville system dynmics, they re chosen vi tril nd error process to chieve the superior trnsient response in the eperimenttion considering the requirement of stility, the limittion of control effort nd the possile operting conditions. The tle,, nd t 1 nd 2 mm-step s re depicted in Fig. 8 nd 8, where respective normlised MSE vlues re nd mm. From the eperimentl results, good trcing responses cn e otined. With the vrition of lod during 6 12 s the tle cn e returned to the quicly. To ehiit the fleile control performnce of the dptive control system, the eperimentl results due to step- chnging from 1 to 2 mm re given in Fig. 9. In Fig. 9, there is no lod vrition. On the contrry, it unlods one iron disc t 2 nd 12 s, nd relods t 4 nd 14 s in Fig. 9. The respective normlised MSE vlues re nd mm. From the eperimentl results the s converge quicly nd the roust un tle tle mm un tle un un tle 1 Fig. 8 Eperimentl results of dptive control system t lodvrition condition 1 mm-step 2 mm-step 1 Fig. 9 Eperimentl results of dptive control system due to step chnging from 1 to 2 mm Nominl condition Lod-vrition condition 1562 IEE Proc.-Electr. Power Appl., Vol. 152, No. 6, Novemer 2005

8 Tle 1: Performnce comprisons of PID, FNN nd dptive control systems Control system PID control FNN control Adptive control Performnce 1 mm 2 mm 1 mm 2 mm 1 mm 2 mm Normlised MSE mm mm mm mm mm mm oustness poor fir good Control frmewor simple comple simple Lerning ility none online online control chrcteristics under the occurrence of different lod vritions nd step s cn e clerly oserved. Compring Figs. 8 nd 9 with Figs. 6 nd 7, it is ovious tht the dptive control system with simple frmewor yields superior control performnce thn the PID nd FNN control systems. In the whole design process no prior nowledge of the controlled plnt ws required nd the stility of the control system cn e gurnteed. It not only hs the lerning ility similr to intelligent control, ut lso its control frmewor is simple lie PID control. 5 Conclusions This study hs successfully implemented the PID, FNN nd dptive control schemes for the levitted ing of hyrid mglev system to demonstrte their individul control diversities. Performnce comprisons of the PID, FNN nd dptive control systems re summrised in Tle 1. The PID control system elongs to n event-sed liner controller. There re lrger normlised MSE vlues under the occurrence of lod vritions; therefore the control gins should e redesigned for different situtions. Moreover, the FNN control system could e designed successfully without comple mthemticl model nd possesses smller normlised MSE vlues. However, this scheme is more complicted thn the PID control system. In ddition, the dptive control system is presented to solve this prolem, nd it not only hs good trcing response ut lso mes this system more roust under different step s nd lod vritions. From these performnce comprisons the dptive control system is more suitle to the control of the hyrid mglev system thn the PID nd FNN control systems. Note tht this study just demonstrtes three specific model-free control strtegies, not ll possile control methods suggested intheliterture.the min contriutions of this ppliction-oriented study re summrised s follows. Derivtion of the dynmic model of hyrid mglev system. Development of PID, FNN nd dptive control strtegies for this hyrid mglev system. Implementtion of these model-free control schemes for the control of the hyrid mglev system considering the possile occurrence of uncertinties. Comprisons of individul control performnces to provide designers with preliminry guideline for mnipulting the hyrid mglev system efficiently. 6 Acnowledgments The uthors would lie to cnowledge the finncil support of the Ntionl Science Council of Tiwn,.O.C. through grnt NSC E nd epress their grtitude to the referees nd Associte Editor for their useful comments nd suggestions. In ddition, the uthors would lie to thn Prof. Seng-Chi Chen for his ssistnce in supporting the mglev equipment. 7 eferences 1 Nshim, H.: The superconducting mgnet for the Mglev trnsport system, IEEE Trns. Mgn., 1994, 30, (4), pp Powell, J.., nd Dny, G.T.: Mglev vehicles-rising trnsporttion dvnces of the ground, IEEE Trns. Pot., 1996, 15, (4), pp Chen, M.Y., Wng, M.J., nd Fu, L.C.: Modeling nd controller design of mglev guiding system for ppliction in precision ing, IEEE Trns. Ind. 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