Computer Aided Design of a Linear Positioning System

Loránd SZABÓ – Ioan-Adrian VIOREL – Zoltán KOVÁCS Technical University of Cluj-Napoca, Romania

Abstract: Countless precise linear positioning systems used in industrial and laboratory processes are driven by permanent magnet excited variable reluctance linear motors. Thus rotary to linear gear-boxes or belt and pulleys, needed with rotary motors for linear drives are avoided. The greatest difficulty in the design of these frequently utilized motors consists of the necessity to consider the complex toothed configuration, the iron core saturation and the permanent magnet operating point change due to air-gap reluctance modifications and to control m.m.f. The dynamic performances and the positioning capabilities of the motor can be improved by operating it under a closed-loop control. An e.m.f. sensing based control strategy was developed in order to obtain optimum behavior for the motor. Results obtained by dynamic simulation of the linear positioning system confirm the advantages of the selected motor type and of the proposed optimal control strategy. Cite as: Szabó, L. – Viorel, I.A. – Kovács, Z.: Computer Aided Design of a Linear Positioning System, Proceedings of the Power Electronics, Motion Control Conference (PEMC '96), Budapest (Hungary), vol. II., pp. 263-267, 1996.

See attached the scan of the paper

REFERENCES

1. VIOREL, I.A. – KOVACS, Z. – SZABO, L.: Sawyer Type Linear Motor Modelling, Proceedings of the International Conference on Electrical Machines (ICEM '92), Manchester (UK), pp. 697-701, 1992.

2. EBIHARA, D.: Design of a PM Type Linear Stepping Motor for Automatic Conveyer System, Proceedings of the International Conference on Electrical Machines Design and Applications, London (UK), pp. 265-269, 1985.

3. VIOREL, I.A. – BIRÓ, K. – SZABÓ L.: Transformer Transient Behavior Simulation by a Coupled Circuit-Field Model, Proceedings of the International Conference on Electrical Machines (ICEM '94), Paris (France), pp. 654-659, 1994.

4. SZABO, L. – VIOREL, I.A. – KOVACS, Z.: Computer Simulation of a Closed-Loop Linear Positioning System, Proceedings of the Power Conversion & Intelligent Motion Conference (PCIM '93), Nürnberg (Germany), vol. Intelligent Motion, pp. 142-151, 1993.

5. VEIGNAT, N. – SIMON-VERMOT, M. – KARMOUS, M.: Stepper Motors Optimization Use, Proceedings of the International Conference on Electrical Machines (ICEM '94), Paris (France), pp. 13-16, 1994.

6. JENKINS, M.K. – HOWE, D. – BIRCH, T.S.: An Improved Design Procedure for Hybrid Stepper Motors, IEEE Transactions on Magnetics, vol. 26., no. 5. (Sept. 1990), pp. 2535-2538.

7. SZABÓ, L. – VIOREL, I.A.: Variable Reluctance Permanent Magnet Linear Motor Computer Aided Design, Proceedings of the International Conference on Optimization of Electric and Electronic Equipments (OPTIM '98), Braşov (Roamnia), pp. 305-310, 1998.

8. VIOREL, I.A. – SZABÓ, L.: Permanent magnet variable reluctance linear motor control, Electromotion, vol. 1, no. 1, pp. 31-38, 1994.

worthwbile to identify this ilem again, since this may deteriorate the estimation of other parameters. A promising solution for the stator resistance effect could be setting this parameter as a constant value in the motor transfer function (equations 4 and equation 1). Then it is necessary to perform the broadband excitation test at the same temperature in wbich the stalor resistance is defined or measured otherwise errors will result in estimated rOtor inductance. Figure 6 illustrates the results of the another test while the stator resistance fixed to the 150 mO (according to the motor data sbeet).

·�t:�j o 5 10 15 20 I.,(A)

3r,--�--�--�--r--. 00 00000 o o 0

b 2

oL.(mH) 1L---�--�--�--��

o 5 10 15 20

Bgu.re 6. Results d the idectif\fd induction rootor inductances using broadband ex.citation lest: a. rotor indt.tctance (0) in comparison with no-load lest (continued line) b • eslimalM t""'lleakage (0)

It follows from figure 6-a !bat. as expected, there is a very good agreement between the identified rotor inductance from broadband excitation and the corresponding values obtained from classical no-load tesL The effect of the low level iron nonlinearity can be seen from the reSUlts. TIle identified lowest current level inductance (first measured point) is smaller than !be unsaturated inductllnce. This proves that the employed tangent hyperboliC model for magnetizing curve is not an accurate model for low current levels. Figure 6-b sltows that the rotor flux dependency on leakage inductance is negligible, verifying the assumption wbich has been made in most of the practical applications (at.. : constant).

CONCLUSION

Tbe application o f an advanced identification technique to estimate the induction motor parameters is tested. Tbe results obtained coincide with that of the traditional no-load test. Static inductance of a machine can be easily obtained from no-load tesl However, calculation of the dynamic inductance is always confronted with large errors in analytical methods because of differentiation or modeling errors.

Therefore, precise and direct identification parameter is very important and this is the of the proposed tecbnique. The use of power the setup configuration enables the test to be at actual magnetic saturation levels of the with sufficiently large signals to avoid small cycle problem. Tbis tecbnique, in contrast load test, has lhe advantages lhat the mOlor sbould not be disconnected from the load. many cases the macbine is imbedded in thaI the mechanical c' nnections can nOI removed from the motor sbafL Another the proposed tecbnique lies in its complete identification procedure takes an bour. The test, therefore. can be performed the maintenance period or at the commissioning

REFERENCES

{II Beya K .• !'inielon R.. s_ ... I .• !.at'"" P .•

Mpaoda-Mabwe B. aDd Delbaye M .• : lde:DLificalioo �"'" I"'amelen wing Broadband &ciWi. '. IEEE Energy Conversioll, 912. 1994. pp. 'l7()'280. 121 BUn' A. and Grotsl<>lkn H .. : p......,..er identification '" fed induction motor at standstill with a correlation n�, 97·102. \31 F.cher I. and Moser U. H.. : Die magoetU:ictunpkur'veR durch tin fache algebraisd\e: funktiooea. Archi'V tUt Elek1rotecbnik. Eingegngen am, 195-5. 295. {4] G.bii A...o t.alaire P.: Ro,,,, time commnt induction JlX'I{or in iodUecf vectoc cont.roUed drives. EPE9S Spain, Vol. I. pp. 1.431-1.436. 15J lEEE Standard !l5·A 1987. -SlaOdard proce<!ur<o roc syndlrOll<lW madli.. 1"'''''''''''' by .... dstill Ji:"lUCncy ...ung·. (supplement 10 ANSII!EEE. Sid. 115·1987).

.

16] K.yl>ani A. : Syncluoo_ � .. I"'a Electrical macrunes and Power Systems. 1992, No. m Kelemen A. and ........ M., 1992. "Vecta cooLroi I". Omikk Publisher, Budapes� Hungary. (S) !(hal'" F. H .• Lorenz R. D., Novotny D. W. and Tang cl n� level in fieJd oriented induction m.ad'tiue C(l OObSiderntioll d magnetic saturalion dl'tcts. IEEE Trans. 1A.23.-No. 2. 1987.pp. 276-281. 191 KI"", N.R: Parameter identification d. •• induction regard to dependencies on ;.atucation, IEEE Trans. on Ind. No. 6. 1993. pp. 1135-1140.

) Koll.u 1..1993. "Prequeocy domain system idenLlf",w ...., with MAlLAB, use(s g1Jide', The MATWORKS

Seri<s. Ill) Levi E.: Method for magnetizing curve identification controlled induct"'" madlines, ElE'. Vol. 2, No. S. SepJOc 309·314. {l2} Rull. M .. and Grotstollen H. : Identification of the _iii induc\tluO!: dan asyndu"ooous mol« at �dstiU by sq=es algootbm. Proceeding. d. EPE93 England. PI'­Ill} ScIJouk ... I. and Pin!<lon, II.. 1991. -!<i.mil systc:n\S. a �tical guideline to accurate modeling" I

I)K. 114} S<>iiman. S. A. and a.:w ...... G. S, Modeling d. ,..-s from Slandstill !requeucy � .... '" .00 • C$llmation a1Cocilhm. Electric Machines and power Syswns.

123·136. [IS} Van 0.. Boos"" A. P .. 1989. "Ph. DTh .... •• S ....

2/262

GeIll.&lgium. . (161 Vas. P .. 1m, 'Electrical madlind .00 dri""'·. 0Jif�. PubUcatioos. USA. (171 Vas P .. 1993. "Parameter �timatioo. condit.ioD di>gnmjs d. .1e<Ui<:al machi ... •• OJiJood scieocc Publio (18} W.lis 1. R • ...o _.; Deviarioo '" induction """'" O(ondAilllr"l".CY _ ....... IEEE Tr.tu. On EnersY Vol. 4. December 1989. pp. 605·613.

.

COMPUTER AIDED DESIGN OF A LINEAR POSITIONING SYSTEM

L. Szabo, 1.1. Viorel, Z. lovacs

Technical University of Cluj. Romania

� Countless precise linear positioning systems used in industrial and laboratory processes are driven by permanent magnet elcited variable reluctance linear motors. Thus rotary to linear gear-bOles or belt and pulleys, needed with rotary motors for linear drives are avoided. The greatest difficulty in the design of these frequently utilized motors consists of the neeessity to consider the complex toothed configuration, the iron core saturation and the permanent magnet operating point change due to air-gap reluctance modifications and to control l.IJ. The dynamic performances and the positioning capabilities of the lotor can be improved by operating it under a closed-loop controL An e.IL sensing based control strategy was developed in order to obtain optimum hehavior for the lotor. Results obtained by dynalie simulation of the linear positioning systel confirm the advantages of the selected lIotor type and of the proposed optimal control strategy.

� precise linear positioning system, permanent sagnet excited variahle reluctance linear motor, �omputer aided design, e.'.f. sensing, optimal control strategy.

linear positioning systems are used by ayriad and laboratory processes (industrial robot

tools, measuring systems, computer 1s tile movement have to be performed

of linear direct drives are to linear gear-boxes or belt

leys, needed with rotary motors for linear The interest in these systems has been given

of a steady increese in requirements for accuracy, while, at the same time placing

the l1axillum speed and on the constancy of such purposes the permanent magnet excited �luctance linear motor is one of the best

due to the recent availability of high energy IBagnets. It offers many advantages such as

accurate positioning, high servo stiffness, and fast settling times.

magnet etcHed variable reluctance linear a simple �onstruction Ill. The moveable

(the mover) consists of tvo electromagnets '01 coils. A perllanent magnet serves as a bias

lach electromagnet has tvo poles, and all poles sale number of teeth. The mover is suspended

fixed stator I the pla ten), a toothed ferromag­structure having the same fine teeth pitch lith

. The tangential force is produced riable reluctance principle, Le. the

of the teeth of that pole in which tbe nux was concentrated to align vith the platen ThlS way the mover changes its position function

of the current pulses that energi ze the

The first step in the computer aided design of a linear positioning eyste. is the driver motor sizing (21. This paper presents a novel computer aided design lethodo­logy of the permanent magnet excited variable reluc· tance linear motor. The design relationships were obtained frollt a combined circuit-field motor lodel presented in several previous papers Ill, !H. The model takes account of saturation throughout tbe motor (the nonlinearity of the S/R characteristics of the iron parts) and allows for variations in penanent 1l3gnet lorking point due to the variable air-gap permeance and control amperturns. The computer programs elaborated by the autbors help the pmtidng engineer to design the aotor. Some of tbe motor dimensions and material characteristics can be changed by the computer

in order to optimize the permanent magnet and the motor leight, improving this vay the

cost/performance ratio. The computer is completely under the direct control of the user, together with all needed data files on convenient.

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The second step in the computer aided linear pOSitioning system consists in establlShiDg an optimal control strategy of the permanent lIagnet excited variable reluctance linear motor in order to obtain the best perforianteS lSI. By some analytical computations the optimal commutation angle of the control coil current pulses is determined in function of the actualilover position, obtained frol the induced e . • . f. of an un· energized motor coil. This vay the tangential force ripple is reduced to a .inhum value and the expensive position sensors are avoided. Finally the authors presents some results obtained by means of computer dynuic simulation of the linear positioning system using the designed permanent magnet excited variable reluctance linear motor and the above

mentioned optimal control strategy. The obtained results confir; the validity of the control strategy and demonstrates the advantages of the selected motor type.

Tl!B 1I0TOR DBSIGII

The design of a pertaneal aagnet excited variable reluctance linear lotor is quite different than designing a classical electric motor. The cOllplex toothed configuration, the aagnetic saturation of the iron cores and the peraanent magnet operating point change due to air-gap variable reluctance and control •.•. f. arise a lot of problems. Therefore an accurate desigu lethodology conception and the developllent of computer programs based on it is a step towards the direction of cutting down drastically the Dumber of experilents. The design procedure is based on equations obtained analytically froll the coupled circuit-field lotor 1II0del. This vay the computations are accurate enough and requite short cOlputation tile. They can be easily i.pleafnted in computer prograls. The softvare developed by the authors is flexible and easy to use. Only seconds are required for the user to determine the effects aade by changing any one of all the parameters that fully influence the 1I0tor behavior. It enables the designer to optili:e sOle lotor cOllponents in order to at taiD tbe best performances possible vith a good performance to costs ratio. The user can influence the design procedure as little or as luch as he wants it, setting a few inputs and leaving the rest of design for the cOllputer. The developed design lethodology bas four lain parts, in fact the stages have to go througb the designing process: iI The required basic design data establishment. In any case the future application of the Ilotor imposes particular specifications on the basic design data. iii The selection of the utilized aaterials and the cal eulation of all the lotor dimensions. iiil The optillization of SOle motor dimensions in order to increase the final performances and to reduce the costs. ivl The tbermal and electrolagnetic examination of the designed IIOtor. In the first phase of the motor design procedure the following required design data lUSt be prescribed, depending on the needs of the application in which the aotor will be used (61: tbe laximal tangential [tractionl force developed by the lotor, the resolution of tile positioning (taking into account the possibili­ties of the selected control stratesyl, the length and width of the running track. At tbe beginning of the second stage, which is the lain part of the design procedure, the shes of the tootbed air-gap structure lust be computed. Tbe tootb pitch

(1:) is given by the ilposed positioning Tbe air-gap length (�) lOst be as siall as being lilited only by the lechanical constrains and cost of manufacturing. The next step consists iI cboosing the active netieal materials used for the lotor constrnrH.: Bxtrelely ilportant is the per.anent laquet the lost expensive and sensitive assembly of the taking into account the illposed tetlperature rise lover and the motor cost to performaDce ratio. earth aagnets are needed to leet the high thrust unit volume necessities "I. The movu armature is aade of silicon steel having high saturation level aud loy specific The platen is fabricated of soft iron. The ,orking point of the peraanent aagnet 00· demagnetization characteristic lust be determi such a vay as to euure the desired flux density in the lover and platen cores. Tbe permanent dimensions can be deterained by cOlputing its active surface and thickness:

F S -k to­� - l? BrJJpm

t =k BrJJr pm "Ha(Br-Bpm)

where Bp is the illposed flux density in the poles, respectively B" and He are the reaanent flux density and the comitive force of the selected magnet. The. two designing constants (k" and kpl have to be determined conditionally on the selected air-gap length and tooth width to tooth pitch ratio f1J. The length of the lagnet initially is taken equal to the pre-' scribed width of the platen. The pole width and th number of the pole teeth (Z) is cOllputed f rOI the resulted pole area (Spl. Tbe lover core has

. a

constant cross-section equal to the cOllputed pole area. This peraits an efficient magnetic utilization; avoiding local core saturations.

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The control coil design has to be aade in a ray to ensure the necessary cOiland aagnetic flux throughout' the poles. This directs the aagnetic flux due to the penanent magnet (011 pml in such a way as to maximize, respectively minimize the total aagnetic flux in the tva corresponding poles of one electromagnet. The·· equation relating to the control coil a.m.L can be expressed as:

whence

6 '" 2Za- 011 c Spllo(2Z+A.-1) pm

a-"'k� �

). is the equivalent air-gap permeance coefficient andkc is Carter's factor. Tbe main factor that can be improved to lake the permanent magnet excited variable reluctance linear

'" -

·.ore attractive is its cost. To achieve this an ,Iation of the lotor magnetic circuit has to be The best results in cost illprovements can be made

the permanent .agnet volule optilization. A lIyriad possibilities m to select the three magnet sizes achieve the sale aagnetic load. The ideal ugnet

can be selected in a way as to achieve lIiniaal volule and, of course, the smallest cost. An

vay to decrease the lover core volule is to the optimull width to length ratio of the

coil (kc(>il)' 'tep of the design procedure is the electro­and thermal checking of tbe just designed

a computer progra., based on the previous­mathematical motor lodel !41, the laXilal

force and the highest flux densities in motor portions can be calculated for the

ted control current. The thewl analysis in order to deteraine the te.perature over the whole cross-section. Tbe

of temperature at all points is very ilportant, specially for the permanent .3gnet and for

... the linding insulation. In a simplified fol'l the . lent aagnet excited variable reluctance linear can be considered as an assembly of the following

lIasie bodies: the Calland windings, the lover, respectively the stiltor core [71. The temperature in each body depends not only on tbe losses in the uspective body, but also on the heat generated in the surrounding areas, as well as on tbe beat flov path throoghout tbe lotor. The temperature rise in the basic constructing elements can be computed by sol vlug the

. differential equation system, that describes the heat �equilibrium in the 10tOr.

The peraanent aagnet excited variable reluctance linear IOtor can be operated in open loop or in closed loop drive lode. In the first case the supplying control sequence is executed at a given frequency, existing a peril of losing the synchronism !4l. The closed loop control systell laintai os the prescribed lotor speed lith no dependence of load variation. In this case the operating frequency is variable and depends on the IOtor capability to achieve an imposed displacement under given conditions as load and input source limits. The control systel enables significant motor efficien­ey, eliminates mechanical resonances and allows stable operation. The control syste. has to assure the imposed velocity profile and the positioning precision. The speed is depending on tbe resulting tangential force and the COntrol has to be in a certain relationship ,ith the IOyer position, acting also on the control currents. As it las already proved !81, if the cOlland currents have an ideally square shape, the tangential force

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depends aainly on the 'lover position. Therefore the control system has to assure the change of excitation through the coamand coils at a certain value of the displace.ent to assure the maximum value of the average tangential force. To achieve tbis the optilul COHuta­tion angle has to be determined. The total tangential force can be obtained by adding the tangential forces due to the four poles:

Ft=Kp E ' sincz; (5) 4( 011. )2 • ,-1. 1 +mcosa:.l

where � i is the magnetic flUI through pole i and a: 1 is the corresponding angular displace.ent. The tangential force constant can be expressed by:

.here:

K - 2lt Zo m (6) l'e - - --r .. S (2Z+).-1) r-o l?

). 1+1 (2Z-1) (7) m= 2 2Z+).-1

Differentiating the expression of the average total tangential force and setting it to 0 tbe optimal comllutation angle can be obtained:

ex = ar:csin '2 t & lBl ( 1 - l�l-+ �(2-mk...,....,)�2 ) op v� 4mke

whence the e.m.f. constant can be expressed by: P +P

k=N6 � (Il .. pm 4 .here Po, is the peneance of the equivalent air-gap under the pole i. In order to detect the position of the lover the induced e .•. f. through an un-energized control coil can be of real help:

e=k"msinex �� (10)

where v""du./ dt is the speed of the lover, which can be computed by lIonitoring the variation in tile of the displacement.

ilSULTs·m COICLUSIOHS

The above mentioned lotor design procedure and progr.�s has been used to design a permanent lagnet excited variable reluctance linear lotor baving four cOIIIand coils placed on each pole. Tbis vas selected because of the simplicity of its ilono-polar supply converter needs and because of the possibility to apply tile above mentioned sensories! optiul control strategy. The following required design data vere prescribed for the permanent .agnet excited variable reluctance linear lotor:

,ff::

:¥; ,n,'_,;' •

iD:-' ��): . �t·,� :, illl: .fr.:. �fi'" �

--

'i';'�' •

.� :. ,' i;::( " 'K � :.: .

f/

;� �,,:.�"-;r ,','1-\, :.; ...... , t". � ,·r .,. 'I{

.,,� �

;::,�: !).�:;:.�

F <w.x "SON Xi," 0 • 5mm ls=200mm 1=70mm

(ll)

lext all the lotor dimensions iere established. It vas lain stress on the best tooth geoletry selection. The optimal value for the tooth width to tooth pitch ratio us found out as to be 0.42. Prol the point of viev of aanufacturing the rectangular teeth form is the lost suitahle. In this case the luilom tangential force is great and the shape of the tangential force-displace· lent static characteristic is near optimal, assuring high stiffness and therefore high positional accuracy. The minilu. magnet volulle vas obtained for a magnet length of 1=810. kco1l" 3 was selected for the optimul width to length ratio of the control coil. This way the core and winding volume vas ainilbed. Sale of the lost ilportant parameters of the designed lotors are presented in Table 1: Table 1

air-gap O.1mm

tooth pitcb 2l1li

tooth width o .84mm

slot width 1.1611111

nuaher of teeth per pole

The selected perillanent magnet is of VACOllAX-1!S type, baving residual flux density of 0.91 and comitive force of 650lA/a. The cross-section of the designed permanent laqnet excited variable reluctance linear lotor and its aain dimensions are shown in Figure l. Next the electroillagnetic and tbenal verification of tbe designed permanent lagnet excited variable

reluctance linear lotor vas perforled. Using a separate" cOlputer progra. the maximal tangential force and tbe highest flux densities in different 'QtOf portions vere calculated by leans of the above lentioned cOlbined" circuit-field lathenticallOdel. All these parill eters vere found as in accordance vith the imposed data. By solving the differential equation syste. that describes tbe heat equilihriul of the motor the over-temperatures. in all the lotor portions were cOlputed. The strictest tellperature limits {the maliau! temperature of the permanent magnet vithout the risk of dalaging its lagnetic properties and the greatest linding tempera­ture, that is in relation vith its electric insulationl vere not reached. It can be concluded that the designed penanent aagnet excited variable reluctance linear IOtor fulfills the required perfor.ances and cO'plies all the imposed magnetic and thermal Haits. Therefore it can be considered as designed suitably. The proposed computer aided design methodology not only" shortens the design process, but also gives lore economical, efficient and higher quality alternatives. The control unit of the precise linear pOSitioning systelll, presented in Figure 2, is a colbination of an intelligent controller, of circuits for the captation of the e .•. f. through the un-en_erghed cOlllmand coils and of tvo dual motion control integrated circuits for '. the PHM current control.

v· -'INTELLIGENT CONTROLLER

v·s L)

ligure 2

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------------------------.... """'f!1"n',.'"nnnn n n: l" , • • , ' <

ne intelligent controller is the 'brain' of the entire control 5yste., which operates upon the above presented opti.al control strategy. It coordinates the .. ovuent

" of the permanent magnet excited variable reluctance lotor in function of the unigue external input

'. "signal. the iaposed speed (v'l, and generates the

four imposed comland coil current signals (�"I in dependence of the detected e .•. f. (el. The pover aulti-chip lodules (of SLA10HM type, produced by Allegro MicroSystems Inc. 1I.S.A.) enables efficient PWM .otor control. They require only an external current

, sensing resistor {RI, a single fixed reference input I Vee) and a logical input (INI. the perforwces of the designed precise linear positioning syste. can be analyzed by leans of computer silalation performed using the above lIentioned combined

,. circuiHield matbematical model. It is a very accurate tool for designers because all the lotor parameters can

. be detenined this

'" time (""5)

Sale results of the linear positioning 5yste. dynaaic silulation are presented in Figure J (the current in one of the co_nd coils, the tangential force, the speed and the displace.ent. of the lOver venus tilel. The simulated pick&place kind positioning task ilposed for the system is the following: the lOt or loves 50 to tbe right without load at a speed of 0.8./5. It stays stopped lOIs. After this the lotor is loved 1m. with a 0.5kg load at a lover (0.51/sl speed. Trapezo· idal velocity profiles were adopted. As it can be seen frol the results the i.posed task vas successfully fulfilled. The cOlllland current and the resulting thrust have great values during the tyO accelerations. When the lotor is loving at slew speed the tangent ial force is ·near constant. In order to decelerate the lotor negative tangential forces are exercised. During the lovements the displacement variation is Dear linear. The lOt or paraaeters and the linear positioning Slstell eharacteristics obtained via computer sillUlation stand by to sustain tbe theoretical basis of the utilized mathematical lodel and to conlin the validity of the opti,al control strategy presented in tbis paper.

lEFXmCES

III VIom LA.-KovAcS s. -sm6 L.: SawyerType Linear Motor Modelling, Proceedings of the International Conference on Blectrical Machines, Manchester, 1m, pp. £91·101. [21 EBlum D.; Design of a PI! Type Linear Stepping Motor for Automatic Conveyer Systea, Proceedings of the International Conference on Blectrical Machines Design and Applications, London, 1985, pp. 265-269. tlI VIOm LA. ·BIRO [.-SZABO L.: Transforer Transient Behavior Si.ulation by a Coupled Circuit-Field Model, Proceedings of the International Conference on Rlectrical Machines, Paris, 1994, pp. m·659. BJ SZAB6 L. -VIOm U..IOVACS Z.: COlputer Simulation of a Closed-Loop Linear Positioning S1stel, Proceedings of the peIM-Intelligent Motion Conference, Blirnherg, 1993, pp. 142·151. IS) VSICNAT I.-SIMOH-VERHOT M.·lliM01lS M.: Stepper Kotors Optilization Ose, Proceedings of the Interna· tional Conference on Blectrical Machines, Paris, 1994, pp. 13-16. 161 JlmBS et al.: In Improved Design Procedure for Hybrid Stepper Motors, Proceedings of the IHTBRMAG 190 in IBRB Transactions on Magnetics, Vol. 26., Bo. 5. (sept. 19901. pp. 2535·2538. 111 sm6 L. ·VIOUL LA.: Variable leluctauce Penanent Magnet Linear Motor Co_poter Aided Design, paper to be presented at the International Conference on Rlectrical Machines, Vigo, 1996-181 VIORSL LA.-sma L.: Pertanent-magnet variable reluctance linear lotor control, Blectlo.otion, vol. 1., nr. 1. (19941, pp. 11-38.

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