Radial Active Magnetic Bearing Control using Fuzzy Logic

Transcription

1 AMSE JOURNALS-16-Series: Mdelling A; Vl. 89; N 1; pp 9-1 Submitted July 16; Revised Oct. 1, 16, Accepted Nv. 15, 16 Radial Active Magnetic Bearing Cntrl using Fuzzy Lgic Nabila. Bubaya*, Belhamdi Saad*, Mrad. Maazuz** Abstract *Electrical Engineering Lab., LGE, University f M sila, M sila, Algeria ** Mechanical Engineering Dept, University f M sila, M sila, Algeria (bsaad1@yah.fr - nabila.bubaya@yah.fr) presented in this paper is a fuzzy lgic apprach t imprve perfrmance f a radial active magnetic bearing cntrl system.classical,linear design technique are mst ften used t cntrl the natural instability f these bearing, but magnetic nnlinearities limit cntrl effectiveness and the regin f stable perfrmance. therefre,the a idea here is t adjust the linear cntrller signal in such a way that nnlinear effects are better cmpensated.the relatinships f attractive frce t the electrmagnet currents and air gap are describe d and cmpensated using fuzzy principles, rather than a precise mdel-based cntrl apprach. Cmputer simulatins are used t cnfirm that a fuzzy descriptin f nnlinear cmpensatin des indeed imprve system perfrmance, withut requiring an exact mdel f the bearing nnlinearities. Keywrds: Active Magnetic Bearing, Magnetic Levitatin, Fuzzy lgic. 1. Intrductin Active magnetic bearings are being increasingly used in industrial applicatins where minimum frictin is desired r in harsh envirnments where traditinal bearings and their assciated lubricatin systems are cnsidered unacceptable (Chi 6 and L.O Cnner 199).cmmercially available technlgy was pineered by the French in the early 197 s and is licensed by several American and Japanese firms. Typical applicatins fr active bearings include turb mlecular vacuum pumps, gas pipeline centrifugal cmpressrs, sealed pumps, and electric utility pwer plant equipment.applicatin f the magnetic bearing in aerspace and crygenic envirnments is als being examined. Bearings that als emply permanent magnets have been recently develped, but the majrity f systems use electrmagnets. Since the alt magnetic bearing is an active device, it can als generate beneficial characteristics that are impssible t achieve with traditinal rlling element and fluid film bearings (Y.Zhang, 1991 and 9

2 E.Maslen,P.Hermann 1989).In thery, lads can be mved and frce disturbances can be gracefully damped (Schweitzer, G, 9 and H.M.Chen 1988),rather than bearing passed nt the remainder f the mechanical system. Despite the great ptential, the highly nnlinear and naturally unstable dynamic characteristic make AMB systems difficult t cntrl. initial studies were cncentrated firstly n the classical linear cntrl techniques which were based n prprtinal integral derivative (PID)r prprtinal derivative (PD) type cntrllers and then fllwed by the mdern cntrllers such as LQG and H which were als based n linear cntrl thery. These linear cntrllers are designed by linear zing the dynamic mdel f a magnetic bearing abut a nminal equilibrium pint (Ming-Ma Hsu, Seng-Chi Chen, 15 and M.Fujita,F.Mastsumura 199).The main cntrllers used fr AMB in mst practical installatin are the traditinal PID type.whilst the perfrmance f the PID cntrller is generally satisfactry fr mst practical applicatins. This type f cntrller becmes ineffective when the rtr is subjected t extreme perating cnditins.thus, several nn- linear cntrl techniques have been prpsed t deal with the nn-linear dynamics f the AMB (S. C. Chen, 13). Research wrk n nn-linear cntrl f AMB has been undertaken by several authrs t vercme the shrtcming f the linear PID cntrllers. Yeh prpsed a sliding cntrl scheme t deal with the nn-linear dynamics f AMB systems (T.J.Yeh, Y.J.Chung, 1). Marci S. used a back stepping apprach as cmpensatin fr parametric uncertainly and eliminating state measurements (Seng-Chi Chen, 14),.hwever, these cntrllers are mre cmplicated cmpared with their linear cunterparts.at this pint, a fuzzy lgic cntrller (FLC) is seen as a slutin fr bth f these prblems (Belhamdi, S, 15).Hng S.K. used a rbust fuzzy cntrl scheme fr magnetic bearing (MB) systems. Hung J.Y. Cmbined an FLC with a PID cntrller fr adjusting the utput f the PID cntrller in such a way that nnlinear effects are better cmpensated (Belhamdi, S, 13).Maki K.H. used an FLC t tune the gains f the linear PD cntrller t imprve the perfrmance f the AMB cntrl system (T. Dimnd, 1).. Active magnetic bearing mdel A typical AMB cnfiguratin cnsists f a statr and a rtr. The cils are wund arund each ple f the statr Each rtr axis has a pair f amplifiers t prvide current t the bearing cils and an attractive frce t adjust the psitin f the rtr alng the particular axis. The current carrying cil wrapped arund the statr f an AMB system creates a magnetic field within the statr, the rtr and air gap between the rtr and the statr. 93

3 In the derivatin f the frces that are generated in the magnetic field, the fllwing assumptins hld. Leakage f magnetic flux is neglected. Fringing effect i.e. the spreading f magnetic flux in the air gap is neglected. The magnetic irn is perating belw saturatin level. The expressin fr the electrmagnetic frce that is generated in a single acting actuatr is given in (1), where is the permeability f air, N is the number f the cil turns n the magnetic actuatr, S is the area f the ne magnetic ple, I is the cil current, and C is the length f ne air gap N S. i F (1) 4C In the actual peratin f the AMB, a pair f magnetic actuatrs cunter- acting each ther is used. This cnfiguratin is knwn as the difference driving mde Figure.1 shws the basic principle f an active magnetic bearing. Y Y I+I c Z y C F Z I-I c Figure1. Representatin f a AMB with 1 DLL The frce prduced in this system can be determined by assuming that the current in the decreasing air gap is (I+Ic) and the current in the ppsite side is (I-Ic).the air gap is (C-y)in the decreasing side,and (C+y) in the ppsite side.ic is the cntrl current and C is the nminal air gap i.e. the gap at equilibrium psitin in the Y- axis, and y is the displacement f the rtr frm its equilibrium psitin in the Y-directin.F1 and F dente the frces f the tw cunter-acting actuatrs respectively, whilst F dentes the resultant frce,then the nnlinear frce equatin fr the difference driving mde is (). S N I I c I I c F F1 F 4 C y C y 94 ()

4 Applicatin f the Newtn s secnd law t the AMB systems gives (3). Where m y is the mass f the rtr; I Ic I Ic K (3) C y C y K 4 S N, which is the frce cnstant. Equatin (3) is the mdel used in the simulatins, and plant parameters are shwn in table. 3. Simulatin mdel f AMB with linear cntrllers The mathematical mdel that has been develped in sectin II is implemented using Matlab /simulink develpment AMB is the instability f the rtr.the mst cmmn PID cntrller is used t calculate the cntrl current. The regulatr represented in the figure.. The frm f the regulatr is given by equatin 4. G c 1 T s 1 Td 1. s N s K. 1 T. s (4) p i d y - G c (s) AMB y Figure.1. Diagram blck f the AMB in clsed Fr calculated the gains f the regulatr ne uses a methd f apprach fast, cnsist in taking T T / 1 et T T / 4 with T : the dminant time-cnstant f the prcess and ne i d i generally chses N abut 1. Results f simulatins f the AMB in lp clsed with filtered regulatr PID (KP=8, Ti=8, Td=, N=1) and y ref =3% are cnsigned in the figure.3. We nte that the active magnetic bearing is currently stable in clsed lp time(s) a) : Displacement f the AMB Ic(A) b) : Cntrl f the AMB Figure.3. applicatin 95 f PID t the AMB

5 4. Design f the FLC cntrller Fuzzy lgic thery was first established in Zadeh s seminal paper in 1965.Mamdani applied fuzzy lgic t dynamics abut 1 years later.the Mamdani architecture f a fuzzy lgic cntrller is based n qualitative and empirical knwledge f human beings. Later Takagi and Sugen established a fuzzy mdel, called the Takagi-Sugen mdel, which can be mre easily used fr analytical purpses. Mamdani architecture is used here t build a nn-linear rule-based fuzzy lgic cntrl system. Fuzzy lgic cntrllers fr active magnetic bearings are synthesized and designed fr stabilizing the system during the cmmand fllwing prcess. The antecedent and cnsequent f each rule are defined in terms f input and utput variables in predefined membership functin. These membership functins pssess qualitative descriptin, which generalize the ntin f assigning a single degree t a specific respnse severity r crrective actin level. The expert's experience is incrprated int a knwledge base with 5 rules (5 x 5). This experience is synthesized by the chice f the input-utput (I/O) membership functins and the rule base. Then, in the secnd stage f the FLC, the inference engine, based n the input fuzzy variables e and Δe, uses apprpriate IF-THEN rules in the knwledge base t imply the rules in the knwledge base t imply the final utput fuzzy sets as shwn in the Table1, where NB, N, Z, P, PB, crrespnd t Negative Big, Negative, Zer, Psitive, Psitive Big respectively (Belhamdi, 13). e NB N Z P PB NB NB NB N N Z N NB N N Z PB Δe Z N N Z P PB P N Z P P PB PB Z P P PB PB Table1. Fuzzy rule fr type-1 FLCs 96

6 4. Simulatin Results The AMB whse parameters are shwn in table I is simulated by using MATLAB. Equatin (3) f the magnetic bearing system is built with S-functin f MATLAB, and the basic fuzzy lgic cntrller is built with the Fuzzy Inference System tlbx f MATLAB. The figure (4) presents the evlutin f the exit (displacement) and the manipulated variable. It is nticed well that displacement fllws its reference well time(s) a) : Displacement f AMB b) : Cntrl f the AMB Figure.4. Applicatin f FLC t the AMB Figure.7 shws the cmparisn between the respnses f the traditinal PID cntrller and the FL cntrller.it can be seen frm fig (5) that when the FL cntrl methd is adpted, the versht f the rtr displacement is less than 4% and the rising time is less than. secnd. In cntrast, the versht is bigger and the rising time is lnger when the traditinal PID methd is adpted.. 4 FLC REF PID Figure 6. Cmparisn between the PID and FLC 97

7 4.1 In the presence f a disturbance in level In this case we apply a disturbance f frm square f perid equal t s and f amplitude equalizes at 1.5%.the curves represented by figure FLC REF PID Figure.7. Applicatin f PID and FLC t AMB 4. In the presence f a sinusidal disturbance Nw; we apply a disturbance f sinusidal frm f frequency equal t.8 rad/s and f amplitude equalizes t 1.5%.the curves represented by figure.8. 4 FLC REF PID Figure 8. Applicatin f PID and FLC t AMB It can be seen that the FL cntrller has strnger disturbance rejectin ability cmpared with the traditinal PID cntrller. 5. Cnclusin The fuzzy lgic and PID type cntrllers fr AMB have been studied. Initially, dynamic mdel f the AMB has been develped. First, a PID type cntrller has been applied t the system and the step respnse f the cntrller btained. Owing t the small air gap, gd results were achieved with linear cntrller with reasnable psitin errrs. Since AMB have a nnlinear structure, the 98

8 influence f the parameters n the perfrmance f the system is clear. Thus, a nnlinear cntrller is frmed in the simulatin mdel by Fuzzy reasning. Simulatin results shw that system perfrmance is imprved with FLC. It is bserved that fuzzy cntrl is giving better respnse than cnventinal cntrller. TABLE Appendix PARAMETERS OF THE AMB SIMULATION MODEL S m I C (m²) N 4 x 1e-7 9.8e-6 1 (kg) 8.5 (A) 35e-3 (m) 1e-3 i, y (,) References 1 Chi, H., Gregry, B. and Nathan, G., Neural Rbust Cntrl f a High-Speed Flexible Rtr Supprted n Active Magnetic Bearings, American Cntrl Cnference IEEE, pp , June 6. 1 L.O Cnner, Active magnetic bearing give systems a left, mech. Eng., vl.114, Nº.7,pp.5-57,July 199. Y.Zhang Static characteristics f magnetized jurnal bearing lubricated with ferrfluid, trans. ASMEJ triblgy, vl 113, pp , July K.R.Brnstein, Dynamic lad capabilities f electrmagnetic bearings, Trans, ASME J.Triblgy, vl.113, pp , July E.Maslen,P.Hermann,and M.Sctt, pratical limits t the perfrmance f magnetic bearings:peack frce,slew rate,and displacement sensitivity,trans. ASMEJ Triblgy,vl.111,pp ,Apr Schweitzer, G. and Maslen, E. H. Magnetic Bearings-Thery, Design and Applicatin t Rtating Machinery, Springer-Verlag, pp , 9. 6 H.M.Chen and M.S.Darlw, Magneticbearng withrtating frce cntrl Trans. ASME J.Triblgy, vl.11, pp.1-15, Jan

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