Sliding-Mode Control of Synchronous Reluctance Motor

Transcription

1 Internatonal Journal of Electrcal an Computer Engneerng 4: Slng-Moe Control of Synchronous Reluctance Motor Mostafa.A. Fellan, an Dawo.E. Aba Abstract Ths paper presents a controller esgn technue for Synchronous Reluctance Motor to mprove ts ynamc performance wth fast response an hgh accuracy. The slng moe control s the most attractve an sutable metho to use for ths purpose, snce t s smple n esgn an for ts nsenstvty to parameter varatons or external sturbances. When ths metho mplemente t yels fast ynamc response wthout overshoot an a zero steay-state error. The current loop control wth ecentralze slng moe s presente n ths paper. The mathematcal moel for the synchronous machne, the nverter an the controller s evelope. The stablty of the slng moe controller s analyze. Smulaton of synchronous reluctance motor an the controller wth PWM-nverter has been curre out, usng the SIMULINK software package of MATLAB. Smulaton results are presente to show the effectveness of the approach. Keywors Dynamc Smulaton, MATLAB, PWM-nverter, Reluctance Machne, Slng-moe. I. INTRODUCTION HE Synchronous Reluctance Motor (SynRM) has a T mechancally smple an robust structure. It can rotate at hgh spees n hgh temperature envronments because t has no rotor wnng. It rotates at synchronous spees, so the controller s smpler than other types of AC machnes. The most commonly use metho of control for SynRM s fel orente control (FOC) [1]. The FOC represents the attempt to reprouce, for a SynRM, a ynamcal behavor smlar to that of the c machne, characterze by the fact that the evelope torue s proportonal to the moulus of the stator current: to reach ths objectve, t s necessary to keep the rotor flux value constantly eual to the nomnal value, so that, contemporarly, the optmal magnetc crcuts explotaton guarantees the maxmum power effcency [2]. The conventonal lnear controllers such as PI, PID use wth ths structure are senstve to plant parameter varaton an loa sturbance. The performance vares wth operatng contons, an t s also ffcult to tune controller gan both on-lne an off-lne. Another technue to control the torue of the SynRM s the Drect Torue Control (DTC). The name of the DTC s erve from the fact that, on the bass of the errors between the reference an the estmate values of the torue an flux t D.E. Aba (phone: ; e-mal:dawaba@gmal.com) an M.A. Fllan (phone: ; e-mal: Fellan2006@yahoo.com) are wth the Control Engneerng Department, Hgher Insttute of Electroncs, Ben-Wal, Lbya. s possble to rectly control the nverter states n orer to reuce the torue an flux errors wthn the prefxe ban lmts [3]. DTC controller s less sensble to the parameter etunng n comparson wth FOC an t allows goo torue control n steay state an transent operatng contons. Nevertheless DTC presents some rawbacks such as ffculty to control torue an flux at very low spee, hgh nose level at low spee, hgh current an torue rpple, an varable swtchng freuency behavor [2]. Torue sturbances an parameter varatons, prone some mportant problems, whch nee to be mofe. Such problems n rves, partcularly n reluctance synchronous motor are the presence of harmoncs, whch usually leas to hgh torue rpple [4] an conseuently mechancal vbraton. Also, ue to spose the current components n a real coornates, the current control sometmes results n a trackng problem [5] when a multple phase system fe by PWM are rnanufacture. Several methos have been use to reuce vbraton an trackng problem, such as varable structure control strategy an aaptve control [6,7], but the slng moe control s most convenent technue, ue to t's fast ynamc response, nsenstvty to parameter varatons an external sturbance rejecton an of ts smple mplementaton [8]. The theory of slng moe control has been apple to control systems usng brushless c motors [9], nucton motor an synchronous motor rves. However, ts applcaton to the reluctance motor stll not manufacture. Ths paper shows the esgn of the ecentralze slng moe-sgn functon of PWM nverter reluctance motor rve, n terms of current loops controller escrbe n Tow-axs forms. Smulaton s carre out by usng SIMULINK software package of MATLAB for moelng the PWM-nverter an scretng the control laws. A set of slng moe control parameters s esgne an gven. The results show goo performance n spee operaton uner the effect of external sturbances an prove an optmum level of torue wth low rpples. II. SYSTEM MODEL CONSTRUCTION The propose synchronous reluctance motor rve s as shown n Fg. 1. The system conssts of man components: a motor, an nverter an controller. The motor s 3-phase synchronous reluctance wth ampng wnng. The converter conssts of a three phase voltage source nverter whch powers 638

2 Internatonal Journal of Electrcal an Computer Engneerng 4: the stator of the motor. The nverter swtches are rven by a PWM unt, an the gates are trggere by the 3-lne voltage error sgnal of the motor, an carre by a trangular wave of the PWM source. The current an poston sensors are use wth a specfc references for the feeback control, an the Tow-axs transformaton blocks are apple. The sgn functon s esgne for current loop controller n terms of spee error sgnal, whle the resultant tow-axs motor voltage sgnal s transforme back nto 3-phase lne sgnal an fnally fe-back to the PWM-nverter. 3 T e p( L L ) (3) 2 The torue euaton n Laplace oman s T 3 2 p( L L ) ( B + JS) (4) Where, B an J are the ampng fracton an the motor moment of nerta respectvely an p s the number of pole pars an ω r. 2 to3 phase reference frame transformaton Vc 2-axs voltag Sgn functon Slng moe controller S S V a,b,c I re I 0 3 to 2 phase transformaton ω r PWM voltagesource nverter Motor Fg. 1 Block agram of the rve system III. MOTOR DYNAMIC D-Q MODEL The well known - moel of AC machnes s wely use for smulaton purposes. Base on the assumpton that the stator wnngs are snusoally strbute the - moel s a powerful tool for ynamc smulaton of most AC machnes nclung the synchronous reluctance motor. The euatons whch escrbe the behavor of the synchronous reluctance motor n - reference frame can be wrtten as: V V I t RsI + L ωrl I (1) R I L I t s + + ω r L I (2) Where L an L are the rect an uarature axs wnng self nuctance (H), R s the stator wnng resstance (Ω) an ω r s the rotor angular spee n (ra/sec) an t s eual to. IV. PROPOSED CONTROLLER DESIGN A. Current an Spee References The torue an spee control are execute n the - reference frame. A possble strategy to control the spee by slng moe conssts of controllng the rect an uarature currents, so that the motor torue epens on the multplcaton of both current components. Thus, for the current, the reference s specfe n -axs as ref o, an for the spee, the reference s specfe as ωref0 Whle the current n -axs s now epens on both rect current an spee, through the torue euaton. B. Slng Contons Conser S enotes the slng surface an v c s the resultant Tow-axs control voltage vector. The slng moe control can be acheve f there exsts a control law, such that the conton SS < 0 s satsfe [14]. The soluton of v c s therefore: v c v u (5) Where v s the Tow-axs motor voltage components gven n (2) an u s the esgne slng voltage components. Snce the slng moe s obtane by changng the structure of the controller on ether se of the slng surface ''S'' [14] such as the poston error trajectory s force to follow t's tll orgn of the phase plane. Thus, the esgn of v s obtane by an exact feeback lnearzaton of S. Whle u s esgne n such a way to fulfll the conton of the state trajectores to be attracte towar the surface S0. The control law s therefore establshe to follow on the gven slng surfaces below: Subject to: S - 0 an S S <0 The current slng surface s: S - Subject to: S c 0 an S S 0 The spee slng surface s: The electromagnetc torue euaton s: 639

3 Internatonal Journal of Electrcal an Computer Engneerng 4: S c( ) + ( ) 0 (6) These mply: 0, 0 0 an c (7) C. The Sgn Functon The sgn functon s a screte o functon of unty magntue an specfe tme steppng. It s a functon of the slng surface S, such that for both current surface S an spee surface S, the functon takes the form of Fg. 2. Fg. 2 The sgn functon D. The Controller The slng voltage components u are esgne n the form: u k Sgn (S ) an u k Sgn (S ). Takng nto account the exstence conton of the slng control an the stablty conton of the system SS < 0, the two components of the resultant Tow-axs voltage vector v are calculate as follows: From euaton (2) an at no loa (T0) we get: But from (7) Therefore c B + J ( L L ) c Sgn(S) -S 2 -S 1 S hence: ( B J c) ( L L ) v v + u R L + k sgn( S ) s S 1 S 2 (8) (9) (10) v c v + u + k sgn( S ) R s + ( L B Jc + ( L L ) (11) Where, c, k an k are constant parameters, they are tune to obtan an acceptable value of voltage. The resultant Tow-axs voltage vector V c s then transforme back nto 3-phase components. The 3-lne voltage are then njecte to the PWM-nverter an carre by a trangular wave of freuency (3 khz) an ampltue 100, moulate wth voltage control. The c lnk voltage s fxe at 70 V. V. SIMULATION RESULTS Usng the methoology escrbe n the prevous secton, smulaton s carre out by constructng the control moel n the SIMULINK/MATLAB software. Fgs. 3, 4 show the step response of the system to a spee reference of 100 ra/sec an current reference of 0.75 A. The system parameters are: The stator resstance R s 15Ω, -axs nuctance L 0.2 H, -axs nuctance L 0.05 H, the moment of nerta J 0.03 kg.m an the vscous frcton B kg.m 2 /sec. In Fgs. 3, the slng moe control parameters are as shown n Table I. TABLE I SLIDING MODE CONTROL PARAMETERS C 1000 k 100 k 20 S 1 1 S 2 10 S 1 2 S 2 50 In Fgs. 4, the slng moe control parameters are as shown n Table II. TABLE II SLIDING MODE CONTROL PARAMETERS C 10 k 10 k 100 S S 2 1 S S 2 2 S) 640

4 Internatonal Journal of Electrcal an Computer Engneerng 4: Fg. 3a Spee response Fg. 3e -axs controlle voltage Fg. 3b Response of rect current Fg. 4a Spee response Fg. 3c Response of uarature current Fg. 4b Response of rect current Fg. 3 -axs controlle voltage Fg. 4c Response of uarature current 641

5 Internatonal Journal of Electrcal an Computer Engneerng 4: Chatterng an torue rpple are reuce by the control strategy an conseuently the effcency s mprove, snce the effcency s usually hancappe n the electrc rves by chatterng, as s known. The system s reay mae on the MATLAB/SIMULINK, an the smulaton s gven. Fg. 4 -axs controlle voltage Fg. 4e -axs controlle voltage It s clear that there are fferent between the tow sets of fgures above, accorng to the selecte values of the slng moe parameters. For the machne use n ths test, the sutable parameters are gven for Fgs. 3, an those establsh a goo performance of the overall control system. These results show no steay-state error an no chatterng or rpples. Whle parameters lke n Fgs. 4, llustrate lttle swayng n the response of most of varables. Ths mght be because the system s operatng n the nstablty bounary. It has been teste, for the parameters gven for Fgs.4 that the motor s workng at the crtcal stable pont, whch can be recognze by the spee curve. The fgures, however, llustrate a goo effcency of the control strategy, an chatterng of the control an the corresponng rpple are conserably reuce, an are absence n the results of Fgs. 3. REFERENCES [1] p. Pllay, r. Krshnan, Moelng, smulaton, an analyss of permanentmagnet motor rves.. The permanent-magnet synchronous motor rve, IEEE Trans. Inustry Applcatons, Vol 25, n 2 Mar/Apr 1989 pp: [2] m. Roc, k. Jezernk, Spee Sensoless Slng Moe Torue Control of Inucton Motor, IEEE Trans on. Inustral Electroncs, February [3] m. f. Rahman, l. Zong an k. w. Lm, a Drect Torue Controlle Interor Permanent Magnet Synchronous Motor Drve Incorporatng Fel Weakenng, IEEE Trans on. Inustry Applcatons, Vol. 27, N 5, Sep/Oct 1991, pp [4] Carlson, R., Cros, J. & Lajoc, M., 'The analytcal etermnaton of the characterstcs of permanent magnet brushless c rves', Proc. European Conf. On Power Electroncs 1991, Frenze Vol.3, pp [5] Kazrnernowsk, M.P. & Dzenakowsk, M.A., 'Revew of current regulaton methos for VSPWM nverters', Proc. Int. Symposum on Inustral Electroncs 1993, Buapest, pp [6] Marongu, I. & Serr, A., 'Moel reference control of PM synchronous motors', Proc. Electrc rve symposum 1990, Capr, pp [7] Sabanovc, A. & Olnsh, N.K., 'Slng moes n power converters an moton control systems', Int. journal of control Vol.57, No.5, 1993, pp [8] [8]. Ramrez, H.S.,'Slng moe control of slow manfols of c-c power converters', Int. journal of control, No.47, 1988, pp [9] Harashma, F., Hashmoto, H & Kono, S., 'MOSFET converter-fe poston servo system wth slng moe control,'ieee Trans. On Inustral Electroncs, Vol. 1E-32, No.3, 1985, pp [10] Sabanovc, A. & Izosmov, D.B.,'Applcaton of slng moes to nucton motor', IEEE Trans. On Inustral Electroncs, Vol.IA-17, No.1, 1981, pp [11] Benklors, M.F., Deecus, D., Sala, S. & Glumneau, A.,'Dgtal smulaton of slng moe control of brushless servo-motor', Proc. ICEM, France 1994, Vol.2, pp [12] Mostafa, M.A & Nagral, M., 'Dynamc control of synchronous reluctance rve', Proc. AUPEC conference, Syney, 1997, Vol.1, pp [13] Weh, H. an Schroeer, U., 'Statc nverter concepts for multphase machne wth suare wave current fel strbutons', Proc. UPEAC cotf, Brussels, 1985,pp [14] Utkn, V., 'Slng moes an ther applcatons n varable structure systems', Moscow: Mr, VI. CONCLUSION Ths paper hghlghts the applcaton of a slng moe controller to robust spee control of Synchronous reluctance motor rve. The esgn of the slng moe controller s escrbe an both rect current an spee control laws are nvestgate. Reucng of rpples that cause by the hgh freuency of the voltage source nverter can be obtane by usng the sgn functon, whch s esgne to match the reurements of the reluctance motor operaton an mplemente for ths type of control. 642