TORQUE RIPPLE MINIMIZATION, SUPPRESS HARMONICS, AND NOISE OF BRUSHLESS PM SYNCHRONOUS MOTORS DERIVED BY FIELD ORIENTED CONTROL

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1 TORQUE RIPPLE MINIMIZATION, SUPPRESS HARMONICS, AND NOISE OF BRUSHLESS PM SYNCHRONOUS MOTORS DERIVED BY FIELD ORIENTED CONTROL Hamy Mohame Solman 1,* & S. M. Hakm 2 1 General Manger n Caro Metro Greater 2 Department of Electrcal Power an Machnes Engneerng, Caro Unversty Egypt 1 Hamysolman123@gmal.com ABSTRACT Conventonal fel orente control for brushless PM synchronous motor epens upon mathematcal moel so the parameters varatons, nose, electromagnetc nterface, non-snusoal flux an harmoncs n the motor or n power converter wll cause performance eteroratng of the rve system. They are causng spee oscllatons, rpples n torque, rpples n current an an ncrease the total harmoncs storton (THD). Ths paper s aresse these problems an suggeste novel two PI controller for solvng these problems. One for the torque an the other for the flux. The frst PI controller s feeng from the torque error between the reference an estmate torques to get new q-axs current component representng mofer current arses from uncertan thngs such as earlest problems. Ths current wll a to reference q-axs current to get robust new q-axs current to satsfy the rve requrement an solve the torque problem. Wth robust current, the total harmonc storton s a ecrease but oesn t reach the best value so the other PI controller s use to ajust the THD. In ths PI controller, the -axs flux s compare to rotor permanent magnet flux to solve ths problem arses from non-snusoal of the magnetc flux. The output of the PI controller s ntrouce to the reference -axs current. The new -axs current wll reach the best value of THD. The smulaton of the propose controller s compare to the smulaton of conventonal controller to show the avantages of the propose controller. To splay the effectveness of the secon PI controller (flux controller), the result of the new controller s splaye wth new PI torque controller only an wth new two propose controller. MATLAB SIMULINK s use to smulate the rve system. Keywors: PMSM FOC Hysteress Current Controller PI Controller Torque rpple Current rpple THD. 1. INTRODUCTION Permanent magnet synchronous motors (PMSM) are wely use n hgh-performance rves such as nustral robots, electrc vehcles, arcraft an machne tools. These motors have many avantages as: hgh effcency, hgh power ensty an hgh-torque/nerta rato [1].The performance of these motors n rve systems epen up on the motor control an metho of control n power converter. From the most mportant methos to control the power converter are current an voltage controls. The current control s preferable. Ths s because t s smple. The qualty control of ths metho epens upon the qualty of the waveform s generate by current controlle of converter [2-3]. To get goo power waveform ths epens upon the followng factors:- Swtchng frequency of the PWM whch has low harmoncs f t s hgh but t has rawback such as: hgh losses. Moulaton metho whch control the magntue of the output waveform but t has rawback such as: hgh orer of voltage harmoncs an rpple current. Types of current waveform. Ths s because each motor requre own current waveform such as: nucton motor an PMSM requre sne wave but brushless DC motor requre quas square wave form. The metho of motor control s very mportant n the rve system. Ths s because the operaton of the PMSM uner effect of scalar control s suffere from complcate couplng nonlnear ynamc performance. Ths problem can be solve by fel orente control (FOC). PMSM wth FOC emulates the separately excte DC motor. In ths metho of control, the stator current can be ecuple nto flux an torque current components. They can be controlle separately. In four quarant wth keepng magnetc crcut lnear an applyng the prncples operaton of the FOC, the lnear relaton can be escrbe the motor torque. The performance of the motor suffers from uncertantes, parameters varaton, harmoncs n both motor an nverter. These problems affect motor performance. These problems shape ffcult n gettng robust control. They lea to problems n torque an oscllaton n the spee as the seconary problem comes from torque problem. To solve ths problem, the torque must be stue. The motor torque s a sum of mutual torque, reluctance torque an coggng torque. These torques contan harmoncs whch lea to torque rpples. The mutual torque an reluctance 481

2 torque have harmoncs f the stator flux or rotor magnet are non- snusoal. The reluctance torque s exsts only f the nuctance s a functon n the rotor poston. So the torque rpples appear as a sx harmoncs. The coggng torque arses ue to geometry an slots n the PMSM [4]. Other reasons of harmoncs, the swtchng power of nverter causes electromagnetc nterface whch causes nose an ncrease the torque pulsatons. The machne esgn an control technque are use to reuce the torque rpple. The frst metho s complcate an hgh cost so the other metho s preferable. Many control technques are use to mnmze the torque rpple such as: programs to cancelaton the harmoncs but these methos requre full knowlege about the machne parameters. These methos become unesrable f the operatng pont changes [5-6]. The current control scheme wth an aaptve nternal moel s propose n many researches as [7]. Passve flter s use to reucng the torque rpples n [8] but hgher crculatng current arses between flter an nverter. Actve flter s use to reucng the torque rpples but ths metho s hgher cost [9]. Proportonal ntegrator controller (PI), t s the most common controllers use n a we range n the nustral applcatons. The popularty of PI control can be attrbute to ts smplcty. The ntegral controller has rawback such as saturaton. Ths phenomenon can be avoe by ntroucng a lmter to the ntegral part of the controller before ang ts output to the output of the proportonal controller. The output of the PI s use as the nput of controlle voltage source nverter whch s fe to the motor for controllng ts spee [10]. Many researches use PI controller to mprove the poston an spee controllers ths s because t affects the performance of the rve system especally torque an spee oscllatons. The PI controller s senstve to uncertantes varaton such as motor parameters, sturbance an temperature varatons. So In ths stuy two new proportonal ntegrator corrector controller are use to optmze conventonal PI controller. The frst PI controller s use to reuce the nose, storton an rpple torque. The secon PI controller s use to reuce the nose, storton an rpple n the stator currents ths can be one by reucng the storton n the stator flux. Hysteress wth current control are mae. Ths system s smulate by MATLAB Smulnk. The smulate moel wth propose new PI controllers s compare wth conventonal PI controller n orer to nvestgate the avantages of the new propose control. Ths paper s organze as follows. Secton one ntroucton. Secton two FOC rve system of PMSM. Secton three Mathematcal moel of PMSM. In secton four Tratonal control loop of the fel orente control. Secton fve escrbe Hysteress current controller. Secton sx Desgn of PI controller. Secton seven Propose control loop of the fel orente control Secton eght shows the smulaton results. The concluson s n secton nne. 2. FOC DRIVE SYSTEM OF PMSM The FOC ams to control both torque an flux to force the motor to accurately track the esre values. Ths control s performe by regulaton of the motor current. Ths control suffers from unefne thngs such as: parameters varaton, harmoncs an external loa sturbance. To track these problems another fel orente controller rve system s propose as shown n Fgure 1. The etals of the new controller system are scusse later. 3. THE MATHEMATICAL MODEL OF PMSM The mathematcal moel of a PMSM s smlar to that of woun rotor synchronous motor. The rotor wnng of synchronous motor s replace wth hgh resstvty permanent magnet materal, hence, nuce current n the rotor are neglgble. The rotor types of PMSM are shown n Fgure2. The permanent magnets on the rotor are shape n such a way as to prouce snusoal back EMF n stator wnngs The followng equatons represent the moel of PMSM r v L e q q t L (1) q v r q q L q e e t L (2) m m J m L m t (3) 3 [ ( ) ] m m q q q 4 L L (4) e m 2 t (5) 482

3 * c * b * a Hysteress current controller 3 phase nverter c b a * r Reference current regulator m r e Torque an flux estmaton PMSM Fgure 1. Block agram of new controller FOC rve system (a) (b) Fgure 2. The types of the rotor n PMSM: (a) PM surface nset, (b) PM surface nteror (bure) Due to the control varables are measure n synchronous reference frame an the actual values are measure n statonery reference frame, the park an Clark must be performe an vse versa. The followng matrx can be apple to transform from abc to q 2 4 cos cos( ) cos( ) S a 2 e e e S 3 3 b S (6) S q sn sn( ) sn( ) e e e 3 3 S c An transformaton matrx from q to abc s cos sn e e S a 2 2 S S cos( ) sn( ) b e e 3 (7) 3 S q S c 4 4 cos( ) sn( ) e e 3 3 Uner base spee the -axs current s force to zero then the torque can be controlle through the q-axs current component only an the electromagnetc torque can be calculate as 3 [ ] e m q 4 (8) 4. TRADITIONAL CONTROL LOOP OF THE FIELD ORIENTED CONTROL Conventonal fel orente control can be apple as shown n Fgure 3. One PI controller s use. It s use to regulate the spee. The nput of PI controller s the spee error whch comes from comparng the reference an measure spees. The output of ths PI controller s a reference torque. Wth a of constant torque an the output of PI controller the torque current component ( ) can be euce. The -axs current component ( q ) s set to zero ths s because the operaton of the PMSM n a constant flux regon. Wth a of rotor poston an two reference 483

4 current components ( ), the three phase reference current can be euce. They comparng to the actual three q phase current through hysteress current controller to get pulse sgnals of nverter. Fgure 3. Conventonal fel orente control 5. HYSTERESIS CURRENT CONTROLLER In ths work, the current control of converter s a hysteress current controller. It s use ue to smple, fast ynamc response an nsenstve to loa parameters. Fgure4. represents the hysteress current controller. In ths metho each phase conssts of comparator an hysteress ban. The swtchng sgnals are generate ue to error n the current. The error comes from comparng between the reference current an actual current. The man task of ths metho of control s to force the nput current to follow the reference current n each phase. The evaton of these currents (error current) represents the current storton whch can be calculate as storton % I rms ( ) T 2 act ref t (9) In ths metho of control, the evaton of the current between the upper an lower n the hysteress ban s lmte. In any phase, f the actual current becomes more than the upper lmt of hysteress ban ( ref HB ) the upper swtch of the nverter arm s turne off, the lower swtch s turne on an the current starts to ecay. In contrast f the actual current reaches lower lmt or less than of hysteress ban ( ref HB ) the lower swtch of the nverter arm s turne off, the upper swtch s turne on an the current comes back nto the hysteress ban. The ban wth calculates the swtchng frequency an current rpple. The ban wth s rectly to current rpple an nversely proportonal to swtchng frequency so the selecton of the ban wth means performance of nverter. Ths s because the ncreasng n the ban wth wll ncrease the current rpple n contrast; a ecrease n the ban wth wll ncrease the swtchng losses. Fgure 4. Hysteress current controller basc structure an concept 484

5 6. DESIGN OF PI CONTROLLER PI controller s a type of feeback controller whch has output epenng upon the error. Ths error s use to ajust the nput of the other process. Two parameters are use to esgn ths controller. These parameters are proportonal gan ( ) an ntegral gan ( ). Ths controller can represent as k p k k k GS ( ) (10) p S Proportonal gan s use to mprove the rse tme an ntegral gan s use to elmnate the steay state error. These parameters can be euce by many methos such as: tral an error, Zegler-Nchols metho an nternal moel of control. The parameters of the PI controller are etermne epenng upon [11-12]. 7. PROPOSED CONTROL LOOP OF THE FIELD ORIENTED CONTROL In tratonal control (FOC), the rve s nfluence by uncertantes, electromagnetc nterface, non-snusoal of stator current an permanent magnet rotor flux or all of them. They reflect on the torque an current causng unwante problems such as rpple an nose. The eal case of electromagnetc torque s (8) but when takes nto account the effect of harmoncs, t becomes 3 m [ q ( q ) q ( sn(6 ) sn(12 )) 4 m L L 6 12 ( cos(6 ) cos(12 )) ] q6 q12 q The frst term s the mutual torque, the secon t s reluctance torque an the other terms represent the harmonc torques. Due to * s force to zero so the terms whch contan ths current aren t most energy effectve. So the torque equaton can be represente as 3 [ cos(6 ) cos(12 )] m q 4 (13) m q 6 q12 Ths torque can be consere as m em e 6h (14) e12h Also q-axs current component s 4 m 1 q (15) 3 [ cos(6 ) cos(12 )] m q 6 q12 (12) So the PI spee controller whch s use to generate the q-axs current sn't suffcent to overcome the nose an rpples n torque an current. To mnmze the rpple an nose n the torque another PI controller s use; the nput of the new PI controller s the error n the torque. Ths error comes from the output of comparator whch comparng the reference torque to estmate torque. The output of the new PI controller s a new q-axs current ( ). Ths current s a to the reference of q-axes current to get robust current ( rpple an uncertantes nse the machne. qrobust qref qsol qrobust qsol ) representng the soluton for nose, Wth ths enhance n the q-axs current component, the storton of the current oesn t reach the best value ths can be seen n table 1 an n later fgures. To reach the best value another PI controller s use. The nput of ths PI controller arses from comparng the estmate -axs flux wth permanent magnet flux. The output of ths PI controller s ae to the reference -axs current whch s force to zero at constant flux regon. The new -axs current s reuce the storton as shown n table 1 an as n later fgures. the new q-axes current wth rotor poston are use to generate the new reference current. The new propose controller s shown n Fgure 5. (10) 485

6 Fgure 5. Propose controller 8. SIMULATION STUDY Here the three moels are compare. These moels are conventonal moel, mofe moel wth PI torque controller an mofe moel wth two PI controllers an one for the torque an the other for flux controller. These comparsons are use to show the effectveness of each moel an to show whch of them s robust moel. Table 2 shows the motor parameters. Durng the smulatons, the torque set value s lmte to 2 N.m. In all fgures the tme axs s n secons. Here the smulaton stues two cases 1. Motor startng wth loang. 2. Suen apple loa. Where t s foun that, 8.1. The frst case In fgure 6, q axes currents are smulate. In conventonal moel fgure 6. (a), the q axes currents s hghly storte. In mofe moel wth PI torque current controller fgure 6. (b), the q-axs current s mofe an closest to the best value whle the -axs current s mprove but sn t reache the best value. In mofe moel wth two PI controllers (PI controllers for torque an flux) fgure 6. (c), both q-axs current component an -axs current component are closest to the best value. 486

7 Fgure 6. (a) Iq-axs current wth conventonal metho Fgure 6. (b) Iq -axs current wth mofe PI controller for torque only Fgure 6. (c) Iq -axs current wth mofe PI controllers for torque an flux In fgure7, the stator flux s smulate. Wth mofe control (PI controllers for torque an flux) fgure 7. (c), the storton n the flux s suppresse f t s compare to conventonal metho fgure 7. (a), an mofe metho wth one PI controller (torque current controller) fgure 7. (b). 487

8 Fgure 7. (a) Stator flux wth conventonal metho Fgure 7. (b) Stator flux wth mofe PI controller for torque only Fgure 7. (c) Stator flux wth mofe PI controller for torque an flux The torque response n fgure 8 showe that, the torque rpple s approxmately vanshe wth two mofe control (two PI controllers an one PI controller) fgure 8. (c) an fgure 8. (b) f t s compare to the conventonal metho fgure 8. (a). Ths s because the mprovement occurre n q-axs current component. 488

9 Fgure 8. (a) Torque wth conventonal metho Fgure 8. (b) Torque wth mofe PI controller for torque only Fgure 8. (c) Torque wth mofe PI controller for torque an flux Fgure 9 shows some nose n the spee wth conventonal metho fgure 9. (a) f t s compare to the mofe metho (two PI controllers an one PI controller) fgure 9. (c) an fgure 9. (b). Ths s because the torque rpple reaches the best value wth mofe methos. 489

10 Fgure 9. (a) Spee wth conventonal metho Fgure 9. (b) Spee wth mofe PI controller for torque only Fgure 9. (c) Spee wth mofe PI controller for torque an flux In fgure 10, the stator currents become smoother wth mofe metho (PI controllers for torque an flux) fgure 10. (c) but wth usng torque current controller only fgure 10. (b), the mofe n the current s less smoother. Ths occurs ue to hghly reucton of the nose n the stator flux an suppresses n electromagnetc nterference wth two PI controllers. In conventonal metho fgure 10. (a), the stator current s hghly storte ue to nose n the stator flux an electromagnetc nterference. 490

11 Fgure 10. (a) Stator current wth conventonal metho Fgure 10. (b) Stator current wth mofe PI controller for torque only Fgure 10. (c) Stator current wth mofe PI controller for torque an flux 8.2. The secon case Here the motor start wthout loa, at 0.1 sec. suen loa s apple, at 0.25 the loa s suenly remove where t s foun that, hghly storte n q-axs currents wth conventonal metho even wth startng wthout loa but wth moulate metho (PI controllers for torque an flux) the storton s vansh. In the mofe metho wth one PI 491

12 torque current controller, the q-axs current becomes mprovement but the mprovement n the -axs current component s lmte. Ths s shown n fgure 11. Fgure 11. (a) Iq -axs current wth conventonal metho Fgure 11. (b) Iq -axs current wth mofe PI controller for torque only Fgure 11. (c) Iq -axs current wth mofe PI controller for torque an flux In fgure 12 when compare to the stator flux wth three methos uner scusson( conventonal fel orente control, fel orente control wth PI torque current control an fel orente control wth two PI controllers for torque an flux ), t s best mprovement occurrng wth PI controllers for torque an flux. 492

13 Fgure 12. (a) Stator flux wth conventonal metho Fgure 12. (b) Stator flux wth mofe PI controller for torque only Fgure 12. (c) Stator flux wth mofe PI controller for torque an flux In fgure 13. The rpple torque s reuce wth mofe methos ths occurs ue to less n the electromagnet nterface. 493

14 Fgure 13. (a) torque wth conventonal metho Fgure 13. (b) torque wth mofe PI controller for torque only Fgure 13. (c) Torque wth mofe PI controllers for torque an flux Fgure 14 shows some nose n the spee wth conventonal metho f t s compare to the mofe methos. 494

15 Fgure 14. (a) spee wth conventonal metho Fgure 14. (b) Spee wth mofe PI controller for torque only Fgure 14. (c)spee wth mofe PI controller for torque an flux In Fgure 15, the stator currents become smoother wth mofe metho (PI controllers for torque an flux) ue to reucton of the nose n the stator flux an suppresses n electromagnetc nterference. Wth two PI controllers, the stator currents become approxmately zero uner no loa but wth conventonal metho these currents on t equal to zero ue to nose, harmoncs an electromagnet nterface. 495

16 Fgure 15. (a) Stator current wth conventonal metho Fgure 15. (b) Stator current wth mofe PI controller for torque only Fgure15. (c) Stator current wth mofe PI controller for torque an flux 9. CONCLUSION Ths paper s ntrouce two new PI controllers to suppress the harmoncs, torque rpples, nose an electromagnetc nterference. These PI controllers are affectng the nverter swtchng frequency. These controllers are reucng the rpples n the torque an current. The stator currents become smoother wave form. The results show that, the q-axs current becomes smoother whch reflects on the motor torque to keep qut operaton. The -axs current reuce to zero whch reflects on the stator flux lnkage. It becomes storton less an leas to reucng the coggng torque. 496

17 Type of control Tratonal metho Propose metho wth mofe PI controller for torque only Propose metho wth mofe PI controllers one for the torque an other for flux Table 1 Rpple torque THD n the % current % Table 2 Number of pole P 4 Stator resstance r 5.8 Ohm -axs nuctance 44.8 mh q-axs nuctance Permanent magnet flux L L q m mh 533 mwb Inerta constant J N.m S 2 Frcton constant 0 Loa torque T Reference spee L m Abbrevatons: DC: Drect current motor. FOC: Fel orente control. PM: Permanent magnet. PMSM: Permanent magnet synchronous motor. Lst of symbol 2 N.m 70 ra/s,, as bs : The nstantaneous stator phase currents. cs : -axs stator current referre to rotor. * : -axs stator reference current referre to rotor. : q-axs stator current referre to rotor. q * : q-axs stator reference current referre to rotor. q J : Moment of nerta k k L L p q : Proportonal gan : ntegral gan : -axs nuctance. : q-axs nuctance. P : Number of pole r T : Stator resstance m em L e6h : Develope torque. : Mutual torque. : Loa torque. : Sx harmoncs torque : Frcton constant : fferentaton operator. t m : mechancal spee of the motor. e : The electrcal frequency. r : The electrcal rotor spee. : Permanent magnet flux m, : Sx an twelve -axs flux 6 12, : Sx an twelve q-axs flux q6 q12 REFERENCES [1]. Goe, I. a Slva an P. Jose, A. Sern, A hybr controller for the spee control of a permanent magnet synchronous motor rve, Control Engneerng Practce, Vol. 16, Issue 3, pp , March, [2]. J. Dxon, S. Tepper an L. Moran, Practcal evaluaton of fferent moulaton technques for current controlle voltage-source nverters, IEE Proc,-Electr. Power appl, vol. 143, no. 4, July, 1996, pp [3]. M. P. Kazmerkowsk, an L. Malesan, Current control technques for three-phase voltage-source PWM converters: a survey, IEEE Trans. In. Electron., vol. 45, no. 5, October, 1998, pp [4]. V.Petrovc an R.Ortega, Desgn an Implementaton of an Aaptve Controller for Torque Rpple Mnmzaton n PM Synchronous Motors, IEEE Transactons on Power Electroncs, VOL. 15, NO. 5, 2000, pp [5]. J. Y. Hung an Z. Dng, Desgn of currents to reuce torque rpple n brushless permanent magnet motors, Proc. Inst. Elect. Eng. B, vol. 140, no. 4, 1993, pp [6]. J. Holz an L. Sprngob, Ientfcaton an compensaton of torque rpple n hgh-precson permanent magnet motor rves, IEEE Trans. In. Electron., vol. 43, Aprl, 1996, pp [7]. Vlaan Petrovc, Romeo Ortega, Aleksanar M. Stankovc, an Glea Tamor, Desgn an Implementaton of an Aaptve Controller for Torque Rpple Mnmzaton n PM Synchronous Motors, IEEE Transactons on Power Electroncs, VOL. 15, NO. 5,, pp , SEP [8]. K. Gulez, A.A. Aam, I.E. Buzcu, H. Pastacı, Usng passve flters to mnmze torque pulsatons an noses n surface PMSM erve fel orente control, Smulaton Moelng Practce an Theory pp th August, [9]. K. Gulez, A.A. Aam, Reucton of torque pulsaton an noses n PMSM wth hybr flter topology, Smulaton Moelng Practce an Theory pp , 19th August, [10]. Ln Mathew1 an Vvek Kumar Paney Desgn an evelopment of fuzzy logc controller to control the spee of permanent magnet synchronous motor, Journal of Electrcal an Electroncs Engneerng Research Vol. 3(3), pp.52-61,feb [11]. L. Harnefors an H.-P. Nee, Moel-base current control of AC machnes usng the nternal moel control metho, IEEE Transactons on Inustry Applcatons, vol. 34, no. 1, pp , Jan./Feb [12]. L. Harnefors, K. Petl anen an L. Gertmar, Torque maxmzng fel weakenng control: esgn, analyss an parameter selecton, IEEE Transactons on Inustral Electroncs, vol. 48, no. 1, pp , Feb