INSTANTANEOUS TORQUE CONTROL OF MICROSTEPPING BIPOLAR PWM DRIVE OF TWO-PHASE STEPPING MOTOR

Transcription

1 The 5 th PSU-UNS Internatonal Conference on Engneerng and 537 Technology (ICET-211), Phuket, May 2-3, 211 Prnce of Songkla Unversty, Faculty of Engneerng Hat Ya, Songkhla, Thaland 9112 INSTANTANEOUS TORQUE CONTROL OF MICROSTEPPING BIPOLAR PWM DRIE OF TWO-PHASE STEPPING MOTOR Weerasak Chachan 1, Mongkol Konghrun 1, and Kanokvate Tungpmolrut 2 1 Kng Mongkut s Unversty of Technology Thonbur (KMUTT),Faculty of Engneerng Department of Electrcal Engneerng, Thaland 2 Natonal Electroncs and Computer Technology Center, Thaland Authors to correspondence should be addressed va emal: sakchachan@hotmal.com Abstract: Tradtonally, the speed of hybrd steppng motor s manly controlled by adjustng the steppng rate. The motor s generally drven by the rated motor current such that t can drve as hgh load torque as possble. The open-loop drve s also preferred due to smplcty. Unfortunately, ths s not effcent way of motor operaton, especally at lght load condtons. In addton, the tradtonal full-step and half-step controls could cause the problems related to the torque and speed rpples. Ths paper proposes the nstantaneous torque control to solve the mentoned known problems. The mcrosteppng bpolar PWM drve for two-phase steppng motor s mplemented. A three-phase voltage source nverter s employed to drve the two-phase steppng motor, usng space-vector pulse wdth modulaton (SPWM) technque. The step resoluton can be adjusted by usng the confgurable zero-order-hold (ZOH). The nstantaneous torque control of mcrosteppng drve s mplemented on a fxed-pont TMS32F2812 DSP. The expermental results have shown the successfully mplemented system. Key Words: Instantaneous Torque /Mcrosteppng /PI Controller /Steppng motor /Zero-Order-Hold 1. INTRODUCTION Hybrd steppng motors are popular n the poston control such as CNCs, plotters, etc. because ther control schemes are easy. The tradtonal full-step and half-step controls could cause oscllaton, resonance, rpples of torque and speed [1]. In addton, the motor drven wth the rated current s not effcent way, especally at lght load condtons. In hgh performance applcatons, the mcrosteppng drve and the nstantaneous torque control are necessary to solve these problems. In lteratures, the current control schemes for mcrosteppng drve usng a three-phase voltage source nverter have been presented n [2] and [3]. The three-phase voltage source nverter s manly controlled by usng space-vector pulse wdth modulaton (SPWM) scheme for a two-phase motor. In [4] and [5], the torque control schemes of steppng motor are presented. However, the poston sensor was used n these researches. Thus, the total cost of the control scheme s ncreased. In [6], the nstantaneous torque of hybrd steppng motor was presented. The topology of converter crcut s the conventonal H-brdge. The dsadvantages of the H-brdge converter when compared wth the three-phase nverter were well descrbed n [2]. In ths paper, the nstantaneous torque control of mcrosteppng bpolar PWM based dgtal for two-phase steppng motor s proposed to mprove the motor operaton. The topology of converter crcut s the conventonal three-phase nverter, usng space vector pulse wdth modulaton (SPWM) technque. 2. TECHNICAL BACKGROUNDS 2.1. Electromagnetc torque of two-phase hybrd steppng motor Electromagnetc torque equaton for two-phase hybrd steppng motor has been well descrbed n [7]. Bascally, the motor torque s produced by the nfluence of stator and rotor flux lnkages. The magntude of stator flux lnkage depends on the phase current. Two phase currents of steppng motor n the mcrosteppng drve can be expressed as follows: I s the magntude of phase current; ω s the exctaton frequency; t s the tme. (1) (2)

2 538 Also, two stator flux lnkages can be calculated n equatons (3) and (4), respectvely. The magntude of total stator flux equaton can be wrtten as k 1 (3) (4) (5) s the total stator flux magntude;, s the phase A and phase B flux lnkages, respectvely; s the torque constant (same for both phases). The electromagnetc torque of each phase wndng of steppng motor has already been derved as τ s the electromagnetc torque; Φ R s the rotor flux magntude; δ (6) s the angle between the stator and rotor flux lnkages (.e., load angle). Accordng to equaton (6), the electromagnetc torque vares as a snusodal functon of the load angle for any gven constant magntude of phase current. Stator and rotor flux lnkage vectors relatve to an orthogonal statonary reference frame s shown n Fg. 1. Phase dfference between stator and rotor flux lnkage vectors s actually the load angle, varyng between - radans. SPWM scheme. Upper and lower swtchng devces n each leg (.e., S1-S2, S3-S4, S5-S6) are always excted alternatvely and formulated as S2=1-S1, S4=1-S3, S6=1-S5 Sx = or 1. In Table 1, all possble voltage vectors generated by the three-phase nverter crcut for two-phase motor s shown [8]. As seen n ths Table, the phase voltage has three values:,, or. All voltage vectors can be drawn n the voltage spacevector dagram for three-phase nverter drvng twophase motor n the Fg. 3. Notce that the and 7 are zero voltage vectors. Accordng to ths dagram, the waveforms of two-phase voltages generated by these voltage vectors can be depcted n Fg S1 S2 a S3 S4 b S5 S6 Hybrd SM Fg 2. Three-phase nverter crcut for two-phase steppng motor. Referrng to Fg. 2, the phase voltages n the statonary reference frame can smply be calculated by the nverter leg voltages as follow., are the motor phase voltages n the statonary frame;,, are the nverter leg voltages; s. For the reference phase voltages n statonary reference frame, the references of nverter leg voltages can be computed as follows. c (7) (8) wher, are the reference phase voltages. The can be calculated n Eq. (9) for SPWM. (9) Fg 1. Stator and rotor flux lnkage vectors n statonary reference frame 2.2. SPWM scheme for two-phase steppng motor. The SPWM scheme for two-phase steppng motor drven by three-phase nverter crcut s mplemented n ths paper. Three-phase voltage source nverter connectng to two stator wndngs of motor s shown n Fg. 2. All swtchng devces are controlled by means of s the dc bus voltage;, s the maxmum and mnmum voltages, respectvely. These voltages are defned as follow. (1) (11)

3 539 Table 1. oltage vectors generated by three-phase nverter for two-phase steppng motor S1 S3 S5 α β I 5 III,7 q-axs 3 6 II I I 1 2 d-axs Fg 3 oltage space-vector dagram for three-phase nverter drvng two-phase steppng motor. I II III I I I the torque block. The outputs of ths block s the dq-axs reference currents ( and ). Ths would be vared accordng to the load torque. Then, the d-axs reference currents ( ) s smply computed n Eq. (12). As changed, the measured peak current ( ) s changed as well. The measured peak current ( ) can be smply calculated n Eq. (13). Thus, the dq-axs reference currents ( and ) can be obtaned. The PI current s are used to control each axs n the current loop, gvng the dq-axs reference voltages ( and ). Next, the SPWM block obtans these voltages transformed to the reference phase voltages n αβ-axs reference frame through the nverse park transformaton wth the dscrete angle ( ). The current feedback ( and ) can be obtaned through the transformaton from the αβ-axs reference current ( and ) to dq-axs reference current feedback ( and ) by the park transformaton, then the current loop s realzed. Fnally, the nstantaneous torque control s establshed. The step resoluton for mcrosteppng drve can be adjusted by the confgurable zero-order-hold ZOH block. The measured stator currents are converted to dgtal sgnals by on-chp 1-bt ADC nsde the DSP. The overall flowchart of nstantaneous torque control of mcrosteppng bpolar PWM based dgtal for two-phase steppng motor s shown n Fg 6. Notce that the torque control loop s confgured to be executed slower than the current loops because the mechancal tme constant s longer than the electrcal tme constant. In ths paper, the prescaler s set to 2. In Fg 6, ths prescaler has been establshed by ntroducng the condtonal branch of <count = 2 >. (12) dc dc dc t t (13), are the dq-axs reference currents, respectvely; s the measured peak current;, are the measured currents n the statonary frame. dc Fg 4 Motor phase voltages. 3. INSTANTANEOUS TORQUE CONTROL OF MICROSTEPPING BIPOLAR PWM DRIE Overall block dagram of the mplementng system s shown n Fg. 5. In ths Fg., the snusodal functon of the load angle s computed n the error computaton block. In the error computaton block, the snusodal functon of the load angle ( ) s computed and sent to Error computaton S dsc. con. Torque d q q d ZOH Current Current d q q d dsc. 2 phase SPWM Inverse Park Trans. dsc. Park transformaton PWM1 PWM2 PWM3 PWM4 PWM5 PWM6 Hybrd Steppng motor Fg 5 Overall block dagram of proposed system 3-phase nverter

4 54 ISR start Current meas. Generate Ramp Generate Angle by ZOH module Park Trans. Calculate the load angle Count = prescaler?? Yes Count = Torque Controller d,q currents PIs. Inverse Park Trans. No Count + 1 Error Computaton Space-ector PWM Generate 3 Phase Inverter PWM Fg. 7 Fltered nverter leg voltages at 2 Hz, 1/16 step End Fg 6. Flowchart of proposed system 4. EXPERIMENTAL RESULTS In ths paper, all algorthms are mplemented on a fxed-pont, 15-MHz TMS32F2812 DSP. The ISR/ADC samplng/swtchng frequency s set at 1 khz. The parameters of two-phase steppng motor are summarzed as follows: Phase resstor = 3.4 Ω Phase nductance = 26 mh. Ratng: 3 A and 1.8 º step angle Expermental results can be shown n Fgs 7 through 11. In these results, the dc bus voltage of three-phase nverter s 2 and the output frequency s confgured at 2 Hz. The step resoluton s adjusted by the confgurable zero-order-hold. In the test, the motor s operated at 1/16 of full step (.e.,.1125º/step). Fg. 7 shows the fltered nverter leg voltages, whch are computed by equaton (8). The characterstc of SPWM technque s depcted. In Fg. 8, the fltered phase voltages computed by equaton (7) and formulated as α= a-c, β= b-c s shown. Clearly, two fundamental phase voltages are snusodal waveform and have 9 o dfference. Fg. 9 shows the phase currents responses when the motor was runnng at a lght load (T L =.15 N.m). Fgs. 1 and 11 show the results of phase currents when the load torque s ncreased to.3 and.6 N.m, respectvely. Referrng to these results, the phase currents can be vared when the load torque s changed. Thus, the mplementng system can effectvely drve the steppng motor n the effcent way. Fg 8 Fltered phase voltages at 2 Hz, 1/16 step Fg. 9 Torque and phase currents at 2 Hz, 1/16 step, and T L =.15 N.m (lght load).

5 6. ACKNOWLEDGMENT 541 The fnancal support from Thaland graduate nsttute of scence and technology (TGIST) s acknowledged. The scholarshp recpent code s the TG M. Fg. 1 Torque and phase currents at 2 Hz, 1/16 step, and T L =.3 N.m Fg. 11 Torque and phase currents at 2 Hz, 1/16 step, and T L =.6 N.m 5. CONCLUSIONS In ths paper, the nstantaneous torque control scheme of mcrosteppng bpolar PWM drve system for twophase steppng motor has been proposed. The drve optmzes the phase current level of steppng motor vares accordng to the load torque. The topology of converter crcut s the three-phase voltage source nverter, usng space vector pulse wdth modulaton (SPWM) technque. The step resoluton s adjusted by usng the confgurable zero-order-hold (ZOH). Accordng to the expermental results, the overall hardware and software algorthms of proposed system have been successfully mplemented. The magntude of two phase currents s effectvely vared as load changes. The expermental results have confrmed the successful nstantaneous torque control of mcrosteppng bpolar PWM based dgtal 7. REFERENCES [1] K. Inaba, Y. Noda, T. Myosh and K. Terashma, Drvng Control consderng Torsonal braton Suppresson n a Steppng Motor wth a Full-step Drve, IEEE Internatonal conference. Industral Electroncs, pp , 29. [2] S.-M. Yang, F.-C. Ln, and M.-T. Chen, Mcrosteppng control of a two-phase lnear steppng motor wth three-phase SI nverter for hgh-speed applcaton, IEEE Transacton on ndustry Applcatons, vol.4, no.5, pp , September/October 24. [3] C. Yodsant, and M. Konghrun, Implementaton of two-axs hghly accurate poston control of spacevector PWM based mcrosteppng bpolar drve, IEEE Internatonal conference. Electrcal machnes and systems, pp , October 28. [4] G. Hanyng, C. Shukang, and K. Erlang, Maxmum torque/current control of 2-phase hybrd steppng motor, IEEE Internatonal aeqean conference. Electrcal machnes and Drve, vol.3, pp , 23. [5] X. Danguo, W. Panha, Integrated Poston Sensor Based Self-tunng PI Speed Controller for Hybrd Steppng Motor Drve, IEEE Internatonal conference. Power Electroncs and Moton Control, vol.3, pp ,24. [6] N. Matsu, M. Nakamura and T. Kosaka, Instantaneous Torque Analyss of Hybrd Steppng Motor, IEEE Transacton on ndustral Applcatons, vol.32, no.5, pp , September/October [7] J.D. Wale, C. Pollock, A low-cost sensorless technque for load torque estmaton n a hybrd steppng motor, IEEE Transacton on ndustral Electroncs, vol.46, no.4, pp , Aug [8] M.B. de R. Correa, C. B. Jacobna, A. M. N. Lma, and E. R. C. da Slva, A three-leg voltage source nverter for two-phase ac motor drve system, IEEE power Electroncs Specalsts Conference, vol. 3, pp , 21.