Published in IET Electric Power Applications Received on 16th January 2008
Revised on 9th April 2008 doi: 10.1049/iet-epa:20080017
ISSN 1751-8660
Low-speed performance comparisons
of back-EMF detection circuits with
position-dependent load torque
H.-C. Chen T.-Y. Tsai C.-K. Huang
*
Department of Electrical and Control Engineering, National Chiao Tung University, Hsinchu, Taiwan, Republic of China
*Also an associate researcher in the Energy and Environment Laboratories, Industrial Technology Research Institute, Hsinchu, Taiwan, Republic of China
E-mail: [email protected]
Abstract: Because of the widely used brushless DC motors (BDCMs) in high-efficiency variable-speed compressors, many sensorless controls with square-wave operation had been developed in the literatures. Recently, more and more low-production-cost BDCM-type compressors with position-dependent load torque, such as rotary compressors, are applied to the residential products, which lead to the importance of low-speed performance of sensorless control. The authors address the low-low-speed performance comparisons between two common back-EMF detecting circuits (BEDCs). Without using the actual refrigerant system, a Motor-Generator set coupled with a disk and copper cylinder are also built up to serve as the experimental position-dependent load torque. From the simulated and experimental results, one of the BEDCs is better than the other one for the low-speed application of position-dependent load torque.
1
Introduction
Because of the rotor permanent-magnetic field, brushless DC motors (BDCMs) possess higher efficiency than the popular induction motors (IMs). Additionally, for variable-speed IMs, only relatively sinusoidal-current operations can be used to maintain efficiency. But in the control of variable-speed BDCMs, square-wave current with rich harmonic currents can be drawn without the loss of high efficiency. Therefore more and more BDCMs are used in high-efficiency residential applications – variable-speed refrigerant systems, including compressor motors and fan motors.
In the normal operations of BDCMs, the discrete rotor positions should be monitored by the mounted position sensors to yield adequate current commutations. However, in refrigerant system, the temperature in the hermetic compressors is usually more than 90 8C, which would result in the failures of Hall position sensors. It follows that the sensorless control techniques without position sensors become important in the applications of BDCMs to variable-speed refrigerant systems.
In the last decades, many sensorless controls with square-current operation had been proposed in the literature and they can be divided into several groups [1]. The group of back-EMF detecting methods commutates the winding currents according to the detected rotor positions from the back-EMF detecting circuits (BEDCs) because the rotor position can be found from the back-EMFs of BDCMs and back-EMFs can be sensed from the terminal voltages of the unexcited phase[2 – 9].
Based on the frequency responses of passive filters, one type of back-EMF detecting circuit (named BEDC-I) including band-pass and low-pass filters had been proposed in [2 – 7]. In [2 – 4], three Y-connected band-pass filters are used to attenuate the dc and high-frequency PWM voltages in the terminal voltages. The position signals are estimated from the comparisons of three filtered signals with their pseudo-neutral signal. In [5, 6], position signals are obtained from the comparisons of two of the three filtered signals. Low-cost back-EMF detecting circuit including only one band-pass filter and using one terminal voltage had been used in [7] to obtain the position signal.
The detailed analysis of band-pass filter and discussion can be found in[5, 6].
Meanwhile, another type of back-EMF detecting circuit (named BEDC-II) with three Y-connected low-pass filters used in[8, 9]can also be found. It is noted that these low-pass filters are used to attenuate the injected noise, rather than to attenuate the PWM voltage components. The position signals can be estimated by comparing the three filtered signals with the filtered DC-link voltage. However, in BEDC-II, the feedback position signals with PWM fluctuations cannot be directly used to commutate the motor currents. Therefore a complicated phase shift function should be implemented in the BEDC-II’s commutating signal generator with integrated circuit [8]
and MCU/DSP[9].
Recently, because of the low-cost trend of high-efficiency variable-speed refrigerant products, low-production-cost rotary compressors are widely used in the residential applications. From the view of load characteristics, the rotary compressor possesses position-dependent load torque[10, 11]
where its maximum load torque in specific position may be near four times its minimum load torque. It follows that the instantaneous speed of BDCM fluctuates around its average speed. Unfortunately, this speed deviation becomes relatively large, especially at low speed, which would introduce disparate position errors to BEDCs and degrade the low-speed performance of the sensorless control.
In fact, compressor motors in variable-speed refrigerant products run at low speed most of the time. That is, the low-speed performance of sensorless BDCMs control is more important than the high-speed performance. In[12], the high-speed performances of sensorless control with PWM inverter and variable DC-link inverter had been addressed. It shows that the current commutation error resulting from PWM period has a great effect on the high-speed performances of sensorless control. However, no low-speed performance comparisons of sensorless BDCM control can be found in the literatures.
Therefore in this paper, the low-speed performances of two sensorless controls with circuits BEDC-I and BEDC-II are studied and analysed. The result shows that position-dependent load torque would produce significant position-dependent detecting errors, especially at low speed. That is, the low-speed performance of sensorless control is highly related to the induced position-dependent detecting error. The simulation and experiment including both BEDCs and their sensorless controls had been finished. The simulated and experimental data demonstrate the results of analysis.
2
Sensorless BDCM control
Compared with the variable-speed IMs, BDCMs can be controlled with square-wave currents without loss of their
efficiencies. Both 1208-conduction method and 1808 -conduction method are able to draw square-wave currents and the main difference between them is that there is always one unexcited phase in the former, and no unexcited phase in the latter. Therefore the former is always used in the square-current sensorless controls [2– 9, 11 – 13] for that the motor positions can be known by sensing the zero crossing points (ZCPs) of back-EMFs from the approximations of motor terminal voltage and the BDCM back-EMF in the unexcited phase.
In addition, adjusting the average motor terminal voltages to regulate the motor speed is the simplest variable-speed control of BDCMs in refrigerant systems. By considering the complication of implementation, pulse width modulation (PWM) scheme with six power switches to adjust the average motor terminal voltages is better than the scheme of changing the dc-link voltage because of its extra switch[12].
Therefore the configuration of square-current sensorless control with PWM scheme is illustrated in Fig. 1 where BEDC obtains the position signals HU, HV and HW from
the inverter and motor terminal voltages VP, VN, VU, VV
and VW. By using the above position signals HU, HV and
HW, commutation signal H and speed vr can be obtained
and then, the speed controller tunes the PWM duty ratio adequately according to the speed difference between speed command vr and the estimated speed vr. Then, the
switching signal generator yields the six gate signals GT 1,
GT 2, GT 3, GT 4, GT 5and GT 6according to the commutation
signal H and PWM duty ratio to yield square-wave currents adequately. Voltages eU, eV and eW are the
back-EMFs of the two identified BDCMs coupled together.
Four common 1208 square-wave PWMs (SWPWMs) as shown in Fig. 2 can be found in the sensorless BDCM control where only upper or lower switch of one leg is conducting with PWM. The 1208 SWPWMs from
Fig. 2a– 2d are named fully upper PWM (FUPWM)[2 –7, 11], fully lower PWM (FLPWM) [13], alternatively leading PWM (ALeadPWM) [12] and alternatively lagging PWM (ALagPWM)[8, 9], respectively.
The waveforms of terminal voltages for various SWPWMs can be found in Fig. 2and all their expressions for various switching-signal states are tabulated in Table 1. The states A, B, C, D, E, F can be found in ALagPWM and the states I, J, K, L, M, N can be found in ALeadPWM. In addition, FUPWM and FDPWM include states A, C, E, J, L, N and states B, D, F, I, K, M, respectively.
3
BEDC-I
BEDC-I is plotted in Fig. 3 where three identical circuit networks are Y-connected and four terminal voltages VN,
HV and HW are generated from the comparisons between the
pseudo-neutral signal vn and the filtered signals vU, vV, vW, respectively. Since the commutation intervals are 608 electrical degrees in 1208 SWPWM, the desired winding current commutation should occur at (308 þ k 608) lagging behind the ZCPs of back-EMFs where k is an integer to operate BDCM efficiently. Thus, by using the phase response of circuit networks, BEDC-I is designed to detect the points of 908 lagging behind the ZCPs of back-EMFs.
3.1 Circuit analysis
The individual circuit network can be seen as a low-pass filter cascaded with a band-pass filter where the former provides 908-delay relation and the latter keeps the signal gain constant during the BDCM speed range from vrlow
through vrhigh in rpm. when a P-poles BDCM operating at
vr(rpm), the fundamental frequency f1¼pvr=120 (Hz) of
back-EMF and terminal voltage is located in the range from flow to fhigh
fLow¼ PvrLow 120 f1 ¼ Pvr 120 PvrHigh 120 ¼fHigh (1) To keep near 908 phase shifting during BDCM speed range in (1), the lowest fundamental frequency fLowfrom the lowest
speed vrLow should be significantly higher than the
cut-frequency fLPI of the low-pass filter
fLowfLPI¼
R11þR12
2pR11R12C11
(2)
The frequency response of band-pass filter shown inFig. 3
can be derived as FBP( jf1) ¼ jf1 fBP1 1 þ jf1=fBP1 1 1 þ jf1=fBP2 (3)
where fBP1 and fBP2 (,fBP1) are the corner frequencies of
band-pass filter. Figure 2 1208 SWPWMs a FUPWM b FLPWM c ALeadPWM d ALagPWM
fBP1 ¼ 1 2pC12R13 (4) fBP2 ¼ 1 2pC13R14 (5)
To keep the magnitude of the filtered constant during the BDCM speed range, the lowest fundamental frequency fLow should be larger than the corner frequency fBP1 and
the highest fundamental frequency fHigh should be smaller
than the corner frequency fBP2. On the other hand, the
PWM frequency fPWM should be larger than the corner
frequency fBP2 to attenuate the PWM voltage components
Table 1 Expressions of terminal voltages for all switching states
State Always OFF Always ON PWM ON/OFF VU VV VW
A GT 2GT 3GT 4GT 5 GT 1 GT 6ON Vdc 0 0.5Vdcþ 1.5eW GT 6OFF Vdc Vdc Vdcþ 1.5eW B GT 3GT 4GT 5GT 6 GT 2 GT 1ON Vdc 0.5Vdcþ 1.5eV 0 GT 1OFF 0 1.5eV 0 C GT 1GT 4GT 5GT 6 GT 3 GT 2ON 0.5Vdcþ 1.5eU Vdc 0 GT 2OFF Vdcþ 1.5eU Vdc Vdc D GT 1GT 2GT 5GT 6 GT 4 GT 3ON 0 Vdc 0.5Vdcþ 1.5eW GT 3OFF 0 0 1.5eW E GT 1GT 2GT 3GT 6 GT 5 GT 4ON 0 0.5Vdcþ 1.5eV Vdc GT 4OFF Vdc Vdcþ 1.5eV Vdc F GT 1GT 2GT 3GT 4 GT 6 GT 5ON 0.5Vdcþ 1.5eU 0 Vdc GT 5OFF 1.5eU 0 0 I GT 2GT 3GT 4GT 5 GT 6 GT 1ON Vdc 0 0.5Vdcþ 1.5eW GT 1OFF 0 0 1.5eW J GT 3GT 4GT 5GT 6 GT 1 GT 2ON Vdc 0.5Vdcþ 1.5eV 0 GT 2OFF Vdc Vdcþ 1.5eV Vdc K GT 1GT 4GT 5GT 6 GT 2 GT 3ON 0.5Vdcþ 1.5eU Vdc 0 GT 3OFF 1.5eU 0 0 L GT 1GT 2GT 5GT 6 GT 3 GT 4ON 0 Vdc 0.5Vdcþ 1.5eW GT 4OFF Vdc Vdc Vdcþ 1.5eW M GT 1GT 2GT 3GT 6 GT 4 GT 5ON 0 0.5Vdcþ 1.5eV Vdc GT 5OFF 0 1.5eV 0 N GT 1GT 2GT 3GT 4 GT 5 GT 6ON 0.5Vdcþ 1.5eU 0 Vdc GT 6OFF Vdcþ 1.5eU Vdc Vdc Figure 3 BEDC-I
at the filtered voltages vU, vV and vW. Consequently, the
relation of above critical frequencies can be expressed as fLPIfBP1, fLow f1 fHigh, fBP2 , fPWM (6)
3.2 1208 SWPWM
Using various 1208 SWPWM in BDCM operation results in various motor terminal voltages as shown inFig. 2. It is noted that all the various terminal voltages possess the same magnitudes of fundamental and harmonic voltages. Consequently, all four 1208 SWPWM in Fig. 2 can be used with BEDC-I because the design of BEDC-I is based on the frequency response of passive filters. Fig. 4
shows the illustrated waveforms of BEDC-I where the filtered signal vU can be found to be 908 lagging behind
the ZCPs of back-EMFs. The position signals HU, HV and HWare square waveforms 1208 out of phase with each
other. To obtain adequate current commutation, the desired commutation signals H should be generated as shown inFig. 4.
3.3 Commutation signal generator
FromFig. 4, we can find that the edges of position signals HU, HV and HW occur at the desired commutation
instants. Thus, the block diagram of the commutation signal generator is plotted in Fig. 5 where the combined signal HX is generated from the exclusive-or (XOR)
operation of three position signals HU, HV and HW. Then,
the commutation signal H can be generated by using the common edge-trigger function. That is, it is easy to
implement the commutation signal generator for BEDC-I by using the general-purpose DSP/MCU [2, 3, 7].
3.4 Position-dependent load torque
For constant load torque, the instantaneous motor speed vr
in steady state can be seen as constant and equal to its average value ¯vr. Thus, all harmonic frequencies fh of
terminal voltage are integral multiples of the fundamental frequency f1corresponding to the motor speed vr.
fh¼hf1¼h
Pvr
120 (7)
where h is an odd integer .1. At low speeds, the fundamental frequency f1 is near the lowest fundamental frequency fLow
and thus, the lowest harmonic frequency 3f1 may be
smaller than the corner frequency fBP2 as shown inFig. 6a.
It follows that some low-speed position detection error may occur with constant load torque.
For position-dependent load torque, the instantaneous motor speed vr is varying around its steady-state average
value ¯vr. For 2-poles BDCMs, electrical frequency is equal
to the mechanical frequency and thus the speed variations due to position-dependent load torque would contribute to the same harmonic frequencies as the case of constant load torque in (7).
However, for multi-pole-pairs BDCMs (even pole number P . 2), electrical frequency is P/2 times the mechanical frequency and thus, the speed variations due to position-dependent load torque would lead to not only the harmonics fh in (7) but also the interharmonics fih in the
motor terminal voltages. For P-poles BDCMs (even P . 2), the interharmonic frequencies fih are
fih ¼hf1 1 +
2 k P
(8) where k is an integer from 1 to P 2 1 except 0.5P. For example, for a 4-pole BDCM, the induced interharmonic Figure 4 Illustrated waveforms for BEDC-I with FUPWM
Figure 5 Commutation signal generator for BEDC-I
Figure 6 Terminal voltage frequency spectrum and relationship between the various frequencies being discussed
a With constant load torque
frequency fih would be 0.5f1, 1.5f1, 4.5f1 . . . as shown in
Fig. 6b.
Obviously, from (8) and Fig. 6b, some resulting interharmonic frequencies fih are inevitably located in the
frequency band of band-pass filter from fBP1 to fBP2. It
means that the interharmonic frequencies fih due to
position-dependent load torque cannot be easily attenuated by the band-pass filter and would result in the undesired interharmonics. That is, additional undesired position detection error due to position-dependent load torque will be introduced into sensorless control through BEDC-I, especially at low speed.
4
BEDC-II
FromTable 1, when the SWPWM switching state is ON, the terminal voltages of unexcited phase are equal to
VX ¼0:5Vdcþ1:5eX (9)
where X may be U, V and W. t implies that comparing the terminal voltage Vxwith half DC-link voltage 0.5Vdcis able
to detect the ZCPs of back-EMF. Therefore BEDC-II is developed as plotted in Fig. 7 where four identified low-pass filters and all terminal voltages VP, VN, VU, VVand VW
are used[8, 9].
4.1 Circuit analysis
However, the equality in (9) is satisfied only when the PWM switching signal is ON. To exactly separate the ‘ON’ duration, the waveforms of terminal voltage must be preserved, not filtered. Therefore it follows that the low-pass filter in BEDC-II is not designed to attenuate the PWM component in the terminal voltage, but to reject the
switching noises. It follows that the cut-frequency fLPII of
the low-pass filter in BEDC-II must be much larger than PWM frequency fPWM
fLPII¼
R21þR22
2pR21R22C
fPWM (10)
It is noted that the PWM frequency fPWM for BEDC-I is
significantly larger than fLPI as shown in (6). Comparing
(10) with (6) also shows the main difference of circuit design between BEDC-I and BEDC-II.
To obtain filtered signal vpfrom the terminal voltages Vp
and VN, the value of resistor R23 must be the sum of the
values of R21and R22.
R23¼R21þR22 (11)
4.2 1208 SWPWM
From Fig. 2, we can find that the comparisons of the unexcited-phase terminal voltage and half DC-link voltage between commutation instants can be divided into two types. One type initially keeps fixed and then turns to change with PWM frequency until the coming of ZCPs of back-EMFs as shown in the dashed-block of Fig. 8. The other type initially changes with PWM frequency and then keeps fixed after ZCPs of back-EMFs. Using the common edge-trigger function is able to identify the ZCPs of back-EMFs from the former type.
Therefore strictly speaking, all four 1208 SWPWM in
Fig. 2 can be used with BEDC-II. However, by considering the complication of required edge-trigger function, only ALagPWM in Fig. 2d is suitable for BEDC-II for that all the comparisons are divided into the former types as shown inFig. 8.
4.3 Commutation signal generator
The block of commutation signal generator for BEDC-II is plotted in Fig. 9 where a multiplexer is used to select the unexcited-phase position signal by commutation signal H. To operate BDCM normally, we should commutate current adequately at (308 þ k 608) position behind ZCPs of back-EMFs. It implies that the detections of ZCPs from BEDC-II cannot directly be used as commutation signals. Thus, unlike the commutation signal generator of BEDC-I in Fig. 5, a phase shifter should be included in the commutation signal generator of BEDC-II. Because of the conduction of freewheeling diodes at the current commutation, the terminal voltage would be equal to Vdc or zero until line current returns to zero, which may
result in the failure detection of ZCPs. Therefore in the commutation signal generator, the single-edge-trigger function is designed to capture the first edge-change of signal HMUX and then, hold until the coming of active
reset signal Hreset. The reset signal Hreset is obtained from
Td-delayed commutation signal H. Finally, by shifting the
trigger signal Htrig with p=6, we can obtain the desired
commutation signal H.
4.4 Position-dependent load torque
In general-purpose DSP/MCU, the implementation of p/6 phase shifter is not easy and would take some fixed execution time. Generally speaking, the error of phase shifter at high speed is larger than the near zero error at low speed. It means that the phase shifter would introduce some error into the current commutation for BEDC-II, particularly at high speed and we should pay more attention to the performance of commutation signal generator as shown in
Figs. 5 and 9. Therefore to reduce the effect of phase shifter on commutation signal, many specific MCUs for the purpose of sensorless square-current operations have been developed[3, 14].
Since BEDC-II is designed based on the equality in (9), the ZCPs of back-EMFs can be exactly detected even under varying speed resulting from position-dependent load torque. Therefore the performance of BEDC-I dominates the performance of sensorless square-current operation. But for BEDC-II, its cooperating commutation signal generator would degrade the performance of sensorless square-current operation.
5
Simulation results
To evaluate the position detecting error Du of BEDC-I and BEDC-II, some simulation results are provided in this section. According to the circuit analysis in (1) – (11), the simulated parameters for various BEDCs are listed as
R11 ¼470 kV, R12 ¼47 kV, R13¼30 kV
R14 ¼2 kV, C11¼C12¼2:2 mF, C13¼470 nF
R21 ¼300 kV, R22¼12 kV, R23 ¼312 kV, C ¼ 330 pF
(12)
To evaluate the position detecting errors of both BEDCs fairly and avoid the error from commutation signal generators, the operations of BDCMs in simulation are operated with ‘sensor-feedback’. That is, the commutation signal H is directly generated from the position sensor. In addition, PWM duty ratio in simulation is given, not automatically tuned by speed loop. It follows that the simulated position detecting errors Du are introduced only from BEDCs. The parameters of simulated 4-pole BDCM are listed inTable 2.
5.1 Constant load torque
When a BDCM is operating with constant load torque, the motor speed can be seen as fixed and the resulting position error is constant. For constant load torque 1 N-m, the obtained average detecting errors Du by keeping the PWM duty ratio fixed from 20 to 80% can be tabulated in
Table 3. From Table 3, we can find that the position detection error Du of BEDC-II is small and near constant during the speed range. But for BEDC-I, the position detection error Du varies from negative value to positive value because of its frequency-dependent (i.e. speed-dependent) performance.
Figure 9 Commutation signal generator for BEDC-II
Table 2 Simulated parameters
stator resistance 0.7V
stator inductance Lq¼ 10.5 mH, Ld¼ 4 mH
voltage constant (line-to-line)
23.63 mVrms/rpm
speed range vr,Low¼ 1200 rpm,
vr,High¼ 6000 rpm
motor inertia 0.0004 kg2 m2
DC link voltage 300 V
PWM frequency 5 kHz
5.2 Position-dependent load torque
In the following simulation, the position-dependent load torque is given as
TL¼1 þ 0:5 sin ur(N m) (13)
where ur is the rotor position and its average torque is also
equal to the same value 1 N-m as the constant load torque in the previous section. By keeping the PWM duty ratio fixed at 20%, 50% and 80%, the simulated position detecting errors Du are plotted in Fig. 10a and 10b, respectively.
From Fig. 10a, we can find that position detecting error Du of BEDC-I changes with the rotor position ur,
especially at low speed. At high speed, the speed variation due to position-dependent load torque becomes small and thus the position detecting error Du is almost constant under various rotor positions ur. The simulated errors
shown in Fig. 10b indicate that both position detecting error of BEDC-II and its variation are small.
5.3 Comments
The error resulting from commutation signal generator has been removed in the above simulation. Obviously, the simulated results in Table 3 and Fig. 10 indicate that BEDC-II is better than BEDC-I during the entire speed range. However, the performance of sensorless operation is dependent on the commutation error, not only on the position detecting error of BEDC. It means that the performance of sensorless operation with BEDC-II may or may not be better than that with BEDC-I during various speeds.
6
Experimental results
To evaluate the low-speed performances of various BEDCs under position-dependent load torque, an experimental system is set up in the laboratory. It mainly consists of two identified BDCMs coupled to each other as plotted in
Fig. 1, an aluminium disk and a copper cylinder where the cylinder is fixed on the disk as shown in Fig. 11. All the motors and the disk are coupled to the unique shaft. The circuit parameters of used BEDCs and motor parameters of two used BDCMs in experiments are the same as (12) andTable 2.
The two coupled BDCMs can be seen as a Motor-Generator (M-G) set where the Motor-Generator-end terminals are connected to the Y-connected resistors as shown in
Fig. 1 to provide a constant load torque regardless of the rotor position. Besides, the copper cylinder on the disk contributes to a position-dependent load torque because of the unified direction of the gravity force. Since the weight
Figure 10 Simulated position detecting error with position-dependent load torque for
a BEDC-I b BEDC-II
Table 3 Position detection errorDu at constant load torque Duty Du 20% 30% 40% 50% 60% 70% 80% 1280 rpm 2000 rpm 2740 rpm 3470 rpm 4210 rpm 4940 rpm 5690 rpm BEDC-I 216.58 29.178 23.128 2.1558 6.6858 11.998 16.438 BEDC-II 3.4268 0.298 1.0748 1.018 0.8948 1.0828 0.668
of copper cylinder is 203.58 g and its distance to the couple is 5 cm, the resulting peak torque is near 0.2 N-m.
As shown in the dashed line of Fig. 1, all sensorless functions including commutation signal generator, speed estimation, speed controller and switching signal generator are digitally implemented in general-purpose MCU. The BDCM speed vr is estimated by the period TH of the
signal H vr ¼ 1 6TH 60 P=2¼ 20 PTH (rpm) (14)
The p=6 phase shifter is implemented by delaying the input signal Htrig with its half period Ttrig. It is noted that the
smaller the period Ttrig is, the larger is the delay error
caused by constant MCU execution time. Therefore the performance of commutation signal generators cannot be neglected in evaluating the performance of sensorless control. At low speeds (i.e. near vr,Low), the error due to fixed
execution time is relatively small and can be neglected. Therefore the current commutation error is dominated by the position detecting error of BEDC. The smaller position error may lead to small current commutation error and thus small current and small power at low speed.
Consequently, we turn to record the input power with various BDCM speed and position-dependent load torques. Relatively small input power implies that small position detecting error exists in the experiment. The Generator-end terminals are connected to three 5 V resistors to run at a relatively low speed.
With position-dependent load torque, the recorded BDCM speed vr and input power Pin for BEDC-I and
BEDC-II are plotted in Fig. 12. From Fig. 12, we can find that with the same BDCM speed, less power is required for BEDC-II than that for BEDC-I. Thus, BEDC-II actually yields better performance than BEDC-I at low speeds.
With the increase in speed, the fixed execution time would result in a relatively large phase error. Therefore the Figure 11 Experimental position-dependent load torque
Figure 13 Experimental waveforms of position signal HU,
motor winding current iU and terminal voltage VUfor
a BEDC-I with FUPWM b BEDC-II with FLagPWM
Figure 12 BDCM speed and input power with position-dependent load torque
commutation error for BEDC-II may be larger than that for BEDC-I at high speed (i.e. near vr,High ), though BEDC-II
is better than BEDC-I from simulation results.
At low speed (i.e. near vr,Low), the detection error of BEDC
can be well judged in the experiment. At high speed (i.e. near vr,High), it is hard to separate the BEDC error from the commutation error. Therefore the authors carefully claim that BEDC-II performs better than BEDC-I at low speeds, especially with position-dependent load torque.
The measured waveforms of position signal HU, current iU
and terminal voltage VU for BEDC-I with FUPWM and
BEDC-II with FLagPWM at near 1000 rpm are plotted in Fig. 13a and 13b, respectively. From Table 3, the simulated position error is about 168 at about 1000 rpm. Therefore BDCM sensorless control with BEDC-I work well with large position error. However, from the view of the simplicity of commutation signal generator, BEDC-I possesses competitive advantage in the high-speed application of sensorless control.
7
Conclusion
In this paper, the low-speed performances and comparisons of two BEDCs and their sensorless controls are studied under position-dependent load torque. The implementation of commutation signal generation is the only difference between the sensorless control of BEDC-I and BEDC-II. From the analysis, the implementation of sensorless control for BEDC-I is simpler than that for BEDC-II. However, BEDC-II yields less position detecting error than BEDC-I, especially at low speed. The simulation and experimental results also demonstrate the analysis result. It follows that BEDC-II is suitable in low-speed application of BDCMs.
8
Acknowledgment
This work was supported by the Energy R&D foundation funding provided by the Bureau of Energy, Ministry of Economic Affairs, in Taiwan.
9
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