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. 4.1, an aluminum disk and a copper cylinder where the cylinder is fixed on the disk as shown in Fig. 4.11. 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 (4.12) and Table 4.2.

The two coupled BDCMs can be seen as a Motor-Generator (M-G) set where the Generator-end terminals are connected to the Y-connected resistors as shown in Fig. 4.1 in order 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 of copper cylinder is 203.58g and its distance to the couple is 5cm, the resulting peak torque is near 0.2N-m.

MCU SPMC75F2413A is used to implement the control loop shown in Fig. 4.1. This MCU is able to provide two channels of 16 bit phase detecting control (PDC) timers for

capture function and PWM operation. The PDC timers are very useful for mechanical speed calculation.

Fig. 4.11. Experimental position-dependent load torque.

As shown in the dashed line of Fig. 4.1, 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

ω

_r is estimated by the period

T of the signal H

_H

) 20 (

2 / 60 6

1

rpm

PT P

T

_{H H}

r = × =

ω

(4.14)

The π

/ 6

phase shifter is implemented by delaying the input signal

H with its half

_trig

period

T . It is noted that the smaller period

_trig

T is, the larger delay error due to constant

_trig MCU execution time is. Therefore, the performance of commutation signal generators can not be neglected in evaluating the performance of sensorless control.

At low speeds (i.e. near

ω

_r,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.

copper cylinder

aluminum disk coupling

Copper Cylinder

Aluminum Disk Coupling

copper cylinder

aluminum disk coupling

Copper Cylinder

Aluminum Disk

Coupling

Consequently, we turn to record the input power with various BDCM speed and position-dependent load torque. Relatively small input power implies that small position detecting error exists in experiment. The Generator-end terminals are connected to three 5Ω resistors (

R

_g =5Ω) in order to run at relatively low speed.

With position-dependent load torque, the recorded BDCM speed

ω

_r and input power

P for BEDC-I and BEDC-II are plotted in Fig. 4.12. From Fig. 4.12, we can find that with

in

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 speed.

)(rpmrω

) (W

P_in

I BEDC − II

BEDC −

Fig. 4.12. BDCM speed and input power with position-dependent load torque.

With the increase of speed, the fixed execution time would result in relatively large phase error. Therefore, the commutation error for BEDC-II may be larger than that for BEDC-I at high speed (i.e. near

ω

_r,High), though BEDC-II is better than BEDC-I from simulation results.

At low speed (i.e. near

ω

_r,Low), the detection error of BEDC can be well judged in 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

H , current

_a

i and terminal voltage

_a

V

_a for BEDC-I with

120

^o SWPWM type-01_01 and BEDC-II with

120

^o SWPWM type-01_01 at near 1000rpm are plotted in Fig. 4.13(a) and Fig. 4.13(b), respectively. From Table 4.3, the simulated position error is about

16 °

at about 1000rpm. 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 sensolrss control.

5V

10A

200V 5ms Ha

ia

Va

(a)

5V

10A

200V 5ms Ha

ia

Va

(b)

Fig. 4.13. Experimental waveforms of position signal

H , motor winding current

_a

i and

_a terminal voltage

V for: (a) BEDC-I with

_a

120

^o SWPWM type-11_00; and (b) BEDC-II with

120

o SWPWM type-01_01

CHAPTER 5

TWELVE-STEP

BDCM SENSORLESS CONTROL

5.1 Introduction

In Chapter 2 and Chapter 3, we had studied the characteristics of various SWPWMs and understood that modified

150

^o SWPWM is better than

150

^o SWPWM. In chapter 4, the performances of sensorless control via BEDC with

120

^o SWPWM are reviewed. We find that BEDC-II is better than BEDC-I and not all linear

120

^o SWPWM types can be used in the sensorless control due to the commutation signal generator of BEDC-II. In addition, since there is no floating phase in

180

^o SWPWM, no linear

180

^o SWPWM types can be used in BDCM sensorless control.

Due to the six two-switch conducting states of the twelve states in

150

^o SWPWM,

150

^o SWPWM can be used in sensorless control. In this chapter, we first sieve out the

150

^o SWPWM types that can be used in sensorless control (namely sensorless

150

^o SWPWM types) from linear

150

^o SWPWM types. Then, we propose the commutation signal generator and speed estimation adopted for

150

^o SWPWM. Finally, the simulated and experimental results are provided to show the performance improvement from using twelve-step

150

^o SWPWM.

5.2 Sensorless SWPWM Types

From Chapter 2, we know that there are 9 linear

120

^o SWPWM types. However, from the complication of commutation signal generator discussed in Chapter 4, we know that not all linear

120

^o SWPWM types can be used in the sensorless control via BEDC-II as

sensorless

120

^o SWPWM types. Correspondingly, not all linear

150

^o SWPWM types can be used in the sensorless control via BEDC-II as sensorless

150

^o SWPWM types.

5.2.1 Sensorless 120

^o

SWPWM Types

In order to find out the sensorless

120

^o SWPWM types form 9 linear

120

^o SWPWM types, all position sensing signals

H of 9 linear

_a

120

^o SWPWM types generated from BEDC-II are plotted in Fig. 5.1.

Due to the use of a single-edge trigger function in the

120

^o SWPWM commutation signal generator plotted in Fig. 4.9, the position signals

H during the floating periods

_a (illustrated with dashed line in Fig. 5.1) must be the following patterns listed in Fig. 5.2(a) and Fig. 5.2(b) in order to detect the correct zero-crossing points of motor back-EMFs. On the other hand, some linear

120

^o SWPWM cannot be used in sensorless control, once the patterns listed in Fig. 5.2(c) are found in the position signals

H .

_a

It follows that only types-01_01, 01_11, 11_01 and 11_11 can be sensorless

120

^o SWPWM types tabulated in Table 5.1[4-9]. However, types-01_01 is better than other three ones due to its minimum effective transition rate α¹²⁰_PWM^° discussed in Chapter 2[5].

Table 5.1. Sensorless

120

^o SWPWM types

2 1U U

=00

2 1U U

=01

2 1U U

=10

2 1U U

=11

2 1L L =00

2 1L L =01

2 1L L =10

2 1L L =11

Fig. 5.1. Position sensing signals

H of linear

_a

120

^o SWPWM types from BEDC-II.

00 _ 11

01 _ 01

01 _ 11

10 _ 11

11 _ 11 11 _ 01

11 _ 10 10 _ 10

11 _ 00

Ha H_a

(a)

Ha H_a

(b)

Ha H_a

(c)

Fig. 5.2. (a),(b) Acceptable and (c) unacceptable position signals during the floating periods.

5.2.2 Sensorless 150

^o

SWPWM Types

Likewise, we should check the position signals

H of all linear

_a

150

^o SWPWM types in order to identify the sensorless

150

^o SWPWM types. By following the searching guidelines listed in the above section, all 225 linear

150

^o SWPWM types can be classified into Table 3.4 according to their position signals

H . It shows that there are 100 sensorless

_a

150

^o SWPWM types tabulated in Table 5.2 can be used in sensorless control and they are named sensorless

150

^o SWPWM.

Obviously,

150

^o SWPWM type-00110_00110 is the best sensorless

150

^o SWPWM for its minimum effective transition rate α¹⁵⁰_PWM^° and good thermal distributionF_G¹⁵_,TD^0o . However, from the voltage harmonics, the modified

150

^o SWPWM. is better than original

150

^o SWPWM. It follows that the modified

150

^o SWPWM type-00110_00110 is used in the sensorless control in the following sections.

Table 5.2. Sensorless

150

^o SWPWM types U₁U₂U₃U₄U₅

5 4 3 2 1LLLL

L 00000 00001 00010 00011 00100 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011 11100 11101 11110 11111 00000

00001 00010 00011 00100 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011 11100 11101 11110 11111

Sensorless

150

^o SWPWM types

5.3 Twelve-Step BDCM Sensorless Control

5.3.1 Sensorless Control Scheme

By using BEDC-II and applying

150

^o SWPWM type-00110_00110, the illustrated waveforms are plotted in Fig. 5.3. Obviously, from three position signals

H ,

_a

H and

_b

H ,

_c the six ZCP instants shown in signal

H

_trig can be easily obtained by simple trigger function.

However, there should be twelve commutations in

150

^o SWPWM. Two commutation signals H₁ and H₂ are obtained by following each ZCP instant with delayed phase π

/ 12

and π

/ 4

, respectively.

Va

ea

va

vp

Htrig

H

reset

H

π 12

π 4

Td

Ha

Hb

Hc

H1

H2

TH

HMUX

Fig. 5.3. Illustrated waveforms of type-00110_00110 via BEDC-II.

In order to bypass the conduction time of freewheeling diode, the reset signal

H

_reset should be a time-delay

T signal from the latest commutation signal commutation signal

_d

H2 to reset the single-edge trigger function. Then, the final commutation signal H can be synthesized from the OR operation of signals H₁ and H₂. The commutation signal generator used in

150

^o SWPWM can be plotted in Fig. 5.4.

From Fig. 5.4, a multiplexer is used to select the position signal of unexciting phase by commutation signal H₂. In order to operate BDCM normally, we should commutate current adequately at (15^o + k×30^o) position behind ZCPs of back-EMFs with modified

150

^o SWPWM. Due to the conduction of freewheeling diodes at the current commutation, the terminal voltage would be equal to

V or zero until line current returns to zero, which may

_dc 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

H

_MUX and then, hold until the coming of active reset signal

H

_reset. The reset signal

H

_reset is obtained from

T -delayed from signal

_d H₂. Finally, using OR gate integrates two commutation signals H₁, H₂ and obtain the desired commutation signal H. By detecting the periods T_H of signal H, the estimated speed ω can be obtained as _r

H H

r

T P PT

10 2

60 12

1 × =

ω

= (5.1)

Ha

Hb

Hc H

ds

e⁻T

Htrig reset

H

HMUX

12 jπ

e ¹

H H2 4 jπ

e

Fig. 5.4. Commutation signal generator for

150

^o SWPWM.

5.3.2 Starting Strategy

In this study, the proposed starting strategy of BDCM is divided into alignment mode and synchronization mode. The rotor is forced to locate in a given position in alignment mode. In synchronizing mode, the six switching signals start changing to generate a synchronous rotating magnet field with increasing rotating speed. When the standstill characteristics are known, an optimal accelerating speed rate and the accompanying voltage (PWM duty) can be obtained to lead the rotor rotating in specified speed synchronously to some speed where the sensorless circuits are able to function well.

5.4 Simulation Results

In this section, some simulation results are provided to evaluate the performance of six-step BDCM sensorless control (

120

^o SWPWM) and twelve-step BDCM sensorless control (

150

^o SWPWM). The configuration of sensorless control had been plotted in Fig. 4.1 and the simulated program in PSIM software is plotted in Fig. 5.5.

As shown in Fig. 5.5, the PSIM program involves four parts: three phase inverter which is fed by dc voltage 300V, BEDC-II, DLL block which involves the sensorless function of commutation signal generator, speed estimator, switching signal generator, and two coupled motors where one is called motor and the other is seen as a generator connected to Y-connected resistances

R .

_g

According to the BEDC-II analysis in (4.9)~(4.11), the simulated parameters for BEDC-II are listed as (4.12) and BEDC-II obtains the position signals

H ,

_a

H and

_b

H from the

_c inverter and motor terminal voltages V_P,

V ,

_a

V and

_b

V . By inputting the above position

_c signals

H , H and H into the DLL block, commutation signal H and the estimated

speed ω can be obtained from (5.1). Then, the speed controller tunes the PWM duty ratio _r adequately according to the speed difference between speed command

ω

^*_r and the estimated speed ω . At the same time, the switching signal generator yields the six gate signals _r according to the commutation signal

H and PWM duty ratio to yield square-wave currents

adequately.

The parameters of motor and inverter have been listed in Table 3.5, and those of generator are tabulated in Table 5.3.

Table 5.3. Simulated generator parameters Stator resistance

2 . 2 Ω

Stator inductance L_q

= 3 . 43

mH,

L

_d =2.73

mH

Voltage constant (Line-to-Line) 65

Vp / krpm

Pole number 4 pole

Motor inertia 1.92

kg

−

cm

²

With speed command ω_r^∗

= 3000

rpm, the simulated BDCM current waveforms

i and

_a the corresponding back-EMFs

e under various SWPWM for

_a

R

_g =100Ω and

R

_g = 20Ω are plotted in Fig. 5.6 and Fig. 5.7, respectively. We can find that both six-step and twelve-step sensorless controls work stably. In addition, it is noted that current harmonics in motor windings would not only result in the excess copper loss, but also contribute to the torque ripple at the shaft, the vibration and acoustic noise. It follows that current harmonics should be reduced as far as possible.

As shown in Fig. 5.6, when the yielding motor current is small (i.e. light load), the listed

THD and WTHD values show that six-step sensorless control is preferred. On the other hand,

when the yielding current becomes large (i.e. heavy load), the listed THD and WTHD values in Fig. 5.7 implies that twelve-step sensorless control is better than six-step sensorless control.

Ha

Hb

Hc

Fig. 5.5. Simulated model in PSIM.

2A

2A

5.5 Experimental Results

With

R

_g =100Ω and six-step 120^o SWPWM type-01_01, the measured gate signals

1

GT and G_T4, position sensing signal

H and motor winding current

_a

i under various

_a speed are plotted in Fig. 5.8. Likewise, the measured waveforms for

R

_g =100Ω and twelve-step 10Modified150^o SWPWM type-00110_001 are plotted in Fig. 5.9. The calculated THD and WTHD values are tabulated in Table 5.4 and plotted in Fig. 5.10.

Obviously, due to the current harmonics, sensorless BDCM control with six-step 01

_ 01 type SWPWM

120^o is better than that with Modified

150

^o SWPWM

10 1 0 0 _ 0 1 01 0

type with

R

_g =100Ω (i.e. light load).

Table 5.4.

THD and

_i

WTHD of experimented current waveform with

_i

R

_g =100Ω

SWPWM

120

^o

type-01_01

Modified

150

^o SWPWM type-00110_00110 SWPWM

ω (rpm) r

THD (%)

_i

WTHD (%)

_i

THD (%)

_i

WTHD (%)

_i

1000 65.66 20.43 85.75 34.04 1500 56.79 16.30 79.83 30.00 2000 48.81 15.94 78.94 27.29 2500 43.60 13.10 69.63 25.41 3000 41.67 13.03 51.51 20.69

A

speed ω equal to: (a)_r 1000

rpm

; (b)1500rpm; (c)2000rpm; (d)2500rpm; (e)3000rpm.

A Fig. 5.9. Experimental waveforms of Modified

150

^o SWPWM type-00110_00110 with

Ω 00

=1

R

g and speed ω equal to: (a)_r 1000

rpm

; (b)1500rpm; (c)2000rpm; (d)2500rpm;

(e)3000rpm.

1000 2000 3000

1000 2000 3000

)

With

R

_g = 20Ω, the measured gate signals G_T1 and G_T4, position sensing signal

H

_a and motor winding current

i with six-step

_a 120^o SWPWM type-01_01 and twelve-step

10 1 0 0 _ 0 1 01 0 type SWPWM 150

Modified ^o are plotted in Fig. 5.11 and Fig. 5.12,

respectively. The calculated THD and WTHD values are tabulated in Table 5.5 and plotted in Fig. 5.10.

From Table 5.5, we can find that the current harmonics of six-step sensorless control is less than that of twelve-step sensorless control when the motor speed ω is smaller than _r 1500rpm. However, when the speed becomes higher than 1500rpm, the current harmonics of six-step sensorless control is larger than that of twelve-step sensorless control.

Consequently, it is preferred to use twelve-step sensorless control at those conditions closed to the rated condition.

Table 5.5.

THD and

_i

WTHD of experimented current waveform with

_i

R

_g =20Ω

SWPWM

120

^o

type-01_01

Modified

150

^o SWPWM type-00110_00110 SWPWM

ω (rpm) r

THD (%)

_i

WTHD (%)

_i

THD (%)

_i

WTHD (%)

_i

1000 38.94 13.82 46.69 17.86 1500 37.01 13.77 36.47 13.81 2000 36.58 13.69 33.85 12.67 2500 33.78 12.84 30.21 11.69 3000 31.83 11.98 26.05 10.23

A

speed ω equal to: (a)_r 1000

rpm

; (b)1500rpm; (c)2000rpm; (d)2500rpm; (e)3000rpm.

ms Fig. 5.12. Experimental waveforms of Modified

150

^o SWPWM type-00110_00110 with

Ω 0

=2

R

g and speed ω equal to: (a)_r 1000

rpm

; (b)1500rpm; (c)2000rpm; (d)2500rpm;

(e)3000rpm.

CHAPTER 6

CONCLUSION

In order to integrate the small-sized motor drivers into SOC design, we should minimize the power consumption due to gate driving circuit, reduce temperature rise and eliminate possible hot spot in the PWM motor driver. With the common six-switch circuit topology, best selection of SWPWM scheme is an effective way to overcome the SOC challenges – power consumption and thermal balance. After the classification of linear modulation, effective PWM transition rate

α

_PWM , power loss unbalanced ratio and experimental demonstration, this thesis recommends the following best SWPWM schemes for SOC design type 01_01 and 10_10 for

120

^° SWPWM and type 010_010 for

180

^° SWPWM. The results are very important for small-sized motor drivers in some portable and electric equipment powered by batteries.

In addition, 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.

Based on the study of SWPWM and BEDC, the proposed twelve-step BDCM sensorless control had been designed and implemented. The result shows that twelve-step BDCM sensorless control is better than six-step BDCM sensorless control at those conditions close to the rated condition. The performance evaluation of position-dependent load torque will be the

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A ^PPENDIX A

The Fig. A.1 and Fig. A.2 shows the experimental environment which we used in chapter 5

Fig. A.1. MCU and BDEC-II.

Fig. A.2. Structure of BDCM sensorless control.

在文檔中 方波脈寬調變及其於直流無刷馬達無感測控制之應用 (頁 87-0)