T YPICAL C OMMUTATION P RINCIPLE

between electromagnetic torque and back-EMFs could be represented as

e

According to the Newton law, the electromechanical equation can be expressed as

(

_{m e L}

) (

_e

which could be rearranged as

(

_{e m e L}

e

J ω B ω T

T

= 2

p

& + +

)

^(2-21)

where J is the motor’s inertia, Bm is the viscous damping, TL is the load torque

2.3 Typical Commutation Principle

The model of the 3-phase Y-connected BLDC motor consists of winding resistances, winding inductances, and back-EMF voltage sources [23]. The typical commutation for a BLDC motor is accomplished by controlling the six inverter switches according to the six-step sequence to produce the phase current waveforms as shown in Fig.2.4. Ideally, the currents are in rectangular shapes, and the stator inductance voltage drop may be neglected [7]. Thus, the sequence of the conducting

phase will be shown in Table 2.1 from Fig.2.4.

e

a

Phase A

i

a

0

e

b

Phase B

i

b

0

e

c

Phase C

i

c

0

0° 60° 120° 180° 240° 300° 360°

Fig.2.4 Ideal back-EMF and phase current waveform of a BLDC motor

The accurate rotor position sensors are required since the torque production performance largely depends on the relationship between excitation currents and back-EMFs. The rotor position sensing can be achieved by using the Hall-effect sensors for low-cost applications, or by resolving and optical encoders for high-performance applications. In reality, Hall-effect sensors are used most widely for electronic commutation of BLDC motor drives. Fig.2.5 shows the system schematic block diagram of the commutation control for a BLDC motor. This figure is included of the inverter circuit, the equivalent model of a BLDCM, and the feedback the signals of Hall-effect sensor.

The inverter circuit of single-phase is cascaded by two power transistors, such as MOSFETs or IGBTs, as the active elements. Both of them can not conduct at the same time to avoid burning under over-current. Generally, NMOSFETs are selected to be the power transistors for small power motors. Based on the devices characteristics, to turn ON the NMOSFETs, a high gate voltage should be applied [21]. In addition, the six segments are processed in order, which is implemented by the six-step drive.

Generally, the typically commutation is based on the rotor position which is measured by three Hall-effect sensors located in the motor. The Hall-effect signals which would send the position massages are related to the back-EMFs . When the phase back-EMF is through the positive zero-crossing, its Hall signal will become high after 30° delay. On the contrary, when the phase back-EMF is through the negative

Hall-effect sensor Hc

Commutation Logic Hb Duty

ratio

PWM control

Ha

Fig.2.5 System schematic of typical commutation control for a BLDC motor

zero-crossing, its Hall signal will become low after 30° delay. The timing diagram of back-EMFs and Hall-effect signals are shown in Fig.2.6.

Back-emfs

0

e

c

e

b

e

a

H

a

H

b

H

c

0° 60° 120° 180° 240° 300° 360°

Fig.2.6 The timing diagram of back-EMFs and Hall-effect signals

Since the BLDC motor should be separated in six segments, the three Hall-effect sensors can produce digital signals in three bits as shown in Table 2.1. In the traditional control experiment, it is easy to know the rotor position and velocity because it just decodes the digital signals from Hall-effect sensors and differential the variance of one digital signal.

Table 2.1 Position based of six segments with Hall-effect sensors signals Electrical angle segment Switch on Hall-effect

0 ~o 60 ^o CB ^S3, S5 001

60 ~o 120^o A B S_1, S₅ 101

120 ~o 180^o A C S_1, S₆ 100

180 ~o 240^o BC S2, S6 110

240 ~o 300^o BA S1, S4 010

300 ~o 360^o CA S_3, S₄ 011

Ideally, the conducted current waveforms are in rectangular shapes because only two phases are excited at any instant and the effect of free-wheeling diodes is ignored.

Hence, the phase current can not be changed suddenly because the inductance exists.

In order to analyze the characteristics during the phase commutation, the commutation from phase a-c to phase a-b is considered as an example. First, the diode S1 and S6 in Fig.2.5 will be conducted so that the current of the phase b will pass through the diode.

Immediately after switching off Q6, the current of the phase b still pass through the diode until decaying to zero as shown in Fig.2.7. Hence, there exists commutation period between the two-phase conduction period. On the other hand, during the two-phase conducting period, two conducting phase currents are opposite and another one is zero. Therefore, the sum of three phase currents will still equal to zero at any time.

Two-phase conducting period

Commutation period Current

i

a

i

c

Time

i

b

Fig.2.7 Two-phase conducting period and commutation period

Chapter 3

Sensorless Commutation Control for BLDC Motors

Since BLDC Motors use permanent magnets for excitation, rotor position sensors are needed to perform electrical commutation. Commonly, three Hall-effect sensors installed inside the BLDC motor are used to detect rotor position. However, the rotor position sensors present several drawbacks from the viewpoint of total system cost, size, and reliability. Therefore, resent investigators have paid more and more attentions to sensorless control without any Hall-effect sensors and proposed many sensorless-related technologies.

Section 3.1 introduces three sensorless control methods. Besides, back-EMF based position detection is more useful than others since the back-EMFs proportional to the rotating angular velocity should be recognized directly or indirectly and the hardware could be realized easily. Hence the back-EMF based position detection will be narrowly described clearly in Section 3.2.

3.1 Review of Sensorless Control Methods for BLDC Motors

Since the knowledge of six communication instants per electrical is only needed for BLDC motors. In order to reduce cost and motor size, the elimination of the rotor position sensors is a very desirable objective in many applications. Furthermore, the sensorless control is the only way for some applications and many methods via sensorless control have been researched, such as back-EMF based position estimation method [1], [2], [3], [19], Kalman-filter based method [4], third-harmonics voltage position detection method [5], and free-wheeling diode conducting method [6]. More details about back-EMF based position estimation method will be discussed in Section 3.2.

3.1.1 Kalman-filter based method

A method which uses the extended Kalman filter (EKF) to estimate speed and rotor position of a BLDC motor is illustrated in [4]. The estimation algorithm is based on the state-space model of the motor and a statistical description of the uncertainties which is modeled by covariance matrices, including P(t), Q(t), and R(t). Define that

P(t) is for the system state vector, Q(t) is for the model uncertainty, and R(t) is for the

measurement uncertainty.

Since the EKF is an efficient state estimator for nonlinear system and consists of

the prediction and correlation equations, the drive system could be described as

( ) t f [ x ( ) ( ) t ,u t ,t ] n ( ) t

x & = +

(3-1)

where the initial state vector is modeled as a Gaussian random vector with mean and covariance , while is a zero-mean white Gaussian noise independent of and with a covariance matrix

( ) t

0

x

x

0

P

₀

n ( ) t

( ) t

0

x Q ( ) t

. The measurement are modeled as

( ) ^t

_i

^h [ ^x ( ) ^t

_i

^t,

_i

] ^v ( ) ^t

_i

y

= + (3-2)

where is a zero-mean white Gaussian noise independent of and with a covariance matrix . Hence, the EKF would generate a minimum-variance estimator since it has a predictor-corrector structure.

( ) ^t

_i

v x ( ) t

0

( ) ^t

_i

R

However, there exists a critical part since the design is to use accurate initial value for the various covariance matrices. In principle, these initial matrices need to be obtained by considering the stochastic properties of the corresponding noises. Since these noises are usually unknown, trial-and-error method is used for tuning the initial estimates of these matrices to obtain the best tradeoff between filter stability and convergence time.

3.1.2 Third-harmonics voltage based detection method

This method in [5] deals with the use of the third harmonic component of the back-EMF for indirect sensing the rotor flux position. The six step inverters switch the

stator excitation at every ^π₃ electrical degree. The switching can be detected by monitoring the third-harmonic voltage of the back-EMF. The stator voltage equation for phase a, for instance, is written as

( )

_{as as}

Similar expressions can be written for the other two stator phases. The phase stator resistance and inductance are represented as Rs and Ls respectively. The term eas

represents the back-EMF voltage. For a full pitch magnet and full pitch stator phase winding, the back-EMF voltages contains the following frequency components

( ^{cosω t k cos 3 ω t k cos 5 ω t k cos 7 ω t ...} )

Because of Y-connected stator windings, the third-harmonic voltage component at the terminal voltage is only due to the back-EMF. The summation of the three stator phase voltages is a zero sequence which contains a dominant third-harmonic component and high frequency components, expressed as

high_freq

where v3 is the third-harmonic voltage and

v

_{high_freq} is the high frequency components.

Therefore, the rotor flux can be estimated from this third-harmonic signal by integrating the resultant voltage v3,

(3-8)

∫

=

v dt

λ

_{r3 3}

Since the third harmonic flux linkage lags the third harmonic of the back-EMF voltages by 30 degrees, the commutation signals can be obtained by directly detecting the zero-crossing of the third harmonic flux linkage without any phase delay. Fig.3.1 shows the relationship between the back-EMFs, the third harmonic voltage and the rotor flux linkage; it is clearly to see that the zero-crossing of is the commutation instant. The result of the summation of the three phase voltages contain the third-harmonic voltage and high frequency sequence components that can be easily eliminated by a low-pass filter.

r3

λ

To sum up, the important advantages of this method are easy to implementation

v

3

0

0° 60° 120° 180° 240° 300° 360°

Fig.3.1 Relationship between the back-EMFs, the third harmonic voltage and the rotor flux linkage

e

a

e

b

e

c

0

λ3 0

and low susceptibility to electrical noise. On the other hand, signal detection at low speeds with this method is possible because the third harmonic signal has a frequency three times higher than the fundamental back-EMF, allowing operation in a wider speed range than techniques based on sensing the motor back-EMF. However, it is difficult to sense the neutral point voltage. Therefore, the neutral terminal is not available due to the cost and structure constrains in application.

3.1.3 Free-Wheeling diode conducting method

Since the back-EMF is quite small and hard to detect during the low-speed operation, it is difficult to precisely detect the rotor position based on the back-EMF only. Recently, some approaches have included other information besides back-EMF to detect the rotor position, for example the work by S. Ogasawara and H. Akagi [6].

Their approach proposed a method on the basis of the conducting state of free-wheeling diodes connected with power transistors. Fig.3.2 shows the circuit with phase a-b conducted, which means the active signal is given to S1 and S5. If S1 is on state, the dc link voltage increases the main current i. If S1 turn off, the current i continues to flow through the free-wheeling diode D4 and decreases. Then, the voltage equation of this loop can be derived as

=0

where VCE and VF denote the forward voltage drop of the transistors and diode. From (3-9), the voltage drop of the motor winding as

2

The neutral voltage vn which also shown in Fig.3.2, is given by

a

Substitution (3-10) into (3-11) gives the following equation

2

Equation (3-13) holds good even in transient states because no motor constant are included. The conducting condition of the diode D6 is given by

F

c

V

v

<− (3-14)

Substituting (3-13) into (3-14) gives the following equation

2

Since the back-EMF are assumed in ideal trapezoidal waveform, is approximately zero near the zero point of . Therefore, the conducting condition of D6 is given by

In general, VCE and VF are much smaller than the back-EMF. When the back-EMF

e

c become negative, the open-phase current flows through the negative-sign diode D6.

Therefore, the zero-crossing point of the non-excited phase back-EMF can be equivalently obtained by detecting corresponding diode conducting condition.

Fig.3.3(a) shows a current waveform in an open phase, and Fig.3.3(b) shows a specially designed circuit to detect whether the free-wheeling diodes are conducting or not. A resistor and a diode are connected to a comparator for voltage clamping. The reference voltage is slightly smaller than the forward voltage drop of the

free-wheeling diode. After detecting the diode conducting instant in the non-excited phase, a digital phase shifter is realized to generate the correct commutation signal.

However, the detecting circuit needs two isolated power supplies and the external hardware circuit is required.

V

ref

V

_F

Fig.3.2 Free-wheeling conducting circuit in active signal S1 to S5

V

dc

i

VCE

VF

Fig.3.3 Free-wheeling diode conducting method: (a) current waveform in an open phase, (b) Diode conducting detecting circuit

3.2 Back-EMF Based Position Estimation Method

The rotor position is obtained directly by measurement of the back-EMFs induced in the stator windings. In the basic operation of a BLDC motor, only two phases are energized at any instant with the other phase unexcited. Therefore, each of the motor terminal voltages contains the back-EMF information that can be used to derive the commutation instants [1], [19]. The zero-crossing method is employed to determine the switching sequence by detecting the instant where the back-EMF in the unexcited phase crosses zero. After detecting the commutation instant, the phase shifter is needed to get the correct commutation signal.

3.2.1 Zero-crossing detection

Generally, with Y-connected stator windings, the terminal voltages va, vb and vc can be derived as the three unexcited phase. From (3-17) to (3-19) can be derived as

(

_{an bn cn}

)

_n

c b

a

v v v v v v

v

+ + = + + +3 (3-20)

Note that the current of the non-excited phase is zero if all the winding currents applied to the three phases are assumed to possess ideal rectangular shape without any disturbance. Hence, from (3-17) to (3-20), the back-EMF of the non-excited phase a can be derived as

The relationship between three terminal voltages and the waveform of back-EMF produced from (3-22) are shown in Fig.3.4. Therefore, the positions of the zero-crossing point could be detected from the back-EMF of phase a ( ) when the electrical angles in the region of 0°-60° and 180°-240° as shown in Fig.3.4. In additional,

and could be found in the same way.

e

a

non

e

b₋

e

_c−non

V

dc

v

a

After comparing the signals as presented in Fig.3.5, It could be found the relationship between the non-excited phase back-EMF ( ) and Hall-effect signals (Ha). Thus, the zero-crossing points of the non-excited phases are required to be

e

a

Fig.3.4 Ideal three terminal voltages and the waveform of back-EMF

delayed with 30 electrical degrees for generating the corresponding commutation signals instead of Hall-effect signals. The System schematic of sensorless BLDC motor drive is presented in Fig.3.6. Compared with System schematic of typical commutation control in Fig.2.5, the zero-crossing detection has replaced three Hall-effect sensors.

Zero-crossing signal

Ha

e

a

0° 60° 120° 180° 240° 300° 360°

Fig.3.5 The relationship between the non-excited phase back-EMF and Hall-effect signals

The method can be realized by using voltage sensors and low pass filters.

However, the modulation noise is eliminated by using the low pass filters which is produced a phase delay varies with the frequency of the excited signal for the desired speed. Besides, since the back-EMF is zero at standstill and proportional to rotor speed, this method can not be used at zero speed and realizes difficultly at startup or very low situation.

3.2.2 Commutation phase shifter

After recognizing the zero-crossing signal of the estimated non-excited phase back-EMF, an additional 30° phase shift is required to perform correct commutation.

Since the precision of the sensorless commutation control depends on the rotor speed, a

a b c n

Phase Voltage Zero-crossing detection Commutation Logic

PWM control Duty

ratio

Fig.3.6 System schematic of sensorless BLDC motor drive

novel frequency-independent phase shifter (FIPS) [3] has been proposed. The algorithm of this phase shifter has been proven independent of input signal frequencies.

However, the computation effort is quite large for real-time application; hence the

digital simplified-type FIPS has been proposed in [1] as shown in Fig.3.7. Define the variable γ as the ratio of decreasing to increasing increments for the counters,

c

_p

( ) k

and , which are limited by a positive value L to avoid overflow condition at very low speed. Thus, and . Fig.3.8 illustrates the operational waveform of the proposed phase shifter. Assume that the input signal

k

n

( ) ^k

⁻

^c ( ^k

⁻¹

)

^<0

c

_{n n}

( ) k

x

in Fig.3.7 is the zero-crossing signal of the

non-excited phase back-EMF as shown in Fig.3.5, and the output is the corresponding commutation signal. Also, since commutations exist every 180° in Fig.3.5,

( ) k y

γ can be represented as

φ*

γ = π (3-27)

where is the desired degrees of the phase shift. Therefore, the decreasing increments are six-times larger than the increasing increments in order to make the phase shift = 30°. Besides, k

φ*

φ* zn denotes the time when nth zero-crossing of input signal

x ( ) k

occurs, and kcn denotes the time when the commutation occurs. By definition, kp is the largest k when

c

_p

( ) k

−

c

_p

( k

−¹

)

<⁰, hence kp

=k

c1 when k=kc1. As a result, the output signal

y ( ) k

is changed from +1 to −1 at kc1 and the counter of

c

_p

( ) k

is disabled until next zero-crossing is triggered. On the other hand, is the largest k when

k

n

( ) ^k

⁻

^c ( ^k

⁻¹

)

^<0

c

_{n n} , hence kn

=k

c2 when k=kc2. As a result, the output signal is changed from −1 to +1 at k

( ) k

y

c2 and the counter of

c

_n

( ) k

is disabled until next

zero-crossing is triggered. Therefore, the proposed digital phase shifter not only

performs the frequency-independent characteristics, but also reduces computation effort.

xP

( )k c_n xN

( )k c_p

Fig.3.7 Block diagram of simplified-type FIPS

kp= kc1

kp= kc1

kp=0

kn= kc2

kn=0 kn=0

0

0

1 -1

( ) k

x

₀

k

k

k

( ) k k y

( ) ^k

c

_n

( ) k c

_p

k_z1 kc1 k_z2 kc2 k_z3 k_c3

Fig.3.8 The operational waveform of the proposed phase shifter

Chapter 4

Start-up Strategy and Procedure for BLDC Motors

The start-up strategy is necessary since there is little or no back-EMF to sense when the motor is standstill or at a low speed. This chapter will introduce the start-up strategy in detail and the implementation of initial position detection and the start-up procedure for the BLDC motors.

4.1 Start-up Strategy

Since the back-EMF detection based position detection method cannot be used at start-up or low-speed, the additional start-up strategies are needed to solve these problems. Generally, the open-loop start-up algorithm can avoid this problem, in which strong current is flown to the output driver to force the rotor to move to the known rotor position [1], [20]. This open-loop algorithm has disadvantages of slow start and possibility of initial backward rotation [6]. Instead of open-loop start-up, inductive sense start-up algorithm is widely used in BLDC motor applications nowadays [10], [21]. In this section, these two methods will be introduced in detail.

4.1.1 Open-loop start-up method

The open-loop start-up method is accomplished by providing a rotating stator field which increases gradually in frequency. Once the rotor field begins to become

attracted to the stator field enough to overcome friction and inertia, the rotor begins to turn. However, the drawback of this method is the initial rotor movement is not predictable, which is inadequate for disk drives. Thus, the initial position detection is important in this method.

The motor starting procedure will be illustrated as follows: first, the rotor would be aligned from an unknown position to a certain position. Then set control signals to the driver circuit with a conducting sequence. If the initial position could be known accurately, this method could succeed in high probability.

4.1.2 Inductive sense start-up method

The main idea of this method is to utilize the fact that the inductance of the motor winding varies as the rotor position changes. The magnetic flux generated by the current in the stator winding can increase or decrease the flux density in the stator depending on the rotor position, leading to decrease or increase in induction due to the saturation of the stator. The relationship between inductance and flux linkage is shown

as

+

Li

= _PM

Phase λ

λ (4-1)

where λ_Phase is the summation of the flux from the permanent magnet, λ , and the _PM flux from the current i. L is the inductance of the excited phase. Supply the current with positive or negative direction to the phase, as shown in Fig.4.1 [10]. The

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