B ACKGROUND

Nowadays, BLDC motors become more and more attractive for many industrial applications, such as electrical vehicles, compressors and DVD players etc. Comparing with other motors, BLDC motors possess some distinct advantages such as high torque, high power density and high efficiency. Since BLDC motors use permanent magnet for excitation, rotor position sensors are needed to perform electrical commutation.

Conventionally, three Hall-effect sensors are used as rotor position sensors for BLDC motors. However, the sensors lead to several disadvantages, such as cost, size and reliability. In addition, the sensors may be sensitive to the motor temperature inside.

Therefore, the sensorless control methods have been widely studied in recent years, such as back-EMF based position estimation method [1]-[3], third harmonic voltage position detection method [5], free-wheeling diode conducting method [6], and Kalman-filter method [4]. The first two methods both use the detected back-EMFs which should be measured at the instant of the unexcited phase. The third method, free-wheeling diode conducting method, uses indirect sensing of the zero-crossing of the back-EMFs to obtain the switching instants of BLDC motors. The Kalman-filter method is a stochastic observer in the least-square sense for estimating the states of

dynamic non-linear systems and it is viable for the on-line determination of the rotor position and velocity of a motor.

Among these control methods, the back-EMF based position estimation method is often used since the back-EMFs could be measured indirectly from the motor’s terminal voltages. When a motor is running, back-EMF is induced in the coil, and the position information of a rotor can be detected by the back-EMF. However, back-EMF is only generated while a motor is running, which requires another initial position detection and start-up algorithm when a motor is at standstill or at low speed with insufficient back-EMF. Many researchers have focused on the open-loop start-up method [6] and inductive sense start-up method [10]-[11]. In this thesis, the detailed realization issues of the sensorless algorithm will be introduced, and be implemented by using a PC-based feedback control system. In addition, the start-up problem will be overcome in the experiment.

1.2 Thesis Organization

The thesis is organized as follows. First, the basic concepts of BLDC motors are introduced in Chapter 2, including the characteristics, mathematical modeling and commutation principle of BLDC motors. Among them, the commutation principle would focus on the conventional electrical commutation with Hall-effect sensors.

In Chapter 3, some snesorless control method will be introduced. First, Kalman-filter based method, third-harmonics voltage position detection method, and free-wheeling diode conducting method will be described. Then the back-EMF based position estimation method used in experiment will be introduced in detail.

Chapter 4 will discuss the start-up strategies, such as open-loop start-up method and inductive sense start-up method. The initial position of the rotor will be detected to avoid the temporary reverse rotation. An additional modified open-loop start-up method will be proposed to solve the start-up problem. Then the start-up procedure used in the implementation will be presented, including initial position detection and start-up from standstill.

Chapter 5 will describe the hardware setup and implementation of sensorless drive. The sensorless control method and start-up method are implemented by the software, Matlab^®−Simulink^®. This toolbox can help designer establish them easily and directly. Besides, the hardware circuit which is included in the driver circuit and filter circuit is set up by Real-Time workshop^® (RTW) of Matlab^®. The main idea of the hardware circuit is to realize and verify the sensorless control method. Chapter 6 will show the experimental results to demonstrate the success of BLDC motor drive.

Finally, Chapter 7 gives the conclusions.

Chapter 2

Basic Concepts of BLDC Motors

A brushless DC (BLDC) motor is a rotating electric machine where the stator is a classic three-phase stator like that of an induction motor and the rotor has surface-mounted permanent magnets. In this chapter, the basic configuration and the characteristics of BLDC motors will be described in Section 2.1. Then the mathematical modeling will be represented in Section 2.2. Furthermore, a BLDC motor requires an inverter and a position sensor to perform “commutation” because a permanent magnet synchronous motor takes the place of dc motor with brushes and commutators [8]. Thus, the detail commutation and excited procedure will be illustrated in Section 2.3.

2.1 Characteristics of BLDC Motors

In general, a BLDC motor consists of a permanent magnet synchronous motor that converts electrical energy to mechanical energy. The basic configuration of BLDC motors are shown in Fig.2.1. In this figure, it’s clear to see that and the excitation of BLDC motors which consists of permanent magnets is on the rotor and the armature is on the stator. On the other hand, BLDC motors come in 2-phase, 3-phase and 4-phase configuration. Corresponding to its type, the stator has the same numbers of windings.

Out of these, 3-phase motors are the most popular and widely used since 2-phase and 4-phase motors are usually used in small power condition [22]. Furthermore, the hall elements are installed inside the stator to detect the rotor position. Since the 3-phase BLDC motors have three windings which are distributed with 120° in electrical degree apart to each other, the driver structure including the six-step inverters using PWM signals. Thus, the principle of switching is based on electrical angular position information, which is decoded by three Hall-effect sensors.

Permanent magnet rotor Winding

Hall element

Fig.2.1 The basic configuration of BLDC motors

2.2 Mathematical Modeling of BLDC Motors

In general, a BLDC motor has a permanent-magnet rotor and its stator windings are wound to generate the trapezoidal back electromotive force (back-EMF), and thus it requires rectangular-shaped stator phase current to produce constant torque. Besides, the two-axis transformation (d, q model) [9], [22], commonly used in PMSM, is not necessary the best choice for modeling and simulating the BLDC motors.

The dynamic equations of BLDC motors with Y-connected stator windings are

shown in Fig.2.2. When the neutral point is isolated, the phase currents of BLDC, ias(t),

i

bs(t), and ics(t), can be expressed as

( ) ^t

⁺

ⁱ ( ) ^t

⁺

ⁱ ( ) ^t

⁼⁰

i

_{as bs cs} (2-1)

i

as

i

bs

i

cs

Fig.2.2 Equivalent modeling for a BLDC Motor Because the three windings are distributed with

3 2π

in electrical degree apart to each other, the stator current in vector space is generally represented as

( )

_as

( )

_bs

( )

^j23π _cs

( )

^j43π where Lms and Ls respectively represent the mutual inductance and the self-inductance

of the stator. Besides, λ_pm is the flux magnitude produced by the permanent magnets, which are assumed sinusoidally distributed in the air-gap.

With a cylindrical stator, the self-inductances of the field windings are independent of the rotor position θ when the harmonic effects of stator slot openings are neglected. Hence, the self-inductance is constant, commonly further decomposed as

where takes into account the space-fundamental component of air-gap flux and is corresponding to the field-leakage flux.

L

ss

L

ls

The mutual inductances can be found on the assumption that the mutual inductance is due solely to space-fundamental air-gap flux. Because the phases are

displayed by

cos

, the mutual inductances are

L

_ms

L

_ss

2

−1

= (2-7)

The phase-a flux linkage (2-3) can be rewritten as

( ) (

_{e ss sl}

) ( )

_{as ss}

(

_bs

( )

_cs

( ) )

_{pm e}

as θ

t, L L i t L i t i t

λ

cos

θ

λ = + − + +

2

1 (2-8)

With balanced three-phase currents, substitution of (2-1) gives

(

_e

)

_{ss sl as pm e}

Besides, since the rotor would be engaged by the excited phase, the torque of a

motor is produced in this moving process. The equation of the instant torque could be

where

W

_co is the co-energy defined in Fig.2.3, and represented as

∫

Fig.2.3 Characteristic for co-energy

In general, for a p-pole 3-phase motor, the total electrical energy could be shown as

[ ] [ ]

From (2-14) and (2-16), the electromagnetic torque would be formulated by three phase currents, given as

( )

_⎥

Then the back-EMFs could be shown in matrix form from (2-13) as

⎥⎥ 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

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

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