seminar report

OBSEVER-BASED SENSORLESS CONTROL OF A FIVE-PHASE BRUSHLESS DC MOTOR 2012-2013

Dept. of EEE, Dr. T. T. I. T, K. G. F


TECHNICAL SEMINAR REPORT

On“OBSERVER-BASED SENSORLESS CONTROL OF A

FIVE-PHASE BRUSHLESS DC MOTOR”

Submitted in the partial fulfillment of the Requirement for the VIII Semester, Seminar – 06EES86

For the award of degree of

Bachelor of EngineeringIn

Electrical & Electronics EngineeringVisvesvaraya Technological University

Belgaum

By

SAMHITA .V 1GV09EE024

Under the Guidance ofMr. SOMASHEKAR. B, M. TechLecturer, Dept. of EEE, Dr.T. T. I. T

2012 –2013

Dr. T.THIMMAIAH INSTITUTE OF TECHNOLOGY(Formerly Golden Valley Institute of Technology)

Department of Electrical & Electronics Engineering



Oorgaum, Kolar Gold Fields – 563120.

CHAPTER 1

ABSTRACT

This report presents a rotor position estimation technique for a five-

phase permanent magnet synchronous motor with independent phases,

based on a back-EMF observer. The method involves the use of a proper

linear transformation which allows representing the five-phase motor by an

equivalent two-phase model. Due to its characteristics, the sensorless

strategy can be used in multi-phase motors having non-sinusoidal back-EMF

shape; such is the case of brushless DC motors used in fault-tolerant

applications. After an overview of the back-EMF model for the five-phase

motor, the linear transformation and the observer-based estimation

technique are used.And the experimental results are also shown.



CHAPTER 2

INTRODUCTION

Permanent magnet synchronous motors (PMSM) are widely employed

for their high efficiency, silent Operation, compact form, reliability, and low

maintenance. Depending on the application, different types of motors are

used, with different rotor structure (surface or buried magnets), winding type

(distributed or concentrated), and back-emf shape (sinusoidal or

trapezoidal).

Recently, multi-phase PMSM with independent phases have been

proposed for safety critical applications such as aircraft brakes, spoiler or

flap actuators. In these cases, the multi-phase machine is fed by a multi-

phase power converter, and the whole drive system must satisfy severe

fault-tolerant requirements, which involve the control hardware and the drive

sensors too.



2.1. BLDC MOTOR

The brushless DC motor differ from normal DC motor in that it

employs electrical commutation of the armature current rather than the

mechnical commutation. The construction of brushless DC motor is similar to

a permanent magnet synchronous motor.

The five-phase winding is placed on the stator (armature) while

rotor consists of Permanent Magnets. The word Brushless DC motor is used

to define the combination of motor, its electronic drive circuit and rotor

position sensors.

The electronic drive is an inverter which consists of transistors,

which feeds stator windings. The transistors are controlled by the pulses

generated by rotor position sensors.

Brushless DC (BLDC) motors are preferred, with magnets

mounted on the rotor surface and trapezoidal shaped back-EMF. Hall-effect

bipolar sensors can be used as primary position transducers, in a quite

simple and reliable assessment: each stator-fixed Hall sensor, one for each

phase, directly detects the polarity of the undergoing rotor magnets with a

proper angular displacement. The digital signals are processed by the

controller and the rotor position information is computed with the resolution

necessary for the electronic commutation of the motor.



2.1. SENSORLESS STRATEGY

Machine drive system without rotor position sensors are called

sensorless drives. It has gained the increasing popularity in the industrial

applications due to the inherent drawbacks of rotor position sensors.

Drawback of these sensors is the performance degradation

owing to the vibration or humidity. Furthermore these external sensors will

result in added cost and increasing the size of the drives.

The Permanent magnet drives of sensorless control has widely

found its application fields on the high performance machine drives because

of the ripple free torque characteristics and simple control rule.



2.3. BLOCK-DIAGRAM

Fig.1. Basic block-diagram

The input DC supply is given to the power converter circuit such that

five-phase AC supply is obtained. The five phase supply from the electronic

drive circuit is given to the α-β model. Linear transformation technique is

used to transform five-phase into an equivalent two-phase (α-β) model. This

equivalent two-phase model is fed to Back-EMF observer which estimates the

equivalent back-EMF. Phase detection algorithm estimates angular speed

and rotor position when it is fed from Back-EMF.


α-β MODE

L

BACK-EMF

OBSERVER

PHASEDETECTI

ONALGORIT

HM

POWER CONVER

TER

DCsupply

speed

angle


CHAPTER 3

FIVE PHASE BRUSHLESS DC MOTOR

Fig. 2 cross section of the five-phase PM BLDC motor

Fig. 1 shows a cross section of the five-phase PM BLDC motor. It has 18

rotor poles and 20 stator slots (4 slots per phase). Each phase consists of two

series coils mounted on diametrically displaced stator teeth. Due to this

structure, independent feeding of each phase is provided.

3.1. RATINGS:

The motor parameters are as given below in table I.



3.2. POWER CONVERTER:

Fig.3. Power converter for independent phase feeding

Independent H-bridge modules are used as power converter for

independent feeding of each phase as shown in the Fig.3. It results that,

motor phases are independent from each other, in the sense of electrical,

thermal and magnetic interactions, a suitable feature to avoid a single phase

faults to affect the remaining safe phases.

An H bridge is an electronic circuit that enables a voltage to be applied

across a load in either direction. The term HBridge is derived from the typical

graphical representation of such a circuit. An H bridge is built with four

switches (solid-state or mechanical). When the switches dA1 and



d’A2(according to the first figure) are closed (and dA2 and d’

A1are open) a

positive voltage will be applied across the motor and vice-versa.

A common use of the H Bridge is an inverter.



3.3. FIVE-PHASE MODEL:

Dealing with the description of such kind of independent-phase

machine, we can write down the following generalized voltage equation:

V x=RI x+Ld I xdt

+Ex(θr) (1)

Where,

Subscript “x” (x=A, B, C, D, E) indicates a generic phase of

the motor.

θr= pθm , the rotor (electric) angle.

The instantaneous value of the back-EMF is given by the time

derivative of the magnet flux linkage in the phase, which in turn depends

from the position of the rotor:

E x (θ r )=d Ψ Mx(θ r)

dt=d Ψ Mx(θr)d θr

∙d θrdt

=d Ψ Mx(θ r)dθ r

∙ωr (2)

Where,

ωris the rotor speed.

In order to generalize the voltage balance in case of non-

sinusoidal machines, the normalized back-EMF shape function is

defined as follows:

f x (θr )=Ex (θ r)K e ∙ωr

(3)

Where, Ke is the back-EMF constant.



From that, we can modify the machine equations into the

following form:

V x=RI x+Ld I xdt

+K eωr f x (θr) (4)

The shape functions of the motor considered is as shown in Fig.4.

Fig. 4. Back-EMF shape functions of the five-phase motor (design data).

Depending on the motor design, the back-EMF waveforms are quasi-

trapezoidal and they are symmetrically displaced over just one-half of the

electrical period, which gives the machine an intrinsic asymmetry.

Regarding to the electromagnetic torque, it can be expressed in

theparticular case of a multi-phase machine in the following way:

Using the shape functions one obtains:



3.4. SPACE VECTOR REPRESENTATION:

In order to set-up the sensorless strategy with a minimum number of

equations, an equivalent space-vector representation of the five-phase motor

has been developed. The objective is to achieve sine/cosine shapes for the

components of the equivalent shape function (i.e. backEMF) space-vector, in

order to set-up a two-phase observer similar to that employed in more

standard three-phase motors.

To this purpose, the linear transformation given by matrix (7) can be

considered, which allows to represents the five-phase motor by a couple of

space-vectors with components denoted as αβandα’β’ and an homopolar

component.

In (7) the first two rows are achieved by the projection of the magnetic axes

of the five phase motor as shown in Fig. 4, they define a direct sequence

space-vector. The third, fourth and fifth rows are defined considering the

virtual inversion of the magnetic axis direction of phases B and D, i.e. the

equivalent motor of phases A,C,E,-B,-D, symmetrically displaced of 2π/5

electrical degrees. The third row defines the homopolar (zero sequence)

component, while the fourth and fifth rows define an inverse sequence

space-vector whose values would be null in case of purely sinusoidal motor

and safe operation.



The application of the transformation (7) to the backEMF shape

functions of the five-phase motor gives the results reported in Fig. 5.

Fig. 5. Shape functions of the transformed equivalent model.

Due to the quasi-trapezoidal back-EMF nature of the BLDC motor, both

the zero sequence and the inverse sequence components are not equal to

zero, nevertheless this aspect will not affect the proposed sensorless

strategy.

In fact, in the following we will consider only the direct sequence

components for the set-up of the observer-based sensorless strategy. In fact,

the information on the rotor position can be extracted by the first harmonic

of the direct sequence component independently on the values of the zero

and inverse sequence ones.



3.5. TWO-PHASE EQUIVALENT REPRESENTATION:

Owing to the aim of implementing a sensorless scheme, an equivalent

two-phase representation of the five-phase motor has been developed. The

first step in this process is the transformation of the five-phase model using a

proper linear transformation capable to preserve the information on the rotor

axis position. First of all the space-vector representation of the motor

quantities must be taken into account, as reported in Fig. 4. Choosing a

stationary reference frame - and considering the projections onto these axes

a linear matrix can be constructed as in (8), which corresponds to define the

components of an equivalent direct sequence space-vector. Homopolar and

inverse sequence components could be defined in order to achieve a full

analytical description of the five-phase machine. Anyway, being the rotor

position information already present in the direct sequence components,

only these last will be considered to implement the sensorless control.

Hence, in the transformed α-βquantities, the back-EMF dependence on

rotor magnet position is then arranged in the following general form:



Where the periodic shape factors are expressed through the Fourier

series expansion and for the conventions assumed in the linear

transformation one has:

These considerations are made under the hypotheses of:

- Slow time-variations of the rotor speed;

- accounting for the effect of the first harmonic back-EMF only;

- Considering the back-EMF dynamical model related to these first

harmonics.



3.6. EQUIVALENT BACK-EMF MODEL:

Considering the equivalent two-phase stator-fixed alpha-beta model

associated to the direct sequence space-vectorof the five-phase motor, the

following state form (matrix) equation is obtained:

Where:

And

These are matrices of constant system parameters.

The back-EMF dependence on rotor magnet position can be arranged

as in the equation (9).

According to (6), the rotor (magnet) position information is contained

in the sine/cosine shapes of the 1stharmonic back-EMFs. If the speed is

assumed as a constant (that is the case of speed steady-state operation), the

following relations are achieved by time derivatives of these fundamentals:



Being:

a speed dependent matrix.

By associating (11) and (13) the following extended model is obtained, which

represents the motor dynamics in terms of 1st harmonics back-EMFs at

speed steady-state:

Where:

Equation (15) represents state variables.

Equation (16) represents system matrices.

In the extended model (14) the currents acts as the system outputs

(measurable state-variables), the applied voltages are the system inputs,

while the back-EMF components take the role of internal (nonmeasurable)

state-variables.



CHAPTER 4

OBSERVER-BASED SENSORLESS STRATEGY

Physical sensors have shortcomings that can degrade a control

system.There are at least four common problems caused by sensors. First,

sensors are expensive. Sensor cost can substantially raise the total cost of a

control system. In many cases, the sensors and their associated cabling are

among the most expensive components in the system. Second, sensors and

their associated wiring reduce the reliability of control systems. Third, some

signals are impractical to measure. The objects being measured may be

inaccessible for such reasons as harsh environments and relative motion

between the controller and the sensor (for example, when trying to measure

the temperature of a motor rotor). Fourth, sensors usually induce significant

errors such as stochastic noise, cyclical errors, and limited responsiveness.

Hence observers are used to augment or replace sensors in a control

system. Observers are algorithms that combine sensed signals with other

knowledge of the control system to produce observed signals. These

observed signals can be more accurate, less expensive to produce, and more

reliable than sensed signals. Observers offer designers an inviting alternative

to adding new sensors or upgrading existing ones.



4.1. BACK-EMF OBSERVER

From the previous extended model a linear state observer can be built

as follows (Luenberger-like observer):

d Xdt

=[ A (ωr ) ] X+ [B ]V αβ+ [K ] (I αβ− I αβ) (17)

With X=[ I α , I β , Eα , Eβ ]T estimated state variables and:

gain matrices (with k1 and g constant gains), where the parameter g stands

for a generic proportionality factor that can be used to weight more heavily

the back-emfs estimates with respect to the currents estimates.

The observer is used to estimate the run-time waveforms of the 1st

harmonic motor back-EMFs. From these we canretrieve the angular position

and the speed of the rotor magnet axis by a proper phase detection

algorithm asdescribed in the next subsection.



4.2. ROTOR SPEED & POSITION DETECTION:

The block scheme of the algorithm employed for rotor speed and

position detection is shown in Fig. 6. The basic principle refers to a

quadrature Phase Locked Loop (PLL). It involves the generation of an error

signal from the phase difference between harmonic input signals (in our case

the estimated back-EMF components) and corresponding quadrature

feedback functions of the estimated angle.

Assuming for the estimated 1st harmonics of the backEMF the phase relation

given by (9) and (10), and using the Werner’s formula we can write the

following expression of the error signal:

ε ( t )∝(sin~θ r cos θr−cos

~θ r sin θ r)∝ sin (~θ r−θ r) (18)

where~θ rrepresents the argument of the input waveforms (assumed as known

references) and θr is theargument of the feedback signals, i.e. the estimated

angle. For small deviations between them one obtains:

ε ( t )≈(~θr−θr) (19)

Hence, a Proportional Integral (PI) regulator can be used to generate

the closed loop feedbacks, in order to correct the angle deviation and

bringing the estimated angle to converge to the reference one. The

estimated speed signal can be obtained by introducing a further integration

block between the output of the PI regulator and the generation of the

feedback signals.

Fig. 6. Phase detector scheme.



Hence, the observer-based sensorless strategy for the five-phase BLDC

motor can be resumed by the functional blocks shown in Fig. 8: first, the five-

phase motor currents and voltages are measured and transformed into the

equivalent αβ components using the first two rows of the linear

transformation (7); second, using these measurements, the time-varying

alpha-beta components of the 1st harmonic back-EMF are estimated in the

back-EMF observer; third, from these estimates, the rotor speed and magnet

axis position are computed by the phase detection algorithm.

Due to the dependence of the observer sub-matrix [A22]from the rotor

speed, the estimate of this signal must be used as an additional run-time

input of the observer.

Fig.7. Observer-based sensorless strategy



4.3. SENSORLESS DRIVE SCHEME:

The drive scheme incorporating the observer-based sensorless

strategy is shown in Fig.8.

Fig.8. BLDC sensorless control scheme

Modular architecture is used in current control. Five independent

current control loops regulate the phasecurrents. In each current loop a

comparison between reference and measured current is performed, error is

PIregulated and correction is applied through five independent H-bridges in

the voltage-source inverter. An external loop regulates the speed by

comparison with the respective feedback, the speed error is regulated

through a PIregulator and torque requirement in term of current reference is

generated.



Fig. 9. BLDC control strategy.

The commutation logic used to compute the current references is

shown in Fig. 9. According to the BLDC control strategy, constant torque is

generated by feeding the motor phases with constant current in constant

back-EMF wave region. To achieve this behavior the rotor electric turn is

divided into ten sectors; in each sector only four back-EMFs are constant so

that the motor is fed by four quasi-square back-EMF synchronous currents,

while the remaining current is controlled at zero.



CHAPTER 5

EXPERIMENTAL SET-UP AND RESULTS

The experimental set-up arranged to verify the performance of the

sensorless strategy for the five-phase BLDC motor is shown in Fig. 10.

Fig. 10. Drive board description and experimental system set-up.

The experimental set-up arranged to verify the performance of the

sensorless strategy for the five-phase BLDC motor is shown in Fig. 10. The

control unit is based on a TMS320F2806 digital signal controller (DSC), whose

enhanced peripheral capabilities are used for interfacing the power hardware

both for control and diagnostic purposes.

Position sensors are provided, in order to set-up and evaluate the

performance of sensorless control: five Hall sensors are used to generate the

magnet field sector information needed for the BLDC commutation logic; a

square-wave quadrature encoder with 536 (134 x 4) pulses-per-revolution is

also present, employed for speed computation.

The experimental set-up includes a host PC, a Digital-toAnalog

Converter (DAC) and a scope. The host PC runs the DSC development and


POWER HARDWAR

E

CONTROL

HARDWARE

5ФBLDCMOTOR

DAC

SCOPE

DRIVE BOARD


debugger tools and the user interface, this last allows data exchange with

the control firmware. The scope is used for displaying the variables

computed by the control algorithm in real-time, through a 4 channel DAC.

RESULTS:

Figures 11 to 13 report some test results of the five-phase sensorless drive

prototype. In a first development step, tests have been carried out with the

observer in openloop, i.e. the estimated speed and position are not used for

motor control.

Fig. 11 shows the estimated alpha and beta back-EMF components

versus the commutation sector evolution (measured from the Hall sensors)

during a no-load test at about rated speed (570 rpm, equal to 85.5 Hz).

Fig. 11. Alpha (black trace) and Beta (blue trace) components of the back-EMFs, commutation sector (magenta) and speed (green) @ 570 rpm (voltage is

scaled to 50V/div).

According to what expected from theory the shapes of the estimated

back-EMFs are close to pure sinusoids, the alpha-beta components are in

quadrature with the first one leading on the second one. Being the “zero” of

the actual position located on the center of the first sector (see Fig. 9), this



test would prove an estimation error of about one-half sector, i.e. 18

electrical degrees. Investigation about this error is out of the scope of the

present paper. Nevertheless, due to intrinsic implementation delays in the

acquisition of the Hall sensor signals, the position estimation error computed

from the scope outputs represents just an indication.

Fig. 12 shows the response of the back-EMF observer when it operates at low

speed condition (60 rpm, equal to 9 Hz). The shapes of the back-EMFs are

estimated correctly even in this situation. Also the electrical position is

shown: in this case the position reference is aligned with the alpha axis

localized in the center of the first sector, leading to position estimation error

apparently equal to zero.

Fig. 12. Commutation sector (magenta), estimated position (black) and estimated Alpha and Beta back-EMFs (green and blue respectively) @ 60 rpm (voltage is scaled to 20V/div).



Finally, in Fig. 13 are shown the estimated electric position and speed

and the corresponding measured signals in a more large speed transition

from low to about rated value. It can be noticed that the estimated speed is

consistent with the measured speed in a quite satisfactory way.

Fig. 13.Commutation sector (magenta) and actual speed (blue) are reportedin the upper axis, estimated position (black) and estimated speed (green) are reported in the lower axis, during a speed transition from 60 to 570 rpm(speed is scaled to 300rpm/div).



CHAPTER 6

ADVATAGES, DISADVANTAGES & APPLICATIONS

Advantages:

Lower cost.

Reduced hardware complexity.

Reduced size, no sensor cable.

Increased reliability.

Less maintenance requirements.

Better noise immunity.

Disadvantages:

Poor precision.

Offset problem of the integral algorithm.

Sudden changes in the load can cause the back-EMF loop to lose sync

resulting in a loss of speed and torque

Applications:

Appliance and automotive industries

Electric and Hybrid vehicles-propulsion

Motor choice for model aircrafts including Helicopters.

Popularity has also risen in the radio controlled car.



CHAPTER 7

CONCLUSION

An approach to the rotor speed and position estimation in a five-phase BLDC

motor is proposed, based on a back-EMF observer. A linear transformation is

developed to represent the five-phase motor by an equivalent two-phase

model. The position is extracted from the estimated back-EMFs using a PLL

algorithm.

The presence of saturation is not taken into account because the two-phase

linear model developed in this study is able to correctly describe the

behavior of the system with good approximation.

The proposed strategy has been validated by experimental results with the

observer operating in open-loop, the analysis has pointed out that the rotor

position and speed are estimated with good reliability both at high and low

speed.

Estimation errors reported at high frequency operation such as the influence

of the observer gains set-up require a deeper analysis and will be

investigated in the next step of this research.


seminar report

Documents

based sensorless

based sensorless

bldc control

direct sequence

inverse sequence

electronic

rotor magnet

phase bldc