o

Abstrakt

Diplomová práce je zaměřena na problematiku bezsenzorového řízení BLDC

motoru pomocí Rozšířeného Kálmánova filtru. V první části je popsán proces

implementace EKF pro odhad rychlosti a elektrického natočení rotoru. K určení

odhadovaných stavů používá EKF nelineární model BLDC motoru a měření některých

veličin zahrnujících šum. Druhá část práce se zabývá návrhem metodiky měření a

odhadem kvality bezsenzorového řízení BLDC motoru. Nejlepších výsledků bylo dosaženo

analýzou zvlnění celkového proudu vstupujícího do výkonové elektroniky motoru.

V závěru práce bylo ohodnoceno několik algoritmů pro bezsenzorové řízení BLDC

motoru.

Abstract

This thesis is focused on the sensorless control of BLDC motor using the Extended

Kalman filter. In the first section, process of EKF implementation for estimating rotor

speed and electrical angle is described. For this estimation, EKF uses non-linear BLDC

motor model and some measurement containing random noise. Second part deals with

designing methodology to measure and estimate the quality of BLDC motor sensorless

control. Best results were achieved with total current entering power electronics ripple

analyzation. In the last section, several BLDC sensorless control algorithms were

evaluated.

Bibliographic reference

HRBÁČ, Z. Bezsensorové řízení BLDC motoru. Brno: Vysoké učení technické v

Brně, Fakulta strojního inženýrství, 2014. 57 s. Vedoucí diplomové práce Ing. Václav

Sova.

Statutory declaration

I statutory declare, that I wrote master’s thesis “Sensorless control of BLDC motor”

by myself using references mentioned in the list annexed to this thesis.

In Brno: ……………… ……………………

Bc. Zbyněk Hrbáč

Acknowledgements

I would like to thank my supervisor Ing. Václav Sova for methodological,

pedagogical and technical support and valuable advices during the process of completing

this thesis.

List of figures

Figure 1: One slot on pole and phase [1] ............................................................................. 12

Figure 2: Two slots on pole and phase [1] .......................................................................... 13

Figure 3: BLDC motor used during experiments ................................................................ 14

Figure 4: Hall sensor position [2] ........................................................................................ 14

Figure 5: BLDC commutation logic .................................................................................... 15

Figure 6: Back-EMF integration: Zero crossing point [2] ................................................... 16

Figure 7: Kalman filter principle diagram [14] ................................................................... 17

Figure 8: Matlab Function used to calculate KF in Simulink ............................................. 21

Figure 9: Diagram of BLDC motor ..................................................................................... 24

Figure 10: Back-EMF and current ideal wave form ............................................................ 26

Figure 11: Back-EMF function derivation .......................................................................... 29

Figure 12: BLDC with EKF simulation .............................................................................. 30

Figure 13: EKF Matlab function ......................................................................................... 31

Figure 14: Estimated and “measured” speed with error displayed ...................................... 32

Figure 15: Estimated and “measured” rotor’s electrical angle with error displayed ........... 33

Figure 16: Simulated and “measured” Hall sensor output .................................................. 34

Figure 17: BLDC motor sensorless control block diagram ................................................. 35

Figure 18: Sensorless control Simulink model overview .................................................... 36

Figure 19: Control block overview ...................................................................................... 36

Figure 20: Sensorless start block ......................................................................................... 38

Figure 21: Sensorless start Stateflow diagram .................................................................... 39

Figure 22: Simulated and measured Hall position sensor signal comparison ..................... 40

Figure 23: dSPACE ControlDesk ........................................................................................ 41

Figure 24: BLDC signals waveform at 1000 rpm ............................................................... 42

Figure 25: Frequency spectrum of total current at 1000 rpm .............................................. 42

Figure 26: BLDC motor, torque meter and cylindrical break experimental setup .............. 44

Figure 27: Torque meter output ........................................................................................... 45

Figure 28: Torque meter output frequency spectrum .......................................................... 45

Figure 29: One phase current............................................................................................... 46

Figure 30: One phase current frequency spectrum .............................................................. 47

Figure 31: Total current ....................................................................................................... 48

Figure 32: Total current frequency spectrum ...................................................................... 48

Figure 33: Method comparison overview ............................................................................ 49

Figure 34: Torque meter output frequency spectrum .......................................................... 50

Figure 35: Calculated torque frequency spectrum ............................................................... 50

Figure 36: Methods performance comparison ..................................................................... 52

Contents

1 Introduction ................................................................................................................ 11

2 Research ..................................................................................................................... 12

2.1 BLDC motor principles ........................................................................................ 12

2.2 BLDC motor control ............................................................................................. 13

2.2.1 Sensor control ................................................................................................ 14

2.2.2 Sensorless control .......................................................................................... 15

2.3 Kalman Filtration .................................................................................................. 16

2.3.1 State space representation – continuous system ............................................ 17

2.3.2 State space representation – discrete system ................................................. 18

2.3.3 Covariance matrices ...................................................................................... 19

2.3.4 Algorithm steps ............................................................................................. 20

2.3.5 Extended Kalman filter .................................................................................. 21

3 Solution goals ............................................................................................................. 22

4 Solution procedures and results ................................................................................. 23

4.1 BLDC motor equations for Kalman filter ............................................................. 23

4.1.1 Electrical part ................................................................................................. 23

4.1.2 Mechanical part ............................................................................................. 26

4.1.3 State space representation .............................................................................. 27

4.1.4 Extension for EKF ......................................................................................... 28

4.1.5 Simulations using BLDC motor Simulink model ......................................... 29

4.2 Sensorless control using EKF ............................................................................... 34

4.2.1 Used hardware ............................................................................................... 35

4.2.2 Used software ................................................................................................ 35

4.2.3 Simulink algorithm ........................................................................................ 36

4.2.4 Algorithm performance ................................................................................. 39

4.2.5 dSPACE ControlDesk GUI ........................................................................... 40

4.3 Methodology of torque ripple evaluation ............................................................. 41

4.3.1 Torque sensor measurement .......................................................................... 43

4.3.2 Current sensor measurement ......................................................................... 46

4.3.3 Method comparison ....................................................................................... 49

4.4 BLDC motor sensorless control evaluation .......................................................... 51

5 Conclusion ................................................................................................................. 53

6 References .................................................................................................................. 54

7 Symbols and abbreviations ........................................................................................ 56

8 List of attachments ..................................................................................................... 57

11

1 Introduction

BLDC motors are becoming widely used in the industry, from small motors in PC

fans to high power traction ones in electric vehicles. The main advantages of BLDC motor

are high reliability, greater efficiency and longer operating life compared to DC motor.

One of the biggest disadvantages is output torque ripple. In applications, where there is a

need for accurate motor movement, precise position sensors have to be used. If lowest cost

is demanded, sensorless control techniques may be applied.

This thesis is called Sensorless control of BLDC motor, which may be somewhat

confusing. In all applications sensors need to be utilized to control the motor. Sensorless

control means using electrical measurements (phase current, phase voltage, etc.) instead of

Hall position sensors mounted on motor’s non driving side.

This thesis is divided into two main parts. First part (research) provides short

overview of basic BLDC motor principles with possibilities of its control and introduction

to Kalman filter. Second part (solution procedures and results) discusses implementation

of EKF into BLDC motor sensorless control. Also issues with output torque ripple and its

evaluation are described in this section.

12

2 Research

2.1 BLDC motor principles

Brushless direct current motor (BLDC), sometimes called electronically

commutated motor (EC), is structurally similar to synchronous motor with permanent

magnets on the rotor. From synchronous motor, BLDC motor varies by different back-

EMF waveform and distribution of windings in slots. Also, BLDC motor is designed to be

driven by a rectangular shape input voltage. Ideal back-EMF and current waveforms are

shown in Figure 10. At all times, there is one phase without current (commutating phase)

and at the two remaining, current in one is going in the opposite direction as in the other

one.

Three main types of winding distribution are: one slot per pole and phase, two slots

per pole and phase, segmental stator with one coil per pole and phase. All three types are

designed to work with rectangular shape voltages.

One slot per pole and pair is the simplest winding distribution (Figure 1).

Theoretically, output torque should be always constant, independent on rotor electrical

angle. Due to pole coverage, winding inductance and slot spacing (problems with

reluctance torque) output torque is changing with rotation.

Figure 1: One slot on pole and phase [1]

Two slots per pole and pair have lower output torque ripple, because slot spacing is

smaller. At the same number of poles, the number of slots is doubled (Figure 2).

13

Figure 2: Two slots on pole and phase [1]

Motors with segmental stator use different type of winding. Windings are three

separate coils with no crossing. Having constant motor construction volume, output torque

is higher by about 20% compared to the previous two types.

BLDC motor behaves similar to a DC motor, meaning it has a linear relationship

between voltage and rpm, current and torque. Main advantage of BLDC motor is that there

is no mechanical commutation, so the motor is low-maintenance and the lifetime is longer

compared to conventional DC motor. Commutation, or phase change, is done using

feedback signal from Hall position sensor. Based on how the rotor is turned, the converter

switches between phases and rotary motion is created (see Figure 5).

BLDC motor can be bought at a variety of sizes, shapes and power outputs. From

small motors in hard drives to high power traction motors. By shape, motors are divided

into cylindrical and disc-like. Both groups are also split to machines with inner and outer

rotor. More about theory of BLDC motors can be found in [1] and [5].

2.2 BLDC motor control

For correct BLDC motor commutation, it is not necessary to know the rotor’s

electrical angle exactly, but just in which of the six segments (each 60° (1/3π rad) wide) it

is located. This information can be obtained either by using position sensors (sensor

control) or electrical measurements (sensorless control).

14

Figure 3: BLDC motor used during experiments

2.2.1 Sensor control

In a majority of applications, where sensor BLDC control is used, position

information is obtained from a Hall sensors mounted on the motor’s non driving side.

Based on signals from the Hall sensors (Figure 4), transistors in the power electronics are

switched on at a correct sequence to drive the motor (Figure 5).

Figure 4: Hall sensor position [2]

15

Rotor el. angle

Hall sensor states Transistor states

A B C Top A Bot A Top B Bot B Top C Bot C

0π÷1/3π 1 1 0 Off On Off Off On Off

1/3π÷2/3π 1 0 0 Off On On Off Off Off

2/3π÷π 1 0 1 Off Off On Off Off On

π÷4/3π 0 0 1 On Off Off Off Off On

4/3π÷5/3π 0 1 1 On Off Off On Off Off

5/3π÷2π 0 1 0 Off Off Off On On Off Figure 5: BLDC commutation logic

2.2.2 Sensorless control

In cases, where position sensors are eliminated, several methods may be used to

obtain position information. These methods are based on back-EMF, phase voltage and

phase current sensing. Signal-to-noise ratio is rather low at lower speeds, which is a reason

that sensorless control techniques don’t work well at near zero speeds. There is a need for

open loop commutation to start-up the motor. All methods also have to deal with PWM

ripple induction, when PWM control strategies are used. Analog to digital converter should

be synchronized with the PWM frequency to obtain a signal with low noise. When

synchronization is not possible, a low-pass filter needs to be inserted into measuring

process.

Some of sensorless control approaches include: Back-EMF zero crossing detection,

Back-EMF integration, Model based and estimation methods. Detailed description of

BLDC motor sensorless control methods can be found in [2], [3] and [4].

Back-EMF zero crossing detection

Back-EMF zero crossing detection method is one of the simplest sensorless control

techniques. As stated in its name, this approach detects a point, where back-EMF crosses

zero. This happens exactly in half of a commutating phase period, 30° before desired

commutation (Figure 10). When zero crossing is detected, delay of 30° electrical is

realized and then the phases are commutated. This delay varies with rotor speed. Correct

delay is constantly maintained by the control algorithm (counter, etc.).

Back-EMF integration

This technique uses exactly the same zero crossing point as the Back-EMF zero

crossing detection method does. Difference is how the 30° delay is realized. Integration of

16

the back-EMF is used to indicate the correct commutation point. The integrated area stays

approximately the same at different speeds. When the integrator reaches a pre-defined

threshold value, phases are commutated and a reset signal is applied onto the integrator.

Integrator is held in reset state until next zero crossing point occurs. Phase switching

advance can be easily realized by changing the integrator threshold value.

Figure 6: Back-EMF integration: Zero crossing point [2]

Model based and estimation methods

These methods combine system’s model knowledge to produce some kind of

estimate which is then compared with measurement and corrected. These algorithms

include: Adaptive Observer, Extended Kalman Filter, Model Reference Adaptive System

or Artificial Neural Network. Sensorless control method based on Extended Kalman

Filtration, is thoroughly described in this thesis. Papers, also describing theory of EKF

sensorless BLDC motor control method: [7], [8], [9] and [10].

2.3 Kalman Filtration

Kalman filter (KF) is an algorithm for unknown states estimation of state space

system. It uses knowledge of the system and some state measurement containing random

noise. Simple Kalman filter is for linear systems only, for non-linear systems Extended

Kalman filter (EKF) has to be used.

In BLDC sensorless control Kalman filtration was applied to estimate rotor speed

and rotor electrical angle, the simulated Hall sensor signal is then determined from this

signal.

17

Figure 7: Kalman filter principle diagram [14]

2.3.1 State space representation – continuous system

Kalman filter calculates estimate x of state vector x, which cannot be measured

directly. This estimate is done based on the knowledge of the system (linear state space

representation in discrete time), taking into account model’s inaccuracy (covariance matrix

of state noise Q) and inaccuracy of measurement (covariance matrix of measurement R).

Linear state description of the system:

(1)

(2)

, where:

x … state vector

u … input vector

w … state noise vector

y … output vector

v … measurement noise vector

A … state matrix

B … input matrix

18

C … output matrix

D … feedforward matrix (usually = 0)

G … noise matrix

2.3.2 State space representation – discrete system

For KF state space representation in discrete time is needed. State matrix Φ, input

matrix Γ and noise matrix Λ in discrete time:

(3)

(4)

(5)

, where:

Ts … sample time

I … unit matrix

Taking equations (1) and (2) and transferring them to discrete time, we get

(neglecting feedforward matrix D):

(6)

(7)

Transfer from continuous to discrete system can also be easily done by the c2d

command in Matlab, where inputs are the continuous system, sample time Ts, and method

of discretization.

19

2.3.3 Covariance matrices

Covariance matrices set behavior of the filter. One matrix consists of variances and

covariance of two (or more) vectors. Variance defines how one vector is spread out.

Covariance says how much one vector changes with other.

Let’s say we have two vectors X and Y. Equations for mean, variance and

covariance are following (both vectors with finite measured length N):

∑

(8)

∑

(9)

∑

(10)

∑

(11)

∑

(12)

Covariance matrix Q is then:

[

] (13)

If the two vectors are independent, which we suppose they are, covariance equals

zero and covariance matrix simples out:

[

] (14)

Covariance matrices basically define weights of system’s model and measurement.

Matrix Q describes properties of state noise vector w, matrix R describes properties of

20

measurement noise vector v. The bigger the value on diagonals, the less I “trust”

model/measurement.

2.3.4 Algorithm steps

Inputs into Kalman filter are from previous step: state estimate x, covariance

estimate P and system input u. Measurement y is done in the actual step. In following,

notation k|k-1 means calculation in k-th time step considering measurement from k-1 time

step.

First step in the algorithm is prediction based on model, consisting of state estimate

and estimate error covariance matrix:

(15)

(16)

Next step is state and covariance correction based on measurement (output vector

update, output vector error, update covariance, Kalman gain, state estimate update,

covariance estimate update):

(17)

(18)

(19)

(20)

(21)

(22)

At this point, state and error covariance estimates are calculated for current time

step, which are also input for k+1 time step.

21

Figure 8: Matlab Function used to calculate KF in Simulink

2.3.5 Extended Kalman filter

Previous algorithm can be only applied on linear systems. By broadening simple

Kalman filter (Extended Kalman Filter – EKF), states of non-linear systems can be

estimated. State matrix Φ and input matrix Γ ale replaced by local linearization in current

state x, which is calculated in every time step. This linearization leads on using Jacobian

matrix.

Having non-linear system:

(23)

Replacing it with first two terms of Taylor series:

(24)

New equations for state estimate (using Euler integration) and state matrix:

(25)

( ) (26)

Other equations in the algorithm are same as in KF.

22

3 Solution goals

Officially set tasks:

1. Implement and verify advanced method of BLDC sensorless control based on

Extended Kalman Filter.

2. Design methodology to measure and estimate the quality of BLDC sensorless

control, focused on motor’s torque ripple.

3. Apply this designed methodology and compare several BLDC sensorless controls.

Implementation and verification of sensorless control of BLDC motor method

based on Extended Kalman Filter is the first task described in solution procedures and

results. In the beginning, simulations were done to see how EKF behaves with BLDC

motor non-linear model. EKF sensorless control method was then implemented into the

dSPACE Real-time hardware and fine-tuned for best performance.

Methodology to measure and estimate the quality of BLDC sensorless control is

presented in the second part. Torque of a motor can be measured by two main methods:

direct torque sensing and current sensing. Current is then recalculated to torque. Torque

ripple is evaluated from both of these methods. Both methods are also compared to each

other.

Application of proposed methodology and comparison of some BLDC sensorless

control algorithms is shown at the end of the solution procedures and results.

23

4 Solution procedures and results

4.1 BLDC motor equations for Kalman filter

4.1.1 Electrical part

Electrical circuit of a wye wound BLDC motor can be described by following

equations (according to Figure 9):

(27)

(28)

(29)

, where:

u … phase voltage

i … phase current

R … winding resistance

L … winding inductance

M … mutual inductance

e … back-EMF

24

Figure 9: Diagram of BLDC motor

Kirchhoff’s first circuit law:

(30)

If symmetrical motor is supposed:

(31)

(32)

(33)

Considering symmetrical motor (equations 31÷33), Kirchhoff’s first law (equation

30), total inductance substitution Ls = L – M and equations for BLDC motor (27÷29) lead

to following:

25

( )

( )

(34)

(35)

(36)

Back-EMF of each phase is depending on rotor’s speed. The shape is trapezoidal

(Figure 10), with immediate value:

(37)

(38)

(39)

, where:

e … back-EMF

λ … voltage constant depending on motor’s design

ωm … rotor speed (mechanical)

f(φel) … back-EMF prototype function, depending on rotor’s electrical angle

(similar as on Figure 10, but with amplitude of 1)

26

Figure 10: Back-EMF and current ideal wave form

4.1.2 Mechanical part

BLDC motor torque equation:

(40)

, where:

Mi … motor’s inner torque

J … rotor inertia

B … viscous friction coefficient

Mz … torque load

27

Inner torque:

(41)

Equivalence between rotor’s speed and rotor’s electrical angle:

(42)

, where:

p … number of pole pairs

4.1.3 State space representation

Equations 34 ÷ 42 rewritten for state space representation:

(43)

(44)

(45)

(46)

(47)

28

First state equation ẋ = Ax + Bu:

[

]

[

]

[

]

[

]

[

]

(48)

Second state equation y = Cx + Du:

[

] [

]

[

]

[

] [

] (49)

4.1.4 Extension for EKF

Non-linear system representation ẋ = f(x,u):

[

]

[

]

(50)

29

Jacobian matrix:

[

]

[

]

(51)

(52)

Derivations ∂f(x5)/ ∂ x5 are described in Figure 11.

φel ∂fa/dx5 ∂fb/dx5 ∂fc/dx5

0π÷1/3π 6/π 0 0

1/3π÷2/3π 0 0 -6/π

2/3π÷π 0 6/π 0

π÷4/3π -6/π 0 0

4/3π÷5/3π 0 0 6/π

5/3π÷2π 0 -6/π 0

Figure 11: Back-EMF function derivation

4.1.5 Simulations using BLDC motor Simulink model

Main purpose of doing Simulink simulation was to check how the EKF behaves

with BLDC motor system and if it is possible to calculate unknown states from BLDC

motor non-linear model and measurements provided. Simulation with simple KF was done

as well, but KF output signals weren’t corresponding well with BLDC outputs. This was

because KF works with linear models only and cannot fully represent non-linear system as

BLDC motor.

30

Simulations were done with BLDC motor model used in [3]. Outputs of this model

were all necessary signals for EKF (phase voltages, phase currents and torque load), Hall

signals and also rotor speed and rotor electrical angle which were compared with signals

leaving EKF. Simulation layout is shown in Figure 12. Input signals to Kalman are vector

of measured signals y with white noise and input vector u. Output vector is state estimate

x_est.

Figure 12: BLDC with EKF simulation

Main part of whole algorithm, the EKF Matlab function, is shown in Figure 13.

Inputs of this function are: measurement y at current time step, system input u, state

estimate xest and estimate error covariance matrix P from the previous time step, output

matrix C, covariance matrices Q and R, BLDC motor parameters (winding resistance R,

winding inductance L, rotor inertia J, viscous friction coefficient B, voltage constant λ,

number of pole pairs p), time step Ts, back-EMF prototype function f(φel) and its

derivation.

Function was divided into three parts: calculation of linearized matrix Φ, prediction

step and correction step. State matrix was calculated according to equation 26, prediction

step according to equations 25 and 16 and correction step according to 17÷22.

31

Figure 13: EKF Matlab function

Simulation results are shown in Figure 14 and Figure 15. Ripple, in shown

waveforms, is due to the nature of EKF as it is just the best estimate, based on model and

actual inputs.

32

Figure 14: Estimated and “measured” speed with error displayed

33

Figure 15: Estimated and “measured” rotor’s electrical angle with error displayed

Simulated Hall position sensor output was derived out of estimated rotor’s

electrical angle information. Depending on, in which one of six segments (according to

Figure 5) rotor was located, logical signal was sent to the output. This signal was then

compared with “measured” Hall signal (Figure 16).

34

Figure 16: Simulated and “measured” Hall sensor output

4.2 Sensorless control using EKF

After successful simulation shown previously, EKF was implemented into real

BLDC motor control algorithm. The motor was driven sensorlessly using non-linear BLDC

motor model combined with phase current and phase voltage measurements. Sensorless

control algorithm was designed in Matlab/Simulink, then compiled and sent to dSPACE.

ControlDesk functioned as the control environment for model, while compiled and

running. Block diagram showing sensorless control in Figure 17.

35

Figure 17: BLDC motor sensorless control block diagram

Algorithm was running at a frequency of 10 kHz. Better performance couldn’t be

achieved due to EKF high computational requirements.

4.2.1 Used hardware

List of hardware used during experiments:

dSPACE modular hardware (DS2202 HIL I/O Board, DS1006 Processor board)

Three phase Low voltage power module (Microchip MC1L)

BLDC motor (Fulling Motor FL86BLS125)

Torque meter (Burster 8645-5005)

DC motor for torque load

4.2.2 Used software

List of software used during experiments:

Matlab 2011b with Simulink

dSPACE Real-Time Interface

dSPACE ControlDesk

36

4.2.3 Simulink algorithm

BLDC motor sensorless control algorithm in Simulink is split into two main parts

called BLDC motor and Control (Figure 18).

Figure 18: Sensorless control Simulink model overview

BLDC motor block incorporates all inputs and outputs from and to motor and the

Three phase low voltage power module. Transistor logic, Duty and Reset signals were sent

to the power module microcontroller. Fault signal was the fault detection read out of power

module microcontroller. Voltage was sensed directly on dSPACE ADC input terminal.

Phase currents were the Isolated Phase current feedback signals out of power module H-

bridge. Motor load was calculated from the current sensor, reading total current

consumption of power electronics, and the data-sheet torque constant. Hall signal is the

rotor electrical angle indicator from Hall position sensors mounted on motor’s non driving

side.

BLDC motor was driven by a pulse width modulation (PWM). Because of lack of

ADC with PWM synchronization possibility in our dSPACE hardware, digital low pass

filters had to be applied to filter both voltage and current inputs. This led to some

difficulties which are described later.

The control block is a bit more diverse, as shown in Figure 19.

Figure 19: Control block overview

37

EKF Hall sim block is very much similar to one described in 4.1.5. When

initializing the open-loop starting sequence, the EKF occasionally started to approximate to

the opposite direction as the rotor was turning, which led to fault states. That is why a

direction signal was added to the EKF Matlab function (1 indicating stop state and forward

rotation, -1 backward rotation). Outputs of this block were simulated Hall position sensor

logical signal and rotor speed.

Rotor speed is one of two estimated states from EKF used in sensorless control.

Due to use of a low-pass filter, some signal delay was introduced, but more significantly

the sensorless control algorithm wasn’t working well with BLDC motor data sheet

parameters anymore. There was a need for some experimental fine-tuning of parameters to

achieve better performance. Simulated Hall position sensor signals had to exactly

correspond with the measured ones. Simulated Hall position sensor signals were derived

from rotor’s electrical angle, which is an integral of rotor speed. So, when fine-tuning the

parameters of BLDC motor in the model, the main emphasis was on precise match of

simulated and real Hall position sensor signal, not on estimated rotor speed. This is a

reason why the speed output had to be calibrated using a third degree polynomial, to equal

the real rotor speed. Phase switching advance can be easily adjusted by either adding or

subtracting constant out of estimated rotor electrical angle.

Hall signal and direction switch block is a block where simulated and real Hall

position sensor signals were switched between. On the output, there was the Hall logical

signal, sensorless control indicator (0 indicating sensor control, 1 sensorless control) and

direction indicators (1/-1 as described previously and 1 indicating forward rotation, 0 stop

state and -1 backward rotation).

Speed regulator block is just a simple PI regulator to maintain demanded speed,

with duty cycle as an output.

Sensorless start block takes care of open loop initial starting sequence. The main

part is Stateflow chart shown in Figure 21, which then switches between inputs of Hall

switch and Duty switch. Initial state is sensor running state. From here, states can be

switched between sensorless running state and stop state. If stop state and sensorless input

1 are valid, sensorless start open loop sequence is initiated. Rotor turns into certain

position, waits for 0,4 sec and starts to rotate with open loop commutation. When rotor

speed rises above pre-defined value, states change to sensorless running and rotor runs in

closed loop using EKF estimations.

38

Figure 20: Sensorless start block

39

Figure 21: Sensorless start Stateflow diagram

Commutation logic block transferred Hall position sensor signal into transistor

logic signal. Commutation table shown in Figure 5.

4.2.4 Algorithm performance

BLDC sensorless control algorithm presented in this thesis was able to run from

approximately 50 rpm to 3100 rpm (power supply maximum voltage limit). When using

load, algorithm was working without problems up to around 2 Nm of load, then stalled

because of power supply current limit.

Finding covariance matrices was an iteration process to accomplish best EKF

performance. Increasing Q and R meant more noise in process and higher uncertainty in

model or measurement.

40

As stated before, EKF was used to estimate rotor speed and rotor electrical angle,

from which the simulated Hall position sensor signal, used to drive the motor, was derived.

Comparison of real measured and simulated Hall position sensor signal shown in Figure

22.

Figure 22: Simulated and measured Hall position sensor signal comparison

4.2.5 dSPACE ControlDesk GUI

dSPACE ControlDesk was used to control algorithm while compiled and running.

In this algorithm, ControlDesk includes switches to demand rotation direction, speed

demand, sensor or sensorless control and reset button. Hall states indicators, sensorless

indicator and speed display are also incorporated. dSPACE ControlDesk works as an

oscilloscope, with sampling frequency set by Simulink model. Waveforms of any kind can

be displayed and recorded, in Figure 23 phase current and phase voltage shown.

41

Figure 23: dSPACE ControlDesk

4.3 Methodology of torque ripple evaluation

Output torque ripple is one of the biggest issues when using BLDC motor drives. If

torque ripple is significant, it can reduce life-time of accessories connected to BLDC

motor, such as gearbox, etc.

Torque ripple (output torque in general) can be measured by two main transducing

methods: torque sensor or current sensor, current is then recalculated to torque by the

torque constant. In this thesis both methods are described and compared.

Figure 24 provides an overview of BLDC motor signals in time: phase voltage and

phase current on phase A, one of three Hall position sensor signals and total current (total

current measured with the external LEM current sensor). Crosses indicate moment of

phase commutation. This waveform was captured when using sensor control. Frequency

spectrum of total current is in Figure 25.

42

Figure 24: BLDC signals waveform at 1000 rpm

Figure 25: Frequency spectrum of total current at 1000 rpm

43

The most significant frequency is the one at approximately 400Hz, which is the

commutating frequency of BLDC motor:

(53)

, where:

fCOM … commutating frequency

fω … rotor speed in [Hz]

n … number of phase commutations per electrical revolution

p … number of pole pairs

Since the commutating frequency was the most significant element of frequency

spectrum, this was the most focused on frequency, when evaluating output torque ripple.

Mean squared error (MSE) was the method used to evaluate the actual torque

ripple. MSE is a performance function, which measures how much a vector spreads out.

∑

(54)

, where:

N … number of samples

xk …k-th sample of signal

μx … mean

At all methods described subsequently, torque ripple evaluation is shown at 1000

RPM (commutating frequency of 400Hz) to easily compare one technique to another.

Detailed analysis of torque ripple is in [11], [12] and [13].

4.3.1 Torque sensor measurement

Experimental setup can be seen in Figure 26 with BLDC motor, cylindrical break

and torque meter in the middle. When evaluating torque ripple out of torque meter, no

phase switching ripple appears with no load connected. Some loading device has to be

44

attached at all times. Also the breaking device has to rotate as smoothly as possible. When,

for example, a DC motor is linked, the transducer is showing DC motor commutation and

reluctance moment instead of BLDC motor phase switching. This information would be

useless for our purposes.

Figure 26: BLDC motor, torque meter and cylindrical break experimental setup

Figure 27 displays waveform of torque meter output with DC motor acting as a

break, BLDC motor commutation moments are marked. Frequency spectrum is shown in

Figure 28. The most significant frequency is the DC motor commutation at 133 Hz.

Torque meter output with smoother load shown later in this thesis (in Figure 33 and Figure

34).

45

Figure 27: Torque meter output

Figure 28: Torque meter output frequency spectrum

46

4.3.2 Current sensor measurement

When assessing torque ripple out of current sensor measurement, no load needs to

be connected. Ripple is clearly visible from low to high speeds.

Torque ripple can be evaluated by two different current measurements: phase

current and total current. Phase current would be more suitable, since phase current sensors

are already utilized in EKF sensorless control algorithm. Waveform of this measurement

(measured without load) is demonstrated in Figure 29 frequency spectrum in Figure 30.

Figure 29: One phase current

47

Figure 30: One phase current frequency spectrum

As we can see on the figures above, commutation torque ripple cannot be clearly

visible. This method is therefore useless for our purposes.

Measuring total current entering power electronics demonstrated best results.

Commutation torque ripple is clearly visible in waveform in Figure 31 and also in

frequency spectrum in Figure 32.

48

Figure 31: Total current

Figure 32: Total current frequency spectrum

49

4.3.3 Method comparison

Method comparison was done to see how the total current method is compared with

torque meter output. Series of measurement was done at different rotor speeds with and

without load. Waveform shown below is at 500RPM. Smooth cylindrical break connected

to torque meter (Figure 26) acted as a breaking mechanism. Figure 33 shows both methods

compared in time. Frequency spectrum of torque sensor measurement is in Figure 34,

torque measurement using current sensor frequency spectrum in Figure 35.

Waveforms of both methods are similar at lower speeds. From about 800 RPM

commutation ripple on torque meter output begins to be less visible. This is due to high

mechanical time constant of BLDC motor, torque meter and cylindrical break system.

Cutoff frequency of the transducer is 1 kHz, which shouldn’t influence output at these

speeds.

Figure 33: Method comparison overview

50

Figure 34: Torque meter output frequency spectrum

Figure 35: Calculated torque frequency spectrum

51

4.4 BLDC motor sensorless control evaluation

Taking into account all methods described above, technique using total current

entering power electronics was chosen as the best one to evaluate sensorless control. This

method does not need any measuring device or load connected to BLDC motor output

shaft, so the ripple assessed is the one that is really caused by phase commutation. For

better ADC scaling, the external Hall current sensor was connected to the FPGA card

incorporated in the dSPACE modular hardware and then processed. Sampling frequency of

the input signal was 10 kHz. No filter was applied to smooth out or adjust the signal. Mean

squared error was the performance criteria.

Several BLDC sensorless controlling techniques were evaluated: sensorless method

using EKF described in this thesis, sensorless method using EKF with phase switching

advance of -0.1 rad, sensorless method described in [4] and a commercially accessible

controller (RC speed regulator). Also the sensor control method was compared.

Sensorless methods using EKF and described in [4] behaved similar with sensor

control. Second mentioned stopped working at about 1350 RPM. Commercially accessible

controller showed the worst performance. Lastly evaluated was the EKF method with

phase switching advance. At lower speeds, this method performed better than the one

without phase advance. At higher speeds, both variations were the same. Figure 36 shows

performance of all methods evaluated.

52

Figure 36: Methods performance comparison

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

100 300 500 700 900 1100 1300 1500

MSE

[N

m2 ]

Rotor speed [RPM]

Method comparison

Sensors

EKF

Sensorless [4]

Commercial

EKF - Phase adv.

53

5 Conclusion

The thesis thoroughly described implementation of Extended Kalman filter into

brushless direct current motor sensorless control algorithm. This control method was

working well from low to high speeds with or without load. Open loop commutation was

needed to start-up the motor.

First part (research) delivered an overview of BLDC motor principles and described

some methods used to control the motor (both with position sensors and sensorlessly).

Also, short introduction to Kalman filter was provided here.

Second section (solution procedures and results) described application of EKF into

BLDC motor sensorless control. After simulations, EKF was implemented into real BLDC

motor control algorithm. Control technique presented in this thesis was able to run from

approximately 50 rpm to 3100 rpm (power supply maximum voltage limit). When using

load, algorithm was working without problems up to around 2 Nm of load, then stalled

because of power supply current limit.

Possible methodologies to measure and estimate the quality of BLDC sensorless

control (with focus on output torque ripple) were discussed in the last part of this thesis.

Technique using total current entering power electronics provided best results during

experiments. Mean squared error was the performance criteria. At the end, several BLDC

motor control algorithms were evaluated. Sensorless method using EKF behaved similar as

the sensor control.

54

6 References

[1] VOREL, P.: Synchronní stroje s permanentními magnety. Brno: Akademické

nakladatelství CERM, s.r.o., 2005. 80-7204-417-6.

[2] GAMAZO, J.C.; VÁZQUEZ, E.; GÓMEZ, J.: Position and Speed Control of Brushless

DC. Valladolid, Spain: University of Valladolid, 2010.

[3] KRIŽAN, J.: Bezsenzorové řízení BLDC motoru. Brno: Vysoké učení technické v Brně,

Fakulta strojního inženýrství, 2012. str. 70. Vedoucí diplomové práce doc. Ing. Robert

Grepl, Ph.D.

[4] SOVA, V.: Využití FPGA pro řízení a modelování BLDC motoru. Brno: Vysoké učení

technické v Brně, Fakulta strojního inženýrství, 2013. str. 67. Vedoucí diplomové

práce doc. Ing. Robert Grepl, Ph.D.

[5] SKALICKÝ, J.: Elektrické servopohony. Brno: Vysoké učení technické v Brně, Fakulta

elektrotechniky a komunikačních technologií, 2002. 80-214-1978-4.

[6] GREPL, R.: Podklady a příklady k předmětu RPO: Pohonové soustavy. Brno: Vysoké

učení technické v Brně, Fakulta strojního inženýrství, 2013.

[7] VESELÝ, L. Algoritmy bezsnímačového řízení synchronního motoru s permanentními

magnety. Brno: Vysoké učení technické v Brně, Fakulta elektrotechniky a

komunikačních technologií, 2013. 122s. Vedoucí disertační práce doc. Ing. Pavel

Václavek, Ph.D.

[8] LENINE, D.; RAMI REDDY, B.; VIJAY KUMAR, S.: Estimation of speed and rotor

position of BLDC motor using Extended Kalman filter. International Conference on

Information and Communication Technology in Electrical Sciences. 2007.

[9] DHAOUADI, R.; MOHAN, N.; NORUM, L.: Design and implementation of an

extended Kalman filter for the state estimation of a permanent magnet synchronous

motor. IEEE Transactions on Power Electronics. 1991.

[10] TERZIC, B.; JADRIC, M.: Design and implementation of the extended Kalman filter

for the speed and rotor position estimation of brushless DC motor. IEEE Transactions

on Industrial Electronics. 2001.

[11] ZIAEINEJAD, S.; SANGSEFIDI, Y.; SHOULAIE, A.: Analysis of commutation

torque ripple of BLDC motors and a simple method for its reduction. International

Conference on Electrical Engineering and Informatics (ICEEI). 2011.

55

[12] BYOUNG-HEE, K.; CHOEL-JU, K.; HZUNG-SU, M,; GYU-HA C.: Analysis of

torque ripple in BLDC motor with commutation time. IEEE International Symposium

on Industrial Electronics, 2001.

[13] RANSARA, H.K.S.; MADAWALA, U.K.: A technique for torque ripple

compensation of a low cost BLDC motor drive. IEEE International Conference on

Industrial Technology. 2013.

[14] EM, veidt.: General State Estimation Techniques. [Online] 12. August 2013. [Citace:

4. May 2014.] http://wiki.ldv.ei.tum.de/tiki-

index.php?page=2.+General+State+Estimation+Techniques.

[15] Matlab/Simulink, Mathworks, Inc.: http://www.mathworks.com, 2014

[16] Modular Hardware, dSPACE GmbH: http://www.dspace.com, 2014.

[17] BLDC motor FL86BLS125, Smart Motor Devices OÜ: http://www.stepmotor.biz,

2014

[18] Three phase Low voltage power module MC1L, Microchip Technology, Inc.:

http://www.microchip.com, 2014

[19] Torque meter 86445-5005, burster praezisionsmesstechnik gmbh & co kg,

http://www.burster.com, 2014

56

7 Symbols and abbreviations

Symbol Meaning

A State matrix

ADC Analog to digital converter

B Input matrix

B Viscous friction coefficient

C Output matrix

D Feedforward matrix

e Back-EMF

EKF Extended Kalman filter

f(φel) Back-EMF prototype function

fCOM Commutating frequency

fω Rotor speed

G Noise matrix

I Unit matrix

i Phase current

J Jacobian matrix

J Rotor inertia

K Kalman gain

KF Kalman filter

L Winding inductance

Ls Inductance substitution

M Mutual inductance

Mi Motor inner torque

Mz Torque load

n No. of phase commutations

N Number of samples

P Covariance estimate

p Number of pole pairs

Q Model covariance matrix

R Measurement covariance matrix

R Phase resistance

S Covariance update

Ts Sample time

u Input vector

u Phase voltage

v Measurement noise vector

w State noise vector

x State vector

y Output vector

Γ Input matrix (discrete time)

Λ Noise matrix (discrete time)

λ Voltage constant

Φ State matrix (discrete time)

φel Rotor electrical angle

ωm Mechanical rotor speed

57

8 List of attachments

EKF simulation with BLDC motor files:

(1) Simulation_EKF_BLDC.m

(2) Simulation_BLDC_EKF.mdl

EKF sensorless BLDC motor control files:

(3) dSPACE_EKF_BLDC.m

(4) dSPACE_BLDC_EKF.mdl

Datasheets:

(5) BLDC_FL86BLS125.pdf

(6) Power_module_MC1L.pdf

(7) Torque_meter_8645-5005.pdf