speed control of a switched reluctance motor benjamin pilley...switched reluctance motor. further...
TRANSCRIPT
Speed Control of a Switched Reluctance Motor
Benjamin Pilley
2nd November 2005
A thesis submitted in partial fulfilment of the requirements for the degree of
Bachelor of Engineering in Electrical Engineering at The University of
Newcastle, Australia.
i
Abstract The aim of this project is to control the speed of a Switched Reluctance Motor. A
current controller, utilising a Mitsubishi M16C microcontroller, from a previous attempt at
this project will be used. The switched reluctance motor was originally from a washing
machine but required a new controller for research into a general purpose drive. A speed
control loop has been placed around the existing current controller and a PI speed controller
now controls the motor. The speed is measured using the position encoder and filtered to
reduce the effects of noise. A means of varying the commutation turn on and turn off angles
has been implemented to give greater control on the production of torque. The drive and user
interface circuitry has been mounted in an instrument case for teaching purposes. Extra
functionality has been added in the form of protection, ramping of the speed set-point and an
LCD.
Further work has been undertaken into investigating methods that remove the need
for a mechanical position sensor. The ruggedness and reliability of the SRM makes it suitable
for applications in harsh environments and removing the dedicated shaft position sensor
further improves its potential in these applications.
ii
Acknowledgments I would like to take this opportunity to thank the many people that have helped me
throughout the project. It has been a challenging, but rewarding experience and it is only
fitting that I acknowledge those that have helped me get to this point.
To my Parents, family and friends who supported me along the way and helped in
anyway they could. This is dedicated to you.
I would like to thank Colin Coates, my academic supervisor for the guidance, support
and ideas provided throughout the year.
Finally I would like to thank all the technical staff in the electrical engineering
department, but especially Nick Hawryluk and Chris Jones who readily provided equipment
when needed.
Thankyou,
Benjamin Pilley
iii
List of Contributions Contributions that have been made during this project include:
• Reconstruction of previous project.
• Implementation and tuning of PI speed controller.
• Improvement on position detection techniques using position estimation.
• Design and construction of enclosure.
• Addition of an LCD.
• Adjustable commutation angles.
• Calculation of optimal turn on angle.
• Long and short dwell commutation schemes.
• Modification of current transformers.
• State machine background software.
• Improved reliable starting method.
• Ability to reverse while already running.
• Agitation demonstration mode.
• Accurate measurement of speed.
• Filtering of measured speed.
• Stall and current protection.
• Investigation into position sensor-less methods.
• Measuring inductance profile.
• Trialling of a position sensor-less method.
Signed,
Benjamin Pilley Colin Coates
______________ ________________
2/10/2005 2/10/2005
iv
Table of Contents
ABSTRACT...................................................................................................................................... I
ACKNOWLEDGMENTS ............................................................................................................... II
LIST OF CONTRIBUTIONS ........................................................................................................III
TABLE OF CONTENTS ...............................................................................................................IV
LIST OF FIGURES...................................................................................................................... VII
1. INTRODUCTION........................................................................................................................ 1
1.1 SCOPE....................................................................................................................................... 1 1.2 OVERVIEW OF SWITCHED RELUCTANCE MOTORS ....................................................................... 2 1.3 ADVANTAGES AND DISADVANTAGES ......................................................................................... 2 1.4 APPLICATIONS........................................................................................................................... 3 1.5 OUTLINE OF REPORT ................................................................................................................. 4
2. THEORIES AND PRINCIPLES.................................................................................................. 5
2.1 VARIATION OF INDUCTANCE WITH ROTOR POSITION................................................................... 5 2.2 THE VOLTAGE EQUATION .......................................................................................................... 8 2.3 CONTROL METHODS................................................................................................................ 11
2.3.1 Energising the SRM......................................................................................................... 11 2.3.2 Voltage Control............................................................................................................... 12 2.3.3 Current Control............................................................................................................... 12 2.3.4 Single Pulse Mode ........................................................................................................... 13 2.3.5 Commutation and Firing Angles ...................................................................................... 14
3. HARDWARE AND BACKGROUND SOFTWARE................................................................. 17
3.1 HARDWARE............................................................................................................................. 17 3.1.1 SRM and Converter Circuit ............................................................................................. 17 3.1.2 Microcontroller............................................................................................................... 18 3.1.3 Current Feedback............................................................................................................ 18 3.1.4 Position Encoder............................................................................................................. 19 3.1.5 User Interface ................................................................................................................. 20 3.1.6 Interface Board ............................................................................................................... 21 3.1.7 Enclosure ........................................................................................................................ 21 3.1.8 Power Supplies................................................................................................................ 21
3.2 BACKGROUND SOFTWARE ....................................................................................................... 22 3.2.1 Initialisation, Reset and Off State..................................................................................... 22 3.2.2 Motor Start Procedure..................................................................................................... 24 3.2.3 On State .......................................................................................................................... 25
v
3.2.4 Reverse State................................................................................................................... 26 3.2.5 Agitate State.................................................................................................................... 26
4. FOREGROUND SOFTWARE AND CONTROLLER ............................................................. 28
4.1 POSITION ESTIMATION............................................................................................................. 28 4.2 COMMUTATION ANGLES .......................................................................................................... 31
4.2.1 Advance Angle................................................................................................................. 31 4.2.2 Turn Off angle................................................................................................................. 32
4.3 COMMUTATOR ........................................................................................................................ 33 4.4 CURRENT CONTROLLER........................................................................................................... 35 4.5 OVER CURRENT PROTECTION .................................................................................................. 35 4.6 USER INTERFACE TIMER .......................................................................................................... 35 4.7 SPEED MEASUREMENT AND FEEDBACK .................................................................................... 36 4.8 SPEED FILTER ......................................................................................................................... 37 4.9 SPEED SET POINT CREATION AND RAMPING.............................................................................. 38 4.10 STALL PROTECTION ............................................................................................................... 38 4.11 PI SPEED CONTROLLER.......................................................................................................... 39
4.11.1 Tuning the Speed Controller .......................................................................................... 39 4.11.2 Implementing the Speed Controller ................................................................................ 40
4.12 INTERRUPT PRIORITIES .......................................................................................................... 40 4.13 PROCESSOR LOADING ............................................................................................................ 41
5. RESULTS ................................................................................................................................... 42
5.1 SPEED MEASUREMENT ............................................................................................................ 42 5.2 POSITION ESTIMATION............................................................................................................. 42 5.3 CURRENT CONTROL ................................................................................................................ 44 5.4 SPEED CONTROL ..................................................................................................................... 46
6. POSITION SENSOR-LESS TECHNIQUES ............................................................................. 49
6.1 REVIEW OF POSITION SENSOR-LESS TECHNIQUES ..................................................................... 49 6.1.1 Flux-linkage.................................................................................................................... 50 6.1.2 Observation of the Phase Current Waveform.................................................................... 50 6.1.3 Active Probing................................................................................................................. 51
6.2 INVESTIGATION INTO ACTIVE PROBING .................................................................................... 52 6.2.1 Measurement of the Inductance Profile ............................................................................ 52 6.2.2 Implementation of Active Probing .................................................................................... 53 6.2.3 Results and Issues............................................................................................................ 55
7. CONCLUSION........................................................................................................................... 57
7.1 WORK BEFORE OPEN DAY....................................................................................................... 57 7.2 FUTURE WORK........................................................................................................................ 57 7.2 CONCLUSIONS ......................................................................................................................... 57
vi
REFERENCES............................................................................................................................... 59
Appendix A- Software in C code
Appendix B-Ports and connections
Appendix C-Speed calculation errors
Appendix D-Current setpoint
Appendix E-Speed controller tuning
Appendix F-Circuit diagrams
Appendix G-Photos
vii
List of Figures FIGURE 2.1 2/2 SWITCHED RELUCTANCE MOTOR [8]. ............................................................................................ 6
FIGURE 2.2: INDUCTANCE PROFILE FOR THE SINGLE PHASE 2/2 SRM....................................................................... 6
FIGURE 2.3 3 PHASE 6/4 SRM [2] ........................................................................................................................ 7
FIGURE 2.4: 12/8, 3 PHASE SWITCHED RELUCTANCE MOTOR [2] ............................................................................ 7
FIGURE 2.5: FLUX LINKAGE VERSUS CURRENT CURVES AT VARIOUS ROTOR POSITIONS FOR A) IDEAL, B) PRACTICAL. . 8
FIGURE 2.6: EQUIVALENT CIRCUIT FOR A SINGLE PHASE......................................................................................... 9
FIGURE 2.7 HALF-BRIDGE INVERTER [2] .............................................................................................................11
FIGURE 2.8 CURRENT CONTROL METHODS ..........................................................................................................13
FIGURE 2.9: TORQUE SPEED CURVE FOR A SRM [13]...........................................................................................14
FIGURE 2.10: PHASE INDUCTANCE PROFILES WITH ENCODER PATTERN FOR THE 12/8 THREE PHASE SRM ..................15
FIGURE 2.11: DETERMINING THE TURN ON ANGLE. ...............................................................................................16
FIGURE 3.1: HARDWARE OVERVIEW [2] ..............................................................................................................17
FIGURE 3.2: BACKGROUND SOFTWARE FLOW .......................................................................................................23
FIGURE 3.3: STARTING PROCEDURE.....................................................................................................................25
FIGURE 3.4: REVERSE AND AGITATE MODES OF OPERATION ..................................................................................27
FIGURE 4.1: BLOCK DIAGRAM OF SPEED AND CURRENT CONTROLLERS..................................................................28
FIGURE 4.2: FOREGROUND SOFTWARE .................................................................................................................29
FIGURE 4.3: A) POSITION ENCODER EDGE DETERMINATION AND B) LOGIC OF POSITION ESTIMATION .........................30
FIGURE 4.4: A) COMMUTATION WITH NO OVERLAP B) COMMUTATION WITH OVERLAP ............................................34
FIGURE4.5: SPEED CALCULATION, DISPLAY AND RETURN FUNCTION.......................................................................37
FIGURE 4.6: INTERRUPTS IN ORDER OF PRIORITIES ................................................................................................41
FIGURE 5.1: ESTIMATION OF POSITION AT 1 RPS ..................................................................................................43
FIGURE 5.2: ESTIMATION OF POSITION AT 10RPS.................................................................................................43
FIGURE 5.3: POSITION ESTIMATION AT 25 RPS.....................................................................................................44
FIGURE 5.4: OVERLAPPED CURRENT WAVEFORMS AT 13RPS.................................................................................45
FIGURE 5.5: NON-OVERLAPPED CURRENT WAVEFORM AT 13 RPS..........................................................................45
FIGURE 5.6: CURRENT WAVEFORMS AT 7RPS. .....................................................................................................46
FIGURE 5.7: START-UP WITH NO LOAD. ................................................................................................................47
FIGURE 5.8: START-UP WITH LOAD......................................................................................................................47
FIGURE 5.9: SPEED REFERENCE CHANGE AND RESULTING MOTOR SPEED. ................................................................48
FIGURE 5.10: CHANGED IN LOAD AT FIXED SPEED.................................................................................................48
FIGURE 6.1: COMBINED FIGURE SHOWING RISE/FALL TIME AND CHANGE OF SLOPE METHODS....................................51
FIGURE 6.2: ACTIVE PROBING IN AN UNEXCITED PHASE.........................................................................................52
FIGURE 6.3: INDUCTANCE CURVES AT VARIOUS MECHANICAL ANGLES AND CURRENTS. ...........................................53
FIGURE 6.4: ACTIVE PROBING METHOD................................................................................................................54
FIGURE 6.5: ACTIVE PROBING OF PHASE A...........................................................................................................55
FIGURE 6.6: RESULTS OF ACTIVE PROBING METHOD..............................................................................................55
1
1. Introduction The increase in need for variable speed drives in industry and consumer applications
has seen renewed interest in the Switched Reluctance Motor (SRM). Reluctance machines
have been around in one form or another since the 1830s [1]. The introduction of
semiconductor power switching technology in the 1960s saw the first modern SRM become a
reality, however it was not until the late 1980s that the interest in SRMs increased. Since then
much research and development on these motors has taken place. Only a small number of
commercial products presently use SRMs. However the advantages of the SRM over other
drives, particularly in applications requiring reliability and adjustable speed, continue to fuel
research on these motors.
1.1 Scope
The primary aim of this project is to design and implement a speed controller for a
Switched Reluctance Motor. Further work is to be done to research methods of advanced
control using sensor-less control. Finally the drive will be packaged in a more user friendly
arrangement to ease further work on the motor.
The switched reluctance machine and its associated drive electronics were obtained
from a washing machine. In 2003, Mathew Tildesley designed a current controller for the
motor [2] and this project builds on this and adds speed control. The existing current
controller uses the Mitsubishi M16C microcontroller, bypassing the original controller. The
original drive circuit still remains. This project will continue using this arrangement as the
microcontroller has the ability to handle the planned speed controller.
The further work undertaken into removing the need for a mechanical position sensor
by investigating position sensor-less control is motivated by one of the main advantages of
the SRM. The ruggedness and reliability of the SRM makes it suitable for applications in
harsh environments and removing the dedicated shaft position sensor further improves its
potential in these applications.
The installation of the drive circuit and various interfacing electronics inside an
enclosure increases the safety of the user when running the motor at voltages above the safe
levels specified in AS/NZS3000:2000. It will also increase the ease of use in demonstrations
and for future final year projects, teaching or use in the laboratories.
2
1.2 Overview of Switched Reluctance Motors
All electrical machines can be classified into two different categories depending on
how they produce torque. The first is electromagnetic, where motion is produced from the
interaction of the two magnetic fields produced by the stator and the rotor. This produces an
electromagnetic torque that tends to bring the fields into alignment. The vast majority of
motors fall into this category, such as DC and induction motors, but they differ on how their
magnetic fields are generated.
The second type, of which the SRM is included, produces its torque “by the tendency
of its moveable part to move to a position where the inductance of the excited winding is
maximized” [3]. These motors are known as variable reluctance motors. The tendency of the
rotor is to move to a position of minimum reluctance, in order to close the flux path, thereby
producing torque. The term ‘switched’ derives from the switching of the currents in the
individual stator phases, more accurately described as commutation. This switching creates
momentary magnetic circuits which cause the rotor to continuously move to a position of
minimum reluctance. By controlling the switching strategy, and the current flowing through
the stator coils, we can control the torque and the speed of the motor.
1.3 Advantages and Disadvantages
The SRM has no permanent magnets; therefore its construction is very simple. It has
windings on the stator, but not on the rotor. The rotor is quite basic, consisting of steel
laminations stacked around the shaft. This attributes a number of advantages to the SRM. The
costs “and problems associated with permanent magnets (such as magnetization and
demagnetization) are avoided” [3]. The rotor is easier to manufacture and weighs less, giving
the shaft a low inertia, therefore increasing its ability to accelerate and its ability to operate at
high speed. The lack of windings produces minimal heat, eliminating the difficulties that arise
from the need to cool the inside of the motor.
The SRM is able to operate over a very wide speed range without any special
arrangements or modifications. Due to the simple construction and lack of brushes, they are
very robust and suitable for operation in harsh environments. This also means that in simple
applications such as a general drive, little maintenance is required and a long life can be
expected.
Unfortunately, the SRM has some shortcomings. The most important is that its
control characteristics are nonlinear. This is caused by a number of factors including fringing,
magnetic saturation and the reliance on a single excitation source. Another disadvantage,
compared to other types of motors, is the commutation of the SRM has to be done
3
electronically, rather than being operated from an AC source or DC bus like other more
popular motors. This requires a microcontroller and power electronics to control the
commutation of the motor’s phases.
The need to provide the controller with rotor position information requires the use of
a mechanical encoder, typically a slotted disc with photo interrupters or Hall Effect sensors.
The dependence on these mechanical sensors increases “the cost and complexity, and tend to
reduce the reliability of the drive system. The discrete sensors are also undesirable in space
restricted applications.”[4]. The alternative is to use a sensor-less method of position
detection that relies on online measurements of motor parameters. This eliminates the
mechanical position encoders but typically requires extra software overheads such as a fast
processor or reasonable amounts of memory.
Another disadvantage is the ripple in the production of torque. This is due to the
switching of the current in the phases. This ripple can be attributed to the period when a stator
phase is energized, but the rotor is in an unaligned position and therefore unable to produce
the maximum amount of torque. The switching of the current can also produce an amount of
acoustic noise if the switching frequency is in the audible range of frequencies.
1.4 Applications
The advantages of Switched Reluctance Motors, such as reliability and speed range,
have seen them adopted into a variety of applications. For example the motor that this project
is concerned with originated in a washing machine. Below are some examples of real world
applications.
• CompAir Broomwade Limited uses switched reluctance motors in some of its
variable speed compressors.
• Besam AB uses switched reluctance motors in its Besam EMD 3000 sliding door
operating system
• Smallfry utilises a compact SRM in its “next generation of food processors” [5].
• SR Drives Manufacturing Ltd manufactures switched reluctance motors for use in
hazardous environments such as mines.
• Automotive applications such as power steering[6].
With continuing research and development into overcoming the disadvantages of torque
ripple and the need for a rotor position sensor, the adoption of the SRM as a general purpose
drive will start to take place.
4
1.5 Outline of Report
Chapter 2 provides a look at the basic principles of the SRM. The properties of the motor
are discussed with reference to the voltage equation and the torque equation is developed. A
brief look at the circuit used to control the SRM and some of the methods of control are
introduced.
Chapter 3 outlines the hardware involved in the project and the background software.
Chapter 4 presents the controller and supporting functionality that occurs during the
interrupts.
Chapter 5 presents the results of the drive with the speed controller.
Chapter 6 contains some background, work and results on position sensor-less methods
of control.
Chapter 7 concludes the report, presenting what has been achieved, the road to the open
day and some future possibilities for projects involving this motor.
5
2. Theories and Principles This section will outline the basic principles of operation of the SRM and expand on
the relevant information required for the discussion of the project. The motor that this project
is based on is a 12/8, 3-phase SRM, with 12 stator poles and 8 rotor poles. References will be
made to different stator/rotor layouts to explain the basic principles. Firstly a 2/2 motor will
be used to explain the variation of inductance with rotor position and then the process of
torque production. A 6/4 motor will then be used to explain the methods of rotation. The
torque equation will be derived using the voltage equation. Finally the circuit used to energise
the SRM will be introduced and the typical methods used to produce torque.
2.1 Variation of Inductance with Rotor Position
The 2/2 SRM shown in figure 2.1 is a simple machine that can only produce torque
over a limited arc of rotation, but will serve as the basis of a discussion on one of the main
principles of SRMs, the variation of inductance with respect to rotor position. From the theory
of electromagnetism, reluctance is the “opposition offered to the establishment of magnetic
lines of force in a magnetic circuit”[7] and is defined as
Al
µ=ℜ H-1
where l is the length (m) and A is the cross-sectional area (m2) of the magnetic circuit. The
permeability is µ (Hm-1). The inductance is inversely related to reluctance and is defined as
ℜ=
2nL Hm-1
where n is equal to the number of turns. When the windings around the stator coil are
energised and the stator and rotor poles are not aligned, the lines of flux will have to travel
across a large amount of air. The reluctance of the circuit will be a maximum, making the
inductance minimal. As the rotor pole moves to overlap the stator pole, the flux lines will be
able to find a path of lower reluctance through the air-gap between the poles. When the two
poles are aligned, the reluctance will be at a minimum and the inductance at a maximum. A
typical inductance profile for a single phase of an SRM can be seen in figure 2.2.
6
Figure 2.1 2/2 Switched Reluctance Motor [8].
Figure 2.2: Inductance profile for the single phase 2/2 SRM
The 2/2 SRM in figure 2.1 is unable to produce continuous unidirectional torque.
Obviously there needs to be more phases so that gaps in the production of torque can be
accounted for by the other phases. Figure 2.3 shows a 6/4, 3-phase SRM. When the phase pair
A-A’ are energized, by supplying current to the coils around each pole, the rotor pole pair X-
Y will rotate to align with A-A’ in order to close the flux path and increase inductance. If
rotation is required in the clockwise direction, A-A’ is switched off and the pair C-C’ is
energized, causing the rotor poles W and Z respectively to rotate to align with the C poles.
The B pair are energized next, acting on X and Y and so on. “The cycle of torque production
associated with one current pulse is called a stroke” [3]. The stroke is also definable as the
step angle, which can be calculated using the following equation.
radqN r
πε
2=
Where rN is equal to the number of rotor poles and q is the number of phases. For the 6/4
motor, the stroke is equal to 0.523 rad or 30 degrees.
7
Figure 2.3 3 phase 6/4 SRM [2]
Thus when the rotor is aligned with phase A as in figure 2.3, and the next phase is activated,
in this case C, the rotor will move 30 degrees to a position of maximum inductance. For the
12/8 SRM involved in this project (see figure 2.4) the stroke is 0.26 rad or 15 degrees. To
complete a full revolution, the 12/8 motor needs 24 steps.
Figure 2.4: 12/8, 3 phase Switched Reluctance Motor [2]
8
2.2 The Voltage Equation
By examining the voltage equation and determining an expression for torque we can
learn a great deal about the operation of the SRM. By undertaking a linear analysis we assume
that the inductance is unaffected by the current. In a practical SRM, saturation occurs as the
current in the phase increases beyond a certain point contributing to the machines non-linear
nature. In figure 2.5 we see a typical set of magnetisation curves for a SRM. The ideal curves
are shown next to these. For this analysis the ideal case will suffice. We can also ignore the
fringing flux about the pole corners and make the assumption that the flux crosses the air gap
in a radial manner. The mutual coupling between phases is ignored in this case as its effect is
negligible. These assumptions can be made to simplify the analysis, without eliminating the
important characteristics.
Figure 2.5: Flux linkage versus current curves at various rotor positions for A) Ideal, B) Practical.
The expression Vo is the applied voltage to one phase [9]:
dtd
RiVo)(θλ
+=
Where, Vo is the voltage across the phase winding, R is the winding resistance, ? (?) is the
flux linkage that varies with position and is expressed as:
iL ⋅= )()( θθλ
dtiLd
RiVo))(( ⋅
+=θ
Using the product rule:
θωθ
ddL
idtdi
LRiVo ⋅++= )( eq 1
9
The three terms on the right hand side of this equation relate to the resistive voltage drop, the
inductive voltage drop and the induced EMF respectively. Note that the induced EMF is
dependent on the rotor position, shaft speed and the current and so can be difficult to
calculate. The equivalent circuit for a single phase of a SRM can be seen in figure 2.6.
Multiplying both sides of the equations with the current gives the instantaneous power.
θθ
ωθd
dLi
dtdi
iLRiiVP oi)(
)( 22 ⋅++== eq 2
The energy stored by an inductor is given by
2
21
LiW =
Power in an inductor is given as the change in energy over time. The product rule gives
dtdi
LiddL
idtdi
LidtdL
iLidtd
pL +=+=
=
θω222
21
21
21
eq 3
Using the law of conservation of energy the mechanical power can be found by subtracting
the power loss due to the winding resistance and the inductor. Subtracting equation 3 and Ri2
from equation 2 will give
θθ
ωd
dLiPi
)(21 2 ⋅=
The electro-mechanical torque is equal to power over the speed of rotation. Applying that to
the equation above will leave us with the result
θθ
ddL
iTe)(
21 2=
Figure 2.6: Equivalent circuit for a single phase.
10
Further investigation into this equation reveals some key concepts in the operation of the
SRM.
1. The torque produced by the motor is independent of the direction of the current due to
the i2 term.
2. The dL/d? term is the slope of the inductance curve shown in figure 2.2. Due to the i2
term, the direction of the torque is dependent on the slope of the inductance curve.
Therefore to produce positive or motoring torque, current should be applied only
where the slope of the inductance is rising. Likewise negative or braking torque can
be produced by applying current when the slope of the inductance curve is negative.
3. While motoring, current in the energised phase needs to exit the windings before the
rotor reaches the aligned position. Current left in the energised phase after this would
produce negative torque, reducing the efficiency of the motor.
4. The second property implies that where the slope of the inductance profile is small,
the torque produced will be smaller than when the slope is at a maximum. Therefore
about the aligned and unaligned positions of each of the phases of the SRM, the
torque produced will be much smaller than where the slope is a maximum. This has
implications for the starting of the motor, where the starting phase cannot produce
enough torque to rotate the shaft.
5. While this is a linear analysis, in reality the inductance curve is a function of the
position as well as the current, making further development of the equivalent circuit
and model difficult.
6. The i2 term is proportional to the torque, giving the SRM good starting torque. The
lack of windings or magnets on the shaft also contributes.
7. Property two also implies that the SRM is capable of four quadrant operation.
Switched reluctance generators have been popular with researchers and show many
promising advantages over other generators especially in applications requiring
“robustness, high speed and fault tolerance”[10].
8. The direction of rotation is determined by the order in which the phases are energised.
This is a simple operation to perform.
9. The SRM requires a converter circuit and a method of controlling it. It cannot be
operated directly from a DC bus or three phase power supply. This relegates the SRM
to use as a variable speed drive to justify the cost and complexity of the converter
circuit.
The instantaneous change of the current waveform cannot be reproduced in practice
and effective ways to approximate and control this will be discussed next.
11
2.3 Control Methods
There are three common techniques for energising and controlling the current applied
to the stator phases. These are Single Pulse Mode, Voltage control and Current control. The
basic principles are outlined below after an introduction into the circuit used to energise the
SRM.
2.3.1 Energising the SRM
The SRM in this project is energised using an Asymmetric Half Bridge Inverter
shown in figure 2.7. This is a common topology used for this type of motor as it allows each
phase to be energised independently. There are three voltages that can be applied to the stator
windings. Taking Phase A for example, if both the Hi FET and Lo FET are switched on the
voltage applied to the stator winding will be +Vpos, or in the case of this project, +30V. This
is assuming that Vneg is 0Volts, which is the case in this project. The stator winding will
experience 0Volts if only one of the FETs is switched on and –Vpos if both of the FETs are
off and the current is free wheeling through the two diodes.
There are two common methods of switching, soft chopping and hard chopping. Soft
chopping has only one FET doing the chopping, steering the current through the windings.
The other FET continues to conduct throughout the excitation. In this case the stator windings
experience either +30V or 0V. The other method, hard chopping, switches both FETs on or
off together or between +30V and -30V. This method “generally produces more acoustic and
electrical noise, and increased current ripple…” [11] so soft chopping is generally preferred
and is used in this project.
Figure 2.7 Half-Bridge Inverter [2]
12
2.3.2 Voltage Control
Voltage control does not use measurements of the current to control the excitation of
the phases. This would make it suitable for a low cost drive, but in this case its inability to
control and limit the current makes it undesirable. This limitation means there is no control
over the torque output and smooth torque production is difficult to achieve. It is performed
using a fixed frequency Pulse Width Modulation (PWM) with variable duty cycle which is set
by the outer speed control loop. However this was not a previously implemented method of
controlling the current for this project so warrants no further discussion.
2.3.3 Current Control
The most common methods of current control for a SRM involve measuring the
current and then chopping either the current or the voltage to achieve the desired effect.
Chopping is the switching on/off of the power transistors at a high frequency, compared to the
fundamental frequency of the phase current waveform. The current chopping method of
current control is a hysteresis type control. The power transistors are switched off if the
specified current set point is exceeded by the measured current. When the measured current
falls below the set point, the transistors are switched back on. The supply voltage remains the
same in this case, but the switching frequency changes. This can “cause a subsonic noise in
the SRM”[12] which increases the noise produced by the motor. This makes it an undesirable
choice for some applications.
The Chopping Voltage method of current control is the one that has been previously
implemented for this project. It involves chopping the supply voltage at a fixed frequency to
maintain the measured current about a set point. The duty cycle is determined by the
difference between the measured current and the set point set by the speed controller. Figure
2.8 shows the voltage being chopped in order to maintain the current within an error band.
This method of control was chosen as it is possible to control the torque quite accurately.
Voltage control does not take the stator current into account and therefore the torque that is
produced is not as smooth or constant as that produced by a current controller.
13
Figure 2.8 Current Control Methods
2.3.4 Single Pulse Mode
The previously mentioned current control methods are suitable for low to medium
speed operation. However once the ‘base’ speed is reached (see figure 2.9), the back-EMF
produced by the motor will increase to the point where the power transistors will have to
remain on throughout the stroke to maintain the required current. Should the supply voltage
be chopped, the average voltage would fall. This would have the effect of reducing the current
and hence reducing torque.
To increase the speed further there are two possible solutions. The first is to increase
the period that the phase is conducting. This conduction period is also known as the dwell
angle. The second involves keeping the dwell angle constant and advancing the turn on angle.
A combination of these methods is also possible. If we advance the turn on angle so that the
“phase commutation begins sooner, we gain the advantage of producing current in the
winding while the inductance is low, and also of having additional time to reduce the current
in the winding before the rotor reaches the negative torque region”[13]. This method of
current control has not been used in this project. At the low to medium speeds of this motor in
its present configuration the previously mentioned voltage chopping method of current
control will be used.
14
Figure 2.9: Torque Speed Curve for a SRM [13]
2.3.5 Commutation and Firing Angles
The design of the SRM requires that the commutation of the phases be managed by
the controller unlike a DC motor which uses commutator brushes. The choice of commutation
angles for the SRM has a large effect on the performance. The commutation angles are
chosen “in such a way that they optimise the overall performance of the motor; e.g. minimise
currents or maximise efficiency”[14]. This flexibility allows the varying of the turn on angle
online to optimise performance.
Throughout the report references will be made to mechanical angles and electrical
angles. A portion of a typical inductance profile for the three phases of a 12/8 SRM can be
seen in figure 2.10. The phase inductance repeats every 45 degrees. The mechanical angle
refers to the physical angle between the shaft and the body of the motor where one revolution
is equal to 360 degrees. With the angle relative to the aligned position of phase C, one period
of the phase inductance is said to be 360 electrical degrees.
The 12/8 SRM has a stroke of 15 degrees, so each phase needs to be energised so that
it produces torque for an angle equal 15 degrees. This will ensure that there are no gaps in the
production of torque. It is also possible to energise a phase for an angle greater than 15
degrees. In this case two phases will be conducting at the same time.
15
Figure 2.10: Phase inductance profiles with encoder pattern for the 12/8 three phase SRM
This overlap will eliminate the small periods of no torque production that occur in the real
implementation of the controller where a small delay may exist between the changing of
phases.
The choice of the turn on and turn off angles at which a phase is energised to produce
torque and then turned off have a significant impact on the overall performance of the SRM.
The maximisation of the mean torque is the main objective in this case which will give a
“wider torque-speed envelope and faster transient response”[15]. The same paper presents a
set of criteria in order to achieve the maximisation of torque. The turn off angle can be chosen
to maximise torque while the turn on angle is chosen to maximise efficiency. The most
common method used to determine the optimal turn on angle is presented next followed by
the choice of the turn off angle.
Turn on angle
Close to the unaligned position of any of the phases, the inductance is at its minimum
value. If the current to the phase is applied while the inductance is at a minimum, it will rise
at a faster rate compared to applying it further away from the unaligned position where the
inductance is higher. If we utilise this property we can establish the required current in the
phase before the inductance increases. From the voltage equation presented in section 2.2 we
can neglect the voltage drop due to resistance in this case as the resistance is small and the
second term as the inductance can be assumed constant in the unaligned position. We now
have:
ωθ
⋅⋅=d
dLiV ph
phph
16
This can be rearranged to the following to obtain the turn on angle as a function of
other variables.
ωθ ⋅⋅=ph
phphon V
Li
Figure 2.11 demonstrates the application of the equation to the turn on angle. As the
speed and desired current or torque demand increases, the turn on angle is increased, giving
the current more time to reach its required value.
Turn off angle
The turn off angle can be calculated in a number of ways. If the phases are to conduct
one at a time and not overlap, the choice of the turn off angle would simply be 120 electrical
degrees or 15 mechanical degrees after the turn on angle. If some overlap is required then the
turn off angle can be chosen to “maximise the mean torque”[15].
Figure 2.11: Determining the turn on angle.
17
3. Hardware and Background Software This section provides an overview of the hardware relevant to this project and the
software that runs in the background. The hardware is discussed first, outlining the additions
and changes made to the components since the previous project. The background software is
discussed next, detailing the movement between the states of operation depending on inputs
from the user. A description of the starting algorithm is presented as well.
3.1 Hardware
3.1.1 SRM and Converter Circuit
The SRM and its drive circuitry were originally obtained from a washing machine.
The SRM in question is a three phase motor with 12 stator teeth and 8 rotor teeth. The stator
poles are 90 degrees apart and the arrangement can be seen in figure 2.4. The converter circuit
houses all the power electronics used to control the current in the stator windings. The circuit
uses the Asymmetric Half Bridge Inverter, seen in figure 2.7, to switch a voltage across the
stator coils. The current controller controls the current flowing in the stator by switching the
Field Effect Transistors (FETs) according to the control algorithm used. The implementation
of this can be seen in section 4.4.
Figure 3.1: Hardware overview [2]
18
For safety reasons the circuit has been modified to allow operation from a much
lower voltage than originally intended. The original converter and SRM operated from a
voltage supplied by rectifying 110VAC. The rectifying diodes have been bypassed and a
supply voltage of 30VDC is provided by a bench power supply ensuring that no dangerous
voltages may harm the user. A circuit diagram of the power supply can be found in the
appendices. The maximum speed and torque will be limited by the reduction of supply
voltage, increasing safety, but limiting performance.
With the completion of the speed controller and housing of the circuitry in an
enclosure the supply voltage can be increased as there is insulated barrier provided between
the user and the circuits. This presents an opportunity to increase the performance of the
motor and to validate the current and speed controllers at the original specifications.
3.1.2 Microcontroller
Mitsubishi’s M16C Microcontroller is a 16-bit microcontroller and is used to control
the SRM in this project. A full description of its features can be found by looking at the
appropriate datasheets available through the School [16].
Various features that are used in this project are I/O ports, timers and ADCs. The I/O
ports are being used for many purposes including switching the devices on the converter
circuit, reading user inputs, and outputting data to a Liquid Crystal Display (LCD). Four ports
are configured to repeatedly convert the analogue voltages produced by three Current
Transformers and a potentiometer, located on the user interface board, into digital values
between 0 and 1024. The conversion time is 2µs, which is adequate for this application[2].
Numerous timers have been set up to enable time critical components of the controller to
function in the foreground. Two external interrupt pins INT2 and INT3 are used to inform the
controller of increments made by the encoder. The roles of these timers and interrupts will be
discussed in later sections.
3.1.3 Current Feedback
In order to control the motor using the voltage chopping current control method, the
phase currents need to be measured so that it is possible to chop the voltage to keep the
current around the set point. The current is measured using one LEM LTS 25-NP Current
Transformer (CT) for each phase. These devices produce a voltage that is converted to a
digital number by the M16C’s 10-bit analogue to digital converters. The CT is ideal as it also
provides a high level of isolation between the microcontroller and the higher voltages of the
motor circuit.
Previously, the CTs were set up with a nominal current measurement of 2.5 Amps.
Being a 10-bit ADC and having a maximum and minimum measurement of 5 and 0 volts
19
respectively, the resolution of the conversion would be 4.88mV. The CT outputs a voltage of
3.125V for a measurement of 2.5 Amps, the rated current of this particular SRM. Over this
current range we have 128 different levels resulting in a resolution of 19.5mA. We can
increase the performance of the CT by improving the resolution.
By increasing the turns on the primary side of the CT, we reduce the nominal current
measurement to 1.78A. The CT can still operate up to 2.5A (output voltage would be
3.775V), but the resolution is increased to 13.9mA. This is the realistic limit of the device as
no more turns could be achieved on the primary side due to the gauge of the wire required to
handle the current. The voltage, once converted into digital is compared to the controller’s set
point in its unmodified 10-bit number to ensure that an accurate comparison is made [2].
3.1.4 Position Encoder
Knowledge of the position of the rotor with respect to the stator is important in the
control of a SRM. The rotary position encoder that is mounted on the shaft of the SRM is
used to provide the controller feedback on the position of the rotor. The encoder uses an
optical sensor which is conditioned by some simple circuitry to produce an output voltage of
0V for a gap and 5V for a block. The output signal is passed to the microcontroller through
two interrupt on change ports (INT), one each to capture the rising or falling edge. The
encoder voltage supply of 9V will be discussed in section 3.1.8.
The encoder is implemented as an incremental encoder, which records the number of
times a known sequence passes the sensor. This is a simple way to operate the encoder
compared to operating it as an absolute encoder. The absolute encoder method measures the
width of the pulse and decides if it is a ‘big’ or ‘small’ pulse and compares it to the previous
pulse. The main disadvantage is that acceleration or deceleration of the shaft might cause
errors in the measurement of the pulses. While it is possible to avoid this by limiting the rate
of change of speed, accuracy cannot be guaranteed and therefore the encoder is operated as an
incremental encoder [2].
The main problem with the incremental encoder method is the need to start the motor
from a known position in order to initialise the count. The start up routine is discussed in
section 3.2.2. Once the encoder has been initialised subsequent increments will advance the
count in the appropriate direction.
For rotation in the clockwise direction, the encoder count is incremented on the
positive edges and for anti-clockwise rotation on the negative edges. The pattern of the
encoder can be seen in figure 2.10. Each increment of the counter corresponds to a movement
of 7.5 mechanical degrees of the rotor or 60 electrical degrees. This gives six increments over
the electrical period and 48 over the complete revolution of the shaft.
20
3.1.5 User Interface
The user interface (UI) allows the user to control the motor using simple intuitive
controls. It consists of an On/Off momentary push button, Single Pole, Double Throw (SPDT)
direction switch, SPDT mode switch, potentiometer speed setting, LED On/Off indicator, four
line LCD display, LED rotation indicator and a piezo beeper. A momentary on push button
was chosen as it allowed the motor to be turned off by the software in the protection
functions. The LCD display is used to display the speed, direction of rotation, mode and other
information such as the current set-point, advance angle, and anything else used during tuning
or debugging.
After applying power and loading the software, the motor is controlled from the UI.
The user can turn the motor on by pressing the on/off button. To turn the motor off, the same
button is pressed. A green LED will light to show that the motor is turned on. A potentiometer
is used for the setting of the speed command. A switch is provided to set the direction of
rotation and the present setting can be seen on the LCD display. A mode switch allows the
user to toggle between different control methods or between normal and the agitation mode.
The final role of this control has not been determined yet, but will likely assist in the
demonstration on open day. A red LED and piezo beeper alert the user to an over current
protection issue or a stalled shaft.
A Liquid Crystal Display (LCD) has been added to the project. Originally a pair of
seven segment LED displays informed the user of the speed of the motor. However, they were
no longer part of the project equipment at the start of this year. To replace them, and to
provide more information to the user, a 4x20 character LCD display was interfaced to the
M16C. The data lines for the LCD use the same ports that were previously used for the
LED’s. An LCD display was chosen as the modules were readily available, easy to interface
and could display a large amount of information. However there were also disadvantages such
as slow update times and larger software overheads compared to the LED solution. This was
overcome by only updating the display once a second.
The LCD is operated from a series of sub-routines called from the main function and
at times when a value needs to be displayed. The LCD controller contained on the LCD
module is an industry standard Hitachi HD44780 compatible controller. The LCD needs to be
initialised before use. The LCD initialisation is run with the other initialisation routines before
the motor is operated and contains control words sent at specified time intervals. The routine
also writes any words or information to the screen that will remain constant throughout the
motors operation. This will save the need to write this in one of the timer interrupts and waste
processor time.
21
When a value that needs to be displayed is updated, a function is run that takes this
value as an argument and copies it for later display. When the 100 Hz user interface interrupt
occurs one hundred times, one second will have elapsed and the value that has been copied
will be displayed. As the copy function runs each time the value is computed or updated, the
value displayed will be the most recent. In most cases, the one second update time will be
sufficient. The number of variables that can be displayed is only limited by the size of the
display.
3.1.6 Interface Board
Before mounting in the enclosure, the UI and some other circuitry were located on a
piece of Vero board. The UI components are now located on the front panel of the enclosure,
but the Vero board is still used to mount the current transformers, noise filtering capacitors,
and optical isolators for each of the high and low side gate switches for each phase. All
connections made to the microprocessor from the UI elements, the isolators, position encoder
and current transformers still go through the Vero board.
The isolation is provided by six 4N36 Phototransistor opto-couplers produced by
Fairchild. This protects the microcontroller from possible faults on the current converter side
that might result in a high voltage being applied to the microcontroller and destroying it. The
15VDC necessary for the high side of the opto-couplers is provided by a 15VDC supply on
the current converter circuit. The 5VDC power supply for the remaining circuity is provided
by the microcontroller development board.
3.1.7 Enclosure
To increase the safety and useability of the project, the circuits have been placed
inside an enclosure. A plastic junction box was chosen due to the insulating properties of
plastic, the ease of machining and the large sizes available. The enclosure is large enough to
mount the two circuit boards side by side and is hinged along one side, allowing ease of
access. As mentioned previously the components of the user interface are mounted on the top
of the enclosure. The rear of the enclosure contains the connections to the microprocessor, the
motor and the power supply.
3.1.8 Power Supplies
At present the 5V power supply for the CTs and other circuits on the interface board
and the 9V for the position encoder circuit are provided by the M16C development board and
its switch mode power supply respectively. With the mounting of the two circuits in the
22
enclosure it would be elegant to provide the power for these circuits from another source
located within the enclosure. A 15V supply derived from a zener diode provides the high side
voltages for the isolation drives and could be used for this purpose. However this will
eliminate the isolation that presently exists between the converter circuit and the
microcontroller. Further possibilities are being explored.
3.2 Background Software
The software follows a state machine type of operation which controls the operation
of the controller and hence the motor, with time critical operations operating from timer and
INT interrupts. The user controls the movement between states based on the input from the
UI. A flow chart depicting the movement through the software based on the UI settings can be
seen in figure 3.2. A brief outline of the operation of the software will be followed by a more
in depth look at each of the states and the operations performed in the interrupts.
3.2.1 Initialisation, Reset and Off State
When power is first applied the software will initialise itself and the LCD display and
set up the required peripherals. This only needs to occur once. The software enters the reset
phase once this is done, disables the speed controller and commutation functions and
initialises the encoder counts, the current set point and other counts and flags to their
appropriate values. Disabling the speed controller and commutation functions prevents them
from interfering with the start up routine. After initialisation and reset have been completed,
the software enters the Off state. The Off state consists of a simple ‘while’ loop that exits only
when the user starts the motor from the UI.
23
Initialisation
Reset
Off
on/off switch?
Startup
On Do direction reverse
Agitate
Reverse switch?on/off switch?
Turn off agitation?
offl
on
on
off
no changel
reverse
on
off
offl
on
Agitate switch?
Figure 3.2: Background software flow
24
3.2.2 Motor Start Procedure
To start the motor turning in the correct direction the controller needs to know where
the shaft is so it can energise the correct phase next to start rotation. The position encoder
needs to be initialised to a known position for subsequent position information to be accurate
and useful. To overcome these problems the encoder is always initialised in alignment with
phase C.
Originally the starting routine had some issues with rotating to align with phase C.
The problem occurred when the rotor was in such a position that no torque was produced by
the energised phase C due to the rotor poles not overlapping the stator poles. The new routine
corrects this problem by energising both phase B and C at the same time. This will cause to
rotor to turn regardless of its initial position. After a short wait, phase B is turned off and only
phase C is left energised, aligning the rotor pole with phase C. This process can be seen in
figure 3.3.
When the rotor has aligned with phase C, a wait of approximately 0.8s occurs. This
allows the rotor to become stationary and the encoder to be initialised to the correct position
before the encoder software is enabled. After this wait is over, the direction command set by
the user is checked and the encoder software is enabled. If rotation is required in the
clockwise direction, phase B and C are energised, causing the shaft to kick in the clockwise
direction. If an anti-clockwise direction is required, phases A and C are energised. This initial
kick will provide the encoder with an edge to act upon and update the position so that the
appropriate next phase is energised in order to ensure rotation. After the kick has been
completed, the starting procedure is completed. Operation now passes to the On state
discussed in the next section.
The rotor needs to overcome any load to move to the energised phase and setting the
current at a high arbitrary set point will not always guarantee a successful start. If the load is
too great for the motor to start a stall detection routine will identify the problem, turn the
drive off and alert the user. In the future a more advanced starting algorithm could identify
this problem and increase the current set-point up to the limit in an effort to move the shaft.
25
Energise Phase B & C
Start command received
Energise Phase C
Wait a small time
Wait 0.8s
Energise Phase B & C
Energise Phase A & CDirection
Continue to normal operation Continue to normal operation
Anti-clockwise
Clockwise
Figure 3.3: Starting procedure.
3.2.3 On State
Like the Off state the On state consists of a while loop that waits until a user input
causes it to exit. A reverse of direction, enabling agitation or turning off the motor will cause
the while loop to exit and return to the off state.
26
3.2.4 Reverse State
The reverse state is entered when the user requests a change in direction of rotation.
To rotate the motor in the opposite direction only requires that the phase sequence order is
changed. However the motor needs to be stopped and restarted again. The method used
closely resembles the start-up method discussed previously. Ideally it would also use a
hesitation free method where by the motor could stop at any point and be restarted again.
Once the reverse function is entered its first task is to stop the shaft. A flowchart of
the process can be seen in figure 3.4. The commutation and speed control routines are
disabled, phase C is enabled and the current is set to approximately one ampere. This will
cause the motor to brake and slow down, eventually stopping aligned to phase C. The
software waits for a predetermined time until it assumes the rotor is stationary. This time was
determined during testing to give a minimal wait time between the changing of direction. The
position is reset as the rotor is aligned with phase C. A routine similar to the start up routine
discuss in section 3.2.2 now restarts the motor in the new direction. The speed controller and
the commutator are enabled and Control returns to the On state with the motor rotating in the
new direction.
3.2.5 Agitate State
The agitate state is a demonstration mode that operates to continuously change the
direction of the motor. Its purpose is not to emulate the previous role of this motor, but to
provide a simple display mode. Its operation is similar to the reverse state with the exception
that control remains with this state until the mode is turned off.
The agitate demonstration mode is entered from the On state by the user engaging the
mode on the UI. Control passes to the agitate state which is contained in a while loop that
continues to loop until the user disengages the agitation mode on the UI and control is passed
back to the off state. The agitate state operates by disabling the speed control and
commutator, then braking the motor in the same way as the reverse state. Once the shaft has
settled the direction of rotation is reversed, the position reset and the commutation function
enabled. The shaft is kicked in the required direction and then the function waits until it has
reached the speed set on the UI. Once the motor reaches this speed, the function loops back to
the start, braking the motor. This operation continues until the user turns the agitation mode
off and control is diverted to the reset and then off state. Figure 3.4 demonstrates the
operation of this mode.
27
Direction change
Disable speed control and commutator
Brake using phase C
Reset position and wait until stationary
What is the new direction?
Set direction to anti-clockwise
Exit rotating anti-clockwise Exit rotating clockwise
Clockwise
Anti-clockwise
Set direction to clockwise
Agitate mode
Disable speed control and commutator
Brake using phase C
Reset position and wait until stationary
Toggle direction
Are we at the maximumspeed?
Has the mode been turned off?
Start motor in new direction
Enable speed control and commutator
Has the mode been turned off?
Return to off state
Yes
No
No
Yes
Yes No
Figure 3.4: Reverse and Agitate modes of operation
28
4. Foreground Software and Controller The primary aim of this project is to design and implement a speed controller for use
with the motor and its existing current controller. The speed controller will consist of speed
measurement, feedback of the speed and at least a Proportional Integral (PI) controller to
control the speed. The controllers, the position estimation, commutation and other supporting
software are executed using interrupts. This section discusses the operation of the software
that is run in the foreground by the interrupts. The background and implementation of the
speed controller and its place within the overall drive is also discussed.
4.1 Position Estimation The position encoder provides the position information that is essential to the
operation of the SRM. As previously mentioned the encoder consists of a slotted disk and a
photo detector and provides the exact location of the rotor with respect to the stator every 7.5
mechanical degrees. Originally the commutation angles of the controller were fixed to these
encoder edges. To allow greater efficiency and higher speeds than were possible under the
previous method, the commutation angles should be variable. While the position encoder
provides accurate information at discrete positions, in between encoder edges the position of
the shaft is not known. To determine the position of the shaft between encoder edges, a
position estimation routine has been implemented.
Figure 4.1: Block diagram of Speed and Current Controllers
29
-Estimate or update position-Calculate turn on angle-Commutation-Current control-Speed control at 1kHz
-Read input controls-Write to LEDs-Create setpoint-Write to LCD-Ramp Logic-Debounce On/Off
-Calculate Speed
-Positive edge-Update count if required
-Negative edge-Update count if required
5kHz Timer
10Hz Timer
100Hz Timer
INT 2 INT 3
Figure 4.2: Foreground software
To allow flexibility and ease of tuning, the electrical angle is now represented by a
16-bit number with a range of 0 to 65535. One electrical degree is equal to 182.04 bits, while
1 bit is equal to 0.0055 degrees. Obviously due to errors in obtaining exact position
information with the encoders, this degree of accuracy is not required. However, since the
M16C is a 16-bit microprocessor there will be no large overheads required and so the full 16-
bit range will be used. Common angles such as 60 degrees and 120 degrees are defined in the
header file to allow ease of reading.
The position encoder uses two interrupt on change pins, INT2 and INT3 to interface
with the M16C for the positive and negative edges respectively. As mentioned in section
3.1.4, rotation in the clockwise direction requires that the encoder count is incremented on the
positive edges and for anti-clockwise rotation on the negative edges. This is handled in
software by keeping track of the edges, and on the required edge, be it positive or negative,
the counter is incremented. A flowchart of the procedure can be seen in figure 4.3A. After six
increments the counter is reset as the motor has completed one electrical revolution. At the
maximum set speed of 2000rpm, there will be 1584 edges every second or one every 631.2µs.
The updating of the position of the rotor takes place at 5 kHz or once every 200 µs giving
plenty of time for the edge to be recognised.
30
Has there been an edge?
Enter 5 kHz Interrupt
Is the rotor initialised and kick started?
Is the rotor initialised and kick started?
EndEstimate position using present speed
Determine which edge using encoder count
Clear edge flag
Edge from encoder
Direction?
Positive or negative edge? Positive or negative edge?
Set positive edge flag
Exit without updating
increment count and reset if 6
Also incrementspeed count
Exit
Was the previous edge positive?
Anti-clockwise
Positive
Negative
Clockwise
Positive
Negative
Yes Yes
NoNo
Yes
No
Was the previousedge negative?
Set negative edge flag
Increment edge count and reset if 6
Also increment speed count
Exit without updatingExit
Positive
Negative
Negative
positive
A)
B) Figure 4.3: A) Position encoder edge determination and B) logic of position estimation
At each valid encoder edge, a flag is set signifying that an encoder edge has just taken
place. This flag notifies the position estimation routine that operates in the 5 kHz timer that an
encoder edge has just occurred. A function is run that determines which edge just occurred
and updates the appropriate 16-bit representation of the angle to the estimated position
31
variable. This will provide the controller with exact position information at the six discrete
angles. The flow of the software can be seen in figure 4.3B.
If no encoder edge has occurred the software runs the routine to estimate the position
of the shaft. This routine uses the following equation to update the position of the shaft.
sfnnn
1)(ˆ)1(ˆ)(ˆ ⋅+−= ωθθ
This equation takes the last position updated either by the encoder or the previous
execution of the estimation algorithm and adds the distance travelled since the last update.
This is measured by multiplying the speed of the shaft by the period between updates. As the
updates occur at a regular frequency the speed can be multiplied by a constant that takes into
account the scaling as well as the frequency of updates. This constant is calculated as below.
162360
65535)(1
360(sec)60
(min)1(sec)1)(60_ESTK_POSITION ⋅
°⋅
°⋅⋅⋅=
revfsrps
In this case the frequency is set to 5 kHz and we obtain a result of 858972.
4.2 Commutation Angles
In the original current controller, the commutation angles coincided with edges of the
position encoder and so were fixed. The present controller allows the commutation angles to
be varied due to the position estimation performed between encoder edges. This enables the
turn on and off angles to be adjusted for optimum performance of the SRM. The choice of
these angles was discussed in section 2.3.5. This section will discuss the calculation of the
commutation angles and their implementation into the controller.
4.2.1 Advance Angle
The turn on angle is referred to as the ‘advance angle’ in this case as it advances as
the speed and current set-point increase (see figure 2.11). The advanced angle is calculated in
the commutation function that runs in the 5 kHz timer interrupt. It takes the desired current
output from the speed controller and the speed of rotation and produces the advanced angle in
terms of the 16 bit angle. The assumption is made that the phase voltage used in the
calculation is equal to the voltage of the DC bus, in this case 30V. During the period in
question, i.e. from turn on to the current demand is met, both FET switches will be on and the
full bus voltage minus the voltage drop across the FETs will be applied to the phase. As
accuracy is not paramount in this case, the voltage drop across the FETs can be neglected.
The inductance around the unaligned position is relatively flat so the inductance used in this
equation can be considered constant. Below is the explanation of the software that is
32
responsible for the calculation of the advance angle and how it adjusts the turn on angle. The
code is based on the method presented in [13].
The speed is first obtained from the speed function and multiplied with the current set
point specified by the speed controller. The result of this multiplication is scaled by dividing
by 4 using the shift command (a/4 = a>>2) to ensure that the code runs as fast as possible.
This scaling accounts for the DC bus voltage, the inductance at the unaligned position and the
units and was calculated as below.
( ))(360)(65535
)(1)(8
)(1)(360
(sec)60(min)1
)(585)(1
601
1
elecbits
elecmech
revmech
bitsA
rpsV
LConst
DCun °
×°°
×°
××××××=
With the unaligned inductance equal to approximately 7mH and the DC bus voltage
at 30V, we obtain a value of 5.31. At the increased operating voltage of 120V a scaling value
of 19.23 is required. If we round this down to 4 and 16 respectively we can take advantage of
the shift by two or shift by 4 operations which are simpler for the M16C to accomplish. The
errors associated with this rounding are at most half of an electrical degree which is
acceptable for this application. To further increase the accuracy, the DC bus voltage could be
measured online and the result could be used to take into account the changes in winding
resistance due to temperature changes and the voltage drop across the semi conductors.
Once the advance angle has been calculated, it is combined with the estimated
position by summing the two together to provide the electrical angle. As either the current
demand or the speed increases, the advance angle and hence the electrical angle will increase
also. Thus when the commutator is deciding when to commutate the phases, a larger advance
angle will cause the phase to commutate sooner.
4.2.2 Turn Off angle
As noted previously the turn off angle has two possibilities that depend whether
overlap is required. For no overlap the turn off angle is calculated simply by addition of 120
degrees to the turn on angle. If overlap is required then the turn off angle is fixed to the most
effective angle for each phase. The amount of overlap is selected offline and defined as a
constant in software. The overlap is chosen so that the current still has time to exit the
windings before the stator and rotor poles overlap, but the period of overlap is long enough to
provide the maximum amount of torque. Through experimentation and observation over time
the ideal amount of overlap is deemed to be 30 electrical degrees.
33
4.3 Commutator
The commutation decisions are made in the 5 kHz timer interrupt after the calculation
of the advance angle. The commutator makes the decision based on the advance angle, the
reference turn on angle for phase A and the estimated position. As stated in section 4.2.1 the
advance angle is combined with the estimated position and it is the result of this addition that
the commutator acts upon. A reference turn on angle is specified for phase A, which would
normally be the start of overlap of the rotor and stator poles, and from this the turn on angle is
calculated for the other two phases through offsetting by ±120 electrical degrees. This enables
the user to specify the reference angle in order to experiment or fine tune the operation of the
motor. The commutator also takes into account the 20 electrical degree offset of the position
encoder. Previously when the turn on and off angles were fixed, the leeway of 20 electrical
degrees or 2.5 mechanical degrees allowed the current in the phase to exit the winding before
entering the negative torque region. The offset was not changed on the encoder, but is
accounted for in the software by a constant.
The commutator consists of a series of if statements or rules that determine which
phase to enable based on the position of the rotor. Various constant angles such as p and p/2
are represented in software as a 16 bit number in the same format discussed previously. The
commutation angles are different depending on the direction of rotation.
Two versions of commutator rules were completed. The first does not overlap the
phases and uses a constant dwell angle and varying turn off angle. This was used for most of
the time as it was simple and provided adequate performance. Recently the turn off angle was
fixed, as discussed previously and the excitation of the phases was made to overlap. This is
the second version of rules. The new set of rules theoretically provides more torque and fewer
ripples in the torque waveform and is referred to as the long dwell mode. Presently the long
dwell mode is activated when the current set-point specified by the speed controller exceeds
approximately 0.3A. When the motor is running under normal conditions with a minimal
load, the non-overlap method is engaged, but in the future a more advanced system could be
implemented. A flow chart of these two rules can be seen in figure 4.4.
34
Start of Commutation
Calculate advance angle and add this to the estimated position
Angle within phase A rules?
Angle within phase B rules?
Angle within phase C rules?
Enable Phase A Enable Phase B Enable Phase C
End of Commutation
No No
Yes Yes Yes
No
Start of long dwell Commutation
Calculate advance angle and add this
to the estimated position
Angle within phase A rules?
Angle within phase A&B rules?
Angle within phase B rules?
A)
Angle within phase A&B rules?
Angle within phase B rules?
Angle within phase A&B rules?
Enable Phase A
Enable Phase A&B
Enable Phase B
Enable Phase B&C
EnablePhase C
Enable Phase C&A
End of long dwell commutation
No
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
No
B) Figure 4.4: A) Commutation with no overlap B) Commutation with overlap
35
4.4 Current Controller
The soft voltage chopping current control method used is executed by a timer that
runs at 5 kHz. This timer is set up to have the highest priority of all the timer interrupts, which
enables it to run even while executing the lengthy LCD routines. Only the INT pins used to
capture the pulses of the encoder have a higher priority, due to the critical nature of the
information.
The controller identifies which phase has been enabled by the commutation sequence
and activates its low side FET. The controller compares the measured current values to the set
point, created either by the user or the speed controller, and switches the high side FET on if
the measured current is below the set point. This places 30V across the winding and causes
the current in the coil to increase. If the measured current is above the set point, the high side
FET is turned off, placing 0V across the coil. A theoretical result for this method can be seen
in figure 2.8.
4.5 Over Current Protection Over current protection is an essential safety and reliability mechanism. Since this
project uses a current sensor for each phase we can use this to provide a measure of over
current protection in software. As a first precaution the speed controller has a limit on the
maximum current it can demand from the current controller. This is set at the 2.5 amps that
the motor is rated for. The primary over current protection occurs within the current
controller. When the currents are measure the software checks to see if it exceeds the limit. If
so the drive is turned off. The limit is set at the rated current of 2.5Amps. If the over current
protection is enabled, the red light on the UI is turned on and the buzzer is activated. The user
can turn these off by pressing the on/off button. Another press of the on/off button will start
the drive again.
4.6 User Interface timer
The user interface timer takes care of the tasks involving the user interface. The
direction and mode switches are checked and the LED’s are set to the appropriate values. The
value of the potentiometer is read and converted into a speed set-point with a value between 1
RPS and 32RPS. De-bouncing of the on/off push button also takes place using this interrupt.
Writing to the LCD occurs after one hundred executions of the interrupt (i.e. at one second).
This was most appropriate as a large amount of time, 10ms, is required to communicate with
the LCD. Sending the data any quicker would be a waste of processor time and the user does
36
not need the information updated any more than this. The ramping of the speed set-point
occurs every half a second. The on/off button is read and de-bounced from this timer as well.
4.7 Speed Measurement and Feedback
The rotational speed must be known so that the speed controller can act on the current
controller to increase or decrease the speed to the reference set by the user. Previously the
speed was only calculated every second so that it could be displayed for the user’s
information. While the updating of the rotors speed every second was suitable for display
purposes, the speed is now updated more frequently allowing for a faster response by the
speed controller. This has been achieved by placing the speed calculation routine into a timer
driven interrupt that occurs at a frequency of 10Hz.
All tasks related to the calculation, formatting for display and query of present speed
are accomplished through the use of the speed calculation function. The required task is run
depending on the argument passed to the function. The flow diagram in figure 4.5 shows the
operation of the function. The count update task is called every time a relevant encoder edge
occurs and increments a counter. The relevant edge for clockwise rotation is positive and for
anti-clockwise it is negative. This counter is used in the calculation task that is performed in
the 10Hz timer interrupt. This task calculated the speed and will be discussed shortly. The
display task is used to display the speed of the SRM on the LCD. It is called from the user
interface timer interrupt once every second. The final task runs whenever the controller needs
to know the speed. It simply returns the most recent value of the speed in RPS.
The speed is calculated by counting the number of encoder position increments that
occur in a known time frame. For each encoder increment, the rotor has turned through 7.5
degrees. Therefore 48 increments of the encoder will occur in one rotation. If calculated over
the period of a second, the number of increments divided by 48 will give the speed in
Revolutions per Second (RPS). This calculation is scaled up by 128 to avoid the elimination
of the fractional part that results from the division by 48. This method avoids using floating
point arithmetic for which the M16C is not equipped. To calculate the speed at the faster rate
of 10 times every second, the same calculation is carried out, with the result being multiplied
by 10 to give a result in RPS.
The difference between desired speed and the measured speed of the motor gives the
input to the speed controller. The speed controller then acts on this information to produce the
current set point. The potentiometer on the user panel produces a voltage from 0 to 5V which
is then converted to a 10-bit digital number using the onboard ADC. This number is scaled to
the speed range we require by using a simple algorithm. The final speed range that will be
used a maximum of 2000 revolutions per minute (RPM) and a minimum of 60 RPM.
37
Speed Calculation function called
Perform countupdate?
Calculate speed?
Display speedon LCD
Return presentspeed
Increment count
Exit
Calculate speed
Run LCD display function
Return withpresent speed
Reset counter
Label
No
No
No
No
Yes
Yes
Yes
Yes
Figure4.5: Speed calculation, display and return function.
4.8 Speed Filter
During testing it was determined that a filter was needed on the speed feedback signal
to smooth out the speed measurement. The encoder and the software that calculates the speed
are not perfect and problems can arise due to interrupts delaying the calculation of speed and
general rounding errors introduced by the integer arithmetic used to calculate the speed. This
could cause the speed to oscillate between various values and the speed controller would act
to try and rectify this. By filtering the speed signal, the speed controller does not act on the
errors and a much smoother response is obtained.
A simple Finite Impulse Response (FIR) was chosen for this requirement. This was
mainly due to its simple implementation. A second order filter was designed in Matlab to
operate in the speed control function that operates at 1 kHz, filtering the speed signal at 10Hz.
The coefficients obtained using a Hamming window were [0.0689 0.862 0.0689] which were
38
scaled by 27 and rounded off. The filtering takes place before the speed control algorithm. We
can see that the filter takes into account the previous two values of the speed. Although a
higher order or more complex filter could have been implemented, the second order FIR filter
produces adequate results without imposing large software overheads on the microprocessor.
4.9 Speed Set point Creation and Ramping
The set point for the speed controller is created in the user interface interrupt. The 0-
5V signal created by the potentiometer is converted into a 10 bit number by the onboard
ADC. This 10 bit number is scaled to give a range of 1 RPS to 33 RPS, in 1 RPS increments.
This gives an operating range of 60 RPM to approximately 2000RPM. While the SRM is
capable of higher speeds (up to 3000RPM in testing) the speed has been limited. This is
because the time between encoder edges reduces to the point where the estimation of the shaft
position does not have time to take place.
To prevent problems caused by the user changing the speed set point at too fast a rate,
a simple ramping algorithm has been implemented. This limits the rate of change of the speed
set point and takes place in the UI timer interrupt. If the new speed set by the user differs
from the previous measured set point by a value greater than 5 rps ever 0.5 seconds, the rate
of change is fixed to an increase of 5rps every 0.5s until the set point is within 5rps of the new
set point. The rate of change decelerating is different to the rate of accelerating as the motor is
able to increase speed far quicker then it can reduce speed, especially with no load. The rate
of change for the set point while decelerating is set to 3rps every 0.5 seconds.
4.10 Stall Protection
The stall protection module of the controller will stop the energising of the phases
and warn the user if it detects that the rotor has stalled. The shaft will stall when the motor
cannot produce enough torque to overcome the load. At the reduced supply voltage, the shaft
can be stopped with the load provided by someone’s hands. If the rotor was stationary and the
controller was applying the full rated current there is a chance that the coils on the stator can
burn out. Stalling also causes problems for the position estimation and the measurement of
speed as no encoder edges occur. By stopping the motor from energising any of the phases
and returning to the Off state, we can eliminate these problems.
The stall detection occurs in the one second portion of the user interface interrupt.
Each time an encoder edge occurs a flag is set in software. This flag is checked in the
interrupt and if it is set then operation carries on as usual and the flag is rest. If the flag has
not been set, then it can be assumed that the shaft has stopped turning and the controller is
39
turned off and control passed back top the off state. At the motors minimum speed of 1rps,
there will be 48 edges so there is no chance of a stall being detected, however if the rotor
stops, no edges will occur and the stall will be detected. In a similar manner to the over
current protection, the buzzer will sound, but the red LED will blink at one second intervals.
This helps to distinguish which protection has stopped operation of the drive. The buzzer and
the blinking LED can be cancelled by pressing the on/off button. Another press will restart
the motor.
4.11 PI Speed Controller
The speed controller that is used in this project is a Proportional plus Integral
Controller (PI). The PI controller is widely used in industry as it is a simple and effective
controller for applications that do not require a more sophisticated approach. For the speed
control of this SRM, the PI controller has been deemed adequate. The gains from using a
more complex, higher-order type of controller are unlikely to improve the operation of the
SRM by any great margin. Investigation of a more complex controller could be a future aim.
The PI controller will act on the error signal calculated from the user set point and the
measured speed. The proportional part of the controller “provides a contribution which
depends on the instantaneous value of the control error” [17]. However a proportional
controller cannot remove steady state errors that are caused by disturbances. To remove these
errors, integral action is added to the control. Integral action “gives a controller output that is
proportional to the accumulated error” [17] and so the controller will always work to reduce
the error signal to zero. The transfer function of a PI controller is:
sK
KsT
KC Ip
rPPI +=+= )
11(
where KP is the proportional gain, Tr is the reset time and KI is the integral gain that is equal
to KP/ Tr .
4.11.1 Tuning the Speed Controller
The speed controller for this SRM was tuned using empirical methods, due to the lack
of a model for the SRM. The Ziegler-Nichols reaction curve method was used to obtain a
starting point for further tuning. As specified in the tuning rules, the speed controller was
disabled, allowing the current set-point to be controlled by the user. The motor was placed at
a stable operating point with a light load on the shaft and a step in the set-point was made.
The resulting speed curve was captured by an oscilloscope, downloaded to a PC and plotted
in Matlab. The plot and the calculations used to obtain the two gains can be seen in the
appropriate appendix. The proportional gain obtained was 9.15 and the integral gain was 5.08.
40
Through further testing and tuning that took place throughout the project, the integral gain
was increased to 11, and the proportional gain rounded up to 10. This gave a slightly faster
rise time and a better response to changes in the load.
4.11.2 Implementing the Speed Controller
The speed controller is called at a frequency of 1 kHz in the timer function that
handles the commutation and current control. The speed is filtered in this function as
discussed previously. The error between the set-point specified by the user and the filtered
speed of the SRM is calculated and the result is passed to the integrator. The integrator is a
simple summation of the previous errors. An integral limit is applied at this point to avoid
windup of the integrator. The limit was determined through testing. The result of the
integrator is multiplied by the integrator gain, which is scaled (212 ×1000) to account for the
sampling rate of the integrator, and the proportional gain to give the current set-point. Before
the routine is complete, the controller checks to see if the set-point exceeds the rated current
of the motor and applies a limit if needed.
4.12 Interrupt Priorities
The priority of the interrupts can be seen in figure 4.6. The two INT pin interrupts
have the highest priority as this will ensure the feedback of the position is as accurate as
possible. The timer interrupt that runs the current control, commutation and the speed control
has the next highest interrupt. This is due to its importance in the control of the motor and the
time critical functions that are performed like the estimation of the position. The timer that
contains the speed calculation routine is the next most important. Finally the UI timer has the
lowest priority as the controls on the UI do not change at a high frequency and there are no
time critical tasks.
41
INT 2 - Encoder signal, positive edge
INT 3 -Encoder signal, negative edge
5kHz Timer - Speed and current control- Commutation
10Hz Timer - Speed calculation
100Hz Timer - User interface
Figure 4.6: Interrupts in order of priorities
4.13 Processor Loading
The M16C is more than capable for the implementation of the speed controller in its
present form. However care was taken when writing the software to keep the code as fast as
possible. Below is a table outlining the typical times required for the execution of the
interrupts. The task that requires the most time is the LCD display routine. As this is in a low
priority interrupt, this is not an issue. There is still the capability for more functionality,
however investigation into more advanced techniques of torque control or high performance
sensor-less control would benefit from a Digital Signal Processor (DSP).
Interrupt Task Frequency of execution
Execution Time
5 kHz Timer Commutation and current control 5kHz 50us
Speed control 1kHz 32us 100 Hz Timer UI tasks 100 Hz 11us
Write to LCD 1 Hz 75ms 10 Hz Speed calculation 10 Hz 8us INT Encoder edges depends on speed 19us
Total with LCD write=75.12ms Total without LCD write=120us
Table 1: Typical execution times.
42
5. Results The results obtained are presented in this chapter. The results were captured using an
Agilent 4-channel oscilloscope. The speed, set-points and position information were
measured by outputting the required data to the two onboard Digital to Analog Converters
(DAC).
5.1 Speed Measurement
The accuracy of the speed measurement depends on the speed of the motor and the
delay caused by interrupts. Measurements were taken to confirm the accuracy of the speed
determined by the encoder using an oscilloscope to measure the time between negative edges
on the encoder. The distance between negative edges is known from section 2.1.4 as 7.5
degrees or one forty eighth of a revolution. The errors ranged from 23% at two revolutions
per second (120 RPM) to a minimum of 0% at twenty revolutions per second (1200 RPM).
In-between the errors were varied and may have been prone to measurement errors such as
noise and parallax error. The measurements taken can be seen in the appropriate appendix.
The general trend of the errors can be explained. At low speed the time between
encoder edges is longer than at high speed and in this time the shaft could be accelerating due
to disturbances. The count of encoder edges will also be much lower than at a higher speed.
For example at four revolutions per second there will be 19.2 encoder edges between speed
calculation interrupts, while at fourteen revolutions per second there will be 67.2 edges. The
fixed point arithmetic used has a higher precision at higher speed as it has more encoder
edges giving a larger scaled number. When the scaling is removed, the rounding will have a
larger impact on the lower number.
5.2 Position Estimation
By its nature, the estimation of the position is prone to errors. The following figures
5.1, 5.2 and 5.3 show the output of the position encoder at the top, the estimated position in
the middle and the position as it was calculated previously at the bottom. At 1RPS, there is a
distinct step in the estimate when the encoder edge updates the position. This is mainly due to
the long time in-between edges, the variations in speed and errors in the constant used to
calculate the position. At 10RPS, the estimate is more accurate, with no noticeable steps. At
25RPS the time to perform the estimate has decreased and so while the estimate is still
accurate, fewer cycles of the estimation routine take place. This accounts for the tiny steps
seen in the relevant figure.
43
Figure 5.1: Estimation of position at 1 RPS
Figure 5.2: Estimation of position at 10RPS
44
Figure 5.3: Position estimation at 25 RPS.
Overall the position estimation routine performs its function well and allows more flexible
choices of commutation angles.
5.3 Current Control
While the current controller itself has not changed, the turn on and turn off angles
have and this affects the current waveform. As discussed, there are two methods of
commutation, the long dwell angle mode and the normal mode. As expected the long dwell
mode did not require as high a current set-point as the normal mode. At 13RPS with the same
load, the overlapped method had a set-point of 0.45A while the non-overlapped method had a
set-point of 0.53A. The plots of the current in the three phases obtained from the CTs as well
as the encoder output for the overlapped and normal method in figures 5.4 and 5.5
respectively. In both cases, phase A is at the top and phase C is at the bottom.
The chopping of the current around the set-point can be seen in all the current
waveforms. Figure 5.6 shows a typical set of waveforms at a 7RPS with no load. The current
regulation in this figure is not as expected. Ideally the current should rise to the set-point and
then remain flat topped until the turn off angle which is clearly not the case. In this case the
problem is exaggerated by the lack of load on the motor. One of the reasons that the current is
so poorly regulated is the early turn on angle.
45
Figure 5.4: Overlapped current waveforms at 13RPS.
Figure 5.5: Non-overlapped current waveform at 13 RPS
As shown previously, the inductance of the stator coils is at a minimum when the phases are
unaligned. By turning the phase on early we can take advantage of the low inductance, but
this causes the current to increase so rapidly that the current controller does not have the
chance to turn the phase off before the current overshoots. This is not a large issue when there
is a load and when the inductance is larger i.e. closer to the aligned position. For example
with the overlap and a load, as in figure 5.4, after the initial overshoot, the current is a much
more ‘sensible’ shape. The increasing inductance can be clearly seen in this figure as the rise
and fall times of the current increase as the aligned position is approached.
46
Figure 5.6: Current waveforms at 7RPS.
5.4 Speed Control
With the completion of the PI speed controller the speed is regulated about the users
command. Figure 5.7 shows the motor’s starting response with no load and figure 5.8 shows
the response with a load. The speed set-point was set to 1500RPM and the motor turned on.
The delay of two seconds between the point of turn on and the movement of the rotor is due
to the starting algorithm. The no load case exhibits some overshoot and a settling time of
approximately five seconds, while the load case shows little if no overshoot and a settling
time of about 3 seconds. This is an improvement on the result of 10 seconds with no load
presented in the interim report.
The response to speed set-point changes with a load can be seen in figure 5.9. The
motor is quick to increase speed to match the set-point, but is not so quick when slowing
down as the motor is just coasting. Only the results for the case with a load are shown. The
results without a load are similar, but display overshoot like the start-up case and is slower in
reducing the speed.
Figure 5.10 shows the speed response for the loading and unloading of the motor. The
first small increase in speed is due to the load being removed from the shaft. The load in this
case is provided by weight acting on a block of wood which can be seen in the photos
contained in the appendices. The motor is then loaded, which decreases the speed. The motor
is unloaded and loaded again. The actual speed only varies by 2RPS.
47
Due to the relatively low voltage that the motor is operating at, the speed controller
has difficulty dealing with loads above a certain magnitude. This was noticeable at speeds
above 2000RPM, prompting the speed to be limited. Due to the empirical method of tuning,
fine tuning of the gains has been an on going process. This is likely to continue through until
open day.
Figure 5.7: Start-up with no load.
Figure 5.8: Start-up with load.
48
Figure 5.9: Speed reference change and resulting motor speed.
Figure 5.10: Changed in load at fixed speed.
49
6. Position Sensor-less Techniques The reliance on a position sensor to provide accurate phase switching information is
one of the significant limitations that has prevented the wide spread adoption of the SRM. A
mechanical position sensor adds cost to the drive and reduces the reliability. As one of the
major applications of the SRM is in situations that are hostile to mechanical sensors, the
elimination of this sensor would be a significant advantage. The use of methods to determine
the position without a mechanical sensor will be referred to from here on as sensor-less
methods. This was the motivation behind further study into this area.
This chapter investigates the previous work done in this area and the possible
solutions to the problem. A closer look at the method that was chosen for further investigation
and the difficulties faced will follow. Finally the results of the work completed to date are
presented and discussed.
6.1 Review of Position Sensor-less Techniques
The techniques used for determining the position of the rotor without a mechanical
sensor can be divided into two groups. One group uses measurements taken from the
energised phase and are non intrusive. That is they do not impose any further waveforms or
signals on the motor. Examples of techniques that fit into this group are state observers, flux-
linkage measurements and observation of the current waveform. These methods are generally
computationally intensive and suited for use at high speeds. The second group uses one of the
phases that is not producing torque and injects a low voltage test signal. Examples include
active probing and modulated signal injection. The intrusive nature of this method implies
that some negative torque will be produced due to the injection of the test signal in the region
of negative inductance slope. Some variations require large amounts of storage for inductance
profiles, however, they are not as demanding on the processor and work well at low speeds.
A number of methods from both groups were considered for further investigation due
to their chance of success and their ease of integration into the present drive. For the active
phase techniques, state observers were not considered due to the need for a mathematical
model of the system which was not attempted in this project. The injection of a modulated
signal was also not attempted. This was due to the external hardware required to supply the
modulated signal to the inactive phase. The extra cost and complication eliminated further
investigation into this method. The methods that were deemed suitable are discussed below.
50
6.1.1 Flux-linkage
Methods using the measurement of the flux-linkage in the active phase are among the
most popular sensor-less techniques. The use of the unique relationship between the flux,
angle and phase current was first proposed by Lyons et al [18]. The equation below is used
along with the flux verses current curves for various angles as presented in figure 2.5.
∫ ⋅−= dtiRVph )(ψ
where Vph is the applied voltage to the phase, R is the winding resistance and i is the phase
current. From this equation we know that with the knowledge of the flux and the current we
can determine the inductance and hence position.
The method can be used to continuously update the position, however this requires a
large amount of data to be stored. A more common alternative proposed identifies only one
inductance value per stroke, reducing the need for a complete set of stored flux curves.
This method can provide good accuracy and is suitable for use in the medium and
high speed range. It is not intrusive and normally requires no extra hardware. The main
limitations of this method centre on the “integration of the phase voltage”[19]. The variation
of the phase resistance with temperature can produce errors that are more prominent at low
speeds due to the long periods of integration. The complexity of computation requires a fast
processor to be able to operate at high speeds and depending on the method used a large
amount of storage space. The accuracy of the magnetisation curves also has an effect on the
accuracy of this method.
6.1.2 Observation of the Phase Current Waveform
Many different techniques fall under this category and all use measurements and
observations of the current waveform used to produce torque. The rise time and fall time
methods use measurements of the current rise and fall times in the chopping waveform. As
the inductance increases the time taken for the current to rise or fall a set amount will
increase. This would be easy to implement, however accuracy is affected significantly by the
back-EMF which varies with rotor speed and position.
Another method uses the change in slope of the current as the rotor passes the aligned
position and enters the falling inductance region. This method is easy to implement, but is
only suitable for low speed operation and can produce significant negative torque. A
combined representation of these two methods can be seen in figure 6.1. Other methods exist
that fall under this category but due to complexity or incompatibility with the current
controller or motor were not considered.
51
Figure 6.1: Combined figure showing rise/fall time and change of slope methods.
6.1.3 Active Probing
Active probing methods use measurement pulses injected into one or both of the
phases that are not used for torque production in order to determine the position. To minimise
the effect of back-EMF, negative torque and saturation, the signal injected is of a low voltage
and short duration. The use of the existing power electronic circuit to inject these pulses
reduces the need for external circuits and makes the implementation of these methods simple.
Alcarnley et al [20] first suggested the use of a low current waveform in a non-torque
producing phase. The pulses are injected using the power circuit at a high frequency with the
peak of the current in the order of 10% of the rated current. This helps reduce the production
of negative torque and the effect of saturation and back-EMF. Using equation 1 and assuming
a low current level for a short period of time, eliminating the first and third term we have:
it
VLti
LV∆∆
≈⇒∆∆
≈ )()( θθ eq 6.1
The most significant problem with this method is the mutual coupling between the
phase producing torque and the phase or phases used for measurement particularly if the
torque producing phase is undergoing high frequency chopping. Eddy current effects also
impact on the accuracy of this method. The method is suitable only at low speeds where there
is sufficient time to inject these pulses. Accurate inductance profiles are also needed, as well
as the capacity to store the data, however this can be eliminated by identifying one inductance
value every stroke. Other variations of this method that use the same principles exist
including using the flux-linkage method presented earlier. An ideal application of this method
is presented in figure 6.2.
52
Figure 6.2: Active probing in an unexcited phase.
6.2 Investigation into Active Probing
The active probing method of determining the position of the shaft was chosen for
further work. The choice was made due to the ease of implementation and the possible
difficulties in achieving suitable performance using the flux calculation method at low speeds
and the limitations of the M16C [19]. For this method to be successful, the inductance profile
of the SRM needs to be known. The measurement of this profile at various positions and
current levels is presented next. The implementation of the probing software is also discussed,
followed by the results and finally suggestions that could benefit any future work conducted
in this area.
6.2.1 Measurement of the Inductance Profile
The measurement of the inductance at various rotor positions and levels of current
was achieved by locking the shaft in a fixed position, applying pulses of varying width and
measuring the change in current using a current probe and an oscilloscope. A small vice was
used to hold the shaft in place and a protractor was used to measure the angles from the
aligned position. The pulses were applied using the converter circuit in the present
arrangement with the M16C applying a train of pulses to the phase being measured. The rise
time and the change in current were recorded for increasing pulse widths until the current was
reached. Measurements were taken at five mechanical degree increments or 40 electrical
degrees. The results were entered into an Excel spreadsheet and the inductance calculated
using equation 6.1. Due to the large amount of data generated, the results have been included
53
in an excel file located on the accompanying CD. The resulting curves for phase A can be
seen in figure 6.3.
Figure 6.3: Inductance curves at various mechanical angles and currents.
As expected the inductance has a higher value when the stator and rotor poles are
aligned, compared to the inductance when the poles are not aligned. Although not many
curves at different positions were obtained, the overall trend can still be seen with the large
gap between 5 and 15 degrees and 15 and 20 degrees suggesting a sharp change in the slope
of the inductance at a fixed current level (see figure2.2). The reason some of the curves do not
extend out to 2.5A is due to concerns about the safety of the motor and the vice holding the
shaft. Due to the measurement technique (the protractor could only provide an approximate
position) the curves are not smooth and the graph is not completely accurate. Ideally due to
the symmetrical nature of these motors, the curves measured for phase A should be the same
as the other phases. Obviously this is not always the case, but in this case the assumption was
made. The inductance in phase C was measured to confirm this assumption, and the results
were very similar.
6.2.2 Implementation of Active Probing
The method used to measure the inductance profiles above was implemented into the
working speed controller code with appropriate modifications and no overlapping of the
current waveforms. The phase to be energised next was selected as the measurement phase
54
and enabled at the required time by the commutator. The injection of pulses was performed in
the On state. A simple flow chart in figure 6.4 outlines the method.
To apply the pulses to the measurement phase, the FET switches were enabled,
supplying 30V to the phase windings. After a small period of time (0.6ms to 6ms were
trialled) the phase was turned off and the current measured. Ideally this current would have a
direct relationship to the position of the rotor. Figure 6.5 shows the current in phase A, with
the thin pulses being the result of the measurement routine. The plot was obtained using
Matlab and a serial connection to a digital oscilloscope. Please excuse the axes, which in this
case are not important.
While other variations on this method were tried, including fixing the current and
measuring the rise time, the basics principles remained the same. The results obtained are
explained next.
Enter On state
Turn on Hi and Lo switches
Is phase A the measurement phase?
Continue to rest of On state
Wait a small time
Turn off switchsMeasure current and
send to serial port
No
Yes
Figure 6.4: Active probing method.
55
500 550 600 650 700 750 800 850 900 950 1000-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
Time (Samples)
Cur
rent
(no
uni
ts)
Figure 6.5: Active probing of phase A.
6.2.3 Results and Issues
As shown in figure 6.5, the pulses were successfully injected into the phase under
measurement. During operation the drive was able to function normally and the probing only
had a small effect on the performance of the motor, with a slightly higher (5-10%) set-point
required. However closer inspection of figure 6.5 reveals that the assumption of the current
being proportional to the position is invalid. Ideally we would like to see the currents increase
continuously throughout the measurement period.
Figure 6.6: Results of active probing method.
56
Figure 6.6 shows the inductance measured by the sensor-less routine for three cases.
The required data was passed to a PC using the M16C’s serial port and the inductance
computed in Excel. An accurate online routine had not been designed as the method was still
under testing. Clearly there is a large amount of inaccuracy present. The result is typical of
what was achieved, however occasionally a number of measurements coincided, suggesting
that this method still has merit.
The most likely reason for the errors is mutual coupling and switching interference
between the phase that is producing torque and the phase that is used for measurement.
Enough time was not available before the completion of this report to reliably measure the
effect of the mutual coupling. One possible method would be to lock the rotor down and
energise one phase in the normal manner while measuring its affect on another phase.
A solution to this problem involving co-ordination between the measurement and
torque producing phases that only injects a pulse when an ‘ideal’ time, for instance when the
current is at a minimum, was trialled. However a reliable solution was not obtained.
57
7. Conclusion
7.1 Work Before Open Day
The time before open day will be spent mainly on the presentation of the enclosure.
Labels will be added to the controls and the wiring and connections tidied up. A more
permanent method of mounting the LCD also will be achieved as well as a power supply for
the position encoder and finalisation of the connections. The drive may be tested at its
original voltage using a 240V to 120V transformer, but it is likely that the lower voltage of
30V will be used on open day. Any further time that may arise will be spent on the sensor-less
work, but this is unlikely.
7.2 Future Work
The next step in this project addresses the position sensor-less problem. There are
various methods that can be used and a complete investigation into a number of these
methods could be a further project. The replacement of the mechanical position encoder with
a reliable and accurate sensor-less method is an important step along the way to increasing the
competitiveness of the SRM in the variable speed drives marketplace.
Further extensions could see the development of an accurate model of the SRM and
controllers. This would enable easier tuning and investigation into advanced methods of
torque, current or speed control.
7.2 Conclusions
The primary aim of this project was to design and implement a speed controller for a
Switched Reluctance Motor. Further to this aim, work has been done to research methods of
advanced control using sensor-less control. Finally the drive has been packaged in a user
friendly arrangement to ease further work on the motor.
The speed controller and its supporting functions have been completed. The PI speed
controller was tuned using empirical methods, and the tuning of the gains is an ongoing
process. The speed controller was built around the previously designed current controller and
acceptable results were achieved, provided the load was not too great. In order to gain greater
control over the turn on and turn off angles, a method of estimating the position of the shaft
between encoder updates was devised. The turn on angle is now variable and calculated
online. The estimation proved to be accurate enough for the purpose and the ability to vary
58
the commutation angles increased the speed envelope. The top speed (above 3000RPM) of
the motor is much greater than was previously possible with fixed commutation angles (about
1800RPM). An overlapped commutation of current was also implemented to eliminate gaps
in the production of torque. This also has the benefit of increasing the torque during situations
such as start-up and operation with a high load. Features such as the filtering of speed, stall
protection, reversing and ramping of the speed set-point add reliability and improve the
performance of the motor.
The installation of the drive circuit and various interfacing electronics inside an
enclosure increased the safety of the user and also reduced occasional breakages that occurred
while setting up each day. It also increases the ease of use in demonstrations and for future
use by people that do not have an intimate understanding of the circuits and connections.
The further work undertaken into removing the need for a mechanical position sensor
by investigating position sensor-less control was motivated by one of the main advantages of
the SRM, its ruggedness and reliability. The inductance of the phases at various currents and
positions was obtained through an experiment. The results were to be used to determine the
position of the rotor using pulses injected into one of the unused phases. While an attempt
was made, the results show that large errors can occur. However this method still has merit
and requires more knowledge of the coupling between the phases.
59
References [1] A. F. Anderson, "Development history," in Electronic Control of Switched
Reluctance Machines, T. J. E. Miller, Ed.: Newnes, 2001. [2] M. Tildesley, "Switched Reluctance Motor Drive," in Department of Electrical &
Computer Engineering. Newcastle: The University of Newcastle, 2003, pp. 56 + Appendices.
[3] T. J. E. Miller, "Introduction," in Electronic Control of Switched Reluctance Machines, T. J. E. Miller, Ed.: Newnes, 2001.
[4] T. Perl, I. Husain, and M. Elbuluk, "Design trends and trade-offs for sensorless operation of switched reluctance motor drives," presented at Industry Applications Conference, 1995. Thirtieth IAS Annual Meeting, IAS '95., Conference Record of the 1995 IEEE, 1995.
[5] S. Drives. http://www.srdrives.co.uk/fr_index.htm [6] D. A. Torrey and J. M. Kokernak, "Power Steering: Brushless DC or Switched-
Reluctance?," in Power Electronics Technology, 2002. [7] A. Mychael, Electric Circuits and Machines, 2nd ed. Sydney: McGraw-Hill Book
Company, 1977. [8] T. J. E. Miller, "Optimal design of switched reluctance motors," IEEE Transactions
on Industrial Electronics, vol. 49, pp. 15-27, 2002. [9] R. Krishnan, Switched Reluctance Motor Drives: CRC Press, 2001. [10] T. Sawata, "The switched reluctance generator," in Electronic Control of Switched
Reluctance Machines, T. J. E. Miller, Ed. Oxford: Newnes, 2001. [11] T. J. E. Miller, "Average Torque Control," in Electronic Control of Switched
Reluctance Machines, T. J. E. Miller, Ed.: Newnes, 2001. [12] F. Blaabjerg, P. C. Kjaer, P. O. Rasmussen, and C. Cossar, "Improved digital current
control methods in switched reluctance motor drives," Power Electronics, IEEE Transactions on, vol. 14, pp. 563-572, 1999.
[13] M. T. DiRenzo, "Switched Reluctance Motor Control – Basic Operation and Example Using the TMS320F240, Texas Instruments Application Note," 2000.
[14] R. C. Becerra, M. Ehsani, and T. J. E. Miller, "Commutation of SR motors," Power Electronics, IEEE Transactions on, vol. 8, pp. 257-263, 1993.
[15] J. J. Gribble, P. C. Kjaer, C. Cossar, and T. J. E. Miller, "Optimal commutation angles for current controlled switched reluctance motors," presented at Power Electronics and Variable Speed Drives, 1996. Sixth International Conference on (Conf. Publ. No. 429), 1996.
[16] Mitsubishi, "M16C/62 Family Datasheet," 2000. [17] G. C. Goddwin, S. F. Graebe, and M. E. Salgado, Control System Design, 1st ed.
New Jersey: Prentice Hall, 2001. [18] J. P. Lyons, S. R. MacMinn, and M. A. Preston, "Flux/current methods for SRM rotor
position estimation," IEEE IAS Annual meeting, pp. 483-487, 1991. [19] G. Gallegos-Lopez, "Sensorless control," in Electronic Control of Switched
Reluctance Machines, T. J. E. Miller, Ed.: Newnes, 2001, pp. 133-170. [20] P. P. Acarnley, R. J. Hill, and C. W. Hooper, "Detection of rotor position in stepping
and switched reluctance motors by monitoring of current waveforms," IEEE Transactions, vol. IE-32, pp. 215-222, 1985.
A-1
Appendix Appendix A Software in C code
Appendix B Ports and connections
Appendix C Speed calculation errors
Appendix D Current setpoint
Appendix E Speed controller tuning
Appendix F Circuit diagrams
Appendix G Photos
A-2
Appendix A Software in C code
The source files are included on the CD. The most up to date version will be available on the website by open day. The code was too long to include and was difficult to read.
Three versions are included on the CD. • -Speed Control- This is the most up to date snapshot of the software. Does
not include any sensorless code. • Sensorless 1 and Sensorles 2 are examples of my attempts to eliminate the
shaft encoder. They are not well commented, but may be of use in the future.
A-3
Appendix B Ports and connections
Note that the wiring is likely to change by open day due to the installation of the LCD in a more permanent manner. An updated list of connections will be available on the day.
A-4
Appendix C Speed calculation errors
rps rpm real rps real rpm %error 2 120 2.48 148.5149 19.20 4 240 4.31 258.6207 7.20 6 360 6.41 384.6154 6.40 8 480 7.87 472.4409 -1.60
10 600 10.31 618.5567 3.00 12 720 11.63 697.6744 -3.20 14 840 13.89 833.3333 -0.80 16 960 15.87 952.381 -0.80 18 1080 18.02 1081.081 0.10 20 1200 20.00 1200 0.00 22 1320 21.51 1290.323 -2.30 24 1440 23.26 1395.349 -3.20 26 1560 25.64 1538.462 -1.40 28 1680 27.62 1657.459 -1.36 30 1800 29.85 1791.045 -0.50 32 1920 31.25 1875 -2.40
A-5
Appendix D Current setpoint
A-6
Appendix E Speed controller tuning
0 200 400 600 800 1000 1200 1400 1600 1800 2000-40
-30
-20
-10
0
10
20
30
40
Time (samples)
Vol
ts (
repr
esen
ts s
peed
)Reaction curve
Above is the waveform capture from a Tektronix TDS220 DSO using Matlab. Due to the setup at the time the capture was not of the best quality and another DSO was not available. The plant inputs, outputs and time constants were recorded using the DSO and the information on the LCD display. The following is my working calculation of the gains using the Ziegler-Nichols reaction curve method.
Yinitial = 5 RPS Yfinal = 29RPS Uinitial = 546 (10-bit number) Ufinal = 563 (10-bit number) t0 = 0s t1 = 600ms t2 = 9.2s Parameters computed as follows
41.11724
5465635290 ==
−−
=−−
=∞
∞
oo uu
yyK
mstt 600010 =−=τ
A-7
stt 6.8120 =−=υ Therefore
15.96.041.1
6.89.09.0
00
0 =×
==τ
υK
K p
8.16.033 =×=⋅= orT τ
From section 4.11.1, we have the final gains:
08.58.115.9
15.9
===
=
r
PI
p
TK
K
K
A-8
Appendix F Circuit diagrams
Scan of Mathew Tildsley’s Inverter circuit diagram Scan of Mathew Tildsley’s Power circuit diagram
A-9
A-10
A-11
Appendix G Photos
Project setup
Original setup
A-12
Front User Interface
Inside the enclosure