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Open Access Dissertations Theses and Dissertations
Fall 2013
Electric Machine Differential For Vehicle TractionControl And Stability ControlSandun Shivantha KuruppuPurdue University
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Recommended CitationKuruppu, Sandun Shivantha, "Electric Machine Differential For Vehicle Traction Control And Stability Control" (2013). Open AccessDissertations. 135.https://docs.lib.purdue.edu/open_access_dissertations/135
Graduate School ETD Form 9 (Revised 12/07)
PURDUE UNIVERSITY GRADUATE SCHOOL
Thesis/Dissertation Acceptance
This is to certify that the thesis/dissertation prepared
By
Entitled
For the degree of
Is approved by the final examining committee:
Chair
To the best of my knowledge and as understood by the student in the Research Integrity and Copyright Disclaimer (Graduate School Form 20), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy on Integrity in Research” and the use of copyrighted material.
Approved by Major Professor(s): ____________________________________
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Approved by: Head of the Graduate Program Date
Sandun Shivantha Kuruppu
Electric Machine Differential for Vehicle Traction Control and Stability Control
Doctor of Philosophy
N. Athula Kulatunga Anthony B. Will
Kartik B. Ariyur
Steven D. Pekarek
John M. Starkey
N. Athula Kulatunga
James L. Mohler 11/01/2013
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ELECTRIC MACHINE DIFFERENTIAL FOR VEHICLE TRACTION CONTROL
AND STABILITY CONTROL
A Dissertation
Submitted to the Faculty
of
Purdue University
by
Sandun Shivantha Kuruppu
In Partial Fulfillment of the
Requirements for the Degree
of
Doctor of Philosophy
December 2013
Purdue University
West Lafayette, Indiana
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!
~~ මාගේ ආදරනය අමමා, තාතතා සහ මලල වෙත… ~~ *
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ACKNOWLEDGEMENTS
The journey of a graduate student is a unique experience. The graduate student parting
on this long journey experiences a far more different intellectual challenge. The approach
for higher studies in the 21st century may be dissimilar to that of the times of Aleksandr
Lyapunov or Sir Isaac Newton; yet the individual interests that drives the progression of
our understanding of the world still exists. My experience at Purdue University was very
unique and I am extremely grateful to the individuals who were instrumental in
supporting me and guiding me throughout the journey.
I would like to take this opportunity to thank my major advisor and all my committee
members. I am most grateful to Dr. Athula Kulatunga, my major advisor for accepting
me as a graduate student at the International Rectifiers Power Electronics Development
and Applications Lab (IR-PEDAL); a high caliber research lab. I appreciate his patience
and guidance in enabling my creative thinking to develop new technology. Dr. Kartik
Ariyur was most kind and patient with me while assisting me on improving my
theoretical understanding of material. He enforced mathematical rigger in my studies on a
daily basis and continuously encouraged me in every way possible. I’m most thankful for
his patience as I was novice to rigorous mathematics and controls. Dr. Steven Pekarek
guided me with his expertise on energy conversion and motor controls at every possible
opportunity. His teachings and teaching style in ECE610 influenced me in understanding
the basics behind energy conversion in electromechanical systems. I’m most grateful to
Dr. John Starkey for helping me understand vehicle dynamics at such short notice, during
my vehicle model development phase. His guidance was most useful in developing my
understanding in concepts related to vehicle dynamics and stability control. Dr. Anthony
B. Will of General Motors (GM) was able to provide me feedback on the dissertation
content based on his experience at GM and his research experience. I very much
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appreciate his meticulous feedback and taking time from his busy work schedule to read
through the dissertation.
My two internships at Delphi Electronics and Safety had a significant influence on my
studies and in developing a practical understanding in my area of studies. I would like to
thank Timothy R. Porter, Dr. Charles J. Sullivan, James Walters, Mark Henderson, Bart
Gilbert, Chris Jones, Ronald Krefta and Huimin Zhou of Delphi and all the members of
my team at Delphi for providing me a unique opportunity to hone my skills. As a
colleague and a good friend, Huimin Zhou was always prepared to help me and scrutinize
my work to improve the quality. I’m most thankful for her efforts. James Walters was
kind enough to provide me guidance and advise on application of motor control
algorithms, even after I have left Delphi. His mentorship and feedback was most helpful
in completing my research.
International Rectifiers, Landis + Gyr and General Motors were most generous in
providing the necessary facilities for successful completion of my studies. Professor
James Michael Jacob was most kind to share his expertise with me to help me succeed.
The financial support provided by Dr. Gary Bertoline, the Dean of College of
Technology and Dr. James L. Mohler, the Associate Dean for Academic Affairs and
Diversity was invaluable in completing my studies.
The members of the Sri Lankan community in West Lafayette were there for me every
step of the way helping me in numerous ways. They made West Lafayette my home away
from home. I’m very much thankful to Agnid Benarjee and Kaushika De Silva for their
patience, advice and limitless friendship. The life as it is, ‘is full of change’. Yet
Dooshaye Moonshiram helped me experience it and encouraged me to be strong, positive
and hardworking by example. Last but not least, I would like to express my heartfelt
gratitude towards my loving mother, father and brother for their continued patience,
encouragement and support all throughout my life as a son, a brother, and a student.
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TABLE OF CONTENTS
Page
LIST OF TABLES ........................................................................................................... viii
LIST OF FIGURES ........................................................................................................... ix
NOMENCLATURE ........................................................................................................ xiii
ABSTRACT ...................................................................................................................... xv
CHAPTER 1. INTRODUCTION ................................................................................. 1
1.1 Introduction ................................................................................................1
1.2 Research Question ......................................................................................2
1.3 Contributions and Summary of Results .....................................................3
CHAPTER 2. LITERATURE REVIEW ..................................................................... 4
2.1 Vehicle and Tire Properties ........................................................................4
2.2 Related Work – Traction Control ...............................................................9
2.3 Related Work – Vehicle Stability Control ...............................................11
2.4 Related Work – Electric Machines for EV, HEV Applications ...............14
2.5 Related Work – Electric Machine Differential ........................................16
CHAPTER 3. ELECTRIC MACHINE DIFFERENTIAL DEVELOPMENT. ......... 19
3.1 System Overview .....................................................................................19
3.2 Vehicle Selection .....................................................................................20
3.3 Electric Drive Unit Development ............................................................23
3.4 In-System Communication Protocol ........................................................32
3.5 Electric Machine Differential Algorithm .................................................33
3.6 BLDC Machine Properties .......................................................................34
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Page
3.7 BLDC Machine Control Algorithm .........................................................36
3.7.1 Current Controller Development.......................................................38
3.7.2 Speed Controller Development .........................................................43
3.7.3 Final Electric Machine Differential Experimental Setup ..................46
CHAPTER 4. D-Q CURRENT SIGNATURE BASED FAULT DIAGNOSTIC. ... 49
4.1 Introduction ..............................................................................................49
4.2 Problem Statement ...................................................................................51
4.3 Summary of Existing Fault Diagnostic Schemes .....................................54
4.4 Accurate Fault Simulation .......................................................................58
4.5 Fault Detection Algorithm and Faulted Phase Identification ...................64
4.6 Experimental Results ...............................................................................67
4.6.1 Experimental Setup ...........................................................................67
4.6.2 Fault Detection ..................................................................................70
4.6.3 Faulted Phase Identification ..............................................................71
CHAPTER 5. ELECTRIC MACHINE BASED RT-ESSO ALGORITHM. ............ 78
5.1 Introduction ..............................................................................................78
5.2 Background and Motivation .....................................................................80
5.3 Theoretical Model of the System .............................................................83
5.3.1 Unicycle Vehicle Model ...................................................................83
5.3.2 Mechanical Brake Model ..................................................................83
5.3.3 Electric Machine Model ....................................................................84
5.3.4 Road Friction Coefficient Modeling .................................................86
5.4 Extremum Seeking Slip Optimization (ESSO) Controller ......................87
5.4.1 Simplified Explanation of Extremum Seeking Algorithm ................87
5.4.2 Application of Extremum Seeking Algorithm for ABS ....................88
5.5 ESSO Algorithm with Mechanical Brake Actuator .................................90
5.6 ESSO Algorithm with Electric Machine ..................................................92
5.7 Performance Comparison of ABS Schemes (Mech vs Elec) ...................94
5.8 Experimental Setup for Algorithm Verification ......................................98
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Page
5.9 Concluding Remarks ..............................................................................103
CHAPTER 6. EMD BASED YAW STABILITY CONTROL. .............................. 104
6.1 Introduction ............................................................................................104
6.2 Vehicle Model with Two Degrees of Freedom ......................................105
6.3 Vehicle Model with Eight Degrees of Freedom ....................................107
6.3.1 Non-Linear Tire Model ...................................................................109
6.4 Vehicle Model Validation ......................................................................111
6.5 Stability Test Criterion ...........................................................................114
6.6 Stability Control Capability Comparison ...............................................116
6.6.1 Stability Control with Hydraulic Brake System .............................117
6.6.2 Stability Control with Electric Machine Differential ......................119
6.7 Concluding Remarks ..............................................................................121
CHAPTER 7. SUMMARY OF RESEARCH.......................................................... 122
7.1 Electric Machine Differential Hardware Development .........................122
7.2 Novel SPO Fault Diagnostic Algorithm for SM-PMSMs .....................122
7.3 RT-ESSO Algorithm Implementation ...................................................123
7.4 Electric Machine Differential based Yaw Stability Control ..................124
LIST OF REFERENCES ................................................................................................ 125
APPENDIX ..................................................................................................................... 135
VITA ............................................................................................................................... 148
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LIST OF TABLES
Table .............................................................................................................................. Page
Table 3.1 Motor Parameters .............................................................................................. 23
Table 3.2 Central Control Board Sensors and SMPSs ...................................................... 31
Table 3.3 BLDC Machine Specifications and Parameters................................................ 35
Table 4.1 Fault Diagnostic Experimental Setup, Motor Specifications............................ 69
Table 4.2 Comparsion of Simulation and Experimental Results (Fault Diag. Algo.) ...... 75
Table 5.1 Tire Road Friction Coefficient Model Parameters ........................................... 86
Table 5.2 Experimental Setup Component Summary (sensing and actuation) .............. 101
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LIST OF FIGURES
Figure ............................................................................................................................. Page
Figure 2.1 Vehicle reference frame .................................................................................... 4
Figure 2.2 Planar motion of an automobile ........................................................................ 5
Figure 2.3 Tire forces .......................................................................................................... 6
Figure 2.4 Friction coefficient VS. Wheel slip ................................................................... 7
Figure 2.5 Normalized lateral force variation with slip angle ............................................ 8
Figure 2.6 Normalized longitudinal force variation with slip angle. .................................. 8
Figure 2.7 Slip ratio variation with slip angle................................................................... 12
Figure 2.8 Electric vehicle architectures ........................................................................... 17
Figure 3.1 Electric machine differential overview ........................................................... 19
Figure 3.2 Chosen vehicle (Clubcar® Carryall 242) ........................................................ 20
Figure 3.3 Power module connection diagram ................................................................ 24
Figure 3.4 Signal conditioning circuitry ........................................................................... 25
Figure 3.5 Boost converter circuit (LM2578) ................................................................... 26
Figure 3.6 Drive unit PCB top layer layout ...................................................................... 27
Figure 3.7 Drive unit PCB bottom layer layout ................................................................ 27
Figure 3.8 Final PCB design ............................................................................................. 28
Figure 3.9 Chosen heat sink .............................................................................................. 28
Figure 3.10 Final motor drive unit .................................................................................... 29
Figure 3.11 Drive unit efficiency (minimal loading) ........................................................ 30
Figure 3.12 Central control unit ........................................................................................ 31
Figure 3.13 Communication protocol data packet architecture ........................................ 32
Figure 3.14 EMD high level system overview ................................................................. 34
Figure 3.15 Torque vs. Speed and Efficiency vs. Speed .................................................. 36
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Figure ............................................................................................................................. Page
Figure 3.16 Overview of the motor control algorithm ...................................................... 37
Figure 3.17 Motor control algorithm interrupt service routines ....................................... 37
Figure 3.18 Current controller block diagram .................................................................. 38
Figure 3.19.a BLDC machine current controller performance – Bang-Bang Control...... 39
Figure 3.19.b BLDC machine current controller performance (zoomed) ........................ 39
Figure 3.20.a BLDC machine current controller performance - Bang-BangControl ....... 40
Figure 3.20.b BLDC machine current controller performance (zoomed) ........................ 40
Figure 3.21.a BLDC machine current controller performance –PI Regulator .................. 41
Figure 3.21.b BLDC machine current controller performance (zoomed) ........................ 41
Figure 3.22.a BLDC machine current controller performance –PI Regulator .................. 42
Figure 3.22.b BLDC machine current controller performance (zoomed) ........................ 42
Figure 3.23 BLDC motor speed controller ....................................................................... 43
Figure 3.24 Open loop step response for speed command ............................................... 44
Figure 3.25 Speed controller response at low speed ......................................................... 44
Figure 3.26 Speed controller response to load variation-Low speed ................................ 45
Figure 3.27 Speed controller response to load variation-High speed ............................... 45
Figure 3.28 Intergrated electric machine differential setup and test platform .................. 46
Figure 3.29 EMD wheel speed calculation based on Ackerman formula ......................... 47
Figure 4.1 Field oriented control algorithm block diagram .............................................. 52
Figure 4.2 Electromagnetic torque behavior after SPO fault ............................................ 52
Figure 4.3 SM-PMSM stator currents during fault ........................................................... 53
Figure 4.4 and
behavior after SPO fault in FOC SM-PMSMs (experimental) ..... 53
Figure 4.5 Residual generation based SPO fault diagnostic method ................................ 55
Figure 4.6 Matlab® Simulink® simPower® based machine model ................................ 59
Figure 4.7 Ias, Ibs and Ics behavior in a SM-PMSM drive after SPO fault (simulated)...... 60
Figure 4.8
behavior in a SM-PMSM drive after SPO fault (simulated) ......... 60
Figure 4.9 Generic Simulink block based fault simulation scheme.................................. 62
Figure 4.10 Ias, Ibs and Ics behavior in a SM-PMSM drive after SPO fault (simulated) ... 63
Figure 4.11
behavior in a SM-PMSM drive after SPO fault (simulated) ........ 63
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Figure ............................................................................................................................. Page
Figure 4.12 Block diagram of the hardware-in-loop experimental setup ......................... 67
Figure 4.13 Experimental setup ........................................................................................ 68
Figure 4.14 Implementation of field oriented control algorithm ...................................... 69
Figure 4.15 Behavior of fault detection signal (experimental data) ................................. 70
Figure 4.16 Fault detection indicator flag (experimental data) ......................................... 70
Figure 4.17 Phase current behavior after fault occurance (simulated) ............................. 71
Figure 4.18 Behavior of d-q currents after fault occurance (simulated) ........................... 72
Figure 4.19 Faulted phase identification scheme (simulation) ......................................... 72
Figure 4.20.a Faulted phase identification scheme for Phase A (experimental) .............. 73
Figure 4.20.b Faulted phase identification scheme for Phase B (experimental) .............. 74
Figure 4.20.c Faulted phase identification scheme for Phase C (experimental) ............... 74
Figure 4.21 Faulted phase identification for CW vs CCW shaft rotation ......................... 75
Figure 5.1 Friction coefficient variation with wheel slip during braking ......................... 80
Figure 5.2 Unicycle model of a quarter car during braking .............................................. 83
Figure 5.3 Mechanical brake system model ..................................................................... 84
Figure 5.4 Basic Extremum Seeking Scheme ................................................................... 87
Figure 5.5 Extremum seeking brake optimizing controller (without actuator) ................ 89
Figure 5.6 Extremum seeking brake optimizing controller with actuator ........................ 90
Figure 5.7 Simulink implementation of the wheel slip controller with actuator .............. 91
Figure 5.8 Slip optimization algorithm response to varying road conditions (mech) ...... 91
Figure 5.9 Actuator torque response to varying road conditions (mech) ......................... 92
Figure 5.10 Slip optimization algorithm response to varying road conditions (elec)........93
Figure 5.11 Actuator torque response to varying road conditions (elec) .......................... 94
Figure 5.12 Wheel Slip Comparison (hydraulic brakes vs. electric machine).................. 95
Figure 5.13 Actuator torque comparison (hydraulic brakes vs. electric machine) ........... 95
Figure 5.14 Stopping time comparison (hydraulic brakes vs. electric machine) .............. 96
Figure 5.15 Stopping distance comparison (hydraulic brakes vs. electric machine) ........ 96
Figure 5.16 Slip optimizing algorithm response at different perturbation frequencies .... 97
Figure 5.17 Slip optimizing algorithm response at different perturbation frequencies .... 98
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Figure ............................................................................................................................. Page
Figure 5.18 Experimental setup block diagram ................................................................ 99
Figure 5.19 Experimental setup components .................................................................. 100
Figure 5.20 Experimental results of the extremum seeking slip optimization algorithm 102
Figure 6.1 Bicycle model for vehicle dynamics modeling ............................................. 105
Figure 6.2 Wheel rotation dynamics ............................................................................... 105
Figure 6.3 Eight-degrees-of-freedom vehicle model ...................................................... 107
Figure 6.4 Eight DoF vehicle model response at low g maneuver ................................. 111
Figure 6.5 Eight DoF vehicle model response at high g maneuver ................................ 112
Figure 6.6 Vehicle yaw acceleration comparison during high-g maneuver ................... 113
Figure 6.7 Vehicle yaw rate comparison during high-g maneuver ................................. 113
Figure 6.8 Yaw acceleration error and yaw rate error during high-g maneuver ............. 114
Figure 6.9 Steering input for stability control test by USDOT ....................................... 115
Figure 6.10 Yaw control strategy.................................................................................... 116
Figure 6.11 Mechanical braking based yaw controller behaviors at high g maneuver ... 117
Figure 6.12 Mechanical braking based yaw controller wheel torque output .................. 118
Figure 6.13 Electric differential based yaw controller behavior at high-g maneuver .... 119
Figure 6.14 Electric differential based yaw controller wheel torque output ................... 120
Figure 6.15 yaw rate error and yaw acceleration error behavior (with EMD) ............... 120
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NOMENCLATURE
Acceleration in the y-direction
Lateral tire side slip
Bearing friction coefficient
Windage friction in the motor
Cornering stiffness of one tire
Longitudinal stiffness of one tire
Positive constant (feedback linear system)
Steering input to the front wheels
Steered angle of a wheel
Roll axis torsional stiffness
Roll axis torsional damping
Back EMF of Phase A,B and C respectively
Vertical load on one tire
Instantaneous phase current (x = as, bs, cs)
Quadrature axis current in rotor reference frame
Direct axis current in rotor reference frame
Vehicle moment of inertia (z axis)
Vehicle moment of inertia (roll axis)
Sprung mass product of inertia
Rotating tire inertia
Equivalent inertia at one wheel
Wheel inertia
D axis current command
Q axis current command
Zero sequence current
Inertia at motor shaft
Actuator static gain (Chapter 5)
Back EMF constant (Chapter 4)
D axis P.I. controller integral gain
Q axis P.I. controller integral gain
D axis P.I. controller proportional gain
Q axis P.I. controller proportional gain
Ratios of front roll stiffness to the total roll stiffness
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Roll steer coefficient
Q axis inductance
D axis inductance
Leakage inductance
Optimal slip for a given surface
Amplitude of the magnetic flux linkage
Self-inductance
Amplitude of the magnet flux linkage ( )
Mutual inductance
Weight of the quarter car
Vehicle sprung mass
Wheel speed (longitudinal)
Motor rotor speed
Electrical speed
Flux linkage
Sprung mass roll angle (chapter 6)
P Number of poles
Roll rate (chapter 6)
Yaw angle
R Resistance of a phase
Reaction force from the ground (Chapter 5)
Tire rolling radius (Chapter 6)
Wheel radius
Yaw rate (chapter 6)
Motor winding resistance (per phase)
Electrical angle
Drive torque
Electromagnetic torque
Load torque
Lateral wheel base
Braking torque
Vehicle speed
Longitudinal velocity
Lateral velocity
Q axis voltage
D axis voltage
Zero sequence voltage
Phase Voltage of Phase A,B and C respectively
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ABSTRACT
Kuruppu, Sandun S. Ph.D., Purdue University, December 2013. Electric Machine
Differential for Vehicle Traction Control and Stability Control. Major Professor: Athula
Kulatunga.
Evolving requirements in energy efficiency and tightening regulations for reliable
electric drivetrains drive the advancement of the hybrid electric (HEV) and full electric
vehicle (EV) technology. Different configurations of EV and HEV architectures are
evaluated for their performance. The future technology is trending towards utilizing
distinctive properties in electric machines to not only to improve efficiency but also to
realize advanced road adhesion controls and vehicle stability controls. Electric machine
differential (EMD) is such a concept under current investigation for applications in the
near future. Reliability of a power train is critical. Therefore, sophisticated fault detection
schemes are essential in guaranteeing reliable operation of a complex system such as an
EMD. The research presented here emphasize on implementation of a 4kW electric
machine differential, a novel single open phase fault diagnostic scheme, an
implementation of a real time slip optimization algorithm and an electric machine
differential based yaw stability improvement study. The proposed d-q current signature
based SPO fault diagnostic algorithm detects the fault within one electrical cycle. The
EMD based extremum seeking slip optimization algorithm reduces stopping distance by
30% compared to hydraulic braking based ABS.
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CHAPTER 1. INTRODUCTION
1.1 Introduction
Automobile stability control, traction control and antilock braking (ABS) ensure
passengers safety via sophisticated instrumentation and controls. Conventional
techniques rely on brake intervention, differential power control and engine power output
control for non-electric automobiles (Park J.Y. & Kim C.Y.,1999). Not all the above
mentioned control methods are capable of controlling individual tire force to achieve the
desired performance. Dynamic characteristics of each mechanical system influence the
performance of traction control/stability control capability differently. Therefore typically
a combination of systems is utilized to overcome inherent disadvantages in each
mechanical system. The proposed electric machine based differential system based
traction control/stability control presents a significant improvement compared to
conventional systems due to fast torque response in electric machines (Sen P.C.,1990).
Theoretically an electric machine differential is an enabling technology for both
hybrid electric vehicles (HEV) and electric vehicles (EV). Several EV and HEV
architectures are available with unique features. Few of those HEV and EV architectures
facilitate the utilization of the fast torque response capability of the electric machine,
directly in the traction control and stability control process.
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Such architectures utilize electric machines in each wheel (rear wheel drive or all-wheel
drive) in the drive train architecture. Both in-wheel electric machines (inside out machine
design) and shaft coupled machine types are considered. Yet not all EMD architectures
are pragmatic in hybridizing the existing fleet of gasoline power train based automobiles.
In-Wheel electric machine based EMD is one such robust solution in comparison drive
train replacement (Whitehead A.,n/a). Feasible hybridization architecture is only one
aspect; Reliability is also a primary concern in automotive applications. An electric
machine differential (EMD) increases the chance of failure due to the added complex
electrical hardware. Therefore a fault diagnostic system is vital in increasing the
reliability. A novel fault diagnostic scheme was designed and implemented as a first step
towards increasing the overall reliability of the system. The fault condition considered is
a single open phase (SPO) failure in a surface mount permanent magnet synchronous
machine (SM-PMSM). The following section poses the research questions.
1.2 Research Question
I. “Is it possible to detect single open phase fault on a PMSM drive more
efficiently compared to existing methods?”
II. “Is there a significant improvement in vehicle traction control capability of an
electric differential based traction control system compared to
mechanical/hydraulic braking based traction control?”
III. “Is it possible to improve vehicle yaw stabilization capability with an electric
machine differential compared to a mechanical differential?”
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1.3 Chapter Outline and Contributions
Chapter 02 provides a review of existing research towards the concept of electric
machine differential. Methodology for each research questions is discussed with in the
chapter dedicated to the specific question. Chapter 03 provides an overview of the design,
implementation of the 4kW EMD hardware and control algorithm development. Machine
selection, power electronics system development, motor control algorithm and overall
EMD control algorithm is discussed in detail. Chapter 04 is dedicated towards presenting
a novel SPO fault diagnostic algorithm development. The proposed algorithm is capable
of detecting the single open phase in permanent magnet synchronous machines with in
one electrical cycle which is a significant improvement compared to existing methods.
Additionally the algorithm identifies the faulted phase by quadrature and direct axis
current analysis. Chapter 05 presents the results of the real-time extremum seeking slip
optimization (RT-ESSO) algorithm for traction control & antilock braking. The RT-
ESSO algorithm utilizes a sinusoidal perturbation based extremum seeking optimization
algorithm in contrast to variable structure control algorithms available at present. The
algorithm performance was verified with a traction control experimental setup. Chapter
06 is dedicated towards the vehicle model development & yaw stabilization capability
improvement with an electric machine differential. Chapter 07 provides an overall
summary of the contributions and concluding remarks.
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CHAPTER 2. LITERATURE REVIEW
2.1 Vehicle and Tire Properties
Research has shown that 20% -25% of the car accidents resulting injury or fatalities
were due to spinning cars (Van Zantan, 2000). Sixty percent of the accidents with
spinning cars had only one car involved in the accident (Van Zantan, 2000). Lose of
stability of a car causes it to spin or roll, causing injuries or fatalities. Improved stability
control systems improve passenger safety (Erke A., 2008).
Figure 2.1 Vehicle Reference Frame (defined by SAE)
Figure 2.1 above represents the vehicle reference frame based axis system defined for
an automobile, accepted by the Society of Automotive Engineers (SAE). Main focus of
automobile stability is towards yaw moment stabilization and roll moment
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stabilization. Antilock braking and traction control provides additional stability by
preventing excessive wheel slip which could lead to instability. Braking during cornering,
lane changes at high speed and cornering on slippery roads are particular maneuvers that
could render the car in an unstable condition. Instability arises due to lack of road force
on each wheel to complete the maneuver requested by the driver. The vehicle stability
controller monitors the vehicle state and attempts to regain control by controlling braking,
engine power or suspension control.
Figure 2.2 Planar motion of an automobile (Gillespie, T.,1992)
A summary of vehicle yaw instability is presented by Van Zantan, (2000). Rapid turn
maneuvers generate yaw moment that influences the yaw velocity. The yaw moment is a
result of the lateral force generated at tire road contact patch and the slip angle (Van
Zantan, 2000). Ability to influence yaw moment with steering angle decrease with
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increasing slip angle (reaches limit of adhesion). The steer-ability of the car is lost once
the car reaches the physical limit of force between the tire and road is reached. Hence,
limiting slip angle aids stabilize yaw moment while maintaining adequate control (Van
Zantan, 2000). Slip angle control can be achieved with a precise yaw velocity controller
(Park H. & Kim C. Y., 1999). Neither slip nor limit of adhesion (to the road) is directly
measurable but can only be estimated based on measurable quantities.
Tires of an automobile are integral to the vehicle stability as the force generation at
each tire road contact patch is influenced by tire properties. The forces generated at the
tire road contact patch determine the vehicle state of motion. Similar to a vehicle, the tire
itself has six degrees of freedom. There are three directional axis and three rotations
around each directional axis.
FX : Longitudinal Force
FY : Lateral Force
FZ : Normal Force
MZ: Aligning Torque
Α : Slip Angle
V : Total Velocity Vector
Ω : Angular Wheel Speed
Figure 2.3 Tire Forces (Pacejka H.B., 2002)
Typically the tire rolls on the road. The slip angle and the camber angle are two important
parameters for a tire in motion (Wong, J.Y., 2008). The force generated at the tire – road
contact patch is a function of the camber angle and the slip angle. Rolling resistance of a
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pneumatic tire is another important parameter. It is affected by the structure of the tire,
surface conditions, inflation pressure, speed and temperature (Wong, J.Y., 2008).
Tire slip occurs during the process of tractive force/braking force generation. ‘u’ is the
linear speed of the tire center, ‘ ’ is the angular speed and ‘r’ is the wheel radius. Tire
slip is positive during acceleration.
{
⁄
⁄
Eq 2.1
Friction coefficient between the road and the tire is a non-linear function of wheel slip.
The characteristics between the tire and the road vary with tire properties and road
conditions. Figure 2.4 below illustrates example data of the friction coefficient variation
with wheel slip for two types of road conditions, dry asphalt and ice.
Figure 2.4 Friction coefficients vs. wheel slip (Beckman B., 1991)
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
1.2
1.4
Slip / %
Friction C
oeffic
ient
Asphult (Dry)
Ice
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Lateral force on a tire is also known as cornering force. “The relationship between the
tire cornering force and the tire slip angle is of fundamental importance to the
directional control and stability of road vehicles” (Wong, J.Y., 2008). The relationship
between the lateral force and the slip angle is illustrated in Figure 2.5.
Figure 2.5 Normalized lateral force variation with slip angle, reproduced with permission
(Szostak, H.T. et al 1988)
Figure 2.6 Normalized longitudinal force variation with slip angle, reproduced with
permission (Szostak, H.T. et al 1988)
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The slip angle also has an effect on the longitudinal force. Effect of the slip angle on
longitudinal force is shown in Figure 2.6. This discussion is a summary of major tire
properties related to the study presented here. It is understood that there are other factors
that contribute to tire dynamics (aligning torque, pneumatic trail, etc…). Extensive
research on tires and accurate modeling schemes has been conducted by H.B Pacejka,
(2002). Specific tire models utilized in the research will be presented in sub-sequent
chapters.
2.2 Related Work - Traction Control
Anti-lock brake systems (ABS) in automobiles increase safety by preventing wheel
lock-up during braking. ABS reduces stopping distance and enhances steer-ability. ABS
prevents wheel lock up during braking (Will A.B., 1997) (Gerstenmeier J., 1986) whereas
traction control assures optimal friction coefficient during acceleration. Wheel lock up
causes the wheel slip to reach 100%, which significantly decreases the friction coefficient
between the road and the tires. Low friction coefficients cause the vehicle to slide in an
uncontrolled manner. Conventional ABS exploits mechanical braking (or also referred to
as hydraulic brakes) to prevent wheel lock up by controlling wheel slip.
Existing wheel slip control algorithms utilize either, ‘a priori’ knowledge of desired
slip based on direct tire force measurements, estimation of road friction coefficient, by
online search algorithms (Dinçmen E. et al , 2012) or with direct measurement of tire
forces (Nam K. et al, 2011). Most online search algorithm based slip optimization
schemes are based on sliding mode control theory (De Castro R. et al, 2013) (Patra N., et
al, 2012) (Harifi A. et al, 2005) and gradient based search algorithms (Will A.B., 1997).
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10
Sliding mode extremum seeking algorithm based slip optimization algorithms have
been studied in the past (De Castro R. et al, 2013) (Dinçmen E. et al, 2012) (Patra N., et
al, 2012) (Will A.B., 1997). In (De Castro R. et al, 2013) a sliding mode slip controller
based vehicle traction/brake force control scheme with induction motors is proposed. The
proposed slip controller is activated only during excessive tire slip conditions and
assumes that the optimum slip value remains the same for different road conditions. This
assumption restricts the algorithm from reaching the optimum braking force during all
road conditions. Authors of (Dinçmen E. et al, 2012) are proposing a technique
considering the effect of side slip angle variation. The proposed method is self-
optimizing without any user defined data. Yet the inherent chattering in the actuator is
undesirable. Authors of (Will A.B., 1997) present a non-derivative search algorithm for
generating the best slip command which is fed in to a PID sliding mode controller. The
PID sliding mode controller controls the brake actuator. The chattering of the control is
also apparent in the provided results.
Fuzzy logic based antilock braking systems are also under extensive research (Mauer
G.F. et al, 1995) (Shengming X. et al, 2012). In (Shengming X. et al, 2012) a fuzzy rule
based scheme is developed in which, road conditions are categorized in to three groups
based on current wheel slip, predicted wheel slip and brake torque command signal. An
upper limit of useful wheel slip is assumed to be 15%. In (Liu X. et al, 2005), an
implementation of an electric machine based ABS scheme on a vehicle is presented. The
authors also present the advantages of torque response with an electric machine for
traction control applications. However, during implementation, the optimal slip for dry
and ice road conditions are assumed to be ‘1’ and ‘0.2’ respectively. In contrast, we
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propose an algorithm capable of tracking the optimal slip without slip limitations.
Imposing a slip limitation prevents the utilization of the best braking possible on a given
surface. Dynamic behavior of the brake torque actuator is a critical aspect in an antilock
braking system. An electric machine is well known for rapid torque generation capability
compared to mechanical brake actuators (Liu X. et al, 2005) and we attempt to exploit
this property in the proposed design.
2.3 Related Work - Vehicle Stability Control
Vehicle stability is sub divided in to lateral stability, yaw stability and roll stability.
Vehicle stability control assists in reducing under steer, over steer, instability around yaw
axis and roll over conditions. A study on optimal stability control of an automobile is
presented by D. Simic et al (1990) with the use of the bicycle model approximation. The
study investigates the stability of the vehicle considering the effects of the driver and the
environment. The results are based on non-stationary vehicle models. A stable region of
operation for the vehicle is discussed with how the vehicle design characteristic affects
the stability of the vehicle.
Lateral force optimization facilitates stable cornering. The slip angle depends on the
amount of lateral force applied, during a cornering or a turn maneuver. Increasing slip
angle causes the optimal longitudinal slip ratio to shift towards the higher wheel slip
region (Hyeon. J., 2010). But increasing slip ratio reduces the lateral force due to
reduction in lateral friction coefficient. Reduced lateral force limits cornering capability
and increases the chances of a instability. Therefore the researchers are proposing a
variable slip ratio control which simultaneously optimizes both lateral and longitudinal
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12
friction coefficient (Hyeon. J. et al, 2010). PI-regulator based slip ratio controller
proposed by Hyeon et al has shown significant improvement in lateral stability during
cornering on slippery roads and lane change maneuvers at 40kmph. Recent work in this
area has focus towards sliding mode controller based combined lateral and longitudinal
force maximization (Dincmen E. et al, 2012).
Fig 2.7 Slip Variation with Varying Slip Angle
Vehicle yaw stabilization is also a long explored research area for existing
automobiles. Existing techniques vary from brake force control to steering control based
algorithms to stabilize the vehicle. A critical aspect in vehicle stability control is the
accurate prediction of vehicle state/heading and estimation/measurement of road force on
each wheel. Variety of state estimation algorithms, virtual sensors and physical sensors
based techniques exist in the literature.
Masaki Yamamoto (1991) of Toyota Corporation has proposed a yaw stabilization
algorithm based on steering angle feed-forward and yaw velocity feedback. The research
focuses on controlling steer angle, driving/braking force and vertical load for vehicle yaw
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13
control based on the tire adhesion limits (Yamamoto M., 1991). The author investigates
the problem at linear range of tire adhesion and at the non-linear range of tire adhesion.
The steering wheel angle feed-forward function and yaw velocity feedback function
based steering response optimization algorithm for stability control has been effective at
high speed maneuvers when tires maintain adhesion. The effect of steer angle control
renders less effective in the non-linear range of tire adhesion. The author states that, an
alternate algorithm based on roll stiffness distribution control and driving/braking force
control based algorithm is effective in the non-linear range. Several other studies on
active steering are found in the existing literature (Ackermann J. et al, 1999) (Baslamish
S. C., 2006) (Chu L. et al, 2011).
A vehicle dynamics control system for under steer and over steer has been proposed
by Van Zanten et al in 1995. The proposed algorithm utilizes the vehicle slip angle as
information for stability control. The vehicle slip angle is estimated based on
measureable vehicle states such as wheel speed and lateral acceleration. An inner yaw
velocity controller performs yaw control according to the bicycle model, due to the
inaccuracy in the side slip estimation at different driving speeds. The combination of yaw
controller and side slip angle controller with brake pressure control has enabled a stable,
maneuverable vehicle.
Model based vehicle state estimation is common for vehicle stability control purposes.
A robust vehicle state estimation based on an adaptive hybrid integrator/Luenberger type
observer is discussed (Tseng H. E. et al, 1999). Vehicle stability control schemes
facilitate in maintaining the vehicle in a controllable state for the driver. Vehicle side slip
angle estimation is one of the major parameters for the vehicle stability controller. The
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estimation of the slide slip angle is influenced by sensor drift and gravitational
acceleration due to road bank angle. The authors present algorithms with higher accuracy
for side slip angle estimation.
Four wheel steering (4WS) based vehicle yaw stabilization has been proposed as a
means of improving vehicle stability control capability (Will A. B., 1997). A fuzzy model
based rear wheel control strategy has been evaluated by the authors. The author combines
linear quadratic control theory with fuzzy modeling to construct a novel vehicle steering
controller.
Active front steering and rear steering provides improvement in stability control
capability. Electric machine differential provides an additional degree of control due to
the independent wheel torque control capability. Furthermore an electric machine
eliminates the lag in the hydraulic brakes system and provides a faster torque response.
2.4 Related Work - Electric Machines for EV, HEV Applications
Different types of electrical machines are designed and evaluated for automotive
traction applications. Some of the requirements for traction applications are (Zeraoulia et
al, 2006),
High instant power High efficiency
High power density Efficient regenerative braking
High torque at low speeds Reliability and robustness
Wide speed range region Reasonable cost
Fast torque response Wide constant torque region
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15
From the aforementioned requirements, cost of the electric machine, efficiency/loss
and long term return on investment are major concerns in selecting an electric machine
for a traction application. Permanent magnet machines (trapezoidal back emf machines
and sinusoidal back emf machines) and inductions machines are widely used as traction
motors due to their unique advantages. The comparison of electric machines for traction
applications provided by Zeraoulia et al also ranks induction motor the highest,
permanent magnet machine the next and switch reluctance machine and DC machine as
the least preferred.
Permanent magnet electric machines provide good torque density and efficiency
compared to other types of motors (Goss J. et al, 2013). In a more recent study, Goss et al
have evaluated permanent magnet machines and induction machines considering traction
drive profiles and long term cost savings. Fluctuating prices of permanent magnets
prevent automotive manufacturers from utilizing them in applications. Therefore an
induction machine is perceived as a better solution considering the cost reduction, but
relatively provides lower efficiency, power density and power factor (Goss J. et al, 2013).
Several other studies exists which evaluates the different machines for traction
applications (Rahman, K. M., & Ehsani, M., 1996) (Rahman Z., Ehsani, M., & Butler
K.L., 2000).
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16
2.5 Related Work - Electric Machine Differential
A differential in a car allows the wheels on each side of the axle to rotate at different
speeds. Such capability is necessary for safe, efficient cornering/turning of an automobile.
Various types of mechanical differentials are available at present.
Open Differential: Equal torque distribution to each wheel regardless
of the wheel speed.
Locked Differential: Transfers torque to the wheel with the grip.
Limited Slip Differential: Limits full power being delivered to one
wheel
Automatic Torque Biasing Differential
Mechanical differentials vary in mechanical design. The electric machine differential
(EMD) discussed comprises of several advantages over conventional differential. Some
of the advantages are,
Efficiency due to electric power train
Sophisticated control algorithms
Fast dynamic behavior due to electric machine
Ability to alter differential behavior with a control algorithm change
Ability to implement traction control algorithms and ABS algorithms
with minimal hardware requirements
Ability to perform vehicle yaw stability control with minimal
hardware requirements
Different types of EMD architectures are found in literature. Figure 2.8 compares two
of the existing electric machine differential architectures with a typical hybrid drive train
(electric machine placed between the engine and the differential).
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17
Figure 2.8 Electric Vehicle Architectures (Planetary gears based system is not considered)
EMDs equip a unique platform for vehicle stability control, passenger comfort
improvement and range extension of an electric vehicle (EV). Initial research by Yoichi
Hori of University of Tokyo, Japan was based on permanent magnet DC machines
(Furuya T. et al, 1996). In (Hori Y. et al,1998) research outcomes based on an actual
electric vehicle is discussed. A model following control law (MFC) for traction control of
electric machine differential based automobile is presented. In the model, the slip is
represented as a part of vehicle inertia. This MFC reduce the current command of the
motor with the slipping wheel yielding lesser torque to the slipping wheel. Less torque
causes deceleration of the wheel resulting re-adhesion and hence better traction is
achieved.
Further the investigation is extended to an optimal slip ratio control. A road condition
estimator is utilized to estimate the best slip command for the optimal slip ratio controller.
Simulations show that lateral motion stabilization can be achieved with slip ratio based
control on a four wheel driven electric vehicle by implementing slip ratio control (Hori
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18
Y., 2004). Skid detection without vehicle chassis speed is presented therein. Such
advanced adhesion control schemes have proven to be helpful in attenuating yaw
disturbance of an automobile.
Battery life of an electric vehicle is a critical factor in evaluating the performance of
an EV. Miles per charge of an EV estimate the battery pack capacity of it. Limitations in
battery capacity is one of the foremost hurdles, engineers are facing in realizing an
electric vehicle to compete with the driving range capability of a gasoline based
automobile. Researchers confirm a 3% reduction in energy loss by implementing a range
extending traction control algorithm (Fujimoto H. et al, 2011 ).
Yaw moment stabilization and roll moment stabilization of an electric machine based
differential (EMD) is a primary area of study. An observer based yaws and roll moment
control schemes are discussed in (Maeda K. et al, 2011) and (Nam K. et al, 2011)
respectively.
Previous electric differential based traction control and vehicle dynamics stabilization
techniques entail significantly high processing capability due to algorithm complexity.
Authors of (Perez-Pinal F. J. et al, 2009) present a simpler and alternate algorithm for an
electric differential. Mainly the focus of their research is attempting to synchronize the
rear driving wheels to track the vehicle path rather than stabilizing the yaw and roll
moment. Electric machine differential are emerging in the market in several forms. The
unique advantages are appealing towards several industries with a unique drive profiles.
Next section presents the proposed vehicle model and the electric machine control
algorithm utilized in the following sections.
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19
CHAPTER 3. ELECTRIC MACHINE DIFFERENTIAL DEVELOPMENT
The hardware development section presents the followed design criterion, in
developing the brushless DC (BLDC) machine based electric machine differential.
3.1 System Overview
The EMD consists of two electric machines, two drive units, a central control unit.
The initial EMD design is for a rear wheel drive vehicle. The central controller consists
of a lateral accelerometers, longitudinal accelerometers and yaw rate sensors interfaced to
a Microchip® dsPIC304011 microcontroller.
Figure 3.1 Electric Machine Differential Overview
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20
A custom data communication channel was developed between the central controller and
each drive unit to command wheel speed and wheel torque. The central controller is also
interfaced to an accelerator pedal and a steering wheel input to provide information on
drivers intent. Each drive unit is controlled by a Microchip® dsPIC30F4011
microcontroller. The central controller commands the status of the drive (drive disabled,
regenerative braking, open loop operation, closed loop current control, closed loop speed
control) and the respective speed or torque value. Current drive status is communicated
back to the central controller via the same communication channel.
3.2 Vehicle Selection
A small scale vehicle design was considered in sizing the electric machine differential.
A Clubcar® Carryall 242 ® was chosen as the target vehicle.
Figure 3.2 Chosen Vehicle (Clubcar® Carryall 242 ®)
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Vehicle parameters are presented below.
Max Vehicle Weight : 136.1kg (Club Car Carryall 242)
Battery Weight : 22.5kg
(2.25kg x 10, 12Vx5, 2 Parallel Banks of 5, 16Ah, Ub1280F2)
Machine Weight : 28kg (14kg x 2)
Passenger Weight : 120kg (60kg x 2)
Total Weight : 386.1 kg
Acceleration : 0 to 40mph (64kmh) in 13 Seconds
: 0 to 17.8ms-1 in 13 seconds
: 1.37ms-2
Vehicle traction force generation requirements.
Static Friction : 0.8 (Rubber on Dry Asphalt)
Rolling friction : 0.015
Total reaction force on wheels : 390kg x 9.8ms-2
: 3822 N
Reaction Force per Axle : 1911 N
Reaction Force per Wheel : 955.5 N
Force required to overcome rolling friction (per wheel) : μr*R
: 0.015*955.5
: 14.33N per wheel
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22
Acceleration required : 1.37ms-2
Force Required for Acceleration : m x a
: 390kg x 1.37 ms-2
: 535 N
Total Force Required at startup : 535N + 4x14.33N
: 593 N
Force need to be generated by each driving wheel : (593/2) N
: 296 N
Tire specification for the vehicle : 20 x 10-8 All terrain, 4-ply rated
Tire radius : 10 inches (20/2)
: 0.254 m
Torque required at each wheel shaft : 296 N * 0.254 m
: 75.18 Nm per wheel
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Table 3.1
Motor Parameters (BLDC Hub Motors)
Choice
Voltage
/ (V)
Power
/(kW)
Maximum
Speed
/(RPM)
Maximum
Torque
/ (Nm)
Maximum
Current
/ (A)
Weight
/(kg)
Dim.
/(in)
1 60 2.0 774 64.9 46.69 14 10
2 48 3.0 548 157.0 77 22 13
3 60 3.0 n/a n/a n/a 18 13
4 72 4.5 1299 62.6 112 20 13
5 72 4.5 823 105.0 85 20 13
*Information from Kelly Controller LLC data sheets.
A selection of brush-lees DC hub motors were considered for the application. Table 3.1
above summarizes the considered machines. Machine choice #1 highlighted in the table
was chosen for the design considering available development, testing capabilities and
required speed output.
3.3 Electric Drive Unit Development
The design procedure of the DC to AC converter is discussed here. DC to AC
inverters utilizes pulse width modulation to control the desired voltage output. An
International Rectifiers’ IRAM136-3023B intelligent power module was considered to
simplify the design process. The power module contains three half bridges, the necessary
gate drive circuits and thermal shut down circuitry built in to one package.
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24
Figure 3.3 Power Module Connection Diagram (from International Rectifiers datasheet)
The power module is rated for a maximum of 150V and 30A and a maximum
switching frequency of 20 kHz. The gate drive circuitry requires 15V external supply.
The DC link capacitor design is a critical aspect for the drive. It decouples the
inductance from the DC link voltage source by providing a low impedance path for the
ripple currents (Salcone M. et al, 2011). Input capacitor design is guidelines provided by
International Rectifiers were followed.
(
) Eq. 3.1
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25
Therefore a 1000 micro Farad electrolytic capacitor with a voltage rating of 200V was
selected for this application.
Phase current measurements are required for field oriented control algorithm and for
torque regulation in BLDC machines. Shunt resistors, ACS 712 by Allegro Microsystems
LLC and LTS-25NP by LEM USA Inc. were considered for this application. Noise
immunity of LTS-25NP was advantageous and therefore chosen for this application.
Additional transuding circuitry was added to the drive board with the flexibility to choose
the measurement to be interfaced to the microcontroller. Scaling circuitry and analog
filter was implemented in hardware with Linear Technology ® precision zero drift
operational amplifiers.
Figure 3.4 Signal Conditioning Circuitry
The motor drive unit has three voltage levels. A 5V output for microcontroller and
operational amplifiers, a 15V for the gate drive circuitry and a 60V HVDC link for the
motor. The 5V supply is generated with a LM7805 linear voltage regulator. The 15V
supply is generated from a 12V to 15V switch mode boost converter based on Texas
Instruments ® LM2578 integrated circuit. The boost converter lay out is illustrated in the
following figure.
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26
Part Value Part Value
R1 140kΩ C4 0.0022μF
R2 10kΩ L1 330μF
R3 0.15Ω D1 1N5818
R4 200 kΩ Vin 12V
C1 1820pF Vout 15V
C2 470μF Iout 140mA
C3 20pF Vripplr 10mV
Figure 3.5 Boost Converter Circuit (LM2578 data sheet)
Overall drive layout was developed to reduce electromagnetic interference (EMI), and
switching noise on measurements. High current paths were size appropriately and
reinforced to facilitate high current carrying capability. Switch-mode power supply
circuits were separated from the measurement circuitry. Separate ground planes were
placed for measurements and power circuits. Two layered FR4 material was utilized for
the printed circuit board.
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27
Figure 3.6 Drive Unit PCB Top Layer
Figure 3.7 Drive Unit PCB Bottom Layer
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28
Figure 3.8 Final PCB design
The power module required means of removing the heat from the switches to maintain
functionality. A heat sink was designed to remove the excess heat. Figure 3.9 is the
chosen heat sink for this application.
Figure 3.9 Chosen Heat Sink H S MARSTON 96CN-01500-A-200
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29
The power module power dissipation calculation and heat sink calculation was based
on MaximICs’ application note AN1832 and International Rectifiers’ application note
AN1832. The Matlab® script for the calculation is available in the appendix. An
Aluminum alloy based heat sink with a thermal resistance of 0.36OC/W was chosen for
the application. Final drive with the control board mounted on top is show in Fig 3.10.
Figure 3.10 Final Motor Drive Unit
Inverter efficiency is critical in an automotive application due to the limited amount of
energy available. The inverter efficiency was measured under a fixed load up to 430W of
input power. It is noticeable that the inverter has low efficiency at low power levels with
an increasing trend. The selection of the low load was due to limitations in the hardware
platform. The most power loss occurs in the power module. The data sheet states that the
MOSFETs have an RDS_ON that varies between 38mΩ to 122mΩ. The power module total
power loss at 16kHz switching frequency and 24 ARMS output phase current is at 300W.
The efficiency at this power level was 87.50% (Sinusoidal modulation, V+ 100V, TJ =
150OC, Modulation Depth = 0.8, PF = 0.6)(International Rectifiers, 2008).
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30
Figure 3.11 Drive Unit Efficiency Under Minimal Loading
The final central control unit is shown in figure 3.12. It is equipped with one dual axis
accelerometers and two single axis accelerometers for longitudinal and lateral
acceleration sensing. Two yaw rate sensors are also available for yaw variation sensing.
Five analog channels are interfaced to the Microchip® dsPIC30F4011 device for
algorithm development and verification purposes. Two UARTs communicate information
to each drive unit and returns necessary information back to the central controller. Two
voltage levels are available on the central controller. A 15V to 5V switch mode regulator
and a 15V to 3.3V switch mode regulator generate the necessary voltages. The direct
sensor measurements may be filtered and scaled if necessary via the additionally circuitry
provided.
40 60 80 100 120 140 160 180 20026
28
30
32
34
36
38
Speed / (RPM)
Effic
ien
cy / (
%)
31
31
Table 3.2
Central Control Board Sensors and SMPSs (BLDC Hub Motors)
Function Component
5V Regulation LM2576
3.3V Regulation LM2574
Yaw Rate Sensor STEVAL-MKI074V1
Yaw Rate Sensor ANALOG DEVICES-EVAL-ADXRS622Z
Single Axis Accelerometer FREESCALE - MMA2241KEGv
Dual Axis Accelerometer AD22284-A-R2
Figure 3.12 Central Control Unit
A meticulous test procedure with safety precautions were followed during the initial
testing phases. Possible short circuit identification tests were performed to prevent
damage to each drive units. Low voltage testing was performed prior to applying full 60V
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32
to the DC link. Functional verifications on the current sensors and hall sensor interface
were carried out prior to implementing motor control algorithms.
3.4 In-System Communication Protocol
The chosen drive train architecture forced the use of an in-system communication
protocol to be developed in order to reduce computation overhead and better perform
differential action. The communication protocol data transfer rate is 56kbps at 37ms
intervals to both drives, an asynchronous data packet format was chosen to communicate
the data. The data packet structure is illustrated in the following figure.
Figure 3.13 Communication Protocol Data Packet Structure
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33
Each frame is an integer value with the ‘Start Frame’ being ‘0xEE’ (Hexadecimal) and
the end frame being ‘0xDD’ (Hexadecimal). Each drive replies with an acknowledgement
and its’ current status once a data packet is received. This is performed through the
dedicated communication channel available on each drive.
3.5 Electric Machine Differential Algorithm
An overview of the EMD is shown in figure 3.14. The communication protocol
between the wheels and the central command unit assure proper differential functionality.
The central controller estimates the vehicle states based on the yaw rate, accelerometer
measurements and non-driven wheel speed measurements. Stability control algorithms
are initiated only during an unstable condition. Each electric drive receives a status
command and a value for speed and/or torque. Open loop control, Closed loop speed
control, Closed Loop current control, Regenerative braking, Traction Control, Antilock
Braking and Gate drives disabled are the seven status commands. These status commands
and torque/speed commands may be utilized to configure the EMD to different types
(locked differential, variable slip differential, etc) of differential with the use of software.
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34
Figure 3.14 EMD High Level System Overview
3.6 BLDC Machine Manufacturers Data and Characteristics
This section presents the steps followed in developing the speed controller and current
controller. The brushless DC machine was characterized in order to obtain machine
parameters. Machine specifications and obtained parameters are shown in the following
Table. Manufacturer data based Torque vs. Speed characteristic and Efficiency vs. Speed
characteristics are shown in Figure 3.15. Machine commutation sequence was determined
by correlating the phase to phase back emf and hall sensor signal output. The machine is
an inside out type motor or hub motor with the tire.
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35
Table 3.3
BLDC Machine Specifications and Parameters
Parameter Value
Type Trapezoidal Back EMF Permanent Magnet Machine
Rated Voltage 60V
Rated Power 2kW
Position Sensing Hall Sensors
Winding Inductance 6.50mH per phase
Winding Resistance 90mΩ per phase
Back EMF Constant 511 VL-L per kRPM
Poles 24
Wheel Radius 0.229m
Wheel Circumference 1.43m
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36
Figure 3.15 Torque Variation with Speed (Red) and Efficiency Variation with
Speed (Blue)
Following section presents the procedures followed in developing the motor control
algorithm. The motor control algorithm includes the speed controller and current
controller development.
3.7 BLDC Motor Control Algorithm
Initially the motor control algorithm was designed. The drive unit receives necessary
status command and speed/torque commands from the central command unit. The
supervisory algorithm operates at 16kHz. Necessary control outputs are provided to the
microcontroller registers for appropriate control. Two interrupts are utilized in the control
250 300 350 400 450 500 550 600 650 700 750 8000
10
20
30
40
50
60
70
80
90
Speed / (RPM)
Manufacturer Data for the BLDC Machine
Torque / (Nm)
Efficiency / (%)
37
37
algorithm. One interrupt provides the rotor position via the hall sensors and the second
interrupt signals the communication channel data availability. The C codes for the
algorithms are available in the appendix.
Figure 3.16 Overview of the Motor Control Algorithm
Figure 3.17 Motor Control Algorithm Interrupt Service Routines
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38
Initially, motor behavior was observed in open loop mode for system dynamic
behavior. Speed response of the machine was captured for the speed controller design
purposes. Open loop control of the electric machine was preferred in the differential
system as the drive has control over each wheel speed through the accelerator pedal and
the steering wheel adjustment. This will be presented in detail at the end of this chapter.
3.7.1 Current Controller Development
A current controller is important in this application as it leads to torque regulation.
Electromagnetic torque of a BLDC machine is shown in the following expression from
(Texas Instruments, 2010).
(
) (
) (
) Eq 3.2
Only two phases in a BLDC machine is excited at an instant. Therefore only the positive
current of each commutation cycle was measured at an instance. Current rotor position
was utilized in order to determine the phase with positive current flow. Current controller
updated the PWM based on the phase current at 16kHz. A block diagram of the current
control loop is illustrated in Figure 3.18.
Figure 3.18 Current Controller Block Diagram (Texas Instruments, 2010)
39
39
A bang-bang type current controller and a PI type (Proportional and Integral) current
controller were implemented. Step responses of the both current controllers are shown
below. The chosen parameters are given in the table following the figures.
Figure 3.19.a BLDC Machine Current Controller Performance with Bang-Bang type
Controller (Yellow - Phase C current, zoomed & Red - Sampling frequency)
Figure 3.19.b Zoomed Current Waveform from Figure 3.17.a (time base 200μs/div)
Phase C Current
Sampling Instances
Phase C Current
Sampling Instances
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40
Figure 3.17.a above illustrates the bang-bang type current controller regulating Phase
C current. Scale for the yellow waveform is 10.0 A/div (time base 200ms/div). Red
channel in figure 3.17 represents the phase current sampling frequency. The current
regulation set for the above case was set at 11 Amperes.
Figure 3.20.a BLDC Machine Current Controller Performance with Bang-Bang
type Controller (Yellow - Phase C current, & Red - Sampling frequency)
Figure 3.20.b BLDC Machine Current Controller (Zoomed Figure 3.20.a)
Phase C Current
Sampling Instances
Phase C Current
Sampling Instances
41
41
Figure 3.18 below illustrates several electrical cycles of phase C current with the
bang-bang type controller. Higher current command generates sufficient electromagnetic
torque to rotate the machine and accelerate it. The waveform shrinks due to the
acceleration of the electric machine. Figure 3.18.a and b are at 26.6 Amperes of average
phase current regulation.
Figure 3.21.a BLDC Machine Current Controller Performance with PI type
Controller (Yellow - Phase C current, un-zoomed & Red - Sampling frequency)
Figure 3.21.b Zoomed Current Waveform of Figure 3.19.a (Average Current at 11 A)
Phase C Current
Phase C Current
Sampling Instances
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42
Figure 3.22.a BLDC Machine Current Controller Performance with PI type Controller
(Average Current at 20.5 A)
Figure 3.22.b Zoomed Current Waveform of Figure 3.22.a (Average Current at 20.5A)
Figure 3.22 above represents similar results for the PI type current regulator. Several
phase current cycles of the PI regulator based controller is provided in Figure 3.22. The
proportional gain was set to 2.2 and Integral gain was set to 0.111. An integral windup
Phase C Current
Phase C Current
Sampling Instances
43
43
algorithm was also in place that clears the integral value when it increases beyond the set
threshold. Next section presents the procedures followed during the speed controller
development.
3.7.2 Speed Controller Development
Figure 3.23 BLDC Motor Speed Controller (Akin B.et al, 2010)
A block diagram of the speed controller is illustrated in Figure 3.23. Hall sensors are
connected to the change notification interface (CN) that generates an interrupt in the
event of a rising or falling edge. An internal time is utilized to measure the time between
two transitions. The speed is calculated based on the timer value. PI regulator generates
PWM based on the speed command and the current speed. Open loop system response
was observed prior to designing the speed controller. The open loop behavior is
illustrated in Figure 3.24. The delay in the communication channel has been accounted in
the system response. A linear map between the commanded speed and actual speed was
obtained based on the system response.
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44
Figure 3.24 Open Loop Step Response of the Motor
The proportional and integral gains were calculated based on Ziegler-Nicholas method.
The proportional gain was set to 0.9 and the integral gain was set to 0.4. The speed
controller performance at different speeds commands and load variation is presented
below.
Figure 3.25 Speed Controller Response at Low Speed (2.2 rads-1
)
0 2 4 6 8 10
5
10
15
X: 2.253
Y: 4.597Sp
ee
d / (
rad
s-1
)
0 2 4 6 8 100
0.1
0.2
Time / (Seconds)
Sp
ee
d C
om
ma
nd
0 2 4 6 8 100.5
1
1.5
2
2.5
3
Time / (s)
Sp
ee
d / (
rad
ian
s p
er
se
c)
45
45
Figure 3.26 Speed Controller Response to Load Variation (at 12ms-1
, Red – speed set
point)
Figure 3.27 Speed Controller Response to Load Variation (at 17ms-1
, Red – speed set
point)
0 1 2 3 4 5 6 7 810
10.5
11
11.5
12
12.5
13
13.5
Time / (s)
Sp
ee
d (
ms
-1)
0 1 2 3 4 5 6 7 815
15.5
16
16.5
17
17.5
18
18.5
Time / (s)
Sp
ee
d / (
ms
-1)
46
46
Application notes AN957 from Microchip and application note ‘Trapezoidal Control
of BLDC Motors Using Hall Effect Sensors’ from Texas Instruments were very useful in
developing and tuning the controllers.
3.7.3 Final Electric Machine Differential Experimental Setup
The final electric machine differential was integrated and mounted on the test setup as
shown in Figure 3.28. Two non-motorized treadmill platforms allow the system operation
without yaw moment during steady state testing. Each treadmill is mounted with an
industrial grade position transducer to measure actual speed of the road. It should be
noted that the actual speed and wheel speed vary due to wheel slip. Central controller
shown in Figure 3.11 is capable of interfacing to dSPACE® via the five BNC
connections. Simulated vehicle conditions or vehicle control commands are provided
through the analog interface during experimental setup testing.
Figure 3.28 Integrated Electric Machine Differential Setup on Test Platform
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47
Figure 3.29 EMD Wheel Speed Calculation based on Ackerman Formula
Wheel speed command to each wheel is calculated using the Ackerman formula,
based on the throttle position and the steering wheel input (When stability control is not
engaged). The following wheel speed calculation presented is based on the Figure 3.29
shown above (Perez-Pinal F.J. et al, 2009).
Outer wheel speed calculation
(
) (
) (
) (
) Eq. 3.3
(
) Eq. 3.4
Inner wheel speed calculation
(
) (
) (
) (
) Eq. 3.5
(
) Eq. 3.6
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48
The above expressions were utilized in providing speed commands to each wheel of
the electric machine differential. The driver is the speed controller in existing
automobiles, except when cruise control is engaged. Therefore the EMD setup was setup
to either set the PWM duty to each wheel or enable the current control mode. The speed
controller is utilized during cruise control only. The driver has the ability to control the
wheel speeds by controlling the throttle and control the direction of heading (turning
moment) by changing the steering angle. This method also allows the driver to correct for
speed variations that may occur due to parameter mismatch between the two motor-drive
couples. The following section presents the open single phase fault diagnostic algorithm
in detail.
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49
CHAPTER 4. D-Q CURRENT SIGNATURE BASED OPEN SINGLE PHASE FAULT
DETECTION AND FAULTED PHASE IDENTIFICATION FOR SM-PMAC
MACHINE DRIVES
Electric machine differential consists of multiple electric machines and drives.
Therefore reliable operation is critical throughout the life span of an automobile. Fault
diagnostic algorithms are capable of detecting faults in advance and prevent catastrophic
failure in the system as a whole.
4.1 Introduction
Electric machine drive has become one of the key devices enabling efficient energy
conversion in applications varying from transportation to food production to energy
management and power generation. Hence reliable operation is essential in safeguarding
operators and capital investments. Electric machine applications in the transportation
industry are rapidly growing due to electrification of the automobile. Hybridization and
electrification of the automobile include power train, climate control systems, oil pumps,
and power generation (Algrain M. C. et al, 2003). Reliability of aforementioned systems
is critical. Hence fault diagnostic algorithms (On Board Diagnostics or OBD) in the
transportation industry are of great importance (Liu L., 2006)(Wallmark O. et al, 2007).
A single winding Open (SWO) fault or a single phase open (SPO) fault may occur due to
mechanical shock, vibration, thermal shock, and extreme thermal cycling.
50
50
Single winding fault in a permanent magnet AC machine induces undesirable system
behavior in a torque regulated (Field Oriented Controlled-FOC) drive. Further the
resulting behavior of the flux generated by the stator under fault condition may
demagnetize the electromagnets if exposed to the fault for a prolonged period, rendering
the machine in an inoperable state. Therefore a faster SPO fault detection scheme for a
torque controlled surface mount permanent magnet synchronous machines (SM-PMSM)
is of significant value.
Existing SPO fault detection schemes utilize time consuming algorithms. Few of the
techniques are,
Root Mean Squared Calculation (Gajanayake C.J. et al, 2011) (Meinguet F.
et al, 2010)
Frequency domain analysis (Khlaief A. et al, 2010)
Alpha-beta current analysis (Khlaief A. et al, 2010)
Detection time of RMS calculation based methods, extends beyond one electrical cycle.
But the proposed algorithm detects the fault within one electrical cycle via instantaneous
fault signal behavior analysis. Further existing techniques require significantly large
memory (RAM) to calculate RMS values at low speeds with fixed sampling rate. The
proposed algorithm utilizes memory to store the instantaneous data and no data
accumulation is required. Proof of the fault detection scheme is presented through
Matlab® simulation and experimental data from a dSPACE® hardware-in-loop test setup.
The algorithm discussed herewith is of two parts. The first portion detects the fault
quickly with very little processor overhead. The second portion determines the faulted
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51
phase based on the collected data after the fault has been detected. Such techniques are
advantageous in electric drives and solar inverters for fault tolerant operation.
This chapter is organized as follows. Section 4.2 presents the problem definition;
section 4.3 summarize limitations in existing methods; section 4.4 presents accurate fault
simulation methods; section 4.5 derives the faulted phase detection scheme based on the
stationary to rotor reference frame transformation; section 4.6 presents the faulted phase
identification scheme; section 4.7 compares simulation results with experimental results,
improvement in detection time and algorithm complexity.
4.2 Problem Statement
Use of PMSM as a torque regulator is typical in numerous applications due to their
high torque density and higher efficiency (Demmelmyr M. et al, 2011)(Zeraoulia M. E. H.
et al , 2006 )(Goss J. et al, 2013). In FOC drives, torque command is converted in to q-d
current commands in FOC based drives. Electromagnetic torque is a function of d-q
currents as well as machine parameters. Therefore accurate machine parameters results in
an accurate map between torque and current commands. Figure 4.01 below provides an
overview of the SM-PMAC current regulation based torque control scheme implemented
in hardware for testing. The commanded d- q currents are achieved through proportional
and integral regulators (P.I. regulators) in the rotor reference frame. The SPO fault
diagnostic algorithm proposed in this chapter was developed for electric drives with
above mentioned control algorithms.
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52
Figure 4.1 Filed Oriented Control Algorithm Block Diagram
Single phase open (SPO) fault condition is caused by,
1. External cable connection failure
2. Internal motor stator winding failure
3. Failure of the two switches of the same leg (i.e. upper and lower device)
Figure 4.2 Electromagnetic torque before & after SPO fault (Fault occurs at t = 0.5 Sec.)
0.45 0.5 0.55
0
0.01
0.02
0.03
0.04
Time /(s)
Tem
/ (
Nm
)
53
53
Figure 4.3 SM-PMSM Stator Currents during Fault
Figure 4.4 and
behavior during and after fault in a Field Oriented Controlled
(FOC) SM-PMSM
0.1 0.15 0.2 0.25-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Time / (s)
Cu
rre
nt / (A
)
Phase A
Phase B
Phase C
0.1 0.15 0.2 0.25
-1
-0.5
0
0.5
1
1.5
2
2.5
Time / (s)
Cu
rre
nt / (A
)
Id
Iq
54
54
Significant increase in the electromagnetic torque ripple was observed after the SPO
fault (Kuruppu S. S. et al, 2013) (Figure 4.02). Large torque ripple is undesirable for
applications requiring accurate torque regulation such as machine tools, electric vehicles
and medical equipment. The oscillatory electromagnetic torque (at t=0.5 seconds) is due
to the P.I. regulators inability to regulate oscillatory d-q currents caused by the
unbalanced faulty machine. Figures 4.03 and 4.04 illustrate the behavior of phase
currents and d-q current behavior before and after the fault in an actual motor drive setup.
A faster fault detection scheme enables fault prevention without subjecting the machine
to the fault for an extended period of time.
4.3 Summary of Existing Fault Diagnostic Schemes and SPO Fault Diagnostic
Methods
Fault diagnostic systems are classified in to several categories. Failure sensitive filters,
voting systems, multiple hypothesis filter detectors, jump process formulation, and model
based fault diagnostics (also known as innovations based detection systems) (Willsky
A.S., 1976). Model based fault diagnostic schemes are subdivided in to following
categories (Liu L., 2006),
• Fault detection with parity relations
• Fault detection with diagnostic observers
• Fault detection with parameter estimation
Model based fault detection schemes more pronounce in applications. Such algorithms
utilize a residue generation scheme based on specific system parameters (residue is the
normalized deviation found in the system parameter at present compared to the ideal
55
55
value) and a residue evaluation scheme to evaluate the residue value for fault detection
(Liu L., 2006).
Figure 4.5 Residual Generation based SPO Fault Diagnostic Method (Gajanayaka)
The algorithm in (Gajanayaka C.J. et al, 2011) calculates the RMS value of phase
currents in real-time based on instantaneous current waveform sampling. Then a residual
signature/signal is generated based on the RMS current values. An SPO fault causes the
RMS value of the faulted phase current to be zero, causing residue signals related to the
faulted phase to increase beyond the set threshold. A fault indication is generated when
the residue value exceeds the chosen threshold. Several disadvantages exist in the residue
generation method.
√[
] [∫ [ ]
]
Eq. 4.01
Equation 4.01 above illustrates the calculation of RMS value of phase current. RMS
calculation requires samples over one cycle from the periodic signal. Hence the detection
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56
signal is only triggered at best, after one electrical cycle after the fault occurrence (fault
indication is issued after a full cycle time (T_2-T_1)). Further, the memory required for
sample storage is significantly high at low frequency (low speeds) at fixed sampling rate.
Hence, RMS based algorithms may impose a lower speed limit to activate fault detection
algorithm. Alternative algorithms proposed by researchers are discussed below.
Frequency domain analysis method clearly identifies a phase fault by monitoring the
amplitudes of the third harmonic (Khlaief A. et al, 2010). Yet it is incapable of
distinguishing among different phases faulting out. The authors of (Khlaief A. et al, 2010)
are proposing an α – β current signature to identify the faulty phase. The proposed fault
localization scheme performance and complexity is not discussed by the authors.
Wallmark et al in (Wallmark O. et al, 2007) present control algorithms for fault
tolerant PMSM drives. Authors present a fault mode estimation scheme for position
estimation for ‘limping home’ strategy. Fault localization strategy is not discussed. The
proposed algorithm modifies the sensor-less position estimation algorithm to estimate
position after SPO fault.
Authors of (Ribeiro de Araujo R.L. et al, 2004) are proposing a fault detection
scheme based on the error in the inverter pole voltages with respect to the commanded
voltages. Further details of the method are presented in (Riberio R. L. A., et al 2000)
Focus of the proposed method is towards individual switch failure detection rather than
SPO fault.
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57
(Bolognani M. et al, 2000) and (Bolognani M. et al, 1998) investigates a method of
mitigating the electro-magnetic torque ripple caused by a switch failure or failure of two
switches on one leg. The focus of the study is towards a remedial algorithm rather than
detection of the fault.
Several other types of fault schemes and fault detection techniques are discussed in
(Bolognani M. et al, 1998)(Kastha D. et al, 1994)(Fu J.R., 1993)(Liu T. et al,
1993)(Wallace A.K., 1988)(Peuget R. et al, 1998). More recent studies on electric
machine fault diagnostics schemes are discussed in (Liu L. et al, 2005)(Liu L. et al
2006)(Liu L. et al, 2007)(Estima J.O. et al, 2011)(Byoung P. et al, 2011). Parameter
identification based residual generation scheme is proposed in (Ribeiro R.L.A. et al, 2000)
for both sensor faults and process faults. A particle swarm optimization based method is
utilized in (Liu L. et al, 2005) to estimate parameters for fault diagnostics algorithms in
contrast to conventional least square methods for parameter estimation. An algorithm
based on the cumulative summing of a specific fault signal is proposed in (Meinguet F. et
al, 2010) for open circuit fault detection of a five phase PMSM. The fault signature
applied to the CUMSUM (cumulative summing) algorithm is based on the alpha-beta
currents in the stationary reference frame. Yet a simpler robust fault detection scheme
based on torque controlled machine drives utilizing the d-q current behavior has not been
discussed.
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58
Some of the disadvantages in the SPO fault detection methods are discussed in this
section are,
• Algorithm complexity (Khlaief A. et al, 2010) (Wallmark O. et al, 2007)
(Riberio R. L. A., et al 2000) (Liu L. et al, 2005)(Meinguet F. et al, 2010)
• Delay due to RMS calculation (Gajanayake C.J. et al, 2011)( Bolognani S. et
al, 2000)( Bolognani S. et al, 1998)
• Detection time is significantly high (Gajanayake C.J. et al, 2011)( Khlaief A.
et al, 2010)( Riberio R. L. A., et al 2000)( Liu L. et al, 2005)
• Inability to detect the fault at zero speed
The d-q current signature based method proposed here is advantageous considering all
the drawbacks listed above. The algorithm was found to be simple and robust throughout
the speed range.
4.4 Accurate Fault Simulation
Accurate fault recreation in simulation is advantageous in simplifying the fault
diagnostic algorithm development process. Main focus of this section is to discuss
possible accurate SPO fault simulation techniques as d-q machine model (without zero
sequence parameters) is insufficient in faulted machine behavior replication. Fault
simulation without the full state model (i.e. d-q machine model without zero sequence),
results false machine current behavior after the fault which may lead to faulty diagnostic
algorithms.
First step was to identify the behavior of the machine subjected to the SPO fault.
Figures 4.03 and 4.04 illustrate a single phase failure on an actual SM-PMSM recreated
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59
with the experimental setup discussed later. Machine control algorithm and data
collection was performed through a dSPACE® system based test setup. Fault occurs on
phase C, at t=0.18 seconds resulting 180O phase shift between currents in phase A and
phase B. Oscillatory behavior of the d-q currents is a consequence of PI regulators
inability to respond to the resulting d-q current pattern.
Several models were investigated to accurately simulate the fault condition. First
method investigated was based on the D-Q machine model in rotor reference frame.
Simulation results with this method had a significant abnormality from the actual drive
and machine behavior, due to the nature of the stator reference frame to rotor reference
frame transformation and the fault. Hence full state simulation was reasoned necessary to
accurately replicate the fault behavior in simulation (Kuruppu S. S. et al, 2013)
(Gajanayake C.J. et al, 2011). A Matlab® Simulink® simPower® block set based
simulation is proposed in (Gajanayake C.J. et al, 2011). Figure 4.06 illustrates the
machine model and the fault replication scheme.
Figure 4.6 Matlab® Simulink® simPower® based Machine Model (Gajanayake C.J. et al,
2011)
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60
Figure 4.7 Ias, Ibs and Ics behavior before and after the fault (Simulated with
simPower® toolbox)
Figure 4.8
behavior before and after the fault (Simulated with simPower®
toolbox)
0.475 0.48 0.485 0.49 0.495 0.5 0.505 0.51 0.515
-1.5
-1
-0.5
0
0.5
1
1.5
2
Time / (s)
Cu
rre
nt / (A
)
Phase A
Phase B
Phase C
0.48 0.485 0.49 0.495 0.5 0.505 0.51 0.515 0.52
-1
-0.5
0
0.5
1
1.5
2
Time / (s)
Cu
rre
nt / (A
)
D-Axis Current
Q-Axis Current
61
61
Figures 4.07 and 4.08 are simulation results based on the Simulink® simPower® toolbox
based model. The results closely match the actual machine current behavior shown in
Figure 4.03 and 4.04. Alternate simulation strategy based on generic Simulink blocks is
also presented herewith. This simulation requires the implementation of the SM-PMSM
equations. Equations 4.02.1 to 4.02.6 represent the SM-PMSM motor model in stator
reference frame. Equations 4.03.1 to 4.03.3 represent the proposed simulation model.
(x = a,b,c) are phase voltages, phase currents and back e.m.f. of the respective
phase. is the phase resistance. or ‘L’ is the self-inductance and ‘M ‘is the mutual
inductance (Krause P.C. et al, 2002). ‘s’ is the derivative operator in frequency domain.
Eq. 4.02.1
Eq. 4.02.2
Eq. 4.02.3
Eq. 4.02.4
Eq. 4.02.5
Eq. 4.02.6
Equations (1)-(3) can be written in the following form,
[
] [
] [
] Eq. 4.03.1
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62
[
] [
] Eq. 4.03.2
[
] [
] Eq. 4.03.3
Figure 4.9 Generic Simulink Toolbox based Fault Simulation Scheme
Where φ is the flux linkage and ‘K’ is the back emf constant (Gajanayake C.J. et al,
2011). Also, K , amplitude of the flux linkage established by the permanent
magnets. If above model is used to simulate open phase C fault, set , immediately
after the fault. The model needs to be altered to represent the change in the winding
configuration. Further, condition is enforced at the fault occurring instance.
Phase current behavior with the proposed model is shown below in Figure 04.10 and
quadrature and direct axis currents behavior is shown in Figure 04.11.
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63
Figure 4.10 Ias, Ibs and Ics behavior before and after the fault (Simulated with Generic
Simulink toolbox)
Figure 4.11
behavior before and after the fault (Simulated with Generic
Simulink toolbox)
0.49 0.495 0.5 0.505 0.51 0.515 0.52-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Time / (s)
Curr
ent / (A
) , F
ault S
ignal / (U
nits)
Phase A Current
Phase B Current
Phase C Current
Phase A
Phase B
0.49 0.492 0.494 0.496 0.498 0.5 0.502 0.504 0.506 0.508 0.51-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Time / (s)
Cu
rre
nt / (A
)
Iq
Id
64
64
Two methods for accurate fault simulation was presented above. Both methods
provided results that closely match the actual machine current behavior after the fault has
occurred.
4.5
Based Fault Detection Signature & Faulted Phase Identification
Figures 4.04, 4.08 and 4.11 illustrate the behavior of
before and after the
fault. A thorough analysis of the q and d current behavior after the fault revealed a unique
pattern, enabling a simplified method for fault detection. On a surface mount PMAC
motor, Lq ≈ Ld. Hence the electromagnetic torque equation can be written as follows,
(
) (
) [
( )
] Eq. 4.04.1
(
) (
) [
] Eq. 4.04.2
and
are DC quantities during healthy operation and in the
constant torque region. Phase currents after a single phase fault with closed loop PI
regulators are,
& Eq. 4.05
Considering the stator to rotor reference frame transformation,
[ (
) (
) ] Eq. 4.06.1
[ (
) ] Eq. 4.06.2
√ [ (
)] Eq. 4.06.3
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65
[ (
) (
) ] Eq. 4.06.4
[ (
) ] Eq. 4.06.5
√ [ (
)] Eq. 4.06.6
(
) Eq. 4.06.7
D-axis current, is regulated to be zero in FOC algorithms controlling SM-PMSM
machines in the constant torque region. SPO fault causes a significantly large variation in
. The ideal fault detection signal for detecting the SPO fault should show a
significantly distinguishable instantaneous variation compared to the healthy operation
case. Signal significantly amplifies the instantaneous fluctuations in the d-axis
current due to the fault (Kuruppu S. S. et al, 2013). Resolver offset angle is assumed to be
zero. Therefore the signal for fault detection is proposed as,
(
(
⁄
)
)
Eq. 4.07
Detection signal shown above is closer to zero for healthy operation and inhibits false
positive fault indications during startup transients. Further the memory requirement is
significantly reduced compared to RMS calculation as the signal is based upon
instantaneous q and d axis currents in the machine. Once a fault is detected, the following
faulted phase identification algorithm is initiated. The ratio between equations 4.06.3 and
4.06.6 results the following expression.
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66
⁄ (
) Eq. 4.08.1
Similarly, for phase B fault, & ,
⁄ (
) Eq. 4.08.2
For phase A fault, &
⁄ (
) Eq. 4.08.2
Theta ( ) is the electrical angle obtained via the resolver. The phase difference
between the actual electrical angle and the quantity
, for the faulty system
provides a means to uniquely identify the phase containing the fault.
Eq. 4.09
Phase difference between signal , and actual electrical angle based on the resolver
measurement is ⁄ , ⁄ and , for phase C, phase B or phase A SPO fault respectively.
Thus above phase delay of the faulted signal with respect to the actual measured position
provides a unique signature to identify the faulted phase. Fault detection algorithm
discussed in (Kuruppu S. S. et al, 2013) along with the estimated phase shift in S1 was
implemented in simulations and in actual hardware for algorithm verification as
described in the following sections.
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67
4.6 Experimental Results Evaluation
4.6.1 Experimental Setup
Aforementioned fault diagnostic algorithm and faulted phase identification algorithm
was implemented on actual hardware. A 250W Surface Mount Magnet Permanent
Magnet Synchronous Machine coupled to a dSPACE® CLP 1104 Real-time hardware
was utilized. A block diagram of the system is provided below. System information is
provided in the table below.
Figure 4.12 Block diagram of the hardware-in-loop experimental setup
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68
Figure 4.13 Experimental Setup
Parameters of the SM-PMSM are provided in Table 4.1. Figure 4.12 and 4.13 above
illustrates the block diagram of hardware setup and the actual test setup utilized to test the
algorithm. Field oriented control algorithm and the fault diagnostic algorithm was
implemented in Simulink. Model implemented in Simulink was auto-coded and
downloaded to dSPACE environment for real time testing. Parameters of the compiled
code were accessed through dSPACE control desk during runtime. Fault condition was
created by manually disconnecting one phase connecting to the electric machine.
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69
Table 4.1
Fault Diagnostic Experimental Setup Motor Specifications
Parameter Value
Machine Type
Surface Mount Magnet Sinusoidal Back EMF
Synchronous Machine
Manufacturer Motorsolver Inc.
Rated Power 250W
Rated Speed 4000 RPM
Rated Voltage 42 V
Resistance (L-L) 0.19 Ohm
Inductance (L-L) 0.49 mH
Poles 8
Figure 4.14 Implementation of Field Oriented Control Algorithm
70
70
Real time system, execution time step was set at 100μs. DC motor was speed
controlled while the PMSM was torque controlled. Phase currents, q-axis current, d-axis
current, rotor position (electrical), and signal S1 per equation 4.9 were recorded for each
of the phase faulted experiments and analyzed by exporting the data to Matlab. Figure
4.14 below is the torque control algorithm implementation for testing. This is the same
FOC algorithm illustrated in Figure 4.01 implemented using Simulink blocks.
4.6.2 Fault Detection
Faulted phase identification algorithm is initiated upon detection of a fault via the ‘Sss’
signal (Kuruppu S. S. et al, 2013).
Figure 4.15 Behavior of fault detection signal (experimental data)
Figure 4.16 Fault detected flag (experimental data)
0.5 0.55 0.6 0.65 0.7
-1
-0.8
-0.6
-0.4
-0.2
0
Time / (s)
Fau
lt S
ign
al T
rig
ger
0.5 0.55 0.6 0.65 0.7
0
0.5
1
Time / (s)
Fau
lt S
ign
al
Fault Signal
71
71
Behavior of ‘Sss’ before and after the fault is illustrated in Figure 4.15. Fault detection
algorithm compares ‘Sss’ to a preset threshold (-0.8 in this example) and generates a
‘fault detected flag’ (Figure 4.16) in 1.6ms whereas RMS calculation algorithms would
take 30ms to disable the drive unit and initiate the faulted phase identification for the
given speed of rotation (545 RPM).
4.6.3 Faulted Phase Identification
Discussion presented here elaborates the simulation and hardware implementation
results. Both simulations and experimental results support the capability of the proposed
algorithm in accurately detecting the faulted phase. Figures 4.17,4.18 and 4.19 are
simulation results. A single phase fault occurs at t=0.5 seconds. Behavior of phase
currents and d-q currents were presented in the earlier discussion. Phase identification
technique exploits the variation in electrical angle based phase shift in the signal S1.
Figure 4.17 Phase Current Behavior After Fault Occurrence (Simulation Results)
0.475 0.48 0.485 0.49 0.495 0.5 0.505 0.51 0.515
-1.5
-1
-0.5
0
0.5
1
1.5
2
Time / (s)
Cu
rre
nt / (A
)
Phase A
Phase B
Phase C
72
72
Figure 4.18 Behavior of d-q currents after fault (Simulated)
Figure 4.19 Actual rotor position based electrical angle (Red), Signal S1 behavior
corresponding to Phase A (Blue), Phase B (Green), and Phase C (Black) failure
(Simulated)
0.48 0.485 0.49 0.495 0.5 0.505 0.51 0.515 0.52
-1
-0.5
0
0.5
1
1.5
2
Time / (s)
Cu
rre
nt / (A
)
D-Axis Current
Q-Axis Current
0.51 0.512 0.514 0.516 0.518 0.52-2
0
2
Th
eta
/ R
ad
Actual Rotor Position Based Electrical Angle
0.51 0.512 0.514 0.516 0.518 0.52
-1
0
1
Time
Th
eta
/ R
ad
Phase Detection Signal
Phase C Faulted
Phase B Faulted
Phase A Faulted2*pi/ 3pi/ 3
One Electrical Cycle
73
73
Figure 4.19 illustrates the fault signal behavior of a single phase fault on phases ‘A’,’B’
and ‘C’ summarized in to one figure (lower figure of Figure 4.19). Actual electrical angle
(obtained via resolver) is shown in red (top figure of Figure 4.19) emphasizing the phase
shift between the fault signal and the electrical angle. Simulation results agree with the
phase shifts expected from the analytical study. Phase ‘A’ fault signal is in-phase with the
actual electrical angle whereas phase ‘B’ fault has a phase shift of, ⁄ with respect to
actual electrical angle. Single phase open fault on phase ‘C’ results in a fault signal with a
phase shift of ⁄ with respect to the actual electrical angle.
Figures 4.20.a, 4.20.b and 4.20.c, illustrate data from actual hardware based fault
signal (S1) behavior compared with actual electrical angle (red color plot on each figure).
These figures elaborate the phase shift between the actual electrical angles compared to
the signal S1. The phase shift between the fault detection signal (S1) and the actual
electrical angle match the simulation results with an error of degrees. Results are
summarized in Table 4.2.
Figure 4.20.a Actual electrical angle (Red) compared to fault detection signal S1
behavior corresponding to phase A open fault
0.054 0.055 0.056 0.057 0.058 0.059 0.06 0.061 0.062 0.063-2
-1
0
1
2
time / (s)
An
gu
lar
Me
asu
rem
en
t / (r
ad
)
Fault Signal
Actual Electrical Angle
91.9 Deg
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Figure 4.20.b Actual electrical angle (Red) compared to fault detection signal S1
behavior corresponding to phase B open fault
Figure 4.20.c Actual electrical angle (Red) compared to fault detection signal S1
behavior corresponding to phase C open fault
Direction of machine rotation for the hardware implementation was in the counter
clockwise direction whereas the proof and simulation results were established based on a
machine rotating in the clockwise direction. The resolver in the actual implementation
revealed an offset of approximately –𝝅/2. Measurements were corrected with this offset
in table 02. Fault detection signal phase shifts are interchanged for the clockwise and
0.044 0.046 0.048 0.05 0.052 0.054-2
-1
0
1
2
Time / (s)
An
gu
lar
Me
asu
rem
en
t / (r
ad
)
Actual Electrical Angle
Fault Signal
27.9 Deg
0.083 0.084 0.085 0.086 0.087 0.088 0.089 0.09 0.091 0.092-2
-1
0
1
2
Time / (s)
An
gu
lar
Me
asu
rem
en
t / (r
ad
)
Actual Electrical Angle
Fault Signal
29.8 Deg
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counterclockwise direction of motor rotation (Figure 17). It should be noted that the
expected phase angles are interchanged for phase B and phase C fault case when
considering the opposite direction of rotation.
Figure 4.21 Comparison of fault detection signal phase shift for positive and negative
direction of rotation in electrical degrees
Table 4.2
Comparison of Simulation and Experimental Results for Faulted Phase Identification
Faulted Phase
Theoretical Phase
Shift / Deg
Measured Phase
Shift / Deg
Error / Deg
Phase A 0.0 1.9 1.9
Phase B 120.0 117.9 -2.1
Phase C 60.0 60.2 -0.2
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A comparison of faulted phase identification for positive and negative directions of
rotation is illustrated above (Figure 4.21) considering the phase shift between the fault
signal and actual rotor position.
Experimental results shown above justify that the algorithm proposed herewith is
simpler in complexity due to the amount of processing required in detecting the fault as
well as identifying the faulted phase. Fault detection signal only requires two divisions
(floating point), one multiplication and a comparison to the set threshold. Fault detection
flag initiates the faulted phase identification algorithm. Hence the complexity involved
with inverse tangent calculation is not performed until a fault is detected. The fault
detection flag initiates a timer to record the phase difference between the actual electrical
angle and the signal ‘S1’. It should be noted that this algorithm utilizes significantly less
system resources from an embedded microcontroller or a DSP.
This chapter presents a novel single open phase fault diagnostic scheme for surface
mount magnet PMAC machines. A single phase open fault in a torque regulated electric
machine is considered. The fault condition discussed here cause a significantly large
electromagnetic torque ripple. Prolonged operation of the electric machine under this
fault condition may demagnetize the electric machine. Therefore faster detection of the
fault prevents lasting damage to the machine and the system.
Existing SPO fault detection scheme rely on residue generation based scheme which
require time consuming and memory consuming RMS calculation. The proposed scheme
is simple and fast compare to existing methods. Further the proposed algorithm is capable
of identifying the faulty phase by comparing the phase shift in the fault detection signal
(S1) with respect to actual electrical angle. Proof of algorithm has been justified through
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simulations and actual hardware based results. Future studies will be focused towards
detection of other types of faults (such as single switch failure, multiple switch failure) in
an electric machine drive system based on the d-q frame current signatures. Next chapter
presents the implementation of the ABS/traction control algorithm with real time slip
optimization capability.
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CHAPTER 5. ELECTRIC MACHINE BASED REAL TIME EXTREMUM SEEKING
TIRE FORCE MAXIMIZATION
5.1 Introduction
An electric machine based Antilock Braking System (ABS) with a real-time slip
optimization algorithm is presented. This algorithm is capable of reaching the wheel slip
which maximizes the road friction coefficient without any a priori knowledge of the road
condition. Extremum seeking slip optimization algorithm presented in (Ariyur K.B. et al,
2003) was altered to account for actuator dynamics. The results are based on a permanent
magnet synchronous machine and a hydraulic brake system. An improvement of
approximately 30m in stopping distance was observed with an electric machine based
ABS compared to the hydraulic brakes based ABS.
Anti-lock brake systems in automobiles increase safety by preventing wheel lock-up,
by reducing vehicle stopping distance and by enhancing steer-ability. ABS prevents
wheel lock up during braking (Will A.B., 1997) (Gerstenmeier J.,1986) whereas traction
control assures optimal friction coefficient during acceleration. Wheel lock up
significantly decreases the friction coefficient between the road and the tires, causing the
vehicle to slide in an uncontrolled manner (Will A.B., 1997). Existing ABS utilize
mechanical braking (or also referred to as hydraulic brakes) to prevent wheel lock up.
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In-line shaft coupled machines and in-wheel machines are two of the hybrid-electric
(HEV) and full electric vehicle (EV) architectures studied by researchers (Hori Y., 2002)
(Sado H. et al, 1999) (Hori Y. et al, 1997). Such HEVs and EVs facilitate the
implementation of ABS with the use of electric machines. A unique advantage of an
electric machine is the ability to accurately estimate and control the electromagnetic
torque applied to each wheel with the use of phase current measurements. Additionally
wheel slip may be estimated with wheel speed sensors (both driven and non-driven
wheels), enabling real-time wheel slip based brake/traction force maximization. Rough
braking maneuvers increase tire and brake pad wear. Hence such maneuvers are
undesirable. Alternatively, mechanical braking based ABS causes wear in the mechanical
brake systems due to the rapid chatter generated by existing ABS schemes. Regenerative
braking is much more advantageous due to improved energy efficiency and reduced wear
and tear of the system as a whole.
This chapter is organized as follows. Section 5.2 presents a literature review on
antilock braking and electric machine based antilock braking schemes. Section 5.3
presents the vehicle model, the mechanical braking system and the electrical machine
based braking scheme. Section 5.4 introduces the theory related to the extremum seeking
real-time brake force maximization algorithm. Section 5.5 presents the extremum seeking
braking force optimization algorithm applied towards mechanical braking. Section 5.6
presents the electric machine based slip optimization scheme. Section 5.7 provides a
comparison between the mechanical and electrical system based approaches. Section 5.8
presents the BLDC machine based experimental setup and experimental results. Finally
section 5.9 provides concluding remarks related to the work.
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5.2 Background and Motivation
The friction coefficient between the tire and the road is a complex and non-linear
function of wheel slip and the road condition (ice, wet, dry, asphalt, etc ). Wheel slip for a
braking maneuver is defined as,
Eq. 5.01
Where u is the vehicle longitudinal speed, ω is the wheel speed and r is the wheel radius.
Examples of friction coefficient (μ) variation with slip under different road conditions are
illustrated in Figure 01(Will A.B., 1997)
Figure 5.1 Friction coefficient variation with wheel slip during braking
Existing wheel slip control algorithms utilize either, ‘a priori’ knowledge of desired
slip based on direct tire force measurements, estimation of road friction coefficient, by
online search algorithms (Dinçmen M. et al, 2012) or with direct measurement of tire
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
1.2
1.4
Slip / %
Friction C
oeffic
ient
Asphult (Dry)
Ice
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81
forces (Nam K. et al, 2011). Most online search algorithm based slip optimization
schemes are based on sliding mode control theory (De Castro R. et al, 2013) (Dinçmen M.
et al, 2012) (Harifi A. et al, 2005) and gradient based search algorithms (Will A.B., 1997).
Several sliding mode extremum seeking algorithm based slip optimization algorithms
have been studied in the past (De Castro R. et al, 2013) (Dinçmen M. et al, 2012) (Patra
N. & Datta K., 2012) (Will A.B., 1997). In (De Castro R. et al, 2013), a sliding mode slip
controller based vehicle traction/brake force control scheme implemented with induction
motors was studied. The proposed slip controller is activated only during excessive tire
slip conditions and assumes that the optimum slip value remains the same for different
road conditions. This assumption restricts the algorithm from reaching the optimum
braking force during all road conditions. Authors of (Dinçmen M. et al, 2012) are
proposing a technique considering the effect of side slip angle variation. The proposed
method is self-optimizing without any user defined data. Yet the inherent chattering in
the actuation is undesirable. Authors of (Will A.B., 1997) present a non-derivative search
algorithm for generating the best slip command which is fed in to a PID sliding mode
controller. The PID sliding mode controller controls the brake actuator. The chattering of
the control is also apparent in the provided results (Will A.B., 1997).
Fuzzy logic based antilock braking systems are also under extensive research (Mauer
G.F., 1995)(Shengming X. & Huitong W., 2012). In (Mauer G.F., 1995) a fuzzy rule
based scheme is developed in which, road conditions are categorized in to three groups
based on current wheel slip, predicted wheel slip and brake torque command signal. An
upper limit of useful wheel slip is assumed to be 15%. In (Park J.H. & Kim C.Y.,1999),
an implementation of an electric machine based ABS scheme on a vehicle is presented.
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The authors also present the advantages of torque response with an electric machine. In
the implementation, the optimal slip for dry and ice road conditions are assumed to be ‘1’
and ‘0.2’ respectively. In contrast, the proposed algorithm is capable of tracking the
optimal slip without slip limitations. Imposing a slip limitation prevents the utilization of
the best braking possible on a given surface. Dynamic behavior of the brake torque
actuator is a critical aspect in an antilock braking system. An electric machine is well
known for rapid torque generation capability compared to mechanical brake actuators
(Liu X. et al, 2005).
Increasing demand for energy efficiency is making the electric and hybrid electric
vehicle an appealing means of transportation. Significant amount of research is being
conducted towards the evaluation of in-wheel electric machines based hybridization
compared to shaft coupled or other architectures of hybrid drive trains. Advancements in
electric machine research enabled the development of a fault tolerant in-wheel machine
with high power output (Ifedi C.J. et al, 2013). The electric machine based ABS is
compared with its mechanical counterpart. Both types of brake actuators (electric and
mechanical) are equipped with the same extremum seeking brake force optimization
algorithm to maximize the braking force in real-time. The brake force maximization
algorithm compliments the fast torque response capability in the electric machine
enhancing the respective ABS performance compared to the conventional bang-bang type
or sliding mode controller.
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5.3 Theoretical Model of the System
5.3.1 Unicycle Vehicle Model
The simple unicycle model illustrated in Figure 5.02 was chosen for simulating the
control strategy (Ariyur K.B. et al, 2003). A block diagram of the mechanical brake
system model is illustrated in Figure 5.03. It should be noted that the following model has
neglected the load transfer during braking and air resistance in order to simplify the study.
Figure 5.2 Unicycle Model of a Quarter Car During Braking
Eq. 5.02
Eq. 5.03
5.3.2 Mechanical Brake Model
Several techniques exist for modeling mechanical brake systems. Both first order
(Fortina A. et al, 2003)(Raza H. et al, 1997) and second order (Dinçmen M. et al, 2012)
(Wll A.B. & Zak S.H., 1997) brake system models were considered for this study. A first
order mechanical brake system model was utilized based on the work presented in (Raza
H. et al, 1997).
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Figure 5.3 Mechanical Brake System Model
Figure 5.03 represents the mechanical brake model with ‘K’ being the static gain and
‘τ’ being the time constant of the system. The transfer function for the brake torque
response is expressed as,
Eq. 5.04
According to results presented in (Raza H. et al, 1997) the time constant of the brakes
in a Ford® Lincoln Town Car vary between 556 milliseconds to 10 seconds.
5.3.3 Electric Machine Model
A sinusoidal back emf, permanent magnet synchronous machine (SM-PMSM) with
surface mount magnets was considered as the electric machine. The machine is assumed
to be an inside out, in-wheel design or more commonly referred to as a hub design.
Machine equations in the rotor reference frame are presented here (Krause P.C. et al,
2002). Note that ‘p’ is the derivative operator.
( )
Eq. 5.05.1
Eq. 5.05.2
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85
Eq. 5.05.3
(
) (
)
[
] Eq. 5.05.4
(
) (
) Eq. 5.05.5
Electric machine in this application is torque regulated in order to generate the
commanded braking torque. A field oriented control algorithm (FOC) was utilized to
achieve the desired torque command. Proportional and integral regulators regulate
quadrature and direct axis currents enabling accurate torque regulation. Figure 4.01 is a
simplified block diagram of the motor control algorithm. The dynamic model of the
decoupled ( &
), current regulated electric machine is derived as follows,
(
) Eq. 5.06.1
(
) Eq. 5.06.2
Assuming Lq, Ld and are known, decoupled machine equations are expressed by
5.07.1 and 5.07.2. These parameters are provided by the machine manufacturer.
Eq. 5.07.1
Eq. 5.07.2
Decoupled voltage commands with the PI regulators are written as,
(
) ∫(
) Eq.5.08.1
∫(
) Eq.5.08.2
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86
Therefore the transfer functions between the commanded and achieved and
is in
the following form.
(
)
Eq.5.09.1
(
)
Eq.5.09.2
5.3.4 Road Friction Coefficient Modeling
Several techniques exist for representing the friction coefficient between the road and
the tire. Pacejka’s magic formula, lookup tables and linearized model are a few. The road
friction coefficient representation proposed by (Beckman B., 2002) is being utilized for
algorithm verification. The general form of the friction coefficient as a function of the
wheel slip is shown in equation 5.10. Parameters α,β and P corresponding to dry asphalt
and icy road are summarized in Table 5.1.
| | Eq. 5.10
Table 5.1
Tire-Road Friction Coefficient Model Parameters
Parameter Dry Asphalt Road Ice
α 0.1484 -0.07841
β 0.3200 0.04223
P 1.5670 1.59800
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5.4 Extremum Seeking Slip Optimization Controller
5.4.1 Simplified Explanation of Extremum Seeking Algorithm
The extremum seeking algorithm utilized herewith and discussed in detail in (Ariyur
K.B. et al, 2003) uses sinusoidal perturbation in the optimization algorithm. The
extremum seeking for a static map presented here is from the first chapter of (Ariyur K.B.
et al, 2003). The re-presentation here is for the purpose of providing a brief overview of
the algorithm. Rigorous proof of the algorithm can be found in the original text.
Figure 5.4 Basic Extremum Seeking Scheme (Ariyur K.B. et al, 2003)
The static map f(θ) is of the form,
Eq. 5.11
The sinusoidal perturbation extracts the gradient information from the static map passes it
to the feedback loop. The high pass filter removes the DC components and low frequency
components in preparation for the demodulation process. The high pass filter output
contains the gradient information. The demodulation and the integrator enable the
algorithm to converge to the neighborhood of the extremum of the static map.
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88
5.4.2 Application of Extremum Seeking Algorithm for ABS
Relationship between wheel friction coefficient and tire slip is ‘unimodal’. Existing
algorithms maintain wheel slip within an interval that includes the peak friction
coefficient. Such algorithms are incapable of closely tracking the optimal slip. A real
time extremum seeking algorithm is proposed which enables tracking of the optimal
wheel slip for a given road condition in real time (Ariyur K.B. et al, 2003). This
algorithm enables accurate slip based tire force control. The extremum seeking antilock
braking algorithm presented in (Ariyur K.B. et al, 2003) is summarized as follows.
For the extremum seeking case, introduce such that,
Eq. 5.12
Eq. 5.13
Differentiating equation 5.01 with respect to time results,
Eq. 5.14
By substituting with 5.02 and 5.03, is obtained as,
(
)
Eq. 5.15
Therefore the simple feedback linearizing controller,
Eq. 5.16
Positive constant ‘c’ is chosen such that is exponentially stable. The wheel
model under feedback is represented as a cascade of input dynamics and a static map:
Eq. 5.17
Eq. 5.18
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89
Figure 5.5 Extremum seeking brake optimizing controller (without actuator)
Figure 5.05 shown above is a block diagram of the overall slip optimizing algorithm
discussed by authors of (Ariyur K.B. et al, 2003). A wheel model is utilized for
simulation purposes. In an application the wheel model is replaced by the physical system
(i.e. wheel). The actuator dynamics are not considered in this case. A method of
compensation for the actuator dynamics are presented in the following sections as the
actuator dynamics affect overall system behavior during algorithm implementation in a
physical system.
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5.5 Extremum Seeking Brake Force Optimization Algorithm with Mechanical Brake
System
The real time extremum seeking algorithm in (Ariyur K.B. et al, 2003) is designed
without considering the actuator dynamics. This section presents how the algorithm was
modified to compensate for the actuator static gain. Only the static gain was compensated
assuming the actuator dynamics are much faster than the vehicle system dynamics. This
is effectively a use of the method of singular perturbation (Khalil H.K., 2002) though we
do not use it formally. The conditions for this reduction such as the fact the brake
actuation is stable and extremely fast (100x) compared to vehicle dynamics are obviously
satisfied. Therefore the feedback linearization controller expression is of the form,
Eq. 5.19
Further we demonstrate the algorithm behavior during a sudden variation in the road
friction coefficient. Figure 5.06 is a block diagram of the system with the actuator and
Figure 5.07 is a Matlab® Simulink® implementation of the ABS algorithm and the plant
(the wheel model).
Figure 5.6 Extremum seeking brake optimizing controller with actuator
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Figure 5.7 Simulink Implementation of the Slip Controller with Actuator
In the simulation, initially the wheel is on a dry asphalt road. The road condition
changes from dry asphalt to ice. Road conditions depicted as levels 1 and 2 in Figure 5.08
correspond to dry asphalt and icy roads respectively.
Figure 5.8 Road Condition Variations and Slip Optimizer Behavior (τ=250ms)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
1
1.5
2
Ro
ad
Co
nd
itio
n
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.2
0.4
0.6
0.8
1
Time / (Sec)
Wh
ee
l S
lip
1 - Dry Aspahlt2 - Ice
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92
Figure 5.9 Actuator Torque Output with Changing Road Condition
Figures 5.08 and 5.09 illustrate the behavior of the extremum seeking algorithm and
the response of the brake torque actuator with the hydraulic brake system. The variation
of friction coefficient with wheel slip for these two road conditions are illustrated in
Figure 5.01. At t=2.0 seconds the wheel is exposed to an icy surface from an asphalt road.
Extremum seeking algorithm responds rapidly by reducing the brake torque in order to
maintain the optimal slip. Section 5.6 below presents the electric machine based brake
actuation behavior.
5.6 Extremum Seeking Brake Force Optimization Algorithm with Electric Machine
The P.I. current regulator based electromagnetic torque controller was discussed
earlier in section 5.3.3. The transfer functions are given by expressions 5.09.1 and 5.09.2.
Q axis current control is considered in this application. D-axis current is regulated to be
zero.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
200
400
600
800
1000
1200
Time / (Sec)
Actu
ato
r T
orq
ue
/ (
Nm
)
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Results of the behavior of the extremum seeking slip optimization (ESSO) algorithm with
the electric machine are presented in Fig 5.10 and Fig 5.11. Static gain (K) for scaling the
feedback linearization was found to be 1.056 for the chosen electric machine.
Electric machine based system is also subjected to the same condition as the
mechanical braking based ABS. It can be noted that there is no significant variation in the
slip during the slip recovery, after road conditions have changed in comparison to the
mechanical ABS behavior.
Figure 5.10 Road condition variation and slip estimator behavior
.
0 0.5 1 1.5 2 2.5 3 3.5 4
1
1.2
1.4
1.6
1.8
2
Ro
ad
Co
nd
itio
n
0 0.5 1 1.5 2 2.5 3 3.5 40.08
0.1
0.12
0.14
0.16
0.18
Time / (s)
Slip
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Figure 5.11 Motor torque output with changing road condition
5.7 Performance Comparison of Slip Optimizing Anti-lock Braking Schemes
In this section we compare hydraulic braking based ABS with the electric machine
based ABS in order to determine the improvement achieved by the electric machine
based system. Existing automobile mechanical brake system time constants vary around
500ms due to the dynamics of the hydraulic system (Raza H. et al, 1997). It should be
noted that these ABS braking scenarios are considered at 125kmph (78.3mph).
Figures 5.12 compare the wheel slip behavior for the two traction control schemes
during a step change in the road condition. Road condition changes from asphalt to ice at
t=2.0 seconds. The electric machine based systems shows no transient whereas the
mechanical braking (τ = 250ms) based traction control system has a noticeable transient.
0 0.5 1 1.5 2 2.5 3 3.5 40
200
400
600
800
1000
1200
Time / (s)
To
rqu
e /
(Nm
)
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95
Figure 5.12 Wheel Slip Comparison of the electrical machine based ABS with
mechanical ABS system (τ = 250ms) during a road condition
Figure 5.13 illustrates the torque response the mechanical brake actuator and electric
machine during the step change in road condition. The large time constant in the
mechanical brake system causes a drastic variation in the torque output, resulting a
transient in the wheel slip. The electric machine torque response is significantly faster
due to the small time constant.
Figure 5.13 Actuator torque output comparison for the two traction control systems
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.2
0.4
0.6
0.8
1
Time / (Sec)
Wh
ee
l S
lip
Mech. Brakes based Traction Control
Electric Machine based Traction Control
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
200
400
600
800
1000
1200
Time / (Sec)
Actu
ato
r T
orq
ue
/ (
Nm
)
Mech. Braking based ABS
Electric Machine based ABS
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96
Figures 5.14 illustrate the vehicle longitudinal speed profiles with different ABS
schemes. The stopping time of electrical machine based ESSO algorithm is one second
faster than the ESSO algorithm with mechanical brakes (500ms time constant).
Figure 5.14 Stopping time comparison of the electrical machine based ABS with
mechanical ABS system
Figure 5.15 Stopping distance comparison of the electrical machine based ABS with
mechanical ABS system
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
10
20
30
40
Time /(s)
Ve
hic
le L
on
gitu
din
al S
pe
ed
/ (
ms-1
)
Electric Machine
Mechanical Brake (tau = 0.5)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 520
40
60
80
100
120
140
Time / (s)
Sto
pp
ing
Dis
tan
ce
/ (
m)
Electric Machine
Mechanical Brakes (tau = 0.5)
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97
Figure 5.15 illustrates the vehicle stopping distances for ESSO ABS schemes.
Electrical machine based system stopping distance is approximately 30 meters less
compared to the conventional mechanical brake system based ESSO ABS. The electric
machine based system reduces the stopping distance by 30%.
The perturbing frequency (ω) is a crucial parameter for the extremum seeking slip
optimization algorithm as it determines how fast the algorithm will reach the optimal slip.
Both ABS schemes with a range of perturbing frequencies are presented in Figures 5.16
and 5.17. The extremum seeking algorithm has significantly less ripple at higher
frequency compared to the low frequency regardless of the system time constant.
Figure 5.16 Electric machine slip optimizing algorithm response to a road condition
change at different perturbation frequencies
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.08
0.1
0.12
0.14
0.16
0.18
Time / (s)
Slip
Omega = 20 rad per sec
Omega = 200 rad per sec
Omega = 2000 rad per sec
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Figure 5.17 Mechanical braking (τ=2.5ms) based slip optimizing algorithm response to a
road condition change at different perturbation frequencies
It is noteworthy that there is no significant variation in the ABS systems optimal slip
tracking performance due to the perturbing frequency for the chosen range of frequencies
(20 rads-1
to 2000 rads-1
).
5.8 Experimental Setup for Extremum Seeking Slip Optimization Algorithm with a
BLDC Motor Drive System
The experimental setup shown in Figures 5.18 was utilized to provide proof of the
capability of the algorithm to optimize the slip in real time. The experiment optimizes
slip while accelerating rather than braking (due to practical difficulties in recreating a
braking scenario). The same algorithm may be utilized to optimize the brake force during
deceleration. Figure 5.18 is a block diagram of the experimental setup. Figure 5.19
represents each component in the actual setup that corresponds to blocks shown in Figure
5.18.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.05
0.1
0.15
0.2
Time / (s)
Slip
Omega = 20 rad per sec
Omega = 200 rad per sec
Omega = 2000 rad per sec
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Figure 5.18 Experimental setup block diagram
The real-time slip optimization algorithm was developed with Matlab® Simulink®
which was auto-coded in to dSPACE® DS1104 hardware. All input-output signals
(vehicle speed -② in Fig. 5.18, wheel speed –① in Fig 5.18) were interfaced to the
dPACE® hardware through dSPACE CLP 1104 input output board (#3 in Fig 5.19). The
real-time hardware provides the torque command to the control unit (#2 in Fig 5.19). The
control unit communicates the torque command to the 2kW inverter (#1 in Fig 5.19). The
2kW inverter controls the trapezoidal back emf permanent magnet machine (#4 in Fig
5.19) torque output by controlling the PWM signal. The inverter measures the phase
currents and the motor rotor position to enable proper control of the electric machine
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100
Treadmill speed is measured with an Automation Direct® AE1-AN-1A Proximity
Sensor measuring the discrete magnets placed on the shaft of the treadmill. Motor speed
is measured by dSPACE via the hall sensors embedded in the motor.
Figure 5.19 Experimental setup components
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101
Table 5.2
Experimental Setup Component Summary (Sensing and Actuation)
Parameter Value
Motor Drive Power Output 2.0 kW
Motor Drive Microprocessor dsPIC30F4011 (Clock : 120 MHz)
Position Sensor Automation Direct ® AE1-AN-1A
Data Communication Rate 56kbps (every 27ms)
Electric Machine Type
Brushless DC Hub Motor
(Trapezoidal Back EMF)
Electric Machine Voltage Rating 60V
Machine Winding Inductance 6.50 mH per Phase
Machine Winding Resistance 0.09 Ohms per Phase
Machine Back EMF Constant 511Vpeak L-L/lRPM
Number of Magnetic Poles 24
Wheel Radius 0.229m
Test Setup Road Load 24Nm (estimated neglecting losses)
Figure 5.20 below illustrates the behavior of the real-time traction force maximization
algorithm collected via the aforementioned experimental setup. First plot of Figure 5.20
illustrates the slip tracking capability of the algorithm. Slip during acceleration is defined
as,
⁄ Eq. 5.20
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Figure 5.20 Experimental Results with extremum seeking slip optimization
Traction control algorithm was derived similar to the ABS optimization algorithm
presented by equations 5.12 to 5.18. The slip reaches the optimal slip and tracks the value
continuously. Therefore the applied torque is maintained at the optimal value, causing the
wheel and the vehicle to accelerate continuously. The wheel and vehicle acceleration is
shown in the second plot of Figure 5.20.
3.5 4 4.5 5 5.5 6 6.5 7 7.5 80
0.1
0.2
0.3
0.4
Slip
3.5 4 4.5 5 5.5 6 6.5 7 7.5 81
2
3
4
Time / (s)
Sp
ee
d / (
rad
S-1
)
Road Speed
Wheel Speed
Traction Control During Acceleration
103
103
5.9 Concluding Remarks
Proof of advantages in utilizing extremum seeking slip optimization algorithms with
electric machines is provided. Electric machine improves the stopping distance by 30%
and reduces stopping time by 20%. In addition to the above improvements, the electric
machine based system provides a faster torque response due to the electromechanical
system. There are two noteworthy aspects apart from the improved stopping time and
stopping distance. Electric machine based braking utilizes regenerative braking during
the braking process. Therefore energy is recovered while wear and tear in mechanical
brakes is avoided. Additionally, actuator chatter is prevented by the chosen real time
optimization algorithm reducing premature failure of actuators. Simulation results justify
the improvement in stopping time and stopping distance. An example extremum seeking
slip optimization algorithm behavior during a traction control experiment with real
hardware is provided to justify the ability to implement such algorithm in an actual
system/vehicle. Future work includes installing the hardware on an actual vehicle to
analyze the algorithm behavior with varying road conditions.
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CHAPTER 6. ELECTRIC MACHINE DIFFERENTIAL BASED YAW
STABILIZATION CAPABILITY ANALYSIS
6.1 Introduction
Yaw stability control of automobiles is still an active area of research due to
continuous advancement in sensors and actuators. Yaw stability control and roll over
stabilization prevent the vehicle from reaching an unstable state during unforeseen
circumstances. An unstable vehicle poses a threat to the passengers, pedestrians, property
as well as other vehicle on the road. Research on electrification of the power train has
enabled utilization of the faster dynamics available in electric machines to perform better
stability control. U.S. Department of Transportation has set forth a standard for
Electronics Stability Control for motor vehicles under the Standard No.126; Electronic
Stability Control Systems subpart B. The standard requires stability control to be
available beyond 20kmph, unless disabled by the driver. A simulation based yaw stability
control capability improvement with an electric machine differential (EMD) is presented
herewith. The results are compared with conventional yaw stability control schemes.
This chapter is organized as follows. Section 6.2 presents the linear two degrees of
freedom model; Section 6.3 presents the non-linear eight degrees of freedom vehicle
model; Section 6.4 compares the stability control capability of the mechanical/hydraulic
braking based system to the electric machine based stability control system.
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105
6.2 Vehicle Model with Two Degrees of Freedom (2 DoF) and Linear Tire Forces
Two degrees of freedom (yaw and side slip) model was developed based on the model
discussed in (Smith D.E. & Starkey J.M.,1995). The two degrees of freedom model with
linear tire forces enacts the role of an ideal vehicle representing the intended maneuver in
contrast to the actual vehicle behavior. The two DoF model is as follows.
Figure 6.1 Bicycle Model for Vehicle Dynamics Modeling
[ ] Eq. 6.01
[ ] Eq. 6.02
Figure 6.2 Wheel rotation dynamics
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106
[
] Eq. 6.03
‘i’ is the designator for front and rear. If front, i = f and if rear, i = r. Inertia of the ith
wheel is represented as,
Eq. 6.04
Eq. 6.05
It should be noted that the inertia for the wheels of a gasoline engine based automobile is
calculated as above. The wheel inertia for an In-wheel machine type wheel or a shaft
coupled wheel is independent of the gear ratios that are available in a conventional
automobile. Vehicle to global coordinate transform is shown in the equations 6.06 and
6.07.
Eq. 6.06
Eq. 6.07
Slip angles for the front and rear tires are utilized in the tire force calculation.
(
) Eq. 6.08
(
) Eq. 6.09
The 2DoF model utilizes the linear tire modal. Therefore the expression for side force is
as follows,
Eq. 6.09
Next section presents the eight degrees of freedom model of the automobile.
107
107
6.3 Vehicle Model with Eight Degrees of Freedom (8 DoF) and Non-Linear Tire
Forces
The eight degrees of freedom (8DoF) model includes yaw rate, side slip, longitudinal
acceleration, body roll and the dynamics of all four wheels. According to (Smith D.E. &
Starkey J.M., 1995), the 8DoF model is required for accurate simulation results at high
acceleration maneuvers (high g-maneuvers).
Figure 6.3 Eight degrees-of-freedom vehicle model
[ ] Eq. 6.10.1
[ ] Eq. 6.10.2
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108
( ) ( ) (
) ( )
Eq. 6.10.3
Eq. 6.10.4
X and Y direction tire forces are calculated based on the tractive force and side force
on each wheel as follows,
( )
Eq. 6.10.5
Eq. 6.10.6
Total steering angles of the wheels with the roll steer is calculated as follows,
Eq. 6.10.7
Eq. 6.10.8
Longitudinal load transfer and quasi-static lateral load transfer due to acceleration and
roll angle is calculated as follows,
[
] Eq. 6.10.9
[
] Eq. 6.10.10
[
] Eq. 6.10.11
[
] Eq. 6.10.12
Eq. 6.10.13
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109
Vehicle to global coordinate transformation is given by,
Eq. 6.11.1
Eq. 6.11.2
6.3.1 Tire Model for the 8 DoF Vehicle
Each tire has an independent slip angle.
(
⁄ ) Eq. 6.12.1
(
⁄ ) Eq. 6.12.2
(
⁄ ) Eq. 6.12.3
(
⁄ ) Eq. 6.12.4
The longitudinal slip calculation for the cases when the vehicle is accelerating and
decelerating is calculated as follows.
Accelerating :
⁄ Eq. 6.13.1
Braking :
⁄ Eq. 6.13.2
Ut is the speed of the wheel center in the direction of the tire heading. The speed of each
wheel is different for the case of the 8 DoF model.
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110
(
) ( ) Eq. 6.14.1
(
) ( ) Eq. 6.14.2
(
) Eq. 6.14.3
(
) Eq. 6.14.4
Nonlinear tire force model proposed by Dugoff et al is as follows,
[ √
]
√
Eq. 6.15
{
Eq. 6.16
Eq. 6.17
Eq. 6.17
A vehicle model with non-linear properties and eight degrees of freedom is presented
above (Smith D.E. & Starkey J.M., 1995). The model was evaluated based on the vehicle
parameters provided by the authors. Next section presents the model validation results.
111
111
6.4 Vehicle Model Validation
Test conditions provided by the authors in (Smith D.E. & Starkey J.M., 1995) were
utilized in evaluating the model. Results obtained were compared to the results provided
by the authors. Initial model validation test is a low speed lane change maneuver that
results in low lateral acceleration. Figure 6.04 shown below is the vehicle behavior
during the low g maneuver. Second model validation test is a lane change maneuver at
high speed, which results in a high g maneuver. The corresponding results are illustrated
in Figure 6.05. The high g maneuver causes the vehicle to slide away due to lack of
lateral force. The results obtained here match the results presented by D.E. Smith and J.M.
Starkey in their paper.
Figure 6.4 Eight DoF vehicle model response at low g maneuver, U = 10ms-1
0 2 4 6
-2
-1
0
1
2
Time / (sec)
Ste
eri
ng
/ (
De
g)
0 2 4 6
-5
0
5
Time / (sec)
Ya
w R
ate
/ (
De
g/s
)
0 20 40 60-1
-0.5
0
X Direction / (m)
Y D
ire
ctio
n / (
m)
0 2 4 6
-0.1
-0.05
0
0.05
0.1
Time / (sec)
La
tera
l A
cc. / (g
's)
Lin. 2 DoF
Non-Lin. 8 DoF
112
112
Figure 6.5 Eight DoF vehicle model response at high g maneuver, U = 20ms-1
Additional data was collected and studied to develop an appropriate yaw stabilization
strategy. Figure 6.06 illustrates the vehicle yaw acceleration behavior (red curve),
compared to the ideal yaw acceleration (blue curve) obtained with the use of the bicycle
model (2 DoF Model). Figure 6.07 shows the behavior of the actual vehicle yaw rate (red
curve) with respect to the bicycle mode (blue curve). The linear tire force based bicycle
model provides information on the ideal behavior or expected yaw behavior to
successfully complete the maneuver. Yaw control strategy was developed considering
both the error in yaw acceleration and yaw rate (Figure 6.08).
0 2 4 6
-5
0
5
Time / (sec)
Ste
eri
ng
/ (
De
g)
0 2 4 6-20
-10
0
10
20
Time / (sec)
Ya
w R
ate
/ (
De
g/s
)
0 50 100
-20
-10
0
X Direction / (m)
Y D
ire
ctio
n / (
m)
Vehicle Displacement on X-Y Plane
0 2 4 6-0.5
0
0.5
Time / (sec)
La
tera
l A
cc. / (g
's)
Lin 2 DoF
Non-Lin 8 DoF
113
113
Figure 6.6 Vehicle yaw acceleration comparison during high-g maneuver
Figure 6.7 Vehicle yaw rate comparison during high-g maneuver
0 1 2 3 4 5 6 7
-5
0
5
Time / (sec)
Ste
ering I
nput
/ (D
eg)
0 1 2 3 4 5 6 7-2
-1.5
-1
-0.5
0
0.5
1
1.5
Time / (sec)
Yaw
Accela
ration /
(ra
ds
-2)
2 DoF Model
8 DoF Model
0 1 2 3 4 5 6 7
-5
0
5
Time / (sec)
Ste
eri
ng
In
pu
t / (D
eg
)
0 1 2 3 4 5 6 7-30
-20
-10
0
10
20
30
T
Ya
w R
ate
/ (
De
gs-1
)
Time / (sec)
114
114
Figure 6.8 Yaw acceleration error and yaw rate error during the high-g maneuver
6.5 Stability Test Criterion
Vehicle stability and performance of vehicle stability controllers are evaluated in
several different techniques. Stability evaluation is performed based on the transient
behavior and steady state behavior.
(Wong J.Y., 2008) presents several tests for evaluating vehicle handling
characteristics. Constant radius test requires the vehicle to be driven on a curve with a
constant radius at different speeds. Required steering angle and lateral acceleration to
maintain the vehicle on the chosen path is measured for each driving speed. This test
enables the measurement of vehicle under steer coefficient and over steer coefficient.
The second test is a constant speed test. During this test, the vehicle is driven at constant
speed with varying radii. Steering angle and the lateral acceleration required for each case
0 1 2 3 4 5 6 7-1
-0.5
0
0.5
1
Time / (sec)
Ya
w A
cce
lera
tio
n / (
rad
s-2)
0 1 2 3 4 5 6 7
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
Time / (sec)
Ya
w R
ate
/ (
rad
s-1)
115
115
is recorded. The third test is the constant steer angle test, where the steering angle is
maintained fixed during various forward speeds. The lateral acceleration at various
speeds is measured. All three tests above allow the measurement of under steer and over
steer coefficients and study the neutral steer behavior.
Vehicle stability controllers have become a standard feature in automobiles due to the
achievable improvement in vehicle stability. Therefore the Federal Motor Carrier Safety
Administration of the U.S. Department of Transportation (USDOT) established standards
that govern the behavior of the vehicle stability controllers. A vehicle stability controller
evaluation criterion is provided in the Standard No 126 Electronics Stability Control
System. The standards require an initial conditioning phase for vehicle tires and the
brakes. The second phase establishes the yaw rate amplitude requirement for vehicle
stability testing. The third phase applies a sinusoidal steering input with a steering dwell
of 500ms prior to the last quadrant of the sinusoid. The standard also provides the data
processing guidelines for evaluating the performance of the stability controller.
Figure 6.9 Steering input for stability control test by USDOT
2 2.5 3 3.5 4 4.5 5
-6
-4
-2
0
2
4
6
Time / (sec)
Ste
erin
g A
ng
le / (
De
g)
116
116
Alternate vehicle stability controller tests are available in the literature. (Will A.B.,
1997), (Zheng S. et al, 2006) and (Nam K. et al, 2012) presents a lane change maneuver
based stability performance evaluation examples. Therefore the study presented here was
also based on the lane change maneuver at high speeds.
6.6 Stability Control Capability Comparison
The yaw controller implemented and test in this study observes the yaw acceleration
as well as yaw rate. The vehicle yaw acceleration and yaw rate are compared to the two
degrees of freedom (2 DoF) bicycle model based yaw acceleration and yaw rate. An error
is calculated based on the actual value and expected value. The vehicle stability controller
activates the yaw control algorithm during excessive error in either parameter. The
control algorithm commands two different torque values to each wheel in order to
generate a counter torque along the yaw axis.
Figure 6.10 Yaw control strategy
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117
6.6.1 Stability Control with Hydraulic Brake System
The first simulation is based on the hydraulic brake system. The transfer function for
the brake system was derived in section 5.3.2. Identical yaw control algorithms were
utilizes for both the electrical machine based system and hydraulic braking based systems.
These results provide proof of the advantage of using an electric machine.
A lane change maneuver at high speed (20ms-1
) is performed with the mechanical
braking based yaw controller enabled. The vehicle behavior during the above test is
illustrated in Figure 6.11.
Figure 6.11 Mechanical braking based yaw controller behaviors at high g maneuver
0 2 4 6
-6
-4
-2
0
2
4
6
Time / (sec)
Ste
eri
ng
An
gle
/ (
De
g)
0 50 100-20
-15
-10
-5
0
X Direction / (m)
Y D
ire
ctio
n / (
m)
0 1 2 3 4 5 6 7-30
-20
-10
0
10
20
30
Time / (sec)
Ya
w R
ate
/ (
rad
s-1)
0 1 2 3 4 5 6 7
-0.4
-0.2
0
0.2
0.4
0.6
Time / (sec)
La
tera
l A
cc. / (g
's)
118
118
The X-Y plot illustrates the ideal vehicle path (red curve) and the actual vehicle path with
yaw stability control (blue curve). The hydraulic brakes are unable to generate sufficient
counter steering torque along the yaw axis. Therefore the vehicle slides out of the
intended path. The torque induced on each wheel by the yaw control algorithm is shown
in Figure 6.12. The notable disadvantage in the hydraulic braking based scheme is the
inability to generate positive torque on one wheel when a negative force is being
generated on the opposite wheel.
Figure 6.12 Mechanical braking based yaw controller wheel torque output
Above yaw control strategy is effective at speeds less than 13ms-1
. But the same
strategy with the electric machine differential is able to stabilize a vehicle at speeds up to
15ms-1
at the chosen corrective torque values (+/-500Nm).
0 1 2 3 4 5 6 7-500
0
500
1000
Time / (sec)
Left
Wheel T
orq
ue /
(N
m)
0 1 2 3 4 5 6 70
200
400
600
800
Time / (sec)
Rig
ht
Wheel T
orq
ue /
(N
m)
119
119
6.6.2 Stability Control with Electric Machine based Differential
An identical lane change maneuver is considered with the electric machine differential
based vehicle stability controller. Torque commands are distributed to the electric drives
controlling each in-wheel machine. Each wheel on the differential has the capability to
generate traction forces in the opposite directions, in the case of an electric machine
based differential.
Figure 6.13 Electric differential based yaw controller behavior during high-g maneuver
0 2 4 6
-6
-4
-2
0
2
4
6
Time / (sec)
Ste
eri
ng
An
gle
/ (
De
g)
0 50 100 150-10
-8
-6
-4
-2
0
X Direction / (m)
Y D
ire
ctio
n / (
m)
0 2 4 6-30
-20
-10
0
10
20
30
Time / (sec)
Ya
w R
ate
/ (
rad
s-1)
0 2 4 6 8-1
-0.5
0
0.5
1
Time / (sec)
La
tera
l A
cc. / (g
's)
120
120
Figure 6.14 Electric differential based yaw controller wheel torque output
Figure 6.15 Electric differential based yaw controller yaw rate error and yaw acceleration
error behavior with yaw stability controller (high-g maneuver)
0 1 2 3 4 5 6 7-600
-400
-200
0
200
400
600
800
Time / (sec)
Le
ft W
he
el T
orq
ue
/ (
Nm
)
0 1 2 3 4 5 6 7
-500
0
500
Time / (sec)
Rig
ht W
he
el T
orq
ue
/ (
Nm
)
0 1 2 3 4 5 6 7
-0.5
0
0.5
1
Time / (sec)
Ya
w A
cce
lera
tio
n / (
rad
s-2)
0 1 2 3 4 5 6 7-0.15
-0.1
-0.05
0
0.05
0.1
Time / (sec)
Ya
w R
ate
/ (
rad
s-1)
121
121
Figure 6.12 illustrates the vehicle behavior with the electric machine differential based
vehicle yaw controller. In this case the vehicle completes the intended maneuver. The
torque generated by the machine is illustrated in Figure 6.13. Electric machine can
generates road forces with opposite polarity on the two wheels. The opposite forces at
each end of the differential generate more counter torque at the yaw axis compared to
braking one wheel. Figure 6.14 illustrates the error in yaw acceleration and error in yaw
rate during high-g maneuver with the vehicle stability controller.
6.7 Concluding Remarks
This chapter presents simulation results contrasting the advantage in utilizing electric
machine based differential for yaw stability control with respect to mechanical braking
based system. A vehicle model with eight degrees of freedom is considered in the
simulation. The yaw stabilization capability of the vehicle with mechanical brakes
degrades after longitudinal speeds of 65 kmph. The same algorithm in the electric
machine based differential system starts degrading only after 72kmph. Therefore the
electric machine differential shows and improvement in the stability control capability.
Several other criterions related to the hydraulic brakes and electric machines need to
be evaluated prior to implementation. Main concerns are the torque capability of the
electric machine throughout the speed range, continuous brake torque generation
capability of the hydraulic brake system and difference in cost. These aspects are out of
scope for this study. In conclusion, an electric machine differential is advantages
compared to mechanical brakes based yaw stability control.
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122
CHAPTER 7. SUMMARY OF RESEARCH
This section summarizes all the project aspects discussed in detail in preceding
chapters.
7.1 Electric Machine Differential Hardware Development
A 4kW electric machine differential was sized, designed and implemented with two
trapezoidal back emf permanent magnet synchronous machines. Each machine is rated
for 2kW. The electric machine differential (EMD) consists of two 2kW motor drive units
and a central command unit. The central controller and the two drive units are controlled
by Microchip® dsPIC® 30F4011 device. Central controller communicates data to each
drive unit via the UART based data communication protocol. Additionally the central
controller has on board yaw sensors and accelerometers to estimate vehicle stability.
7.2 Novel Open Single Phase Fault Diagnostic Algorithm for SM-PMSMs
Fault diagnostics prevents unintended damage to the overall system while providing
an additional level of safety. Single phase open (SPO) fault phase is one of the critical
faults that require high priority and fast detection.
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123
SPO fault results in a significantly high electromagnetic torque ripple and cause the
permanent magnets to demagnetize if exposed for a prolonged period. Single open phase
fault detection algorithm proposed in this thesis enables faster detection of the fault, with
minimal system resources compared to existing methods. Proof of accurate fault
detection capability is presented through simulation and actual implementation results.
The proposed method is also capable of identifying the actual phase containing the fault.
7.3 Electric Machine Differential based Real Time Extremum Seeking Slip
Optimization Algorithm Implementation
An extremum seeking electric machine based antilock braking scheme for improving
automobile safety compared to mechanical braking based ABS is proposed. At a starting
speed of 125kmph, stopping distance is reduced by 30% compared to mechanical braking
system based ABS, due to the faster torque response in the electric machine (based on
simulation). Further the real-time slip optimization (RT-ESSO) algorithm guarantees
reaching optimal slip under varying road conditions without any high frequency
switching of the actuator found in variable structure controls schemes. Dynamic behavior
of the ABS system under varying road conditions is presented for both the mechanical
and electromechanical actuators. Experimental results based on a setup with the torque
actuator being a 2kW trapezoidal back-emf synchronous motor (BLDC) coupled to a
hardware-in-loop test environment is presented.
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124
7.4 Electric Machine Differential based Yaw Stability Control
This chapter presents a simulation study with the focus of evaluating the advantage of
an electric machine differential for vehicle stability control. The development of an eight
degree of freedom model based on the paper by D.E. Smith and J.M. Starkey (1995) is
discussed. The model is extended to include the dynamics of an electric machine
differential. Preliminary results on a model following yaw stabilization algorithm is
presented. Simulation results provide evidence of the advantage of an electric machine
based yaw stabilization over hydraulic braking based yaw stabilization at high-g
maneuvers.
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125
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APPENDIX
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135
APPENDIX
Algorithm Implementation (C-Code for Motor Controls)
//--------------------------------------------------------------------
// Sensed BLDC Motor Speed Control
// File : Closed_Loop_BLDC_dsPIC30F4011.c
// Author : Sandun S. Kuruppu
// Date : 2013-June-13
// : This is the latest version with current controller. Not a fancy controller. Just
keeps
// the current restricted and well behaved during transients. Lot of improvements
need to
// to be done before this being the final controller.
// V5 : Re-Characterizing torque controller and speed controller for loaded operation
//--------------------------------------------------------------------
// Note that the IRAM Power module has inverted PWM inputs. So increasing PWM
means, decreasing speed
// *** Speed controller refer to AN1078 page 8
//--------------------------------------------------------------------
#include "p30f4011.h"
#include "uart.h"
#define FCY 29000000 // xtal = 5Mhz; PLLx16 -> 20 MIPS (F_CY = F_OSC/4)
//#define BAUDRATE 9600
#define BAUDRATE 57000 //corresponds to 56000 due to clock mismatch
#define FPWM 20000 // 20 kHz, so that no audible noise is present.
#define BRGVAL ((FCY/BAUDRATE)/16)-1
//#define BRGVAL 11
136
136
#define CW 0 // Counter Clock Wise
direction
#define CCW 1 // Clock Wise direction
#define RPMConstant 30*(FCY/256) // ?? Verify 256, 60 for trike motor
#define Ksp 60
#define Ksi 80
#define Ksd 80
void InitMCPWM(void);
void InitADC10(void);
void InitTMR3(void);
void AverageADC(void);
void DelayNmSec(unsigned int N);
void CalculateDC(void);
void GetSpeed(void);
void InitUART2(void);
// Non initialization routines
void ReadDataPkt(void);
void OpenLoop(void);
void SpeedControl(void);
void CurrentControl(void);
void RegenBrake(void);
struct {
unsigned RunMotor : 1;
unsigned Minus : 1;
unsigned unused : 14;
unsigned ClosedLoop : 1;
} Flags;
unsigned int HallValue;
unsigned int Timer3;
unsigned char Count;
unsigned short SpeedCount = 0;
unsigned int AvgSpeed = 0;
int HallPulse;
int Speed = 0;
int PrevSpeed = 0;
int SPEED_CMD;
int ActualSpeed;
int DesiredSpeed;
int SoftSpeedcmd = 1800;
137
137
int TempCount = 0;
int SpeedCtrlActive = 0; // 0 - Skip control loop, 1 - Do speed control
int ForcedCommutation = 1; // 1 - Froced Commutation, 0 - Speed Control
long SpeedError;
long PrevSpeedEr = 0;
long DutyCycle;
int DutyCycle1;
long SpeedIntegralEr;
long Reference;
long DiffSpeedEr;
// Phase Current Measurements
int Current_PH1;
int Current_PH2;
int Current_PH3;
int AvgPhCur;
int Current_Cmd;
int CurError;
int CurIntError;
int CurDifError;
int CurErrorOld;
float ScaledAvgCurr;
// Phase Voltage Measurements
int Voltage_PH1;
int Voltage_PH2;
int Voltage_PH3;
// Closed_Loop, Open_Loop Select
int Status;
// Communication Loop
int Txdata[] = {238,2,85,2,221,'\0'}; // Data to be trnasmitted
//int Rxdata[8];
int i;
int j;
int k; // for soft start
unsigned int Buf[10]; // instead of a char buffer
unsigned int*Receiveddata = Buf;
int vari;
//int*Receiveddata = Buf;
int RX_data;
unsigned int baudvalue; // Value for Baud Register
unsigned int U2MODEvalue; // UART Config Value
unsigned int U2STAvalue; // TX & RX Interrupt information
138
138
//Trike working
//unsigned int StateLoTable[] = {0xFFFF, 0x183F, 0x063F, 0x123F,0x213F, 0x093F,
0x243F, 0xFFFF}; // Reverese
unsigned int StateLoTable[] =
{0xFFFF,0x243F,0x093F,0x213F,0x123F,0x063F,0x183F,0xFFFF}; // (Right side motor
or M1 Motor)
//------------------------------------ Interrupt Routines ------------------------------------------
void __attribute__((interrupt, no_auto_psv)) _CNInterrupt (void)
{
IFS0bits.CNIF = 0;
HallValue = (unsigned int)(PORTB & 0x0007); // mask RB0,1
& 2
OVDCON = StateLoTable[HallValue]; // Load
the overide control register
// Counting Sectors
HallPulse = HallPulse + 1;
TempCount = TempCount + 1;
if (HallPulse == 6)
{
Timer3 = TMR3;
HallPulse = 0;
// Reset timer
TMR3 = 0;
// Calculate Speed
if (Timer3 > 0)
//Speed = RPMConstant/(12*(long)Timer3);
//Speed = 1250000.0/((long)Timer3); // Without Prescaler
//Speed = 4882.8/((long)Timer3); // With 1:256 Prescaler
Speed = 286203.1/((long)Timer3); // With 1:256 Prescaler
if (Speed > 1000)
{
Speed = 0; // To account for erroneous
calculations
}
SpeedCtrlActive = 1;
ForcedCommutation = 0;
// If you divide the Hall pulse by 2 divide Speed by 2 too.
AvgSpeed = (PrevSpeed + Speed)/2;
Flags.ClosedLoop = 1;
}
}
139
139
void __attribute__((interrupt, no_auto_psv)) _ADCInterrupt (void)
{
// Current_PH1 = ADCBUF1 - 704; //3.44V offset compared to 5V and 10bit ADC
// Current_PH2 = ADCBUF2 - 704;
// Current_PH3 = ADCBUF3 - 704;
Current_PH1 = ADCBUF1 - 512; //Using the direct current sensor output without
Current_PH2 = ADCBUF2 - 512; // zero span.
Current_PH3 = ADCBUF3 - 512;
if (HallValue == 4 || HallValue == 5) //Phase 1
{
AvgPhCur = 0.5*(AvgPhCur + Current_PH1);
}
else if (HallValue == 2 || HallValue == 6) //Phase 2
{
AvgPhCur = 0.5*(AvgPhCur + Current_PH2);
}
else if (HallValue == 1 || HallValue == 3) //Phase 3
{
AvgPhCur = 0.5*(AvgPhCur + Current_PH3);
}
ScaledAvgCurr = (AvgPhCur*25.0)/512.0;
ADCON1bits.DONE = 1; // This is software cleared but it will be set when a new
sampling begins
IFS0bits.ADIF = 0;
ADCON1bits.SAMP = 0; // start Converting
}
void __attribute__((interrupt, no_auto_psv)) _U2RXInterrupt(void)
{
Buf[i] = ReadUART2();
if (Buf[i] == 238)
{
i = 0;
Buf[0] = 238;
}
i = i + 1;
if (i>8)
{
140
140
i = 0; // Resetting the data receive read buffer
// Transmitting M1 motor speed
//Disable interrupts
IEC0bits.ADIE = 0; // Disable ADC interrupts
IEC0bits.CNIE = 0; // enable CN interrupts
U2STAbits.UTXEN = 1; // Was important
//SRbits.IPL = 7; // CPU priority highest, All
user interupts disabled
//Transmit the data through the right UART channel (1 or 2)
// Sending Data Packet Manually
j = 0;
for(j = 0 ; j < 6; j++ )
{
RX_data = Txdata[j];
WriteUART2(RX_data);
while(BusyUART2());
}
//Enable interrupts
U2STAbits.UTXEN = 0; // Disabling TX interrupt
IEC0bits.ADIE = 1; // Enable interrupts
IEC0bits.CNIE = 1; // enable CN interrupts
//SRbits.IPL = 0; // Resetting CPU priority
}
IFS1bits.U2RXIF = 0; // clear RX interrupt flag
}
//UART1 Transmit ISR
void __attribute__((interrupt, no_auto_psv)) _U2TXInterrupt(void)
{
IFS1bits.U2TXIF = 0; // clear TX interrupt flag
}
//--------------------------- Begin of Main ------------------------------------------------------------
int main(void)
{
TRISB = 0xFFFF; // Port B as Inputs
TRISE = 0x0100; // PWM pins as outputs, and FLTA as input
TRISD = 0x0000; // For ADC trigger
CNEN1= 0x001C; // CN1,2 and 3 enabled
CNPU1= 0; // Disable all CN pull ups because the pull ups are already in
place through hardware
IFS0bits.CNIF = 0; // clear CNIF
141
141
IEC0bits.CNIE = 1; // enable CN interrupts
SpeedError = 0;
SpeedIntegralEr = 0;
InitTMR3();
InitMCPWM(); // Call Motor Control PWM Initialization
InitADC10(); // Call 10bit ADC Initialization
InitUART2();
while(1)
{
// Obtain the UART data here
// Read Hall position sensors here
HallValue = (unsigned int)(PORTB & 0x0007); // mask RB0,1 & 2
OVDCON = StateLoTable[HallValue]; // Load the overide control register
HallPulse = 0; // Initialize Hall Counter
PTCONbits.PTEN = 1; // Timer Enable bit: ENABLE MCPWM
PWMCON1 = 0b0000111101110111;
T3CON = 0x8030; // Start Timer 3 , 1000 0000 0011 0000
// Conversion between Speed Command and PWM Value (inversly related)
SPEED_CMD = 0;
DutyCycle = 4000;
Flags.RunMotor = 1; // Goes in to the motor control loop
Status = 0;
// Status = 0 is Open Loop, Status = 1 is Closed Loop, Status = -1 is Regen
// Status = 2 is Gate drives disabled
//Add a Startup, Forced Commutation or Soft Start Loop here
//You will enable the RunMotor flag once the commanded current or speed or
momentum has been picked up
//
while(Flags.RunMotor)
{
// Continuous Sampling of Phase Currents
ADCON1bits.SAMP = 1; // start sampling
long Ct1;
for(Ct1 = 0 ; Ct1 < 20; Ct1++ )
{
}
ADCON1bits.SAMP = 0; // start Converting
//while (!ADCON1bits.DONE); // conversion done?
LATDbits.LATD2 = 1;
//Turn off LED1 - generates the sampling inidication or loop
execution time
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for(Ct1 = 0 ; Ct1 < 2; Ct1++ )
{
}
LATDbits.LATD2 = 0; //Turn off LED1
ReadDataPkt(); // Decodes the data packet and sets
the speed and/or current commands
// **** -- SPEED CONTROL -- ****
//Status = 2; // Speed Control
// Dev Only Code - End
*********************************************
if (Status == 0) // GATE DRIVES DISABLED
{
// Diable PWM Module
OVDCON = 0x003F;
//PTCONbits.PTEN = 0; // Timer Enable bit:ENABLE
MCPWM. '0' is Disabled
}
else if (Status == 1) // OPEN LOOP
{
HallValue = (unsigned int)(PORTB & 0x0007);
// mask RB0,1 & 2
OVDCON = StateLoTable[HallValue];
// Load the overide control register
OpenLoop();
}
else if (Status == 2) // SPEED CONTROL & CURRENT
LIMITING
{
HallValue = (unsigned int)(PORTB & 0x0007); // mask RB0,1
& 2
OVDCON = StateLoTable[HallValue];
SpeedControl();
PDC1 = DutyCycle;
PDC2 = PDC1;
PDC3 = PDC1;
PrevSpeed = Speed;
}
else if (Status == 3) // CURRENT CONTROL
{
CurrentControl();
HallValue = (unsigned int)(PORTB & 0x0007); // mask RB0,1 & 2
OVDCON = StateLoTable[HallValue];// Load the override control
register
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}
else if (Status == 4) // REGENERATIVE BRAKING
{
HallValue = (unsigned int)(PORTB & 0x0007); // mask RB0,1 & 2
OVDCON = StateLoTable[HallValue];// Load the override control
register
RegenBrake();
}
else
{
// Diable PWM Module
OVDCON = 0x003F;
}
}
HallValue = (unsigned int)(PORTB & 0x0007); // mask
RB0,1 & 2
OVDCON = StateLoTable[HallValue];
// Load the overide control register
} // End of While(1)
}// End of Void Main
//--------------------------- End of Main --------------------------------------------------------------
//**********************************************************************
void InitMCPWM(void)
{
// Switching frequency at 15kHz PWM 0 ticks to - 4000 ticks
PTPERbits.PTPER = 1999; // = 2000 - 1, Period Value bits 11250 //sets the
frequency, lower value higher frequency
PTCONbits.PTEN = 0; // Timer Enable bit:DISABLE MCPWM
//PWMCON1 = 0b0000111101110111;
PWMCON1 = 0b0000111100000000;
PTCONbits.PTCKPS = 0; // Input Clock Prescale bits: (0=1:1, 1=1:4)
PTCONbits.PTOPS = 0; // Output Clock Postscale bits: 1:1
PTCONbits.PTSIDL = 1; // Stop in Idle Mode: YES
PTCONbits.PTMOD = 0; // Mode Select bits: Free Running Mode
OVDCON = 0x0000; // Allows OVDCON control
PTCONbits.PTEN = 1; // Timer Enable bit: ENABLE MCPWM
/**** PTPER: PWM Time Base Period Register ****/
DTCON1 = 0x0036; // ~3.6 ns of dead time
PDC1 = 4000;
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PDC2 = 4000;
PDC3 = 4000;
return;
}
//**********************************************************************
*******************************************
void InitADC10(void)
{
TRISB = 0xFFFF; // All are inputs
ADPCFG = 0x0007; // RB1, RB2, and RB3 are digital
ADCON2 = 0x0200; // How many S/H channels will be used
ADCON1 = 0x0008; // SAMP bit = 0 ends sampling
// and starts converting
ADCHS = 0x0067; // Select the CH0, CH1, CH2, CH3 configuration
ADCSSL = 0;
ADCON3 = 0x0003; // Manual Sample, Tad = internal 2 Tcy
ADCON1bits.ADON = 1; // turn ADC ON
return;
}
//**********************************************************************
*******************************************
void InitTMR3(void)
{
T3CON = 0x0030;
TMR3 = 0;
PR3 = 0x8000;
}
//**********************************************************************
void InitUART2(void)
{
unsigned int baudvalue; // Value for Baud Register
unsigned int U2MODEvalue; // UART Config Value
unsigned int U2STAvalue; // TX & RX Interrupt information
int RX_data;
U2MODEbits.STSEL = 0; // 1-stop bit
U2MODEbits.PDSEL = 0; // No Parity, 8-data bits
U2MODEbits.ABAUD = 0; // Autobaud Disabled
U2BRG = BRGVAL; // BAUD Rate Setting for 9600
//TX
U2STAbits.UTXISEL = 0; // Interrupt for every data transfer
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IEC1bits.U2TXIE = 0; // Enable UART Transmit interrupt
U2STAbits.UTXEN = 1; // Enable UART Tx
//RX
U2STAbits.URXISEL = 0; // Interrupt after a character is received
// It can be 3, 2 or zero
IEC1bits.U2RXIE = 1; // Enable UART Receive interrupt
U2MODEbits.UARTEN = 1; // Enable UART
}
//**********************************************************************
void ReadDataPkt(void)
{
if (Buf[0]==0x00EE && Buf[8]==0x00DD)
{
SPEED_CMD = Buf[5];
Status = Buf[1]; //M1 Motor Status Select
//Current Command
}
else
{
Status = 0;
SPEED_CMD = 0;
}
}
//**********************************************************************
void SpeedControl(void)
{
//=========================================================
// SPEED CONTROLLER
//=========================================================
if (SpeedCtrlActive == 1)
{
SpeedCtrlActive = 0;
Operation for M1 Motor
DesiredSpeed = 1911.0 - 2.7231*SPEED_CMD;
SpeedError = SPEED_CMD - Speed;
SpeedIntegralEr = SpeedIntegralEr + SpeedError;
DutyCycle = DesiredSpeed - 0.9*SpeedError - 0.4*SpeedIntegralEr;
if (DutyCycle < 200)
DutyCycle = 200;
if (DutyCycle > 3500)
DutyCycle = 3500;
}
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else if (TempCount < 40)
{
OpenLoop();
}
}
//**********************************************************************
void CurrentControl(void)
{
//=========================================================
// CURRENT CONTROLLER
//=========================================================
//---------- Hysteresis Current Control Begin ------------
// if (Current_Cmd - AvgPhCur > 30)
// {
// //DutyCycle = 2000 - 3.5*(Current_Cmd - AvgPhCur);
// DutyCycle = DutyCycle - 1;
// }
// else if (Current_Cmd - AvgPhCur < -30)
// {
// //DutyCycle = 2000 + 3.5*(Current_Cmd - AvgPhCur);
// DutyCycle = DutyCycle + 1;
// }
//---------- Hysteresis Current Control End ------------
//---------- PID Current Control Begin ------------
CurError = Current_Cmd - AvgPhCur;
CurIntError = CurIntError + CurError;
CurDifError = CurError - CurErrorOld;
//DutyCycle = 2000 - 1.2*(CurError) - 0.02*CurIntError;
//DutyCycle = 2000 - 1.9*(CurError) - 1.0*CurDifError- 0.011*CurIntError;
//DutyCycle = 2000 - 1.9*(CurError);
DutyCycle = 2000 - 2.2*(CurError) - 0.111*CurIntError;
//---------- PID Current Control End ------------
// --------- Integral Windup Handler ------------
if (CurIntError > 20000)
{
CurIntError = 10000;
}
else if (CurIntError < -20000)
{
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CurIntError = -10000;
}
CurErrorOld = CurError;
// --------- Integral Windup Handler End ------------
//---------------- DUTY CYCLE LIMITER --------------
if (DutyCycle < 200)
DutyCycle = 200;
if (DutyCycle > 2000)
DutyCycle = 2000;
PDC1 = DutyCycle;
PDC2 = PDC1;
PDC3 = PDC1;
//---------------- DUTY CYCLE LIMITER End--------------
// if (ScaledAvgCurr > 15)
// {
// DutyCycle = DutyCycle + 50;
// }
}
//**********************************************************************
void OpenLoop(void)
{
//SPEED_CMD = 100;
//DesiredSpeed = 3378.6 - 3.3453*SPEED_CMD; //For M1 Motor
DesiredSpeed = 1911.0 - 2.7231*SPEED_CMD;
DutyCycle = DesiredSpeed;
if (DutyCycle < 100)
DutyCycle = 100;
PDC1 = DutyCycle;
PDC2 = PDC1;
PDC3 = PDC1;
PrevSpeed = Speed;
}
//**********************************************************************
void RegenBrake(void)
{
OVDCON = 0x0153F;
PDC1 = 1000;
PDC2 = 1000;
PDC3 = 1000;
}
//**********************************************************************
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VITA
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VITA
Sandun Shivantha Kuruppu
Graduate School, Purdue University
Education
B.Sc. (First Class Honors), Electrical Eng., 2007, University of Peradeniya, Sri Lanka
M.Sc., ECET, 2010, Purdue University, West Lafayette, Indiana
Ph.D., ECET, 2013, Purdue University, West Lafayette, Indiana
Research Interests
Motor Drives Fault Diagnostic Algorithm Development
Machine Control Algorithm Development
Power Electronic Systems Development (DC-DC, DC-AC)
Vehicle Stability Control
Work Experience
2008 - 2013: Graduate Research Assistant at International Rectifiers Power Electronics
Development and Applications Lab, Purdue University, West Lafayette, Indiana
2012: Motor Controls Intern, Delphi E&S, Kokomo, Indiana
2011: Systems Eng. Intern, Delphi E&S, Kokomo, Indiana
2007: Temporary Lecturer, Faculty of Engineering, University of Peradeniya, Sri Lanka
2006: Embedded Systems Intern, Symbol Technologies, Sri Lanka
2003: Pre-University Research Assistant, Institute of Fundamental Studies, Sri Lanka