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Electric Machine Differential For Vehicle TractionControl And Stability ControlSandun Shivantha KuruppuPurdue University

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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): ____________________________________

____________________________________

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


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 3.21.a BLDC machine current controller performance –PI Regulator .................. 41


Figure 3.22.a BLDC machine current controller performance –PI Regulator .................. 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

8

8

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)

9

9

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

12

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

13

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

14

14

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

15

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).

16

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).

17

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

18

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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21

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

25

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.

27

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).

30

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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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

40

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.

44

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.

57

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

59

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.

63

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

65

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

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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

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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

)


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

)


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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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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93

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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94

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



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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




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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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102

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

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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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104

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.

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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.

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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

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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

135

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

{


}

else if (HallValue == 1 || HallValue == 3) //Phase 3

{


}

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


//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


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


SpeedControl();

PDC1 = DutyCycle;

PDC2 = PDC1;

PDC3 = PDC1;

PrevSpeed = Speed;

}

else if (Status == 3) // CURRENT CONTROL

{

CurrentControl();


OVDCON = StateLoTable[HallValue];// Load the override control

register

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}

else if (Status == 4) // REGENERATIVE BRAKING

{


OVDCON = StateLoTable[HallValue];// Load the override control

register

RegenBrake();

}

else

{

// Diable PWM Module

OVDCON = 0x003F;

}

}

HallValue = (unsigned int)(PORTB & 0x0007); // mask

RB0,1 & 2


// 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 --------------


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;


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


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

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