Therst objectiveof this work is to examineand describe theuse of FPGAs
inthereal-timecontrolofhighperformanceAMBrotorsystems. Thecomplete
workingembeddedFPGA-basedcontrolplatformisbuilt,testedandvalidated
AMBcontroller,whichexplorestheadvantagesofthedesignedcontrolplatform,
takes into accountthe bending modes of the rotor (they controllability),and
nonlinearitiesoftheactuator. Therequirementsforthecontrollerincludeahigh
performance and unbalance compensation, at variable rotational speeds. For
theobtainedcontrollerarobustanalysisisconducted. Furthermore,thethesis
focusesnotonlyoncontrolandsystemleveldesignissues,butalsoitaddresses
the hardware description language (HDL) design and testing problems. The
specic designissuesare considered: singlechip controlsolution, emulation of
AMBsystem,built-intesting,designportabilityandreusability,customtailored
digitalarithmetic,on-chipinterconnections,andtheuseofembeddedprocessors.
Theavailableliteraturedoesnotprovideenoughinformationonalltheseissues.
Last but notleast, theresearch was apartof awider work that aimed at
building a completely custom AMB laboratory test rig with AMB actuators
available forexperimental testingof novelcontrol algorithmsand examination
ofrotordynamics atLappeenranta UniversityofTechnology. Theprojectwas
co-nancedbyTEKES 3
.
The dissertation is presented as an introduction to the collection of the
original scientic publications. In addition to that, the thesis includes some
original results, which have not been presented to the wider audience up to
now.
The highlights of the appended publications and the contribution of the
authorsarereportedbelow.
Publication I addressesadesignandimplementationofanapplicationspecic
architecture (of AMB controller), in an FPGA circuit. The publication
presents a prototyping platform that eases the development of control,
testing andintegrationoftestedalgorithmsinto theFPGA. Itshowsthe
FPGA implementation of an AMB currentcontroller of a set of ten
H-bridge switching ampliers. Dierent architectures and data ow of the
AMB controller are examined. The paper shows the opportunities and
threadsofaexibleHDLimplementationofanembeddedcontrolsystem.
Publication II analyzesthe benets of an FPGA-based real-time emulation
formechatronicapplications. Asacasestudy,AMBsforcontactless
sup-portofrigidrotors,areselected. Thispublicationshowsthatforageneral
class ofstate-spacemodels withseparablenonlinearities,itis possibleto
build an optimized hardware implementation of the plant emulator or
stateobserver(abasicpartofastate-spacecontroller). Theemulatorcan
beusedforreal-timevalidationofthecontrolsystemanditscomponents.
PublicationIIusesthe4-DOFrotormodelfromsubsection 3.1.2.
Publication III includes the description of the real-time emulation of
mag-neticsuspensionsystem,withaexiblerotor,in FPGA.Thepublication
comparestherealizationsoftherigidandexiblerotormodels,whichcan
beusedforemulationorfortheimplementationofthecontroller. It
intro-ducestheconceptsof: numericalconditioningof thexed-point
discrete-time model, discreterealizationofdierentialequations,veryhighspeed
integrated circuits hardware description language (VHDL)
implementa-tion of the non-linearactuator model and state-space rotormodel. The
3
emulatorandtheLQcontrollerwithintegralfeedbackaretestedinVHDL
Mentor Graphics
R ModelSim R simulations. PublicationIII utilizesthe exiblerotormodelfromsection3.2.Publication IV presents FEM of the rotorand dierent variantsof theLQ
position control (considered in regard to the rotor model). In the
pub-lication, the rotor model is obtained using the FEM, modal reduction
techniqueandexperimental analysis. PublicationIVincludestheVHDL
implementation of the obtained exible rotor model with the nonlinear
actuator,butitfocusesonthedierentvariantsofthepositioncontroller,
theirHDLimplementations,andonanactivedampingofexiblemodes.
Publication V describes an LQ control and nonlinearities compensation of
a rotorsuspended by AMBs. TheLQ control is based ona state-space
controllerwithanadditionalintegrativefeedback,anddisturbance
estima-tor. Aneectivecompensationofperformancevariationsindynamicforce
characteristicsof radial AMBs is performed using two nonlinear
princi-ples. Thepublicationstudiesthewell-knowninversenonlinearitymethod.
Next,itpresentsanovelmodel reference-basedmethod. It isshownthat
theproposedcompensationprovidescertainadvantagesoverconventional
solutions. Theoverallcontrol istested withtheexible rotormodeland
the nonlinear AMBs. Finally, the paper presents an integration of the
proposedcompensationinto thedigitalcontroller. Accuratemodelingof
the AMB nonlinearities in an FPGA isachievedby using multi-variable
interpolationandlook-uptable.
Publication VI illustratesthetechniqueofanin-circuitvericationwiththe
custommadeembeddedlogicanalyzer. Theanalyzerprovidesthemeans
to monitor internal signals, state of buses, and registers of the
embed-dedcontroller. Theheart ofthetoolcomprisesofthehardcorePowerPC
processor,in theVirtex
TM
-IIProFPGA-circuit. Inaddition to
monitor-ing, thedescribed toolis afeasiblealternativeto thesimilarcommercial
solutions.
Looking at the major contributions to theappended publications, the author
developedallthe programsinVHDL andMatlab, carriedoutthesimulations,
andwasthemainauthorofallthepublicationsbutPublicationVI.Inaddition,
he was involved in the testing, designing of the software part, and
commis-sioningof the FPGA-based AMB rotorprototypingplatform. The text of all
theappended publications, with the exceptionof Publication VI and sections
of PublicationIV, was written bythe author. Theco-author R.Pöllänen
de-veloped the reluctance network model used for obtaining the accurate force
eld of radialAMB. Theco-authorsA. Kärkkäinenand J.Sopanenwrote the
FEMcode,performedthemechanicalmodeling,obtainedtheexiblemodesand
eigenfrequenciesofthetestrotor(the naltestrotor,describedinthethesis,is
dierentthough). TheyalsowrotethesectionsofPublicationIV,whichrequired
expertisein mechanicalengineering. Theremainingsectionsof PublicationIV
waswritten bythe author. Theco-authorA. Penttinen wasthe main author
of PublicationVI. Hedeveloped theC++ code for thePowerPC processorin
ofthecommunicationbetweentheFPGA,PowerPC,andPCconsole. In
Pub-lication VI,theAMB controllerand theconnection betweenthelogicand the
processorwere realizedand tested bytheauthor. Theco-authorsR.Pöllänen
and O. Pyrhönen supervised and inspired the appended publications and the
wholeAMB project.
The main body of the dissertation provides the reader with introductory
information,themaintopictreatedin theorganizedandconsistentmanner,as
well asthe key results and conclusions. Experimental and simulation results
are notorganizedin separate chapters,however, theyfollow throughallparts
ofthedissertation. Themainbodyisorganizedinto sixchapters.
Chapter 1 introducesthehistorical background,properties, applicationsand
principlesofoperationofthemagneticbearings. BasiccontroloftheAMB
rotorsystemisdiscussedin thecontextofdigitalandembeddedsystems.
A briefintroductiontomodern signalprocessingdevicesandtheirusein
embeddedcontrol applicationsisgiven. Therelatedwork andimportant
references in the studied eld are listed. The outline, main goals and
objectivesofthisdissertationarestated.
Chapter 2 considers therotor, magnetic bearings, and control system asan
mechatronic product. The hardware parts and control hardware of the
studiedprototypesystemareintroduced;physicalphenomenabehindtheir
principles of operationare shown. Thenecessarybackgroundforthe
ac-curatesystemmodelingisprepared.
Chapter 3 discusses modeling of the AMB rotor systemfor thecontrol
syn-thesisand itsvalidation. Thereaderis introduced tothe rotormodeling
and main system nonlinearities. The construction of the overall plant
model is presented. The viability of models with dierent complexities
is considered. In particular, a FEM rotormodel is developed and
cor-rected,accordingtoamodalanalysis,tomatchtheprototypesuciently
to designreliablemodel-basedcontrollers. Theeect ofthereduced
pre-magnetization current on the force characteristics of the radial AMB is
discussed.
Chapter 4 studies the design of the controller, its inner and outer control
loops, theirrequirementsand realizations. Theclassicaldecoupled
PID-basedpositioncontrolandLQmodel-basedcontrolmethodsarediscussed.
ThemainconcernareLQcontrolbasedonphysicalquantitiesanddierent
methods of the force-eldlinearization. Special attentionis paid to the
automated LQcontrollerdesignand selectionof theweightingfunctions
fortheLQperformanceindex. Furthermore,theunbalancecompensation,
robust stability analysis, and the controller evaluation accordingto the
selectedcriteriaarepresented.
Chapter 5 focusesontheissuesassociatedwithFPGA-basedcontrolplatform,
suchasthedesignmethodology,hardwaredescriptionlanguagetools,use
ofembeddedprocessorcores,onchipinterconnections,andFPGA
emula-tion. Thesoftwarearchitectureandrealizationofcontrollersub-functions
in VHDL aredescribed. Themeansforecientutilizationof theFPGA
Chapter 6 concludes themain results, summarizes the content and suggests
future researchwork.