Outlook

The outlook for the control algorithms, which eciently utilize the FPGAs

in AMB control is bright. Computationally heavy control algorithms can be

implementedwithoutfearforthelimitedcomputationalpower,numberofI/Os

orinaccuratenumberformatsasmightbeacasewithDSPs. With itsexible

architectures,themodern andlargeFPGAscouldaccommodate verycomplex

controllers. However,toohighcomplexitymayleadto error-pronedesignthat

isdiculttodebug,modifyandmaintain.

AsregardstotheAMBprototype,controlelectronicsandcontrolalgorithms,

therecommendations forfuture work,from thepointof viewofthepresented

thesis(consideredasastartingpoint),areasfollows.

•

^The^laboratory^tests^of^the^AMB^rotor^system^should ^be^continued.

•

^The^unbalancecompensationshouldbetestedexperimentally,after instal-lation ofaspeedsensor.

•

^The^employment^of^robust^control^methods,^theircomputational complex-ityrequirementsandbenetsoverLQmethodsshouldbeexamined.

•

^The^automated^systemidenticationand,basedonit,automated MIMO-adaptivenonlinearcontrollerdesigncouldbeapplied.

•

^Theimprovementsin position sensorsarerequired;thedesignofcustom, moreaordable, accurately positioned and calibrated sensorscould

con-siderablyreduce the costsof control electronicsand risethequalityof a

feedbacksignal.

As to the suggestions for future research work, which involves FPGA-based

AMBcontrollers,theaccentshouldfall onthefollowingtopics.

•

^In^theimplementationwiththeuseofFPGA,thehigh-levelC-based lan-guages,otherhigh-leveldesignenvironments,andready-madeIPlibraries

for hardware-software co-design could alleviate the growing complexity

andworkloadinSoCdesign,releasingtheresearcherandcontrolengineer

fromtediousVHDLcoding.

•

^Thecustom-builtin-chipinterconnectionsandbusesbetweenIPscouldbe replacedwithmoregenericstructures(e.g. busstructuresuchaspresented

byRaumaetal.,2005). ForSoC,whicharemorecomplexthanthestudied

prototype,anetwork-on-a-chip(NoC)couldbeconsidered.TheNoC,that

mightconsistofmultiplepoint-to-pointdata linksconnectedbyswitches

(routers),appliescommunicationmethodssimilar totelecommunications

networksforconnectingprocessorcores,memories,andIP blocks.

•

^Further^ev^aluations ^of^thesingle-chip-embedded FPGA-basedAMB con-trollershould becarriedout. Inorder toachievemoreadditional

experi-mentalresults,animproveduserinterface,integrateddebugginginterface,

andmonitoringarerequired.

•

^Theapplicationofoating-pointarithmeticin theIP forastate-variable

thestate-variableformwith

Ω

^as^a^parameter^and^the^real-time discretiza-tioncouldbeimplemented.

•

^The developmentof akindof anIDE application toprovidefacilitiesto softwareengineerforautomateddesignofcomplexmodel-basedcontrollers

on a single FPGA could be considered. Such an IDE would possibly

combinetheMATLABcontrol toolboxes(forcontroldesign)witha

pro-gramming environment(forautomated code generation)fora

hardware-softwarecontrollerimplementationinFPGA.

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Derivations and algorithms

A.1 Electromagnetic force

Theequation for themagneticforce (2.7) canbe obtainedfrom aprincipleof

virtualwork (Antila, 1998)and (Arkkio et al., 2004). Thevirtual mechanical

workdonebythesystem

W me

^,^the^energy^ofelectromagneticeld

W fe ,

^and^the

total energy of the windings are used in the energy balance of a generalized

electromechanicalsystemwith

N

^circuit^equations^as

N

X

j=1

i j dψ j = dW fe + dW me = dW fe + f · d l ,

^(A.1)

where

i j

ψ j

^and

dl

^are^the^currents^of^the^circuits,^ux ^linkages^of^the^circuits

andthevirtualdisplacement. Consideringthedisplacementandtheactingforce

inx direction,anddeningthevectorcontainingallthecurrentsinthesystem

i

^,^the^energy^and^ux^linkage^dierences^can^be^written^as

dW f e =

Now, weassumethe currents asfree variablessuch that

i =

^constant.

Substi-tutingdierencesinEq. (A.1) andnoticingthat

i

^and

x

^areindependentfrom eachother,theforceequationisobtainedasthepartialderivativeofaco-energy

withrespecttovirtualmovement

f (i, x) =

wheretheelectromagneticco-energyisdenedas

W ce =

N

X

j=1

i j ψ j − W fe ( i , x).

^(A.5)

In document Design and implementation of FPGA-based LQ control of active magnetic bearings (sivua 135-146)

•

•

•

•

•

•

•

•

•

Ω

•

2 nd

2 nd

µ

[

]

H ∞

W me

W fe ,

N

N

X

j=1

i j dψ j = dW fe + dW me = dW fe + f · d l ,

i j

ψ j

dl

i

dW f e =

i =

i

x

f (i, x) =

W ce =

N

X

j=1

i j ψ j − W fe ( i , x).

2 ^nd

2 ^nd