Abstract:
Fractional calculusiswidelyregardedasthecalculusofthe21st century.Itgeneralises
the orderofdifferentialandintegraloperatorstonon-integerorders.Thisthesisisanat-
tempt todevelopefficientandeleganttechniquesfortheorderdiminutionandcontroller
design forageneralfractionalordersystem.Itbeginswithanoutlineofthemathemat-
ical preliminariesofthefractionalcalculusandthefundamentalsofthefractionalorder
systems. Therecentsoftcomputingoptimizationtechniques,i.e.,BigBangBigcrunch
(BBBC) basedalgorithmsiselucidatedindetail.Next,newtechniquesaredeveloped
for theorderreductionofcommensurateandincommensuratefractionalordersystems
respectively.Anexhaustivecomparativeanalysisiscarriedout,whichshowstheeffec-
tivenessoftheproposedtechniqueascomparedtotherecentandexistingtechniques
in theliterature.Further,atechniqueisproposedforthedesignoffractionalorderPID
(FOPID) foranintegerorder(IO)orafractionalorder(FO)system.Theproposed
approach amelioratesthedrawbacksofexistingsoftcomputingalgorithmsandisim-
plemented onwidelydifferentsystems,i.e.,solartrackingsystem,powersystem,an
incommensurate FOsystemandhardwaresetupofadcservosystem.Anextensive
statistical, timeresponseandrobustnessanalysisisalsocarriedouttoauthenticatethe
effectivenessoftheproposedapproach.Theperformanceoftheproposedapproachis
also scrutinizedwithrespecttothekeyperformanceindices.Itisdeducedthatineach
case, theproposedapproachisoneofthebestandoutperformsmanyoftheexisting
techniques intheliterature.TheMATLABcodesimplementedforobtainingtheresults
for thisthesisarealsogivenandmaybeausefulaidforthestudentswhowishtoextend
this workfurtherintheirrelevantareas.Theresultsshowtheefficacyoftheproposed
techniques
