REDUCED ORDER MODELING BASED CONTROLLER DESIGN FOR FRACTIONAL ORDER SYSTEMS

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