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1、IEEETRANSACTIONSONAUTOMATICCONTROL,VOL.48,NO.4,APRIL2003687ANewApproachtoDigitalPIDControllerDesignthisthirdvariablecanbeexactlydetermined.Bysweepingorgriddingoverthethirdvariable,thecompletestabilizingsetcanbedeterminedL.H.Keel,J.I.Rego,andS.P.Bhattacharyya
2、constructively.Thesolutionshowsthatthestabilizingsetforanyplant,whenitisnonempty,consistsofunionsofconvexpolygonsinthespaceofthePIDgains.Abstract—Inthisnote,wepresentanewapproachtotheproblemofTheaforementionedsolutiontechniqueisextendedtosolvetwopre-designin
3、gadigitalproportional-integral-derivative(PID)controllerforagivenbutarbitrarylineartimeinvariantplant.ByusingtheTchebyshevviouslyunsolveddesignproblems.Thefirstproblemisrelatedtodead-representationofadiscrete-timetransferfunctionandsomenewresultsbeatcontrolw
4、hereinoneplacesallclosedloopcharacteristicrootsatonrootcountingwithrespecttotheunitcircle,weshowhowthedigitaltheoriginsothatthetransientsarezeroedoutinafinitenumberofPIDstabilizinggainscanbedeterminedbysolvingsetsoflinearinequali-steps.Ingeneral,deadbeatcont
5、rolisnotpossibleusingPIDsandarea-tiesintwounknownsforafixedvalueofthethirdparameter.Bysweepingorgriddingoverthisparameter,theentiresetofstabilizinggainscanbesonablegoalistoplacetheclosedloopcharacteristicrootsasclosetorecovered.Thepreciseadmissiblerangeofthi
6、sparametercanbepredeter-theoriginaspossiblesothatthetransienterrordecaysquickly.Suchmined.Thissolutionisattractivebecauseitanswersthequestionofwhetherdesignshavebeenadvocatedintheliteratureonsampleddatacontrolthereexistsastabilizingsolutionornotandincasestab
7、ilizationispossiblesystems(seespecifically[15,p.292]).Weshowhowthestabilizationtheentiresetofgainsisdeterminedconstructively.Usingthischaracter-solutionobtainedbyuscanbeexploitedtogiveaconstructivedeter-izationofthestabilizingsetwepresentsolutionstotwodesign
8、problems:1)maximallydeadbeatdesign,wherewedetermineforthegivenplant,theminationofsuch“maximally”deadbeatdesigns.Thesecondproblemsmallestcirclewithintheunitcirclewhereintheclosedloopsystemcharac-
