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1、iiAMathematicalIntroductiontoFeedbackControlSingle-input,single-output,time-invariant,continuoustime, nite-dimensional,deterministic,linearsystemsAndrewD.LewisJanuary{April2002Thisversion:4January2002Thisversion:4January2002ivoftheapproachtakenhere,atleastforthecu
2、riousstudent,isthattheanswertothismoreesotericquestionmaybefoundalongsidethemorestandardadhocmethodsforcontrollerdesign.PrefaceTher^oleofcontroldesignAwordneedstobesaidaboutcontroldesign.GreaterThepurposeofthisprefaceistwo-fold:(1)todiscussthephilosophyoftheapproa
3、chtaken,emphasisisbeingplacedonengineeringdesignintheengineeringundergraduatecurriculum,asitisnonstandardforanintroductorycourse;(2)todiscussthecontentofthebook.andthisisabyallmeansanappropriatetendency.Whenteachingacontrolcourse,onefacesadecisionrelativetodesignc
4、ontent.Shouldthedesignbeintegratedintothecourseateverystage,orshoulditbeseparatedfromtheanalysispartsofthecourse?Inthisbook,theThephilosophytrendinengineeringeducationisbeingbucked,andthelattercourseistaken.Indeed,carehasbeentakentoexplicitlyseparatethebookintothr
5、eeparts,withthedesignpartcomingSincethisbooktakesanuntraditionalapproachtointroductorycontrol,itisworthlast.Onecanjustlyarguethatthisisamistake,butitistheapproachIhavedecidedupon,outliningwhyIhavetakentheapproachIhave.anditseemstowork.Myrationaleforadoptingtheappr
6、oachIdoisthatincontrol,thereisverysimplyalotofanalysistolearnbeforeonecandodesigninaful llingway.ThusIThemathematicalapproachAnintroductorycourseincontrolseemstobeapartgetallthetoolsinplacebeforedesignisundertakeninthelatterstagesofthebook.ofthestandardcurriculumi
7、nmanyoftheengineeringdisciplines.MostsuchcoursesaredirectedtowardsstudentswhosegrasponthefundamentalsubjectsoflinearalgebraandHowtousethebookItisnotpossibletocoverallofthetopicsinthisbookinadi erentialequationsisofteninneedofextensivereview.Thisbookisnotwrittenfor
8、singleterm;atleastitisnotadvisabletoattemptthis.However,itisquiteeasytobreakcourseso eredtosuchstudents.Thepreponderanceoftextsonthesubjecttendtobetheco
