Page - (000013) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

Chapter1 Introduction Iintroducethebasicprinciplesofcontroltheoryinaconciseself-studyguide.Iwrote this guide because I could not find a simple, brief introduction to the foundational concepts. IneededtounderstandthosekeyconceptsbeforeIcouldreadthestandard introductory texts on control or read the more advanced literature. Ultimately, I wanted to achieve sufficient understanding so that I could developmyown line of researchoncontrol inbiological systems. This tutorial does not replicate themany excellent introductory texts on control theory. Instead, I present each key principle in a simple and natural progression through the subject. Theprinciples buildoneachother tofill out thebasic foundation. I leave all the detail tothoseexcellent textsandinsteadfocusonhowtothinkclearlyaboutcontrol. I emphasizewhy thekeyprinciplesare important, andhowtomake themyourown toprovideabasisonwhich todevelopyourownunderstanding. I illustrateeachprinciplewithexamplesandgraphics thathighlightkeyaspects. I include,inafreelyavailablefile,alloftheWolframMathematicasoftwarecodethatI usedtodeveloptheexamplesandgraphics(seePreface).Thecodeprovidesthestart- ingpoint foryourownexplorationof theconceptsand thesubsequentdevelopment ofyourown theoretical studiesandapplications. 1.1 ControlSystemsandDesign Anincominggustofwindtipsaplane.Theplane’ssensorsmeasureorientation.The measured orientation feeds into the plane’s control systems,which send signals to theplane’smechanical components.Themechanics reorient theplane. ©TheAuthor(s)2018 S.A.Frank,ControlTheoryTutorial, SpringerBriefs inAppliedSciences andTechnology,https://doi.org/10.1007/978-3-319-91707-8_1 1