Page - (000014) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

2 1 Introduction An organism’s sensors transform light and temperature into chemical signals. Those chemical signals become inputs for further chemical reactions.Thechainof chemical reactions feeds intophysical systems that regulatemotion. How should components be designed to modulate system response? Different goals leadtodesigntradeoffs.Forexample,asystemthat respondsrapidly tochang- ing inputsignalsmaybeprone toovershootingdesign targets.The tradeoffbetween performanceandstability formsonekeydimensionofdesign. Controltheoryprovidesrichinsightsintotheinevitabletradeoffsindesign.Biolo- gistshavelongrecognizedtheanalogiesbetweenengineeringdesignandtheanalysis ofbiological systems.Biology is, inessence, the scienceof reverseengineering the designoforganisms. 1.2 Overview I emphasize the broad themes of feedback, robustness, design tradeoffs, and opti- mization. Iweave those themes through the threepartsof thepresentation. 1.2.1 Part I:BasicPrinciples Thefirstpartdevelops thebasicprinciplesofdynamicsandcontrol.Thispartbegins withalternativeways inwhich to studydynamics.Asystemchangesover time, the standard description of dynamics. One can often describe changes over time as a combinationof thedifferent frequencies atwhich those changesoccur.Theduality between temporal and frequency perspectives sets the classical perspective in the studyofcontrol. Thefirstpart continuesbyapplying the toolsof temporal andfrequencyanalysis tobasiccontrolstructures.Open-loopcontroldirectlyaltershowasystemtransforms inputs into outputs. Prior knowledgeof the system’s intrinsic dynamics allowsone to design a control process thatmodulates the input–output relation tomeet one’s goals. Bycontrast, closed-loop feedback control allows a system to correct for lackof completeknowledgeabout intrinsic systemdynamics and forunpredictablepertur- bations to the system. Feedback alters the input to be the error difference between the system’soutput and the system’sdesired targetoutput. Byfeedingback theerror into thesystem,onecanmodulate theprocess tomove in the direction that reduces error. Such self-correction by feedback is the single greatestprincipleofdesigninbothhuman-engineeredsystemsandnaturallyevolved biological systems.