Page - (000015) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

1.2 Overview 3 Ipresentafullexampleoffeedbackcontrol. Iemphasizetheclassicproportional, integral, derivative (PID) controller. A controller is a designed component of the systemthatmodulates the system’s intrinsic input–output responsedynamics. In a PID controller, the proportional component reduces or amplifies an input signal to improve theway inwhich feedbackdrives a system toward its target.The integral component strengthens error correctionwhenmoving towardafixed target value.Thederivativecomponentanticipateshowthetargetmoves,providingamore rapid systemresponse tochangingconditions. The PID example illustrates how to use the basic tools of control analysis and design, including the frequency interpretation of dynamics. PIDcontrol also intro- duceskey tradeoffs indesign.Forexample, amore rapid response toward the target setpoint oftenmakes a systemmore susceptible toperturbations andmore likely to becomeunstable. This first part concludes by introducing essentialmeasures of performance and robustness.Performancecanbemeasuredbyhowquicklyasystemmovestowardits targetor,overtime,howfarthesystemtendstobefromitstarget.Thecostofdriving a system toward its target is also ameasurable aspect of performance. Robustness canbemeasuredbyhowlikely it is thatasystembecomesunstableorhowsensitive asystemis toperturbations.Withexplicitmeasuresofperformanceandrobustness, onecanchoosedesigns thatoptimallybalance tradeoffs. 1.2.2 Part II:DesignTradeoffs Thesecondpartappliesmeasuresofperformanceandrobustnesstoanalyzetradeoffs invariousdesignscenarios. Regulationconcernshowquicklyasystemmovestowardafixedsetpoint.Ipresent techniques thatoptimizecontrollers for regulation.Optimalmeans thebestbalance betweendesign tradeoffs.Onefindsanoptimumbyminimizingacost function that combines thevariousquantitativemeasuresofperformanceand robustness. Stabilization considers controller design for robust stability. A robust system maintains its stability evenwhen the intrinsic systemdynamics differ significantly fromthatassumedduringanalysis.Equivalently, thesystemmaintainsstabilityif the intrinsicdynamicschangeor if thesystemexperiencesvariousunpredictablepertur- bations. Changes in systemdynamics or unpredicted perturbations can be thought of asuncertainties in intrinsicdynamics. Thestabilizationchapterpresentsameasureofsystemstabilitywhenacontroller modulates intrinsicsystemdynamics.Thestabilitymeasureprovidesinsight intothe setofuncertainties forwhich thesystemwill remainstable.Thestabilityanalysis is basedonameasureof thedistancebetweendynamical systems, apowerfulway in which tocompareperformanceand robustnessbetweensystems.