Page - (000098) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

Chapter13 TimeDelays Yousuddenlynoticeaballflyingtowardyourhead.Yourfirst reactionhappensafter adelay.Toavoidtheball,youmustconsiderwhereyourheadwillbeafteritsdelayed response in relation towhere theballwill be. Thischapterpresentsmodels fordelaydynamicsanddiscussesacontrolmethod that compensates fordelays. 13.1 Background Delaysoftenoccur in thesignals thatflowbetweencomponentsofacontrol system. Anuncompensated delaymay reduce systemperformance. Suppose, for example, that the sensormeasuring the systemoutput,y, requires δ timeunits toprocess and passon itsmeasuredvalueasa feedbacksignal. The delayed feedback signal reports the system output δ time units before the current time,whichwewrite as y(t−δ). The calculated error between the current referenceinputandthedelayedfeedback,r(t)−y(t−δ),maynotaccuratelyreflect thetrueerrorbetweenthetargetvalueandthecurrentsystemoutputvalue,r(t)−y(t). Delaysmay destabilize a system. If the calculated error overestimates the true error, then the systemmayovercompensate, pushing the systemoutput away from the target referencevalue rather than toward it. The robust control methods discussed in earlier chapters can reduce the insta- bilities created by delays. Robust control creates a significant stabilitymargin. A largestabilitymarginmeans that factorsnotdirectly included in thedesign, suchas unknowndelays,will usuallynotdestabilize the system. ©TheAuthor(s)2018 S.A.Frank,Control Theory Tutorial, SpringerBriefs inAppliedSciences andTechnology,https://doi.org/10.1007/978-3-319-91707-8_13 95