Page - (000038) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

Chapter4 PIDDesignExample I illustrate the principles of feedback control with an example.We start with an intrinsicprocess P(s)= ( a s+a )( b s+b ) = ab (s+a)(s+b). This process cascades two exponential decay systems, each with dynamics as in Eq.2.8 andassociated transfer function as inEq.2.9. For example, if the input into this systemisaunit impulseat timezero, then the systemoutput is y(t)= ab b−a ( e−at −e−bt), expressing thecascadeof twoexponentiallydecayingprocesses. For this example,weuse P(s)= 1 (s+0.1)(s+10) (4.1) as theprocess.Wealsoconsider analternativeprocess P˜(s)= 1 (s+0.01)(s+100). (4.2) Weassumeduringsystemanalysisanddesign thatEq.4.1describes theprocess,but infactEq.4.2isactuallythetrueprocess.Putanotherway,thedifferencebetweenthe twoprocessesmayreflectuncertain informationabout the trueprocessorunknown disturbances that alter the process. Thus,wemay consider howa systemperforms ©TheAuthor(s)2018 S.A.Frank,ControlTheoryTutorial, SpringerBriefs inAppliedSciences andTechnology,https://doi.org/10.1007/978-3-319-91707-8_4 29