Seite - (000051) - in Control Theory Tutorial - Basic Concepts Illustrated by Software Examples

Part II DesignTradeoffs Manyperformancetradeoffsoccur.Asystemthatrespondsquicklytocontrolsignals oftensuffersfromsensitivitytoperturbations.Amorerapidresponsealsoassociates withagreater tendency toward instability. Designofacontrolsystembyanengineermustbalancethecompetingdimensions of performance. Similarly, design of biological systems by evolutionary processes implicitlybalancesthedifferentdimensionsofsuccess. Inengineering,wecanspec- ify performance criteria. In biology,wemust figure out hownatural processes set the relative importanceofdifferentperformancemeasures. Oncewehaveasetofperformancecriteria, howdowefind thecontrol architec- tures andparameters that performwell? Ifwedonot have formal designmethods, thenweendupwithadhocsolutions.Suchsolutionsmayperformwell.Butwedo not have anyway to know if there are better solutions or betterways to formulate thedesigncriteria. Ideally, wewould have an optimizationmethod that provided the best solution for agivenproblemandagiven set ofperformancecriteria.Optimization forcesus to specify the problemwith clarity.Wemustwrite down exactly the performance criteria, the nature of the problem, and all associated assumptions.We then get an answer aboutwhether there is a best design for the given assumptions or a set of comparablealternativedesigns. Optimization is, of course, only as good as the assumptions that wemake. In engineering,wemaybe able to specify design criteria clearly.Or, at least,we can experimentwithvariouscriteria andexamine thealternativeoptimaldesigns. Inbiology,figuringout theappropriate assumptionsandconstraints that express naturalevolutionaryprocessescanbeverydifficult.Wemaymakesomeprogressby tryingdifferentassumptionsashypothesesabout thenaturaldesignprocess.Wecan thentest thematchbetweentheoptimalsolutionsandwhatweactuallysee innature (Parker andMaynardSmith1990). Design by optimization must begin with performance criteria. Three kinds of performancecriteriadominate in typical engineeringapplications. Regulation, or homeostasis, concerns aspects of design that return a system to its setpoint. Good regulation requires insensitivity to perturbations. If the system doesgetpushedawayfromitssetpoint,awell regulatedsystemrapidlyreturns to its equilibrium.Tradeoffsarisebetweentheresponsestodifferentkindsofperturbations.