Date of Graduation

1967

Document Type

Thesis

Abstract

The e f f e c ts o f param eter v a r ia tio n and u n c e rta in ty on optim al process d esign have been s tu d ie d . E quations necessary f o r d e te rmining th e s e n s i t i v i t y of optim al system perform ance to param eter v a ria tio n a re d e riv e d . D esign c r i t e r i a have been developed fo r optim al d esign o f system s th a t a re e i th e r s e n s itiv e to param eter v a ria tio n o r in v o lv in g param eter u n c e rta in ty . The s e n s iti v ity eq u atio n s f o r system s d escrib ed by a lg e b ra ic , d if f e r e n tia l and d iffe re n c e equations a re d eriv ed based on th e Lagrange m u ltip lie r method, P o n try a g in 's maximum p r in c ip le and th e d is c re te v e rsio n o f th e maximum p r in c ip le , re s p e c tiv e ly . Such s e n s iti v ity equ atio n s are li n e a r and can be solved fo r s e n s itiv ity c o e f f ic ie n ts . Two methods a re proposed f o r o p tim al design o f param eters e n s itiv e system s. Design and o p e ra tin g v a ria b le s o f a system are determ ined by reducing s e n s iti v ity such th a t th e re s u ltin g system i s clo se to th e optimum and le s s s e n s itiv e . M odified a l ­ gorithm s o f th e maximum p rin c ip le f o r problems w ith s e n s itiv ity c o n s tra in ts a re p re se n te d . Two design c r i t e r i a are proposed f o r optim al d esign o f systems invo lv in g param eter u n c e rta in ty . One may be used to o b ta in an ap p ro p ria te d e c isio n which w ill keep th e d e v ia tio n o f th e obje c tiv e from th e optim al behavior w ith in a c e rta in to le ra n c e . The o th e r a ssu re s a minimum average norm alized d e v ia tio n o f the o b je c tiv e from th e optim a over th e range o f u n c e rta in ty . Examples in optim al re a c to r 'design are given to dem onstrate th e a p p lic a b ility o f th e proposed methods.

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