Qualitative Reasoning With Higher-Order Derivatives

Considcriiblc progress has been made in qualit‘ltivc rcnsoning ;ibout phycic;rl systems (dc Klccr and Ill-own, 1984) (dc Klccr and I~II)\+ II. 1953,) (J’~rbu~. 1982) (I IilycC, 1979) (Kuipcrs. lS)SZa) (Williams. 1984iI) (Williams, 1984b). IIcscription. cxJ>l;lnation ilnd prediction of cvcnts which occur over short time intcrv,lls is filirly well understood. I lOWC\Cr-, WhCll CnOLl@ time PilSSCS thC lillldillllC~ltill lllOdC Of bCh;lvi()r of the dckicc may change. IIiscovcring lilWS which govern this gross scale time bchuvior IlilS proven illusive. At first sight it ilppcars that the inhcrcnt iimbiguity of qualitative analysis makes it impossible to formulntc pnwcrful Jaws. ‘I’his is not the cast, and wc h,ivc idcnlificd six fundanlcntal IilWS which govern tIlc gross-time behavior of a dcvicc nAic+ rely otl qualiltrtive irtforttlnlion alotte. WC ~;IVC built iI computer progrilm bilscd 011 thcsc laws and tcstcd it out on many cxaniplcs. FOr pLlrJ>OSCS Of CXJ?~illldtiO~l. WC drilW all our cxnmplcs from a simple fluid-mechanical prcssurc-regulator illustrntcd in Figure 1. (dc Klccr and Brown, 1982) prcscnts a theory of causal analysis aJ>plicablc for small time Scales using the prcssurc rcguJ:Hor as an cxamplc. Using that theory it is possible to dctcrminc the direction of change for iIll dcvicc quantities. causal cxplnnations for their change, ilnd idcntificiltion of the ncgativc fccdbnck. In this paper WC address prcssurc regulator cvcnts occurring over a longer time scale. If the input prcssurc rises indcfinitcly, will the valve cvcntually complctcly close? Dots the valve oscillate when a sudden input is applied? Figure 1 : t’rcssurc Regulator