Page - 37 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

3. ModelingMicrowave Heating BasedontheintroductiontomicrowaveheatingandHEPHAISTOSin thepreviouschapter, themathematicalmodelsofthemicrowaveheat- ingprocessinHEPHAISTOSarebuilt inthischapter. Abrief introduc- tionofmathematicalmodelingisgivenfirst, followedbytwodifferent modelingapproaches, thegrey-boxmodelingandtheblack-boxmod- eling. For each modeling approach, the corresponding system identi- fication(SID)algorithms,whichareusedtoestimatetheunknownpa- rameters in themodel,arealsoexplained. Bothapproacheshavebeen implemented, to identify the most suitable modeling scheme for the temperature control system of HEPHAISTOS. The performance com- parisoncanbefoundinchapter 5. In this dissertation, we are focusing on controlling and improving the surface temperature distribution of a rectangular dielectric foil setup, suchasshowninfigure 3.1. Twoassumptionshavebeenmade: 1. The loadreceivesmostofelectromagneticenergy(heatingenergy) fromthetopsurface. 2. The thickness of the load is much smaller than the wavelength of themicrowave( 12.5cm). These two assumptions guarantee that the surface temperature distri- butionof the loadisequivalent to thetemperaturedistributionwithin the load (similar assumptions are used in [CRB08] and [BRS01]). In other words, the temperature difference in the vertical direction (z- direction as in figure 3.1) is sufficiently small. Thus the heat conduc- tion on the vertical direction can be neglected, which simplifies the entire model and following derivations. If the surface temperature 37