Page - 41 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

3.2. Grey-boxModeling adjusted according to the specific situation, which could take a long timeandrequireextraefforts. Althoughblack-boxmodelinghasgreat potential to achieve a good performance, it is normally considered as the last resort and only utilized when no alternative is available [Lju97]. In comparison with black-box modeling, the number of unknown pa- rameters and the amount of experimental data required in grey-box modeling are generally less. Moreover, the first principles used in grey-box modeling also give certain physical interpretations to the parameters being estimated, which double-check the estimation ac- curacy and help to understand the internal physical properties of the system. However, in many cases the first principles are still too com- plicated to be directly applied or not complete to cover all dynamics of theoriginal system. Inordertoidentifythemostsuitablemodelforthemicrowaveheating processandmakeHEPHAISTOSadaptive todifferentheatingscenar- ios, both grey-box and black-box modeling approaches are applied in thisdissertation. 3.2. Grey-boxModeling Therearemainlythreeprocedurestoapplythegrey-boxmodelingap- proach. Thefirst step is to identify thephysicalprinciples thatgovern theentireenergyexchangeprocess. Ifnecessary,certainsimplification and approximation have to be implemented to transfer the original principles intocontrollable forms. The last step is toorganizeanddis- cretize the resulted models, in order to make them suitable for the followingcontrollerdesign. 3.2.1. FirstPrinciples Foranyunitcellonthesurfaceof theheatedloadsuchas infigure 3.1 withsizeof l× l× l (e.g. l=1cm), thecompleteenergy(temperature) 41 changingequationcanbederivedaccordingtothelawofconservation of energy[LNS04], suchas indicatedbytheequation