Page - 39 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

3.1. MathematicalModeling properties of the system can be analyzed. As mentioned in chap- ter 1, a good mathematical model should be able to both describe the main characteristics of a system, but also keep the complexity at a low level. Depending on the nature of different systems, the corre- spondingmathematicalmodelsaredistinguishedintostatic,dynamic, explicit, implicit, deterministic, stochastic or other models. Essen- tially there are three main categories of mathematical modeling ap- proaches. Black-boxmodeling In black-box modeling [Lju97], as the name suggests, the investigated systemis treatedasacompletelyunknownobject. Nophysicalorany otherkindofpriorknowledgeisavailable,andthewholesystemonly consists of three parts: the input, the output and the transfer relation- ship(function)suchasinfigure 3.2. Inablack-box, thechoiceof input and output components is based on observations and requirements accordingly. The critical task is to select an appropriate model and function structure [JHB+95]. For example, for a system with multiple inputandoutputvariables, thestate-spacemodel [Lju97] ispreferable to the transfer function formed model [Lju97]. The principle of select- ing the right model structure is to guarantee that the main features of the system can be reflected by the model. Besides, the number of as- sumptionsshouldbeasfewaspossible. Normallythemodelstructure is chosen on the basis of experimental data or empirical knowledge [SZL+95]. Black-box Model (unknown function) OutputInput Figure3.2. Diagramofblack-boxmodeling. 39