Page - 128 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4. ControlSystemDesign are converging to the target temperature. Using this control task, the number of controlled temperatures can be reduced to 2. For each of them, thenumberofpossiblestatescanalsobereduced. Forexample, in many practical applicationsYmax andYmin does not necessarily to reach the target temperature, and a more realistic objective is to con- strainthemwithinarangeas [Ytar−5,Ytar+5]. In thiscase,bothYmax andYmin canbeassignedwithonly2possiblestates, suchas StateofYmax Smax= { 1, when Ymax<=Ytar+5, 0, Otherwise, (4.51) and StateofYmin Smin= { 1, when Ymax>=Ytar−5, 0, Otherwise. (4.52) Thisdiscretizationmethodabstractall temperaturedistributioninto4 (2×2) different states, which significantly simplifies the whole state space. Due to the limited discretization resolution, several situations are not able to be well represented by the state. Therefore additional controller selectionmechanismhas tobeaddedsuchas Theactivecontroller⇐      MPC/NNC, when Ymax<=Ytar, NoPower, when Ymin>=Ytar, Q(λ) learning, otherwise (4.53) However, unlike other measured temperatures, the positions of the maximum and the minimum temperatures are not fixed and vary- ing along the heating process. In order to successfully control both of them, the informationabout theirpositionsshouldalsobediscretized and included in the state variable. For instance, a rectangular work- piece isheatedintheHEPHAISTOScavityandits thermalpicturecan be shown as in figure 4.13. The whole heating area is divided into 5 different regions (R1, R2, R3, R4, R5) and each region represents one possiblestate for thepositionofYmaxandYmin. Inaddition,according totheempiricalknowledge, theminimumtemperatureYminneveroc- curs in the center region of the workpiece (R3), therefore the number 128