Page - 106 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4. ControlSystemDesign in equation 4.27 that both Y(+)(k) and Y(−)(k) are generated based on Y(k), which means in the sequence (equation 4.28) the controller shouldwaituntilY(+)(k)(Y(k+1))equivalent toY(k) to implement the next control action U(−)(k). This condition requires extra wait- ing time and also brings more disturbances for continuous multiple- output systems, where two adjacent outputs are hardly identical. In addition,theweightupdatefrequencyinthestandardSPSAalgorithm is limited as one update per three control periods, which slows down thewholecontrollerconvergingspeedandcorrespondinglydegrades thecontrolperformance. In order to make the SPSA algorithm more efficient in the practical heating process, a semi-direct NN controller is implemented in this dissertation. The first modification is to change the approximation of thegradient fromequation 4.26 toasimpler formas[SC98] h(w(k)) = J(+)(k) c(k)∆(k) . (4.29) Although the two-measurement strategy (equation 4.26) is gener- ally more preferable, it has been proved in [Spa97] that this one- measurement strategy (equation 4.29) is also suitable for highly non- stationary systems, where the parameters of the plant or external dis- turbancesmightchangeduringonecontrolperiod(fromk+1 tok+2 or fromJ(+)(k) toJ(−)(k)). In order to further speed up the learning process, the control structure is also modified from the direct control scheme to a semi-direct scheme that involves an additional NN esti- mator (figure 4.6 ). In this semi-direct scheme, the NN estimator keeps learning the dy- namics of the real plant and monitoring the error between its predic- tion and real output of the plant. If the prediction of the NN esti- mator is constantly accurate for certain time (the MSE of prediction is lower than a given threshold, described in figure 4.7), it will also be used in the weight update. This NN estimator can be considered as an approximation of the real plant, to provide information such as Yˆ(+)(k), Jˆ(+)(k) to theNNcontroller. Duringeachcontrolperiod, the NN controller can take one or more updates based on the NN estima- tor,andthenumberofupdatespercontrolperiodcanbeadjusted. The principlecanbefoundinthecontrollerdescription(figure 4.7). 106