Page - 58 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

3. ModelingMicrowaveHeating where Kn(k− 1) is defined as the estimation gain vector at time k with the dimension 1× (1 +M). Equation 3.54 indicates that the newestimationθne(k−1)canbeobtainedusingtheformerestimation θne(k−2) plus a correction term. This correction term is proportional to the gain vectorKn(k−1), as well as the difference betweenYnr (k) and Yne (k). A brief illustration of the linear system identification is representedbyfigure 3.3. · Measure the temperature Yn(k) · Estimate the vector θn(k-1) (An(k-1), Bn(k-1)) · Update θne (k-1) using θ n e (k-2) · Consider θne (k-1) as θ n(k) and use it for prediction of Yn(k+1) k-1 k+1k Time Ynr(k-1) Y n r(k) Y n r(k+1) U(k-1) Available: Yn(k), U(k-1), θne (k-2); Target: θ n e (k-1) U(k) θn(k-1) θn(k) Figure3.3. Illustrationof the linearsystemidentificationprocess. Two linear recursive system identification algorithms have been ana- lyzedandtested inourexperiments. 58