Seite - 92 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4. ControlSystemDesign In time-invariant DMC and QDMC, the future temperatures can be predicted (until the time k+ p) using the the current temperature and the current estimated parameters, such as in [Wan09] (1 ≤ l ≤ p) Y(k+ l) = [Cd(k)]Xd(k+ l) = [Cd(k)] ( [Ad(k)]Xd(k+ l−1)+[Bd(k)]∆U(k+ l−1) ) . (4.10) All future temperature vectors from k+ 1 to k+p can be generated usingthisequation Y(k+1 |k) = [Cd(k)][Ad(k)]Xd(k)+[Cd(k)][Bd(k)]∆U(k), Y(k+2 |k) = [Cd(k)][Ad(k)]2Xd(k)+[Cd(k)][Ad(k)][Bd(k)]∆U(k) +[Cd(k)][Bd(k)]∆U(k+1), ... Y(k+p |k) = [Cd(k)][Ad(k)]pXd(k) +[Cd(k)][Ad(k)] p−1 [Bd(k)]∆U(k)+ · ·· +[Cd(k)][Bd(k)]∆U(k+p−1). (4.11) The whole system can be represented in a compact form as [Wan09] Yd(k) = [Fd(k)]Xd(k)+[Ξd(k)]∆Ud(k), (4.12) with [Ξd(k)] =           [Cd(k)][Bd(k)] [ON×M] . .. [ON×M] [Cd(k)][Ad(k)] · [Bd(k)] [Cd(k)][Bd(k)] . .. [ON×M] ... ... ... ... [Cd(k)][Ad(k)] p−1 · [Bd(k)] [Cd(k)][Ad(k)] p−2 · [Bd(k)] . .. [Cd(k)][Bd(k)]           , 92