Page - 96 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4. ControlSystemDesign NonlinearMPC Therearegenerallytwodifferentwaystocontrol thenonlinearsystem 3.46. The first one is to linearize the model and use linear MPC. Ac- cording to the nonlinear model (equation 3.46), the microwave heat- ing termis Ψn(k) =VT(k)[Φn(k)]V(k). Thecorresponding linearizedtermis Ψn(k)≈Ψn(k−1)+ ∂Ψ n ∂V ∣∣∣∣ k−1 ( V(k)−V(k−1)) ≈Ψn(k−1)+2VT(k−1)[Φn(k−1)](V(k)−V(k−1)) ≈2VT(k−1)[Φn(k−1)]V(k)−VT(k−1)[Φn(k−1)]V(k−1) (4.19) which is a ’random walk’ model [ZL03] depending on the former in- put vectorV(k−1). In this case, errors from nonlinear system identi- fication and linearization are accumulated, and this linearized model (equation 4.19)doesnothaveagoodpredictionability for futureout- puts. Therefore the linearization approach is not a good choice and thenonlinearMPCmethodhas tobe implemented. Compared with the popularity of linear MPC, nonlinear MPC was not widely interested and studied until the 1990s [MHL99]. One of the most important driven reasons for the development of nonlinear MPC is the need for more accurate system models and better control performance. As mentioned previously, the control principle of non- linear MPC is the same as linear MPC, except the prediction and con- trol policy are derived from a nonlinear model. In our case, unlike the linear model, there is no analytical control solution derived from the cost function (equation 4.2) using the nonlinear model (equation 3.46). Therefore, a numerical control scheme is proposed combin- ing the idea of bang-bang control [MTA+06] and genetic algorithms [Whi94],which is thebinarygeneticcontrol scheme. Theso-calledbang-bangcontrol[MTA+06],alsoknownasbinarycon- trolorhysteresiscontrol, isacontrol strategywhere thecontrolaction 96