Page - 90 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4. ControlSystemDesign LinearMPC Inthissection,proceduresofhowthecontrolsolutionisderivedinthe linearMPCsystemispresented. LinearMPCachievesgreatsuccesses in a number of applications, e.g. in [QB03] and [MHL99]. By now, the linear MPC theory is widely implemented, and over 90% of MPC applications are linear. Various linear MPC algorithms exist, includ- ing the dynamic matrix control (DMC) [Wan09], predictive functional control (PFC) [HBS11], model algorithmic control (MAC) [GPM89], and generalized predictive control (GPC) [CMT87]. Among these different algorithms, DMC is one of the most powerful and widely implemented MPC algorithms, especially in industry. According to the investigation in [OOH95], all major oil companies apply DMC- like approaches to control process variables such as the temperature and pressure in their new installations or revamps. Compared with other MPC approaches like GPC, DMC is more suitable for multivari- able state-space formed systems as well as ARX types of models. In order to further involve the control input constraints, an improved version of DMC - quadratic DMC (QDMC) [GM86] algorithm is ap- plied. The time-invariant QDMC algorithm is not designed to deal with time-varying systems (such as equation 4.7), but still it is rational to be implementedhere. Thisalgorithmissuitablebecause thecurrently estimated system model (at time k) can predict the future behavior (until time k+p) accurately. In microwave heating applications, the system model parameters are changing slowly, especially when the temperatureof the loadisvaryingwithinasmall range(whenthetar- get temperature is fixed). As long as the current system parameters areestimatedaccurately, it is reasonable toassumethat thecurrentes- timated parameters can be used to predict future outputs with a high accuracy. For instance, it has been demonstrated in [NP97] that the time-invariant MPC approach can keep a suboptimal performance in practical time-varying applications. On the other hand, although a number of MPC approaches have been proposed specialized for spe- cific time-varying systems, such as the approaches in [DC03] [ZL03] and [Ric05], the performance gain of these approaches over conven- tional time-invariant MPC approaches is limited. In this thesis, the time-invariantQDMCalgorithmisselected. 90