Page - 84 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4. ControlSystemDesign a nonlinear equation normally solved by numerical methods. Al- thoughLQRhasasimilarcontrolprincipleasMPC,variousresults [GBTH06] [FKO¨S11] demonstrated that with equal or even more control effort, the performance of LQR is not as good as MPC. It was also suggested in [EDH05] that for MIMO systems which are not fullydecoupled,e.g. HEPHAISTOS,MPCismoresuitable. • H2 and H∞ control [Bur98]: both H2 and H∞ control are powerful and robust methods that can be used for systems with noise and model uncertainties [SP07]. However, high computation costs is still the obstacle that limits their large scale applications. In many cases it is difficult to use these two methods to get analytical solu- tions, and they can only be solved numerically [Bur98]. Moreover, both H2 and H∞ control methods are still too complicated to be applied inhighdimensionalMIMOsystems[vdB07]. • Fuzzy logic control (FLC) [Lee90]: FLC is a control method which is widely applied in systems with unknown dynamics, benefiting fromempiricalknowledgeandexperience. ForSISOorMIMOsys- tems with low dimensions, FLC is easily implemented and tuned. But for MIMO systems with high dimensions, the numbers of both fuzzy rules and membership functions are increasing expo- nentially, which rises the difficulties in the controller design and the tuning of FLC [MSH98]. In addition, for MIMO systems with highly coupled dynamics, empirical knowledge is difficult to be directly used for the generation of fuzzy rules, which leads to a significantperformancedegradationofFLC. Considering above reasons and analyses, two control schemes are in- troduced in this chapter. The first adaptive control scheme includes themodelpredictivecontrol(MPC)[MHL99]andneuralnetworkcon- trol (NNC) methods [CK92], aiming to control temperatures of sep- arated points. The other intelligent control scheme is based on the reinforcement learningcontrol (RLC)method[Bar98]. Insteadof indi- vidual temperatures, it directly controls characteristics of the heating pattern. Both control schemes are optimized according to properties ofHEPHAISTOS, toreducethecomputationcomplexityandimprove thecontrolperformance. 84