Page - 83 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

4. ControlSystemDesign Controller design is the final and most important part in the temper- ature control system. For microwave heating systems with multiple distributedfeedingsourcesas implementedinHEPHAISTOS,several factors have to be considered before the selection of appropriate con- trolalgorithms: • Highlycoupleddynamics; • Highinputandoutputdimensions; • Linearandnonlinearsystemswithmodelinguncertainties; • Time-varyingmodelparameters; • Inputconstraints. A number of currently main stream control methods are briefly ana- lyzedbelow,withrespect toaforementionedproperties: •MIMO PID [MKJ02] : PID is a powerful control scheme that is mostlyappliedinSISOsystems. Theso-calledMIMOPIDis itsex- tension to MIMO systems. The applicable systems are mostly sys- temsthatcanbedecentralizedsuchasin[XCH06]and[PKM13],or smallscalefullycoupledMIMOsystems, forexample,2×2MIMO systems [RLRJGA06] [CC14]. For non-decoupled MIMO systems with high input and output dimensions, the tuning of MIMO PID parameterswillbecomecomplexandinefficient. • Linear quadratic regulator (LQR) [AM07]: LQR is one of the most notable controllers that have been widely used in the last few decades. The objective of LQR is to optimize a cost function based on future system behaviors. Thus essentially it is a predictive con- trolmethod. ThecontrolactionofLQRcomesfromthesolutionof adiscrete-timealgebraicRiccati equation(DARE) [LR95],which is 83