Order reduction and control of hyperbolic, countercurrent distributed parameter systems using method of characteristics

The aim of this paper is to develop a model reduction technique based on method of characteristics (MOC) for control of counter-current distributed parameter systems that are modeled by semi-linear hyperbolic partial differential equations (PDEs). In our previous work, MOC was shown to be a suitable model reduction technique for a class of hyperbolic PDEs. This concept is extended to counter-current systems, wherein the so-called characteristic lines have slopes with opposite signs. Two different approximations are proposed that allow the use of MOC as a model reduction technique. The open-loop results from MOC are compared with a large dimensional model, based on the method of lines. The MOC-based models are used for closed loop simulations within the approximate dynamic programming (ADP) framework. Two case studies are considered: a non-adiabatic plug flow reactor (having characteristics with two different slopes) and a non-adiabatic fixed bed reactor (having characteristics with three different slopes). We demonstrate that using the MOC-based model in an ADP controller results in a significant improvement in computational time, along with a slight improvement in controller performance.