Method of characteristics based model reduction for control of a counter-current reactor using approximate dynamic programming

The aim of this paper is to use the method of characteristics (MOC) as a technique to obtain reduced order model for control of a counter-current reactor. The reactor is described by a system of quasi-linear hyperbolic partial differential equations (PDEs). Due to the counter-current operation, the system exhibits characteristic lines with double slopes; the slope of the characteristics have opposing signs. A reduced order model is obtained by using only a limited number of characteristic lines in the time-space plane. An approximation technique is proposed to obtain state variables at each sampling instance. This reduced-order MOC model is used for control in the approximate dynamic programming (ADP) framework for set-point tracking.