Role of Multiplicity in Control System Design for a Methyl Acetate Reactive Distillation Column

The impact of steady-state multiplicities on the control of a methyl acetate reactive distillation (RD) column is studied. It is shown that input multiplicity, where multiple input values give the same output, can lead to “wrong” control action, leading to poor robustness. A new metric, rangeability, is defined to quantify the severity of input multiplicity in a steady-state input-output (IO) relation. Rangeability can be used in conjunction with conventional sensitivity analysis for the design of robust control structures for RD systems. The design methodology is illustrated for the temperature based control of an industrial scale methyl acetate column. Results for a synthesized control structure shows that controlling the most sensitive reactive tray temperature can lead to poor robustness due to low rangeability resulting in “wrong” control action for large disturbances. Controlling a reactive tray temperature with acceptable sensitivity but larger rangeability gives better robustness. It is also shown that controlling the difference in the temperature of two suitably chosen reactive trays gives better robustness of the control structure due to improved rangeability. The article brings out the importance of IO relations in understanding the complex dynamic behavior of RD systems.