Optimal design and control in a class of distributed parameter systems under uncertainty–application to tubular reactor with catalyst deactivation

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Abstract
Unpredictable variations in the values of plant parameters around their nominal values are often encountered in actual operation of process plants. In order to assure that process performance meets specifications, it is preferable to design and control the process, taking into account the uncertainty in the values of the plant parameters. In this paper, a method to minimize the maximum decrease in the process performance caused by the hypothetical worst parameter variations is proposed. Necessary condition for the worst parameter variations is derived for a class of distributed parameter systems by means of the maximum principle, and then the method for obtaining the optimal design and control subject to the worst parameter variations are discussed. The method is applied to the design of a tubular reactor associated with catalyst activity decay. The reactor obtained is fairly insensitive to the variations in the process parameters while maintaining fairly good performance even at the nominal values of parameters.