OPTIMAL TIME-VARYING CELL-VOLTAGE CONTROL OF A PARALLEL-PLATE REACTOR

As a means to illustrate the calculation of an optimal cell-voltage co ntrol for a parallel-plate reactor, we determine the time-varying cell voltage that maximizes p-aminophenol produced from the electroreducti on of nitrobenzene in a differential-conversion reactor operated in a batch mode; that is, the electrolyte is continuously recirculated from a batch holding tank through the reactor in which a low conversion pe r pass occurs. A rationale is given for restricting the search for the optimal control for this particular reaction network to a chattering- cell voltage that switches between a priori chosen minimum and maximum values. The optimal, time-varying duty cycle is computed using a grad ient-search technique. The predicted concentrations are dependent upon the reaction time; for the conditions examined here, an improvement o f twenty-five percent in the production and nine-hundred percent in th e selectivity of p-aminophenol may be achieved by using the optimal, t ime-varying voltage in comparison to the best steady value. Since a ch attering control is a mathematical construct, we illustrate that a rec tangular, high-frequency waveform may be applied to yield results whic h are indistinguishable from those effected by a chattering cell volta ge. The period of the waveform must be short enough so that surface co ncentrations are time invariant over it and yet, simultaneously, must be long enough so that double-layer charging does not account for a si gnificant passage of coulombs.