In the production of terephthalic acid and isoplithalic acid, a tiny amount of one reactant p-xylene or m-xylene may exist in the unreacted acetic acid, which needs to be purified for reuse by a dehydration column. In our previous study (Huang et al.(1)), it was found that the feed tray location is extremely important for optimizing the operating and the total annual costs. In this paper, the optimal designed processes with and without feed impurity will be further studied in terms of their bifurcation behavior and control. Three cases (one without feed impurity, one with feed impurity and side stream, and one with feed impurity but without side stream) will be studied. In this study, bifurcations due to output multiplicity are observed in two of the cases which have feed impurity but not in the case without. In each bifurcation case, the optimal base case is located on an unstable branch. The overall control at this unstable operating point is thus proposed to deal with disturbance from throughput or feed composition (e.g., water or the impurity) variations. It is found that a dual-temperature control scheme is necessary to keep products at both ends of the column within specifications. For the impurity disturbances, the side strearnflow rate needs to be manipulated accordingly. A novel side-stream operating strategy to maintain the impurity concentration inside the column is proposed for an energy-efficient operation.