Dynamic control structures of many types of reactive distillation columns have been studied in the literature. Both ideal hypothetical chemical systems and real chemical systems have been investigated. Most papers that involve ideal systems consider the quaternary ideal two-reactant, two-product chemistry A + B <-> C + D. This paper explores the control of an ideal ternary system with the chemistry A + B <-> C. Two cases are considered. In the first, there are only three components. In the second, the feed contains another component that does not participate in the reaction but does have a major impact on the structure of the column and the vapor-liquid phase equilibrium. A recent paper [Luyben, W. L. Ind. Eng. Chem. Res. in review] explored the effects of several kinetic and design parameters on the steady-state design of these ternary systems. Significant differences were observed between the systems with and without chemically inert components. The current paper demonstrates that the control structures for these two systems are also quite different. Of particular importance is the finding that a two-temperature control structure provides effective control for the ternary system without inerts; however, this structure does not work when inerts are present, indicating that a direct composition measurement of a column internal composition is required for effective control.