Cyclic distillation is a process intensification technique that allows key benefits such as increased column throughput, lower energy requirements and higher separation performance. Despite these advantages, the application to industrial processes is limited, mainly due to serious controllability concerns. To address this challenge, this study is the first to prove that cyclic distillation is also well controllable, hence being able to provide in practice the expected key economic benefits. In this work we developed a dynamic model which consists of two non-linear functions that map the initial conditions to the system state at the end of vapor and liquid periods, respectively, by solving the dynamic mass balance together with equilibrium relationships. A periodic state is reached when the initial condition is attained after successive application of the two maps. A discrete-time controller is used, with the temperatures in the lower and upper parts of the column as controlled variables and the vapor flow rate and the amount of liquid reflux as manipulated variable. A case study is presented, proving that the discrete PI algorithm in the velocity form gives excellent performance. Thus, the system is able to cope with changes in the feed flow rate and composition.