The two-point composition control problem of binary distillation columns is addressed. First, the exact model-based inventory control problem is studied, yielding the underlying solvability conditions with physical meaning, the limiting behavior attainable with any controller, and its equivalence with nonlinear geometric and MPC controllers. This control behavior is recovered via a measurement-driven linear controller made of a pair of decoupled PI loops and a static interaction compensator. A closed-loop dynamics study formally shows the recovery feature and provides stability conditions coupled with conventional-like tuning rules. The controller implementation needs only four static parameters that have direct physical meaning and can be estimated from plant data and/or simulation packages. The proposed technique is tested with two representative examples in the presence of actuator errors, measurement delays, and load disturbances, matching or improving the behavior obtained with previous schemes.