Distillation Columns—A Class of Dynamic Systems With Multiplicative Inputs

Distillation columns can be described by nonlinear state space equations but which are linear with respect to the inputs for a large domain of working conditions. For adiabatic distillation columns, these state space equations are also homogeneous with respect to the inputs and in this case the inputs act multiplicatively. Three important properties are derived from this structure concerning: 1. The equilibrium points; 2. The time scale around an equilibrium point; 3. The gain around an equilibrium point. These properties depend on the direction and the modulus of the input vector. They have been verified experimentally on the pilot distillation column of Laboratoire d’Automatique de Grenoble. The properties derived from the multiplicative effect of the inputs allow: 1) To implement a simple feedforward control technique for the compensation of the feed flow rate disturbances by maintaining the direction of the input vector. 2) To implement an open loop adaptive feedback control by taking in account the effect of the magnitude of the input vector upon the system dynamics.