A 2-DoF multi-objective H∞/L1 robust controller design for a high purification distillation column using LMIs

In this paper, we propose a robust H_∞/L₁ control system for a high purity distillation column. The original nonlinear model of the column is of high order and it includes parametric uncertainty. A reduced-order linearized model of the distillation column is used to design a 2-DoF multi-objective H_∞/L₁ controller which ensures robust stability of the closed loop system and fulfillment of certain design specifications. The design process is formulated and solved using linear matrix inequalities (LMIs), which is an invaluable tool in control systems. To maintain performance over different values of uncertainty, we reform the uncertainties as polytopic uncertainty, which is easily convertible to LMIs. Then, a simulation of the closed loop system with the nonlinear distillation column model is performed, which shows excellent performance for various reference values tracking and disturbances rejection.