Fractional controller design for a binary distillation column using the method of inequalities

Controller design for a binary distillation column is recognized as a difficult and challenging problem, especially when the controller used is of fractional order. The objective of this paper is to design fractional controllers for a binary distillation column by using the method of inequalities. The design specifications used in the paper are based on conventional step-response criteria and, in keeping with the method of inequalities, are expressed as a set of inequalities. The associated stability problems are resolved by using the numerical procedures recently developed by the authors, whereas the time responses of the system are computed by using the formula for numerical inversion of Laplace transforms based on Zakianpsilas I_MN approximants. The decentralized and full PI controllers of fractional order are obtained and then compared with the PI controllers of integer order that were obtained previously in the literature. The numerical results show that fractional controllers can provide better performances than controllers of integer order.