The fractional PID controllers tuned by genetic algorithms for expansion turbine in the cryogenic air separation process

Abstract

This paper deals with the design of a new algorithm of PID control based on fractional calculus (FC) in production of technical gases, i.e. in a cryogenic air separation process. Production of low pressure liquid air was first introduced by P. L. Kapica and involved expansion in a gas turbine. For application in the synthesis of the control law, for the input temperature and flow of air to the expansion turbine, it is necessary to determine the appropriate differential equations of the cryogenic process of mixing of two gaseous airflows at different temperatures before entrance to the expansion turbine. Thereafter, the model is linearized and decoupled and consequently classical PID and fractional order controllers are taken to assess the quality of the proposed technique. A set of optimal parameters of these controllers are achieved through the genetic algorithm optimization procedure by minimizing a cost function. Our design method focuses on minimizing performance criterion which involves IAE, overshoot, as well as settling time. A time-domain simulation was used to identify the performance of controller with respect to a traditional optimized PID controller.