A fractional order fuzzy PID controller for binary distillation column control

Expert and intelligent control schemes have recently emerged out as a promising solution with robustness which can efficiently deal with the nonlinearities, along with various types of modelling uncertainties, present in different real world systems e.g. binary distillation column. This paper is an attempt to propose an intelligent control system which takes the form of a fractional order fuzzy proportional-integral-derivative (FOFPID) controller which is investigated as a solution to deal with the complex dynamic nature of the distillation column. The FOFPID controller is an extension of an existing formula based self tuning fuzzy proportional integral controller structure, which varies its gains at run time in accordance with the instantaneous error and rate of change of error. The FOFPID controller is a Takagi-Sugeno (TS) model based fuzzy adaptive controller comprising of non-integer order of integration and differentiation operators used in the controller. It has been observed that inclusion of non-integer order of the integration and differentiation operators made the controller scheme more robust. For the performance evaluation of the proposed scheme, the performance of FOFPID controller is compared with that of its integer order counterpart, a fuzzy proportional-integral-derivative (FPID) controller. The parameters of both the controllers were optimized for minimum integral of absolute error (IAE) using a bio-inspired global optimization algorithm, genetic algorithm (GA). Intensive LabVIEWۛ simulation studies were performed which included setpoint tracking with and without uncertainties, disturbance rejection, and noise suppression investigations. For testing the parameter uncertainty handling capability of the proposed controller, uncertain and time varying relative volatility and uncertain tray hydraulic constant were applied. Also, for the disturbance rejection studies, intensive simulations were conducted, which included two most common causes of disturbance i.e. variation in feed composition and variation in feed flow rate. All the simulation investigations clearly suggested that FOFPID controller provided superior performance over FPID controller for each case study i.e. setpoint tracking, disturbance rejection, noise suppression and parameter uncertainties.