In this paper, a single-stage pilot-scale RO (Reverse Osmosis) process is considered. The process is mainly used in various chemical industries such as dye, pharmaceutical, Beverage, and so on. Initially, mathematical modeling of the process is to be done followed by linearization of the system. Here a dual loop construction with a master and a slave is used. The slave uses the conventional PID (Proportional Integral Derivative) with a reference model of the RO process and the master uses the FOPID (Fractional Order Proportional Integral Derivative) with a real time RO process. The slave's output is compared with output of the real time RO process to obtain the error which is in turn used to tune the master. The slave controller is tuned using Ziegler Nicholas method and the error criterion such as IAE (Integral Absolute Error), ISE (Integral Squared Error), ITSE (Integral Time Squared Error), ITAE (Integral Time Absolute Error) are calculated and the minimum among them was chosen as the objective function for the master loop tuning. Hence the tuning of the controller becomes a whole. Therefore two optimization techniques such as PSO (Particle Swarm Optimization) and Bacterial Foraging Optimization Algorithm (BFO) are used for the tuning of the master loop. From the calculations the ITSE was having the minimum value among the performance indices hence it was used as the objective function for the BFO and PSO. The best-tuned values will be obtained with the use of these techniques and the best among all can be considered for various industrial applications. Finally, the performance of the process is compared with both techniques and BFO outperforms the PSO from the simulations.


  • Reverse Osmosis.

  • Multi Input Multi Output.

  • Particle Swarm Optimization.

  • Bacterial Foraging Optimization Algorithm various industrial applications.

Graphical Abstract

Graphical Abstract
Graphical Abstract
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