Comparison of Optimal PI and FOPI Controllers Tuned by PSO Algorithm for FO-TITO Process with Fractional Inverted Decoupling

The Our proposed research aims to put forth an appropriate method for optimal tuning of the fractional order PI Controller applied for non-integer order TITO systems (or fractional order 2-input and 2-output (FO-TITO) processes). The problem of interferences existing between the loops of process is weakened by introducing a fractional inverted decoupler. The scheme of the successful perfect model of the proposed control system design is greatly subject to the careful selection of the adjustment parameters \(\left( {Kp, Ki,\lambda } \right)\) of the FO-PI controller by using a objective function, namely, integral absolute error (IAE). Here, for FO-TITO system, a optimal FO-PI controller design based on the advanced optimization approach called particle swarm optimization (PSO) algorithm is suggested. Finally, an illustrative example of non-integer order TITO process is presented and a comparative study, the results and analysis demonstrate that the performance of the fractional order controllers is better than the classical controllers. The design of the PSO-FOPI controller was studied also with and without inverted decoupling to process to verify the effective role in the use of the fractional inverted decoupling for fractional-order complex process control.