Analytical design of multi-loop fractional IMC-pid-filter controllers for mimo system using equivalent niopdt models

Laifa, Sami http://orcid.org/0000-0001-6245-7581, Badreddine Boudjehemhttp://orcid.org/0000-0001-6245-7581 , and Djalil Boudjehemhttp://orcid.org/0000-0001-6245-7581

Volume 15, PP 383-393,  2020

International Transactions on Systems and Control,




In this paper, a multiloop fractional IMC-PID-filter controller design is proposed for 2x2 multivariable systems (two-input two-output (TITO) system). The MIMO system is decomposed by an inverted decoupler into independent loops (SISO systems) and they are approximated to equivalent new fractional order models known as non integer order plus time delay (NIOPTD). The fractional property of the suggested controller is imposed by choosing the Bode’s ideal closed loop transfer function as the reference model for each loop. The design method is based on the internal model control (IMC) paradigm. Finally, an illustrative example of MIMO process is provided and a comparative study is conducted out to demonstrate the advantages of the proposed method where the simulation results show the superior performance obtained by a multi-loop fractional IMC-PID-filter controllers in comparison with fractional PI/PID controllers based on simplified decoupling smith predictor (Fractional-SDSP and Classical-SDSP) structure as well as classical decentralized PID controllers using root locus method.


Multi-loop fractional IMC-PID-filter controller; internal model control (IMC); MIMO System; NIOPTD model.