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 Hamza Gasmi 

Volume, Issue 2021

International Journal of Dynamics and Control




Our work on this paper aims on developing the strategies of fractional order controller (FOC) design based on use time-domain specifications (Percentage of overshoot (PO) and Settling time (ts)) to control non integer-order models with plus time delay (NIOPTD or fractional order models). Considering a fractional Smith predictor structure, a efficient and simple analytical strategy to tuning a FOC for fractional models is suggested. The design strategy is based on desired time-domain specifications (PO and ts). To achieve these requirements, many tuning analytical formulas are derived using on Bode’s ideal closed-loop transfer function. The resulting new controller can be decomposed into fractional order PID controller cascaded with a fractional order filter. The parameters of the FOPID controller are directly obtained by using the parameters of the fractional order models and the fractional-order filter parameters are easily obtained Using formulas of time-domain specifications (PO and ts). After a successful implementation of the proposed fractional controller on single-input-single-output (SISO) process, it is implemented on the complex system (multi-input multi-output (MIMO) system). Where the simulation results show that the suggested strategy of fractional Smith predictor improves the closed-loop control system compared to other controllers.


Fractional order PID (FOPID) controller, Smith predictor, NIOPTD-II model, Time-domain specifications, Fractional order filter (FOF), MIMO system